Subgroups — C₆₇×#60240 #30739491

Order 17152.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2981	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2980	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2978	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2977	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2974	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2973	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2879	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#550×C₆₇	C₄	1	1	yes	characteristic
35	D₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
36	#548×C₆₇	C₄	1	1	yes	characteristic
37	#548×C₆₇	C₄	1	1	yes	characteristic
38	#547×C₆₇	C₄	1	2	yes	—
39	#547×C₆₇	C₄	1	1	yes	characteristic
40	#546×C₆₇	C₄	1	2	yes	—
41	#546×C₆₇	C₄	1	2	yes	—
42	#546×C₆₇	C₄	1	1	yes	characteristic
43	#546×C₆₇	C₄	1	1	yes	characteristic
44	D₄²×C₆₇	C₄	1	1	yes	characteristic
45	D₄²×C₆₇	C₄	1	2	yes	—
46	#532×C₆₇	C₂²	1	1	yes	characteristic
47	#532×C₆₇	C₂²	1	2	yes	—
48	#525×C₆₇	C₂²	1	1	yes	characteristic
49	#525×C₆₇	C₂²	1	1	yes	characteristic
50	#525×C₆₇	C₂²	1	2	yes	—
51	#525×C₆₇	C₂²	1	2	yes	—
52	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
55	#436×C₆₇	C₂²	1	2	yes	complemented
56	#436×C₆₇	C₂²	1	2	yes	complemented
57	#436×C₆₇	C₂²	1	2	yes	complemented
58	#436×C₆₇	C₂²	1	2	yes	complemented
59	#436×C₆₇	C₂²	1	2	yes	complemented
60	#436×C₆₇	C₂²	1	2	yes	complemented
61	#435×C₆₇	C₂²	1	1	yes	characteristic
62	#435×C₆₇	C₂²	1	1	yes	characteristic
63	#435×C₆₇	C₂²	1	2	yes	—
64	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
67	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
69	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#435×C₆₇	C₂²	1	2	yes	complemented
71	#435×C₆₇	C₂²	1	2	yes	complemented
72	#435×C₆₇	C₂²	1	2	yes	complemented
73	#435×C₆₇	C₂²	1	2	yes	complemented
74	#435×C₆₇	C₂²	1	2	yes	complemented
75	#435×C₆₇	C₂²	1	2	yes	complemented
76	#435×C₆₇	C₂²	1	2	yes	complemented
77	#435×C₆₇	C₂²	1	2	yes	complemented
78	#435×C₆₇	C₂²	1	2	yes	complemented
79	#435×C₆₇	C₂²	1	2	yes	complemented
80	#435×C₆₇	C₂²	1	2	yes	complemented
81	#435×C₆₇	C₂²	1	2	yes	complemented
82	#435×C₆₇	C₂²	1	2	yes	complemented
83	#435×C₆₇	C₂²	1	2	yes	complemented
84	#435×C₆₇	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
88	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
89	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
90	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
91	#433×C₆₇	C₂²	1	2	yes	complemented
92	#433×C₆₇	C₂²	1	2	yes	complemented
93	#433×C₆₇	C₂²	1	2	yes	complemented
94	#433×C₆₇	C₂²	1	2	yes	complemented
95	#432×C₆₇	C₂²	1	2	yes	complemented
96	#432×C₆₇	C₂²	1	2	yes	complemented
97	#432×C₆₇	C₂²	1	2	yes	complemented
98	#431×C₆₇	C₂²	1	2	yes	complemented
99	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#408×C₆₇	C₂²	1	1	yes	characteristic
104	#408×C₆₇	C₂²	1	1	yes	characteristic
105	#408×C₆₇	C₂²	1	1	yes	characteristic
106	#408×C₆₇	C₂²	1	1	yes	characteristic
107	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	#408×C₆₇	C₂²	1	2	yes	complemented
110	#408×C₆₇	C₂²	1	2	yes	complemented
111	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#408×C₆₇	C₂²	1	2	yes	complemented
114	#408×C₆₇	C₂²	1	2	yes	complemented
115	#408×C₆₇	C₂²	1	2	yes	complemented
116	#408×C₆₇	C₂²	1	2	yes	complemented
117	#408×C₆₇	C₂²	1	2	yes	complemented
118	#408×C₆₇	C₂²	1	2	yes	complemented
119	#407×C₆₇	C₂²	1	2	yes	complemented
120	#407×C₆₇	C₂²	1	2	yes	complemented
121	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#407×C₆₇	C₂²	1	2	yes	complemented
124	#407×C₆₇	C₂²	1	2	yes	complemented
125	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
126	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
130	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
131	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	—	4	2	no	—
136	C₂×#41×C₆₇	—	4	2	no	—
137	C₂×#41×C₆₇	—	4	2	no	—
138	C₂×#41×C₆₇	—	4	2	no	—
139	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
140	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
141	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
144	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×#41×C₆₇	C₂³	1	2	yes	—
149	C₂×#41×C₆₇	C₂³	1	2	yes	—
150	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
151	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
152	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
153	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
154	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
155	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
156	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
157	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
158	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
161	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
162	#131×C₆₇	—	4	2	no	—
163	#131×C₆₇	—	4	2	no	—
164	#131×C₆₇	—	4	2	no	—
165	#131×C₆₇	—	4	2	no	—
166	C₂×M₁₆×C₆₇	—	4	2	no	—
167	C₂×M₁₆×C₆₇	—	4	2	no	—
168	C₂×M₁₆×C₆₇	—	4	2	no	—
169	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
176	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
179	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
180	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
181	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
182	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
183	C₂²×C₈×C₆₇	—	4	2	no	—
184	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
185	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
188	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
190	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
193	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
194	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
195	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
196	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
197	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
198	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
199	C₄⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
200	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
201	#127×C₆₇	C₂×C₄	1	2	yes	—
202	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
203	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
204	#124×C₆₇	C₂×C₄	1	2	yes	—
205	#124×C₆₇	C₂×C₄	1	2	yes	—
206	#123×C₆₇	C₂×C₄	1	2	yes	—
207	#123×C₆₇	C₂×C₄	1	2	yes	—
208	#123×C₆₇	C₂×C₄	1	2	yes	—
209	#123×C₆₇	C₂×C₄	1	2	yes	—
210	#123×C₆₇	C₂×C₄	1	2	yes	—
211	#123×C₆₇	C₂×C₄	1	2	yes	—
212	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
213	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
214	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
215	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
216	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
217	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
218	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
219	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
220	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
221	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
222	#121×C₆₇	C₂×C₄	1	2	yes	—
223	#121×C₆₇	C₂×C₄	1	2	yes	—
224	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
225	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
226	#121×C₆₇	C₂×C₄	1	2	yes	—
227	#121×C₆₇	C₂×C₄	1	2	yes	—
228	#121×C₆₇	C₂×C₄	1	2	yes	—
229	#121×C₆₇	C₂×C₄	1	2	yes	—
230	#121×C₆₇	C₂×C₄	1	2	yes	—
231	#121×C₆₇	C₂×C₄	1	2	yes	—
232	#121×C₆₇	C₂×C₄	1	2	yes	—
233	#121×C₆₇	C₂×C₄	1	2	yes	—
234	#120×C₆₇	C₂×C₄	1	2	yes	—
235	#120×C₆₇	C₂×C₄	1	2	yes	—
236	#120×C₆₇	C₂×C₄	1	2	yes	—
237	#120×C₆₇	C₂×C₄	1	2	yes	—
238	#120×C₆₇	C₂×C₄	1	2	yes	—
239	#120×C₆₇	C₂×C₄	1	2	yes	—
240	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
241	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
244	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
245	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
246	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
247	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
248	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
249	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
250	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
251	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
252	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
253	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
254	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₇	C₂³	1	2	yes	—
257	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	C₂³	1	2	yes	—
259	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₆₇	C₂³	1	2	yes	—
261	C₄×D₄×C₆₇	C₂³	1	2	yes	—
262	C₄×D₄×C₆₇	C₂³	1	2	yes	—
263	C₄×D₄×C₆₇	C₂³	1	2	yes	—
264	#117×C₆₇	C₂³	1	1	yes	characteristic
265	#117×C₆₇	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
268	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
271	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
272	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
289	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
290	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
291	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
292	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
293	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
295	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
296	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
297	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
298	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
299	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
300	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
301	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	#97×C₆₇	C₂³	1	1	yes	characteristic
313	#97×C₆₇	C₂³	1	1	yes	characteristic
314	#97×C₆₇	C₂³	1	1	yes	characteristic
315	#97×C₆₇	C₂³	1	1	yes	characteristic
316	#97×C₆₇	C₂³	1	2	yes	—
317	#97×C₆₇	C₂³	1	2	yes	—
318	#97×C₆₇	C₂³	1	2	yes	—
319	C₄×C₈×C₆₇	C₂³	1	2	yes	—
320	C₄×C₈×C₆₇	C₂³	1	2	yes	—
321	C₄×C₈×C₆₇	C₂³	1	2	yes	—
322	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
323	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
324	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
325	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	—	2	2	no	—
329	#41×C₆₇	—	2	2	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	4	2	no	—
333	#41×C₆₇	—	4	2	no	—
334	#41×C₆₇	—	4	2	no	—
335	#41×C₆₇	—	4	2	no	—
336	#41×C₆₇	—	4	4	no	—
337	#41×C₆₇	—	4	4	no	—
338	#41×C₆₇	—	4	2	no	—
339	#41×C₆₇	—	4	2	no	—
340	#41×C₆₇	—	4	2	no	—
341	#41×C₆₇	—	4	2	no	—
342	C₂×Q₈×C₆₇	—	4	2	no	—
343	C₂×Q₈×C₆₇	—	4	2	no	—
344	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
345	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
346	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
347	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
348	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
349	C₂×D₄×C₆₇	—	4	2	no	—
350	C₂×D₄×C₆₇	—	4	2	no	—
351	C₂×D₄×C₆₇	—	4	2	no	—
352	C₂×D₄×C₆₇	—	4	4	no	—
353	C₂×D₄×C₆₇	—	4	4	no	—
354	C₂×D₄×C₆₇	—	4	4	no	—
355	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
356	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
357	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
358	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
360	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
361	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
362	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
363	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
366	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
368	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
369	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
372	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
373	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
374	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
375	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
376	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	2	no	—
379	C₂²×C₄×C₆₇	—	2	2	no	—
380	C₂²×C₄×C₆₇	—	2	2	no	—
381	C₂²×C₄×C₆₇	—	4	2	no	—
382	C₂²×C₄×C₆₇	—	4	2	no	—
383	C₂²×C₄×C₆₇	—	4	2	no	—
384	C₂²×C₄×C₆₇	—	4	2	no	—
385	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
386	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
388	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
389	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
392	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
393	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
394	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
395	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
396	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
397	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
398	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
399	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
400	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
401	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
409	M₁₆×C₆₇	—	2	2	no	—
410	M₁₆×C₆₇	—	2	2	no	—
411	M₁₆×C₆₇	—	2	2	no	—
412	M₁₆×C₆₇	—	2	2	no	—
413	M₁₆×C₆₇	—	4	1	no	—
414	M₁₆×C₆₇	—	4	1	no	—
415	M₁₆×C₆₇	—	4	1	no	—
416	M₁₆×C₆₇	—	4	1	no	—
417	M₁₆×C₆₇	—	4	2	no	—
418	M₁₆×C₆₇	—	4	2	no	—
419	M₁₆×C₆₇	—	4	2	no	—
420	M₁₆×C₆₇	—	4	2	no	—
421	M₁₆×C₆₇	—	4	2	no	—
422	M₁₆×C₆₇	—	4	2	no	—
423	C₂×C₈×C₆₇	—	2	2	no	—
424	C₂×C₈×C₆₇	—	2	2	no	—
425	C₂×C₈×C₆₇	—	2	2	no	—
426	C₂×C₈×C₆₇	—	2	2	no	—
427	C₂×C₈×C₆₇	—	4	1	no	—
428	C₂×C₈×C₆₇	—	4	1	no	—
429	C₂×C₈×C₆₇	—	4	1	no	—
430	C₂×C₈×C₆₇	—	4	1	no	—
431	C₂×C₈×C₆₇	—	4	2	no	—
432	C₂×C₈×C₆₇	—	4	2	no	—
433	C₂×C₈×C₆₇	—	4	2	no	—
434	C₂×C₈×C₆₇	—	4	2	no	—
435	C₂×C₈×C₆₇	—	4	2	no	—
436	C₂×C₈×C₆₇	—	4	2	no	—
437	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
442	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
443	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
444	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
445	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
446	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
447	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
448	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
452	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
454	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
456	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
457	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
458	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
459	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
460	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
461	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
462	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
464	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
465	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
466	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
467	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
468	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
469	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
470	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
471	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
473	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
476	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
477	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
478	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
479	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
480	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
481	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
482	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
483	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
484	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
485	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
486	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
487	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
488	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
489	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
490	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
491	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
492	C₄²×C₆₇	C₂⁴	1	2	yes	—
493	C₂³×C₆₇	—	2	2	no	—
494	C₂³×C₆₇	—	2	2	no	—
495	C₂³×C₆₇	—	2	2	no	—
496	C₂³×C₆₇	—	2	4	no	—
497	C₂³×C₆₇	—	4	1	no	—
498	C₂³×C₆₇	—	4	2	no	—
499	C₂³×C₆₇	—	4	2	no	—
500	C₂³×C₆₇	—	4	1	no	—
501	C₂³×C₆₇	—	4	2	no	—
502	C₂³×C₆₇	—	4	1	no	—
503	C₂³×C₆₇	—	4	2	no	—
504	C₂³×C₆₇	—	4	2	no	—
505	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
506	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
507	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
508	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
509	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
510	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
511	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
512	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
513	Q₈×C₆₇	—	2	2	no	—
514	Q₈×C₆₇	—	2	2	no	—
515	Q₈×C₆₇	—	2	2	no	—
516	Q₈×C₆₇	—	4	2	no	—
517	Q₈×C₆₇	—	4	2	no	—
518	D₄×C₆₇	—	2	4	no	—
519	D₄×C₆₇	—	2	4	no	—
520	D₄×C₆₇	—	2	4	no	—
521	D₄×C₆₇	—	2	2	no	—
522	D₄×C₆₇	—	2	2	no	—
523	D₄×C₆₇	—	2	4	no	—
524	D₄×C₆₇	—	2	2	no	—
525	D₄×C₆₇	—	2	2	no	—
526	D₄×C₆₇	—	2	2	no	—
527	D₄×C₆₇	—	4	1	no	—
528	D₄×C₆₇	—	4	2	no	—
529	D₄×C₆₇	—	4	1	no	—
530	D₄×C₆₇	—	4	2	no	—
531	D₄×C₆₇	—	4	2	no	—
532	D₄×C₆₇	—	4	2	no	—
533	D₄×C₆₇	—	4	2	no	—
534	D₄×C₆₇	—	4	2	no	—
535	D₄×C₆₇	—	4	2	no	—
536	D₄×C₆₇	—	4	2	no	—
537	D₄×C₆₇	—	4	2	no	—
538	D₄×C₆₇	—	4	2	no	—
539	D₄×C₆₇	—	4	2	no	—
540	C₂×C₄×C₆₇	—	2	2	no	—
541	C₂×C₄×C₆₇	—	2	2	no	—
542	C₂×C₄×C₆₇	—	2	2	no	—
543	C₂×C₄×C₆₇	—	2	2	no	—
544	C₂×C₄×C₆₇	—	2	2	no	—
545	C₂×C₄×C₆₇	—	2	2	no	—
546	C₂×C₄×C₆₇	—	2	1	no	—
547	C₂×C₄×C₆₇	—	2	1	no	—
548	C₂×C₄×C₆₇	—	2	1	no	—
549	C₂×C₄×C₆₇	—	2	1	no	—
550	C₂×C₄×C₆₇	—	2	2	no	—
551	C₂×C₄×C₆₇	—	2	2	no	—
552	C₂×C₄×C₆₇	—	2	2	no	—
553	C₂×C₄×C₆₇	—	2	2	no	—
554	C₂×C₄×C₆₇	—	2	1	no	—
555	C₂×C₄×C₆₇	—	2	1	no	—
556	C₂×C₄×C₆₇	—	2	1	no	—
557	C₂×C₄×C₆₇	—	2	1	no	—
558	C₂×C₄×C₆₇	—	2	2	no	—
559	C₂×C₄×C₆₇	—	2	2	no	—
560	C₂×C₄×C₆₇	—	4	2	no	—
561	C₂×C₄×C₆₇	—	4	2	no	—
562	C₂×C₄×C₆₇	—	4	2	no	—
563	C₂×C₄×C₆₇	—	4	2	no	—
564	C₂×C₄×C₆₇	—	4	2	no	—
565	C₂×C₄×C₆₇	—	4	2	no	—
566	C₂×C₄×C₆₇	—	4	1	no	—
567	C₂×C₄×C₆₇	—	4	2	no	—
568	C₂×C₄×C₆₇	—	4	1	no	—
569	C₂×C₄×C₆₇	—	4	2	no	—
570	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
571	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
575	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
582	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
584	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
585	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
587	C₈×C₆₇	—	2	1	no	—
588	C₈×C₆₇	—	2	1	no	—
589	C₈×C₆₇	—	2	1	no	—
590	C₈×C₆₇	—	2	1	no	—
591	C₈×C₆₇	—	2	1	no	—
592	C₈×C₆₇	—	2	1	no	—
593	C₈×C₆₇	—	2	1	no	—
594	C₈×C₆₇	—	2	1	no	—
595	C₈×C₆₇	—	2	2	no	—
596	C₈×C₆₇	—	2	2	no	—
597	C₈×C₆₇	—	2	2	no	—
598	C₈×C₆₇	—	2	2	no	—
599	C₂²×C₆₇	—	2	1	no	—
600	C₂²×C₆₇	—	2	1	no	—
601	C₂²×C₆₇	—	2	1	no	—
602	C₂²×C₆₇	—	2	1	no	—
603	C₂²×C₆₇	—	2	1	no	—
604	C₂²×C₆₇	—	2	1	no	—
605	C₂²×C₆₇	—	2	1	no	—
606	C₂²×C₆₇	—	2	2	no	—
607	C₂²×C₆₇	—	2	2	no	—
608	C₂²×C₆₇	—	2	2	no	—
609	C₂²×C₆₇	—	2	2	no	—
610	C₂²×C₆₇	—	2	1	no	—
611	C₂²×C₆₇	—	2	1	no	—
612	C₂²×C₆₇	—	2	2	no	—
613	C₂²×C₆₇	—	2	1	no	—
614	C₂²×C₆₇	—	2	2	no	—
615	C₂²×C₆₇	—	2	2	no	—
616	C₂²×C₆₇	—	2	1	no	—
617	C₂²×C₆₇	—	2	1	no	—
618	C₂²×C₆₇	—	2	2	no	—
619	C₂²×C₆₇	—	2	2	no	—
620	C₂²×C₆₇	—	2	1	no	—
621	C₂²×C₆₇	—	4	4	no	—
622	C₂²×C₆₇	—	8	4	no	—
623	C₂²×C₆₇	—	8	2	no	—
624	C₂²×C₆₇	—	8	4	no	—
625	C₂²×C₆₇	#518	1	2	yes	—
626	C₂²×C₆₇	#568	1	2	yes	—
627	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
628	C₄×C₆₇	—	2	1	no	—
629	C₄×C₆₇	—	2	1	no	—
630	C₄×C₆₇	—	2	1	no	—
631	C₄×C₆₇	—	2	1	no	—
632	C₄×C₆₇	—	2	2	no	—
633	C₄×C₆₇	—	2	2	no	—
634	C₄×C₆₇	—	2	2	no	—
635	C₄×C₆₇	—	2	1	no	—
636	C₄×C₆₇	—	2	1	no	—
637	C₄×C₆₇	—	2	2	no	—
638	C₄×C₆₇	—	2	1	no	—
639	C₄×C₆₇	—	2	1	no	—
640	C₄×C₆₇	—	2	2	no	—
641	C₄×C₆₇	#518	1	2	yes	—
642	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
643	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
644	#60240	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
645	C₂×C₆₇	—	2	2	no	—
646	C₂×C₆₇	—	2	2	no	—
647	C₂×C₆₇	—	4	1	no	—
648	C₂×C₆₇	—	4	1	no	—
649	C₂×C₆₇	—	4	2	no	—
650	C₂×C₆₇	—	4	2	no	—
651	C₂×C₆₇	—	4	2	no	—
652	C₂×C₆₇	—	4	1	no	—
653	C₂×C₆₇	C₂×#518	1	1	yes	characteristic
654	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
655	C₂×C₆₇	#3573	1	1	yes	characteristic
656	D₄×#41	C₂×C₆₇	1	1	yes	characteristic
657	#2981	C₂×C₆₇	1	2	yes	complemented
658	#2980	C₂×C₆₇	1	2	yes	complemented
659	#2978	C₂×C₆₇	1	2	yes	complemented
660	#2977	C₂×C₆₇	1	2	yes	complemented
661	#2976	C₂×C₆₇	1	2	yes	complemented
662	#2976	C₂×C₆₇	1	2	yes	complemented
663	#2974	C₂×C₆₇	1	2	yes	complemented
664	#2973	C₂×C₆₇	1	2	yes	complemented
665	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
666	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
667	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
668	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
669	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
670	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
671	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
672	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
673	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#2880	C₂×C₆₇	1	1	yes	characteristic, complemented
676	#2880	C₂×C₆₇	1	1	yes	characteristic, complemented
677	#2879	C₂×C₆₇	1	1	yes	characteristic, complemented
678	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
679	C₆₇	#60240	1	1	yes	characteristic, direct product factor, Sylow
680	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
681	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
682	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
683	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
684	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
685	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#550	C₄×C₆₇	1	1	yes	characteristic
691	D₄×Q₈	C₄×C₆₇	1	1	yes	characteristic
692	#548	C₄×C₆₇	1	1	yes	characteristic
693	#548	C₄×C₆₇	1	1	yes	characteristic
694	#547	C₄×C₆₇	1	2	yes	—
695	#547	C₄×C₆₇	1	1	yes	characteristic
696	#546	C₄×C₆₇	1	2	yes	—
697	#546	C₄×C₆₇	1	2	yes	—
698	#546	C₄×C₆₇	1	1	yes	characteristic
699	#546	C₄×C₆₇	1	1	yes	characteristic
700	D₄²	C₄×C₆₇	1	1	yes	characteristic
701	D₄²	C₄×C₆₇	1	2	yes	—
702	#532	C₂²×C₆₇	1	1	yes	characteristic
703	#532	C₂²×C₆₇	1	2	yes	—
704	#525	C₂²×C₆₇	1	1	yes	characteristic
705	#525	C₂²×C₆₇	1	1	yes	characteristic
706	#525	C₂²×C₆₇	1	2	yes	—
707	#525	C₂²×C₆₇	1	2	yes	—
708	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
709	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
710	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
711	#436	C₂²×C₆₇	1	2	yes	complemented
712	#436	C₂²×C₆₇	1	2	yes	complemented
713	#436	C₂²×C₆₇	1	2	yes	complemented
714	#436	C₂²×C₆₇	1	2	yes	complemented
715	#436	C₂²×C₆₇	1	2	yes	complemented
716	#436	C₂²×C₆₇	1	2	yes	complemented
717	#435	C₂²×C₆₇	1	1	yes	characteristic
718	#435	C₂²×C₆₇	1	1	yes	characteristic
719	#435	C₂²×C₆₇	1	2	yes	—
720	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
723	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	#435	C₂²×C₆₇	1	2	yes	complemented
727	#435	C₂²×C₆₇	1	2	yes	complemented
728	#435	C₂²×C₆₇	1	2	yes	complemented
729	#435	C₂²×C₆₇	1	2	yes	complemented
730	#435	C₂²×C₆₇	1	2	yes	complemented
731	#435	C₂²×C₆₇	1	2	yes	complemented
732	#435	C₂²×C₆₇	1	2	yes	complemented
733	#435	C₂²×C₆₇	1	2	yes	complemented
734	#435	C₂²×C₆₇	1	2	yes	complemented
735	#435	C₂²×C₆₇	1	2	yes	complemented
736	#435	C₂²×C₆₇	1	2	yes	complemented
737	#435	C₂²×C₆₇	1	2	yes	complemented
738	#435	C₂²×C₆₇	1	2	yes	complemented
739	#435	C₂²×C₆₇	1	2	yes	complemented
740	#435	C₂²×C₆₇	1	2	yes	complemented
741	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
742	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
743	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
744	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
745	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
746	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
747	#433	C₂²×C₆₇	1	2	yes	complemented
748	#433	C₂²×C₆₇	1	2	yes	complemented
749	#433	C₂²×C₆₇	1	2	yes	complemented
750	#433	C₂²×C₆₇	1	2	yes	complemented
751	#432	C₂²×C₆₇	1	2	yes	complemented
752	#432	C₂²×C₆₇	1	2	yes	complemented
753	#432	C₂²×C₆₇	1	2	yes	complemented
754	#431	C₂²×C₆₇	1	2	yes	complemented
755	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
757	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
759	#408	C₂²×C₆₇	1	1	yes	characteristic
760	#408	C₂²×C₆₇	1	1	yes	characteristic
761	#408	C₂²×C₆₇	1	1	yes	characteristic
762	#408	C₂²×C₆₇	1	1	yes	characteristic
763	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
764	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
765	#408	C₂²×C₆₇	1	2	yes	complemented
766	#408	C₂²×C₆₇	1	2	yes	complemented
767	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
768	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
769	#408	C₂²×C₆₇	1	2	yes	complemented
770	#408	C₂²×C₆₇	1	2	yes	complemented
771	#408	C₂²×C₆₇	1	2	yes	complemented
772	#408	C₂²×C₆₇	1	2	yes	complemented
773	#408	C₂²×C₆₇	1	2	yes	complemented
774	#408	C₂²×C₆₇	1	2	yes	complemented
775	#407	C₂²×C₆₇	1	2	yes	complemented
776	#407	C₂²×C₆₇	1	2	yes	complemented
777	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
778	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
779	#407	C₂²×C₆₇	1	2	yes	complemented
780	#407	C₂²×C₆₇	1	2	yes	complemented
781	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
782	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
783	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
784	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
785	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
786	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
787	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
788	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
789	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
790	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
791	C₂×#41	—	4	2	no	—
792	C₂×#41	—	4	2	no	—
793	C₂×#41	—	4	2	no	—
794	C₂×#41	—	4	2	no	—
795	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
796	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
797	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
798	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
799	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
800	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
801	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
802	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
803	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
804	C₂×#41	C₂³×C₆₇	1	2	yes	—
805	C₂×#41	C₂³×C₆₇	1	2	yes	—
806	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
807	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
808	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
809	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
810	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
811	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
812	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
813	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
814	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
815	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
817	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
818	#131	—	4	2	no	—
819	#131	—	4	2	no	—
820	#131	—	4	2	no	—
821	#131	—	4	2	no	—
822	C₂×M₁₆	—	4	2	no	—
823	C₂×M₁₆	—	4	2	no	—
824	C₂×M₁₆	—	4	2	no	—
825	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
826	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
827	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
828	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
829	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
830	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
831	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
832	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
833	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
834	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
835	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
836	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
837	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
838	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
839	C₂²×C₈	—	4	2	no	—
840	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
841	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
842	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
843	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
844	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
845	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
846	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
847	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
848	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
849	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
850	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
851	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
852	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
853	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
854	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
855	C₄⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
856	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
857	#127	C₂×C₄×C₆₇	1	2	yes	—
858	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
859	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
860	#124	C₂×C₄×C₆₇	1	2	yes	—
861	#124	C₂×C₄×C₆₇	1	2	yes	—
862	#123	C₂×C₄×C₆₇	1	2	yes	—
863	#123	C₂×C₄×C₆₇	1	2	yes	—
864	#123	C₂×C₄×C₆₇	1	2	yes	—
865	#123	C₂×C₄×C₆₇	1	2	yes	—
866	#123	C₂×C₄×C₆₇	1	2	yes	—
867	#123	C₂×C₄×C₆₇	1	2	yes	—
868	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
869	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
870	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
871	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
872	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
874	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
875	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
876	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
877	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
878	#121	C₂×C₄×C₆₇	1	2	yes	—
879	#121	C₂×C₄×C₆₇	1	2	yes	—
880	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
881	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
882	#121	C₂×C₄×C₆₇	1	2	yes	—
883	#121	C₂×C₄×C₆₇	1	2	yes	—
884	#121	C₂×C₄×C₆₇	1	2	yes	—
885	#121	C₂×C₄×C₆₇	1	2	yes	—
886	#121	C₂×C₄×C₆₇	1	2	yes	—
887	#121	C₂×C₄×C₆₇	1	2	yes	—
888	#121	C₂×C₄×C₆₇	1	2	yes	—
889	#121	C₂×C₄×C₆₇	1	2	yes	—
890	#120	C₂×C₄×C₆₇	1	2	yes	—
891	#120	C₂×C₄×C₆₇	1	2	yes	—
892	#120	C₂×C₄×C₆₇	1	2	yes	—
893	#120	C₂×C₄×C₆₇	1	2	yes	—
894	#120	C₂×C₄×C₆₇	1	2	yes	—
895	#120	C₂×C₄×C₆₇	1	2	yes	—
896	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
897	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
898	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
899	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
900	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
901	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
902	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
903	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
904	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
905	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
906	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
907	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
908	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
909	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
912	C₄×D₄	C₂³×C₆₇	1	2	yes	—
913	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
914	C₄×D₄	C₂³×C₆₇	1	2	yes	—
915	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
916	C₄×D₄	C₂³×C₆₇	1	2	yes	—
917	C₄×D₄	C₂³×C₆₇	1	2	yes	—
918	C₄×D₄	C₂³×C₆₇	1	2	yes	—
919	C₄×D₄	C₂³×C₆₇	1	2	yes	—
920	#117	C₂³×C₆₇	1	1	yes	characteristic
921	#117	C₂³×C₆₇	1	2	yes	—
922	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
923	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
924	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
927	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
928	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
929	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
930	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
931	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
932	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
933	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
934	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
935	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
936	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
937	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
938	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
939	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
940	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
941	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
942	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
944	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
945	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
946	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
948	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
951	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
953	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
954	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
955	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
956	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
957	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
960	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
961	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
967	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
968	#97	C₂³×C₆₇	1	1	yes	characteristic
969	#97	C₂³×C₆₇	1	1	yes	characteristic
970	#97	C₂³×C₆₇	1	1	yes	characteristic
971	#97	C₂³×C₆₇	1	1	yes	characteristic
972	#97	C₂³×C₆₇	1	2	yes	—
973	#97	C₂³×C₆₇	1	2	yes	—
974	#97	C₂³×C₆₇	1	2	yes	—
975	C₄×C₈	C₂³×C₆₇	1	2	yes	—
976	C₄×C₈	C₂³×C₆₇	1	2	yes	—
977	C₄×C₈	C₂³×C₆₇	1	2	yes	—
978	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
979	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
980	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
981	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	2	2	no	—
987	#41	—	2	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	2	no	—
990	#41	—	4	2	no	—
991	#41	—	4	2	no	—
992	#41	—	4	4	no	—
993	#41	—	4	4	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	#41	—	4	2	no	—
998	C₂×Q₈	—	4	2	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
1001	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
1002	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
1003	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
1004	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	4	4	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	4	no	—
1011	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1012	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1013	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1014	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1015	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1016	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1017	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1018	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1019	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1020	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1021	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1022	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1023	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1024	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1025	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1026	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1027	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1028	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1029	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1030	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1031	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1032	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	—	4	2	no	—
1041	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1048	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1050	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1051	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1052	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1053	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1054	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1055	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1056	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
1057	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1062	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1063	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	M₁₆	—	2	2	no	—
1066	M₁₆	—	2	2	no	—
1067	M₁₆	—	2	2	no	—
1068	M₁₆	—	2	2	no	—
1069	M₁₆	—	4	1	no	—
1070	M₁₆	—	4	1	no	—
1071	M₁₆	—	4	1	no	—
1072	M₁₆	—	4	1	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	M₁₆	—	4	2	no	—
1076	M₁₆	—	4	2	no	—
1077	M₁₆	—	4	2	no	—
1078	M₁₆	—	4	2	no	—
1079	C₂×C₈	—	2	2	no	—
1080	C₂×C₈	—	2	2	no	—
1081	C₂×C₈	—	2	2	no	—
1082	C₂×C₈	—	2	2	no	—
1083	C₂×C₈	—	4	1	no	—
1084	C₂×C₈	—	4	1	no	—
1085	C₂×C₈	—	4	1	no	—
1086	C₂×C₈	—	4	1	no	—
1087	C₂×C₈	—	4	2	no	—
1088	C₂×C₈	—	4	2	no	—
1089	C₂×C₈	—	4	2	no	—
1090	C₂×C₈	—	4	2	no	—
1091	C₂×C₈	—	4	2	no	—
1092	C₂×C₈	—	4	2	no	—
1093	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1094	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1095	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1096	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1097	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1098	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1099	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1100	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1101	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1102	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1103	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1104	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1105	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1106	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1107	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1108	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1109	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1110	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1111	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1112	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1113	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1114	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1116	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1117	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1118	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1119	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1123	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1125	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1127	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1129	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1132	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1133	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1134	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1135	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1136	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1137	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1138	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1139	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1140	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1141	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1142	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1143	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1144	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1145	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1146	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1147	C₄²	C₂⁴×C₆₇	1	2	yes	—
1148	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	4	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	1	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1162	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1163	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1164	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1165	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1166	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1167	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1168	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	2	no	—
1172	Q₈	—	4	2	no	—
1173	Q₈	—	4	2	no	—
1174	D₄	—	2	4	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	2	4	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	2	2	no	—
1179	D₄	—	2	4	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	1	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	1	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	2	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1227	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1228	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1229	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1230	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1231	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1232	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1233	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1234	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1235	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1236	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1237	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1238	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1239	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1240	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1241	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1242	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1243	C₈	—	2	1	no	—
1244	C₈	—	2	1	no	—
1245	C₈	—	2	1	no	—
1246	C₈	—	2	1	no	—
1247	C₈	—	2	1	no	—
1248	C₈	—	2	1	no	—
1249	C₈	—	2	1	no	—
1250	C₈	—	2	1	no	—
1251	C₈	—	2	2	no	—
1252	C₈	—	2	2	no	—
1253	C₈	—	2	2	no	—
1254	C₈	—	2	2	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	2	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	2	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	4	4	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	8	4	no	—
1281	C₂²	#518×C₆₇	1	2	yes	—
1282	C₂²	#568×C₆₇	1	2	yes	—
1283	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	2	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	2	2	no	—
1297	C₄	#518×C₆₇	1	2	yes	—
1298	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1299	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1300	C₂	—	2	2	no	—
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	4	1	no	—
1306	C₂	—	4	2	no	—
1307	C₂	—	4	2	no	—
1308	C₂	C₂×#518×C₆₇	1	1	yes	characteristic
1309	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1310	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	D₄×#41×C₆₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₆₇×#2981	C₂	semidirect
3. C₆₇×#2980	C₂	semidirect
4. C₆₇×#2978	C₂	semidirect
5. C₆₇×#2977	C₂	semidirect
6. C₆₇×#2976	C₂	semidirect
7. C₆₇×#2976	C₂	semidirect
8. C₆₇×#2974	C₂	semidirect
9. C₆₇×#2973	C₂	semidirect
10. C₆₇×#2935	C₂	semidirect
11. D₄×M₁₆×C₆₇	C₂	semidirect
12. C₆₇×#2933	C₂	semidirect
13. C₆₇×#2933	C₂	semidirect
14. C₆₇×#2932	C₂	semidirect
15. C₆₇×#2930	C₂	semidirect
16. C₆₇×#2929	C₂	semidirect
17. C₂×#435×C₆₇	C₂	semidirect
18. C₆₇×#2925	C₂	semidirect
19. C₆₇×#2923	C₂	semidirect
20. C₆₇×#2880	C₂	semidirect
21. C₆₇×#2880	C₂	semidirect
22. C₆₇×#2879	C₂	semidirect
23. C₂×#408×C₆₇	C₂	semidirect
26. C₂×#131×C₆₇	C₂²	semidirect
27. C₂×#131×C₆₇	C₂²	semidirect
28. C₂×#131×C₆₇	C₂²	semidirect
29. C₂×#131×C₆₇	C₂²	semidirect
30. C₂²×M₁₆×C₆₇	C₂²	semidirect
31. C₂²×M₁₆×C₆₇	C₂²	semidirect
32. C₂²×M₁₆×C₆₇	C₂²	semidirect
33. C₂³×C₈×C₆₇	C₂²	semidirect
55. #436×C₆₇	C₂²	semidirect
56. #436×C₆₇	C₂²	semidirect
57. #436×C₆₇	C₂²	semidirect
58. #436×C₆₇	C₂²	semidirect
59. #436×C₆₇	C₂²	semidirect
60. #436×C₆₇	C₂²	semidirect
64. #435×C₆₇	C₂²	semidirect
65. #435×C₆₇	C₂²	semidirect
66. #435×C₆₇	C₂²	semidirect
67. #435×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #435×C₆₇	C₂²	semidirect
71. #435×C₆₇	C₂²	semidirect
72. #435×C₆₇	C₂²	semidirect
73. #435×C₆₇	C₂²	semidirect
74. #435×C₆₇	C₂²	semidirect
75. #435×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. #435×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. #435×C₆₇	C₂²	semidirect
80. #435×C₆₇	C₂²	semidirect
81. #435×C₆₇	C₂²	semidirect
82. #435×C₆₇	C₂²	semidirect
83. #435×C₆₇	C₂²	semidirect
84. #435×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
87. C₈×D₄×C₆₇	C₂²	semidirect
88. C₈×D₄×C₆₇	C₂²	semidirect
89. C₈×D₄×C₆₇	C₂²	semidirect
90. C₈×D₄×C₆₇	C₂²	semidirect
91. #433×C₆₇	C₂²	semidirect
92. #433×C₆₇	C₂²	semidirect
93. #433×C₆₇	C₂²	semidirect
94. #433×C₆₇	C₂²	semidirect
95. #432×C₆₇	C₂²	semidirect
96. #432×C₆₇	C₂²	semidirect
97. #432×C₆₇	C₂²	semidirect
98. #431×C₆₇	C₂²	semidirect
99. #424×C₆₇	C₂²	semidirect
100. #424×C₆₇	C₂²	semidirect
101. #423×C₆₇	C₂²	semidirect
102. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
107. #408×C₆₇	C₂²	semidirect
108. #408×C₆₇	C₂²	semidirect
109. #408×C₆₇	C₂²	semidirect
110. #408×C₆₇	C₂²	semidirect
111. #408×C₆₇	C₂²	semidirect
112. #408×C₆₇	C₂²	semidirect
113. #408×C₆₇	C₂²	semidirect
114. #408×C₆₇	C₂²	semidirect
115. #408×C₆₇	C₂²	semidirect
116. #408×C₆₇	C₂²	semidirect
117. #408×C₆₇	C₂²	semidirect
118. #408×C₆₇	C₂²	semidirect
119. #407×C₆₇	C₂²	semidirect
120. #407×C₆₇	C₂²	semidirect
121. #407×C₆₇	C₂²	semidirect
122. #407×C₆₇	C₂²	semidirect
123. #407×C₆₇	C₂²	semidirect
124. #407×C₆₇	C₂²	semidirect
125. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
126. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
127. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
128. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
129. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
130. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
131. #405×C₆₇	C₂²	semidirect
132. #405×C₆₇	C₂²	semidirect
133. C₄×M₁₆×C₆₇	C₂²	semidirect
134. C₂×#97×C₆₇	C₂²	semidirect
644. #60240	C₆₇	direct (N × H)
657. #2981	C₂×C₆₇	semidirect
658. #2980	C₂×C₆₇	semidirect
659. #2978	C₂×C₆₇	semidirect
660. #2977	C₂×C₆₇	semidirect
661. #2976	C₂×C₆₇	semidirect
662. #2976	C₂×C₆₇	semidirect
663. #2974	C₂×C₆₇	semidirect
664. #2973	C₂×C₆₇	semidirect
665. #2935	C₂×C₆₇	semidirect
666. D₄×M₁₆	C₂×C₆₇	semidirect
667. #2933	C₂×C₆₇	semidirect
668. #2933	C₂×C₆₇	semidirect
669. #2932	C₂×C₆₇	semidirect
670. #2930	C₂×C₆₇	semidirect
671. #2929	C₂×C₆₇	semidirect
672. C₂×#435	C₂×C₆₇	semidirect
673. #2925	C₂×C₆₇	semidirect
674. #2923	C₂×C₆₇	semidirect
675. #2880	C₂×C₆₇	semidirect
676. #2880	C₂×C₆₇	semidirect
677. #2879	C₂×C₆₇	semidirect
678. C₂×#408	C₂×C₆₇	semidirect
679. C₆₇	#60240	direct (N × H)
682. C₂×#131	C₂²×C₆₇	semidirect
683. C₂×#131	C₂²×C₆₇	semidirect
684. C₂×#131	C₂²×C₆₇	semidirect
685. C₂×#131	C₂²×C₆₇	semidirect
686. C₂²×M₁₆	C₂²×C₆₇	semidirect
687. C₂²×M₁₆	C₂²×C₆₇	semidirect
688. C₂²×M₁₆	C₂²×C₆₇	semidirect
689. C₂³×C₈	C₂²×C₆₇	semidirect
711. #436	C₂²×C₆₇	semidirect
712. #436	C₂²×C₆₇	semidirect
713. #436	C₂²×C₆₇	semidirect
714. #436	C₂²×C₆₇	semidirect
715. #436	C₂²×C₆₇	semidirect
716. #436	C₂²×C₆₇	semidirect
720. #435	C₂²×C₆₇	semidirect
721. #435	C₂²×C₆₇	semidirect
722. #435	C₂²×C₆₇	semidirect
723. #435	C₂²×C₆₇	semidirect
724. #435	C₂²×C₆₇	semidirect
725. #435	C₂²×C₆₇	semidirect
726. #435	C₂²×C₆₇	semidirect
727. #435	C₂²×C₆₇	semidirect
728. #435	C₂²×C₆₇	semidirect
729. #435	C₂²×C₆₇	semidirect
730. #435	C₂²×C₆₇	semidirect
731. #435	C₂²×C₆₇	semidirect
732. #435	C₂²×C₆₇	semidirect
733. #435	C₂²×C₆₇	semidirect
734. #435	C₂²×C₆₇	semidirect
735. #435	C₂²×C₆₇	semidirect
736. #435	C₂²×C₆₇	semidirect
737. #435	C₂²×C₆₇	semidirect
738. #435	C₂²×C₆₇	semidirect
739. #435	C₂²×C₆₇	semidirect
740. #435	C₂²×C₆₇	semidirect
741. C₈×D₄	C₂²×C₆₇	semidirect
742. C₈×D₄	C₂²×C₆₇	semidirect
743. C₈×D₄	C₂²×C₆₇	semidirect
744. C₈×D₄	C₂²×C₆₇	semidirect
745. C₈×D₄	C₂²×C₆₇	semidirect
746. C₈×D₄	C₂²×C₆₇	semidirect
747. #433	C₂²×C₆₇	semidirect
748. #433	C₂²×C₆₇	semidirect
749. #433	C₂²×C₆₇	semidirect
750. #433	C₂²×C₆₇	semidirect
751. #432	C₂²×C₆₇	semidirect
752. #432	C₂²×C₆₇	semidirect
753. #432	C₂²×C₆₇	semidirect
754. #431	C₂²×C₆₇	semidirect
755. #424	C₂²×C₆₇	semidirect
756. #424	C₂²×C₆₇	semidirect
757. #423	C₂²×C₆₇	semidirect
758. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
763. #408	C₂²×C₆₇	semidirect
764. #408	C₂²×C₆₇	semidirect
765. #408	C₂²×C₆₇	semidirect
766. #408	C₂²×C₆₇	semidirect
767. #408	C₂²×C₆₇	semidirect
768. #408	C₂²×C₆₇	semidirect
769. #408	C₂²×C₆₇	semidirect
770. #408	C₂²×C₆₇	semidirect
771. #408	C₂²×C₆₇	semidirect
772. #408	C₂²×C₆₇	semidirect
773. #408	C₂²×C₆₇	semidirect
774. #408	C₂²×C₆₇	semidirect
775. #407	C₂²×C₆₇	semidirect
776. #407	C₂²×C₆₇	semidirect
777. #407	C₂²×C₆₇	semidirect
778. #407	C₂²×C₆₇	semidirect
779. #407	C₂²×C₆₇	semidirect
780. #407	C₂²×C₆₇	semidirect
781. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
782. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
783. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
784. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
785. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
786. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
787. #405	C₂²×C₆₇	semidirect
788. #405	C₂²×C₆₇	semidirect
789. C₄×M₁₆	C₂²×C₆₇	semidirect
790. C₂×#97	C₂²×C₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×#41×C₆₇	2
C₆₇×#2981	2
C₆₇×#2980	2
C₆₇×#2978	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2974	2
C₆₇×#2973	2
C₆₇×#2935	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2932	2
C₆₇×#2930	2
C₆₇×#2929	2
C₂×#435×C₆₇	2
C₆₇×#2925	2
C₆₇×#2923	2
C₆₇×#2880	2
C₆₇×#2879	2
C₂×#408×C₆₇	2
#60240	67

Subgroups — C67×#60240 #30739491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60240 #30739491