Subgroups — C₆₇×#60324 #30739575

Order 17152.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3481	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2978	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2973	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×M₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
20	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
22	C₆₇×#2930	C₂	1	2	yes	maximal, complemented
23	C₂×#436×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
25	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
27	#559×C₆₇	C₄	1	1	yes	characteristic
28	#554×C₆₇	C₄	1	1	yes	characteristic
29	#554×C₆₇	C₄	1	1	yes	characteristic
30	#553×C₆₇	C₄	1	1	yes	characteristic
31	#553×C₆₇	C₄	1	1	yes	characteristic
32	#553×C₆₇	C₄	1	2	yes	—
33	#551×C₆₇	C₄	1	2	yes	—
34	#551×C₆₇	C₄	1	2	yes	—
35	#546×C₆₇	C₄	1	2	yes	—
36	#546×C₆₇	C₄	1	1	yes	characteristic
37	#546×C₆₇	C₄	1	1	yes	characteristic
38	D₄²×C₆₇	C₄	1	1	yes	characteristic
39	#532×C₆₇	C₂²	1	1	yes	characteristic
40	#529×C₆₇	C₂²	1	1	yes	characteristic
41	#529×C₆₇	C₂²	1	2	yes	—
42	#529×C₆₇	C₂²	1	1	yes	characteristic
43	#525×C₆₇	C₂²	1	2	yes	—
44	#525×C₆₇	C₂²	1	2	yes	—
45	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
46	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#446×C₆₇	C₂²	1	2	yes	complemented
54	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	#436×C₆₇	C₂²	1	1	yes	characteristic
58	#436×C₆₇	C₂²	1	1	yes	characteristic
59	#436×C₆₇	C₂²	1	1	yes	characteristic
60	#436×C₆₇	C₂²	1	1	yes	characteristic
61	#436×C₆₇	C₂²	1	2	yes	complemented
62	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#436×C₆₇	C₂²	1	2	yes	complemented
64	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
66	#436×C₆₇	C₂²	1	2	yes	complemented
67	#436×C₆₇	C₂²	1	2	yes	complemented
68	#436×C₆₇	C₂²	1	2	yes	complemented
69	#436×C₆₇	C₂²	1	2	yes	complemented
70	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
71	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#436×C₆₇	C₂²	1	2	yes	complemented
74	#436×C₆₇	C₂²	1	2	yes	complemented
75	#435×C₆₇	C₂²	1	1	yes	characteristic
76	#435×C₆₇	C₂²	1	2	yes	—
77	#435×C₆₇	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
83	#435×C₆₇	C₂²	1	2	yes	complemented
84	#435×C₆₇	C₂²	1	2	yes	complemented
85	#435×C₆₇	C₂²	1	2	yes	complemented
86	#435×C₆₇	C₂²	1	2	yes	complemented
87	#435×C₆₇	C₂²	1	2	yes	complemented
88	#435×C₆₇	C₂²	1	2	yes	complemented
89	#435×C₆₇	C₂²	1	2	yes	complemented
90	#435×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#435×C₆₇	C₂²	1	2	yes	complemented
92	#435×C₆₇	C₂²	1	2	yes	complemented
93	#435×C₆₇	C₂²	1	2	yes	complemented
94	#435×C₆₇	C₂²	1	2	yes	complemented
95	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
96	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
97	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
99	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#433×C₆₇	C₂²	1	2	yes	complemented
103	#433×C₆₇	C₂²	1	2	yes	complemented
104	#433×C₆₇	C₂²	1	2	yes	complemented
105	#433×C₆₇	C₂²	1	2	yes	complemented
106	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#432×C₆₇	C₂²	1	2	yes	complemented
108	#432×C₆₇	C₂²	1	2	yes	complemented
109	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#424×C₆₇	C₂²	1	2	yes	complemented
115	#424×C₆₇	C₂²	1	2	yes	complemented
116	#423×C₆₇	C₂²	1	2	yes	complemented
117	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#408×C₆₇	C₂²	1	2	yes	complemented
121	#408×C₆₇	C₂²	1	2	yes	complemented
122	#408×C₆₇	C₂²	1	2	yes	complemented
123	#407×C₆₇	C₂²	1	2	yes	complemented
124	#407×C₆₇	C₂²	1	2	yes	complemented
125	#407×C₆₇	C₂²	1	2	yes	complemented
126	#407×C₆₇	C₂²	1	2	yes	complemented
127	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
128	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
129	#405×C₆₇	C₂²	1	2	yes	complemented
130	#405×C₆₇	C₂²	1	2	yes	complemented
131	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₆₇	C₂³	1	2	yes	—
138	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
139	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
140	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	#131×C₆₇	—	4	4	no	—
144	C₂×M₁₆×C₆₇	—	4	4	no	—
145	C₂×M₁₆×C₆₇	—	4	4	no	—
146	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
148	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
149	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
163	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
164	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
167	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
168	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
169	#126×C₆₇	C₂×C₄	1	2	yes	—
170	#126×C₆₇	C₂×C₄	1	2	yes	—
171	#126×C₆₇	C₂×C₄	1	2	yes	—
172	#126×C₆₇	C₂×C₄	1	2	yes	—
173	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
174	#125×C₆₇	C₂×C₄	1	2	yes	—
175	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
176	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
177	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
178	#124×C₆₇	C₂×C₄	1	2	yes	—
179	#124×C₆₇	C₂×C₄	1	2	yes	—
180	#123×C₆₇	C₂×C₄	1	2	yes	—
181	#123×C₆₇	C₂×C₄	1	2	yes	—
182	#123×C₆₇	C₂×C₄	1	2	yes	—
183	#123×C₆₇	C₂×C₄	1	2	yes	—
184	#123×C₆₇	C₂×C₄	1	2	yes	—
185	#123×C₆₇	C₂×C₄	1	2	yes	—
186	#123×C₆₇	C₂×C₄	1	2	yes	—
187	#123×C₆₇	C₂×C₄	1	2	yes	—
188	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
189	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
190	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
191	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
193	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
194	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
195	#121×C₆₇	C₂×C₄	1	2	yes	—
196	#121×C₆₇	C₂×C₄	1	2	yes	—
197	#121×C₆₇	C₂×C₄	1	2	yes	—
198	#121×C₆₇	C₂×C₄	1	2	yes	—
199	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
200	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
201	#121×C₆₇	C₂×C₄	1	2	yes	—
202	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
203	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
204	#121×C₆₇	C₂×C₄	1	2	yes	—
205	#120×C₆₇	C₂×C₄	1	2	yes	—
206	#120×C₆₇	C₂×C₄	1	2	yes	—
207	#120×C₆₇	C₂×C₄	1	2	yes	—
208	#120×C₆₇	C₂×C₄	1	2	yes	—
209	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
210	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
211	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
214	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
215	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
217	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
218	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
219	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
220	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
222	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
223	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
225	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
228	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	2	yes	—
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	C₄×D₄×C₆₇	C₂³	1	2	yes	—
234	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₆₇	C₂³	1	2	yes	—
237	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₇	C₂³	1	2	yes	—
240	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
241	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
242	#117×C₆₇	C₂×C₄	1	2	yes	—
243	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
244	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
245	#117×C₆₇	C₂³	1	2	yes	—
246	#117×C₆₇	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
250	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
251	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
252	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
253	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
254	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
258	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
259	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
262	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
263	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
265	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
266	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
267	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
269	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
270	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
271	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
272	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
273	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
274	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
276	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
289	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
294	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
296	#97×C₆₇	C₂³	1	1	yes	characteristic
297	#97×C₆₇	C₂³	1	1	yes	characteristic
298	#97×C₆₇	C₂³	1	2	yes	—
299	#97×C₆₇	C₂³	1	1	yes	characteristic
300	#97×C₆₇	C₂³	1	1	yes	characteristic
301	#97×C₆₇	C₂³	1	2	yes	—
302	#97×C₆₇	C₂³	1	2	yes	—
303	#97×C₆₇	C₂³	1	2	yes	—
304	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₆₇	C₂³	1	2	yes	—
309	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
314	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
315	#41×C₆₇	—	4	2	no	—
316	#41×C₆₇	—	4	2	no	—
317	#41×C₆₇	—	4	2	no	—
318	#41×C₆₇	—	4	2	no	—
319	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
320	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₆₇	—	4	2	no	—
323	C₂×D₄×C₆₇	—	4	2	no	—
324	C₂×D₄×C₆₇	—	4	4	no	—
325	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
329	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
331	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
333	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
335	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
336	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
337	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
338	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
339	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₆₇	—	4	2	no	—
341	C₂²×C₄×C₆₇	—	4	2	no	—
342	C₂²×C₄×C₆₇	—	4	2	no	—
343	C₂²×C₄×C₆₇	—	4	2	no	—
344	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
350	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
351	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
353	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
354	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
355	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
356	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
357	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
358	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
364	M₁₆×C₆₇	—	2	2	no	—
365	M₁₆×C₆₇	—	2	4	no	—
366	M₁₆×C₆₇	—	2	4	no	—
367	M₁₆×C₆₇	—	2	2	no	—
368	M₁₆×C₆₇	—	4	2	no	—
369	M₁₆×C₆₇	—	4	2	no	—
370	M₁₆×C₆₇	—	4	2	no	—
371	M₁₆×C₆₇	—	4	2	no	—
372	M₁₆×C₆₇	—	4	1	no	—
373	M₁₆×C₆₇	—	4	2	no	—
374	M₁₆×C₆₇	—	4	2	no	—
375	M₁₆×C₆₇	—	4	1	no	—
376	M₁₆×C₆₇	—	4	2	no	—
377	C₂×C₈×C₆₇	—	2	2	no	—
378	C₂×C₈×C₆₇	—	2	4	no	—
379	C₂×C₈×C₆₇	—	4	2	no	—
380	C₂×C₈×C₆₇	—	4	1	no	—
381	C₂×C₈×C₆₇	—	4	2	no	—
382	C₂×C₈×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	—	4	2	no	—
384	C₂×C₈×C₆₇	—	4	2	no	—
385	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
386	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
387	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
388	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
412	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
438	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
443	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
444	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
447	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
448	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
452	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
453	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
454	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄²×C₆₇	C₂⁴	1	2	yes	—
456	C₂³×C₆₇	—	2	4	no	—
457	C₂³×C₆₇	—	4	2	no	—
458	C₂³×C₆₇	—	4	2	no	—
459	C₂³×C₆₇	—	4	2	no	—
460	C₂³×C₆₇	—	4	2	no	—
461	C₂³×C₆₇	—	4	2	no	—
462	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
463	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
465	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
466	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
468	Q₈×C₆₇	—	2	2	no	—
469	Q₈×C₆₇	—	4	2	no	—
470	Q₈×C₆₇	—	4	1	no	—
471	D₄×C₆₇	—	2	2	no	—
472	D₄×C₆₇	—	2	4	no	—
473	D₄×C₆₇	—	2	2	no	—
474	D₄×C₆₇	—	2	2	no	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	2	no	—
477	D₄×C₆₇	—	4	2	no	—
478	D₄×C₆₇	—	4	2	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	4	2	no	—
481	D₄×C₆₇	—	4	2	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	2	no	—
484	D₄×C₆₇	—	4	1	no	—
485	D₄×C₆₇	—	4	2	no	—
486	C₂×C₄×C₆₇	—	2	2	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	1	no	—
491	C₂×C₄×C₆₇	—	2	2	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	1	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	2	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	4	2	no	—
505	C₂×C₄×C₆₇	—	4	2	no	—
506	C₂×C₄×C₆₇	—	4	2	no	—
507	C₂×C₄×C₆₇	—	4	2	no	—
508	C₂×C₄×C₆₇	—	4	2	no	—
509	C₂×C₄×C₆₇	—	4	1	no	—
510	C₂×C₄×C₆₇	—	4	1	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
513	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
518	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
519	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
520	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
522	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
525	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
527	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
528	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
529	C₈×C₆₇	—	2	2	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	2	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	—	2	2	no	—
534	C₈×C₆₇	—	2	1	no	—
535	C₈×C₆₇	—	2	1	no	—
536	C₈×C₆₇	—	2	2	no	—
537	C₈×C₆₇	—	2	1	no	—
538	C₈×C₆₇	—	2	1	no	—
539	C₈×C₆₇	—	2	1	no	—
540	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
541	C₂²×C₆₇	—	2	1	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	2	no	—
545	C₂²×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	1	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	2	no	—
552	C₂²×C₆₇	—	2	1	no	—
553	C₂²×C₆₇	—	2	2	no	—
554	C₂²×C₆₇	—	2	2	no	—
555	C₂²×C₆₇	—	2	2	no	—
556	C₂²×C₆₇	—	2	2	no	—
557	C₂²×C₆₇	—	2	2	no	—
558	C₂²×C₆₇	—	8	4	no	—
559	C₂²×C₆₇	—	8	4	no	—
560	C₂²×C₆₇	#568	1	2	yes	—
561	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	2	no	—
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	1	no	—
569	C₄×C₆₇	—	2	1	no	—
570	C₄×C₆₇	—	2	1	no	—
571	C₄×C₆₇	—	2	1	no	—
572	C₄×C₆₇	—	2	1	no	—
573	C₄×C₆₇	—	2	1	no	—
574	C₄×C₆₇	—	2	2	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	2	no	—
577	C₄×C₆₇	#568	1	2	yes	—
578	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
579	C₄×C₆₇	#585	1	1	yes	characteristic
580	#60324	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
581	C₂×C₆₇	—	2	2	no	—
582	C₂×C₆₇	—	4	1	no	—
583	C₂×C₆₇	—	4	2	no	—
584	C₂×C₆₇	—	4	2	no	—
585	C₂×C₆₇	—	4	1	no	—
586	C₂×C₆₇	—	4	2	no	—
587	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
589	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
590	#3481	C₂×C₆₇	1	1	yes	characteristic
591	#2995	C₂×C₆₇	1	2	yes	complemented
592	#2994	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#2993	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#2990	C₂×C₆₇	1	1	yes	characteristic, complemented
595	#2989	C₂×C₆₇	1	1	yes	characteristic, complemented
596	#2981	C₂×C₆₇	1	1	yes	characteristic, complemented
597	#2978	C₂×C₆₇	1	2	yes	complemented
598	#2976	C₂×C₆₇	1	2	yes	complemented
599	#2975	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#2973	C₂×C₆₇	1	2	yes	complemented
602	#2971	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#2969	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#2967	C₂×C₆₇	1	2	yes	complemented
605	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2965	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2935	C₂×C₆₇	1	1	yes	characteristic, complemented
608	D₄×M₁₆	C₂×C₆₇	1	2	yes	complemented
609	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#2933	C₂×C₆₇	1	2	yes	complemented
611	#2930	C₂×C₆₇	1	2	yes	complemented
612	C₂×#436	C₂×C₆₇	1	1	yes	characteristic, complemented
613	C₆₇	#60324	1	1	yes	characteristic, direct product factor, Sylow
614	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
615	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
616	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
617	#559	C₄×C₆₇	1	1	yes	characteristic
618	#554	C₄×C₆₇	1	1	yes	characteristic
619	#554	C₄×C₆₇	1	1	yes	characteristic
620	#553	C₄×C₆₇	1	1	yes	characteristic
621	#553	C₄×C₆₇	1	1	yes	characteristic
622	#553	C₄×C₆₇	1	2	yes	—
623	#551	C₄×C₆₇	1	2	yes	—
624	#551	C₄×C₆₇	1	2	yes	—
625	#546	C₄×C₆₇	1	2	yes	—
626	#546	C₄×C₆₇	1	1	yes	characteristic
627	#546	C₄×C₆₇	1	1	yes	characteristic
628	D₄²	C₄×C₆₇	1	1	yes	characteristic
629	#532	C₂²×C₆₇	1	1	yes	characteristic
630	#529	C₂²×C₆₇	1	1	yes	characteristic
631	#529	C₂²×C₆₇	1	2	yes	—
632	#529	C₂²×C₆₇	1	1	yes	characteristic
633	#525	C₂²×C₆₇	1	2	yes	—
634	#525	C₂²×C₆₇	1	2	yes	—
635	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
636	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
637	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
639	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
640	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#446	C₂²×C₆₇	1	2	yes	complemented
644	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
646	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#436	C₂²×C₆₇	1	1	yes	characteristic
648	#436	C₂²×C₆₇	1	1	yes	characteristic
649	#436	C₂²×C₆₇	1	1	yes	characteristic
650	#436	C₂²×C₆₇	1	1	yes	characteristic
651	#436	C₂²×C₆₇	1	2	yes	complemented
652	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
653	#436	C₂²×C₆₇	1	2	yes	complemented
654	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#436	C₂²×C₆₇	1	2	yes	complemented
657	#436	C₂²×C₆₇	1	2	yes	complemented
658	#436	C₂²×C₆₇	1	2	yes	complemented
659	#436	C₂²×C₆₇	1	2	yes	complemented
660	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
662	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#436	C₂²×C₆₇	1	2	yes	complemented
664	#436	C₂²×C₆₇	1	2	yes	complemented
665	#435	C₂²×C₆₇	1	1	yes	characteristic
666	#435	C₂²×C₆₇	1	2	yes	—
667	#435	C₂²×C₆₇	1	1	yes	characteristic
668	#435	C₂²×C₆₇	1	2	yes	complemented
669	#435	C₂²×C₆₇	1	2	yes	complemented
670	#435	C₂²×C₆₇	1	2	yes	complemented
671	#435	C₂²×C₆₇	1	2	yes	complemented
672	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
673	#435	C₂²×C₆₇	1	2	yes	complemented
674	#435	C₂²×C₆₇	1	2	yes	complemented
675	#435	C₂²×C₆₇	1	2	yes	complemented
676	#435	C₂²×C₆₇	1	2	yes	complemented
677	#435	C₂²×C₆₇	1	2	yes	complemented
678	#435	C₂²×C₆₇	1	2	yes	complemented
679	#435	C₂²×C₆₇	1	2	yes	complemented
680	#435	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	#435	C₂²×C₆₇	1	2	yes	complemented
682	#435	C₂²×C₆₇	1	2	yes	complemented
683	#435	C₂²×C₆₇	1	2	yes	complemented
684	#435	C₂²×C₆₇	1	2	yes	complemented
685	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
686	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
687	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
689	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#433	C₂²×C₆₇	1	2	yes	complemented
693	#433	C₂²×C₆₇	1	2	yes	complemented
694	#433	C₂²×C₆₇	1	2	yes	complemented
695	#433	C₂²×C₆₇	1	2	yes	complemented
696	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
697	#432	C₂²×C₆₇	1	2	yes	complemented
698	#432	C₂²×C₆₇	1	2	yes	complemented
699	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
700	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#424	C₂²×C₆₇	1	2	yes	complemented
705	#424	C₂²×C₆₇	1	2	yes	complemented
706	#423	C₂²×C₆₇	1	2	yes	complemented
707	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#408	C₂²×C₆₇	1	2	yes	complemented
711	#408	C₂²×C₆₇	1	2	yes	complemented
712	#408	C₂²×C₆₇	1	2	yes	complemented
713	#407	C₂²×C₆₇	1	2	yes	complemented
714	#407	C₂²×C₆₇	1	2	yes	complemented
715	#407	C₂²×C₆₇	1	2	yes	complemented
716	#407	C₂²×C₆₇	1	2	yes	complemented
717	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
718	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
719	#405	C₂²×C₆₇	1	2	yes	complemented
720	#405	C₂²×C₆₇	1	2	yes	complemented
721	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
723	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
726	C₂×#41	C₂×C₄×C₆₇	1	1	yes	characteristic
727	C₂×#41	C₂³×C₆₇	1	2	yes	—
728	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
729	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
730	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
731	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
732	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
733	#131	—	4	4	no	—
734	C₂×M₁₆	—	4	4	no	—
735	C₂×M₁₆	—	4	4	no	—
736	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
738	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
739	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
741	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
742	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
743	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
747	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
749	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
751	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
752	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
753	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
754	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
755	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
756	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
757	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
758	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
759	#126	C₂×C₄×C₆₇	1	2	yes	—
760	#126	C₂×C₄×C₆₇	1	2	yes	—
761	#126	C₂×C₄×C₆₇	1	2	yes	—
762	#126	C₂×C₄×C₆₇	1	2	yes	—
763	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
764	#125	C₂×C₄×C₆₇	1	2	yes	—
765	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
766	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
767	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
768	#124	C₂×C₄×C₆₇	1	2	yes	—
769	#124	C₂×C₄×C₆₇	1	2	yes	—
770	#123	C₂×C₄×C₆₇	1	2	yes	—
771	#123	C₂×C₄×C₆₇	1	2	yes	—
772	#123	C₂×C₄×C₆₇	1	2	yes	—
773	#123	C₂×C₄×C₆₇	1	2	yes	—
774	#123	C₂×C₄×C₆₇	1	2	yes	—
775	#123	C₂×C₄×C₆₇	1	2	yes	—
776	#123	C₂×C₄×C₆₇	1	2	yes	—
777	#123	C₂×C₄×C₆₇	1	2	yes	—
778	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
779	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
780	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
781	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
782	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
785	#121	C₂×C₄×C₆₇	1	2	yes	—
786	#121	C₂×C₄×C₆₇	1	2	yes	—
787	#121	C₂×C₄×C₆₇	1	2	yes	—
788	#121	C₂×C₄×C₆₇	1	2	yes	—
789	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
790	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
791	#121	C₂×C₄×C₆₇	1	2	yes	—
792	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
793	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
794	#121	C₂×C₄×C₆₇	1	2	yes	—
795	#120	C₂×C₄×C₆₇	1	2	yes	—
796	#120	C₂×C₄×C₆₇	1	2	yes	—
797	#120	C₂×C₄×C₆₇	1	2	yes	—
798	#120	C₂×C₄×C₆₇	1	2	yes	—
799	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
800	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
802	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
803	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
804	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
805	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
806	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
807	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
808	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
809	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
810	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
811	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
812	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
813	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
814	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
815	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
818	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₆₇	1	2	yes	—
821	C₄×D₄	C₂³×C₆₇	1	2	yes	—
822	C₄×D₄	C₂³×C₆₇	1	2	yes	—
823	C₄×D₄	C₂³×C₆₇	1	2	yes	—
824	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×D₄	C₂³×C₆₇	1	2	yes	—
827	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
831	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
832	#117	C₂×C₄×C₆₇	1	2	yes	—
833	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
834	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
835	#117	C₂³×C₆₇	1	2	yes	—
836	#117	C₂³×C₆₇	1	2	yes	—
837	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
839	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
843	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
844	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
846	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
847	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
853	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
855	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
856	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
857	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
859	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
860	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
865	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
866	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
873	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
876	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
885	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
886	#97	C₂³×C₆₇	1	1	yes	characteristic
887	#97	C₂³×C₆₇	1	1	yes	characteristic
888	#97	C₂³×C₆₇	1	2	yes	—
889	#97	C₂³×C₆₇	1	1	yes	characteristic
890	#97	C₂³×C₆₇	1	1	yes	characteristic
891	#97	C₂³×C₆₇	1	2	yes	—
892	#97	C₂³×C₆₇	1	2	yes	—
893	#97	C₂³×C₆₇	1	2	yes	—
894	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
898	C₄×C₈	C₂³×C₆₇	1	2	yes	—
899	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
901	C₄×C₈	C₂³×C₆₇	1	2	yes	—
902	C₄×C₈	C₂³×C₆₇	1	2	yes	—
903	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
904	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
910	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
911	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	4	no	—
915	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
916	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
917	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
918	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
920	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
921	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
922	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
923	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
924	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
925	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
926	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
927	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
928	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
929	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
936	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
937	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
938	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
941	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
943	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
944	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
945	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
946	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
947	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
954	M₁₆	—	2	2	no	—
955	M₁₆	—	2	4	no	—
956	M₁₆	—	2	4	no	—
957	M₁₆	—	2	2	no	—
958	M₁₆	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	M₁₆	—	4	2	no	—
961	M₁₆	—	4	2	no	—
962	M₁₆	—	4	2	no	—
963	M₁₆	—	4	1	no	—
964	M₁₆	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	1	no	—
967	C₂×C₈	—	2	2	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	—	4	2	no	—
972	C₂×C₈	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	1	no	—
975	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
979	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
984	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
985	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
986	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
990	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
995	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
996	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1001	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1002	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1003	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1004	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1005	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1006	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1007	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1008	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1009	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1014	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1019	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1020	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1021	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1022	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1023	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1026	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1029	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1030	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1031	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1032	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1033	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1034	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1035	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1036	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1037	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1038	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1039	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1040	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₆₇	1	2	yes	—
1044	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1046	C₂³	—	2	4	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	4	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1053	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1054	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1055	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1056	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1057	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1058	Q₈	—	2	2	no	—
1059	Q₈	—	4	1	no	—
1060	Q₈	—	4	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	1	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	2	no	—
1075	D₄	—	4	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1103	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1105	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1106	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1107	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1108	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1112	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1113	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1114	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1115	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1116	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1117	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1118	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1119	C₈	—	2	2	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	2	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	1	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	1	no	—
1148	C₂²	—	8	4	no	—
1149	C₂²	—	8	4	no	—
1150	C₂²	#568×C₆₇	1	2	yes	—
1151	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	1	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	#568×C₆₇	1	2	yes	—
1168	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1169	C₄	#585×C₆₇	1	1	yes	characteristic
1170	C₂	—	2	2	no	—
1171	C₂	—	4	1	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1177	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1178	C₂	C₂×#568×C₆₇	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	C₆₇×#3481	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×#2995	C₂	semidirect
3. C₆₇×#2994	C₂	semidirect
4. C₆₇×#2993	C₂	semidirect
5. C₆₇×#2990	C₂	semidirect
6. C₆₇×#2989	C₂	semidirect
7. C₆₇×#2981	C₂	semidirect
8. C₆₇×#2978	C₂	semidirect
9. C₆₇×#2976	C₂	semidirect
10. C₆₇×#2975	C₂	semidirect
11. C₆₇×#2974	C₂	semidirect
12. C₆₇×#2973	C₂	semidirect
13. C₆₇×#2971	C₂	semidirect
14. C₆₇×#2969	C₂	semidirect
15. C₆₇×#2967	C₂	semidirect
16. C₆₇×#2966	C₂	semidirect
17. C₆₇×#2965	C₂	semidirect
18. C₆₇×#2935	C₂	semidirect
19. D₄×M₁₆×C₆₇	C₂	semidirect
20. D₄×M₁₆×C₆₇	C₂	semidirect
21. C₆₇×#2933	C₂	semidirect
22. C₆₇×#2930	C₂	semidirect
23. C₂×#436×C₆₇	C₂	semidirect
24. C₂×#131×C₆₇	C₂²	semidirect
25. C₂²×M₁₆×C₆₇	C₂²	semidirect
26. C₂²×M₁₆×C₆₇	C₂²	semidirect
50. #446×C₆₇	C₂²	semidirect
51. #446×C₆₇	C₂²	semidirect
52. #446×C₆₇	C₂²	semidirect
53. #446×C₆₇	C₂²	semidirect
54. #446×C₆₇	C₂²	semidirect
55. C₈×Q₈×C₆₇	C₂²	semidirect
56. C₈×Q₈×C₆₇	C₂²	semidirect
61. #436×C₆₇	C₂²	semidirect
62. #436×C₆₇	C₂²	semidirect
63. #436×C₆₇	C₂²	semidirect
64. #436×C₆₇	C₂²	semidirect
65. #436×C₆₇	C₂²	semidirect
66. #436×C₆₇	C₂²	semidirect
67. #436×C₆₇	C₂²	semidirect
68. #436×C₆₇	C₂²	semidirect
69. #436×C₆₇	C₂²	semidirect
70. #436×C₆₇	C₂²	semidirect
71. #436×C₆₇	C₂²	semidirect
72. #436×C₆₇	C₂²	semidirect
73. #436×C₆₇	C₂²	semidirect
74. #436×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. #435×C₆₇	C₂²	semidirect
86. #435×C₆₇	C₂²	semidirect
87. #435×C₆₇	C₂²	semidirect
88. #435×C₆₇	C₂²	semidirect
89. #435×C₆₇	C₂²	semidirect
90. #435×C₆₇	C₂²	semidirect
91. #435×C₆₇	C₂²	semidirect
92. #435×C₆₇	C₂²	semidirect
93. #435×C₆₇	C₂²	semidirect
94. #435×C₆₇	C₂²	semidirect
95. C₈×D₄×C₆₇	C₂²	semidirect
96. C₈×D₄×C₆₇	C₂²	semidirect
97. C₈×D₄×C₆₇	C₂²	semidirect
98. C₈×D₄×C₆₇	C₂²	semidirect
99. C₈×D₄×C₆₇	C₂²	semidirect
100. C₈×D₄×C₆₇	C₂²	semidirect
101. C₈×D₄×C₆₇	C₂²	semidirect
102. #433×C₆₇	C₂²	semidirect
103. #433×C₆₇	C₂²	semidirect
104. #433×C₆₇	C₂²	semidirect
105. #433×C₆₇	C₂²	semidirect
106. #432×C₆₇	C₂²	semidirect
107. #432×C₆₇	C₂²	semidirect
108. #432×C₆₇	C₂²	semidirect
109. #432×C₆₇	C₂²	semidirect
110. #431×C₆₇	C₂²	semidirect
111. #431×C₆₇	C₂²	semidirect
112. #431×C₆₇	C₂²	semidirect
113. #431×C₆₇	C₂²	semidirect
114. #424×C₆₇	C₂²	semidirect
115. #424×C₆₇	C₂²	semidirect
116. #423×C₆₇	C₂²	semidirect
117. #423×C₆₇	C₂²	semidirect
118. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
119. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
120. #408×C₆₇	C₂²	semidirect
121. #408×C₆₇	C₂²	semidirect
122. #408×C₆₇	C₂²	semidirect
123. #407×C₆₇	C₂²	semidirect
124. #407×C₆₇	C₂²	semidirect
125. #407×C₆₇	C₂²	semidirect
126. #407×C₆₇	C₂²	semidirect
127. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
128. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
129. #405×C₆₇	C₂²	semidirect
130. #405×C₆₇	C₂²	semidirect
131. C₄×M₁₆×C₆₇	C₂²	semidirect
132. C₄×M₁₆×C₆₇	C₂²	semidirect
133. C₄×M₁₆×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
580. #60324	C₆₇	direct (N × H)
591. #2995	C₂×C₆₇	semidirect
592. #2994	C₂×C₆₇	semidirect
593. #2993	C₂×C₆₇	semidirect
594. #2990	C₂×C₆₇	semidirect
595. #2989	C₂×C₆₇	semidirect
596. #2981	C₂×C₆₇	semidirect
597. #2978	C₂×C₆₇	semidirect
598. #2976	C₂×C₆₇	semidirect
599. #2975	C₂×C₆₇	semidirect
600. #2974	C₂×C₆₇	semidirect
601. #2973	C₂×C₆₇	semidirect
602. #2971	C₂×C₆₇	semidirect
603. #2969	C₂×C₆₇	semidirect
604. #2967	C₂×C₆₇	semidirect
605. #2966	C₂×C₆₇	semidirect
606. #2965	C₂×C₆₇	semidirect
607. #2935	C₂×C₆₇	semidirect
608. D₄×M₁₆	C₂×C₆₇	semidirect
609. D₄×M₁₆	C₂×C₆₇	semidirect
610. #2933	C₂×C₆₇	semidirect
611. #2930	C₂×C₆₇	semidirect
612. C₂×#436	C₂×C₆₇	semidirect
613. C₆₇	#60324	direct (N × H)
614. C₂×#131	C₂²×C₆₇	semidirect
615. C₂²×M₁₆	C₂²×C₆₇	semidirect
616. C₂²×M₁₆	C₂²×C₆₇	semidirect
640. #446	C₂²×C₆₇	semidirect
641. #446	C₂²×C₆₇	semidirect
642. #446	C₂²×C₆₇	semidirect
643. #446	C₂²×C₆₇	semidirect
644. #446	C₂²×C₆₇	semidirect
645. C₈×Q₈	C₂²×C₆₇	semidirect
646. C₈×Q₈	C₂²×C₆₇	semidirect
651. #436	C₂²×C₆₇	semidirect
652. #436	C₂²×C₆₇	semidirect
653. #436	C₂²×C₆₇	semidirect
654. #436	C₂²×C₆₇	semidirect
655. #436	C₂²×C₆₇	semidirect
656. #436	C₂²×C₆₇	semidirect
657. #436	C₂²×C₆₇	semidirect
658. #436	C₂²×C₆₇	semidirect
659. #436	C₂²×C₆₇	semidirect
660. #436	C₂²×C₆₇	semidirect
661. #436	C₂²×C₆₇	semidirect
662. #436	C₂²×C₆₇	semidirect
663. #436	C₂²×C₆₇	semidirect
664. #436	C₂²×C₆₇	semidirect
668. #435	C₂²×C₆₇	semidirect
669. #435	C₂²×C₆₇	semidirect
670. #435	C₂²×C₆₇	semidirect
671. #435	C₂²×C₆₇	semidirect
672. #435	C₂²×C₆₇	semidirect
673. #435	C₂²×C₆₇	semidirect
674. #435	C₂²×C₆₇	semidirect
675. #435	C₂²×C₆₇	semidirect
676. #435	C₂²×C₆₇	semidirect
677. #435	C₂²×C₆₇	semidirect
678. #435	C₂²×C₆₇	semidirect
679. #435	C₂²×C₆₇	semidirect
680. #435	C₂²×C₆₇	semidirect
681. #435	C₂²×C₆₇	semidirect
682. #435	C₂²×C₆₇	semidirect
683. #435	C₂²×C₆₇	semidirect
684. #435	C₂²×C₆₇	semidirect
685. C₈×D₄	C₂²×C₆₇	semidirect
686. C₈×D₄	C₂²×C₆₇	semidirect
687. C₈×D₄	C₂²×C₆₇	semidirect
688. C₈×D₄	C₂²×C₆₇	semidirect
689. C₈×D₄	C₂²×C₆₇	semidirect
690. C₈×D₄	C₂²×C₆₇	semidirect
691. C₈×D₄	C₂²×C₆₇	semidirect
692. #433	C₂²×C₆₇	semidirect
693. #433	C₂²×C₆₇	semidirect
694. #433	C₂²×C₆₇	semidirect
695. #433	C₂²×C₆₇	semidirect
696. #432	C₂²×C₆₇	semidirect
697. #432	C₂²×C₆₇	semidirect
698. #432	C₂²×C₆₇	semidirect
699. #432	C₂²×C₆₇	semidirect
700. #431	C₂²×C₆₇	semidirect
701. #431	C₂²×C₆₇	semidirect
702. #431	C₂²×C₆₇	semidirect
703. #431	C₂²×C₆₇	semidirect
704. #424	C₂²×C₆₇	semidirect
705. #424	C₂²×C₆₇	semidirect
706. #423	C₂²×C₆₇	semidirect
707. #423	C₂²×C₆₇	semidirect
708. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
709. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
710. #408	C₂²×C₆₇	semidirect
711. #408	C₂²×C₆₇	semidirect
712. #408	C₂²×C₆₇	semidirect
713. #407	C₂²×C₆₇	semidirect
714. #407	C₂²×C₆₇	semidirect
715. #407	C₂²×C₆₇	semidirect
716. #407	C₂²×C₆₇	semidirect
717. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
718. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
719. #405	C₂²×C₆₇	semidirect
720. #405	C₂²×C₆₇	semidirect
721. C₄×M₁₆	C₂²×C₆₇	semidirect
722. C₄×M₁₆	C₂²×C₆₇	semidirect
723. C₄×M₁₆	C₂²×C₆₇	semidirect
724. C₂×C₄×C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3481	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2981	2
C₆₇×#2978	2
C₆₇×#2976	2
C₆₇×#2975	2
C₆₇×#2974	2
C₆₇×#2973	2
C₆₇×#2971	2
C₆₇×#2969	2
C₆₇×#2967	2
C₆₇×#2966	2
C₆₇×#2965	2
C₆₇×#2935	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2930	2
C₂×#436×C₆₇	2
#60324	67

Subgroups — C67×#60324 #30739575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60324 #30739575