Subgroups — C₆₇×#60314 #30739565

Order 17152.

1900 conjugacy classes of subgroups.

The subgroup lattice has 1056 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×#2992	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2989	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2980	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2978	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2977	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2976	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2974	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2973	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2970	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2968	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2967	C₂	1	2	yes	maximal, complemented
14	D₄×M₁₆×C₆₇	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2933	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#435×C₆₇	C₂	1	2	yes	maximal, complemented
20	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	complemented
23	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
24	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
25	#559×C₆₇	C₄	1	1	yes	characteristic
26	#554×C₆₇	C₄	1	2	yes	—
27	#553×C₆₇	C₄	1	2	yes	—
28	#553×C₆₇	C₄	1	2	yes	—
29	#551×C₆₇	C₄	1	1	yes	characteristic
30	#551×C₆₇	C₄	1	2	yes	—
31	#551×C₆₇	C₄	1	1	yes	characteristic
32	#546×C₆₇	C₄	1	2	yes	—
33	#546×C₆₇	C₄	1	2	yes	—
34	D₄²×C₆₇	C₄	1	1	yes	characteristic
35	#532×C₆₇	C₂²	1	1	yes	characteristic
36	#529×C₆₇	C₂²	1	2	yes	—
37	#529×C₆₇	C₂²	1	2	yes	—
38	#525×C₆₇	C₂²	1	1	yes	characteristic
39	#525×C₆₇	C₂²	1	1	yes	characteristic
40	#525×C₆₇	C₂²	1	2	yes	—
41	C₄×#41×C₆₇	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
44	#446×C₆₇	C₂²	1	2	yes	complemented
45	#446×C₆₇	C₂²	1	2	yes	complemented
46	#446×C₆₇	C₂²	1	2	yes	complemented
47	#446×C₆₇	C₂²	1	2	yes	complemented
48	#436×C₆₇	C₂²	1	2	yes	complemented
49	#436×C₆₇	C₂²	1	2	yes	complemented
50	#436×C₆₇	C₂²	1	2	yes	complemented
51	#436×C₆₇	C₂²	1	2	yes	complemented
52	#436×C₆₇	C₂²	1	2	yes	complemented
53	#436×C₆₇	C₂²	1	2	yes	complemented
54	#435×C₆₇	C₂²	1	2	yes	—
55	#435×C₆₇	C₂²	1	2	yes	—
56	#435×C₆₇	C₂²	1	2	yes	—
57	#435×C₆₇	C₂²	1	2	yes	—
58	#435×C₆₇	C₂²	1	2	yes	complemented
59	#435×C₆₇	C₂²	1	2	yes	complemented
60	#435×C₆₇	C₂²	1	2	yes	complemented
61	#435×C₆₇	C₂²	1	2	yes	complemented
62	#435×C₆₇	C₂²	1	2	yes	complemented
63	#435×C₆₇	C₂²	1	2	yes	complemented
64	#435×C₆₇	C₂²	1	2	yes	complemented
65	#435×C₆₇	C₂²	1	2	yes	complemented
66	#435×C₆₇	C₂²	1	2	yes	complemented
67	#435×C₆₇	C₂²	1	2	yes	complemented
68	#435×C₆₇	C₂²	1	2	yes	complemented
69	#435×C₆₇	C₂²	1	2	yes	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	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
79	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
80	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
81	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
82	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
83	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
84	#433×C₆₇	C₂²	1	2	yes	complemented
85	#433×C₆₇	C₂²	1	2	yes	complemented
86	#433×C₆₇	C₂²	1	2	yes	complemented
87	#433×C₆₇	C₂²	1	2	yes	complemented
88	#432×C₆₇	C₂²	1	2	yes	complemented
89	#432×C₆₇	C₂²	1	2	yes	complemented
90	#432×C₆₇	C₂²	1	2	yes	complemented
91	#432×C₆₇	C₂²	1	2	yes	complemented
92	#431×C₆₇	C₂²	1	2	yes	complemented
93	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#424×C₆₇	C₂²	1	2	yes	complemented
96	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#423×C₆₇	C₂²	1	2	yes	complemented
98	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
99	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#408×C₆₇	C₂²	1	2	yes	complemented
104	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#407×C₆₇	C₂²	1	2	yes	complemented
107	#407×C₆₇	C₂²	1	2	yes	complemented
108	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
109	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
110	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
111	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#405×C₆₇	C₂²	1	2	yes	complemented
114	C₄×M₁₆×C₆₇	C₂²	1	2	yes	complemented
115	C₂×#97×C₆₇	C₂²	1	2	yes	complemented
116	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
118	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
119	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	#131×C₆₇	—	4	2	no	—
126	#131×C₆₇	—	4	2	no	—
127	C₂×M₁₆×C₆₇	—	4	4	no	—
128	C₂×M₁₆×C₆₇	—	4	2	no	—
129	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
130	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
132	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
133	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
134	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
139	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₆₇	—	4	2	no	—
142	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
143	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
147	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
149	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
154	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
155	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
156	#126×C₆₇	C₂×C₄	1	2	yes	—
157	#126×C₆₇	C₂×C₄	1	2	yes	—
158	#126×C₆₇	C₂×C₄	1	2	yes	—
159	#126×C₆₇	C₂×C₄	1	2	yes	—
160	#125×C₆₇	C₂×C₄	1	2	yes	—
161	#125×C₆₇	C₂×C₄	1	2	yes	—
162	#124×C₆₇	C₂×C₄	1	2	yes	—
163	#124×C₆₇	C₂×C₄	1	2	yes	—
164	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
165	#124×C₆₇	C₂×C₄	1	1	yes	characteristic
166	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
167	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
168	#123×C₆₇	C₂×C₄	1	2	yes	—
169	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
170	#123×C₆₇	C₂×C₄	1	1	yes	characteristic
171	#123×C₆₇	C₂×C₄	1	2	yes	—
172	#123×C₆₇	C₂×C₄	1	2	yes	—
173	#123×C₆₇	C₂×C₄	1	2	yes	—
174	#123×C₆₇	C₂×C₄	1	2	yes	—
175	#123×C₆₇	C₂×C₄	1	2	yes	—
176	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
177	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
178	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
179	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
180	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
181	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
182	#121×C₆₇	C₂×C₄	1	2	yes	—
183	#121×C₆₇	C₂×C₄	1	2	yes	—
184	#121×C₆₇	C₂×C₄	1	2	yes	—
185	#121×C₆₇	C₂×C₄	1	2	yes	—
186	#121×C₆₇	C₂×C₄	1	2	yes	—
187	#121×C₆₇	C₂×C₄	1	2	yes	—
188	#121×C₆₇	C₂×C₄	1	2	yes	—
189	#121×C₆₇	C₂×C₄	1	2	yes	—
190	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
191	#120×C₆₇	C₂×C₄	1	2	yes	—
192	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
193	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
194	#120×C₆₇	C₂×C₄	1	2	yes	—
195	#120×C₆₇	C₂×C₄	1	1	yes	characteristic
196	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
197	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
198	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
199	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
200	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
201	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
202	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
203	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
204	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
205	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
206	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
207	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
208	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
209	C₄×D₄×C₆₇	C₂³	1	2	yes	—
210	C₄×D₄×C₆₇	C₂³	1	2	yes	—
211	C₄×D₄×C₆₇	C₂³	1	2	yes	—
212	C₄×D₄×C₆₇	C₂³	1	2	yes	—
213	C₄×D₄×C₆₇	C₂³	1	2	yes	—
214	C₄×D₄×C₆₇	C₂³	1	2	yes	—
215	C₄×D₄×C₆₇	C₂³	1	2	yes	—
216	C₄×D₄×C₆₇	C₂³	1	2	yes	—
217	C₄×D₄×C₆₇	C₂³	1	2	yes	—
218	#117×C₆₇	C₂×C₄	1	2	yes	—
219	#117×C₆₇	C₂×C₄	1	2	yes	—
220	#117×C₆₇	C₂×C₄	1	2	yes	—
221	#117×C₆₇	C₂³	1	1	yes	characteristic
222	#117×C₆₇	C₂³	1	1	yes	characteristic
223	#117×C₆₇	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
225	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
226	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
227	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
228	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
229	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
230	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
233	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
234	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
235	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
238	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
239	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
240	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
241	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
242	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
243	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
244	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
245	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
247	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
248	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
249	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
250	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
251	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
252	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
253	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
254	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
255	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
259	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
260	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
261	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
262	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
263	#97×C₆₇	C₂³	1	2	yes	—
264	#97×C₆₇	C₂³	1	2	yes	—
265	#97×C₆₇	C₂³	1	2	yes	—
266	#97×C₆₇	C₂³	1	2	yes	—
267	#97×C₆₇	C₂³	1	2	yes	—
268	#97×C₆₇	C₂³	1	2	yes	—
269	#97×C₆₇	C₂³	1	2	yes	—
270	#97×C₆₇	C₂³	1	2	yes	—
271	C₄×C₈×C₆₇	C₂³	1	2	yes	—
272	C₄×C₈×C₆₇	C₂³	1	2	yes	—
273	C₄×C₈×C₆₇	C₂³	1	2	yes	—
274	C₄×C₈×C₆₇	C₂³	1	2	yes	—
275	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
277	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
278	#41×C₆₇	—	4	1	no	—
279	#41×C₆₇	—	4	1	no	—
280	#41×C₆₇	—	4	1	no	—
281	#41×C₆₇	—	4	1	no	—
282	#41×C₆₇	—	4	4	no	—
283	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
284	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
285	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
286	C₂×D₄×C₆₇	—	4	4	no	—
287	C₂×D₄×C₆₇	—	4	4	no	—
288	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
289	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
291	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
292	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
297	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
298	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
299	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
300	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
301	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	—	4	1	no	—
303	C₂²×C₄×C₆₇	—	4	2	no	—
304	C₂²×C₄×C₆₇	—	4	1	no	—
305	C₂²×C₄×C₆₇	—	4	1	no	—
306	C₂²×C₄×C₆₇	—	4	2	no	—
307	C₂²×C₄×C₆₇	—	4	1	no	—
308	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
309	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
315	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
319	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
326	M₁₆×C₆₇	—	2	4	no	—
327	M₁₆×C₆₇	—	2	4	no	—
328	M₁₆×C₆₇	—	4	2	no	—
329	M₁₆×C₆₇	—	4	2	no	—
330	M₁₆×C₆₇	—	4	2	no	—
331	M₁₆×C₆₇	—	4	1	no	—
332	M₁₆×C₆₇	—	4	2	no	—
333	M₁₆×C₆₇	—	4	1	no	—
334	M₁₆×C₆₇	—	4	1	no	—
335	M₁₆×C₆₇	—	4	1	no	—
336	M₁₆×C₆₇	—	4	1	no	—
337	M₁₆×C₆₇	—	4	1	no	—
338	C₂×C₈×C₆₇	—	2	4	no	—
339	C₂×C₈×C₆₇	—	2	2	no	—
340	C₂×C₈×C₆₇	—	2	2	no	—
341	C₂×C₈×C₆₇	—	2	2	no	—
342	C₂×C₈×C₆₇	—	4	2	no	—
343	C₂×C₈×C₆₇	—	4	1	no	—
344	C₂×C₈×C₆₇	—	4	2	no	—
345	C₂×C₈×C₆₇	—	4	1	no	—
346	C₂×C₈×C₆₇	—	4	2	no	—
347	C₂×C₈×C₆₇	—	4	2	no	—
348	C₂×C₈×C₆₇	—	4	1	no	—
349	C₂×C₈×C₆₇	—	4	2	no	—
350	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
352	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
354	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
355	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
358	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
359	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
362	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
372	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
375	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
397	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
399	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
402	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
403	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
404	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
405	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
406	C₄²×C₆₇	C₂⁴	1	2	yes	—
407	C₄²×C₆₇	C₂⁴	1	2	yes	—
408	C₄²×C₆₇	C₂⁴	1	2	yes	—
409	C₂³×C₆₇	—	2	4	no	—
410	C₂³×C₆₇	—	2	4	no	—
411	C₂³×C₆₇	—	4	1	no	—
412	C₂³×C₆₇	—	4	2	no	—
413	C₂³×C₆₇	—	4	1	no	—
414	C₂³×C₆₇	—	4	2	no	—
415	C₂³×C₆₇	—	4	2	no	—
416	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
417	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
418	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
419	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
420	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
421	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
422	Q₈×C₆₇	—	4	1	no	—
423	Q₈×C₆₇	—	4	1	no	—
424	Q₈×C₆₇	—	4	2	no	—
425	D₄×C₆₇	—	2	4	no	—
426	D₄×C₆₇	—	2	4	no	—
427	D₄×C₆₇	—	2	4	no	—
428	D₄×C₆₇	—	2	4	no	—
429	D₄×C₆₇	—	4	2	no	—
430	D₄×C₆₇	—	4	2	no	—
431	D₄×C₆₇	—	4	2	no	—
432	D₄×C₆₇	—	4	2	no	—
433	D₄×C₆₇	—	4	1	no	—
434	D₄×C₆₇	—	4	1	no	—
435	D₄×C₆₇	—	4	2	no	—
436	D₄×C₆₇	—	4	1	no	—
437	D₄×C₆₇	—	4	1	no	—
438	D₄×C₆₇	—	4	2	no	—
439	C₂×C₄×C₆₇	—	2	4	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	2	2	no	—
445	C₂×C₄×C₆₇	—	2	2	no	—
446	C₂×C₄×C₆₇	—	2	2	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	4	1	no	—
453	C₂×C₄×C₆₇	—	4	2	no	—
454	C₂×C₄×C₆₇	—	4	1	no	—
455	C₂×C₄×C₆₇	—	4	2	no	—
456	C₂×C₄×C₆₇	—	4	2	no	—
457	C₂×C₄×C₆₇	—	4	2	no	—
458	C₂×C₄×C₆₇	—	4	2	no	—
459	C₂×C₄×C₆₇	—	4	2	no	—
460	C₂×C₄×C₆₇	—	4	2	no	—
461	C₂×C₄×C₆₇	—	4	2	no	—
462	C₂×C₄×C₆₇	—	4	2	no	—
463	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
468	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
471	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
472	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
476	C₈×C₆₇	—	2	2	no	—
477	C₈×C₆₇	—	2	1	no	—
478	C₈×C₆₇	—	2	1	no	—
479	C₈×C₆₇	—	2	1	no	—
480	C₈×C₆₇	—	2	2	no	—
481	C₈×C₆₇	—	2	2	no	—
482	C₈×C₆₇	—	2	2	no	—
483	C₈×C₆₇	—	2	2	no	—
484	C₈×C₆₇	—	2	2	no	—
485	C₈×C₆₇	H(5,𝔽₂)	1	2	yes	—
486	C₂²×C₆₇	—	2	2	no	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	1	no	—
490	C₂²×C₆₇	—	2	1	no	—
491	C₂²×C₆₇	—	2	2	no	—
492	C₂²×C₆₇	—	2	1	no	—
493	C₂²×C₆₇	—	2	2	no	—
494	C₂²×C₆₇	—	2	2	no	—
495	C₂²×C₆₇	—	2	2	no	—
496	C₂²×C₆₇	—	2	2	no	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	2	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	4	4	no	—
501	C₂²×C₆₇	—	8	4	no	—
502	C₂²×C₆₇	—	8	2	no	—
503	C₂²×C₆₇	#568	1	4	yes	—
504	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
505	C₄×C₆₇	—	2	2	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	1	no	—
508	C₄×C₆₇	—	2	1	no	—
509	C₄×C₆₇	—	2	2	no	—
510	C₄×C₆₇	—	2	1	no	—
511	C₄×C₆₇	—	2	2	no	—
512	C₄×C₆₇	—	2	2	no	—
513	C₄×C₆₇	—	2	2	no	—
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	2	2	no	—
516	C₄×C₆₇	—	2	2	no	—
517	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
518	C₄×C₆₇	#585	1	1	yes	characteristic
519	#60314	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
520	C₂×C₆₇	—	2	4	no	—
521	C₂×C₆₇	—	4	1	no	—
522	C₂×C₆₇	—	4	1	no	—
523	C₂×C₆₇	—	4	1	no	—
524	C₂×C₆₇	—	4	2	no	—
525	C₂×C₆₇	—	4	2	no	—
526	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂×C₆₇	C₂×#568	1	2	yes	—
528	#3481	C₂×C₆₇	1	1	yes	characteristic
529	#2995	C₂×C₆₇	1	2	yes	complemented
530	#2992	C₂×C₆₇	1	2	yes	complemented
531	#2989	C₂×C₆₇	1	2	yes	complemented
532	#2980	C₂×C₆₇	1	1	yes	characteristic, complemented
533	#2978	C₂×C₆₇	1	1	yes	characteristic, complemented
534	#2977	C₂×C₆₇	1	1	yes	characteristic, complemented
535	#2976	C₂×C₆₇	1	2	yes	complemented
536	#2974	C₂×C₆₇	1	2	yes	complemented
537	#2973	C₂×C₆₇	1	2	yes	complemented
538	#2970	C₂×C₆₇	1	2	yes	complemented
539	#2968	C₂×C₆₇	1	2	yes	complemented
540	#2967	C₂×C₆₇	1	2	yes	complemented
541	D₄×M₁₆	C₂×C₆₇	1	2	yes	complemented
542	#2933	C₂×C₆₇	1	2	yes	complemented
543	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
546	C₂×#435	C₂×C₆₇	1	2	yes	complemented
547	C₆₇	#60314	1	1	yes	characteristic, direct product factor, Sylow
548	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
550	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	complemented
551	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
553	#559	C₄×C₆₇	1	1	yes	characteristic
554	#554	C₄×C₆₇	1	2	yes	—
555	#553	C₄×C₆₇	1	2	yes	—
556	#553	C₄×C₆₇	1	2	yes	—
557	#551	C₄×C₆₇	1	1	yes	characteristic
558	#551	C₄×C₆₇	1	2	yes	—
559	#551	C₄×C₆₇	1	1	yes	characteristic
560	#546	C₄×C₆₇	1	2	yes	—
561	#546	C₄×C₆₇	1	2	yes	—
562	D₄²	C₄×C₆₇	1	1	yes	characteristic
563	#532	C₂²×C₆₇	1	1	yes	characteristic
564	#529	C₂²×C₆₇	1	2	yes	—
565	#529	C₂²×C₆₇	1	2	yes	—
566	#525	C₂²×C₆₇	1	1	yes	characteristic
567	#525	C₂²×C₆₇	1	1	yes	characteristic
568	#525	C₂²×C₆₇	1	2	yes	—
569	C₄×#41	C₂²×C₆₇	1	2	yes	—
570	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
571	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
572	#446	C₂²×C₆₇	1	2	yes	complemented
573	#446	C₂²×C₆₇	1	2	yes	complemented
574	#446	C₂²×C₆₇	1	2	yes	complemented
575	#446	C₂²×C₆₇	1	2	yes	complemented
576	#436	C₂²×C₆₇	1	2	yes	complemented
577	#436	C₂²×C₆₇	1	2	yes	complemented
578	#436	C₂²×C₆₇	1	2	yes	complemented
579	#436	C₂²×C₆₇	1	2	yes	complemented
580	#436	C₂²×C₆₇	1	2	yes	complemented
581	#436	C₂²×C₆₇	1	2	yes	complemented
582	#435	C₂²×C₆₇	1	2	yes	—
583	#435	C₂²×C₆₇	1	2	yes	—
584	#435	C₂²×C₆₇	1	2	yes	—
585	#435	C₂²×C₆₇	1	2	yes	—
586	#435	C₂²×C₆₇	1	2	yes	complemented
587	#435	C₂²×C₆₇	1	2	yes	complemented
588	#435	C₂²×C₆₇	1	2	yes	complemented
589	#435	C₂²×C₆₇	1	2	yes	complemented
590	#435	C₂²×C₆₇	1	2	yes	complemented
591	#435	C₂²×C₆₇	1	2	yes	complemented
592	#435	C₂²×C₆₇	1	2	yes	complemented
593	#435	C₂²×C₆₇	1	2	yes	complemented
594	#435	C₂²×C₆₇	1	2	yes	complemented
595	#435	C₂²×C₆₇	1	2	yes	complemented
596	#435	C₂²×C₆₇	1	2	yes	complemented
597	#435	C₂²×C₆₇	1	2	yes	complemented
598	#435	C₂²×C₆₇	1	2	yes	complemented
599	#435	C₂²×C₆₇	1	2	yes	complemented
600	#435	C₂²×C₆₇	1	2	yes	complemented
601	#435	C₂²×C₆₇	1	2	yes	complemented
602	#435	C₂²×C₆₇	1	2	yes	complemented
603	#435	C₂²×C₆₇	1	2	yes	complemented
604	#435	C₂²×C₆₇	1	2	yes	complemented
605	#435	C₂²×C₆₇	1	2	yes	complemented
606	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
607	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
608	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
609	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
610	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
611	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
612	#433	C₂²×C₆₇	1	2	yes	complemented
613	#433	C₂²×C₆₇	1	2	yes	complemented
614	#433	C₂²×C₆₇	1	2	yes	complemented
615	#433	C₂²×C₆₇	1	2	yes	complemented
616	#432	C₂²×C₆₇	1	2	yes	complemented
617	#432	C₂²×C₆₇	1	2	yes	complemented
618	#432	C₂²×C₆₇	1	2	yes	complemented
619	#432	C₂²×C₆₇	1	2	yes	complemented
620	#431	C₂²×C₆₇	1	2	yes	complemented
621	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
622	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	#424	C₂²×C₆₇	1	2	yes	complemented
624	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#423	C₂²×C₆₇	1	2	yes	complemented
626	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
627	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#408	C₂²×C₆₇	1	2	yes	complemented
632	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	#407	C₂²×C₆₇	1	2	yes	complemented
635	#407	C₂²×C₆₇	1	2	yes	complemented
636	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
637	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
638	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
639	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#405	C₂²×C₆₇	1	2	yes	complemented
642	C₄×M₁₆	C₂²×C₆₇	1	2	yes	complemented
643	C₂×#97	C₂²×C₆₇	1	2	yes	complemented
644	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
646	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
648	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
649	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
650	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
652	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
653	#131	—	4	2	no	—
654	#131	—	4	2	no	—
655	C₂×M₁₆	—	4	4	no	—
656	C₂×M₁₆	—	4	2	no	—
657	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
658	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
659	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
660	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
661	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
662	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
663	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
664	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
665	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
667	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
668	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
669	C₂²×C₈	—	4	2	no	—
670	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
671	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
672	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
673	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
674	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
675	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
676	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
677	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
678	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
679	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
680	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
681	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
682	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
683	#127	C₂×C₄×C₆₇	1	1	yes	characteristic
684	#126	C₂×C₄×C₆₇	1	2	yes	—
685	#126	C₂×C₄×C₆₇	1	2	yes	—
686	#126	C₂×C₄×C₆₇	1	2	yes	—
687	#126	C₂×C₄×C₆₇	1	2	yes	—
688	#125	C₂×C₄×C₆₇	1	2	yes	—
689	#125	C₂×C₄×C₆₇	1	2	yes	—
690	#124	C₂×C₄×C₆₇	1	2	yes	—
691	#124	C₂×C₄×C₆₇	1	2	yes	—
692	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
693	#124	C₂×C₄×C₆₇	1	1	yes	characteristic
694	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
695	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
696	#123	C₂×C₄×C₆₇	1	2	yes	—
697	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
698	#123	C₂×C₄×C₆₇	1	1	yes	characteristic
699	#123	C₂×C₄×C₆₇	1	2	yes	—
700	#123	C₂×C₄×C₆₇	1	2	yes	—
701	#123	C₂×C₄×C₆₇	1	2	yes	—
702	#123	C₂×C₄×C₆₇	1	2	yes	—
703	#123	C₂×C₄×C₆₇	1	2	yes	—
704	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
705	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
706	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
707	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
708	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
709	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
710	#121	C₂×C₄×C₆₇	1	2	yes	—
711	#121	C₂×C₄×C₆₇	1	2	yes	—
712	#121	C₂×C₄×C₆₇	1	2	yes	—
713	#121	C₂×C₄×C₆₇	1	2	yes	—
714	#121	C₂×C₄×C₆₇	1	2	yes	—
715	#121	C₂×C₄×C₆₇	1	2	yes	—
716	#121	C₂×C₄×C₆₇	1	2	yes	—
717	#121	C₂×C₄×C₆₇	1	2	yes	—
718	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
719	#120	C₂×C₄×C₆₇	1	2	yes	—
720	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
721	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
722	#120	C₂×C₄×C₆₇	1	2	yes	—
723	#120	C₂×C₄×C₆₇	1	1	yes	characteristic
724	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
725	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
726	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
727	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
728	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
729	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
730	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
731	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
732	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
733	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
734	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
735	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
736	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
737	C₄×D₄	C₂³×C₆₇	1	2	yes	—
738	C₄×D₄	C₂³×C₆₇	1	2	yes	—
739	C₄×D₄	C₂³×C₆₇	1	2	yes	—
740	C₄×D₄	C₂³×C₆₇	1	2	yes	—
741	C₄×D₄	C₂³×C₆₇	1	2	yes	—
742	C₄×D₄	C₂³×C₆₇	1	2	yes	—
743	C₄×D₄	C₂³×C₆₇	1	2	yes	—
744	C₄×D₄	C₂³×C₆₇	1	2	yes	—
745	C₄×D₄	C₂³×C₆₇	1	2	yes	—
746	#117	C₂×C₄×C₆₇	1	2	yes	—
747	#117	C₂×C₄×C₆₇	1	2	yes	—
748	#117	C₂×C₄×C₆₇	1	2	yes	—
749	#117	C₂³×C₆₇	1	1	yes	characteristic
750	#117	C₂³×C₆₇	1	1	yes	characteristic
751	#117	C₂³×C₆₇	1	2	yes	—
752	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
753	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
758	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
759	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
760	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
761	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
762	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
763	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
764	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
765	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
766	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
767	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
768	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
769	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
770	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
771	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
772	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
791	#97	C₂³×C₆₇	1	2	yes	—
792	#97	C₂³×C₆₇	1	2	yes	—
793	#97	C₂³×C₆₇	1	2	yes	—
794	#97	C₂³×C₆₇	1	2	yes	—
795	#97	C₂³×C₆₇	1	2	yes	—
796	#97	C₂³×C₆₇	1	2	yes	—
797	#97	C₂³×C₆₇	1	2	yes	—
798	#97	C₂³×C₆₇	1	2	yes	—
799	C₄×C₈	C₂³×C₆₇	1	2	yes	—
800	C₄×C₈	C₂³×C₆₇	1	2	yes	—
801	C₄×C₈	C₂³×C₆₇	1	2	yes	—
802	C₄×C₈	C₂³×C₆₇	1	2	yes	—
803	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
804	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
805	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
806	#41	—	4	1	no	—
807	#41	—	4	1	no	—
808	#41	—	4	1	no	—
809	#41	—	4	1	no	—
810	#41	—	4	4	no	—
811	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
812	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
813	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
814	C₂×D₄	—	4	4	no	—
815	C₂×D₄	—	4	4	no	—
816	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
817	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
818	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
819	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
820	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
821	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
822	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
823	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
824	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
825	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
826	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
827	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
828	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
829	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
830	C₂²×C₄	—	4	1	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
837	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
838	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
839	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
840	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
841	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
842	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
843	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
844	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
845	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
846	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
847	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
849	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
850	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
853	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
854	M₁₆	—	2	4	no	—
855	M₁₆	—	2	4	no	—
856	M₁₆	—	4	2	no	—
857	M₁₆	—	4	2	no	—
858	M₁₆	—	4	2	no	—
859	M₁₆	—	4	1	no	—
860	M₁₆	—	4	1	no	—
861	M₁₆	—	4	1	no	—
862	M₁₆	—	4	1	no	—
863	M₁₆	—	4	1	no	—
864	M₁₆	—	4	2	no	—
865	M₁₆	—	4	1	no	—
866	C₂×C₈	—	2	4	no	—
867	C₂×C₈	—	2	2	no	—
868	C₂×C₈	—	2	2	no	—
869	C₂×C₈	—	2	2	no	—
870	C₂×C₈	—	4	2	no	—
871	C₂×C₈	—	4	1	no	—
872	C₂×C₈	—	4	2	no	—
873	C₂×C₈	—	4	1	no	—
874	C₂×C₈	—	4	2	no	—
875	C₂×C₈	—	4	2	no	—
876	C₂×C₈	—	4	1	no	—
877	C₂×C₈	—	4	2	no	—
878	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
879	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
880	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
881	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
882	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
883	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
884	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
886	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
887	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
888	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
889	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
890	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
891	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
892	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
893	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
894	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
895	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
896	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
897	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
898	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
899	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
900	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
901	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
902	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
903	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
912	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
913	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
914	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
915	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
916	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
917	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
918	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
919	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
920	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
921	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
922	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
923	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
924	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
925	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
926	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
927	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
928	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
929	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
930	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
931	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
932	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
933	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
934	C₄²	C₂⁴×C₆₇	1	2	yes	—
935	C₄²	C₂⁴×C₆₇	1	2	yes	—
936	C₄²	C₂⁴×C₆₇	1	2	yes	—
937	C₂³	—	2	4	no	—
938	C₂³	—	2	4	no	—
939	C₂³	—	4	1	no	—
940	C₂³	—	4	2	no	—
941	C₂³	—	4	1	no	—
942	C₂³	—	4	2	no	—
943	C₂³	—	4	2	no	—
944	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
945	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
946	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
947	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
948	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
949	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
950	Q₈	—	4	2	no	—
951	Q₈	—	4	1	no	—
952	Q₈	—	4	1	no	—
953	D₄	—	2	4	no	—
954	D₄	—	2	4	no	—
955	D₄	—	2	4	no	—
956	D₄	—	2	4	no	—
957	D₄	—	4	2	no	—
958	D₄	—	4	2	no	—
959	D₄	—	4	2	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	1	no	—
963	D₄	—	4	1	no	—
964	D₄	—	4	2	no	—
965	D₄	—	4	1	no	—
966	D₄	—	4	1	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	4	1	no	—
981	C₂×C₄	—	4	2	no	—
982	C₂×C₄	—	4	1	no	—
983	C₂×C₄	—	4	2	no	—
984	C₂×C₄	—	4	2	no	—
985	C₂×C₄	—	4	2	no	—
986	C₂×C₄	—	4	2	no	—
987	C₂×C₄	—	4	2	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	4	2	no	—
991	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
992	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
993	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
994	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
995	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
996	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1001	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1002	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1003	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1004	C₈	—	2	2	no	—
1005	C₈	—	2	1	no	—
1006	C₈	—	2	1	no	—
1007	C₈	—	2	1	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	2	2	no	—
1010	C₈	—	2	2	no	—
1011	C₈	—	2	2	no	—
1012	C₈	—	2	2	no	—
1013	C₈	H(5,𝔽₂)×C₆₇	1	2	yes	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	4	4	no	—
1029	C₂²	—	8	4	no	—
1030	C₂²	—	8	2	no	—
1031	C₂²	#568×C₆₇	1	4	yes	—
1032	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1033	C₄	—	2	2	no	—
1034	C₄	—	2	2	no	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	1	no	—
1045	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1046	C₄	#585×C₆₇	1	1	yes	characteristic
1047	C₂	—	2	4	no	—
1048	C₂	—	4	1	no	—
1049	C₂	—	4	2	no	—
1050	C₂	—	4	1	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	1	no	—
1053	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1054	C₂	C₂×#568×C₆₇	1	2	yes	—

	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×#2992	C₂	semidirect
4. C₆₇×#2989	C₂	semidirect
5. C₆₇×#2980	C₂	semidirect
6. C₆₇×#2978	C₂	semidirect
7. C₆₇×#2977	C₂	semidirect
8. C₆₇×#2976	C₂	semidirect
9. C₆₇×#2974	C₂	semidirect
10. C₆₇×#2973	C₂	semidirect
11. C₆₇×#2970	C₂	semidirect
12. C₆₇×#2968	C₂	semidirect
13. C₆₇×#2967	C₂	semidirect
14. D₄×M₁₆×C₆₇	C₂	semidirect
15. C₆₇×#2933	C₂	semidirect
16. C₆₇×#2932	C₂	semidirect
17. C₆₇×#2930	C₂	semidirect
18. C₆₇×#2929	C₂	semidirect
19. C₂×#435×C₆₇	C₂	semidirect
20. C₂×#131×C₆₇	C₂²	semidirect
21. C₂×#131×C₆₇	C₂²	semidirect
22. C₂²×M₁₆×C₆₇	C₂²	semidirect
23. C₂²×M₁₆×C₆₇	C₂²	semidirect
24. C₂³×C₈×C₆₇	C₂²	semidirect
44. #446×C₆₇	C₂²	semidirect
45. #446×C₆₇	C₂²	semidirect
46. #446×C₆₇	C₂²	semidirect
47. #446×C₆₇	C₂²	semidirect
48. #436×C₆₇	C₂²	semidirect
49. #436×C₆₇	C₂²	semidirect
50. #436×C₆₇	C₂²	semidirect
51. #436×C₆₇	C₂²	semidirect
52. #436×C₆₇	C₂²	semidirect
53. #436×C₆₇	C₂²	semidirect
58. #435×C₆₇	C₂²	semidirect
59. #435×C₆₇	C₂²	semidirect
60. #435×C₆₇	C₂²	semidirect
61. #435×C₆₇	C₂²	semidirect
62. #435×C₆₇	C₂²	semidirect
63. #435×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. C₈×D₄×C₆₇	C₂²	semidirect
79. C₈×D₄×C₆₇	C₂²	semidirect
80. C₈×D₄×C₆₇	C₂²	semidirect
81. C₈×D₄×C₆₇	C₂²	semidirect
82. C₈×D₄×C₆₇	C₂²	semidirect
83. C₈×D₄×C₆₇	C₂²	semidirect
84. #433×C₆₇	C₂²	semidirect
85. #433×C₆₇	C₂²	semidirect
86. #433×C₆₇	C₂²	semidirect
87. #433×C₆₇	C₂²	semidirect
88. #432×C₆₇	C₂²	semidirect
89. #432×C₆₇	C₂²	semidirect
90. #432×C₆₇	C₂²	semidirect
91. #432×C₆₇	C₂²	semidirect
92. #431×C₆₇	C₂²	semidirect
93. #424×C₆₇	C₂²	semidirect
94. #424×C₆₇	C₂²	semidirect
95. #424×C₆₇	C₂²	semidirect
96. #423×C₆₇	C₂²	semidirect
97. #423×C₆₇	C₂²	semidirect
98. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
99. #408×C₆₇	C₂²	semidirect
100. #408×C₆₇	C₂²	semidirect
101. #408×C₆₇	C₂²	semidirect
102. #408×C₆₇	C₂²	semidirect
103. #408×C₆₇	C₂²	semidirect
104. #407×C₆₇	C₂²	semidirect
105. #407×C₆₇	C₂²	semidirect
106. #407×C₆₇	C₂²	semidirect
107. #407×C₆₇	C₂²	semidirect
108. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
109. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
110. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
111. #405×C₆₇	C₂²	semidirect
112. #405×C₆₇	C₂²	semidirect
113. #405×C₆₇	C₂²	semidirect
114. C₄×M₁₆×C₆₇	C₂²	semidirect
115. C₂×#97×C₆₇	C₂²	semidirect
116. C₂×#97×C₆₇	C₂²	semidirect
519. #60314	C₆₇	direct (N × H)
529. #2995	C₂×C₆₇	semidirect
530. #2992	C₂×C₆₇	semidirect
531. #2989	C₂×C₆₇	semidirect
532. #2980	C₂×C₆₇	semidirect
533. #2978	C₂×C₆₇	semidirect
534. #2977	C₂×C₆₇	semidirect
535. #2976	C₂×C₆₇	semidirect
536. #2974	C₂×C₆₇	semidirect
537. #2973	C₂×C₆₇	semidirect
538. #2970	C₂×C₆₇	semidirect
539. #2968	C₂×C₆₇	semidirect
540. #2967	C₂×C₆₇	semidirect
541. D₄×M₁₆	C₂×C₆₇	semidirect
542. #2933	C₂×C₆₇	semidirect
543. #2932	C₂×C₆₇	semidirect
544. #2930	C₂×C₆₇	semidirect
545. #2929	C₂×C₆₇	semidirect
546. C₂×#435	C₂×C₆₇	semidirect
547. C₆₇	#60314	direct (N × H)
548. C₂×#131	C₂²×C₆₇	semidirect
549. C₂×#131	C₂²×C₆₇	semidirect
550. C₂²×M₁₆	C₂²×C₆₇	semidirect
551. C₂²×M₁₆	C₂²×C₆₇	semidirect
552. C₂³×C₈	C₂²×C₆₇	semidirect
572. #446	C₂²×C₆₇	semidirect
573. #446	C₂²×C₆₇	semidirect
574. #446	C₂²×C₆₇	semidirect
575. #446	C₂²×C₆₇	semidirect
576. #436	C₂²×C₆₇	semidirect
577. #436	C₂²×C₆₇	semidirect
578. #436	C₂²×C₆₇	semidirect
579. #436	C₂²×C₆₇	semidirect
580. #436	C₂²×C₆₇	semidirect
581. #436	C₂²×C₆₇	semidirect
586. #435	C₂²×C₆₇	semidirect
587. #435	C₂²×C₆₇	semidirect
588. #435	C₂²×C₆₇	semidirect
589. #435	C₂²×C₆₇	semidirect
590. #435	C₂²×C₆₇	semidirect
591. #435	C₂²×C₆₇	semidirect
592. #435	C₂²×C₆₇	semidirect
593. #435	C₂²×C₆₇	semidirect
594. #435	C₂²×C₆₇	semidirect
595. #435	C₂²×C₆₇	semidirect
596. #435	C₂²×C₆₇	semidirect
597. #435	C₂²×C₆₇	semidirect
598. #435	C₂²×C₆₇	semidirect
599. #435	C₂²×C₆₇	semidirect
600. #435	C₂²×C₆₇	semidirect
601. #435	C₂²×C₆₇	semidirect
602. #435	C₂²×C₆₇	semidirect
603. #435	C₂²×C₆₇	semidirect
604. #435	C₂²×C₆₇	semidirect
605. #435	C₂²×C₆₇	semidirect
606. C₈×D₄	C₂²×C₆₇	semidirect
607. C₈×D₄	C₂²×C₆₇	semidirect
608. C₈×D₄	C₂²×C₆₇	semidirect
609. C₈×D₄	C₂²×C₆₇	semidirect
610. C₈×D₄	C₂²×C₆₇	semidirect
611. C₈×D₄	C₂²×C₆₇	semidirect
612. #433	C₂²×C₆₇	semidirect
613. #433	C₂²×C₆₇	semidirect
614. #433	C₂²×C₆₇	semidirect
615. #433	C₂²×C₆₇	semidirect
616. #432	C₂²×C₆₇	semidirect
617. #432	C₂²×C₆₇	semidirect
618. #432	C₂²×C₆₇	semidirect
619. #432	C₂²×C₆₇	semidirect
620. #431	C₂²×C₆₇	semidirect
621. #424	C₂²×C₆₇	semidirect
622. #424	C₂²×C₆₇	semidirect
623. #424	C₂²×C₆₇	semidirect
624. #423	C₂²×C₆₇	semidirect
625. #423	C₂²×C₆₇	semidirect
626. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
627. #408	C₂²×C₆₇	semidirect
628. #408	C₂²×C₆₇	semidirect
629. #408	C₂²×C₆₇	semidirect
630. #408	C₂²×C₆₇	semidirect
631. #408	C₂²×C₆₇	semidirect
632. #407	C₂²×C₆₇	semidirect
633. #407	C₂²×C₆₇	semidirect
634. #407	C₂²×C₆₇	semidirect
635. #407	C₂²×C₆₇	semidirect
636. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
637. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
638. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
639. #405	C₂²×C₆₇	semidirect
640. #405	C₂²×C₆₇	semidirect
641. #405	C₂²×C₆₇	semidirect
642. C₄×M₁₆	C₂²×C₆₇	semidirect
643. C₂×#97	C₂²×C₆₇	semidirect
644. 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
C₆₇×#3481	2
C₆₇×#2995	2
C₆₇×#2992	2
C₆₇×#2989	2
C₆₇×#2980	2
C₆₇×#2978	2
C₆₇×#2977	2
C₆₇×#2976	2
C₆₇×#2974	2
C₆₇×#2973	2
C₆₇×#2970	2
C₆₇×#2968	2
C₆₇×#2967	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2932	2
C₆₇×#2930	2
C₆₇×#2929	2
C₂×#435×C₆₇	2
#60314	67

Subgroups — C67×#60314 #30739565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60314 #30739565