Subgroups — C₆₇×#62759 #30742010

Order 17152.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3551	C₂	1	4	yes	maximal, complemented
2	C₆₇×#3550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3548	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3547	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3546	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3545	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3544	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3543	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3542	C₂	1	8	yes	maximal, complemented
11	C₆₇×#3529	C₂	1	4	yes	maximal, complemented
12	C₆₇×#3483	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3481	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3475	C₂	1	4	yes	maximal, complemented
15	D₄×#41×C₆₇	C₂	1	4	yes	maximal, complemented
16	C₆₇×#3460	C₂	1	8	yes	maximal, complemented
17	C₆₇×#3449	C₂	1	4	yes	maximal, complemented
18	C₆₇×#3444	C₂	1	2	yes	maximal, complemented
19	C₂×#532×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₇	C₂²	1	2	yes	complemented
21	C₂²×#41×C₆₇	C₂²	1	4	yes	complemented
22	#563×C₆₇	C₂²	1	8	yes	complemented
23	#563×C₆₇	C₂²	1	4	yes	complemented
24	#562×C₆₇	C₂²	1	16	yes	complemented
25	#562×C₆₇	C₂²	1	8	yes	complemented
26	H(3,𝔽₄)×C₆₇	C₂²	1	4	yes	complemented
27	#560×C₆₇	C₂²	1	16	yes	complemented
28	#560×C₆₇	C₂²	1	8	yes	complemented
29	#559×C₆₇	C₂²	1	2	yes	complemented
30	Q₈²×C₆₇	C₂²	1	2	yes	complemented
31	#556×C₆₇	C₂²	1	4	yes	complemented
32	#555×C₆₇	C₂²	1	8	yes	complemented
33	#555×C₆₇	C₂²	1	2	yes	complemented
34	#555×C₆₇	C₂²	1	8	yes	complemented
35	#555×C₆₇	C₂²	1	4	yes	complemented
36	#554×C₆₇	C₂²	1	4	yes	complemented
37	#554×C₆₇	C₂²	1	4	yes	complemented
38	#553×C₆₇	C₂²	1	8	yes	complemented
39	#553×C₆₇	C₂²	1	8	yes	complemented
40	#552×C₆₇	C₂²	1	8	yes	complemented
41	#552×C₆₇	C₂²	1	8	yes	complemented
42	#551×C₆₇	C₂²	1	16	yes	complemented
43	#551×C₆₇	C₂²	1	8	yes	complemented
44	#550×C₆₇	C₂²	1	8	yes	complemented
45	#550×C₆₇	C₂²	1	4	yes	complemented
46	#550×C₆₇	C₂²	1	4	yes	complemented
47	D₄×Q₈×C₆₇	C₂²	1	4	yes	complemented
48	#548×C₆₇	C₂²	1	8	yes	complemented
49	#547×C₆₇	C₂²	1	8	yes	complemented
50	#547×C₆₇	C₂²	1	4	yes	complemented
51	#547×C₆₇	C₂²	1	4	yes	complemented
52	#546×C₆₇	C₂²	1	8	yes	complemented
53	#546×C₆₇	C₂²	1	16	yes	complemented
54	#546×C₆₇	C₂²	1	8	yes	complemented
55	#546×C₆₇	C₂²	1	8	yes	complemented
56	D₄²×C₆₇	C₂²	1	8	yes	complemented
57	D₄²×C₆₇	C₂²	1	2	yes	complemented
58	D₄²×C₆₇	C₂²	1	4	yes	complemented
59	#544×C₆₇	C₂²	1	8	yes	complemented
60	#542×C₆₇	C₂²	1	8	yes	complemented
61	#542×C₆₇	C₂²	1	8	yes	complemented
62	#542×C₆₇	C₂²	1	16	yes	complemented
63	#540×C₆₇	C₂²	1	8	yes	complemented
64	#540×C₆₇	C₂²	1	16	yes	complemented
65	#540×C₆₇	C₂²	1	8	yes	complemented
66	#538×C₆₇	C₂²	1	16	yes	complemented
67	#538×C₆₇	C₂²	1	16	yes	complemented
68	#537×C₆₇	C₂²	1	8	yes	complemented
69	#537×C₆₇	C₂²	1	8	yes	complemented
70	#537×C₆₇	C₂²	1	8	yes	complemented
71	#536×C₆₇	C₂²	1	8	yes	complemented
72	#536×C₆₇	C₂²	1	4	yes	complemented
73	#536×C₆₇	C₂²	1	4	yes	complemented
74	#535×C₆₇	C₂²	1	8	yes	complemented
75	#535×C₆₇	C₂²	1	8	yes	complemented
76	#535×C₆₇	C₂²	1	8	yes	complemented
77	#535×C₆₇	C₂²	1	4	yes	complemented
78	#535×C₆₇	C₂²	1	4	yes	complemented
79	#534×C₆₇	C₂²	1	8	yes	complemented
80	#534×C₆₇	C₂²	1	8	yes	complemented
81	#533×C₆₇	C₂²	1	2	yes	complemented
82	#533×C₆₇	C₂²	1	2	yes	complemented
83	#533×C₆₇	C₂²	1	2	yes	complemented
84	#532×C₆₇	C₂²	1	1	yes	characteristic
85	#532×C₆₇	C₂²	1	1	yes	characteristic
86	#532×C₆₇	C₂²	1	2	yes	—
87	#532×C₆₇	C₂²	1	2	yes	complemented
88	#532×C₆₇	C₂²	1	8	yes	complemented
89	#532×C₆₇	C₂²	1	2	yes	complemented
90	#532×C₆₇	C₂²	1	4	yes	complemented
91	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#532×C₆₇	C₂²	1	2	yes	complemented
93	#532×C₆₇	C₂²	1	2	yes	complemented
94	#532×C₆₇	C₂²	1	4	yes	complemented
95	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#532×C₆₇	C₂²	1	8	yes	complemented
97	#532×C₆₇	C₂²	1	8	yes	complemented
98	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
100	#529×C₆₇	C₂²	1	4	yes	complemented
101	#529×C₆₇	C₂²	1	16	yes	complemented
102	#529×C₆₇	C₂²	1	4	yes	complemented
103	#529×C₆₇	C₂²	1	4	yes	complemented
104	#529×C₆₇	C₂²	1	4	yes	complemented
105	#529×C₆₇	C₂²	1	4	yes	complemented
106	#529×C₆₇	C₂²	1	4	yes	complemented
107	#529×C₆₇	C₂²	1	8	yes	complemented
108	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
109	#525×C₆₇	C₂²	1	8	yes	complemented
110	#525×C₆₇	C₂²	1	16	yes	complemented
111	#525×C₆₇	C₂²	1	4	yes	complemented
112	#525×C₆₇	C₂²	1	4	yes	complemented
113	#525×C₆₇	C₂²	1	4	yes	complemented
114	#525×C₆₇	C₂²	1	8	yes	complemented
115	#525×C₆₇	C₂²	1	8	yes	complemented
116	C₂×#121×C₆₇	C₂²	1	4	yes	complemented
117	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
118	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
119	C₄×#41×C₆₇	C₂²	1	4	yes	complemented
120	C₄×#41×C₆₇	C₂²	1	8	yes	complemented
121	C₂×C₄×D₄×C₆₇	C₂²	1	4	yes	complemented
122	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
123	C₂×#117×C₆₇	C₂²	1	4	yes	complemented
124	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	C₂×#41×C₆₇	—	4	8	no	—
126	C₂×#41×C₆₇	—	4	16	no	—
127	C₂×#41×C₆₇	C₂³	1	4	yes	—
128	C₂×#41×C₆₇	C₂³	1	4	yes	—
129	C₂×#41×C₆₇	C₂³	1	4	yes	—
130	C₂×#41×C₆₇	C₂³	1	8	yes	—
131	C₂×#41×C₆₇	C₂³	1	2	yes	—
132	C₂×#41×C₆₇	C₂³	1	4	yes	—
133	C₂×#41×C₆₇	C₂³	1	8	yes	—
134	C₂×#41×C₆₇	C₂³	1	2	yes	—
135	C₂×#41×C₆₇	C₂³	1	2	yes	—
136	C₂×#41×C₆₇	C₂³	1	4	yes	—
137	C₂×#41×C₆₇	C₂³	1	2	yes	—
138	C₂×#41×C₆₇	C₂³	1	8	yes	—
139	C₂×#41×C₆₇	C₂³	1	8	yes	—
140	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
141	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
142	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
143	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
147	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
148	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
150	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₇	C₂³	1	8	yes	—
152	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
155	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
157	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
160	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
161	C₄⋊Q₈×C₆₇	C₂³	1	8	yes	—
162	#127×C₆₇	C₂³	1	1	yes	characteristic
163	#127×C₆₇	C₂³	1	4	yes	—
164	#127×C₆₇	C₂³	1	1	yes	characteristic
165	#127×C₆₇	C₂³	1	2	yes	—
166	#127×C₆₇	C₂³	1	2	yes	—
167	#127×C₆₇	C₂³	1	8	yes	—
168	#127×C₆₇	C₂³	1	8	yes	—
169	#127×C₆₇	C₂³	1	8	yes	—
170	#126×C₆₇	C₂³	1	8	yes	—
171	#126×C₆₇	C₂³	1	8	yes	—
172	#126×C₆₇	C₂³	1	16	yes	—
173	#126×C₆₇	C₂³	1	16	yes	—
174	#126×C₆₇	C₂³	1	16	yes	—
175	#125×C₆₇	C₂³	1	4	yes	—
176	#125×C₆₇	C₂³	1	4	yes	—
177	#125×C₆₇	C₂³	1	4	yes	—
178	#125×C₆₇	C₂³	1	16	yes	—
179	#125×C₆₇	C₂³	1	8	yes	—
180	#124×C₆₇	C₂³	1	2	yes	—
181	#124×C₆₇	C₂³	1	2	yes	—
182	#124×C₆₇	C₂³	1	8	yes	—
183	#124×C₆₇	C₂³	1	2	yes	—
184	#124×C₆₇	C₂³	1	2	yes	—
185	#124×C₆₇	C₂³	1	4	yes	—
186	#124×C₆₇	C₂³	1	4	yes	—
187	#124×C₆₇	C₂³	1	4	yes	—
188	#124×C₆₇	C₂³	1	8	yes	—
189	#124×C₆₇	C₂³	1	16	yes	—
190	#124×C₆₇	C₂³	1	8	yes	—
191	#124×C₆₇	C₂³	1	8	yes	—
192	#124×C₆₇	C₂³	1	8	yes	—
193	#124×C₆₇	C₂³	1	8	yes	—
194	#124×C₆₇	C₂³	1	16	yes	—
195	#123×C₆₇	C₂³	1	8	yes	—
196	#123×C₆₇	C₂³	1	8	yes	—
197	#123×C₆₇	C₂³	1	8	yes	—
198	#123×C₆₇	C₂³	1	8	yes	—
199	#123×C₆₇	C₂³	1	8	yes	—
200	#123×C₆₇	C₂³	1	16	yes	—
201	#123×C₆₇	C₂³	1	8	yes	—
202	#123×C₆₇	C₂³	1	8	yes	—
203	#123×C₆₇	C₂³	1	16	yes	—
204	#123×C₆₇	C₂³	1	16	yes	—
205	#123×C₆₇	C₂³	1	16	yes	—
206	#123×C₆₇	C₂³	1	16	yes	—
207	#123×C₆₇	C₂³	1	16	yes	—
208	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
209	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
210	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
216	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
217	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
218	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
219	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
220	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
221	C₂²⋊Q₈×C₆₇	C₂³	1	16	yes	—
222	#121×C₆₇	C₂³	1	4	yes	—
223	#121×C₆₇	C₂³	1	4	yes	—
224	#121×C₆₇	C₂³	1	4	yes	—
225	#121×C₆₇	C₂³	1	8	yes	—
226	#121×C₆₇	C₂³	1	4	yes	—
227	#121×C₆₇	C₂³	1	8	yes	—
228	#121×C₆₇	C₂³	1	4	yes	—
229	#121×C₆₇	C₂³	1	4	yes	—
230	#121×C₆₇	C₂³	1	4	yes	—
231	#121×C₆₇	C₂³	1	4	yes	—
232	#121×C₆₇	C₂³	1	4	yes	—
233	#121×C₆₇	C₂³	1	4	yes	—
234	#121×C₆₇	C₂³	1	16	yes	—
235	#121×C₆₇	C₂³	1	8	yes	—
236	#121×C₆₇	C₂³	1	8	yes	—
237	#121×C₆₇	C₂³	1	16	yes	—
238	#121×C₆₇	C₂³	1	16	yes	—
239	#121×C₆₇	C₂³	1	16	yes	—
240	#121×C₆₇	C₂³	1	8	yes	—
241	#121×C₆₇	C₂³	1	16	yes	—
242	#121×C₆₇	C₂³	1	16	yes	—
243	#121×C₆₇	C₂³	1	16	yes	—
244	#121×C₆₇	C₂³	1	16	yes	—
245	#121×C₆₇	C₂³	1	16	yes	—
246	#121×C₆₇	C₂³	1	8	yes	—
247	#121×C₆₇	C₂³	1	8	yes	—
248	#121×C₆₇	C₂³	1	16	yes	—
249	#120×C₆₇	C₂³	1	8	yes	—
250	#120×C₆₇	C₂³	1	8	yes	—
251	#120×C₆₇	C₂³	1	8	yes	—
252	#120×C₆₇	C₂³	1	16	yes	—
253	#120×C₆₇	C₂³	1	8	yes	—
254	#120×C₆₇	C₂³	1	8	yes	—
255	#120×C₆₇	C₂³	1	16	yes	—
256	#120×C₆₇	C₂³	1	16	yes	—
257	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
258	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
259	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
260	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
261	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
262	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
263	C₄×Q₈×C₆₇	C₂³	1	8	yes	—
264	C₄×D₄×C₆₇	C₂³	1	4	yes	—
265	C₄×D₄×C₆₇	C₂³	1	4	yes	—
266	C₄×D₄×C₆₇	C₂³	1	4	yes	—
267	C₄×D₄×C₆₇	C₂³	1	16	yes	—
268	C₄×D₄×C₆₇	C₂³	1	8	yes	—
269	C₄×D₄×C₆₇	C₂³	1	4	yes	—
270	C₄×D₄×C₆₇	C₂³	1	8	yes	—
271	C₄×D₄×C₆₇	C₂³	1	4	yes	—
272	C₄×D₄×C₆₇	C₂³	1	8	yes	—
273	C₄×D₄×C₆₇	C₂³	1	8	yes	—
274	C₄×D₄×C₆₇	C₂³	1	16	yes	—
275	C₄×D₄×C₆₇	C₂³	1	4	yes	—
276	C₄×D₄×C₆₇	C₂³	1	8	yes	—
277	C₄×D₄×C₆₇	C₂³	1	8	yes	—
278	C₄×D₄×C₆₇	C₂³	1	16	yes	—
279	C₄×D₄×C₆₇	C₂³	1	8	yes	—
280	C₄×D₄×C₆₇	C₂³	1	8	yes	—
281	C₄×D₄×C₆₇	C₂³	1	8	yes	—
282	C₄×D₄×C₆₇	C₂³	1	8	yes	—
283	C₄×D₄×C₆₇	C₂³	1	4	yes	—
284	C₄×D₄×C₆₇	C₂³	1	4	yes	—
285	C₄×D₄×C₆₇	C₂³	1	4	yes	—
286	C₄×D₄×C₆₇	C₂³	1	4	yes	—
287	C₄×D₄×C₆₇	C₂³	1	16	yes	—
288	C₄×D₄×C₆₇	C₂³	1	8	yes	—
289	#117×C₆₇	C₂³	1	4	yes	—
290	#117×C₆₇	C₂³	1	8	yes	—
291	#117×C₆₇	C₂³	1	8	yes	—
292	#117×C₆₇	C₂³	1	4	yes	—
293	#117×C₆₇	C₂³	1	4	yes	—
294	#117×C₆₇	C₂³	1	8	yes	—
295	#117×C₆₇	C₂³	1	4	yes	—
296	#117×C₆₇	C₂³	1	4	yes	—
297	#117×C₆₇	C₂³	1	8	yes	—
298	#117×C₆₇	C₂³	1	8	yes	—
299	#117×C₆₇	C₂³	1	8	yes	—
300	#117×C₆₇	C₂³	1	16	yes	—
301	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
302	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
303	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
304	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
305	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
306	C₂×C₂²⋊C₄×C₆₇	C₂³	1	16	yes	—
307	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
308	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
310	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
315	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
316	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
317	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
318	C₂⁴×C₆₇	C₂⁴	1	4	yes	—
319	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
321	#41×C₆₇	—	2	16	no	—
322	#41×C₆₇	—	4	4	no	—
323	#41×C₆₇	—	4	8	no	—
324	#41×C₆₇	—	4	4	no	—
325	#41×C₆₇	—	4	8	no	—
326	#41×C₆₇	—	4	4	no	—
327	#41×C₆₇	—	4	4	no	—
328	#41×C₆₇	—	4	16	no	—
329	#41×C₆₇	—	4	8	no	—
330	#41×C₆₇	—	4	16	no	—
331	#41×C₆₇	—	4	16	no	—
332	#41×C₆₇	—	4	8	no	—
333	#41×C₆₇	—	4	16	no	—
334	C₂×Q₈×C₆₇	—	4	4	no	—
335	C₂×Q₈×C₆₇	—	4	8	no	—
336	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
337	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
338	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
339	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
340	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
341	C₂×Q₈×C₆₇	C₂⁴	1	8	yes	—
342	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
343	C₂×D₄×C₆₇	—	4	8	no	—
344	C₂×D₄×C₆₇	—	4	16	no	—
345	C₂×D₄×C₆₇	—	4	8	no	—
346	C₂×D₄×C₆₇	—	4	4	no	—
347	C₂×D₄×C₆₇	—	4	8	no	—
348	C₂×D₄×C₆₇	—	4	16	no	—
349	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
350	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
351	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
352	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
353	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
354	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
355	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
356	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
357	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
358	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
359	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
360	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
361	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
362	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
363	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
364	C₂×D₄×C₆₇	C₂⁴	1	8	yes	—
365	C₂×D₄×C₆₇	C₂⁴	1	16	yes	—
366	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
367	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
368	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₆₇	—	2	4	no	—
370	C₂²×C₄×C₆₇	—	2	16	no	—
371	C₂²×C₄×C₆₇	—	4	4	no	—
372	C₂²×C₄×C₆₇	—	4	16	no	—
373	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
380	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
381	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
382	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
383	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
386	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
387	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
388	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
389	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
390	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
391	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
392	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
393	C₂²×C₄×C₆₇	C₂⁴	1	16	yes	—
394	C₂²×C₄×C₆₇	C₂⁴	1	8	yes	—
395	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
397	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
398	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
399	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
400	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
401	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
402	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
403	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
404	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
405	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
406	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
407	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
408	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
409	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
410	C₄⋊C₄×C₆₇	C₂⁴	1	16	yes	—
411	C₄⋊C₄×C₆₇	C₂⁴	1	8	yes	—
412	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
413	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
414	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
415	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
416	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
417	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
418	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
419	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
420	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
421	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
422	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
423	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
424	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
425	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
426	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
427	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
428	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
429	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
430	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
431	C₂²⋊C₄×C₆₇	C₂⁴	1	8	yes	—
432	C₂²⋊C₄×C₆₇	C₂⁴	1	16	yes	—
433	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
434	C₄²×C₆₇	C₂⁴	1	2	yes	—
435	C₄²×C₆₇	C₂⁴	1	2	yes	—
436	C₄²×C₆₇	C₂⁴	1	2	yes	—
437	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
438	C₄²×C₆₇	C₂⁴	1	2	yes	—
439	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
441	C₄²×C₆₇	C₂⁴	1	8	yes	—
442	C₄²×C₆₇	C₂⁴	1	8	yes	—
443	C₄²×C₆₇	C₂⁴	1	8	yes	—
444	C₄²×C₆₇	C₂⁴	1	8	yes	—
445	C₄²×C₆₇	C₂⁴	1	2	yes	—
446	C₄²×C₆₇	C₂⁴	1	2	yes	—
447	C₄²×C₆₇	C₂⁴	1	8	yes	—
448	C₂³×C₆₇	—	2	2	no	—
449	C₂³×C₆₇	—	2	8	no	—
450	C₂³×C₆₇	—	4	2	no	—
451	C₂³×C₆₇	—	4	8	no	—
452	C₂³×C₆₇	—	4	8	no	—
453	C₂³×C₆₇	—	4	16	no	—
454	C₂³×C₆₇	C₂⁵	1	4	yes	—
455	C₂³×C₆₇	C₂⁵	1	8	yes	—
456	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
457	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
458	C₂³×C₆₇	C₂⁵	1	4	yes	—
459	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
460	Q₈×C₆₇	—	2	8	no	—
461	Q₈×C₆₇	—	2	8	no	—
462	Q₈×C₆₇	—	4	2	no	—
463	Q₈×C₆₇	—	4	4	no	—
464	Q₈×C₆₇	—	4	2	no	—
465	Q₈×C₆₇	—	4	8	no	—
466	Q₈×C₆₇	—	4	4	no	—
467	D₄×C₆₇	—	2	16	no	—
468	D₄×C₆₇	—	2	8	no	—
469	D₄×C₆₇	—	2	8	no	—
470	D₄×C₆₇	—	2	8	no	—
471	D₄×C₆₇	—	2	8	no	—
472	D₄×C₆₇	—	4	8	no	—
473	D₄×C₆₇	—	4	16	no	—
474	D₄×C₆₇	—	4	4	no	—
475	D₄×C₆₇	—	4	4	no	—
476	D₄×C₆₇	—	4	2	no	—
477	D₄×C₆₇	—	4	4	no	—
478	D₄×C₆₇	—	4	4	no	—
479	D₄×C₆₇	—	4	2	no	—
480	D₄×C₆₇	—	4	4	no	—
481	D₄×C₆₇	—	4	8	no	—
482	D₄×C₆₇	—	4	16	no	—
483	D₄×C₆₇	—	4	8	no	—
484	D₄×C₆₇	—	4	4	no	—
485	D₄×C₆₇	—	4	8	no	—
486	D₄×C₆₇	—	4	16	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	8	no	—
489	C₂×C₄×C₆₇	—	2	8	no	—
490	C₂×C₄×C₆₇	—	2	8	no	—
491	C₂×C₄×C₆₇	—	2	8	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	2	no	—
494	C₂×C₄×C₆₇	—	2	8	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	2	no	—
497	C₂×C₄×C₆₇	—	2	16	no	—
498	C₂×C₄×C₆₇	—	2	4	no	—
499	C₂×C₄×C₆₇	—	2	4	no	—
500	C₂×C₄×C₆₇	—	2	4	no	—
501	C₂×C₄×C₆₇	—	2	16	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	8	no	—
506	C₂×C₄×C₆₇	—	4	16	no	—
507	C₂×C₄×C₆₇	—	4	8	no	—
508	C₂×C₄×C₆₇	—	4	16	no	—
509	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
510	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
511	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
512	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
513	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
514	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
515	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
517	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
518	C₂×C₄×C₆₇	C₂⁵	1	8	yes	—
519	C₂×C₄×C₆₇	C₂⁵	1	4	yes	—
520	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂⁵	1	2	yes	—
522	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
523	C₂²×C₆₇	—	2	2	no	—
524	C₂²×C₆₇	—	2	4	no	—
525	C₂²×C₆₇	—	2	1	no	—
526	C₂²×C₆₇	—	2	1	no	—
527	C₂²×C₆₇	—	2	4	no	—
528	C₂²×C₆₇	—	2	8	no	—
529	C₂²×C₆₇	—	2	2	no	—
530	C₂²×C₆₇	—	2	2	no	—
531	C₂²×C₆₇	—	2	8	no	—
532	C₂²×C₆₇	—	2	8	no	—
533	C₂²×C₆₇	—	2	8	no	—
534	C₂²×C₆₇	—	2	8	no	—
535	C₂²×C₆₇	—	4	4	no	—
536	C₂²×C₆₇	—	8	8	no	—
537	C₂²×C₆₇	—	8	16	no	—
538	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
539	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
540	C₄×C₆₇	—	2	4	no	—
541	C₄×C₆₇	—	2	1	no	—
542	C₄×C₆₇	—	2	1	no	—
543	C₄×C₆₇	—	2	4	no	—
544	C₄×C₆₇	—	2	8	no	—
545	C₄×C₆₇	—	2	2	no	—
546	C₄×C₆₇	—	2	2	no	—
547	C₄×C₆₇	—	2	8	no	—
548	C₄×C₆₇	—	2	2	no	—
549	C₄×C₆₇	—	2	8	no	—
550	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
551	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
552	C₄×C₆₇	#585	1	4	yes	—
553	#62759	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
554	C₂×C₆₇	—	2	2	no	—
555	C₂×C₆₇	—	4	1	no	—
556	C₂×C₆₇	—	4	1	no	—
557	C₂×C₆₇	—	4	4	no	—
558	C₂×C₆₇	—	4	8	no	—
559	C₂×C₆₇	—	4	4	no	—
560	C₂×C₆₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂×C₆₇	C₂×#585	1	2	yes	—
562	#3551	C₂×C₆₇	1	4	yes	complemented
563	#3550	C₂×C₆₇	1	1	yes	characteristic, complemented
564	#3549	C₂×C₆₇	1	1	yes	characteristic, complemented
565	#3548	C₂×C₆₇	1	2	yes	complemented
566	#3547	C₂×C₆₇	1	4	yes	complemented
567	#3546	C₂×C₆₇	1	4	yes	complemented
568	#3545	C₂×C₆₇	1	4	yes	complemented
569	#3544	C₂×C₆₇	1	2	yes	complemented
570	#3543	C₂×C₆₇	1	2	yes	complemented
571	#3542	C₂×C₆₇	1	8	yes	complemented
572	#3529	C₂×C₆₇	1	4	yes	complemented
573	#3483	C₂×C₆₇	1	2	yes	complemented
574	#3481	C₂×C₆₇	1	2	yes	complemented
575	#3475	C₂×C₆₇	1	4	yes	complemented
576	D₄×#41	C₂×C₆₇	1	4	yes	complemented
577	#3460	C₂×C₆₇	1	8	yes	complemented
578	#3449	C₂×C₆₇	1	4	yes	complemented
579	#3444	C₂×C₆₇	1	2	yes	complemented
580	C₂×#532	C₂×C₆₇	1	1	yes	characteristic, complemented
581	C₆₇	#62759	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²×#41	C₂²×C₆₇	1	2	yes	complemented
583	C₂²×#41	C₂²×C₆₇	1	4	yes	complemented
584	#563	C₂²×C₆₇	1	8	yes	complemented
585	#563	C₂²×C₆₇	1	4	yes	complemented
586	#562	C₂²×C₆₇	1	16	yes	complemented
587	#562	C₂²×C₆₇	1	8	yes	complemented
588	H(3,𝔽₄)	C₂²×C₆₇	1	4	yes	complemented
589	#560	C₂²×C₆₇	1	16	yes	complemented
590	#560	C₂²×C₆₇	1	8	yes	complemented
591	#559	C₂²×C₆₇	1	2	yes	complemented
592	Q₈²	C₂²×C₆₇	1	2	yes	complemented
593	#556	C₂²×C₆₇	1	4	yes	complemented
594	#555	C₂²×C₆₇	1	4	yes	complemented
595	#555	C₂²×C₆₇	1	8	yes	complemented
596	#555	C₂²×C₆₇	1	2	yes	complemented
597	#555	C₂²×C₆₇	1	8	yes	complemented
598	#554	C₂²×C₆₇	1	4	yes	complemented
599	#554	C₂²×C₆₇	1	4	yes	complemented
600	#553	C₂²×C₆₇	1	8	yes	complemented
601	#553	C₂²×C₆₇	1	8	yes	complemented
602	#552	C₂²×C₆₇	1	8	yes	complemented
603	#552	C₂²×C₆₇	1	8	yes	complemented
604	#551	C₂²×C₆₇	1	16	yes	complemented
605	#551	C₂²×C₆₇	1	8	yes	complemented
606	#550	C₂²×C₆₇	1	4	yes	complemented
607	#550	C₂²×C₆₇	1	8	yes	complemented
608	#550	C₂²×C₆₇	1	4	yes	complemented
609	D₄×Q₈	C₂²×C₆₇	1	4	yes	complemented
610	#548	C₂²×C₆₇	1	8	yes	complemented
611	#547	C₂²×C₆₇	1	8	yes	complemented
612	#547	C₂²×C₆₇	1	4	yes	complemented
613	#547	C₂²×C₆₇	1	4	yes	complemented
614	#546	C₂²×C₆₇	1	16	yes	complemented
615	#546	C₂²×C₆₇	1	8	yes	complemented
616	#546	C₂²×C₆₇	1	8	yes	complemented
617	#546	C₂²×C₆₇	1	8	yes	complemented
618	D₄²	C₂²×C₆₇	1	8	yes	complemented
619	D₄²	C₂²×C₆₇	1	4	yes	complemented
620	D₄²	C₂²×C₆₇	1	2	yes	complemented
621	#544	C₂²×C₆₇	1	8	yes	complemented
622	#542	C₂²×C₆₇	1	8	yes	complemented
623	#542	C₂²×C₆₇	1	8	yes	complemented
624	#542	C₂²×C₆₇	1	16	yes	complemented
625	#540	C₂²×C₆₇	1	8	yes	complemented
626	#540	C₂²×C₆₇	1	16	yes	complemented
627	#540	C₂²×C₆₇	1	8	yes	complemented
628	#538	C₂²×C₆₇	1	16	yes	complemented
629	#538	C₂²×C₆₇	1	16	yes	complemented
630	#537	C₂²×C₆₇	1	8	yes	complemented
631	#537	C₂²×C₆₇	1	8	yes	complemented
632	#537	C₂²×C₆₇	1	8	yes	complemented
633	#536	C₂²×C₆₇	1	8	yes	complemented
634	#536	C₂²×C₆₇	1	4	yes	complemented
635	#536	C₂²×C₆₇	1	4	yes	complemented
636	#535	C₂²×C₆₇	1	8	yes	complemented
637	#535	C₂²×C₆₇	1	4	yes	complemented
638	#535	C₂²×C₆₇	1	4	yes	complemented
639	#535	C₂²×C₆₇	1	8	yes	complemented
640	#535	C₂²×C₆₇	1	8	yes	complemented
641	#534	C₂²×C₆₇	1	8	yes	complemented
642	#534	C₂²×C₆₇	1	8	yes	complemented
643	#533	C₂²×C₆₇	1	2	yes	complemented
644	#533	C₂²×C₆₇	1	2	yes	complemented
645	#533	C₂²×C₆₇	1	2	yes	complemented
646	#532	C₂²×C₆₇	1	1	yes	characteristic
647	#532	C₂²×C₆₇	1	1	yes	characteristic
648	#532	C₂²×C₆₇	1	2	yes	—
649	#532	C₂²×C₆₇	1	4	yes	complemented
650	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
651	#532	C₂²×C₆₇	1	2	yes	complemented
652	#532	C₂²×C₆₇	1	4	yes	complemented
653	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#532	C₂²×C₆₇	1	2	yes	complemented
655	#532	C₂²×C₆₇	1	2	yes	complemented
656	#532	C₂²×C₆₇	1	2	yes	complemented
657	#532	C₂²×C₆₇	1	8	yes	complemented
658	#532	C₂²×C₆₇	1	8	yes	complemented
659	#532	C₂²×C₆₇	1	8	yes	complemented
660	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
662	#529	C₂²×C₆₇	1	4	yes	complemented
663	#529	C₂²×C₆₇	1	4	yes	complemented
664	#529	C₂²×C₆₇	1	4	yes	complemented
665	#529	C₂²×C₆₇	1	4	yes	complemented
666	#529	C₂²×C₆₇	1	4	yes	complemented
667	#529	C₂²×C₆₇	1	4	yes	complemented
668	#529	C₂²×C₆₇	1	8	yes	complemented
669	#529	C₂²×C₆₇	1	16	yes	complemented
670	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
671	#525	C₂²×C₆₇	1	4	yes	complemented
672	#525	C₂²×C₆₇	1	4	yes	complemented
673	#525	C₂²×C₆₇	1	4	yes	complemented
674	#525	C₂²×C₆₇	1	8	yes	complemented
675	#525	C₂²×C₆₇	1	8	yes	complemented
676	#525	C₂²×C₆₇	1	8	yes	complemented
677	#525	C₂²×C₆₇	1	16	yes	complemented
678	C₂×#121	C₂²×C₆₇	1	4	yes	complemented
679	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
680	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
681	C₄×#41	C₂²×C₆₇	1	4	yes	complemented
682	C₄×#41	C₂²×C₆₇	1	8	yes	complemented
683	C₂×C₄×D₄	C₂²×C₆₇	1	4	yes	complemented
684	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
685	C₂×#117	C₂²×C₆₇	1	4	yes	complemented
686	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	C₂×#41	—	4	8	no	—
688	C₂×#41	—	4	16	no	—
689	C₂×#41	C₂³×C₆₇	1	4	yes	—
690	C₂×#41	C₂³×C₆₇	1	4	yes	—
691	C₂×#41	C₂³×C₆₇	1	4	yes	—
692	C₂×#41	C₂³×C₆₇	1	8	yes	—
693	C₂×#41	C₂³×C₆₇	1	2	yes	—
694	C₂×#41	C₂³×C₆₇	1	4	yes	—
695	C₂×#41	C₂³×C₆₇	1	8	yes	—
696	C₂×#41	C₂³×C₆₇	1	2	yes	—
697	C₂×#41	C₂³×C₆₇	1	2	yes	—
698	C₂×#41	C₂³×C₆₇	1	4	yes	—
699	C₂×#41	C₂³×C₆₇	1	2	yes	—
700	C₂×#41	C₂³×C₆₇	1	8	yes	—
701	C₂×#41	C₂³×C₆₇	1	8	yes	—
702	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
703	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
704	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
705	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
706	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
707	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
708	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
709	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
710	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
711	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂³×C₄	C₂³×C₆₇	1	8	yes	—
713	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
714	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
715	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
716	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
717	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
718	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
719	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
720	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
721	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
722	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
723	C₄⋊Q₈	C₂³×C₆₇	1	8	yes	—
724	#127	C₂³×C₆₇	1	1	yes	characteristic
725	#127	C₂³×C₆₇	1	4	yes	—
726	#127	C₂³×C₆₇	1	1	yes	characteristic
727	#127	C₂³×C₆₇	1	2	yes	—
728	#127	C₂³×C₆₇	1	2	yes	—
729	#127	C₂³×C₆₇	1	8	yes	—
730	#127	C₂³×C₆₇	1	8	yes	—
731	#127	C₂³×C₆₇	1	8	yes	—
732	#126	C₂³×C₆₇	1	8	yes	—
733	#126	C₂³×C₆₇	1	8	yes	—
734	#126	C₂³×C₆₇	1	16	yes	—
735	#126	C₂³×C₆₇	1	16	yes	—
736	#126	C₂³×C₆₇	1	16	yes	—
737	#125	C₂³×C₆₇	1	4	yes	—
738	#125	C₂³×C₆₇	1	4	yes	—
739	#125	C₂³×C₆₇	1	4	yes	—
740	#125	C₂³×C₆₇	1	16	yes	—
741	#125	C₂³×C₆₇	1	8	yes	—
742	#124	C₂³×C₆₇	1	2	yes	—
743	#124	C₂³×C₆₇	1	2	yes	—
744	#124	C₂³×C₆₇	1	8	yes	—
745	#124	C₂³×C₆₇	1	2	yes	—
746	#124	C₂³×C₆₇	1	2	yes	—
747	#124	C₂³×C₆₇	1	4	yes	—
748	#124	C₂³×C₆₇	1	4	yes	—
749	#124	C₂³×C₆₇	1	4	yes	—
750	#124	C₂³×C₆₇	1	8	yes	—
751	#124	C₂³×C₆₇	1	16	yes	—
752	#124	C₂³×C₆₇	1	8	yes	—
753	#124	C₂³×C₆₇	1	8	yes	—
754	#124	C₂³×C₆₇	1	8	yes	—
755	#124	C₂³×C₆₇	1	8	yes	—
756	#124	C₂³×C₆₇	1	16	yes	—
757	#123	C₂³×C₆₇	1	8	yes	—
758	#123	C₂³×C₆₇	1	8	yes	—
759	#123	C₂³×C₆₇	1	8	yes	—
760	#123	C₂³×C₆₇	1	8	yes	—
761	#123	C₂³×C₆₇	1	8	yes	—
762	#123	C₂³×C₆₇	1	16	yes	—
763	#123	C₂³×C₆₇	1	8	yes	—
764	#123	C₂³×C₆₇	1	8	yes	—
765	#123	C₂³×C₆₇	1	16	yes	—
766	#123	C₂³×C₆₇	1	16	yes	—
767	#123	C₂³×C₆₇	1	16	yes	—
768	#123	C₂³×C₆₇	1	16	yes	—
769	#123	C₂³×C₆₇	1	16	yes	—
770	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
771	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
772	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
773	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
774	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
775	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
776	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
777	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
778	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
779	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
780	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
781	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
782	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
783	C₂²⋊Q₈	C₂³×C₆₇	1	16	yes	—
784	#121	C₂³×C₆₇	1	4	yes	—
785	#121	C₂³×C₆₇	1	4	yes	—
786	#121	C₂³×C₆₇	1	4	yes	—
787	#121	C₂³×C₆₇	1	8	yes	—
788	#121	C₂³×C₆₇	1	4	yes	—
789	#121	C₂³×C₆₇	1	8	yes	—
790	#121	C₂³×C₆₇	1	4	yes	—
791	#121	C₂³×C₆₇	1	4	yes	—
792	#121	C₂³×C₆₇	1	4	yes	—
793	#121	C₂³×C₆₇	1	4	yes	—
794	#121	C₂³×C₆₇	1	4	yes	—
795	#121	C₂³×C₆₇	1	4	yes	—
796	#121	C₂³×C₆₇	1	16	yes	—
797	#121	C₂³×C₆₇	1	8	yes	—
798	#121	C₂³×C₆₇	1	8	yes	—
799	#121	C₂³×C₆₇	1	16	yes	—
800	#121	C₂³×C₆₇	1	16	yes	—
801	#121	C₂³×C₆₇	1	16	yes	—
802	#121	C₂³×C₆₇	1	8	yes	—
803	#121	C₂³×C₆₇	1	16	yes	—
804	#121	C₂³×C₆₇	1	16	yes	—
805	#121	C₂³×C₆₇	1	16	yes	—
806	#121	C₂³×C₆₇	1	16	yes	—
807	#121	C₂³×C₆₇	1	16	yes	—
808	#121	C₂³×C₆₇	1	8	yes	—
809	#121	C₂³×C₆₇	1	8	yes	—
810	#121	C₂³×C₆₇	1	16	yes	—
811	#120	C₂³×C₆₇	1	8	yes	—
812	#120	C₂³×C₆₇	1	8	yes	—
813	#120	C₂³×C₆₇	1	8	yes	—
814	#120	C₂³×C₆₇	1	16	yes	—
815	#120	C₂³×C₆₇	1	8	yes	—
816	#120	C₂³×C₆₇	1	8	yes	—
817	#120	C₂³×C₆₇	1	16	yes	—
818	#120	C₂³×C₆₇	1	16	yes	—
819	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
820	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
821	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
822	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
823	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
824	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
825	C₄×Q₈	C₂³×C₆₇	1	8	yes	—
826	C₄×D₄	C₂³×C₆₇	1	4	yes	—
827	C₄×D₄	C₂³×C₆₇	1	4	yes	—
828	C₄×D₄	C₂³×C₆₇	1	4	yes	—
829	C₄×D₄	C₂³×C₆₇	1	16	yes	—
830	C₄×D₄	C₂³×C₆₇	1	8	yes	—
831	C₄×D₄	C₂³×C₆₇	1	4	yes	—
832	C₄×D₄	C₂³×C₆₇	1	8	yes	—
833	C₄×D₄	C₂³×C₆₇	1	4	yes	—
834	C₄×D₄	C₂³×C₆₇	1	8	yes	—
835	C₄×D₄	C₂³×C₆₇	1	8	yes	—
836	C₄×D₄	C₂³×C₆₇	1	16	yes	—
837	C₄×D₄	C₂³×C₆₇	1	4	yes	—
838	C₄×D₄	C₂³×C₆₇	1	8	yes	—
839	C₄×D₄	C₂³×C₆₇	1	8	yes	—
840	C₄×D₄	C₂³×C₆₇	1	16	yes	—
841	C₄×D₄	C₂³×C₆₇	1	8	yes	—
842	C₄×D₄	C₂³×C₆₇	1	8	yes	—
843	C₄×D₄	C₂³×C₆₇	1	8	yes	—
844	C₄×D₄	C₂³×C₆₇	1	8	yes	—
845	C₄×D₄	C₂³×C₆₇	1	4	yes	—
846	C₄×D₄	C₂³×C₆₇	1	4	yes	—
847	C₄×D₄	C₂³×C₆₇	1	4	yes	—
848	C₄×D₄	C₂³×C₆₇	1	4	yes	—
849	C₄×D₄	C₂³×C₆₇	1	16	yes	—
850	C₄×D₄	C₂³×C₆₇	1	8	yes	—
851	#117	C₂³×C₆₇	1	4	yes	—
852	#117	C₂³×C₆₇	1	8	yes	—
853	#117	C₂³×C₆₇	1	8	yes	—
854	#117	C₂³×C₆₇	1	4	yes	—
855	#117	C₂³×C₆₇	1	4	yes	—
856	#117	C₂³×C₆₇	1	8	yes	—
857	#117	C₂³×C₆₇	1	4	yes	—
858	#117	C₂³×C₆₇	1	4	yes	—
859	#117	C₂³×C₆₇	1	8	yes	—
860	#117	C₂³×C₆₇	1	8	yes	—
861	#117	C₂³×C₆₇	1	8	yes	—
862	#117	C₂³×C₆₇	1	16	yes	—
863	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
864	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
865	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
866	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
867	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
868	C₂×C₂²⋊C₄	C₂³×C₆₇	1	16	yes	—
869	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
870	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
871	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
872	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
873	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
874	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
875	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
876	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
877	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
878	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
879	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
880	C₂⁴	C₂⁴×C₆₇	1	4	yes	—
881	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
882	C₂⁴	C₂⁴×C₆₇	1	8	yes	—
883	#41	—	2	16	no	—
884	#41	—	4	4	no	—
885	#41	—	4	8	no	—
886	#41	—	4	4	no	—
887	#41	—	4	8	no	—
888	#41	—	4	4	no	—
889	#41	—	4	4	no	—
890	#41	—	4	16	no	—
891	#41	—	4	8	no	—
892	#41	—	4	16	no	—
893	#41	—	4	16	no	—
894	#41	—	4	8	no	—
895	#41	—	4	16	no	—
896	C₂×Q₈	—	4	4	no	—
897	C₂×Q₈	—	4	8	no	—
898	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
899	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
900	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
901	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
902	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
903	C₂×Q₈	C₂⁴×C₆₇	1	8	yes	—
904	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
905	C₂×D₄	—	4	8	no	—
906	C₂×D₄	—	4	8	no	—
907	C₂×D₄	—	4	16	no	—
908	C₂×D₄	—	4	4	no	—
909	C₂×D₄	—	4	8	no	—
910	C₂×D₄	—	4	16	no	—
911	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
912	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
913	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
914	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
915	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
916	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
917	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
918	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
919	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
920	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
921	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
922	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
923	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
924	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
925	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
926	C₂×D₄	C₂⁴×C₆₇	1	8	yes	—
927	C₂×D₄	C₂⁴×C₆₇	1	16	yes	—
928	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
929	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
930	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
931	C₂²×C₄	—	2	4	no	—
932	C₂²×C₄	—	2	16	no	—
933	C₂²×C₄	—	4	16	no	—
934	C₂²×C₄	—	4	4	no	—
935	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
936	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
937	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
938	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
939	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
940	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
945	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
946	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
947	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
948	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
949	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
950	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
952	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
954	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
955	C₂²×C₄	C₂⁴×C₆₇	1	16	yes	—
956	C₂²×C₄	C₂⁴×C₆₇	1	8	yes	—
957	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
958	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
959	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
960	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
961	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
962	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
963	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
964	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
965	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
966	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
967	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
968	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
969	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
970	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
971	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
972	C₄⋊C₄	C₂⁴×C₆₇	1	16	yes	—
973	C₄⋊C₄	C₂⁴×C₆₇	1	8	yes	—
974	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
975	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
976	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
977	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
978	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
979	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
980	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
981	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
982	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
983	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
984	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
985	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
986	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
987	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
988	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
989	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
990	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
991	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
992	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
993	C₂²⋊C₄	C₂⁴×C₆₇	1	8	yes	—
994	C₂²⋊C₄	C₂⁴×C₆₇	1	16	yes	—
995	C₄²	C₂⁴×C₆₇	1	2	yes	—
996	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₄²	C₂⁴×C₆₇	1	2	yes	—
998	C₄²	C₂⁴×C₆₇	1	8	yes	—
999	C₄²	C₂⁴×C₆₇	1	2	yes	—
1000	C₄²	C₂⁴×C₆₇	1	2	yes	—
1001	C₄²	C₂⁴×C₆₇	1	2	yes	—
1002	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1003	C₄²	C₂⁴×C₆₇	1	2	yes	—
1004	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1005	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1006	C₄²	C₂⁴×C₆₇	1	8	yes	—
1007	C₄²	C₂⁴×C₆₇	1	8	yes	—
1008	C₄²	C₂⁴×C₆₇	1	8	yes	—
1009	C₄²	C₂⁴×C₆₇	1	8	yes	—
1010	C₂³	—	2	2	no	—
1011	C₂³	—	2	8	no	—
1012	C₂³	—	4	2	no	—
1013	C₂³	—	4	8	no	—
1014	C₂³	—	4	8	no	—
1015	C₂³	—	4	16	no	—
1016	C₂³	C₂⁵×C₆₇	1	4	yes	—
1017	C₂³	C₂⁵×C₆₇	1	8	yes	—
1018	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1019	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1020	C₂³	C₂⁵×C₆₇	1	4	yes	—
1021	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
1022	Q₈	—	2	8	no	—
1023	Q₈	—	2	8	no	—
1024	Q₈	—	4	2	no	—
1025	Q₈	—	4	4	no	—
1026	Q₈	—	4	2	no	—
1027	Q₈	—	4	8	no	—
1028	Q₈	—	4	4	no	—
1029	D₄	—	2	16	no	—
1030	D₄	—	2	8	no	—
1031	D₄	—	2	8	no	—
1032	D₄	—	2	8	no	—
1033	D₄	—	2	8	no	—
1034	D₄	—	4	4	no	—
1035	D₄	—	4	4	no	—
1036	D₄	—	4	2	no	—
1037	D₄	—	4	4	no	—
1038	D₄	—	4	4	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	4	4	no	—
1041	D₄	—	4	8	no	—
1042	D₄	—	4	16	no	—
1043	D₄	—	4	8	no	—
1044	D₄	—	4	16	no	—
1045	D₄	—	4	8	no	—
1046	D₄	—	4	4	no	—
1047	D₄	—	4	8	no	—
1048	D₄	—	4	16	no	—
1049	C₂×C₄	—	2	2	no	—
1050	C₂×C₄	—	2	8	no	—
1051	C₂×C₄	—	2	8	no	—
1052	C₂×C₄	—	2	8	no	—
1053	C₂×C₄	—	2	8	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	2	8	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	2	no	—
1059	C₂×C₄	—	2	16	no	—
1060	C₂×C₄	—	2	4	no	—
1061	C₂×C₄	—	2	4	no	—
1062	C₂×C₄	—	2	4	no	—
1063	C₂×C₄	—	2	16	no	—
1064	C₂×C₄	—	4	8	no	—
1065	C₂×C₄	—	4	16	no	—
1066	C₂×C₄	—	4	2	no	—
1067	C₂×C₄	—	4	2	no	—
1068	C₂×C₄	—	4	2	no	—
1069	C₂×C₄	—	4	8	no	—
1070	C₂×C₄	—	4	16	no	—
1071	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
1072	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1074	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1075	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1076	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1077	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1078	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1079	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1080	C₂×C₄	C₂⁵×C₆₇	1	8	yes	—
1081	C₂×C₄	C₂⁵×C₆₇	1	4	yes	—
1082	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1083	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1084	C₂×C₄	C₂⁵×C₆₇	1	2	yes	—
1085	C₂²	—	2	2	no	—
1086	C₂²	—	2	4	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	4	no	—
1090	C₂²	—	2	8	no	—
1091	C₂²	—	2	2	no	—
1092	C₂²	—	2	2	no	—
1093	C₂²	—	2	8	no	—
1094	C₂²	—	2	8	no	—
1095	C₂²	—	2	8	no	—
1096	C₂²	—	2	8	no	—
1097	C₂²	—	4	4	no	—
1098	C₂²	—	8	8	no	—
1099	C₂²	—	8	16	no	—
1100	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1101	C₂²	C₂⁶×C₆₇	1	1	yes	characteristic
1102	C₄	—	2	4	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	4	no	—
1106	C₄	—	2	8	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	8	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	2	8	no	—
1112	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1113	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1114	C₄	#585×C₆₇	1	4	yes	—
1115	C₂	—	2	2	no	—
1116	C₂	—	4	1	no	—
1117	C₂	—	4	1	no	—
1118	C₂	—	4	4	no	—
1119	C₂	—	4	8	no	—
1120	C₂	—	4	4	no	—
1121	C₂	C₂²×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1122	C₂	C₂×#585×C₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₆₇
socle	C₂²×C₆₇	C₂⁶
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
1. C₆₇×#3551	C₂	semidirect
2. C₆₇×#3550	C₂	semidirect
3. C₆₇×#3549	C₂	semidirect
4. C₆₇×#3548	C₂	semidirect
5. C₆₇×#3547	C₂	semidirect
6. C₆₇×#3546	C₂	semidirect
7. C₆₇×#3545	C₂	semidirect
8. C₆₇×#3544	C₂	semidirect
9. C₆₇×#3543	C₂	semidirect
10. C₆₇×#3542	C₂	semidirect
11. C₆₇×#3529	C₂	semidirect
12. C₆₇×#3483	C₂	semidirect
13. C₆₇×#3481	C₂	semidirect
14. C₆₇×#3475	C₂	semidirect
15. D₄×#41×C₆₇	C₂	semidirect
16. C₆₇×#3460	C₂	semidirect
17. C₆₇×#3449	C₂	semidirect
18. C₆₇×#3444	C₂	semidirect
19. C₂×#532×C₆₇	C₂	semidirect
20. C₂²×#41×C₆₇	C₂²	semidirect
21. C₂²×#41×C₆₇	C₂²	semidirect
22. #563×C₆₇	C₂²	semidirect
23. #563×C₆₇	C₂²	semidirect
24. #562×C₆₇	C₂²	semidirect
25. #562×C₆₇	C₂²	semidirect
26. H(3,𝔽₄)×C₆₇	C₂²	semidirect
27. #560×C₆₇	C₂²	semidirect
28. #560×C₆₇	C₂²	semidirect
29. #559×C₆₇	C₂²	semidirect
30. Q₈²×C₆₇	C₂²	semidirect
31. #556×C₆₇	C₂²	semidirect
32. #555×C₆₇	C₂²	semidirect
33. #555×C₆₇	C₂²	semidirect
34. #555×C₆₇	C₂²	semidirect
35. #555×C₆₇	C₂²	semidirect
36. #554×C₆₇	C₂²	semidirect
37. #554×C₆₇	C₂²	semidirect
38. #553×C₆₇	C₂²	semidirect
39. #553×C₆₇	C₂²	semidirect
40. #552×C₆₇	C₂²	semidirect
41. #552×C₆₇	C₂²	semidirect
42. #551×C₆₇	C₂²	semidirect
43. #551×C₆₇	C₂²	semidirect
44. #550×C₆₇	C₂²	semidirect
45. #550×C₆₇	C₂²	semidirect
46. #550×C₆₇	C₂²	semidirect
47. D₄×Q₈×C₆₇	C₂²	semidirect
48. #548×C₆₇	C₂²	semidirect
49. #547×C₆₇	C₂²	semidirect
50. #547×C₆₇	C₂²	semidirect
51. #547×C₆₇	C₂²	semidirect
52. #546×C₆₇	C₂²	semidirect
53. #546×C₆₇	C₂²	semidirect
54. #546×C₆₇	C₂²	semidirect
55. #546×C₆₇	C₂²	semidirect
56. D₄²×C₆₇	C₂²	semidirect
57. D₄²×C₆₇	C₂²	semidirect
58. D₄²×C₆₇	C₂²	semidirect
59. #544×C₆₇	C₂²	semidirect
60. #542×C₆₇	C₂²	semidirect
61. #542×C₆₇	C₂²	semidirect
62. #542×C₆₇	C₂²	semidirect
63. #540×C₆₇	C₂²	semidirect
64. #540×C₆₇	C₂²	semidirect
65. #540×C₆₇	C₂²	semidirect
66. #538×C₆₇	C₂²	semidirect
67. #538×C₆₇	C₂²	semidirect
68. #537×C₆₇	C₂²	semidirect
69. #537×C₆₇	C₂²	semidirect
70. #537×C₆₇	C₂²	semidirect
71. #536×C₆₇	C₂²	semidirect
72. #536×C₆₇	C₂²	semidirect
73. #536×C₆₇	C₂²	semidirect
74. #535×C₆₇	C₂²	semidirect
75. #535×C₆₇	C₂²	semidirect
76. #535×C₆₇	C₂²	semidirect
77. #535×C₆₇	C₂²	semidirect
78. #535×C₆₇	C₂²	semidirect
79. #534×C₆₇	C₂²	semidirect
80. #534×C₆₇	C₂²	semidirect
81. #533×C₆₇	C₂²	semidirect
82. #533×C₆₇	C₂²	semidirect
83. #533×C₆₇	C₂²	semidirect
87. #532×C₆₇	C₂²	semidirect
88. #532×C₆₇	C₂²	semidirect
89. #532×C₆₇	C₂²	semidirect
90. #532×C₆₇	C₂²	semidirect
91. #532×C₆₇	C₂²	semidirect
92. #532×C₆₇	C₂²	semidirect
93. #532×C₆₇	C₂²	semidirect
94. #532×C₆₇	C₂²	semidirect
95. #532×C₆₇	C₂²	semidirect
96. #532×C₆₇	C₂²	semidirect
97. #532×C₆₇	C₂²	semidirect
98. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
100. #529×C₆₇	C₂²	semidirect
101. #529×C₆₇	C₂²	semidirect
102. #529×C₆₇	C₂²	semidirect
103. #529×C₆₇	C₂²	semidirect
104. #529×C₆₇	C₂²	semidirect
105. #529×C₆₇	C₂²	semidirect
106. #529×C₆₇	C₂²	semidirect
107. #529×C₆₇	C₂²	semidirect
108. C₂×#124×C₆₇	C₂²	semidirect
109. #525×C₆₇	C₂²	semidirect
110. #525×C₆₇	C₂²	semidirect
111. #525×C₆₇	C₂²	semidirect
112. #525×C₆₇	C₂²	semidirect
113. #525×C₆₇	C₂²	semidirect
114. #525×C₆₇	C₂²	semidirect
115. #525×C₆₇	C₂²	semidirect
116. C₂×#121×C₆₇	C₂²	semidirect
117. C₄×#41×C₆₇	C₂²	semidirect
118. C₄×#41×C₆₇	C₂²	semidirect
119. C₄×#41×C₆₇	C₂²	semidirect
120. C₄×#41×C₆₇	C₂²	semidirect
121. C₂×C₄×D₄×C₆₇	C₂²	semidirect
122. C₂×C₄×D₄×C₆₇	C₂²	semidirect
123. C₂×#117×C₆₇	C₂²	semidirect
124. C₂²×C₄²×C₆₇	C₂²	semidirect
553. #62759	C₆₇	direct (N × H)
562. #3551	C₂×C₆₇	semidirect
563. #3550	C₂×C₆₇	semidirect
564. #3549	C₂×C₆₇	semidirect
565. #3548	C₂×C₆₇	semidirect
566. #3547	C₂×C₆₇	semidirect
567. #3546	C₂×C₆₇	semidirect
568. #3545	C₂×C₆₇	semidirect
569. #3544	C₂×C₆₇	semidirect
570. #3543	C₂×C₆₇	semidirect
571. #3542	C₂×C₆₇	semidirect
572. #3529	C₂×C₆₇	semidirect
573. #3483	C₂×C₆₇	semidirect
574. #3481	C₂×C₆₇	semidirect
575. #3475	C₂×C₆₇	semidirect
576. D₄×#41	C₂×C₆₇	semidirect
577. #3460	C₂×C₆₇	semidirect
578. #3449	C₂×C₆₇	semidirect
579. #3444	C₂×C₆₇	semidirect
580. C₂×#532	C₂×C₆₇	semidirect
581. C₆₇	#62759	direct (N × H)
582. C₂²×#41	C₂²×C₆₇	semidirect
583. C₂²×#41	C₂²×C₆₇	semidirect
584. #563	C₂²×C₆₇	semidirect
585. #563	C₂²×C₆₇	semidirect
586. #562	C₂²×C₆₇	semidirect
587. #562	C₂²×C₆₇	semidirect
588. H(3,𝔽₄)	C₂²×C₆₇	semidirect
589. #560	C₂²×C₆₇	semidirect
590. #560	C₂²×C₆₇	semidirect
591. #559	C₂²×C₆₇	semidirect
592. Q₈²	C₂²×C₆₇	semidirect
593. #556	C₂²×C₆₇	semidirect
594. #555	C₂²×C₆₇	semidirect
595. #555	C₂²×C₆₇	semidirect
596. #555	C₂²×C₆₇	semidirect
597. #555	C₂²×C₆₇	semidirect
598. #554	C₂²×C₆₇	semidirect
599. #554	C₂²×C₆₇	semidirect
600. #553	C₂²×C₆₇	semidirect
601. #553	C₂²×C₆₇	semidirect
602. #552	C₂²×C₆₇	semidirect
603. #552	C₂²×C₆₇	semidirect
604. #551	C₂²×C₆₇	semidirect
605. #551	C₂²×C₆₇	semidirect
606. #550	C₂²×C₆₇	semidirect
607. #550	C₂²×C₆₇	semidirect
608. #550	C₂²×C₆₇	semidirect
609. D₄×Q₈	C₂²×C₆₇	semidirect
610. #548	C₂²×C₆₇	semidirect
611. #547	C₂²×C₆₇	semidirect
612. #547	C₂²×C₆₇	semidirect
613. #547	C₂²×C₆₇	semidirect
614. #546	C₂²×C₆₇	semidirect
615. #546	C₂²×C₆₇	semidirect
616. #546	C₂²×C₆₇	semidirect
617. #546	C₂²×C₆₇	semidirect
618. D₄²	C₂²×C₆₇	semidirect
619. D₄²	C₂²×C₆₇	semidirect
620. D₄²	C₂²×C₆₇	semidirect
621. #544	C₂²×C₆₇	semidirect
622. #542	C₂²×C₆₇	semidirect
623. #542	C₂²×C₆₇	semidirect
624. #542	C₂²×C₆₇	semidirect
625. #540	C₂²×C₆₇	semidirect
626. #540	C₂²×C₆₇	semidirect
627. #540	C₂²×C₆₇	semidirect
628. #538	C₂²×C₆₇	semidirect
629. #538	C₂²×C₆₇	semidirect
630. #537	C₂²×C₆₇	semidirect
631. #537	C₂²×C₆₇	semidirect
632. #537	C₂²×C₆₇	semidirect
633. #536	C₂²×C₆₇	semidirect
634. #536	C₂²×C₆₇	semidirect
635. #536	C₂²×C₆₇	semidirect
636. #535	C₂²×C₆₇	semidirect
637. #535	C₂²×C₆₇	semidirect
638. #535	C₂²×C₆₇	semidirect
639. #535	C₂²×C₆₇	semidirect
640. #535	C₂²×C₆₇	semidirect
641. #534	C₂²×C₆₇	semidirect
642. #534	C₂²×C₆₇	semidirect
643. #533	C₂²×C₆₇	semidirect
644. #533	C₂²×C₆₇	semidirect
645. #533	C₂²×C₆₇	semidirect
649. #532	C₂²×C₆₇	semidirect
650. #532	C₂²×C₆₇	semidirect
651. #532	C₂²×C₆₇	semidirect
652. #532	C₂²×C₆₇	semidirect
653. #532	C₂²×C₆₇	semidirect
654. #532	C₂²×C₆₇	semidirect
655. #532	C₂²×C₆₇	semidirect
656. #532	C₂²×C₆₇	semidirect
657. #532	C₂²×C₆₇	semidirect
658. #532	C₂²×C₆₇	semidirect
659. #532	C₂²×C₆₇	semidirect
660. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
662. #529	C₂²×C₆₇	semidirect
663. #529	C₂²×C₆₇	semidirect
664. #529	C₂²×C₆₇	semidirect
665. #529	C₂²×C₆₇	semidirect
666. #529	C₂²×C₆₇	semidirect
667. #529	C₂²×C₆₇	semidirect
668. #529	C₂²×C₆₇	semidirect
669. #529	C₂²×C₆₇	semidirect
670. C₂×#124	C₂²×C₆₇	semidirect
671. #525	C₂²×C₆₇	semidirect
672. #525	C₂²×C₆₇	semidirect
673. #525	C₂²×C₆₇	semidirect
674. #525	C₂²×C₆₇	semidirect
675. #525	C₂²×C₆₇	semidirect
676. #525	C₂²×C₆₇	semidirect
677. #525	C₂²×C₆₇	semidirect
678. C₂×#121	C₂²×C₆₇	semidirect
679. C₄×#41	C₂²×C₆₇	semidirect
680. C₄×#41	C₂²×C₆₇	semidirect
681. C₄×#41	C₂²×C₆₇	semidirect
682. C₄×#41	C₂²×C₆₇	semidirect
683. C₂×C₄×D₄	C₂²×C₆₇	semidirect
684. C₂×C₄×D₄	C₂²×C₆₇	semidirect
685. C₂×#117	C₂²×C₆₇	semidirect
686. C₂²×C₄²	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×#3551	2
C₆₇×#3550	2
C₆₇×#3549	2
C₆₇×#3548	2
C₆₇×#3547	2
C₆₇×#3546	2
C₆₇×#3545	2
C₆₇×#3544	2
C₆₇×#3543	2
C₆₇×#3542	2
C₆₇×#3529	2
C₆₇×#3483	2
C₆₇×#3481	2
C₆₇×#3475	2
D₄×#41×C₆₇	2
C₆₇×#3460	2
C₆₇×#3449	2
C₆₇×#3444	2
C₂×#532×C₆₇	2
#62759	67

Subgroups — C67×#62759 #30742010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#62759 #30742010