Subgroups — C₆₇×#61733 #30740984

Order 17152.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3353	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3345	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3343	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3335	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3325	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3318	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3310	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3295	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3294	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3188	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3094	C₂	1	2	yes	maximal, complemented
22	C₂×#482×C₆₇	C₂	1	2	yes	maximal, complemented
23	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₆₇	—	2	1	no	—
25	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	#554×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#553×C₆₇	C₂²	1	2	yes	complemented
29	#552×C₆₇	—	2	1	no	—
30	#552×C₆₇	C₂²	1	2	yes	complemented
31	#551×C₆₇	—	2	2	no	—
32	#547×C₆₇	C₂²	1	1	yes	characteristic
33	#547×C₆₇	C₂²	1	2	yes	—
34	#547×C₆₇	C₂²	1	1	yes	characteristic
35	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#546×C₆₇	—	2	1	no	—
37	#546×C₆₇	—	2	1	no	—
38	#546×C₆₇	—	2	2	no	—
39	#546×C₆₇	—	2	1	no	—
40	D₄²×C₆₇	C₂²	1	1	yes	characteristic
41	D₄²×C₆₇	C₂²	1	2	yes	—
42	D₄²×C₆₇	C₂²	1	1	yes	characteristic
43	#537×C₆₇	—	2	1	no	—
44	#534×C₆₇	—	2	2	no	—
45	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#532×C₆₇	C₂²	1	1	yes	characteristic
47	#532×C₆₇	C₂²	1	1	yes	characteristic
48	#529×C₆₇	—	2	2	no	—
49	#529×C₆₇	—	2	1	no	—
50	#525×C₆₇	C₂²	1	2	yes	complemented
51	C₂×#121×C₆₇	C₂²	1	2	yes	—
52	C₂×#121×C₆₇	C₂²	1	2	yes	—
53	C₄×#41×C₆₇	—	2	1	no	—
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
56	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
57	#501×C₆₇	C₂²	1	2	yes	complemented
58	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#498×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	#490×C₆₇	C₂²	1	2	yes	complemented
61	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#486×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#484×C₆₇	C₂²	1	2	yes	complemented
64	#483×C₆₇	C₂²	1	2	yes	complemented
65	#482×C₆₇	C₂²	1	2	yes	complemented
66	#482×C₆₇	C₂²	1	2	yes	complemented
67	#482×C₆₇	C₂²	1	2	yes	complemented
68	#482×C₆₇	C₂²	1	2	yes	complemented
69	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#482×C₆₇	C₂²	1	2	yes	complemented
73	#482×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#482×C₆₇	C₂²	1	2	yes	complemented
75	#482×C₆₇	C₂²	1	2	yes	complemented
76	#481×C₆₇	C₂²	1	2	yes	complemented
77	#481×C₆₇	C₂²	1	2	yes	complemented
78	#481×C₆₇	C₂²	1	2	yes	complemented
79	#480×C₆₇	C₂²	1	2	yes	complemented
80	#480×C₆₇	C₂²	1	2	yes	complemented
81	#480×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#478×C₆₇	C₂²	1	2	yes	complemented
84	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
86	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#476×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#475×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
90	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#474×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#469×C₆₇	C₂²	1	2	yes	complemented
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#468×C₆₇	C₂²	1	2	yes	complemented
95	#468×C₆₇	C₂²	1	2	yes	complemented
96	#466×C₆₇	C₂²	1	2	yes	complemented
97	#466×C₆₇	C₂²	1	2	yes	complemented
98	#465×C₆₇	C₂²	1	2	yes	complemented
99	#465×C₆₇	C₂²	1	2	yes	complemented
100	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#450×C₆₇	C₂²	1	2	yes	complemented
105	#450×C₆₇	C₂²	1	2	yes	complemented
106	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#449×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#449×C₆₇	C₂²	1	2	yes	complemented
109	#447×C₆₇	C₂²	1	2	yes	complemented
110	#447×C₆₇	C₂²	1	2	yes	complemented
111	#442×C₆₇	C₂²	1	2	yes	complemented
112	#440×C₆₇	C₂²	1	2	yes	complemented
113	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#436×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#435×C₆₇	C₂²	1	2	yes	complemented
120	#435×C₆₇	C₂²	1	2	yes	complemented
121	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
125	#428×C₆₇	C₂²	1	2	yes	complemented
126	#428×C₆₇	C₂²	1	2	yes	complemented
127	C₂×#107×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
129	#418×C₆₇	C₂²	1	2	yes	complemented
130	#418×C₆₇	C₂²	1	2	yes	complemented
131	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
132	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
133	#407×C₆₇	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
135	H(5,𝔽₂)×C₆₇	—	4	8	no	—
136	C₂×#41×C₆₇	—	2	1	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	1	no	—
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	—	2	2	no	—
144	C₂²×D₄×C₆₇	—	2	2	no	—
145	C₂²×D₄×C₆₇	—	2	2	no	—
146	C₂²×D₄×C₆₇	—	2	1	no	—
147	C₂²×D₄×C₆₇	—	2	1	no	—
148	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
149	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
150	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
151	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
155	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	#127×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	C₂³	1	1	yes	characteristic
168	#126×C₆₇	—	2	2	no	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#125×C₆₇	—	2	2	no	—
172	#125×C₆₇	—	2	1	no	—
173	#125×C₆₇	C₂³	1	2	yes	—
174	#124×C₆₇	—	2	1	no	—
175	#124×C₆₇	—	2	2	no	—
176	#124×C₆₇	—	2	1	no	—
177	#124×C₆₇	—	2	1	no	—
178	#123×C₆₇	—	2	2	no	—
179	#123×C₆₇	—	2	2	no	—
180	#123×C₆₇	—	2	2	no	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	C₂²⋊Q₈×C₆₇	—	2	1	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	1	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
195	#121×C₆₇	—	2	2	no	—
196	#121×C₆₇	—	2	1	no	—
197	#121×C₆₇	—	2	2	no	—
198	#121×C₆₇	—	2	2	no	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	1	no	—
202	#121×C₆₇	—	2	1	no	—
203	#121×C₆₇	—	2	1	no	—
204	#121×C₆₇	—	2	1	no	—
205	#121×C₆₇	—	2	2	no	—
206	#121×C₆₇	C₂³	1	1	yes	characteristic
207	#121×C₆₇	C₂³	1	1	yes	characteristic
208	#121×C₆₇	C₂³	1	2	yes	—
209	#121×C₆₇	C₂³	1	2	yes	—
210	#121×C₆₇	C₂³	1	2	yes	—
211	#121×C₆₇	C₂³	1	2	yes	—
212	#121×C₆₇	C₂³	1	2	yes	—
213	#121×C₆₇	C₂³	1	2	yes	—
214	#121×C₆₇	C₂³	1	2	yes	—
215	#120×C₆₇	—	2	2	no	—
216	#120×C₆₇	—	2	2	no	—
217	#120×C₆₇	—	2	2	no	—
218	#120×C₆₇	—	2	2	no	—
219	#120×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	—	2	1	no	—
221	C₄×Q₈×C₆₇	—	2	1	no	—
222	C₄×Q₈×C₆₇	—	2	1	no	—
223	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₄×D₄×C₆₇	—	2	1	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	1	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	1	no	—
232	C₄×D₄×C₆₇	—	2	1	no	—
233	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
234	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
235	C₄×D₄×C₆₇	D₄	1	2	yes	—
236	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	2	yes	—
243	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
244	#117×C₆₇	—	2	2	no	—
245	#117×C₆₇	—	2	2	no	—
246	#117×C₆₇	—	2	1	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	1	no	—
249	#117×C₆₇	C₂³	1	1	yes	characteristic
250	#117×C₆₇	C₂³	1	2	yes	—
251	#117×C₆₇	C₂³	1	2	yes	—
252	#117×C₆₇	C₂³	1	2	yes	—
253	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
255	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
256	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
258	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
260	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
261	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
262	C₂×C₄²×C₆₇	—	2	2	no	—
263	C₂×C₄²×C₆₇	—	2	1	no	—
264	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
265	#107×C₆₇	C₂³	1	2	yes	—
266	#107×C₆₇	C₂³	1	2	yes	—
267	#107×C₆₇	C₂³	1	2	yes	—
268	#107×C₆₇	C₂³	1	2	yes	—
269	#107×C₆₇	C₂³	1	2	yes	—
270	#107×C₆₇	C₂³	1	1	yes	characteristic
271	#107×C₆₇	C₂³	1	1	yes	characteristic
272	#106×C₆₇	C₂³	1	2	yes	—
273	#106×C₆₇	C₂³	1	2	yes	—
274	#106×C₆₇	C₂³	1	2	yes	—
275	#106×C₆₇	C₂³	1	2	yes	—
276	#106×C₆₇	C₂³	1	2	yes	—
277	#106×C₆₇	C₂³	1	1	yes	characteristic
278	#106×C₆₇	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	#103×C₆₇	C₂³	1	1	yes	characteristic
284	#103×C₆₇	C₂³	1	2	yes	—
285	#103×C₆₇	C₂³	1	1	yes	characteristic
286	#102×C₆₇	C₂³	1	1	yes	characteristic
287	#102×C₆₇	C₂³	1	2	yes	—
288	#102×C₆₇	C₂³	1	1	yes	characteristic
289	#102×C₆₇	C₂³	1	2	yes	—
290	#102×C₆₇	C₂³	1	2	yes	—
291	#102×C₆₇	C₂³	1	2	yes	—
292	#102×C₆₇	C₂³	1	2	yes	—
293	#102×C₆₇	C₂³	1	2	yes	—
294	#102×C₆₇	C₂³	1	1	yes	characteristic
295	#102×C₆₇	C₂³	1	1	yes	characteristic
296	#102×C₆₇	C₂³	1	1	yes	characteristic
297	#102×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	1	yes	characteristic
299	#102×C₆₇	C₂³	1	2	yes	—
300	#102×C₆₇	C₂³	1	2	yes	—
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	#97×C₆₇	C₂³	1	2	yes	—
311	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₂⁴×C₆₇	—	2	2	no	—
314	C₂⁴×C₆₇	—	2	2	no	—
315	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
316	#41×C₆₇	—	4	1	no	—
317	#41×C₆₇	—	4	1	no	—
318	#41×C₆₇	—	4	4	no	—
319	#41×C₆₇	—	4	4	no	—
320	#41×C₆₇	—	4	8	no	—
321	#41×C₆₇	—	4	4	no	—
322	#41×C₆₇	—	4	4	no	—
323	#41×C₆₇	—	4	4	no	—
324	C₂×Q₈×C₆₇	—	2	1	no	—
325	C₂×Q₈×C₆₇	—	2	1	no	—
326	C₂×Q₈×C₆₇	—	2	1	no	—
327	C₂×Q₈×C₆₇	—	2	1	no	—
328	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₆₇	—	2	4	no	—
330	C₂×D₄×C₆₇	—	2	1	no	—
331	C₂×D₄×C₆₇	—	2	2	no	—
332	C₂×D₄×C₆₇	—	2	2	no	—
333	C₂×D₄×C₆₇	—	2	2	no	—
334	C₂×D₄×C₆₇	—	2	2	no	—
335	C₂×D₄×C₆₇	—	2	2	no	—
336	C₂×D₄×C₆₇	—	2	1	no	—
337	C₂×D₄×C₆₇	—	2	2	no	—
338	C₂×D₄×C₆₇	—	2	1	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	1	no	—
342	C₂×D₄×C₆₇	—	2	1	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	2	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	—	4	2	no	—
347	C₂×D₄×C₆₇	—	4	2	no	—
348	C₂×D₄×C₆₇	—	4	2	no	—
349	C₂×D₄×C₆₇	—	4	2	no	—
350	C₂×D₄×C₆₇	—	4	8	no	—
351	C₂×D₄×C₆₇	—	4	4	no	—
352	C₂×D₄×C₆₇	—	4	8	no	—
353	C₂×D₄×C₆₇	—	4	8	no	—
354	C₂×D₄×C₆₇	—	4	4	no	—
355	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
356	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
357	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
358	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
360	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
361	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₆₇	—	2	2	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	1	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	1	no	—
370	C₂²×C₄×C₆₇	—	2	1	no	—
371	C₂²×C₄×C₆₇	—	2	1	no	—
372	C₂²×C₄×C₆₇	—	4	2	no	—
373	C₂²×C₄×C₆₇	—	4	2	no	—
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
378	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
379	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
381	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
382	SD₁₆×C₆₇	—	4	1	no	—
383	SD₁₆×C₆₇	—	4	2	no	—
384	SD₁₆×C₆₇	—	4	1	no	—
385	D₈×C₆₇	—	4	1	no	—
386	D₈×C₆₇	—	4	2	no	—
387	D₈×C₆₇	—	4	1	no	—
388	M₁₆×C₆₇	—	4	2	no	—
389	M₁₆×C₆₇	—	4	2	no	—
390	C₂×C₈×C₆₇	—	4	2	no	—
391	C₂×C₈×C₆₇	—	4	2	no	—
392	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	—	2	2	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	2	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	2	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	1	no	—
408	C₄⋊C₄×C₆₇	—	2	1	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	1	no	—
412	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
414	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₆₇	—	2	1	no	—
423	C₂²⋊C₄×C₆₇	—	2	2	no	—
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	2	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	1	no	—
437	C₂²⋊C₄×C₆₇	—	2	1	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	2	no	—
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₂²⋊C₄×C₆₇	—	2	1	no	—
442	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₄²×C₆₇	—	2	1	no	—
447	C₄²×C₆₇	—	2	2	no	—
448	C₄²×C₆₇	—	2	1	no	—
449	C₄²×C₆₇	—	2	2	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	1	no	—
452	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₂³×C₆₇	—	2	4	no	—
457	C₂³×C₆₇	—	2	1	no	—
458	C₂³×C₆₇	—	2	2	no	—
459	C₂³×C₆₇	—	2	1	no	—
460	C₂³×C₆₇	—	2	1	no	—
461	C₂³×C₆₇	—	4	2	no	—
462	C₂³×C₆₇	—	4	2	no	—
463	C₂³×C₆₇	—	4	4	no	—
464	C₂³×C₆₇	—	4	4	no	—
465	C₂³×C₆₇	—	8	2	no	—
466	C₂³×C₆₇	—	8	2	no	—
467	C₂³×C₆₇	—	8	2	no	—
468	C₂³×C₆₇	—	8	2	no	—
469	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
470	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
471	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
472	Q₈×C₆₇	—	2	1	no	—
473	Q₈×C₆₇	—	2	1	no	—
474	Q₈×C₆₇	—	4	2	no	—
475	Q₈×C₆₇	—	4	2	no	—
476	Q₈×C₆₇	—	4	2	no	—
477	Q₈×C₆₇	—	8	1	no	—
478	D₄×C₆₇	—	2	4	no	—
479	D₄×C₆₇	—	2	2	no	—
480	D₄×C₆₇	—	2	1	no	—
481	D₄×C₆₇	—	2	1	no	—
482	D₄×C₆₇	—	2	1	no	—
483	D₄×C₆₇	—	2	1	no	—
484	D₄×C₆₇	—	2	2	no	—
485	D₄×C₆₇	—	2	2	no	—
486	D₄×C₆₇	—	2	1	no	—
487	D₄×C₆₇	—	2	1	no	—
488	D₄×C₆₇	—	4	2	no	—
489	D₄×C₆₇	—	4	4	no	—
490	D₄×C₆₇	—	4	2	no	—
491	D₄×C₆₇	—	4	2	no	—
492	D₄×C₆₇	—	4	4	no	—
493	D₄×C₆₇	—	4	4	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	4	4	no	—
496	D₄×C₆₇	—	4	4	no	—
497	D₄×C₆₇	—	4	4	no	—
498	D₄×C₆₇	—	4	2	no	—
499	D₄×C₆₇	—	8	1	no	—
500	D₄×C₆₇	—	8	1	no	—
501	D₄×C₆₇	—	8	2	no	—
502	D₄×C₆₇	—	8	2	no	—
503	D₄×C₆₇	—	8	2	no	—
504	D₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	2	2	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	2	no	—
510	C₂×C₄×C₆₇	—	2	1	no	—
511	C₂×C₄×C₆₇	—	2	1	no	—
512	C₂×C₄×C₆₇	—	2	1	no	—
513	C₂×C₄×C₆₇	—	2	1	no	—
514	C₂×C₄×C₆₇	—	2	1	no	—
515	C₂×C₄×C₆₇	—	2	2	no	—
516	C₂×C₄×C₆₇	—	2	2	no	—
517	C₂×C₄×C₆₇	—	2	2	no	—
518	C₂×C₄×C₆₇	—	2	1	no	—
519	C₂×C₄×C₆₇	—	2	1	no	—
520	C₂×C₄×C₆₇	—	4	2	no	—
521	C₂×C₄×C₆₇	—	4	2	no	—
522	C₂×C₄×C₆₇	—	4	2	no	—
523	C₂×C₄×C₆₇	—	4	1	no	—
524	C₂×C₄×C₆₇	—	4	4	no	—
525	C₂×C₄×C₆₇	—	4	2	no	—
526	C₂×C₄×C₆₇	—	4	4	no	—
527	C₂×C₄×C₆₇	—	4	4	no	—
528	C₂×C₄×C₆₇	—	4	4	no	—
529	C₂×C₄×C₆₇	—	4	2	no	—
530	C₂×C₄×C₆₇	—	4	2	no	—
531	C₂×C₄×C₆₇	—	4	2	no	—
532	C₂×C₄×C₆₇	—	8	1	no	—
533	C₂×C₄×C₆₇	—	8	2	no	—
534	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
542	C₈×C₆₇	—	2	1	no	—
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	2	no	—
545	C₈×C₆₇	—	2	2	no	—
546	C₈×C₆₇	—	2	1	no	—
547	C₈×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	2	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	1	no	—
555	C₂²×C₆₇	—	2	2	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	2	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	4	1	no	—
561	C₂²×C₆₇	—	4	1	no	—
562	C₂²×C₆₇	—	4	2	no	—
563	C₂²×C₆₇	—	4	1	no	—
564	C₂²×C₆₇	—	4	2	no	—
565	C₂²×C₆₇	—	4	1	no	—
566	C₂²×C₆₇	—	4	1	no	—
567	C₂²×C₆₇	—	4	1	no	—
568	C₂²×C₆₇	—	8	4	no	—
569	C₂²×C₆₇	—	16	4	no	—
570	C₂²×C₆₇	—	16	4	no	—
571	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
572	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
573	C₄×C₆₇	—	2	1	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	—	2	1	no	—
576	C₄×C₆₇	—	2	2	no	—
577	C₄×C₆₇	—	2	2	no	—
578	C₄×C₆₇	—	2	1	no	—
579	C₄×C₆₇	—	4	1	no	—
580	C₄×C₆₇	—	4	2	no	—
581	C₄×C₆₇	—	4	1	no	—
582	C₄×C₆₇	—	4	1	no	—
583	C₄×C₆₇	—	4	2	no	—
584	C₄×C₆₇	—	4	1	no	—
585	C₄×C₆₇	—	4	1	no	—
586	C₄×C₆₇	—	4	2	no	—
587	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
588	C₄×C₆₇	#585	1	1	yes	characteristic
589	C₄×C₆₇	#585	1	1	yes	characteristic
590	#61733	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
591	C₂×C₆₇	—	2	4	no	—
592	C₂×C₆₇	—	4	1	no	—
593	C₂×C₆₇	—	4	2	no	—
594	C₂×C₆₇	—	8	1	no	—
595	C₂×C₆₇	—	8	1	no	—
596	C₂×C₆₇	—	8	2	no	—
597	C₂×C₆₇	—	8	1	no	—
598	C₂×C₆₇	#3485	1	1	yes	characteristic
599	C₂×C₆₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
600	C₂×C₆₇	#3584	1	1	yes	characteristic
601	#3496	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#3475	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3354	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3353	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3345	C₂×C₆₇	1	2	yes	complemented
606	#3343	C₂×C₆₇	1	2	yes	complemented
607	#3335	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3334	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#3325	C₂×C₆₇	1	1	yes	characteristic, complemented
610	#3324	C₂×C₆₇	1	1	yes	characteristic, complemented
611	#3318	C₂×C₆₇	1	2	yes	complemented
612	#3310	C₂×C₆₇	1	2	yes	complemented
613	#3295	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#3294	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3235	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3228	C₂×C₆₇	1	1	yes	characteristic, complemented
617	#3194	C₂×C₆₇	1	2	yes	complemented
618	#3188	C₂×C₆₇	1	2	yes	complemented
619	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
620	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
621	#3094	C₂×C₆₇	1	2	yes	complemented
622	C₂×#482	C₂×C₆₇	1	2	yes	complemented
623	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
624	C₆₇	#61733	1	1	yes	characteristic, direct product factor, Sylow
625	C₂×H(5,𝔽₂)	—	2	1	no	—
626	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
627	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#554	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#553	C₂²×C₆₇	1	2	yes	complemented
630	#552	—	2	1	no	—
631	#552	C₂²×C₆₇	1	2	yes	complemented
632	#551	—	2	2	no	—
633	#547	C₂²×C₆₇	1	1	yes	characteristic
634	#547	C₂²×C₆₇	1	2	yes	—
635	#547	C₂²×C₆₇	1	1	yes	characteristic
636	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	#546	—	2	1	no	—
638	#546	—	2	1	no	—
639	#546	—	2	2	no	—
640	#546	—	2	1	no	—
641	D₄²	C₂²×C₆₇	1	1	yes	characteristic
642	D₄²	C₂²×C₆₇	1	2	yes	—
643	D₄²	C₂²×C₆₇	1	1	yes	characteristic
644	#537	—	2	1	no	—
645	#534	—	2	2	no	—
646	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
647	#532	C₂²×C₆₇	1	1	yes	characteristic
648	#532	C₂²×C₆₇	1	1	yes	characteristic
649	#529	—	2	2	no	—
650	#529	—	2	1	no	—
651	#525	C₂²×C₆₇	1	2	yes	complemented
652	C₂×#121	C₂²×C₆₇	1	2	yes	—
653	C₂×#121	C₂²×C₆₇	1	2	yes	—
654	C₄×#41	—	2	1	no	—
655	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
657	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
658	#501	C₂²×C₆₇	1	2	yes	complemented
659	#500	C₂²×C₆₇	1	1	yes	characteristic, complemented
660	#498	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#490	C₂²×C₆₇	1	2	yes	complemented
662	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
663	#486	C₂²×C₆₇	1	1	yes	characteristic, complemented
664	#484	C₂²×C₆₇	1	2	yes	complemented
665	#483	C₂²×C₆₇	1	2	yes	complemented
666	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
667	#482	C₂²×C₆₇	1	2	yes	complemented
668	#482	C₂²×C₆₇	1	2	yes	complemented
669	#482	C₂²×C₆₇	1	2	yes	complemented
670	#482	C₂²×C₆₇	1	2	yes	complemented
671	#482	C₂²×C₆₇	1	2	yes	complemented
672	#482	C₂²×C₆₇	1	2	yes	complemented
673	#482	C₂²×C₆₇	1	2	yes	complemented
674	#482	C₂²×C₆₇	1	1	yes	characteristic, complemented
675	#482	C₂²×C₆₇	1	2	yes	complemented
676	#482	C₂²×C₆₇	1	2	yes	complemented
677	#481	C₂²×C₆₇	1	2	yes	complemented
678	#481	C₂²×C₆₇	1	2	yes	complemented
679	#481	C₂²×C₆₇	1	2	yes	complemented
680	#480	C₂²×C₆₇	1	2	yes	complemented
681	#480	C₂²×C₆₇	1	2	yes	complemented
682	#480	C₂²×C₆₇	1	2	yes	complemented
683	#478	C₂²×C₆₇	1	2	yes	complemented
684	#478	C₂²×C₆₇	1	2	yes	complemented
685	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
686	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
689	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
693	#469	C₂²×C₆₇	1	2	yes	complemented
694	#469	C₂²×C₆₇	1	2	yes	complemented
695	#468	C₂²×C₆₇	1	2	yes	complemented
696	#468	C₂²×C₆₇	1	2	yes	complemented
697	#466	C₂²×C₆₇	1	2	yes	complemented
698	#466	C₂²×C₆₇	1	2	yes	complemented
699	#465	C₂²×C₆₇	1	2	yes	complemented
700	#465	C₂²×C₆₇	1	2	yes	complemented
701	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
702	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
703	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
705	#450	C₂²×C₆₇	1	2	yes	complemented
706	#450	C₂²×C₆₇	1	2	yes	complemented
707	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
708	#449	C₂²×C₆₇	1	1	yes	characteristic, complemented
709	#449	C₂²×C₆₇	1	2	yes	complemented
710	#447	C₂²×C₆₇	1	2	yes	complemented
711	#447	C₂²×C₆₇	1	2	yes	complemented
712	#442	C₂²×C₆₇	1	2	yes	complemented
713	#440	C₂²×C₆₇	1	2	yes	complemented
714	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	#436	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	#435	C₂²×C₆₇	1	2	yes	complemented
721	#435	C₂²×C₆₇	1	2	yes	complemented
722	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
723	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	#428	C₂²×C₆₇	1	2	yes	complemented
727	#428	C₂²×C₆₇	1	2	yes	complemented
728	C₂×#107	C₂²×C₆₇	1	2	yes	complemented
729	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
730	#418	C₂²×C₆₇	1	2	yes	complemented
731	#418	C₂²×C₆₇	1	2	yes	complemented
732	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
733	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
734	#407	C₂²×C₆₇	1	2	yes	complemented
735	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
736	H(5,𝔽₂)	—	4	8	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	—	2	2	no	—
739	C₂×#41	—	2	1	no	—
740	C₂×#41	—	2	1	no	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	—	2	1	no	—
743	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
744	C₂²×D₄	—	2	2	no	—
745	C₂²×D₄	—	2	2	no	—
746	C₂²×D₄	—	2	2	no	—
747	C₂²×D₄	—	2	1	no	—
748	C₂²×D₄	—	2	1	no	—
749	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
750	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
751	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
752	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
755	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
756	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
758	C₂×D₈	C₂³×C₆₇	1	2	yes	—
759	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
760	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
761	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
762	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
763	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
764	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
766	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
767	#127	C₂³×C₆₇	1	1	yes	characteristic
768	#127	C₂³×C₆₇	1	1	yes	characteristic
769	#126	—	2	2	no	—
770	#126	—	2	2	no	—
771	#126	—	2	2	no	—
772	#125	—	2	2	no	—
773	#125	—	2	1	no	—
774	#125	C₂³×C₆₇	1	2	yes	—
775	#124	—	2	1	no	—
776	#124	—	2	2	no	—
777	#124	—	2	1	no	—
778	#124	—	2	1	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	2	2	no	—
800	#121	—	2	2	no	—
801	#121	—	2	2	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	C₂³×C₆₇	1	1	yes	characteristic
808	#121	C₂³×C₆₇	1	2	yes	—
809	#121	C₂³×C₆₇	1	1	yes	characteristic
810	#121	C₂³×C₆₇	1	2	yes	—
811	#121	C₂³×C₆₇	1	2	yes	—
812	#121	C₂³×C₆₇	1	2	yes	—
813	#121	C₂³×C₆₇	1	2	yes	—
814	#121	C₂³×C₆₇	1	2	yes	—
815	#121	C₂³×C₆₇	1	2	yes	—
816	#120	—	2	2	no	—
817	#120	—	2	2	no	—
818	#120	—	2	2	no	—
819	#120	—	2	2	no	—
820	#120	—	2	2	no	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	—	2	1	no	—
824	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
835	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
836	C₄×D₄	D₄×C₆₇	1	2	yes	—
837	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₆₇	1	2	yes	—
842	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₆₇	1	2	yes	—
844	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
845	#117	—	2	2	no	—
846	#117	—	2	2	no	—
847	#117	—	2	1	no	—
848	#117	—	2	2	no	—
849	#117	—	2	1	no	—
850	#117	C₂³×C₆₇	1	1	yes	characteristic
851	#117	C₂³×C₆₇	1	2	yes	—
852	#117	C₂³×C₆₇	1	2	yes	—
853	#117	C₂³×C₆₇	1	2	yes	—
854	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
855	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
856	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
857	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
858	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₂²⋊C₄	—	2	2	no	—
861	C₂×C₂²⋊C₄	—	2	2	no	—
862	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
863	C₂×C₄²	—	2	2	no	—
864	C₂×C₄²	—	2	1	no	—
865	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
866	#107	C₂³×C₆₇	1	1	yes	characteristic
867	#107	C₂³×C₆₇	1	2	yes	—
868	#107	C₂³×C₆₇	1	2	yes	—
869	#107	C₂³×C₆₇	1	2	yes	—
870	#107	C₂³×C₆₇	1	1	yes	characteristic
871	#107	C₂³×C₆₇	1	2	yes	—
872	#107	C₂³×C₆₇	1	2	yes	—
873	#106	C₂³×C₆₇	1	1	yes	characteristic
874	#106	C₂³×C₆₇	1	2	yes	—
875	#106	C₂³×C₆₇	1	2	yes	—
876	#106	C₂³×C₆₇	1	2	yes	—
877	#106	C₂³×C₆₇	1	1	yes	characteristic
878	#106	C₂³×C₆₇	1	2	yes	—
879	#106	C₂³×C₆₇	1	2	yes	—
880	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
881	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
883	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
884	#103	C₂³×C₆₇	1	1	yes	characteristic
885	#103	C₂³×C₆₇	1	1	yes	characteristic
886	#103	C₂³×C₆₇	1	2	yes	—
887	#102	C₂³×C₆₇	1	1	yes	characteristic
888	#102	C₂³×C₆₇	1	1	yes	characteristic
889	#102	C₂³×C₆₇	1	2	yes	—
890	#102	C₂³×C₆₇	1	2	yes	—
891	#102	C₂³×C₆₇	1	2	yes	—
892	#102	C₂³×C₆₇	1	2	yes	—
893	#102	C₂³×C₆₇	1	2	yes	—
894	#102	C₂³×C₆₇	1	2	yes	—
895	#102	C₂³×C₆₇	1	1	yes	characteristic
896	#102	C₂³×C₆₇	1	1	yes	characteristic
897	#102	C₂³×C₆₇	1	2	yes	—
898	#102	C₂³×C₆₇	1	2	yes	—
899	#102	C₂³×C₆₇	1	2	yes	—
900	#102	C₂³×C₆₇	1	2	yes	—
901	#102	C₂³×C₆₇	1	1	yes	characteristic
902	#102	C₂³×C₆₇	1	1	yes	characteristic
903	#102	C₂³×C₆₇	1	2	yes	—
904	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
905	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
911	#97	C₂³×C₆₇	1	2	yes	—
912	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
913	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
914	C₂⁴	—	2	2	no	—
915	C₂⁴	—	2	2	no	—
916	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
917	#41	—	4	1	no	—
918	#41	—	4	1	no	—
919	#41	—	4	4	no	—
920	#41	—	4	4	no	—
921	#41	—	4	8	no	—
922	#41	—	4	4	no	—
923	#41	—	4	4	no	—
924	#41	—	4	4	no	—
925	C₂×Q₈	—	2	1	no	—
926	C₂×Q₈	—	2	1	no	—
927	C₂×Q₈	—	2	1	no	—
928	C₂×Q₈	—	2	1	no	—
929	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
930	C₂×D₄	—	2	4	no	—
931	C₂×D₄	—	2	1	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	2	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	1	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	1	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	4	2	no	—
948	C₂×D₄	—	4	2	no	—
949	C₂×D₄	—	4	2	no	—
950	C₂×D₄	—	4	2	no	—
951	C₂×D₄	—	4	8	no	—
952	C₂×D₄	—	4	4	no	—
953	C₂×D₄	—	4	8	no	—
954	C₂×D₄	—	4	8	no	—
955	C₂×D₄	—	4	4	no	—
956	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
957	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
958	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
959	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
960	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
961	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
962	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₂²×C₄	—	2	2	no	—
964	C₂²×C₄	—	2	2	no	—
965	C₂²×C₄	—	2	2	no	—
966	C₂²×C₄	—	2	2	no	—
967	C₂²×C₄	—	2	1	no	—
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	2	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	4	2	no	—
974	C₂²×C₄	—	4	2	no	—
975	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
976	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
977	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
978	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
979	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
980	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
982	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
983	SD₁₆	—	4	1	no	—
984	SD₁₆	—	4	2	no	—
985	SD₁₆	—	4	1	no	—
986	D₈	—	4	1	no	—
987	D₈	—	4	2	no	—
988	D₈	—	4	1	no	—
989	M₁₆	—	4	2	no	—
990	M₁₆	—	4	2	no	—
991	C₂×C₈	—	4	2	no	—
992	C₂×C₈	—	4	2	no	—
993	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
994	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
998	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	1	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	—	2	1	no	—
1009	C₄⋊C₄	—	2	1	no	—
1010	C₄⋊C₄	—	2	2	no	—
1011	C₄⋊C₄	—	2	2	no	—
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1014	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1016	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1018	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1019	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1020	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1021	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1022	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1023	C₂²⋊C₄	—	2	1	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	2	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1044	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1045	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1046	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	—	2	1	no	—
1050	C₄²	—	2	2	no	—
1051	C₄²	—	2	2	no	—
1052	C₄²	—	2	1	no	—
1053	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1054	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1056	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1057	C₂³	—	2	4	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	2	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	2	1	no	—
1062	C₂³	—	4	2	no	—
1063	C₂³	—	4	2	no	—
1064	C₂³	—	4	4	no	—
1065	C₂³	—	4	4	no	—
1066	C₂³	—	8	2	no	—
1067	C₂³	—	8	2	no	—
1068	C₂³	—	8	2	no	—
1069	C₂³	—	8	2	no	—
1070	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1071	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1072	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1073	Q₈	—	2	1	no	—
1074	Q₈	—	2	1	no	—
1075	Q₈	—	4	2	no	—
1076	Q₈	—	4	2	no	—
1077	Q₈	—	4	2	no	—
1078	Q₈	—	8	1	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	1	no	—
1082	D₄	—	2	1	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	2	no	—
1086	D₄	—	2	2	no	—
1087	D₄	—	2	1	no	—
1088	D₄	—	2	1	no	—
1089	D₄	—	4	2	no	—
1090	D₄	—	4	4	no	—
1091	D₄	—	4	2	no	—
1092	D₄	—	4	2	no	—
1093	D₄	—	4	4	no	—
1094	D₄	—	4	4	no	—
1095	D₄	—	4	2	no	—
1096	D₄	—	4	4	no	—
1097	D₄	—	4	4	no	—
1098	D₄	—	4	4	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	8	2	no	—
1101	D₄	—	8	2	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	1	no	—
1104	D₄	—	8	2	no	—
1105	D₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
1106	C₂×C₄	—	2	2	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	2	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	2	1	no	—
1114	C₂×C₄	—	2	1	no	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	2	no	—
1118	C₂×C₄	—	2	2	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	4	2	no	—
1122	C₂×C₄	—	4	2	no	—
1123	C₂×C₄	—	4	2	no	—
1124	C₂×C₄	—	4	1	no	—
1125	C₂×C₄	—	4	4	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	4	4	no	—
1128	C₂×C₄	—	4	4	no	—
1129	C₂×C₄	—	4	4	no	—
1130	C₂×C₄	—	4	2	no	—
1131	C₂×C₄	—	4	2	no	—
1132	C₂×C₄	—	4	2	no	—
1133	C₂×C₄	—	8	1	no	—
1134	C₂×C₄	—	8	2	no	—
1135	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1136	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1137	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1138	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1139	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1140	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1141	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1142	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1143	C₈	—	2	1	no	—
1144	C₈	—	2	1	no	—
1145	C₈	—	2	2	no	—
1146	C₈	—	2	2	no	—
1147	C₈	—	2	1	no	—
1148	C₈	—	2	1	no	—
1149	C₂²	—	2	2	no	—
1150	C₂²	—	2	2	no	—
1151	C₂²	—	2	1	no	—
1152	C₂²	—	2	2	no	—
1153	C₂²	—	2	1	no	—
1154	C₂²	—	2	2	no	—
1155	C₂²	—	2	1	no	—
1156	C₂²	—	2	2	no	—
1157	C₂²	—	4	2	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	4	1	no	—
1160	C₂²	—	4	1	no	—
1161	C₂²	—	4	1	no	—
1162	C₂²	—	4	1	no	—
1163	C₂²	—	4	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	2	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	8	4	no	—
1170	C₂²	—	16	4	no	—
1171	C₂²	—	16	4	no	—
1172	C₂²	C₂×AGL(1,ℤ/8)×C₆₇	1	4	yes	—
1173	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1174	C₄	—	2	1	no	—
1175	C₄	—	2	1	no	—
1176	C₄	—	2	1	no	—
1177	C₄	—	2	1	no	—
1178	C₄	—	2	2	no	—
1179	C₄	—	2	2	no	—
1180	C₄	—	4	2	no	—
1181	C₄	—	4	1	no	—
1182	C₄	—	4	1	no	—
1183	C₄	—	4	1	no	—
1184	C₄	—	4	2	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	2	no	—
1187	C₄	—	4	1	no	—
1188	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
1189	C₄	#585×C₆₇	1	1	yes	characteristic
1190	C₄	#585×C₆₇	1	1	yes	characteristic
1191	C₂	—	2	4	no	—
1192	C₂	—	4	1	no	—
1193	C₂	—	4	2	no	—
1194	C₂	—	8	1	no	—
1195	C₂	—	8	2	no	—
1196	C₂	—	8	1	no	—
1197	C₂	—	8	1	no	—
1198	C₂	C₆₇×#3485	1	1	yes	characteristic
1199	C₂	C₂²×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
1200	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄×D₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3496	C₂	semidirect
2. C₆₇×#3475	C₂	semidirect
3. C₆₇×#3354	C₂	semidirect
4. C₆₇×#3353	C₂	semidirect
5. C₆₇×#3345	C₂	semidirect
6. C₆₇×#3343	C₂	semidirect
7. C₆₇×#3335	C₂	semidirect
8. C₆₇×#3334	C₂	semidirect
9. C₆₇×#3325	C₂	semidirect
10. C₆₇×#3324	C₂	semidirect
11. C₆₇×#3318	C₂	semidirect
12. C₆₇×#3310	C₂	semidirect
13. C₆₇×#3295	C₂	semidirect
14. C₆₇×#3294	C₂	semidirect
15. C₆₇×#3235	C₂	semidirect
16. C₆₇×#3228	C₂	semidirect
17. C₆₇×#3194	C₂	semidirect
18. C₆₇×#3188	C₂	semidirect
19. C₆₇×#3115	C₂	semidirect
20. C₆₇×#3106	C₂	semidirect
21. C₆₇×#3094	C₂	semidirect
22. C₂×#482×C₆₇	C₂	semidirect
23. C₆₇×#2974	C₂	semidirect
25. #556×C₆₇	C₂²	semidirect
26. #555×C₆₇	C₂²	semidirect
27. #554×C₆₇	C₂²	semidirect
28. #553×C₆₇	C₂²	semidirect
30. #552×C₆₇	C₂²	semidirect
35. #547×C₆₇	C₂²	semidirect
45. #533×C₆₇	C₂²	semidirect
50. #525×C₆₇	C₂²	semidirect
54. C₄×#41×C₆₇	C₂²	semidirect
56. C₂×#117×C₆₇	C₂²	semidirect
57. #501×C₆₇	C₂²	semidirect
58. #500×C₆₇	C₂²	semidirect
59. #498×C₆₇	C₂²	semidirect
60. #490×C₆₇	C₂²	semidirect
61. #486×C₆₇	C₂²	semidirect
62. #486×C₆₇	C₂²	semidirect
63. #484×C₆₇	C₂²	semidirect
64. #483×C₆₇	C₂²	semidirect
65. #482×C₆₇	C₂²	semidirect
66. #482×C₆₇	C₂²	semidirect
67. #482×C₆₇	C₂²	semidirect
68. #482×C₆₇	C₂²	semidirect
69. #482×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #482×C₆₇	C₂²	semidirect
73. #482×C₆₇	C₂²	semidirect
74. #482×C₆₇	C₂²	semidirect
75. #482×C₆₇	C₂²	semidirect
76. #481×C₆₇	C₂²	semidirect
77. #481×C₆₇	C₂²	semidirect
78. #481×C₆₇	C₂²	semidirect
79. #480×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #480×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #478×C₆₇	C₂²	semidirect
84. #477×C₆₇	C₂²	semidirect
85. #476×C₆₇	C₂²	semidirect
86. #476×C₆₇	C₂²	semidirect
87. #476×C₆₇	C₂²	semidirect
88. #475×C₆₇	C₂²	semidirect
89. #474×C₆₇	C₂²	semidirect
90. #474×C₆₇	C₂²	semidirect
91. #474×C₆₇	C₂²	semidirect
92. #469×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
94. #468×C₆₇	C₂²	semidirect
95. #468×C₆₇	C₂²	semidirect
96. #466×C₆₇	C₂²	semidirect
97. #466×C₆₇	C₂²	semidirect
98. #465×C₆₇	C₂²	semidirect
99. #465×C₆₇	C₂²	semidirect
100. #460×C₆₇	C₂²	semidirect
101. #460×C₆₇	C₂²	semidirect
102. #459×C₆₇	C₂²	semidirect
103. #459×C₆₇	C₂²	semidirect
104. #450×C₆₇	C₂²	semidirect
105. #450×C₆₇	C₂²	semidirect
106. #449×C₆₇	C₂²	semidirect
107. #449×C₆₇	C₂²	semidirect
108. #449×C₆₇	C₂²	semidirect
109. #447×C₆₇	C₂²	semidirect
110. #447×C₆₇	C₂²	semidirect
111. #442×C₆₇	C₂²	semidirect
112. #440×C₆₇	C₂²	semidirect
113. C₄×SD₁₆×C₆₇	C₂²	semidirect
114. C₄×SD₁₆×C₆₇	C₂²	semidirect
115. C₄×D₈×C₆₇	C₂²	semidirect
116. C₄×D₈×C₆₇	C₂²	semidirect
117. #436×C₆₇	C₂²	semidirect
118. #436×C₆₇	C₂²	semidirect
119. #435×C₆₇	C₂²	semidirect
120. #435×C₆₇	C₂²	semidirect
121. C₈×D₄×C₆₇	C₂²	semidirect
122. C₈×D₄×C₆₇	C₂²	semidirect
123. #432×C₆₇	C₂²	semidirect
124. #431×C₆₇	C₂²	semidirect
125. #428×C₆₇	C₂²	semidirect
126. #428×C₆₇	C₂²	semidirect
127. C₂×#107×C₆₇	C₂²	semidirect
128. C₂×#106×C₆₇	C₂²	semidirect
129. #418×C₆₇	C₂²	semidirect
130. #418×C₆₇	C₂²	semidirect
131. C₂×#102×C₆₇	C₂²	semidirect
132. C₂×#102×C₆₇	C₂²	semidirect
133. #407×C₆₇	C₂²	semidirect
134. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
590. #61733	C₆₇	direct (N × H)
601. #3496	C₂×C₆₇	semidirect
602. #3475	C₂×C₆₇	semidirect
603. #3354	C₂×C₆₇	semidirect
604. #3353	C₂×C₆₇	semidirect
605. #3345	C₂×C₆₇	semidirect
606. #3343	C₂×C₆₇	semidirect
607. #3335	C₂×C₆₇	semidirect
608. #3334	C₂×C₆₇	semidirect
609. #3325	C₂×C₆₇	semidirect
610. #3324	C₂×C₆₇	semidirect
611. #3318	C₂×C₆₇	semidirect
612. #3310	C₂×C₆₇	semidirect
613. #3295	C₂×C₆₇	semidirect
614. #3294	C₂×C₆₇	semidirect
615. #3235	C₂×C₆₇	semidirect
616. #3228	C₂×C₆₇	semidirect
617. #3194	C₂×C₆₇	semidirect
618. #3188	C₂×C₆₇	semidirect
619. #3115	C₂×C₆₇	semidirect
620. #3106	C₂×C₆₇	semidirect
621. #3094	C₂×C₆₇	semidirect
622. C₂×#482	C₂×C₆₇	semidirect
623. #2974	C₂×C₆₇	semidirect
624. C₆₇	#61733	direct (N × H)
626. #556	C₂²×C₆₇	semidirect
627. #555	C₂²×C₆₇	semidirect
628. #554	C₂²×C₆₇	semidirect
629. #553	C₂²×C₆₇	semidirect
631. #552	C₂²×C₆₇	semidirect
636. #547	C₂²×C₆₇	semidirect
646. #533	C₂²×C₆₇	semidirect
651. #525	C₂²×C₆₇	semidirect
655. C₄×#41	C₂²×C₆₇	semidirect
657. C₂×#117	C₂²×C₆₇	semidirect
658. #501	C₂²×C₆₇	semidirect
659. #500	C₂²×C₆₇	semidirect
660. #498	C₂²×C₆₇	semidirect
661. #490	C₂²×C₆₇	semidirect
662. #486	C₂²×C₆₇	semidirect
663. #486	C₂²×C₆₇	semidirect
664. #484	C₂²×C₆₇	semidirect
665. #483	C₂²×C₆₇	semidirect
666. #482	C₂²×C₆₇	semidirect
667. #482	C₂²×C₆₇	semidirect
668. #482	C₂²×C₆₇	semidirect
669. #482	C₂²×C₆₇	semidirect
670. #482	C₂²×C₆₇	semidirect
671. #482	C₂²×C₆₇	semidirect
672. #482	C₂²×C₆₇	semidirect
673. #482	C₂²×C₆₇	semidirect
674. #482	C₂²×C₆₇	semidirect
675. #482	C₂²×C₆₇	semidirect
676. #482	C₂²×C₆₇	semidirect
677. #481	C₂²×C₆₇	semidirect
678. #481	C₂²×C₆₇	semidirect
679. #481	C₂²×C₆₇	semidirect
680. #480	C₂²×C₆₇	semidirect
681. #480	C₂²×C₆₇	semidirect
682. #480	C₂²×C₆₇	semidirect
683. #478	C₂²×C₆₇	semidirect
684. #478	C₂²×C₆₇	semidirect
685. #477	C₂²×C₆₇	semidirect
686. #476	C₂²×C₆₇	semidirect
687. #476	C₂²×C₆₇	semidirect
688. #476	C₂²×C₆₇	semidirect
689. #475	C₂²×C₆₇	semidirect
690. #474	C₂²×C₆₇	semidirect
691. #474	C₂²×C₆₇	semidirect
692. #474	C₂²×C₆₇	semidirect
693. #469	C₂²×C₆₇	semidirect
694. #469	C₂²×C₆₇	semidirect
695. #468	C₂²×C₆₇	semidirect
696. #468	C₂²×C₆₇	semidirect
697. #466	C₂²×C₆₇	semidirect
698. #466	C₂²×C₆₇	semidirect
699. #465	C₂²×C₆₇	semidirect
700. #465	C₂²×C₆₇	semidirect
701. #460	C₂²×C₆₇	semidirect
702. #460	C₂²×C₆₇	semidirect
703. #459	C₂²×C₆₇	semidirect
704. #459	C₂²×C₆₇	semidirect
705. #450	C₂²×C₆₇	semidirect
706. #450	C₂²×C₆₇	semidirect
707. #449	C₂²×C₆₇	semidirect
708. #449	C₂²×C₆₇	semidirect
709. #449	C₂²×C₆₇	semidirect
710. #447	C₂²×C₆₇	semidirect
711. #447	C₂²×C₆₇	semidirect
712. #442	C₂²×C₆₇	semidirect
713. #440	C₂²×C₆₇	semidirect
714. C₄×SD₁₆	C₂²×C₆₇	semidirect
715. C₄×SD₁₆	C₂²×C₆₇	semidirect
716. C₄×D₈	C₂²×C₆₇	semidirect
717. C₄×D₈	C₂²×C₆₇	semidirect
718. #436	C₂²×C₆₇	semidirect
719. #436	C₂²×C₆₇	semidirect
720. #435	C₂²×C₆₇	semidirect
721. #435	C₂²×C₆₇	semidirect
722. C₈×D₄	C₂²×C₆₇	semidirect
723. C₈×D₄	C₂²×C₆₇	semidirect
724. #432	C₂²×C₆₇	semidirect
725. #431	C₂²×C₆₇	semidirect
726. #428	C₂²×C₆₇	semidirect
727. #428	C₂²×C₆₇	semidirect
728. C₂×#107	C₂²×C₆₇	semidirect
729. C₂×#106	C₂²×C₆₇	semidirect
730. #418	C₂²×C₆₇	semidirect
731. #418	C₂²×C₆₇	semidirect
732. C₂×#102	C₂²×C₆₇	semidirect
733. C₂×#102	C₂²×C₆₇	semidirect
734. #407	C₂²×C₆₇	semidirect
735. C₂×C₂²⋊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×#3496	2
C₆₇×#3475	2
C₆₇×#3354	2
C₆₇×#3353	2
C₆₇×#3345	2
C₆₇×#3343	2
C₆₇×#3335	2
C₆₇×#3334	2
C₆₇×#3325	2
C₆₇×#3324	2
C₆₇×#3318	2
C₆₇×#3310	2
C₆₇×#3295	2
C₆₇×#3294	2
C₆₇×#3235	2
C₆₇×#3228	2
C₆₇×#3194	2
C₆₇×#3188	2
C₆₇×#3115	2
C₆₇×#3106	2
C₆₇×#3094	2
C₂×#482×C₆₇	2
C₆₇×#2974	2
#61733	67

Subgroups — C67×#61733 #30740984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61733 #30740984