Subgroups — C₆₇×#60990 #30740241

Order 17152.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3253	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3241	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3235	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3220	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3199	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3198	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3176	C₂	1	2	yes	maximal, complemented
17	C₆₇×#3122	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	#559×C₆₇	—	2	1	no	—
25	#559×C₆₇	—	2	1	no	—
26	#550×C₆₇	—	2	1	no	—
27	#550×C₆₇	—	2	1	no	—
28	#546×C₆₇	—	2	1	no	—
29	#546×C₆₇	—	2	1	no	—
30	#546×C₆₇	—	2	1	no	—
31	#546×C₆₇	—	2	1	no	—
32	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#542×C₆₇	—	2	1	no	—
34	#542×C₆₇	C₂²	1	1	yes	characteristic
35	#542×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	#540×C₆₇	—	2	1	no	—
37	#540×C₆₇	C₂²	1	1	yes	characteristic
38	#540×C₆₇	C₂²	1	2	yes	—
39	#540×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#540×C₆₇	C₂²	1	2	yes	complemented
41	#538×C₆₇	—	2	1	no	—
42	#538×C₆₇	—	2	1	no	—
43	#537×C₆₇	C₂²	1	1	yes	characteristic
44	#535×C₆₇	C₂²	1	2	yes	—
45	#535×C₆₇	C₂²	1	1	yes	characteristic
46	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
48	#532×C₆₇	—	2	1	no	—
49	#532×C₆₇	C₂²	1	1	yes	characteristic
50	#532×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	C₂²	1	1	yes	characteristic
52	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#532×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#529×C₆₇	—	2	1	no	—
57	#529×C₆₇	C₂²	1	1	yes	characteristic
58	#529×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#525×C₆₇	—	2	1	no	—
60	#525×C₆₇	—	2	1	no	—
61	#518×C₆₇	C₂²	1	2	yes	complemented
62	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
63	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
65	#501×C₆₇	C₂²	1	2	yes	complemented
66	#499×C₆₇	C₂²	1	2	yes	complemented
67	#496×C₆₇	C₂²	1	2	yes	—
68	#493×C₆₇	C₂²	1	2	yes	—
69	#490×C₆₇	C₂²	1	2	yes	complemented
70	#490×C₆₇	C₂²	1	2	yes	complemented
71	#488×C₆₇	C₂²	1	2	yes	complemented
72	#486×C₆₇	C₂²	1	2	yes	complemented
73	#485×C₆₇	C₂²	1	2	yes	complemented
74	#482×C₆₇	C₂²	1	2	yes	—
75	#482×C₆₇	C₂²	1	2	yes	—
76	#482×C₆₇	C₂²	1	2	yes	complemented
77	#482×C₆₇	C₂²	1	2	yes	complemented
78	#482×C₆₇	C₂²	1	2	yes	complemented
79	#481×C₆₇	C₂²	1	2	yes	complemented
80	#480×C₆₇	C₂²	1	2	yes	complemented
81	#478×C₆₇	C₂²	1	2	yes	complemented
82	#478×C₆₇	C₂²	1	2	yes	complemented
83	#477×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	#476×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	2	yes	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	#474×C₆₇	C₂²	1	2	yes	complemented
93	#469×C₆₇	C₂²	1	2	yes	complemented
94	#469×C₆₇	C₂²	1	2	yes	complemented
95	#469×C₆₇	C₂²	1	2	yes	complemented
96	#468×C₆₇	C₂²	1	2	yes	complemented
97	#466×C₆₇	C₂²	1	2	yes	complemented
98	#466×C₆₇	C₂²	1	2	yes	complemented
99	#466×C₆₇	C₂²	1	2	yes	complemented
100	#465×C₆₇	C₂²	1	2	yes	complemented
101	#463×C₆₇	C₂²	1	2	yes	complemented
102	#463×C₆₇	C₂²	1	2	yes	complemented
103	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#460×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#459×C₆₇	C₂²	1	1	yes	characteristic
106	#459×C₆₇	C₂²	1	1	yes	characteristic
107	#459×C₆₇	C₂²	1	1	yes	characteristic
108	#459×C₆₇	C₂²	1	1	yes	characteristic
109	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#459×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#459×C₆₇	C₂²	1	2	yes	complemented
112	#459×C₆₇	C₂²	1	2	yes	complemented
113	#450×C₆₇	C₂²	1	2	yes	complemented
114	#449×C₆₇	C₂²	1	2	yes	complemented
115	#449×C₆₇	C₂²	1	2	yes	complemented
116	#447×C₆₇	C₂²	1	2	yes	—
117	#447×C₆₇	C₂²	1	2	yes	—
118	#447×C₆₇	C₂²	1	2	yes	complemented
119	#447×C₆₇	C₂²	1	2	yes	complemented
120	#447×C₆₇	C₂²	1	2	yes	complemented
121	#442×C₆₇	C₂²	1	2	yes	complemented
122	#442×C₆₇	C₂²	1	2	yes	complemented
123	#442×C₆₇	C₂²	1	2	yes	complemented
124	#440×C₆₇	C₂²	1	2	yes	complemented
125	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
126	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
127	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
128	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
129	#433×C₆₇	C₂²	1	2	yes	complemented
130	#433×C₆₇	C₂²	1	2	yes	complemented
131	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
132	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
133	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	#431×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
137	#408×C₆₇	C₂²	1	2	yes	—
138	#405×C₆₇	C₂²	1	2	yes	complemented
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	—	2	1	no	—
143	C₂×#41×C₆₇	—	2	1	no	—
144	C₂×#41×C₆₇	—	2	1	no	—
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
147	C₂²×D₄×C₆₇	—	2	1	no	—
148	C₂²×D₄×C₆₇	—	2	1	no	—
149	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
150	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₆₇	—	2	1	no	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×D₈×C₆₇	C₂³	1	2	yes	—
155	C₂×D₈×C₆₇	C₂³	1	2	yes	—
156	C₂×D₈×C₆₇	C₂³	1	2	yes	—
157	C₂×D₈×C₆₇	C₂³	1	2	yes	—
158	C₂×D₈×C₆₇	C₂³	1	2	yes	—
159	C₂×D₈×C₆₇	C₂³	1	2	yes	—
160	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
162	C₄⋊Q₈×C₆₇	—	2	1	no	—
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	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
167	#127×C₆₇	—	2	1	no	—
168	#127×C₆₇	—	2	2	no	—
169	#127×C₆₇	—	2	1	no	—
170	#127×C₆₇	—	2	1	no	—
171	#127×C₆₇	C₂³	1	1	yes	characteristic
172	#127×C₆₇	C₂³	1	1	yes	characteristic
173	#127×C₆₇	C₂³	1	1	yes	characteristic
174	#127×C₆₇	C₂³	1	2	yes	—
175	#127×C₆₇	C₂³	1	1	yes	characteristic
176	#126×C₆₇	—	2	1	no	—
177	#126×C₆₇	—	2	1	no	—
178	#126×C₆₇	—	2	1	no	—
179	#126×C₆₇	—	2	1	no	—
180	#125×C₆₇	—	2	1	no	—
181	#125×C₆₇	C₂³	1	1	yes	characteristic
182	#125×C₆₇	C₂³	1	2	yes	—
183	#125×C₆₇	C₂³	1	1	yes	characteristic
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	—	2	2	no	—
186	#124×C₆₇	—	2	1	no	—
187	#124×C₆₇	—	2	1	no	—
188	#124×C₆₇	—	2	1	no	—
189	#124×C₆₇	—	2	1	no	—
190	#124×C₆₇	—	2	1	no	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	—	2	1	no	—
193	#124×C₆₇	—	2	1	no	—
194	#124×C₆₇	C₂³	1	1	yes	characteristic
195	#124×C₆₇	C₂³	1	1	yes	characteristic
196	#123×C₆₇	—	2	1	no	—
197	#123×C₆₇	—	2	1	no	—
198	#123×C₆₇	—	2	1	no	—
199	#123×C₆₇	—	2	1	no	—
200	#123×C₆₇	—	2	1	no	—
201	#123×C₆₇	—	2	1	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	1	no	—
207	#123×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	1	no	—
210	C₂²⋊Q₈×C₆₇	—	2	1	no	—
211	C₂²⋊Q₈×C₆₇	—	2	1	no	—
212	C₂²⋊Q₈×C₆₇	—	2	1	no	—
213	C₂²⋊Q₈×C₆₇	—	2	1	no	—
214	C₂²⋊Q₈×C₆₇	—	2	1	no	—
215	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
216	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	#121×C₆₇	—	2	1	no	—
218	#121×C₆₇	—	2	1	no	—
219	#121×C₆₇	—	2	1	no	—
220	#121×C₆₇	—	2	1	no	—
221	#121×C₆₇	—	2	1	no	—
222	#121×C₆₇	—	2	1	no	—
223	#121×C₆₇	—	2	1	no	—
224	#121×C₆₇	—	2	1	no	—
225	#121×C₆₇	—	2	1	no	—
226	#121×C₆₇	—	2	1	no	—
227	#121×C₆₇	—	2	1	no	—
228	#121×C₆₇	—	2	1	no	—
229	#121×C₆₇	—	2	1	no	—
230	#121×C₆₇	—	2	1	no	—
231	#121×C₆₇	—	2	1	no	—
232	#121×C₆₇	—	2	2	no	—
233	#121×C₆₇	—	2	2	no	—
234	#121×C₆₇	—	2	2	no	—
235	#121×C₆₇	—	2	2	no	—
236	#121×C₆₇	C₂³	1	2	yes	—
237	#121×C₆₇	C₂³	1	2	yes	—
238	#121×C₆₇	C₂³	1	2	yes	—
239	#121×C₆₇	C₂³	1	2	yes	—
240	#121×C₆₇	C₂³	1	1	yes	characteristic
241	#121×C₆₇	C₂³	1	1	yes	characteristic
242	#121×C₆₇	C₂³	1	1	yes	characteristic
243	#121×C₆₇	C₂³	1	1	yes	characteristic
244	#121×C₆₇	C₂³	1	1	yes	characteristic
245	#121×C₆₇	C₂³	1	1	yes	characteristic
246	#120×C₆₇	—	2	1	no	—
247	#120×C₆₇	—	2	1	no	—
248	#120×C₆₇	—	2	2	no	—
249	#120×C₆₇	—	2	2	no	—
250	#120×C₆₇	—	2	1	no	—
251	#120×C₆₇	—	2	1	no	—
252	C₄×Q₈×C₆₇	—	2	1	no	—
253	C₄×Q₈×C₆₇	—	2	1	no	—
254	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
255	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
256	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
257	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₆₇	—	2	1	no	—
259	C₄×D₄×C₆₇	—	2	1	no	—
260	C₄×D₄×C₆₇	—	2	1	no	—
261	C₄×D₄×C₆₇	—	2	1	no	—
262	C₄×D₄×C₆₇	—	2	2	no	—
263	C₄×D₄×C₆₇	—	2	2	no	—
264	C₄×D₄×C₆₇	—	2	1	no	—
265	C₄×D₄×C₆₇	—	2	1	no	—
266	C₄×D₄×C₆₇	—	2	1	no	—
267	C₄×D₄×C₆₇	—	2	1	no	—
268	C₄×D₄×C₆₇	—	2	1	no	—
269	C₄×D₄×C₆₇	—	2	1	no	—
270	C₄×D₄×C₆₇	—	2	1	no	—
271	C₄×D₄×C₆₇	—	2	1	no	—
272	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
273	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
274	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
275	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
276	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
277	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
278	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
279	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₆₇	C₂³	1	2	yes	—
282	C₄×D₄×C₆₇	C₂³	1	2	yes	—
283	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₆₇	C₂³	1	2	yes	—
287	C₄×D₄×C₆₇	C₂³	1	2	yes	—
288	#117×C₆₇	—	2	1	no	—
289	#117×C₆₇	—	2	1	no	—
290	#117×C₆₇	—	2	1	no	—
291	#117×C₆₇	C₂³	1	2	yes	—
292	#117×C₆₇	C₂³	1	1	yes	characteristic
293	#117×C₆₇	C₂³	1	1	yes	characteristic
294	#117×C₆₇	C₂³	1	1	yes	characteristic
295	#117×C₆₇	C₂³	1	1	yes	characteristic
296	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
298	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
299	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
300	C₂×C₄²×C₆₇	—	2	1	no	—
301	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
304	#107×C₆₇	C₂³	1	2	yes	—
305	#107×C₆₇	C₂³	1	2	yes	—
306	#107×C₆₇	C₂³	1	2	yes	—
307	#107×C₆₇	C₂³	1	2	yes	—
308	#106×C₆₇	C₂³	1	2	yes	—
309	#106×C₆₇	C₂³	1	2	yes	—
310	#106×C₆₇	C₂³	1	2	yes	—
311	#106×C₆₇	C₂³	1	2	yes	—
312	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
313	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
318	#103×C₆₇	C₂³	1	2	yes	—
319	#103×C₆₇	C₂³	1	2	yes	—
320	#102×C₆₇	C₂³	1	2	yes	—
321	#102×C₆₇	C₂³	1	2	yes	—
322	#102×C₆₇	C₂³	1	2	yes	—
323	#102×C₆₇	C₂³	1	2	yes	—
324	#102×C₆₇	C₂³	1	2	yes	—
325	#102×C₆₇	C₂³	1	2	yes	—
326	#102×C₆₇	C₂³	1	2	yes	—
327	#102×C₆₇	C₂³	1	2	yes	—
328	#102×C₆₇	C₂³	1	2	yes	—
329	#102×C₆₇	C₂³	1	2	yes	—
330	#102×C₆₇	C₂³	1	2	yes	—
331	#102×C₆₇	C₂³	1	2	yes	—
332	#102×C₆₇	C₂³	1	2	yes	—
333	#102×C₆₇	C₂³	1	2	yes	—
334	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
335	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
336	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
337	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
338	#97×C₆₇	C₂³	1	2	yes	—
339	#97×C₆₇	C₂³	1	2	yes	—
340	C₄×C₈×C₆₇	C₂³	1	2	yes	—
341	C₄×C₈×C₆₇	C₂³	1	2	yes	—
342	C₂⁴×C₆₇	—	2	2	no	—
343	C₂⁴×C₆₇	—	2	1	no	—
344	#41×C₆₇	—	4	1	no	—
345	#41×C₆₇	—	4	1	no	—
346	#41×C₆₇	—	4	1	no	—
347	#41×C₆₇	—	4	1	no	—
348	#41×C₆₇	—	8	2	no	—
349	#41×C₆₇	—	8	2	no	—
350	#41×C₆₇	—	8	2	no	—
351	#41×C₆₇	—	8	2	no	—
352	#41×C₆₇	—	8	2	no	—
353	#41×C₆₇	—	8	2	no	—
354	C₂×Q₈×C₆₇	—	2	1	no	—
355	C₂×Q₈×C₆₇	—	2	1	no	—
356	C₂×Q₈×C₆₇	—	2	1	no	—
357	C₂×Q₈×C₆₇	—	2	1	no	—
358	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
359	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	1	no	—
362	C₂×D₄×C₆₇	—	2	1	no	—
363	C₂×D₄×C₆₇	—	2	2	no	—
364	C₂×D₄×C₆₇	—	2	2	no	—
365	C₂×D₄×C₆₇	—	2	2	no	—
366	C₂×D₄×C₆₇	—	2	2	no	—
367	C₂×D₄×C₆₇	—	2	1	no	—
368	C₂×D₄×C₆₇	—	2	1	no	—
369	C₂×D₄×C₆₇	—	2	1	no	—
370	C₂×D₄×C₆₇	—	2	1	no	—
371	C₂×D₄×C₆₇	—	2	1	no	—
372	C₂×D₄×C₆₇	—	2	2	no	—
373	C₂×D₄×C₆₇	—	2	1	no	—
374	C₂×D₄×C₆₇	—	2	1	no	—
375	C₂×D₄×C₆₇	—	2	1	no	—
376	C₂×D₄×C₆₇	—	2	1	no	—
377	C₂×D₄×C₆₇	—	2	1	no	—
378	C₂×D₄×C₆₇	—	2	1	no	—
379	C₂×D₄×C₆₇	—	2	1	no	—
380	C₂×D₄×C₆₇	—	2	1	no	—
381	C₂×D₄×C₆₇	—	2	2	no	—
382	C₂×D₄×C₆₇	—	2	2	no	—
383	C₂×D₄×C₆₇	—	4	2	no	—
384	C₂×D₄×C₆₇	—	4	2	no	—
385	C₂×D₄×C₆₇	—	4	1	no	—
386	C₂×D₄×C₆₇	—	4	1	no	—
387	C₂×D₄×C₆₇	—	8	2	no	—
388	C₂×D₄×C₆₇	—	8	2	no	—
389	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
392	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
396	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₆₇	—	2	1	no	—
398	C₂²×C₄×C₆₇	—	2	1	no	—
399	C₂²×C₄×C₆₇	—	2	1	no	—
400	C₂²×C₄×C₆₇	—	2	1	no	—
401	C₂²×C₄×C₆₇	—	2	1	no	—
402	C₂²×C₄×C₆₇	—	2	1	no	—
403	C₂²×C₄×C₆₇	—	2	2	no	—
404	C₂²×C₄×C₆₇	—	2	2	no	—
405	C₂²×C₄×C₆₇	—	2	2	no	—
406	C₂²×C₄×C₆₇	—	2	2	no	—
407	C₂²×C₄×C₆₇	—	2	1	no	—
408	C₂²×C₄×C₆₇	—	2	1	no	—
409	C₂²×C₄×C₆₇	—	8	2	no	—
410	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	SD₁₆×C₆₇	—	4	2	no	—
420	SD₁₆×C₆₇	—	4	2	no	—
421	D₈×C₆₇	—	4	2	no	—
422	D₈×C₆₇	—	4	2	no	—
423	D₈×C₆₇	—	4	2	no	—
424	D₈×C₆₇	—	4	2	no	—
425	D₈×C₆₇	—	4	2	no	—
426	D₈×C₆₇	—	4	2	no	—
427	M₁₆×C₆₇	—	4	2	no	—
428	C₂×C₈×C₆₇	—	4	2	no	—
429	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
430	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
431	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
432	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
433	C₄⋊C₄×C₆₇	—	2	1	no	—
434	C₄⋊C₄×C₆₇	—	2	1	no	—
435	C₄⋊C₄×C₆₇	—	2	1	no	—
436	C₄⋊C₄×C₆₇	—	2	1	no	—
437	C₄⋊C₄×C₆₇	—	2	1	no	—
438	C₄⋊C₄×C₆₇	—	2	1	no	—
439	C₄⋊C₄×C₆₇	—	2	1	no	—
440	C₄⋊C₄×C₆₇	—	2	1	no	—
441	C₄⋊C₄×C₆₇	—	2	1	no	—
442	C₄⋊C₄×C₆₇	—	2	1	no	—
443	C₄⋊C₄×C₆₇	—	2	1	no	—
444	C₄⋊C₄×C₆₇	—	2	1	no	—
445	C₄⋊C₄×C₆₇	—	2	1	no	—
446	C₄⋊C₄×C₆₇	—	2	2	no	—
447	C₄⋊C₄×C₆₇	—	2	2	no	—
448	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
449	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
450	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
451	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
452	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
453	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
454	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
459	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
460	C₂²⋊C₄×C₆₇	—	2	2	no	—
461	C₂²⋊C₄×C₆₇	—	2	1	no	—
462	C₂²⋊C₄×C₆₇	—	2	1	no	—
463	C₂²⋊C₄×C₆₇	—	2	1	no	—
464	C₂²⋊C₄×C₆₇	—	2	2	no	—
465	C₂²⋊C₄×C₆₇	—	2	2	no	—
466	C₂²⋊C₄×C₆₇	—	2	2	no	—
467	C₂²⋊C₄×C₆₇	—	2	2	no	—
468	C₂²⋊C₄×C₆₇	—	2	1	no	—
469	C₂²⋊C₄×C₆₇	—	2	1	no	—
470	C₂²⋊C₄×C₆₇	—	2	1	no	—
471	C₂²⋊C₄×C₆₇	—	2	1	no	—
472	C₂²⋊C₄×C₆₇	—	2	1	no	—
473	C₂²⋊C₄×C₆₇	—	2	1	no	—
474	C₂²⋊C₄×C₆₇	—	2	1	no	—
475	C₂²⋊C₄×C₆₇	—	2	1	no	—
476	C₂²⋊C₄×C₆₇	—	2	1	no	—
477	C₂²⋊C₄×C₆₇	—	2	1	no	—
478	C₂²⋊C₄×C₆₇	—	2	1	no	—
479	C₂²⋊C₄×C₆₇	—	2	1	no	—
480	C₂²⋊C₄×C₆₇	—	2	1	no	—
481	C₂²⋊C₄×C₆₇	—	2	1	no	—
482	C₂²⋊C₄×C₆₇	—	2	2	no	—
483	C₂²⋊C₄×C₆₇	—	2	2	no	—
484	C₂²⋊C₄×C₆₇	—	2	2	no	—
485	C₂²⋊C₄×C₆₇	—	2	2	no	—
486	C₂²⋊C₄×C₆₇	—	2	1	no	—
487	C₂²⋊C₄×C₆₇	—	2	1	no	—
488	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
493	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
494	C₄²×C₆₇	—	2	1	no	—
495	C₄²×C₆₇	—	2	1	no	—
496	C₄²×C₆₇	—	2	1	no	—
497	C₄²×C₆₇	—	2	2	no	—
498	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
499	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
500	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
501	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
502	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
503	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
504	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
505	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
506	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
507	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
508	C₂³×C₆₇	—	2	1	no	—
509	C₂³×C₆₇	—	2	1	no	—
510	C₂³×C₆₇	—	2	1	no	—
511	C₂³×C₆₇	—	2	2	no	—
512	C₂³×C₆₇	—	2	2	no	—
513	C₂³×C₆₇	—	4	2	no	—
514	C₂³×C₆₇	—	4	4	no	—
515	C₂³×C₆₇	—	8	1	no	—
516	C₂³×C₆₇	—	8	1	no	—
517	C₂³×C₆₇	—	8	2	no	—
518	C₂³×C₆₇	—	8	2	no	—
519	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
520	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
521	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
522	Q₈×C₆₇	—	2	1	no	—
523	Q₈×C₆₇	—	2	1	no	—
524	Q₈×C₆₇	—	4	1	no	—
525	Q₈×C₆₇	—	4	2	no	—
526	Q₈×C₆₇	—	4	2	no	—
527	Q₈×C₆₇	—	8	1	no	—
528	Q₈×C₆₇	—	8	1	no	—
529	D₄×C₆₇	—	2	1	no	—
530	D₄×C₆₇	—	2	1	no	—
531	D₄×C₆₇	—	2	1	no	—
532	D₄×C₆₇	—	2	1	no	—
533	D₄×C₆₇	—	2	2	no	—
534	D₄×C₆₇	—	2	2	no	—
535	D₄×C₆₇	—	2	1	no	—
536	D₄×C₆₇	—	2	1	no	—
537	D₄×C₆₇	—	2	2	no	—
538	D₄×C₆₇	—	2	2	no	—
539	D₄×C₆₇	—	4	1	no	—
540	D₄×C₆₇	—	4	1	no	—
541	D₄×C₆₇	—	4	1	no	—
542	D₄×C₆₇	—	4	2	no	—
543	D₄×C₆₇	—	4	4	no	—
544	D₄×C₆₇	—	4	2	no	—
545	D₄×C₆₇	—	4	2	no	—
546	D₄×C₆₇	—	4	2	no	—
547	D₄×C₆₇	—	4	2	no	—
548	D₄×C₆₇	—	4	2	no	—
549	D₄×C₆₇	—	8	1	no	—
550	D₄×C₆₇	—	8	1	no	—
551	D₄×C₆₇	—	8	2	no	—
552	D₄×C₆₇	—	8	2	no	—
553	D₄×C₆₇	—	8	1	no	—
554	D₄×C₆₇	—	8	1	no	—
555	D₄×C₆₇	—	8	1	no	—
556	D₄×C₆₇	—	8	1	no	—
557	D₄×C₆₇	—	8	2	no	—
558	D₄×C₆₇	—	8	2	no	—
559	D₄×C₆₇	—	8	1	no	—
560	D₄×C₆₇	—	8	1	no	—
561	D₄×C₆₇	—	8	1	no	—
562	D₄×C₆₇	—	8	1	no	—
563	D₄×C₆₇	—	8	2	no	—
564	D₄×C₆₇	—	8	2	no	—
565	C₂×C₄×C₆₇	—	2	2	no	—
566	C₂×C₄×C₆₇	—	2	2	no	—
567	C₂×C₄×C₆₇	—	2	2	no	—
568	C₂×C₄×C₆₇	—	2	1	no	—
569	C₂×C₄×C₆₇	—	2	1	no	—
570	C₂×C₄×C₆₇	—	2	1	no	—
571	C₂×C₄×C₆₇	—	2	1	no	—
572	C₂×C₄×C₆₇	—	2	1	no	—
573	C₂×C₄×C₆₇	—	2	1	no	—
574	C₂×C₄×C₆₇	—	2	1	no	—
575	C₂×C₄×C₆₇	—	2	1	no	—
576	C₂×C₄×C₆₇	—	2	1	no	—
577	C₂×C₄×C₆₇	—	2	2	no	—
578	C₂×C₄×C₆₇	—	2	2	no	—
579	C₂×C₄×C₆₇	—	2	1	no	—
580	C₂×C₄×C₆₇	—	2	1	no	—
581	C₂×C₄×C₆₇	—	4	1	no	—
582	C₂×C₄×C₆₇	—	4	1	no	—
583	C₂×C₄×C₆₇	—	4	1	no	—
584	C₂×C₄×C₆₇	—	4	2	no	—
585	C₂×C₄×C₆₇	—	4	2	no	—
586	C₂×C₄×C₆₇	—	4	2	no	—
587	C₂×C₄×C₆₇	—	4	2	no	—
588	C₂×C₄×C₆₇	—	8	1	no	—
589	C₂×C₄×C₆₇	—	8	1	no	—
590	C₂×C₄×C₆₇	—	8	1	no	—
591	C₂×C₄×C₆₇	—	8	2	no	—
592	C₂×C₄×C₆₇	—	8	2	no	—
593	C₂×C₄×C₆₇	—	8	2	no	—
594	C₂×C₄×C₆₇	—	8	2	no	—
595	C₂×C₄×C₆₇	—	8	1	no	—
596	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
597	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
598	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
602	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
603	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
604	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
607	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
608	C₈×C₆₇	—	2	2	no	—
609	C₈×C₆₇	—	2	2	no	—
610	C₈×C₆₇	—	2	2	no	—
611	C₈×C₆₇	—	2	2	no	—
612	C₂²×C₆₇	—	2	1	no	—
613	C₂²×C₆₇	—	2	1	no	—
614	C₂²×C₆₇	—	2	1	no	—
615	C₂²×C₆₇	—	2	1	no	—
616	C₂²×C₆₇	—	2	1	no	—
617	C₂²×C₆₇	—	2	1	no	—
618	C₂²×C₆₇	—	2	1	no	—
619	C₂²×C₆₇	—	2	1	no	—
620	C₂²×C₆₇	—	2	1	no	—
621	C₂²×C₆₇	—	4	2	no	—
622	C₂²×C₆₇	—	4	2	no	—
623	C₂²×C₆₇	—	4	1	no	—
624	C₂²×C₆₇	—	4	1	no	—
625	C₂²×C₆₇	—	4	1	no	—
626	C₂²×C₆₇	—	4	1	no	—
627	C₂²×C₆₇	—	4	1	no	—
628	C₂²×C₆₇	—	4	1	no	—
629	C₂²×C₆₇	—	4	2	no	—
630	C₂²×C₆₇	—	4	2	no	—
631	C₂²×C₆₇	—	4	1	no	—
632	C₂²×C₆₇	—	4	1	no	—
633	C₂²×C₆₇	—	4	1	no	—
634	C₂²×C₆₇	—	4	2	no	—
635	C₂²×C₆₇	—	4	2	no	—
636	C₂²×C₆₇	—	8	4	no	—
637	C₂²×C₆₇	—	16	4	no	—
638	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
639	C₄×C₆₇	—	2	1	no	—
640	C₄×C₆₇	—	2	1	no	—
641	C₄×C₆₇	—	2	1	no	—
642	C₄×C₆₇	—	2	1	no	—
643	C₄×C₆₇	—	2	1	no	—
644	C₄×C₆₇	—	2	1	no	—
645	C₄×C₆₇	—	2	1	no	—
646	C₄×C₆₇	—	2	1	no	—
647	C₄×C₆₇	—	2	1	no	—
648	C₄×C₆₇	—	2	1	no	—
649	C₄×C₆₇	—	4	2	no	—
650	C₄×C₆₇	—	4	1	no	—
651	C₄×C₆₇	—	4	1	no	—
652	C₄×C₆₇	—	4	1	no	—
653	C₄×C₆₇	—	4	1	no	—
654	C₄×C₆₇	—	4	1	no	—
655	C₄×C₆₇	—	4	2	no	—
656	C₄×C₆₇	#576	1	2	yes	—
657	C₄×C₆₇	#585	1	1	yes	characteristic
658	C₄×C₆₇	#585	1	1	yes	characteristic
659	#60990	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
660	C₂×C₆₇	—	4	1	no	—
661	C₂×C₆₇	—	4	1	no	—
662	C₂×C₆₇	—	4	1	no	—
663	C₂×C₆₇	—	8	1	no	—
664	C₂×C₆₇	—	8	1	no	—
665	C₂×C₆₇	—	8	1	no	—
666	C₂×C₆₇	—	8	2	no	—
667	C₂×C₆₇	—	8	2	no	—
668	C₂×C₆₇	#3449	1	1	yes	characteristic
669	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
670	C₂×C₆₇	#3585	1	1	yes	characteristic
671	#3508	C₂×C₆₇	1	1	yes	characteristic, complemented
672	#3460	C₂×C₆₇	1	1	yes	characteristic, complemented
673	#3253	C₂×C₆₇	1	1	yes	characteristic, complemented
674	#3251	C₂×C₆₇	1	1	yes	characteristic, complemented
675	#3247	C₂×C₆₇	1	1	yes	characteristic, complemented
676	#3245	C₂×C₆₇	1	1	yes	characteristic, complemented
677	#3241	C₂×C₆₇	1	2	yes	complemented
678	#3235	C₂×C₆₇	1	1	yes	characteristic, complemented
679	#3233	C₂×C₆₇	1	1	yes	characteristic, complemented
680	#3220	C₂×C₆₇	1	2	yes	complemented
681	#3217	C₂×C₆₇	1	1	yes	characteristic, complemented
682	#3205	C₂×C₆₇	1	1	yes	characteristic, complemented
683	#3199	C₂×C₆₇	1	2	yes	complemented
684	#3198	C₂×C₆₇	1	2	yes	complemented
685	#3179	C₂×C₆₇	1	2	yes	complemented
686	#3176	C₂×C₆₇	1	2	yes	complemented
687	#3122	C₂×C₆₇	1	2	yes	complemented
688	#3118	C₂×C₆₇	1	2	yes	complemented
689	#3115	C₂×C₆₇	1	1	yes	characteristic, complemented
690	#3109	C₂×C₆₇	1	1	yes	characteristic, complemented
691	#3106	C₂×C₆₇	1	1	yes	characteristic, complemented
692	#3100	C₂×C₆₇	1	1	yes	characteristic, complemented
693	#2925	C₂×C₆₇	1	1	yes	characteristic, complemented
694	C₆₇	#60990	1	1	yes	characteristic, direct product factor, Sylow
695	#559	—	2	1	no	—
696	#559	—	2	1	no	—
697	#550	—	2	1	no	—
698	#550	—	2	1	no	—
699	#546	—	2	1	no	—
700	#546	—	2	1	no	—
701	#546	—	2	1	no	—
702	#546	—	2	1	no	—
703	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
704	#542	—	2	1	no	—
705	#542	C₂²×C₆₇	1	1	yes	characteristic
706	#542	C₂²×C₆₇	1	1	yes	characteristic, complemented
707	#540	—	2	1	no	—
708	#540	C₂²×C₆₇	1	1	yes	characteristic
709	#540	C₂²×C₆₇	1	2	yes	—
710	#540	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#540	C₂²×C₆₇	1	2	yes	complemented
712	#538	—	2	1	no	—
713	#538	—	2	1	no	—
714	#537	C₂²×C₆₇	1	1	yes	characteristic
715	#535	C₂²×C₆₇	1	2	yes	—
716	#535	C₂²×C₆₇	1	1	yes	characteristic
717	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	#532	—	2	1	no	—
720	#532	C₂²×C₆₇	1	1	yes	characteristic
721	#532	C₂²×C₆₇	1	1	yes	characteristic
722	#532	C₂²×C₆₇	1	1	yes	characteristic
723	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
724	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#532	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	#529	—	2	1	no	—
728	#529	C₂²×C₆₇	1	1	yes	characteristic
729	#529	C₂²×C₆₇	1	1	yes	characteristic, complemented
730	#525	—	2	1	no	—
731	#525	—	2	1	no	—
732	#518	C₂²×C₆₇	1	2	yes	complemented
733	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
734	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
735	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
736	#501	C₂²×C₆₇	1	2	yes	complemented
737	#499	C₂²×C₆₇	1	2	yes	complemented
738	#496	C₂²×C₆₇	1	2	yes	—
739	#493	C₂²×C₆₇	1	2	yes	—
740	#490	C₂²×C₆₇	1	2	yes	complemented
741	#490	C₂²×C₆₇	1	2	yes	complemented
742	#488	C₂²×C₆₇	1	2	yes	complemented
743	#486	C₂²×C₆₇	1	2	yes	complemented
744	#485	C₂²×C₆₇	1	2	yes	complemented
745	#482	C₂²×C₆₇	1	2	yes	—
746	#482	C₂²×C₆₇	1	2	yes	—
747	#482	C₂²×C₆₇	1	2	yes	complemented
748	#482	C₂²×C₆₇	1	2	yes	complemented
749	#482	C₂²×C₆₇	1	2	yes	complemented
750	#481	C₂²×C₆₇	1	2	yes	complemented
751	#480	C₂²×C₆₇	1	2	yes	complemented
752	#478	C₂²×C₆₇	1	2	yes	complemented
753	#478	C₂²×C₆₇	1	2	yes	complemented
754	#477	C₂²×C₆₇	1	1	yes	characteristic, complemented
755	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
756	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
757	#476	C₂²×C₆₇	1	1	yes	characteristic, complemented
758	#476	C₂²×C₆₇	1	2	yes	complemented
759	#475	C₂²×C₆₇	1	1	yes	characteristic, complemented
760	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
761	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
762	#474	C₂²×C₆₇	1	1	yes	characteristic, complemented
763	#474	C₂²×C₆₇	1	2	yes	complemented
764	#469	C₂²×C₆₇	1	2	yes	complemented
765	#469	C₂²×C₆₇	1	2	yes	complemented
766	#469	C₂²×C₆₇	1	2	yes	complemented
767	#468	C₂²×C₆₇	1	2	yes	complemented
768	#466	C₂²×C₆₇	1	2	yes	complemented
769	#466	C₂²×C₆₇	1	2	yes	complemented
770	#466	C₂²×C₆₇	1	2	yes	complemented
771	#465	C₂²×C₆₇	1	2	yes	complemented
772	#463	C₂²×C₆₇	1	2	yes	complemented
773	#463	C₂²×C₆₇	1	2	yes	complemented
774	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
775	#460	C₂²×C₆₇	1	1	yes	characteristic, complemented
776	#459	C₂²×C₆₇	1	1	yes	characteristic
777	#459	C₂²×C₆₇	1	1	yes	characteristic
778	#459	C₂²×C₆₇	1	1	yes	characteristic
779	#459	C₂²×C₆₇	1	1	yes	characteristic
780	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
781	#459	C₂²×C₆₇	1	1	yes	characteristic, complemented
782	#459	C₂²×C₆₇	1	2	yes	complemented
783	#459	C₂²×C₆₇	1	2	yes	complemented
784	#450	C₂²×C₆₇	1	2	yes	complemented
785	#449	C₂²×C₆₇	1	2	yes	complemented
786	#449	C₂²×C₆₇	1	2	yes	complemented
787	#447	C₂²×C₆₇	1	2	yes	—
788	#447	C₂²×C₆₇	1	2	yes	—
789	#447	C₂²×C₆₇	1	2	yes	complemented
790	#447	C₂²×C₆₇	1	2	yes	complemented
791	#447	C₂²×C₆₇	1	2	yes	complemented
792	#442	C₂²×C₆₇	1	2	yes	complemented
793	#442	C₂²×C₆₇	1	2	yes	complemented
794	#442	C₂²×C₆₇	1	2	yes	complemented
795	#440	C₂²×C₆₇	1	2	yes	complemented
796	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
797	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
798	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
799	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
800	#433	C₂²×C₆₇	1	2	yes	complemented
801	#433	C₂²×C₆₇	1	2	yes	complemented
802	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
803	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
804	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
805	#431	C₂²×C₆₇	1	1	yes	characteristic, complemented
806	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
807	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
808	#408	C₂²×C₆₇	1	2	yes	—
809	#405	C₂²×C₆₇	1	2	yes	complemented
810	C₂×#41	—	2	1	no	—
811	C₂×#41	—	2	1	no	—
812	C₂×#41	—	2	1	no	—
813	C₂×#41	—	2	1	no	—
814	C₂×#41	—	2	1	no	—
815	C₂×#41	—	2	1	no	—
816	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
817	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
818	C₂²×D₄	—	2	1	no	—
819	C₂²×D₄	—	2	1	no	—
820	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
821	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
822	C₂³×C₄	—	2	1	no	—
823	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
824	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
825	C₂×D₈	C₂³×C₆₇	1	2	yes	—
826	C₂×D₈	C₂³×C₆₇	1	2	yes	—
827	C₂×D₈	C₂³×C₆₇	1	2	yes	—
828	C₂×D₈	C₂³×C₆₇	1	2	yes	—
829	C₂×D₈	C₂³×C₆₇	1	2	yes	—
830	C₂×D₈	C₂³×C₆₇	1	2	yes	—
831	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
832	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
833	C₄⋊Q₈	—	2	1	no	—
834	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
835	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
836	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
837	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
838	#127	—	2	1	no	—
839	#127	—	2	2	no	—
840	#127	—	2	1	no	—
841	#127	—	2	1	no	—
842	#127	C₂³×C₆₇	1	1	yes	characteristic
843	#127	C₂³×C₆₇	1	1	yes	characteristic
844	#127	C₂³×C₆₇	1	2	yes	—
845	#127	C₂³×C₆₇	1	1	yes	characteristic
846	#127	C₂³×C₆₇	1	1	yes	characteristic
847	#126	—	2	1	no	—
848	#126	—	2	1	no	—
849	#126	—	2	1	no	—
850	#126	—	2	1	no	—
851	#125	—	2	1	no	—
852	#125	C₂³×C₆₇	1	1	yes	characteristic
853	#125	C₂³×C₆₇	1	1	yes	characteristic
854	#125	C₂³×C₆₇	1	2	yes	—
855	#124	—	2	1	no	—
856	#124	—	2	2	no	—
857	#124	—	2	1	no	—
858	#124	—	2	1	no	—
859	#124	—	2	1	no	—
860	#124	—	2	1	no	—
861	#124	—	2	1	no	—
862	#124	—	2	1	no	—
863	#124	—	2	1	no	—
864	#124	—	2	1	no	—
865	#124	C₂³×C₆₇	1	1	yes	characteristic
866	#124	C₂³×C₆₇	1	1	yes	characteristic
867	#123	—	2	1	no	—
868	#123	—	2	1	no	—
869	#123	—	2	1	no	—
870	#123	—	2	1	no	—
871	#123	—	2	1	no	—
872	#123	—	2	1	no	—
873	#123	—	2	2	no	—
874	#123	—	2	2	no	—
875	#123	—	2	2	no	—
876	#123	—	2	2	no	—
877	#123	—	2	1	no	—
878	#123	—	2	1	no	—
879	C₂²⋊Q₈	—	2	1	no	—
880	C₂²⋊Q₈	—	2	1	no	—
881	C₂²⋊Q₈	—	2	1	no	—
882	C₂²⋊Q₈	—	2	1	no	—
883	C₂²⋊Q₈	—	2	1	no	—
884	C₂²⋊Q₈	—	2	1	no	—
885	C₂²⋊Q₈	—	2	1	no	—
886	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
887	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
888	#121	—	2	1	no	—
889	#121	—	2	1	no	—
890	#121	—	2	1	no	—
891	#121	—	2	1	no	—
892	#121	—	2	1	no	—
893	#121	—	2	1	no	—
894	#121	—	2	1	no	—
895	#121	—	2	1	no	—
896	#121	—	2	1	no	—
897	#121	—	2	1	no	—
898	#121	—	2	1	no	—
899	#121	—	2	1	no	—
900	#121	—	2	1	no	—
901	#121	—	2	1	no	—
902	#121	—	2	1	no	—
903	#121	—	2	2	no	—
904	#121	—	2	2	no	—
905	#121	—	2	2	no	—
906	#121	—	2	2	no	—
907	#121	C₂³×C₆₇	1	1	yes	characteristic
908	#121	C₂³×C₆₇	1	1	yes	characteristic
909	#121	C₂³×C₆₇	1	2	yes	—
910	#121	C₂³×C₆₇	1	2	yes	—
911	#121	C₂³×C₆₇	1	1	yes	characteristic
912	#121	C₂³×C₆₇	1	1	yes	characteristic
913	#121	C₂³×C₆₇	1	2	yes	—
914	#121	C₂³×C₆₇	1	2	yes	—
915	#121	C₂³×C₆₇	1	1	yes	characteristic
916	#121	C₂³×C₆₇	1	1	yes	characteristic
917	#120	—	2	1	no	—
918	#120	—	2	1	no	—
919	#120	—	2	2	no	—
920	#120	—	2	2	no	—
921	#120	—	2	1	no	—
922	#120	—	2	1	no	—
923	C₄×Q₈	—	2	1	no	—
924	C₄×Q₈	—	2	1	no	—
925	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
926	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
927	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
928	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
929	C₄×D₄	—	2	1	no	—
930	C₄×D₄	—	2	1	no	—
931	C₄×D₄	—	2	1	no	—
932	C₄×D₄	—	2	1	no	—
933	C₄×D₄	—	2	2	no	—
934	C₄×D₄	—	2	2	no	—
935	C₄×D₄	—	2	1	no	—
936	C₄×D₄	—	2	1	no	—
937	C₄×D₄	—	2	1	no	—
938	C₄×D₄	—	2	1	no	—
939	C₄×D₄	—	2	1	no	—
940	C₄×D₄	—	2	1	no	—
941	C₄×D₄	—	2	1	no	—
942	C₄×D₄	—	2	1	no	—
943	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
944	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
945	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
946	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
947	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
948	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
949	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
950	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
951	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
952	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
953	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
954	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
955	C₄×D₄	C₂³×C₆₇	1	2	yes	—
956	C₄×D₄	C₂³×C₆₇	1	2	yes	—
957	C₄×D₄	C₂³×C₆₇	1	2	yes	—
958	C₄×D₄	C₂³×C₆₇	1	2	yes	—
959	#117	—	2	1	no	—
960	#117	—	2	1	no	—
961	#117	—	2	1	no	—
962	#117	C₂³×C₆₇	1	1	yes	characteristic
963	#117	C₂³×C₆₇	1	2	yes	—
964	#117	C₂³×C₆₇	1	1	yes	characteristic
965	#117	C₂³×C₆₇	1	1	yes	characteristic
966	#117	C₂³×C₆₇	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	—	2	1	no	—
969	C₂×C₂²⋊C₄	—	2	2	no	—
970	C₂×C₂²⋊C₄	—	2	2	no	—
971	C₂×C₄²	—	2	1	no	—
972	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
973	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
974	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
975	#107	C₂³×C₆₇	1	2	yes	—
976	#107	C₂³×C₆₇	1	2	yes	—
977	#107	C₂³×C₆₇	1	2	yes	—
978	#107	C₂³×C₆₇	1	2	yes	—
979	#106	C₂³×C₆₇	1	2	yes	—
980	#106	C₂³×C₆₇	1	2	yes	—
981	#106	C₂³×C₆₇	1	2	yes	—
982	#106	C₂³×C₆₇	1	2	yes	—
983	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
984	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
985	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
986	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
987	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
988	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
989	#103	C₂³×C₆₇	1	2	yes	—
990	#103	C₂³×C₆₇	1	2	yes	—
991	#102	C₂³×C₆₇	1	2	yes	—
992	#102	C₂³×C₆₇	1	2	yes	—
993	#102	C₂³×C₆₇	1	2	yes	—
994	#102	C₂³×C₆₇	1	2	yes	—
995	#102	C₂³×C₆₇	1	2	yes	—
996	#102	C₂³×C₆₇	1	2	yes	—
997	#102	C₂³×C₆₇	1	2	yes	—
998	#102	C₂³×C₆₇	1	2	yes	—
999	#102	C₂³×C₆₇	1	2	yes	—
1000	#102	C₂³×C₆₇	1	2	yes	—
1001	#102	C₂³×C₆₇	1	2	yes	—
1002	#102	C₂³×C₆₇	1	2	yes	—
1003	#102	C₂³×C₆₇	1	2	yes	—
1004	#102	C₂³×C₆₇	1	2	yes	—
1005	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1006	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1007	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1008	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
1009	#97	C₂³×C₆₇	1	2	yes	—
1010	#97	C₂³×C₆₇	1	2	yes	—
1011	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1012	C₄×C₈	C₂³×C₆₇	1	2	yes	—
1013	C₂⁴	—	2	2	no	—
1014	C₂⁴	—	2	1	no	—
1015	#41	—	4	1	no	—
1016	#41	—	4	1	no	—
1017	#41	—	4	1	no	—
1018	#41	—	4	1	no	—
1019	#41	—	8	2	no	—
1020	#41	—	8	2	no	—
1021	#41	—	8	2	no	—
1022	#41	—	8	2	no	—
1023	#41	—	8	2	no	—
1024	#41	—	8	2	no	—
1025	C₂×Q₈	—	2	1	no	—
1026	C₂×Q₈	—	2	1	no	—
1027	C₂×Q₈	—	2	1	no	—
1028	C₂×Q₈	—	2	1	no	—
1029	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
1030	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
1031	C₂×D₄	—	2	1	no	—
1032	C₂×D₄	—	2	1	no	—
1033	C₂×D₄	—	2	1	no	—
1034	C₂×D₄	—	2	2	no	—
1035	C₂×D₄	—	2	2	no	—
1036	C₂×D₄	—	2	2	no	—
1037	C₂×D₄	—	2	2	no	—
1038	C₂×D₄	—	2	1	no	—
1039	C₂×D₄	—	2	1	no	—
1040	C₂×D₄	—	2	1	no	—
1041	C₂×D₄	—	2	1	no	—
1042	C₂×D₄	—	2	1	no	—
1043	C₂×D₄	—	2	2	no	—
1044	C₂×D₄	—	2	1	no	—
1045	C₂×D₄	—	2	1	no	—
1046	C₂×D₄	—	2	1	no	—
1047	C₂×D₄	—	2	1	no	—
1048	C₂×D₄	—	2	1	no	—
1049	C₂×D₄	—	2	1	no	—
1050	C₂×D₄	—	2	1	no	—
1051	C₂×D₄	—	2	1	no	—
1052	C₂×D₄	—	2	2	no	—
1053	C₂×D₄	—	2	2	no	—
1054	C₂×D₄	—	4	2	no	—
1055	C₂×D₄	—	4	2	no	—
1056	C₂×D₄	—	4	1	no	—
1057	C₂×D₄	—	4	1	no	—
1058	C₂×D₄	—	8	2	no	—
1059	C₂×D₄	—	8	2	no	—
1060	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1061	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1062	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1063	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1064	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1065	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
1066	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1067	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
1068	C₂²×C₄	—	2	1	no	—
1069	C₂²×C₄	—	2	1	no	—
1070	C₂²×C₄	—	2	1	no	—
1071	C₂²×C₄	—	2	1	no	—
1072	C₂²×C₄	—	2	1	no	—
1073	C₂²×C₄	—	2	1	no	—
1074	C₂²×C₄	—	2	2	no	—
1075	C₂²×C₄	—	2	2	no	—
1076	C₂²×C₄	—	2	2	no	—
1077	C₂²×C₄	—	2	2	no	—
1078	C₂²×C₄	—	2	1	no	—
1079	C₂²×C₄	—	2	1	no	—
1080	C₂²×C₄	—	8	2	no	—
1081	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1082	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1083	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1084	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1085	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1086	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1087	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1088	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1089	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1090	SD₁₆	—	4	2	no	—
1091	SD₁₆	—	4	2	no	—
1092	D₈	—	4	2	no	—
1093	D₈	—	4	2	no	—
1094	D₈	—	4	2	no	—
1095	D₈	—	4	2	no	—
1096	D₈	—	4	2	no	—
1097	D₈	—	4	2	no	—
1098	M₁₆	—	4	2	no	—
1099	C₂×C₈	—	4	2	no	—
1100	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1101	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1102	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1103	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1104	C₄⋊C₄	—	2	1	no	—
1105	C₄⋊C₄	—	2	1	no	—
1106	C₄⋊C₄	—	2	1	no	—
1107	C₄⋊C₄	—	2	1	no	—
1108	C₄⋊C₄	—	2	1	no	—
1109	C₄⋊C₄	—	2	1	no	—
1110	C₄⋊C₄	—	2	1	no	—
1111	C₄⋊C₄	—	2	1	no	—
1112	C₄⋊C₄	—	2	1	no	—
1113	C₄⋊C₄	—	2	1	no	—
1114	C₄⋊C₄	—	2	1	no	—
1115	C₄⋊C₄	—	2	1	no	—
1116	C₄⋊C₄	—	2	1	no	—
1117	C₄⋊C₄	—	2	2	no	—
1118	C₄⋊C₄	—	2	2	no	—
1119	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1120	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1121	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1122	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1123	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1124	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1125	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1126	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1127	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1128	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1129	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1130	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1131	C₂²⋊C₄	—	2	2	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	—	2	1	no	—
1134	C₂²⋊C₄	—	2	1	no	—
1135	C₂²⋊C₄	—	2	2	no	—
1136	C₂²⋊C₄	—	2	2	no	—
1137	C₂²⋊C₄	—	2	2	no	—
1138	C₂²⋊C₄	—	2	2	no	—
1139	C₂²⋊C₄	—	2	1	no	—
1140	C₂²⋊C₄	—	2	1	no	—
1141	C₂²⋊C₄	—	2	1	no	—
1142	C₂²⋊C₄	—	2	1	no	—
1143	C₂²⋊C₄	—	2	1	no	—
1144	C₂²⋊C₄	—	2	1	no	—
1145	C₂²⋊C₄	—	2	1	no	—
1146	C₂²⋊C₄	—	2	1	no	—
1147	C₂²⋊C₄	—	2	1	no	—
1148	C₂²⋊C₄	—	2	1	no	—
1149	C₂²⋊C₄	—	2	1	no	—
1150	C₂²⋊C₄	—	2	1	no	—
1151	C₂²⋊C₄	—	2	1	no	—
1152	C₂²⋊C₄	—	2	1	no	—
1153	C₂²⋊C₄	—	2	2	no	—
1154	C₂²⋊C₄	—	2	2	no	—
1155	C₂²⋊C₄	—	2	2	no	—
1156	C₂²⋊C₄	—	2	2	no	—
1157	C₂²⋊C₄	—	2	1	no	—
1158	C₂²⋊C₄	—	2	1	no	—
1159	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1160	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1161	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1162	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1163	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1164	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1165	C₄²	—	2	1	no	—
1166	C₄²	—	2	1	no	—
1167	C₄²	—	2	1	no	—
1168	C₄²	—	2	2	no	—
1169	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1170	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1171	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1172	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1173	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1174	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1175	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1176	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1177	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1178	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1179	C₂³	—	2	1	no	—
1180	C₂³	—	2	1	no	—
1181	C₂³	—	2	1	no	—
1182	C₂³	—	2	2	no	—
1183	C₂³	—	2	2	no	—
1184	C₂³	—	4	2	no	—
1185	C₂³	—	4	4	no	—
1186	C₂³	—	8	1	no	—
1187	C₂³	—	8	1	no	—
1188	C₂³	—	8	2	no	—
1189	C₂³	—	8	2	no	—
1190	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1191	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1192	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1193	Q₈	—	2	1	no	—
1194	Q₈	—	2	1	no	—
1195	Q₈	—	4	1	no	—
1196	Q₈	—	4	2	no	—
1197	Q₈	—	4	2	no	—
1198	Q₈	—	8	1	no	—
1199	Q₈	—	8	1	no	—
1200	D₄	—	2	1	no	—
1201	D₄	—	2	1	no	—
1202	D₄	—	2	1	no	—
1203	D₄	—	2	1	no	—
1204	D₄	—	2	2	no	—
1205	D₄	—	2	2	no	—
1206	D₄	—	2	1	no	—
1207	D₄	—	2	1	no	—
1208	D₄	—	2	2	no	—
1209	D₄	—	2	2	no	—
1210	D₄	—	4	1	no	—
1211	D₄	—	4	1	no	—
1212	D₄	—	4	1	no	—
1213	D₄	—	4	2	no	—
1214	D₄	—	4	4	no	—
1215	D₄	—	4	2	no	—
1216	D₄	—	4	2	no	—
1217	D₄	—	4	2	no	—
1218	D₄	—	4	2	no	—
1219	D₄	—	4	2	no	—
1220	D₄	—	8	2	no	—
1221	D₄	—	8	2	no	—
1222	D₄	—	8	1	no	—
1223	D₄	—	8	1	no	—
1224	D₄	—	8	1	no	—
1225	D₄	—	8	1	no	—
1226	D₄	—	8	1	no	—
1227	D₄	—	8	1	no	—
1228	D₄	—	8	1	no	—
1229	D₄	—	8	1	no	—
1230	D₄	—	8	2	no	—
1231	D₄	—	8	2	no	—
1232	D₄	—	8	2	no	—
1233	D₄	—	8	2	no	—
1234	D₄	—	8	1	no	—
1235	D₄	—	8	1	no	—
1236	C₂×C₄	—	2	2	no	—
1237	C₂×C₄	—	2	2	no	—
1238	C₂×C₄	—	2	2	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	2	no	—
1249	C₂×C₄	—	2	2	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	4	1	no	—
1253	C₂×C₄	—	4	1	no	—
1254	C₂×C₄	—	4	1	no	—
1255	C₂×C₄	—	4	2	no	—
1256	C₂×C₄	—	4	2	no	—
1257	C₂×C₄	—	4	2	no	—
1258	C₂×C₄	—	4	2	no	—
1259	C₂×C₄	—	8	1	no	—
1260	C₂×C₄	—	8	1	no	—
1261	C₂×C₄	—	8	2	no	—
1262	C₂×C₄	—	8	2	no	—
1263	C₂×C₄	—	8	2	no	—
1264	C₂×C₄	—	8	2	no	—
1265	C₂×C₄	—	8	1	no	—
1266	C₂×C₄	—	8	1	no	—
1267	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1268	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1269	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1270	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1271	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1272	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1273	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1274	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1275	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1276	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1277	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1278	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1279	C₈	—	2	2	no	—
1280	C₈	—	2	2	no	—
1281	C₈	—	2	2	no	—
1282	C₈	—	2	2	no	—
1283	C₂²	—	2	1	no	—
1284	C₂²	—	2	1	no	—
1285	C₂²	—	2	1	no	—
1286	C₂²	—	2	1	no	—
1287	C₂²	—	2	1	no	—
1288	C₂²	—	2	1	no	—
1289	C₂²	—	2	1	no	—
1290	C₂²	—	2	1	no	—
1291	C₂²	—	2	1	no	—
1292	C₂²	—	4	1	no	—
1293	C₂²	—	4	1	no	—
1294	C₂²	—	4	1	no	—
1295	C₂²	—	4	2	no	—
1296	C₂²	—	4	2	no	—
1297	C₂²	—	4	2	no	—
1298	C₂²	—	4	2	no	—
1299	C₂²	—	4	1	no	—
1300	C₂²	—	4	1	no	—
1301	C₂²	—	4	1	no	—
1302	C₂²	—	4	1	no	—
1303	C₂²	—	4	1	no	—
1304	C₂²	—	4	1	no	—
1305	C₂²	—	4	2	no	—
1306	C₂²	—	4	2	no	—
1307	C₂²	—	8	4	no	—
1308	C₂²	—	16	4	no	—
1309	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1310	C₄	—	2	1	no	—
1311	C₄	—	2	1	no	—
1312	C₄	—	2	1	no	—
1313	C₄	—	2	1	no	—
1314	C₄	—	2	1	no	—
1315	C₄	—	2	1	no	—
1316	C₄	—	2	1	no	—
1317	C₄	—	2	1	no	—
1318	C₄	—	2	1	no	—
1319	C₄	—	2	1	no	—
1320	C₄	—	4	1	no	—
1321	C₄	—	4	1	no	—
1322	C₄	—	4	1	no	—
1323	C₄	—	4	2	no	—
1324	C₄	—	4	2	no	—
1325	C₄	—	4	1	no	—
1326	C₄	—	4	1	no	—
1327	C₄	#576×C₆₇	1	2	yes	—
1328	C₄	#585×C₆₇	1	1	yes	characteristic
1329	C₄	#585×C₆₇	1	1	yes	characteristic
1330	C₂	—	4	1	no	—
1331	C₂	—	4	1	no	—
1332	C₂	—	4	1	no	—
1333	C₂	—	8	1	no	—
1334	C₂	—	8	1	no	—
1335	C₂	—	8	2	no	—
1336	C₂	—	8	2	no	—
1337	C₂	—	8	1	no	—
1338	C₂	C₆₇×#3449	1	1	yes	characteristic
1339	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
1340	C₂	C₆₇×#3585	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 ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3508	C₂	semidirect
2. C₆₇×#3460	C₂	semidirect
3. C₆₇×#3253	C₂	semidirect
4. C₆₇×#3251	C₂	semidirect
5. C₆₇×#3247	C₂	semidirect
6. C₆₇×#3245	C₂	semidirect
7. C₆₇×#3241	C₂	semidirect
8. C₆₇×#3235	C₂	semidirect
9. C₆₇×#3233	C₂	semidirect
10. C₆₇×#3220	C₂	semidirect
11. C₆₇×#3217	C₂	semidirect
12. C₆₇×#3205	C₂	semidirect
13. C₆₇×#3199	C₂	semidirect
14. C₆₇×#3198	C₂	semidirect
15. C₆₇×#3179	C₂	semidirect
16. C₆₇×#3176	C₂	semidirect
17. C₆₇×#3122	C₂	semidirect
18. C₆₇×#3118	C₂	semidirect
19. C₆₇×#3115	C₂	semidirect
20. C₆₇×#3109	C₂	semidirect
21. C₆₇×#3106	C₂	semidirect
22. C₆₇×#3100	C₂	semidirect
23. C₆₇×#2925	C₂	semidirect
32. #544×C₆₇	C₂²	semidirect
35. #542×C₆₇	C₂²	semidirect
39. #540×C₆₇	C₂²	semidirect
40. #540×C₆₇	C₂²	semidirect
46. #535×C₆₇	C₂²	semidirect
47. #533×C₆₇	C₂²	semidirect
52. #532×C₆₇	C₂²	semidirect
53. #532×C₆₇	C₂²	semidirect
54. #532×C₆₇	C₂²	semidirect
55. C₂×#127×C₆₇	C₂²	semidirect
58. #529×C₆₇	C₂²	semidirect
61. #518×C₆₇	C₂²	semidirect
63. C₄×#41×C₆₇	C₂²	semidirect
64. C₂×C₄×D₄×C₆₇	C₂²	semidirect
65. #501×C₆₇	C₂²	semidirect
66. #499×C₆₇	C₂²	semidirect
69. #490×C₆₇	C₂²	semidirect
70. #490×C₆₇	C₂²	semidirect
71. #488×C₆₇	C₂²	semidirect
72. #486×C₆₇	C₂²	semidirect
73. #485×C₆₇	C₂²	semidirect
76. #482×C₆₇	C₂²	semidirect
77. #482×C₆₇	C₂²	semidirect
78. #482×C₆₇	C₂²	semidirect
79. #481×C₆₇	C₂²	semidirect
80. #480×C₆₇	C₂²	semidirect
81. #478×C₆₇	C₂²	semidirect
82. #478×C₆₇	C₂²	semidirect
83. #477×C₆₇	C₂²	semidirect
84. #476×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. #474×C₆₇	C₂²	semidirect
93. #469×C₆₇	C₂²	semidirect
94. #469×C₆₇	C₂²	semidirect
95. #469×C₆₇	C₂²	semidirect
96. #468×C₆₇	C₂²	semidirect
97. #466×C₆₇	C₂²	semidirect
98. #466×C₆₇	C₂²	semidirect
99. #466×C₆₇	C₂²	semidirect
100. #465×C₆₇	C₂²	semidirect
101. #463×C₆₇	C₂²	semidirect
102. #463×C₆₇	C₂²	semidirect
103. #460×C₆₇	C₂²	semidirect
104. #460×C₆₇	C₂²	semidirect
109. #459×C₆₇	C₂²	semidirect
110. #459×C₆₇	C₂²	semidirect
111. #459×C₆₇	C₂²	semidirect
112. #459×C₆₇	C₂²	semidirect
113. #450×C₆₇	C₂²	semidirect
114. #449×C₆₇	C₂²	semidirect
115. #449×C₆₇	C₂²	semidirect
118. #447×C₆₇	C₂²	semidirect
119. #447×C₆₇	C₂²	semidirect
120. #447×C₆₇	C₂²	semidirect
121. #442×C₆₇	C₂²	semidirect
122. #442×C₆₇	C₂²	semidirect
123. #442×C₆₇	C₂²	semidirect
124. #440×C₆₇	C₂²	semidirect
125. C₄×SD₁₆×C₆₇	C₂²	semidirect
126. C₄×D₈×C₆₇	C₂²	semidirect
127. C₄×D₈×C₆₇	C₂²	semidirect
128. C₄×D₈×C₆₇	C₂²	semidirect
129. #433×C₆₇	C₂²	semidirect
130. #433×C₆₇	C₂²	semidirect
131. #432×C₆₇	C₂²	semidirect
132. #432×C₆₇	C₂²	semidirect
133. #431×C₆₇	C₂²	semidirect
134. #431×C₆₇	C₂²	semidirect
135. #423×C₆₇	C₂²	semidirect
136. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
138. #405×C₆₇	C₂²	semidirect
659. #60990	C₆₇	direct (N × H)
671. #3508	C₂×C₆₇	semidirect
672. #3460	C₂×C₆₇	semidirect
673. #3253	C₂×C₆₇	semidirect
674. #3251	C₂×C₆₇	semidirect
675. #3247	C₂×C₆₇	semidirect
676. #3245	C₂×C₆₇	semidirect
677. #3241	C₂×C₆₇	semidirect
678. #3235	C₂×C₆₇	semidirect
679. #3233	C₂×C₆₇	semidirect
680. #3220	C₂×C₆₇	semidirect
681. #3217	C₂×C₆₇	semidirect
682. #3205	C₂×C₆₇	semidirect
683. #3199	C₂×C₆₇	semidirect
684. #3198	C₂×C₆₇	semidirect
685. #3179	C₂×C₆₇	semidirect
686. #3176	C₂×C₆₇	semidirect
687. #3122	C₂×C₆₇	semidirect
688. #3118	C₂×C₆₇	semidirect
689. #3115	C₂×C₆₇	semidirect
690. #3109	C₂×C₆₇	semidirect
691. #3106	C₂×C₆₇	semidirect
692. #3100	C₂×C₆₇	semidirect
693. #2925	C₂×C₆₇	semidirect
694. C₆₇	#60990	direct (N × H)
703. #544	C₂²×C₆₇	semidirect
706. #542	C₂²×C₆₇	semidirect
710. #540	C₂²×C₆₇	semidirect
711. #540	C₂²×C₆₇	semidirect
717. #535	C₂²×C₆₇	semidirect
718. #533	C₂²×C₆₇	semidirect
723. #532	C₂²×C₆₇	semidirect
724. #532	C₂²×C₆₇	semidirect
725. #532	C₂²×C₆₇	semidirect
726. C₂×#127	C₂²×C₆₇	semidirect
729. #529	C₂²×C₆₇	semidirect
732. #518	C₂²×C₆₇	semidirect
734. C₄×#41	C₂²×C₆₇	semidirect
735. C₂×C₄×D₄	C₂²×C₆₇	semidirect
736. #501	C₂²×C₆₇	semidirect
737. #499	C₂²×C₆₇	semidirect
740. #490	C₂²×C₆₇	semidirect
741. #490	C₂²×C₆₇	semidirect
742. #488	C₂²×C₆₇	semidirect
743. #486	C₂²×C₆₇	semidirect
744. #485	C₂²×C₆₇	semidirect
747. #482	C₂²×C₆₇	semidirect
748. #482	C₂²×C₆₇	semidirect
749. #482	C₂²×C₆₇	semidirect
750. #481	C₂²×C₆₇	semidirect
751. #480	C₂²×C₆₇	semidirect
752. #478	C₂²×C₆₇	semidirect
753. #478	C₂²×C₆₇	semidirect
754. #477	C₂²×C₆₇	semidirect
755. #476	C₂²×C₆₇	semidirect
756. #476	C₂²×C₆₇	semidirect
757. #476	C₂²×C₆₇	semidirect
758. #476	C₂²×C₆₇	semidirect
759. #475	C₂²×C₆₇	semidirect
760. #474	C₂²×C₆₇	semidirect
761. #474	C₂²×C₆₇	semidirect
762. #474	C₂²×C₆₇	semidirect
763. #474	C₂²×C₆₇	semidirect
764. #469	C₂²×C₆₇	semidirect
765. #469	C₂²×C₆₇	semidirect
766. #469	C₂²×C₆₇	semidirect
767. #468	C₂²×C₆₇	semidirect
768. #466	C₂²×C₆₇	semidirect
769. #466	C₂²×C₆₇	semidirect
770. #466	C₂²×C₆₇	semidirect
771. #465	C₂²×C₆₇	semidirect
772. #463	C₂²×C₆₇	semidirect
773. #463	C₂²×C₆₇	semidirect
774. #460	C₂²×C₆₇	semidirect
775. #460	C₂²×C₆₇	semidirect
780. #459	C₂²×C₆₇	semidirect
781. #459	C₂²×C₆₇	semidirect
782. #459	C₂²×C₆₇	semidirect
783. #459	C₂²×C₆₇	semidirect
784. #450	C₂²×C₆₇	semidirect
785. #449	C₂²×C₆₇	semidirect
786. #449	C₂²×C₆₇	semidirect
789. #447	C₂²×C₆₇	semidirect
790. #447	C₂²×C₆₇	semidirect
791. #447	C₂²×C₆₇	semidirect
792. #442	C₂²×C₆₇	semidirect
793. #442	C₂²×C₆₇	semidirect
794. #442	C₂²×C₆₇	semidirect
795. #440	C₂²×C₆₇	semidirect
796. C₄×SD₁₆	C₂²×C₆₇	semidirect
797. C₄×D₈	C₂²×C₆₇	semidirect
798. C₄×D₈	C₂²×C₆₇	semidirect
799. C₄×D₈	C₂²×C₆₇	semidirect
800. #433	C₂²×C₆₇	semidirect
801. #433	C₂²×C₆₇	semidirect
802. #432	C₂²×C₆₇	semidirect
803. #432	C₂²×C₆₇	semidirect
804. #431	C₂²×C₆₇	semidirect
805. #431	C₂²×C₆₇	semidirect
806. #423	C₂²×C₆₇	semidirect
807. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
809. #405	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×#3508	2
C₆₇×#3460	2
C₆₇×#3253	2
C₆₇×#3251	2
C₆₇×#3247	2
C₆₇×#3245	2
C₆₇×#3241	2
C₆₇×#3235	2
C₆₇×#3233	2
C₆₇×#3220	2
C₆₇×#3217	2
C₆₇×#3205	2
C₆₇×#3199	2
C₆₇×#3198	2
C₆₇×#3179	2
C₆₇×#3176	2
C₆₇×#3122	2
C₆₇×#3118	2
C₆₇×#3115	2
C₆₇×#3109	2
C₆₇×#3106	2
C₆₇×#3100	2
C₆₇×#2925	2
#60990	67

Subgroups — C67×#60990 #30740241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60990 #30740241