Subgroups — C₆₇×#61488 #30740739

Order 17152.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3524	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3371	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#3336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3321	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3317	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3285	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3175	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3126	C₂	1	2	yes	maximal, complemented
18	C₆₇×#3125	C₂	1	2	yes	maximal, complemented
19	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
20	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	#559×C₆₇	—	2	2	no	—
28	#559×C₆₇	C₂²	1	2	yes	—
29	#557×C₆₇	C₂²	1	2	yes	—
30	#555×C₆₇	—	2	2	no	—
31	#555×C₆₇	C₂²	1	2	yes	—
32	#553×C₆₇	—	2	2	no	—
33	#553×C₆₇	C₂²	1	2	yes	—
34	#552×C₆₇	—	2	2	no	—
35	#552×C₆₇	C₂²	1	2	yes	—
36	#550×C₆₇	C₂²	1	2	yes	—
37	#548×C₆₇	C₂²	1	2	yes	—
38	#548×C₆₇	C₂²	1	2	yes	—
39	#542×C₆₇	—	2	2	no	—
40	#542×C₆₇	C₂²	1	2	yes	—
41	#540×C₆₇	—	2	2	no	—
42	#540×C₆₇	C₂²	1	2	yes	—
43	#529×C₆₇	—	2	2	no	—
44	#529×C₆₇	—	2	2	no	—
45	#529×C₆₇	C₂²	1	2	yes	—
46	#529×C₆₇	C₂²	1	1	yes	characteristic
47	#520×C₆₇	C₂²	1	2	yes	—
48	#519×C₆₇	C₂²	1	2	yes	—
49	C₄×#41×C₆₇	C₂²	1	2	yes	—
50	#500×C₆₇	C₂²	1	1	yes	characteristic
51	#499×C₆₇	C₂²	1	1	yes	characteristic
52	#499×C₆₇	C₂²	1	1	yes	characteristic
53	#495×C₆₇	C₂²	1	1	yes	characteristic
54	#495×C₆₇	C₂²	1	1	yes	characteristic
55	#493×C₆₇	C₂²	1	1	yes	characteristic
56	#490×C₆₇	C₂²	1	2	yes	—
57	#489×C₆₇	C₂²	1	2	yes	—
58	#488×C₆₇	C₂²	1	2	yes	—
59	#485×C₆₇	C₂²	1	2	yes	—
60	#483×C₆₇	C₂²	1	2	yes	—
61	#482×C₆₇	C₂²	1	2	yes	—
62	#482×C₆₇	C₂²	1	2	yes	—
63	#482×C₆₇	C₂²	1	2	yes	—
64	#481×C₆₇	C₂²	1	2	yes	—
65	#479×C₆₇	C₂²	1	2	yes	—
66	#479×C₆₇	C₂²	1	2	yes	—
67	#479×C₆₇	C₂²	1	2	yes	—
68	#478×C₆₇	C₂²	1	2	yes	—
69	#476×C₆₇	C₂²	1	2	yes	—
70	#475×C₆₇	C₂²	1	2	yes	—
71	#469×C₆₇	C₂²	1	2	yes	—
72	#468×C₆₇	C₂²	1	2	yes	—
73	#467×C₆₇	C₂²	1	1	yes	characteristic
74	#467×C₆₇	C₂²	1	1	yes	characteristic
75	#466×C₆₇	C₂²	1	1	yes	characteristic
76	#466×C₆₇	C₂²	1	1	yes	characteristic
77	#466×C₆₇	C₂²	1	1	yes	characteristic
78	#466×C₆₇	C₂²	1	1	yes	characteristic
79	#465×C₆₇	C₂²	1	2	yes	—
80	#464×C₆₇	C₂²	1	2	yes	—
81	#464×C₆₇	C₂²	1	2	yes	—
82	#463×C₆₇	C₂²	1	2	yes	—
83	#463×C₆₇	C₂²	1	2	yes	—
84	#460×C₆₇	C₂²	1	2	yes	—
85	#460×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	—
88	#449×C₆₇	C₂²	1	2	yes	—
89	#449×C₆₇	C₂²	1	2	yes	—
90	#448×C₆₇	C₂²	1	2	yes	—
91	#448×C₆₇	C₂²	1	2	yes	—
92	#446×C₆₇	C₂²	1	1	yes	characteristic
93	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
94	#442×C₆₇	C₂²	1	2	yes	—
95	#441×C₆₇	C₂²	1	2	yes	—
96	#441×C₆₇	C₂²	1	2	yes	—
97	#440×C₆₇	C₂²	1	2	yes	—
98	#440×C₆₇	C₂²	1	2	yes	—
99	#440×C₆₇	C₂²	1	2	yes	—
100	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
102	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
103	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
104	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
106	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
108	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
109	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
113	#436×C₆₇	C₂²	1	1	yes	characteristic
114	#435×C₆₇	C₂²	1	1	yes	characteristic
115	#435×C₆₇	C₂²	1	1	yes	characteristic
116	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
117	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
118	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
119	#433×C₆₇	C₂²	1	1	yes	characteristic
120	#433×C₆₇	C₂²	1	1	yes	characteristic
121	#432×C₆₇	C₂²	1	1	yes	characteristic
122	#427×C₆₇	C₂²	1	1	yes	characteristic
123	#427×C₆₇	C₂²	1	1	yes	characteristic
124	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
125	#419×C₆₇	C₂²	1	2	yes	—
126	#417×C₆₇	C₂²	1	2	yes	—
127	#416×C₆₇	C₂²	1	2	yes	—
128	#405×C₆₇	C₂²	1	1	yes	characteristic
129	#405×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
131	C₂×#41×C₆₇	C₂³	1	2	yes	—
132	C₂×#41×C₆₇	C₂³	1	2	yes	—
133	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
134	#135×C₆₇	—	2	4	no	—
135	#135×C₆₇	—	2	4	no	—
136	C₂×Q₁₆×C₆₇	—	2	4	no	—
137	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
139	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
141	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
143	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
144	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₆₇	C₂³	1	2	yes	—
147	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₆₇	—	2	2	no	—
154	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
155	#127×C₆₇	—	2	2	no	—
156	#127×C₆₇	C₂³	1	2	yes	—
157	#126×C₆₇	—	2	2	no	—
158	#126×C₆₇	—	2	2	no	—
159	#126×C₆₇	—	2	2	no	—
160	#126×C₆₇	—	2	2	no	—
161	#126×C₆₇	D₄	1	1	yes	characteristic
162	#126×C₆₇	D₄	1	1	yes	characteristic
163	#125×C₆₇	—	2	2	no	—
164	#125×C₆₇	—	2	2	no	—
165	#125×C₆₇	—	2	2	no	—
166	#125×C₆₇	D₄	1	1	yes	characteristic
167	#125×C₆₇	C₂³	1	2	yes	—
168	#125×C₆₇	C₂³	1	2	yes	—
169	#124×C₆₇	—	2	2	no	—
170	#124×C₆₇	—	2	2	no	—
171	#124×C₆₇	—	2	2	no	—
172	#124×C₆₇	—	2	2	no	—
173	#124×C₆₇	—	2	2	no	—
174	#124×C₆₇	—	2	2	no	—
175	#124×C₆₇	D₄	1	1	yes	characteristic
176	#124×C₆₇	C₂³	1	2	yes	—
177	#124×C₆₇	C₂³	1	2	yes	—
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	#123×C₆₇	D₄	1	1	yes	characteristic
187	#123×C₆₇	D₄	1	1	yes	characteristic
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
192	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	#121×C₆₇	—	2	2	no	—
195	#121×C₆₇	—	2	2	no	—
196	#121×C₆₇	—	2	2	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	2	no	—
202	#121×C₆₇	D₄	1	1	yes	characteristic
203	#121×C₆₇	C₂³	1	2	yes	—
204	#121×C₆₇	C₂³	1	2	yes	—
205	#121×C₆₇	C₂³	1	2	yes	—
206	#121×C₆₇	C₂³	1	2	yes	—
207	C₄×Q₈×C₆₇	—	2	2	no	—
208	C₄×Q₈×C₆₇	—	2	2	no	—
209	C₄×Q₈×C₆₇	—	2	2	no	—
210	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
211	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
212	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
213	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
214	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
215	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
217	C₄×D₄×C₆₇	—	2	2	no	—
218	C₄×D₄×C₆₇	—	2	2	no	—
219	C₄×D₄×C₆₇	—	2	2	no	—
220	C₄×D₄×C₆₇	—	2	2	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	C₂³	1	2	yes	—
228	C₄×D₄×C₆₇	C₂³	1	2	yes	—
229	C₄×D₄×C₆₇	C₂³	1	2	yes	—
230	C₄×D₄×C₆₇	C₂³	1	2	yes	—
231	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
234	#117×C₆₇	—	2	2	no	—
235	#117×C₆₇	—	2	2	no	—
236	#117×C₆₇	—	2	2	no	—
237	#117×C₆₇	—	2	2	no	—
238	#117×C₆₇	—	2	2	no	—
239	#117×C₆₇	—	2	2	no	—
240	#117×C₆₇	—	2	2	no	—
241	#117×C₆₇	C₂³	1	2	yes	—
242	#117×C₆₇	C₂³	1	2	yes	—
243	#117×C₆₇	C₂³	1	1	yes	characteristic
244	#117×C₆₇	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
246	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
247	C₂×C₄²×C₆₇	—	2	2	no	—
248	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
249	#107×C₆₇	C₂³	1	1	yes	characteristic
250	#107×C₆₇	C₂³	1	1	yes	characteristic
251	#107×C₆₇	C₂³	1	1	yes	characteristic
252	#107×C₆₇	C₂³	1	2	yes	—
253	#107×C₆₇	C₂³	1	2	yes	—
254	#107×C₆₇	C₂³	1	1	yes	characteristic
255	#106×C₆₇	C₂³	1	2	yes	—
256	#106×C₆₇	C₂³	1	2	yes	—
257	#106×C₆₇	C₂³	1	2	yes	—
258	#106×C₆₇	C₂³	1	2	yes	—
259	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
260	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
261	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
263	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
264	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
265	#103×C₆₇	C₂³	1	2	yes	—
266	#103×C₆₇	C₂³	1	2	yes	—
267	#103×C₆₇	C₂³	1	2	yes	—
268	#103×C₆₇	C₂³	1	2	yes	—
269	#103×C₆₇	C₂³	1	2	yes	—
270	#103×C₆₇	C₂³	1	2	yes	—
271	#103×C₆₇	C₂³	1	2	yes	—
272	#103×C₆₇	C₂³	1	2	yes	—
273	#102×C₆₇	C₂³	1	2	yes	—
274	#102×C₆₇	C₂³	1	2	yes	—
275	#102×C₆₇	C₂³	1	2	yes	—
276	#102×C₆₇	C₂³	1	2	yes	—
277	#102×C₆₇	C₂³	1	2	yes	—
278	#102×C₆₇	C₂³	1	2	yes	—
279	#102×C₆₇	C₂³	1	2	yes	—
280	#102×C₆₇	C₂³	1	2	yes	—
281	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	#97×C₆₇	C₂³	1	1	yes	characteristic
288	#97×C₆₇	C₂³	1	1	yes	characteristic
289	#97×C₆₇	C₂³	1	1	yes	characteristic
290	#97×C₆₇	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
297	#41×C₆₇	—	2	4	no	—
298	#41×C₆₇	—	2	4	no	—
299	#41×C₆₇	—	4	2	no	—
300	#41×C₆₇	—	4	2	no	—
301	C₂×Q₈×C₆₇	—	2	2	no	—
302	C₂×Q₈×C₆₇	—	2	2	no	—
303	C₂×Q₈×C₆₇	—	2	4	no	—
304	C₂×Q₈×C₆₇	—	4	2	no	—
305	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
306	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
307	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
308	C₂×D₄×C₆₇	—	2	2	no	—
309	C₂×D₄×C₆₇	—	2	2	no	—
310	C₂×D₄×C₆₇	—	2	2	no	—
311	C₂×D₄×C₆₇	—	2	2	no	—
312	C₂×D₄×C₆₇	—	2	2	no	—
313	C₂×D₄×C₆₇	—	2	2	no	—
314	C₂×D₄×C₆₇	—	2	2	no	—
315	C₂×D₄×C₆₇	—	2	2	no	—
316	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
318	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
319	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	—	2	2	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	2	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	2	no	—
328	C₂²×C₄×C₆₇	—	2	2	no	—
329	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
334	Q₁₆×C₆₇	—	2	4	no	—
335	Q₁₆×C₆₇	—	2	2	no	—
336	Q₁₆×C₆₇	#41	1	4	yes	—
337	SD₁₆×C₆₇	—	2	4	no	—
338	SD₁₆×C₆₇	—	2	4	no	—
339	SD₁₆×C₆₇	—	4	2	no	—
340	SD₁₆×C₆₇	—	4	2	no	—
341	D₈×C₆₇	—	2	2	no	—
342	D₈×C₆₇	—	2	2	no	—
343	D₈×C₆₇	—	4	2	no	—
344	M₁₆×C₆₇	—	4	1	no	—
345	M₁₆×C₆₇	—	4	1	no	—
346	C₂×C₈×C₆₇	—	2	2	no	—
347	C₂×C₈×C₆₇	—	2	2	no	—
348	C₂×C₈×C₆₇	—	2	2	no	—
349	C₂×C₈×C₆₇	—	4	1	no	—
350	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	2	no	—
360	C₄⋊C₄×C₆₇	—	2	2	no	—
361	C₄⋊C₄×C₆₇	—	2	2	no	—
362	C₄⋊C₄×C₆₇	—	2	2	no	—
363	C₄⋊C₄×C₆₇	—	2	2	no	—
364	C₄⋊C₄×C₆₇	—	2	2	no	—
365	C₄⋊C₄×C₆₇	—	2	2	no	—
366	C₄⋊C₄×C₆₇	—	2	2	no	—
367	C₄⋊C₄×C₆₇	—	2	2	no	—
368	C₄⋊C₄×C₆₇	—	2	2	no	—
369	C₄⋊C₄×C₆₇	—	2	2	no	—
370	C₄⋊C₄×C₆₇	—	2	2	no	—
371	C₄⋊C₄×C₆₇	—	2	2	no	—
372	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
374	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
382	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
383	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
384	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	2	no	—
388	C₂²⋊C₄×C₆₇	—	2	2	no	—
389	C₂²⋊C₄×C₆₇	—	2	2	no	—
390	C₂²⋊C₄×C₆₇	—	2	2	no	—
391	C₂²⋊C₄×C₆₇	—	2	2	no	—
392	C₂²⋊C₄×C₆₇	—	2	2	no	—
393	C₂²⋊C₄×C₆₇	—	2	2	no	—
394	C₂²⋊C₄×C₆₇	—	2	2	no	—
395	C₂²⋊C₄×C₆₇	—	2	2	no	—
396	C₂²⋊C₄×C₆₇	—	2	2	no	—
397	C₂²⋊C₄×C₆₇	—	2	2	no	—
398	C₂²⋊C₄×C₆₇	—	2	2	no	—
399	C₂²⋊C₄×C₆₇	—	2	2	no	—
400	C₂²⋊C₄×C₆₇	—	2	2	no	—
401	C₂²⋊C₄×C₆₇	—	2	2	no	—
402	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
405	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
407	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
408	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
409	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
410	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
412	C₄²×C₆₇	—	2	2	no	—
413	C₄²×C₆₇	—	2	2	no	—
414	C₄²×C₆₇	—	2	2	no	—
415	C₄²×C₆₇	—	2	2	no	—
416	C₄²×C₆₇	—	2	2	no	—
417	C₄²×C₆₇	—	2	2	no	—
418	C₄²×C₆₇	—	2	2	no	—
419	C₄²×C₆₇	—	2	2	no	—
420	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
426	C₂³×C₆₇	—	2	2	no	—
427	C₂³×C₆₇	—	2	2	no	—
428	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
429	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
430	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
431	Q₈×C₆₇	—	2	2	no	—
432	Q₈×C₆₇	—	2	2	no	—
433	Q₈×C₆₇	—	2	2	no	—
434	Q₈×C₆₇	—	4	1	no	—
435	Q₈×C₆₇	—	4	4	no	—
436	Q₈×C₆₇	—	8	2	no	—
437	Q₈×C₆₇	C₂×#41	1	4	yes	—
438	D₄×C₆₇	—	2	2	no	—
439	D₄×C₆₇	—	2	2	no	—
440	D₄×C₆₇	—	2	2	no	—
441	D₄×C₆₇	—	2	2	no	—
442	D₄×C₆₇	—	4	1	no	—
443	D₄×C₆₇	—	4	1	no	—
444	D₄×C₆₇	—	4	1	no	—
445	D₄×C₆₇	—	4	4	no	—
446	D₄×C₆₇	—	4	4	no	—
447	D₄×C₆₇	—	8	2	no	—
448	D₄×C₆₇	—	8	2	no	—
449	D₄×C₆₇	—	8	2	no	—
450	D₄×C₆₇	—	8	2	no	—
451	D₄×C₆₇	—	8	2	no	—
452	D₄×C₆₇	—	8	2	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	1	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	4	1	no	—
466	C₂×C₄×C₆₇	—	4	1	no	—
467	C₂×C₄×C₆₇	—	4	4	no	—
468	C₂×C₄×C₆₇	—	4	4	no	—
469	C₂×C₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	8	2	no	—
471	C₂×C₄×C₆₇	—	8	2	no	—
472	C₂×C₄×C₆₇	—	8	2	no	—
473	C₂×C₄×C₆₇	—	8	2	no	—
474	C₂×C₄×C₆₇	—	8	2	no	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
487	C₈×C₆₇	—	2	1	no	—
488	C₈×C₆₇	—	2	1	no	—
489	C₈×C₆₇	—	2	1	no	—
490	C₈×C₆₇	—	2	1	no	—
491	C₈×C₆₇	—	2	1	no	—
492	C₈×C₆₇	—	2	1	no	—
493	C₈×C₆₇	—	2	1	no	—
494	C₈×C₆₇	C₂×#41	1	2	yes	—
495	C₂²×C₆₇	—	2	1	no	—
496	C₂²×C₆₇	—	2	1	no	—
497	C₂²×C₆₇	—	2	1	no	—
498	C₂²×C₆₇	—	2	1	no	—
499	C₂²×C₆₇	—	2	1	no	—
500	C₂²×C₆₇	—	2	1	no	—
501	C₂²×C₆₇	—	2	1	no	—
502	C₂²×C₆₇	—	2	1	no	—
503	C₂²×C₆₇	—	2	1	no	—
504	C₂²×C₆₇	—	4	2	no	—
505	C₂²×C₆₇	—	4	2	no	—
506	C₂²×C₆₇	—	4	2	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₆₇	—	2	1	no	—
512	C₄×C₆₇	—	2	1	no	—
513	C₄×C₆₇	—	2	1	no	—
514	C₄×C₆₇	—	2	1	no	—
515	C₄×C₆₇	—	2	1	no	—
516	C₄×C₆₇	—	2	1	no	—
517	C₄×C₆₇	—	2	1	no	—
518	C₄×C₆₇	—	2	1	no	—
519	C₄×C₆₇	—	2	1	no	—
520	C₄×C₆₇	—	2	1	no	—
521	C₄×C₆₇	—	2	1	no	—
522	C₄×C₆₇	—	2	4	no	—
523	C₄×C₆₇	—	4	2	no	—
524	C₄×C₆₇	—	4	2	no	—
525	C₄×C₆₇	—	4	2	no	—
526	C₄×C₆₇	—	4	2	no	—
527	C₄×C₆₇	—	4	2	no	—
528	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
529	C₄×C₆₇	#585	1	1	yes	characteristic
530	#61488	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
531	C₂×C₆₇	—	4	1	no	—
532	C₂×C₆₇	—	4	1	no	—
533	C₂×C₆₇	—	4	1	no	—
534	C₂×C₆₇	—	8	2	no	—
535	C₂×C₆₇	—	8	2	no	—
536	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
537	C₂×C₆₇	#3584	1	1	yes	characteristic
538	C₂×C₆₇	#3584	1	1	yes	characteristic
539	#3524	C₂×C₆₇	1	2	yes	complemented
540	#3396	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#3383	C₂×C₆₇	1	1	yes	characteristic, complemented
542	#3371	C₂×C₆₇	1	2	yes	complemented
543	#3341	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#3339	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#3336	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#3326	C₂×C₆₇	1	2	yes	complemented
547	#3321	C₂×C₆₇	1	2	yes	complemented
548	#3317	C₂×C₆₇	1	2	yes	complemented
549	#3287	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#3285	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#3285	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#3176	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#3175	C₂×C₆₇	1	1	yes	characteristic, complemented
554	#3168	C₂×C₆₇	1	1	yes	characteristic, complemented
555	#3126	C₂×C₆₇	1	2	yes	complemented
556	#3125	C₂×C₆₇	1	2	yes	complemented
557	#3111	C₂×C₆₇	1	2	yes	complemented
558	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
559	#2951	C₂×C₆₇	1	1	yes	characteristic, complemented
560	#2950	C₂×C₆₇	1	1	yes	characteristic, complemented
561	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
562	C₆₇	#61488	1	1	yes	characteristic, direct product factor, Sylow
563	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
564	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
565	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
566	#559	—	2	2	no	—
567	#559	C₂²×C₆₇	1	2	yes	—
568	#557	C₂²×C₆₇	1	2	yes	—
569	#555	—	2	2	no	—
570	#555	C₂²×C₆₇	1	2	yes	—
571	#553	—	2	2	no	—
572	#553	C₂²×C₆₇	1	2	yes	—
573	#552	—	2	2	no	—
574	#552	C₂²×C₆₇	1	2	yes	—
575	#550	C₂²×C₆₇	1	2	yes	—
576	#548	C₂²×C₆₇	1	2	yes	—
577	#548	C₂²×C₆₇	1	2	yes	—
578	#542	—	2	2	no	—
579	#542	C₂²×C₆₇	1	2	yes	—
580	#540	—	2	2	no	—
581	#540	C₂²×C₆₇	1	2	yes	—
582	#529	—	2	2	no	—
583	#529	—	2	2	no	—
584	#529	C₂²×C₆₇	1	2	yes	—
585	#529	C₂²×C₆₇	1	1	yes	characteristic
586	#520	C₂²×C₆₇	1	2	yes	—
587	#519	C₂²×C₆₇	1	2	yes	—
588	C₄×#41	C₂²×C₆₇	1	2	yes	—
589	#500	C₂²×C₆₇	1	1	yes	characteristic
590	#499	C₂²×C₆₇	1	1	yes	characteristic
591	#499	C₂²×C₆₇	1	1	yes	characteristic
592	#495	C₂²×C₆₇	1	1	yes	characteristic
593	#495	C₂²×C₆₇	1	1	yes	characteristic
594	#493	C₂²×C₆₇	1	1	yes	characteristic
595	#490	C₂²×C₆₇	1	2	yes	—
596	#489	C₂²×C₆₇	1	2	yes	—
597	#488	C₂²×C₆₇	1	2	yes	—
598	#485	C₂²×C₆₇	1	2	yes	—
599	#483	C₂²×C₆₇	1	2	yes	—
600	#482	C₂²×C₆₇	1	2	yes	—
601	#482	C₂²×C₆₇	1	2	yes	—
602	#482	C₂²×C₆₇	1	2	yes	—
603	#481	C₂²×C₆₇	1	2	yes	—
604	#479	C₂²×C₆₇	1	2	yes	—
605	#479	C₂²×C₆₇	1	2	yes	—
606	#479	C₂²×C₆₇	1	2	yes	—
607	#478	C₂²×C₆₇	1	2	yes	—
608	#476	C₂²×C₆₇	1	2	yes	—
609	#475	C₂²×C₆₇	1	2	yes	—
610	#469	C₂²×C₆₇	1	2	yes	—
611	#468	C₂²×C₆₇	1	2	yes	—
612	#467	C₂²×C₆₇	1	1	yes	characteristic
613	#467	C₂²×C₆₇	1	1	yes	characteristic
614	#466	C₂²×C₆₇	1	1	yes	characteristic
615	#466	C₂²×C₆₇	1	1	yes	characteristic
616	#466	C₂²×C₆₇	1	1	yes	characteristic
617	#466	C₂²×C₆₇	1	1	yes	characteristic
618	#465	C₂²×C₆₇	1	2	yes	—
619	#464	C₂²×C₆₇	1	2	yes	—
620	#464	C₂²×C₆₇	1	2	yes	—
621	#463	C₂²×C₆₇	1	2	yes	—
622	#463	C₂²×C₆₇	1	2	yes	—
623	#460	C₂²×C₆₇	1	2	yes	—
624	#460	C₂²×C₆₇	1	2	yes	—
625	#452	C₂²×C₆₇	1	2	yes	—
626	#452	C₂²×C₆₇	1	2	yes	—
627	#449	C₂²×C₆₇	1	2	yes	—
628	#449	C₂²×C₆₇	1	2	yes	—
629	#448	C₂²×C₆₇	1	2	yes	—
630	#448	C₂²×C₆₇	1	2	yes	—
631	#446	C₂²×C₆₇	1	1	yes	characteristic
632	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
633	#442	C₂²×C₆₇	1	2	yes	—
634	#441	C₂²×C₆₇	1	2	yes	—
635	#441	C₂²×C₆₇	1	2	yes	—
636	#440	C₂²×C₆₇	1	2	yes	—
637	#440	C₂²×C₆₇	1	2	yes	—
638	#440	C₂²×C₆₇	1	2	yes	—
639	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
640	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
641	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
642	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
643	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
644	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
645	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
646	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
647	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
648	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
649	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
650	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
651	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
652	#436	C₂²×C₆₇	1	1	yes	characteristic
653	#435	C₂²×C₆₇	1	1	yes	characteristic
654	#435	C₂²×C₆₇	1	1	yes	characteristic
655	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
656	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
657	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
658	#433	C₂²×C₆₇	1	1	yes	characteristic
659	#433	C₂²×C₆₇	1	1	yes	characteristic
660	#432	C₂²×C₆₇	1	1	yes	characteristic
661	#427	C₂²×C₆₇	1	1	yes	characteristic
662	#427	C₂²×C₆₇	1	1	yes	characteristic
663	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
664	#419	C₂²×C₆₇	1	2	yes	—
665	#417	C₂²×C₆₇	1	2	yes	—
666	#416	C₂²×C₆₇	1	2	yes	—
667	#405	C₂²×C₆₇	1	1	yes	characteristic
668	#405	C₂²×C₆₇	1	1	yes	characteristic
669	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
670	C₂×#41	C₂³×C₆₇	1	2	yes	—
671	C₂×#41	C₂³×C₆₇	1	2	yes	—
672	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
673	#135	—	2	4	no	—
674	#135	—	2	4	no	—
675	C₂×Q₁₆	—	2	4	no	—
676	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
677	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
679	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
680	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
681	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
682	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
683	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
684	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
685	C₂×D₈	C₂³×C₆₇	1	2	yes	—
686	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
687	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
688	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
689	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
690	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
694	#127	—	2	2	no	—
695	#127	C₂³×C₆₇	1	2	yes	—
696	#126	—	2	2	no	—
697	#126	—	2	2	no	—
698	#126	—	2	2	no	—
699	#126	—	2	2	no	—
700	#126	D₄×C₆₇	1	1	yes	characteristic
701	#126	D₄×C₆₇	1	1	yes	characteristic
702	#125	—	2	2	no	—
703	#125	—	2	2	no	—
704	#125	—	2	2	no	—
705	#125	D₄×C₆₇	1	1	yes	characteristic
706	#125	C₂³×C₆₇	1	2	yes	—
707	#125	C₂³×C₆₇	1	2	yes	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	—	2	2	no	—
711	#124	—	2	2	no	—
712	#124	—	2	2	no	—
713	#124	—	2	2	no	—
714	#124	D₄×C₆₇	1	1	yes	characteristic
715	#124	C₂³×C₆₇	1	2	yes	—
716	#124	C₂³×C₆₇	1	2	yes	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	—	2	2	no	—
720	#123	—	2	2	no	—
721	#123	—	2	2	no	—
722	#123	—	2	2	no	—
723	#123	—	2	2	no	—
724	#123	—	2	2	no	—
725	#123	D₄×C₆₇	1	1	yes	characteristic
726	#123	D₄×C₆₇	1	1	yes	characteristic
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
731	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
732	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
733	#121	—	2	2	no	—
734	#121	—	2	2	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	—	2	2	no	—
740	#121	—	2	2	no	—
741	#121	D₄×C₆₇	1	1	yes	characteristic
742	#121	C₂³×C₆₇	1	2	yes	—
743	#121	C₂³×C₆₇	1	2	yes	—
744	#121	C₂³×C₆₇	1	2	yes	—
745	#121	C₂³×C₆₇	1	2	yes	—
746	C₄×Q₈	—	2	2	no	—
747	C₄×Q₈	—	2	2	no	—
748	C₄×Q₈	—	2	2	no	—
749	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
750	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
751	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
752	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
753	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
754	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
755	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	2	no	—
759	C₄×D₄	—	2	2	no	—
760	C₄×D₄	—	2	2	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	2	no	—
763	C₄×D₄	—	2	2	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	C₂³×C₆₇	1	2	yes	—
767	C₄×D₄	C₂³×C₆₇	1	2	yes	—
768	C₄×D₄	C₂³×C₆₇	1	2	yes	—
769	C₄×D₄	C₂³×C₆₇	1	2	yes	—
770	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
772	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	—	2	2	no	—
776	#117	—	2	2	no	—
777	#117	—	2	2	no	—
778	#117	—	2	2	no	—
779	#117	—	2	2	no	—
780	#117	C₂³×C₆₇	1	2	yes	—
781	#117	C₂³×C₆₇	1	2	yes	—
782	#117	C₂³×C₆₇	1	1	yes	characteristic
783	#117	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×C₄⋊C₄	—	2	2	no	—
785	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄²	—	2	2	no	—
787	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
788	#107	C₂³×C₆₇	1	1	yes	characteristic
789	#107	C₂³×C₆₇	1	1	yes	characteristic
790	#107	C₂³×C₆₇	1	2	yes	—
791	#107	C₂³×C₆₇	1	1	yes	characteristic
792	#107	C₂³×C₆₇	1	1	yes	characteristic
793	#107	C₂³×C₆₇	1	2	yes	—
794	#106	C₂³×C₆₇	1	2	yes	—
795	#106	C₂³×C₆₇	1	2	yes	—
796	#106	C₂³×C₆₇	1	2	yes	—
797	#106	C₂³×C₆₇	1	2	yes	—
798	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
800	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
802	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
803	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
804	#103	C₂³×C₆₇	1	2	yes	—
805	#103	C₂³×C₆₇	1	2	yes	—
806	#103	C₂³×C₆₇	1	2	yes	—
807	#103	C₂³×C₆₇	1	2	yes	—
808	#103	C₂³×C₆₇	1	2	yes	—
809	#103	C₂³×C₆₇	1	2	yes	—
810	#103	C₂³×C₆₇	1	2	yes	—
811	#103	C₂³×C₆₇	1	2	yes	—
812	#102	C₂³×C₆₇	1	2	yes	—
813	#102	C₂³×C₆₇	1	2	yes	—
814	#102	C₂³×C₆₇	1	2	yes	—
815	#102	C₂³×C₆₇	1	2	yes	—
816	#102	C₂³×C₆₇	1	2	yes	—
817	#102	C₂³×C₆₇	1	2	yes	—
818	#102	C₂³×C₆₇	1	2	yes	—
819	#102	C₂³×C₆₇	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
821	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
822	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
823	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
824	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
825	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
826	#97	C₂³×C₆₇	1	1	yes	characteristic
827	#97	C₂³×C₆₇	1	1	yes	characteristic
828	#97	C₂³×C₆₇	1	1	yes	characteristic
829	#97	C₂³×C₆₇	1	1	yes	characteristic
830	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
831	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
832	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
833	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
834	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
835	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
836	#41	—	2	4	no	—
837	#41	—	2	4	no	—
838	#41	—	4	2	no	—
839	#41	—	4	2	no	—
840	C₂×Q₈	—	2	2	no	—
841	C₂×Q₈	—	2	2	no	—
842	C₂×Q₈	—	2	4	no	—
843	C₂×Q₈	—	4	2	no	—
844	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
845	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
846	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
856	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
857	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
858	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
859	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	2	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	2	2	no	—
867	C₂²×C₄	—	2	2	no	—
868	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
869	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
873	Q₁₆	—	2	4	no	—
874	Q₁₆	—	2	2	no	—
875	Q₁₆	#41×C₆₇	1	4	yes	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	2	4	no	—
878	SD₁₆	—	4	2	no	—
879	SD₁₆	—	4	2	no	—
880	D₈	—	2	2	no	—
881	D₈	—	2	2	no	—
882	D₈	—	4	2	no	—
883	M₁₆	—	4	1	no	—
884	M₁₆	—	4	1	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	2	2	no	—
888	C₂×C₈	—	4	1	no	—
889	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
890	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
892	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
893	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
894	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
895	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
896	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	2	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
912	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
913	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
914	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
915	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
916	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
921	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
922	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
924	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
942	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
943	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
944	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	2	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
960	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
961	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
962	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
968	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
969	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
970	Q₈	—	2	2	no	—
971	Q₈	—	2	2	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	4	1	no	—
974	Q₈	—	4	4	no	—
975	Q₈	—	8	2	no	—
976	Q₈	C₂×#41×C₆₇	1	4	yes	—
977	D₄	—	2	2	no	—
978	D₄	—	2	2	no	—
979	D₄	—	2	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	1	no	—
983	D₄	—	4	1	no	—
984	D₄	—	4	4	no	—
985	D₄	—	4	4	no	—
986	D₄	—	8	2	no	—
987	D₄	—	8	2	no	—
988	D₄	—	8	2	no	—
989	D₄	—	8	2	no	—
990	D₄	—	8	2	no	—
991	D₄	—	8	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	4	1	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	4	4	no	—
1007	C₂×C₄	—	4	4	no	—
1008	C₂×C₄	—	4	4	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	2	no	—
1011	C₂×C₄	—	8	2	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	8	2	no	—
1014	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1025	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1026	C₈	—	2	1	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	C₂×#41×C₆₇	1	2	yes	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	4	2	no	—
1044	C₂²	—	4	2	no	—
1045	C₂²	—	4	2	no	—
1046	C₂²	—	4	2	no	—
1047	C₂²	—	4	2	no	—
1048	C₂²	—	4	2	no	—
1049	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	4	no	—
1062	C₄	—	4	2	no	—
1063	C₄	—	4	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1068	C₄	#585×C₆₇	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	8	2	no	—
1074	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
1075	C₂	C₆₇×#3584	1	1	yes	characteristic
1076	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 ◁ #529×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3524	C₂	semidirect
2. C₆₇×#3396	C₂	semidirect
3. C₆₇×#3383	C₂	semidirect
4. C₆₇×#3371	C₂	semidirect
5. C₆₇×#3341	C₂	semidirect
6. C₆₇×#3339	C₂	semidirect
7. C₆₇×#3336	C₂	semidirect
8. C₆₇×#3326	C₂	semidirect
9. C₆₇×#3321	C₂	semidirect
10. C₆₇×#3317	C₂	semidirect
11. C₆₇×#3287	C₂	semidirect
12. C₆₇×#3285	C₂	semidirect
13. C₆₇×#3285	C₂	semidirect
14. C₆₇×#3176	C₂	semidirect
15. C₆₇×#3175	C₂	semidirect
16. C₆₇×#3168	C₂	semidirect
17. C₆₇×#3126	C₂	semidirect
18. C₆₇×#3125	C₂	semidirect
19. C₆₇×#3111	C₂	semidirect
20. C₆₇×#2966	C₂	semidirect
21. C₆₇×#2951	C₂	semidirect
22. C₆₇×#2950	C₂	semidirect
23. C₄×#135×C₆₇	C₂	semidirect
530. #61488	C₆₇	direct (N × H)
539. #3524	C₂×C₆₇	semidirect
540. #3396	C₂×C₆₇	semidirect
541. #3383	C₂×C₆₇	semidirect
542. #3371	C₂×C₆₇	semidirect
543. #3341	C₂×C₆₇	semidirect
544. #3339	C₂×C₆₇	semidirect
545. #3336	C₂×C₆₇	semidirect
546. #3326	C₂×C₆₇	semidirect
547. #3321	C₂×C₆₇	semidirect
548. #3317	C₂×C₆₇	semidirect
549. #3287	C₂×C₆₇	semidirect
550. #3285	C₂×C₆₇	semidirect
551. #3285	C₂×C₆₇	semidirect
552. #3176	C₂×C₆₇	semidirect
553. #3175	C₂×C₆₇	semidirect
554. #3168	C₂×C₆₇	semidirect
555. #3126	C₂×C₆₇	semidirect
556. #3125	C₂×C₆₇	semidirect
557. #3111	C₂×C₆₇	semidirect
558. #2966	C₂×C₆₇	semidirect
559. #2951	C₂×C₆₇	semidirect
560. #2950	C₂×C₆₇	semidirect
561. C₄×#135	C₂×C₆₇	semidirect
562. C₆₇	#61488	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3524	2
C₆₇×#3396	2
C₆₇×#3383	2
C₆₇×#3371	2
C₆₇×#3341	2
C₆₇×#3339	2
C₆₇×#3336	2
C₆₇×#3326	2
C₆₇×#3321	2
C₆₇×#3317	2
C₆₇×#3287	2
C₆₇×#3285	2
C₆₇×#3176	2
C₆₇×#3175	2
C₆₇×#3168	2
C₆₇×#3126	2
C₆₇×#3125	2
C₆₇×#3111	2
C₆₇×#2966	2
C₆₇×#2951	2
C₆₇×#2950	2
C₄×#135×C₆₇	2
#61488	67

Subgroups — C67×#61488 #30740739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61488 #30740739