Subgroups — C₆₇×#61501 #30740752

Order 17152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3521	C₂	1	2	yes	maximal, complemented
2	C₆₇×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3360	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#3350	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3302	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3267	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3178	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2946	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	—
21	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
22	#556×C₆₇	C₂²	1	2	yes	complemented
23	#556×C₆₇	C₂²	1	2	yes	complemented
24	#554×C₆₇	C₂²	1	2	yes	complemented
25	#553×C₆₇	—	2	2	no	—
26	#553×C₆₇	C₂²	1	2	yes	—
27	#552×C₆₇	—	2	2	no	—
28	#552×C₆₇	C₂²	1	2	yes	—
29	#551×C₆₇	—	2	2	no	—
30	#551×C₆₇	—	2	2	no	—
31	#547×C₆₇	C₂²	1	2	yes	—
32	#546×C₆₇	C₂²	1	2	yes	—
33	#546×C₆₇	C₂²	1	2	yes	complemented
34	#542×C₆₇	C₂²	1	2	yes	—
35	#541×C₆₇	C₂²	1	2	yes	complemented
36	#539×C₆₇	—	2	2	no	—
37	#538×C₆₇	—	2	2	no	—
38	#529×C₆₇	—	2	2	no	—
39	#529×C₆₇	C₂²	1	1	yes	characteristic
40	#529×C₆₇	C₂²	1	2	yes	complemented
41	C₂×#126×C₆₇	—	2	2	no	—
42	#520×C₆₇	C₂²	1	2	yes	—
43	#518×C₆₇	C₂²	1	2	yes	complemented
44	C₄×#41×C₆₇	C₂²	1	2	yes	complemented
45	#501×C₆₇	C₂²	1	2	yes	complemented
46	#499×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#497×C₆₇	C₂²	1	2	yes	complemented
48	#495×C₆₇	C₂²	1	1	yes	characteristic
49	#488×C₆₇	C₂²	1	2	yes	complemented
50	#488×C₆₇	C₂²	1	2	yes	complemented
51	#487×C₆₇	C₂²	1	2	yes	complemented
52	#485×C₆₇	C₂²	1	2	yes	complemented
53	#485×C₆₇	C₂²	1	2	yes	complemented
54	#484×C₆₇	C₂²	1	2	yes	complemented
55	#483×C₆₇	C₂²	1	2	yes	complemented
56	#482×C₆₇	C₂²	1	2	yes	—
57	#482×C₆₇	C₂²	1	2	yes	complemented
58	#479×C₆₇	C₂²	1	2	yes	complemented
59	#479×C₆₇	C₂²	1	2	yes	complemented
60	#478×C₆₇	C₂²	1	2	yes	complemented
61	#478×C₆₇	C₂²	1	2	yes	complemented
62	#476×C₆₇	C₂²	1	2	yes	complemented
63	#474×C₆₇	C₂²	1	2	yes	complemented
64	#470×C₆₇	C₂²	1	2	yes	complemented
65	#468×C₆₇	C₂²	1	2	yes	—
66	#467×C₆₇	C₂²	1	2	yes	complemented
67	#467×C₆₇	C₂²	1	1	yes	characteristic, complemented
68	#466×C₆₇	C₂²	1	1	yes	characteristic
69	#465×C₆₇	C₂²	1	2	yes	—
70	#465×C₆₇	C₂²	1	2	yes	complemented
71	#464×C₆₇	C₂²	1	2	yes	complemented
72	#463×C₆₇	C₂²	1	2	yes	—
73	#463×C₆₇	C₂²	1	2	yes	—
74	#463×C₆₇	C₂²	1	2	yes	—
75	#462×C₆₇	C₂²	1	2	yes	complemented
76	#461×C₆₇	C₂²	1	2	yes	complemented
77	#452×C₆₇	C₂²	1	2	yes	—
78	#452×C₆₇	C₂²	1	2	yes	—
79	#452×C₆₇	C₂²	1	2	yes	complemented
80	#450×C₆₇	C₂²	1	2	yes	complemented
81	#449×C₆₇	C₂²	1	2	yes	—
82	#447×C₆₇	C₂²	1	2	yes	—
83	#446×C₆₇	C₂²	1	1	yes	characteristic, complemented
84	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	#442×C₆₇	C₂²	1	2	yes	—
86	#442×C₆₇	C₂²	1	2	yes	—
87	#441×C₆₇	C₂²	1	2	yes	complemented
88	#440×C₆₇	C₂²	1	2	yes	complemented
89	#440×C₆₇	C₂²	1	2	yes	complemented
90	#440×C₆₇	C₂²	1	2	yes	complemented
91	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
95	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
96	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
98	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×D₈×C₆₇	C₂²	1	2	yes	—
100	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
102	#436×C₆₇	C₂²	1	1	yes	characteristic
103	#435×C₆₇	C₂²	1	2	yes	complemented
104	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
105	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
106	#433×C₆₇	C₂²	1	2	yes	complemented
107	#432×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	#428×C₆₇	C₂²	1	2	yes	complemented
109	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
110	#416×C₆₇	C₂²	1	2	yes	—
111	#416×C₆₇	C₂²	1	2	yes	complemented
112	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
113	#405×C₆₇	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₆₇	C₂³	1	2	yes	—
116	C₂×#41×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
119	#135×C₆₇	—	2	4	no	—
120	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
127	C₂×D₈×C₆₇	C₂³	1	2	yes	—
128	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
133	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
134	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
135	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
136	#126×C₆₇	—	2	2	no	—
137	#126×C₆₇	—	2	2	no	—
138	#126×C₆₇	—	2	2	no	—
139	#126×C₆₇	—	2	2	no	—
140	#126×C₆₇	—	2	2	no	—
141	#126×C₆₇	—	2	2	no	—
142	#126×C₆₇	—	2	2	no	—
143	#126×C₆₇	—	2	2	no	—
144	#126×C₆₇	—	2	2	no	—
145	#126×C₆₇	—	2	2	no	—
146	#126×C₆₇	D₄	1	2	yes	—
147	#125×C₆₇	—	2	2	no	—
148	#125×C₆₇	—	2	2	no	—
149	#125×C₆₇	—	2	2	no	—
150	#125×C₆₇	D₄	1	1	yes	characteristic
151	#125×C₆₇	C₂³	1	2	yes	—
152	#125×C₆₇	C₂³	1	2	yes	—
153	#124×C₆₇	—	2	2	no	—
154	#124×C₆₇	—	2	2	no	—
155	#124×C₆₇	D₄	1	1	yes	characteristic
156	#124×C₆₇	C₂³	1	2	yes	—
157	#124×C₆₇	C₂³	1	2	yes	—
158	#123×C₆₇	—	2	2	no	—
159	#123×C₆₇	—	2	2	no	—
160	#123×C₆₇	—	2	2	no	—
161	#123×C₆₇	—	2	2	no	—
162	#123×C₆₇	—	2	2	no	—
163	#123×C₆₇	—	2	2	no	—
164	#123×C₆₇	—	2	2	no	—
165	#123×C₆₇	—	2	2	no	—
166	#123×C₆₇	D₄	1	2	yes	—
167	C₂²⋊Q₈×C₆₇	—	2	2	no	—
168	C₂²⋊Q₈×C₆₇	—	2	2	no	—
169	C₂²⋊Q₈×C₆₇	—	2	2	no	—
170	C₂²⋊Q₈×C₆₇	—	2	2	no	—
171	C₂²⋊Q₈×C₆₇	—	2	2	no	—
172	C₂²⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
173	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
174	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
175	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
176	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
177	#121×C₆₇	—	2	2	no	—
178	#121×C₆₇	—	2	2	no	—
179	#121×C₆₇	—	2	2	no	—
180	#121×C₆₇	—	2	2	no	—
181	#121×C₆₇	D₄	1	1	yes	characteristic
182	#121×C₆₇	C₂³	1	2	yes	—
183	#121×C₆₇	C₂³	1	2	yes	—
184	#120×C₆₇	—	2	2	no	—
185	#120×C₆₇	—	2	2	no	—
186	C₄×Q₈×C₆₇	—	2	2	no	—
187	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
188	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
189	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
190	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
191	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₆₇	—	2	2	no	—
193	C₄×D₄×C₆₇	—	2	2	no	—
194	C₄×D₄×C₆₇	—	2	2	no	—
195	C₄×D₄×C₆₇	—	2	2	no	—
196	C₄×D₄×C₆₇	—	2	2	no	—
197	C₄×D₄×C₆₇	—	2	2	no	—
198	C₄×D₄×C₆₇	—	2	2	no	—
199	C₄×D₄×C₆₇	—	2	2	no	—
200	C₄×D₄×C₆₇	C₂³	1	2	yes	—
201	C₄×D₄×C₆₇	C₂³	1	2	yes	—
202	C₄×D₄×C₆₇	C₂³	1	2	yes	—
203	C₄×D₄×C₆₇	C₂³	1	2	yes	—
204	C₄×D₄×C₆₇	C₂³	1	2	yes	—
205	C₄×D₄×C₆₇	C₂³	1	2	yes	—
206	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
207	C₄×D₄×C₆₇	C₂³	1	2	yes	—
208	#117×C₆₇	—	2	2	no	—
209	#117×C₆₇	—	2	2	no	—
210	#117×C₆₇	—	2	2	no	—
211	#117×C₆₇	—	2	2	no	—
212	#117×C₆₇	—	2	2	no	—
213	#117×C₆₇	C₂³	1	2	yes	—
214	#117×C₆₇	C₂³	1	2	yes	—
215	#117×C₆₇	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
217	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
218	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
219	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
221	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
224	C₂×C₄²×C₆₇	—	2	2	no	—
225	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
226	#107×C₆₇	C₂³	1	1	yes	characteristic
227	#107×C₆₇	C₂³	1	1	yes	characteristic
228	#107×C₆₇	C₂³	1	2	yes	—
229	#107×C₆₇	C₂³	1	1	yes	characteristic
230	#107×C₆₇	C₂³	1	2	yes	—
231	#107×C₆₇	C₂³	1	1	yes	characteristic
232	#106×C₆₇	C₂³	1	2	yes	—
233	#106×C₆₇	C₂³	1	2	yes	—
234	#106×C₆₇	C₂³	1	2	yes	—
235	#106×C₆₇	C₂³	1	2	yes	—
236	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
237	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
238	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
239	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
240	#103×C₆₇	C₂³	1	2	yes	—
241	#103×C₆₇	C₂³	1	2	yes	—
242	#103×C₆₇	C₂³	1	2	yes	—
243	#103×C₆₇	C₂³	1	2	yes	—
244	#103×C₆₇	C₂³	1	2	yes	—
245	#103×C₆₇	C₂³	1	2	yes	—
246	#103×C₆₇	C₂³	1	2	yes	—
247	#103×C₆₇	C₂³	1	2	yes	—
248	#102×C₆₇	C₂³	1	2	yes	—
249	#102×C₆₇	C₂³	1	2	yes	—
250	#102×C₆₇	C₂³	1	2	yes	—
251	#102×C₆₇	C₂³	1	2	yes	—
252	#102×C₆₇	C₂³	1	2	yes	—
253	#102×C₆₇	C₂³	1	2	yes	—
254	#102×C₆₇	C₂³	1	2	yes	—
255	#102×C₆₇	C₂³	1	2	yes	—
256	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
257	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
258	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
259	#97×C₆₇	C₂³	1	2	yes	—
260	#97×C₆₇	C₂³	1	2	yes	—
261	C₄×C₈×C₆₇	C₂³	1	2	yes	—
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	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
266	C₂⁴×C₆₇	—	2	2	no	—
267	#41×C₆₇	—	2	4	no	—
268	#41×C₆₇	—	2	4	no	—
269	#41×C₆₇	—	4	2	no	—
270	#41×C₆₇	—	4	2	no	—
271	C₂×Q₈×C₆₇	—	2	2	no	—
272	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
273	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
275	C₂×D₄×C₆₇	—	2	4	no	—
276	C₂×D₄×C₆₇	—	2	2	no	—
277	C₂×D₄×C₆₇	—	2	2	no	—
278	C₂×D₄×C₆₇	—	2	2	no	—
279	C₂×D₄×C₆₇	—	2	2	no	—
280	C₂×D₄×C₆₇	—	2	2	no	—
281	C₂×D₄×C₆₇	—	4	2	no	—
282	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
284	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
285	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₆₇	—	2	2	no	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	2	no	—
292	C₂²×C₄×C₆₇	—	2	2	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	Q₁₆×C₆₇	—	2	2	no	—
300	Q₁₆×C₆₇	—	4	1	no	—
301	Q₁₆×C₆₇	—	4	2	no	—
302	SD₁₆×C₆₇	—	2	4	no	—
303	SD₁₆×C₆₇	—	2	4	no	—
304	SD₁₆×C₆₇	—	2	4	no	—
305	SD₁₆×C₆₇	—	4	2	no	—
306	D₈×C₆₇	—	2	4	no	—
307	D₈×C₆₇	—	4	1	no	—
308	D₈×C₆₇	#41	1	4	yes	—
309	M₁₆×C₆₇	—	2	4	no	—
310	C₂×C₈×C₆₇	—	2	2	no	—
311	C₂×C₈×C₆₇	—	4	1	no	—
312	C₂×C₈×C₆₇	—	4	2	no	—
313	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
315	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
317	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
318	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	2	2	no	—
321	C₄⋊C₄×C₆₇	—	2	2	no	—
322	C₄⋊C₄×C₆₇	—	2	2	no	—
323	C₄⋊C₄×C₆₇	—	2	2	no	—
324	C₄⋊C₄×C₆₇	—	2	2	no	—
325	C₄⋊C₄×C₆₇	—	2	2	no	—
326	C₄⋊C₄×C₆₇	—	2	2	no	—
327	C₄⋊C₄×C₆₇	—	2	2	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
338	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
340	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
342	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
345	C₂²⋊C₄×C₆₇	—	2	2	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	2	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	2	no	—
351	C₂²⋊C₄×C₆₇	—	2	2	no	—
352	C₂²⋊C₄×C₆₇	—	2	2	no	—
353	C₂²⋊C₄×C₆₇	—	2	2	no	—
354	C₂²⋊C₄×C₆₇	—	2	2	no	—
355	C₂²⋊C₄×C₆₇	—	2	2	no	—
356	C₂²⋊C₄×C₆₇	—	2	2	no	—
357	C₂²⋊C₄×C₆₇	—	2	2	no	—
358	C₂²⋊C₄×C₆₇	—	2	2	no	—
359	C₂²⋊C₄×C₆₇	—	2	2	no	—
360	C₂²⋊C₄×C₆₇	—	2	2	no	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
365	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₄²×C₆₇	—	2	2	no	—
369	C₄²×C₆₇	—	2	2	no	—
370	C₄²×C₆₇	—	2	2	no	—
371	C₄²×C₆₇	—	2	2	no	—
372	C₄²×C₆₇	—	2	2	no	—
373	C₄²×C₆₇	—	2	2	no	—
374	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
377	C₄²×C₆₇	C₂⁴	1	2	yes	—
378	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	4	4	no	—
382	C₂³×C₆₇	—	8	2	no	—
383	C₂³×C₆₇	—	8	2	no	—
384	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
385	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	Q₈×C₆₇	—	2	2	no	—
387	Q₈×C₆₇	—	2	2	no	—
388	Q₈×C₆₇	—	2	2	no	—
389	Q₈×C₆₇	—	2	2	no	—
390	Q₈×C₆₇	—	4	1	no	—
391	Q₈×C₆₇	—	8	2	no	—
392	D₄×C₆₇	—	2	2	no	—
393	D₄×C₆₇	—	2	2	no	—
394	D₄×C₆₇	—	2	2	no	—
395	D₄×C₆₇	—	4	1	no	—
396	D₄×C₆₇	—	4	2	no	—
397	D₄×C₆₇	—	4	4	no	—
398	D₄×C₆₇	—	4	4	no	—
399	D₄×C₆₇	—	4	4	no	—
400	D₄×C₆₇	—	8	2	no	—
401	D₄×C₆₇	—	8	2	no	—
402	D₄×C₆₇	C₂×#41	1	4	yes	—
403	C₂×C₄×C₆₇	—	2	1	no	—
404	C₂×C₄×C₆₇	—	2	2	no	—
405	C₂×C₄×C₆₇	—	2	2	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	2	no	—
408	C₂×C₄×C₆₇	—	2	2	no	—
409	C₂×C₄×C₆₇	—	2	2	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	2	no	—
412	C₂×C₄×C₆₇	—	2	2	no	—
413	C₂×C₄×C₆₇	—	4	1	no	—
414	C₂×C₄×C₆₇	—	4	1	no	—
415	C₂×C₄×C₆₇	—	4	4	no	—
416	C₂×C₄×C₆₇	—	4	4	no	—
417	C₂×C₄×C₆₇	—	8	2	no	—
418	C₂×C₄×C₆₇	—	8	2	no	—
419	C₂×C₄×C₆₇	—	8	2	no	—
420	C₂×C₄×C₆₇	—	8	2	no	—
421	C₂×C₄×C₆₇	—	8	2	no	—
422	C₂×C₄×C₆₇	—	8	2	no	—
423	C₂×C₄×C₆₇	—	8	2	no	—
424	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
430	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
432	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
433	C₈×C₆₇	—	2	1	no	—
434	C₈×C₆₇	—	2	2	no	—
435	C₈×C₆₇	—	2	1	no	—
436	C₈×C₆₇	—	2	1	no	—
437	C₈×C₆₇	—	2	2	no	—
438	C₈×C₆₇	C₂×#41	1	2	yes	—
439	C₂²×C₆₇	—	2	1	no	—
440	C₂²×C₆₇	—	2	1	no	—
441	C₂²×C₆₇	—	2	2	no	—
442	C₂²×C₆₇	—	2	2	no	—
443	C₂²×C₆₇	—	2	1	no	—
444	C₂²×C₆₇	—	2	2	no	—
445	C₂²×C₆₇	—	2	4	no	—
446	C₂²×C₆₇	—	4	2	no	—
447	C₂²×C₆₇	—	4	2	no	—
448	C₂²×C₆₇	—	4	2	no	—
449	C₂²×C₆₇	—	4	2	no	—
450	C₂²×C₆₇	—	4	2	no	—
451	C₂²×C₆₇	—	16	4	no	—
452	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₆₇	—	2	1	no	—
454	C₄×C₆₇	—	2	1	no	—
455	C₄×C₆₇	—	2	1	no	—
456	C₄×C₆₇	—	2	1	no	—
457	C₄×C₆₇	—	2	2	no	—
458	C₄×C₆₇	—	2	2	no	—
459	C₄×C₆₇	—	2	1	no	—
460	C₄×C₆₇	—	2	2	no	—
461	C₄×C₆₇	—	4	2	no	—
462	C₄×C₆₇	—	4	2	no	—
463	C₄×C₆₇	—	4	2	no	—
464	C₄×C₆₇	—	4	2	no	—
465	C₄×C₆₇	—	4	2	no	—
466	C₄×C₆₇	—	4	2	no	—
467	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
468	C₄×C₆₇	#585	1	1	yes	characteristic
469	#61501	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
470	C₂×C₆₇	—	4	1	no	—
471	C₂×C₆₇	—	4	2	no	—
472	C₂×C₆₇	—	4	4	no	—
473	C₂×C₆₇	—	8	2	no	—
474	C₂×C₆₇	D₄×#41	1	1	yes	characteristic
475	C₂×C₆₇	#3584	1	1	yes	characteristic
476	C₂×C₆₇	#3584	1	1	yes	characteristic
477	#3521	C₂×C₆₇	1	2	yes	complemented
478	#3402	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#3389	C₂×C₆₇	1	1	yes	characteristic, complemented
480	#3360	C₂×C₆₇	1	2	yes	complemented
481	#3352	C₂×C₆₇	1	1	yes	characteristic, complemented
482	#3350	C₂×C₆₇	1	2	yes	complemented
483	#3302	C₂×C₆₇	1	2	yes	complemented
484	#3297	C₂×C₆₇	1	2	yes	complemented
485	#3296	C₂×C₆₇	1	2	yes	complemented
486	#3273	C₂×C₆₇	1	1	yes	characteristic, complemented
487	#3267	C₂×C₆₇	1	2	yes	complemented
488	#3178	C₂×C₆₇	1	2	yes	complemented
489	#3168	C₂×C₆₇	1	1	yes	characteristic, complemented
490	#3120	C₂×C₆₇	1	2	yes	complemented
491	#3118	C₂×C₆₇	1	2	yes	complemented
492	#3111	C₂×C₆₇	1	2	yes	complemented
493	#2966	C₂×C₆₇	1	1	yes	characteristic, complemented
494	#2946	C₂×C₆₇	1	2	yes	complemented
495	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
496	C₆₇	#61501	1	1	yes	characteristic, direct product factor, Sylow
497	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	—
498	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
499	#556	C₂²×C₆₇	1	2	yes	complemented
500	#556	C₂²×C₆₇	1	2	yes	complemented
501	#554	C₂²×C₆₇	1	2	yes	complemented
502	#553	—	2	2	no	—
503	#553	C₂²×C₆₇	1	2	yes	—
504	#552	—	2	2	no	—
505	#552	C₂²×C₆₇	1	2	yes	—
506	#551	—	2	2	no	—
507	#551	—	2	2	no	—
508	#547	C₂²×C₆₇	1	2	yes	—
509	#546	C₂²×C₆₇	1	2	yes	—
510	#546	C₂²×C₆₇	1	2	yes	complemented
511	#542	C₂²×C₆₇	1	2	yes	—
512	#541	C₂²×C₆₇	1	2	yes	complemented
513	#539	—	2	2	no	—
514	#538	—	2	2	no	—
515	#529	—	2	2	no	—
516	#529	C₂²×C₆₇	1	1	yes	characteristic
517	#529	C₂²×C₆₇	1	2	yes	complemented
518	C₂×#126	—	2	2	no	—
519	#520	C₂²×C₆₇	1	2	yes	—
520	#518	C₂²×C₆₇	1	2	yes	complemented
521	C₄×#41	C₂²×C₆₇	1	2	yes	complemented
522	#501	C₂²×C₆₇	1	2	yes	complemented
523	#499	C₂²×C₆₇	1	1	yes	characteristic, complemented
524	#497	C₂²×C₆₇	1	2	yes	complemented
525	#495	C₂²×C₆₇	1	1	yes	characteristic
526	#488	C₂²×C₆₇	1	2	yes	complemented
527	#488	C₂²×C₆₇	1	2	yes	complemented
528	#487	C₂²×C₆₇	1	2	yes	complemented
529	#485	C₂²×C₆₇	1	2	yes	complemented
530	#485	C₂²×C₆₇	1	2	yes	complemented
531	#484	C₂²×C₆₇	1	2	yes	complemented
532	#483	C₂²×C₆₇	1	2	yes	complemented
533	#482	C₂²×C₆₇	1	2	yes	—
534	#482	C₂²×C₆₇	1	2	yes	complemented
535	#479	C₂²×C₆₇	1	2	yes	complemented
536	#479	C₂²×C₆₇	1	2	yes	complemented
537	#478	C₂²×C₆₇	1	2	yes	complemented
538	#478	C₂²×C₆₇	1	2	yes	complemented
539	#476	C₂²×C₆₇	1	2	yes	complemented
540	#474	C₂²×C₆₇	1	2	yes	complemented
541	#470	C₂²×C₆₇	1	2	yes	complemented
542	#468	C₂²×C₆₇	1	2	yes	—
543	#467	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	#467	C₂²×C₆₇	1	2	yes	complemented
545	#466	C₂²×C₆₇	1	1	yes	characteristic
546	#465	C₂²×C₆₇	1	2	yes	—
547	#465	C₂²×C₆₇	1	2	yes	complemented
548	#464	C₂²×C₆₇	1	2	yes	complemented
549	#463	C₂²×C₆₇	1	2	yes	—
550	#463	C₂²×C₆₇	1	2	yes	—
551	#463	C₂²×C₆₇	1	2	yes	—
552	#462	C₂²×C₆₇	1	2	yes	complemented
553	#461	C₂²×C₆₇	1	2	yes	complemented
554	#452	C₂²×C₆₇	1	2	yes	—
555	#452	C₂²×C₆₇	1	2	yes	—
556	#452	C₂²×C₆₇	1	2	yes	complemented
557	#450	C₂²×C₆₇	1	2	yes	complemented
558	#449	C₂²×C₆₇	1	2	yes	—
559	#447	C₂²×C₆₇	1	2	yes	—
560	#446	C₂²×C₆₇	1	1	yes	characteristic, complemented
561	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	#442	C₂²×C₆₇	1	2	yes	—
563	#442	C₂²×C₆₇	1	2	yes	—
564	#441	C₂²×C₆₇	1	2	yes	complemented
565	#440	C₂²×C₆₇	1	2	yes	complemented
566	#440	C₂²×C₆₇	1	2	yes	complemented
567	#440	C₂²×C₆₇	1	2	yes	complemented
568	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
569	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
570	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
572	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
573	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
574	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
575	C₄×D₈	C₂²×C₆₇	1	2	yes	—
576	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
577	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
578	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
579	#436	C₂²×C₆₇	1	1	yes	characteristic
580	#435	C₂²×C₆₇	1	2	yes	complemented
581	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
582	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
583	#433	C₂²×C₆₇	1	2	yes	complemented
584	#432	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	#428	C₂²×C₆₇	1	2	yes	complemented
586	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
587	#416	C₂²×C₆₇	1	2	yes	—
588	#416	C₂²×C₆₇	1	2	yes	complemented
589	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
590	#405	C₂²×C₆₇	1	2	yes	complemented
591	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
592	C₂×#41	C₂³×C₆₇	1	2	yes	—
593	C₂×#41	C₂³×C₆₇	1	2	yes	—
594	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
595	AGL(1,ℤ/8)	—	2	8	no	—
596	#135	—	2	4	no	—
597	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
598	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
599	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
602	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
603	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
604	C₂×D₈	C₂³×C₆₇	1	2	yes	—
605	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
606	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
607	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
608	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
609	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
610	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
611	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
612	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#126	—	2	2	no	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	D₄×C₆₇	1	2	yes	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	D₄×C₆₇	1	1	yes	characteristic
628	#125	C₂³×C₆₇	1	2	yes	—
629	#125	C₂³×C₆₇	1	2	yes	—
630	#124	—	2	2	no	—
631	#124	—	2	2	no	—
632	#124	D₄×C₆₇	1	1	yes	characteristic
633	#124	C₂³×C₆₇	1	2	yes	—
634	#124	C₂³×C₆₇	1	2	yes	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	#123	D₄×C₆₇	1	2	yes	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	—	2	2	no	—
648	C₂²⋊Q₈	—	2	2	no	—
649	C₂²⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
650	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
651	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
652	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
653	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
654	#121	—	2	2	no	—
655	#121	—	2	2	no	—
656	#121	—	2	2	no	—
657	#121	—	2	2	no	—
658	#121	D₄×C₆₇	1	1	yes	characteristic
659	#121	C₂³×C₆₇	1	2	yes	—
660	#121	C₂³×C₆₇	1	2	yes	—
661	#120	—	2	2	no	—
662	#120	—	2	2	no	—
663	C₄×Q₈	—	2	2	no	—
664	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
665	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
666	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
667	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
668	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	C₂³×C₆₇	1	2	yes	—
678	C₄×D₄	C₂³×C₆₇	1	2	yes	—
679	C₄×D₄	C₂³×C₆₇	1	2	yes	—
680	C₄×D₄	C₂³×C₆₇	1	2	yes	—
681	C₄×D₄	C₂³×C₆₇	1	2	yes	—
682	C₄×D₄	C₂³×C₆₇	1	2	yes	—
683	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
684	C₄×D₄	C₂³×C₆₇	1	2	yes	—
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	C₂³×C₆₇	1	2	yes	—
691	#117	C₂³×C₆₇	1	2	yes	—
692	#117	C₂³×C₆₇	1	2	yes	—
693	C₂×C₄⋊C₄	—	2	2	no	—
694	C₂×C₄⋊C₄	—	2	2	no	—
695	C₂×C₄⋊C₄	—	2	2	no	—
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	—	2	2	no	—
698	C₂×C₂²⋊C₄	—	2	2	no	—
699	C₂×C₂²⋊C₄	—	2	2	no	—
700	C₂×C₂²⋊C₄	—	2	2	no	—
701	C₂×C₄²	—	2	2	no	—
702	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
703	#107	C₂³×C₆₇	1	1	yes	characteristic
704	#107	C₂³×C₆₇	1	1	yes	characteristic
705	#107	C₂³×C₆₇	1	2	yes	—
706	#107	C₂³×C₆₇	1	1	yes	characteristic
707	#107	C₂³×C₆₇	1	1	yes	characteristic
708	#107	C₂³×C₆₇	1	2	yes	—
709	#106	C₂³×C₆₇	1	2	yes	—
710	#106	C₂³×C₆₇	1	2	yes	—
711	#106	C₂³×C₆₇	1	2	yes	—
712	#106	C₂³×C₆₇	1	2	yes	—
713	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
714	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
715	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
716	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
717	#103	C₂³×C₆₇	1	2	yes	—
718	#103	C₂³×C₆₇	1	2	yes	—
719	#103	C₂³×C₆₇	1	2	yes	—
720	#103	C₂³×C₆₇	1	2	yes	—
721	#103	C₂³×C₆₇	1	2	yes	—
722	#103	C₂³×C₆₇	1	2	yes	—
723	#103	C₂³×C₆₇	1	2	yes	—
724	#103	C₂³×C₆₇	1	2	yes	—
725	#102	C₂³×C₆₇	1	2	yes	—
726	#102	C₂³×C₆₇	1	2	yes	—
727	#102	C₂³×C₆₇	1	2	yes	—
728	#102	C₂³×C₆₇	1	2	yes	—
729	#102	C₂³×C₆₇	1	2	yes	—
730	#102	C₂³×C₆₇	1	2	yes	—
731	#102	C₂³×C₆₇	1	2	yes	—
732	#102	C₂³×C₆₇	1	2	yes	—
733	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
734	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
735	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
736	#97	C₂³×C₆₇	1	2	yes	—
737	#97	C₂³×C₆₇	1	2	yes	—
738	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
739	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
740	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
742	C₄×C₈	C₂³×C₆₇	1	2	yes	—
743	C₂⁴	—	2	2	no	—
744	#41	—	2	4	no	—
745	#41	—	2	4	no	—
746	#41	—	4	2	no	—
747	#41	—	4	2	no	—
748	C₂×Q₈	—	2	2	no	—
749	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
750	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
751	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
752	C₂×D₄	—	2	4	no	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	2	no	—
758	C₂×D₄	—	4	2	no	—
759	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
760	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
761	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
762	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	2	no	—
767	C₂²×C₄	—	2	2	no	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
773	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
776	Q₁₆	—	2	2	no	—
777	Q₁₆	—	4	1	no	—
778	Q₁₆	—	4	2	no	—
779	SD₁₆	—	2	4	no	—
780	SD₁₆	—	2	4	no	—
781	SD₁₆	—	2	4	no	—
782	SD₁₆	—	4	2	no	—
783	D₈	—	2	4	no	—
784	D₈	—	4	1	no	—
785	D₈	#41×C₆₇	1	4	yes	—
786	M₁₆	—	2	4	no	—
787	C₂×C₈	—	2	2	no	—
788	C₂×C₈	—	4	1	no	—
789	C₂×C₈	—	4	2	no	—
790	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
793	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
794	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
795	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
813	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
815	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
816	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
817	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
818	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
821	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
841	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
842	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
843	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
844	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	2	2	no	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
852	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
853	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₄²	C₂⁴×C₆₇	1	2	yes	—
856	C₂³	—	2	2	no	—
857	C₂³	—	2	2	no	—
858	C₂³	—	4	4	no	—
859	C₂³	—	8	2	no	—
860	C₂³	—	8	2	no	—
861	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
862	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
863	Q₈	—	2	2	no	—
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	2	2	no	—
867	Q₈	—	4	1	no	—
868	Q₈	—	8	2	no	—
869	D₄	—	2	2	no	—
870	D₄	—	2	2	no	—
871	D₄	—	2	2	no	—
872	D₄	—	4	1	no	—
873	D₄	—	4	2	no	—
874	D₄	—	4	4	no	—
875	D₄	—	4	4	no	—
876	D₄	—	4	4	no	—
877	D₄	—	8	2	no	—
878	D₄	—	8	2	no	—
879	D₄	C₂×#41×C₆₇	1	4	yes	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	4	1	no	—
891	C₂×C₄	—	4	1	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	2	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	2	no	—
898	C₂×C₄	—	8	2	no	—
899	C₂×C₄	—	8	2	no	—
900	C₂×C₄	—	8	2	no	—
901	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
903	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
904	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
905	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
906	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
907	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
908	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
909	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
910	C₈	—	2	1	no	—
911	C₈	—	2	2	no	—
912	C₈	—	2	1	no	—
913	C₈	—	2	1	no	—
914	C₈	—	2	2	no	—
915	C₈	C₂×#41×C₆₇	1	2	yes	—
916	C₂²	—	2	1	no	—
917	C₂²	—	2	1	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	1	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	16	4	no	—
929	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
930	C₄	—	2	1	no	—
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
945	C₄	#585×C₆₇	1	1	yes	characteristic
946	C₂	—	4	2	no	—
947	C₂	—	4	1	no	—
948	C₂	—	4	4	no	—
949	C₂	—	8	2	no	—
950	C₂	D₄×#41×C₆₇	1	1	yes	characteristic
951	C₂	C₆₇×#3584	1	1	yes	characteristic
952	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×#3521	C₂	semidirect
2. C₆₇×#3402	C₂	semidirect
3. C₆₇×#3389	C₂	semidirect
4. C₆₇×#3360	C₂	semidirect
5. C₆₇×#3352	C₂	semidirect
6. C₆₇×#3350	C₂	semidirect
7. C₆₇×#3302	C₂	semidirect
8. C₆₇×#3297	C₂	semidirect
9. C₆₇×#3296	C₂	semidirect
10. C₆₇×#3273	C₂	semidirect
11. C₆₇×#3267	C₂	semidirect
12. C₆₇×#3178	C₂	semidirect
13. C₆₇×#3168	C₂	semidirect
14. C₆₇×#3120	C₂	semidirect
15. C₆₇×#3118	C₂	semidirect
16. C₆₇×#3111	C₂	semidirect
17. C₆₇×#2966	C₂	semidirect
18. C₆₇×#2946	C₂	semidirect
19. C₄×#135×C₆₇	C₂	semidirect
22. #556×C₆₇	C₂²	semidirect
23. #556×C₆₇	C₂²	semidirect
24. #554×C₆₇	C₂²	semidirect
33. #546×C₆₇	C₂²	semidirect
35. #541×C₆₇	C₂²	semidirect
40. #529×C₆₇	C₂²	semidirect
43. #518×C₆₇	C₂²	semidirect
44. C₄×#41×C₆₇	C₂²	semidirect
45. #501×C₆₇	C₂²	semidirect
46. #499×C₆₇	C₂²	semidirect
47. #497×C₆₇	C₂²	semidirect
49. #488×C₆₇	C₂²	semidirect
50. #488×C₆₇	C₂²	semidirect
51. #487×C₆₇	C₂²	semidirect
52. #485×C₆₇	C₂²	semidirect
53. #485×C₆₇	C₂²	semidirect
54. #484×C₆₇	C₂²	semidirect
55. #483×C₆₇	C₂²	semidirect
57. #482×C₆₇	C₂²	semidirect
58. #479×C₆₇	C₂²	semidirect
59. #479×C₆₇	C₂²	semidirect
60. #478×C₆₇	C₂²	semidirect
61. #478×C₆₇	C₂²	semidirect
62. #476×C₆₇	C₂²	semidirect
63. #474×C₆₇	C₂²	semidirect
64. #470×C₆₇	C₂²	semidirect
66. #467×C₆₇	C₂²	semidirect
67. #467×C₆₇	C₂²	semidirect
70. #465×C₆₇	C₂²	semidirect
71. #464×C₆₇	C₂²	semidirect
75. #462×C₆₇	C₂²	semidirect
76. #461×C₆₇	C₂²	semidirect
79. #452×C₆₇	C₂²	semidirect
80. #450×C₆₇	C₂²	semidirect
83. #446×C₆₇	C₂²	semidirect
84. C₈×Q₈×C₆₇	C₂²	semidirect
87. #441×C₆₇	C₂²	semidirect
88. #440×C₆₇	C₂²	semidirect
89. #440×C₆₇	C₂²	semidirect
90. #440×C₆₇	C₂²	semidirect
91. C₄×Q₁₆×C₆₇	C₂²	semidirect
92. C₄×Q₁₆×C₆₇	C₂²	semidirect
93. C₄×Q₁₆×C₆₇	C₂²	semidirect
94. C₄×SD₁₆×C₆₇	C₂²	semidirect
95. C₄×SD₁₆×C₆₇	C₂²	semidirect
96. C₄×SD₁₆×C₆₇	C₂²	semidirect
97. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. #435×C₆₇	C₂²	semidirect
105. C₈×D₄×C₆₇	C₂²	semidirect
106. #433×C₆₇	C₂²	semidirect
107. #432×C₆₇	C₂²	semidirect
108. #428×C₆₇	C₂²	semidirect
109. #427×C₆₇	C₂²	semidirect
111. #416×C₆₇	C₂²	semidirect
112. C₂×#102×C₆₇	C₂²	semidirect
113. #405×C₆₇	C₂²	semidirect
114. C₂×C₄×C₈×C₆₇	C₂²	semidirect
469. #61501	C₆₇	direct (N × H)
477. #3521	C₂×C₆₇	semidirect
478. #3402	C₂×C₆₇	semidirect
479. #3389	C₂×C₆₇	semidirect
480. #3360	C₂×C₆₇	semidirect
481. #3352	C₂×C₆₇	semidirect
482. #3350	C₂×C₆₇	semidirect
483. #3302	C₂×C₆₇	semidirect
484. #3297	C₂×C₆₇	semidirect
485. #3296	C₂×C₆₇	semidirect
486. #3273	C₂×C₆₇	semidirect
487. #3267	C₂×C₆₇	semidirect
488. #3178	C₂×C₆₇	semidirect
489. #3168	C₂×C₆₇	semidirect
490. #3120	C₂×C₆₇	semidirect
491. #3118	C₂×C₆₇	semidirect
492. #3111	C₂×C₆₇	semidirect
493. #2966	C₂×C₆₇	semidirect
494. #2946	C₂×C₆₇	semidirect
495. C₄×#135	C₂×C₆₇	semidirect
496. C₆₇	#61501	direct (N × H)
499. #556	C₂²×C₆₇	semidirect
500. #556	C₂²×C₆₇	semidirect
501. #554	C₂²×C₆₇	semidirect
510. #546	C₂²×C₆₇	semidirect
512. #541	C₂²×C₆₇	semidirect
517. #529	C₂²×C₆₇	semidirect
520. #518	C₂²×C₆₇	semidirect
521. C₄×#41	C₂²×C₆₇	semidirect
522. #501	C₂²×C₆₇	semidirect
523. #499	C₂²×C₆₇	semidirect
524. #497	C₂²×C₆₇	semidirect
526. #488	C₂²×C₆₇	semidirect
527. #488	C₂²×C₆₇	semidirect
528. #487	C₂²×C₆₇	semidirect
529. #485	C₂²×C₆₇	semidirect
530. #485	C₂²×C₆₇	semidirect
531. #484	C₂²×C₆₇	semidirect
532. #483	C₂²×C₆₇	semidirect
534. #482	C₂²×C₆₇	semidirect
535. #479	C₂²×C₆₇	semidirect
536. #479	C₂²×C₆₇	semidirect
537. #478	C₂²×C₆₇	semidirect
538. #478	C₂²×C₆₇	semidirect
539. #476	C₂²×C₆₇	semidirect
540. #474	C₂²×C₆₇	semidirect
541. #470	C₂²×C₆₇	semidirect
543. #467	C₂²×C₆₇	semidirect
544. #467	C₂²×C₆₇	semidirect
547. #465	C₂²×C₆₇	semidirect
548. #464	C₂²×C₆₇	semidirect
552. #462	C₂²×C₆₇	semidirect
553. #461	C₂²×C₆₇	semidirect
556. #452	C₂²×C₆₇	semidirect
557. #450	C₂²×C₆₇	semidirect
560. #446	C₂²×C₆₇	semidirect
561. C₈×Q₈	C₂²×C₆₇	semidirect
564. #441	C₂²×C₆₇	semidirect
565. #440	C₂²×C₆₇	semidirect
566. #440	C₂²×C₆₇	semidirect
567. #440	C₂²×C₆₇	semidirect
568. C₄×Q₁₆	C₂²×C₆₇	semidirect
569. C₄×Q₁₆	C₂²×C₆₇	semidirect
570. C₄×Q₁₆	C₂²×C₆₇	semidirect
571. C₄×SD₁₆	C₂²×C₆₇	semidirect
572. C₄×SD₁₆	C₂²×C₆₇	semidirect
573. C₄×SD₁₆	C₂²×C₆₇	semidirect
574. C₄×SD₁₆	C₂²×C₆₇	semidirect
580. #435	C₂²×C₆₇	semidirect
582. C₈×D₄	C₂²×C₆₇	semidirect
583. #433	C₂²×C₆₇	semidirect
584. #432	C₂²×C₆₇	semidirect
585. #428	C₂²×C₆₇	semidirect
586. #427	C₂²×C₆₇	semidirect
588. #416	C₂²×C₆₇	semidirect
589. C₂×#102	C₂²×C₆₇	semidirect
590. #405	C₂²×C₆₇	semidirect
591. C₂×C₄×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×#3521	2
C₆₇×#3402	2
C₆₇×#3389	2
C₆₇×#3360	2
C₆₇×#3352	2
C₆₇×#3350	2
C₆₇×#3302	2
C₆₇×#3297	2
C₆₇×#3296	2
C₆₇×#3273	2
C₆₇×#3267	2
C₆₇×#3178	2
C₆₇×#3168	2
C₆₇×#3120	2
C₆₇×#3118	2
C₆₇×#3111	2
C₆₇×#2966	2
C₆₇×#2946	2
C₄×#135×C₆₇	2
#61501	67

Subgroups — C67×#61501 #30740752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61501 #30740752