Subgroups — C₆₇×#61330 #30740581

Order 17152.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3374	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3372	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3369	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3367	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3364	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3363	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3360	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3359	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3137	C₂	1	2	yes	maximal, complemented
12	C₂×#487×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3082	C₂	1	2	yes	maximal, complemented
14	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3046	C₂	1	2	yes	maximal
16	C₆₇×#3039	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
19	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic
20	C₂×#137×C₆₇	C₂²	1	2	yes	—
21	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
22	Q₈²×C₆₇	C₂²	1	2	yes	—
23	#557×C₆₇	C₂²	1	2	yes	—
24	#557×C₆₇	C₂²	1	2	yes	—
25	#557×C₆₇	C₂²	1	2	yes	—
26	#556×C₆₇	C₂²	1	2	yes	—
27	#556×C₆₇	C₂²	1	2	yes	—
28	#554×C₆₇	—	2	2	no	—
29	#554×C₆₇	C₂²	1	2	yes	—
30	#552×C₆₇	—	2	2	no	—
31	#552×C₆₇	—	2	2	no	—
32	D₄×Q₈×C₆₇	—	2	2	no	—
33	D₄×Q₈×C₆₇	C₂²	1	2	yes	—
34	#544×C₆₇	—	2	2	no	—
35	#544×C₆₇	C₂²	1	2	yes	—
36	#541×C₆₇	—	2	2	no	—
37	#536×C₆₇	C₂²	1	2	yes	—
38	#533×C₆₇	—	2	1	no	—
39	#533×C₆₇	—	2	1	no	—
40	#533×C₆₇	—	2	1	no	—
41	#533×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Q₈×C₆₇	—	2	1	no	—
43	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
45	#520×C₆₇	C₂²	1	2	yes	—
46	#519×C₆₇	C₂²	1	2	yes	—
47	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
49	#491×C₆₇	C₂²	1	4	yes	—
50	#489×C₆₇	C₂²	1	4	yes	—
51	#488×C₆₇	C₂²	1	4	yes	—
52	#487×C₆₇	C₂²	1	4	yes	—
53	#487×C₆₇	C₂²	1	2	yes	—
54	#487×C₆₇	C₂²	1	2	yes	—
55	#487×C₆₇	C₂²	1	2	yes	—
56	#487×C₆₇	C₂²	1	2	yes	—
57	#479×C₆₇	C₂²	1	4	yes	—
58	#479×C₆₇	C₂²	1	4	yes	—
59	#477×C₆₇	C₂²	1	2	yes	—
60	#477×C₆₇	C₂²	1	4	yes	—
61	#476×C₆₇	C₂²	1	2	yes	—
62	#475×C₆₇	C₂²	1	2	yes	—
63	#475×C₆₇	C₂²	1	4	yes	—
64	#474×C₆₇	C₂²	1	2	yes	—
65	#464×C₆₇	C₂²	1	4	yes	—
66	#463×C₆₇	C₂²	1	4	yes	—
67	#462×C₆₇	C₂²	1	2	yes	—
68	#462×C₆₇	C₂²	1	2	yes	—
69	#462×C₆₇	C₂²	1	4	yes	—
70	#461×C₆₇	C₂²	1	2	yes	—
71	#461×C₆₇	C₂²	1	2	yes	—
72	#461×C₆₇	C₂²	1	4	yes	—
73	#446×C₆₇	C₂²	1	2	yes	—
74	#446×C₆₇	C₂²	1	2	yes	—
75	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
76	C₈×Q₈×C₆₇	C₂²	1	2	yes	—
77	#441×C₆₇	C₂²	1	4	yes	—
78	#440×C₆₇	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
80	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	—
81	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
82	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
83	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	—
84	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
85	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
86	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
87	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
88	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
89	#428×C₆₇	C₂²	1	2	yes	—
90	#427×C₆₇	C₂²	1	1	yes	characteristic
91	#424×C₆₇	C₂²	1	2	yes	—
92	#423×C₆₇	C₂²	1	1	yes	characteristic
93	#419×C₆₇	C₂²	1	2	yes	—
94	#417×C₆₇	C₂²	1	2	yes	—
95	#416×C₆₇	C₂²	1	1	yes	characteristic
96	#416×C₆₇	C₂²	1	1	yes	characteristic
97	C₂×#103×C₆₇	C₂²	1	2	yes	—
98	C₂×#103×C₆₇	C₂²	1	2	yes	—
99	#405×C₆₇	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
101	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₆₇	—	2	2	no	—
104	C₂²×Q₈×C₆₇	—	2	1	no	—
105	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
106	#137×C₆₇	—	2	8	no	—
107	#135×C₆₇	—	2	4	no	—
108	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
109	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
111	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
115	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
117	C₄⋊Q₈×C₆₇	—	2	2	no	—
118	C₄⋊Q₈×C₆₇	—	2	2	no	—
119	C₄⋊Q₈×C₆₇	—	2	2	no	—
120	C₄⋊Q₈×C₆₇	—	2	4	no	—
121	C₄⋊Q₈×C₆₇	—	2	1	no	—
122	C₄⋊Q₈×C₆₇	—	2	1	no	—
123	C₄⋊Q₈×C₆₇	—	2	1	no	—
124	C₄⋊Q₈×C₆₇	—	2	1	no	—
125	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
126	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
127	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
129	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
130	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₆₇	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
133	#126×C₆₇	—	2	4	no	—
134	#126×C₆₇	—	2	4	no	—
135	#125×C₆₇	—	2	2	no	—
136	#125×C₆₇	—	2	2	no	—
137	#125×C₆₇	—	2	2	no	—
138	#125×C₆₇	—	2	4	no	—
139	#125×C₆₇	—	2	4	no	—
140	#125×C₆₇	—	2	4	no	—
141	#125×C₆₇	D₄	1	2	yes	—
142	#125×C₆₇	C₂³	1	4	yes	—
143	#124×C₆₇	C₂³	1	4	yes	—
144	#123×C₆₇	—	2	4	no	—
145	C₂²⋊Q₈×C₆₇	—	2	2	no	—
146	C₂²⋊Q₈×C₆₇	—	2	2	no	—
147	C₂²⋊Q₈×C₆₇	—	2	2	no	—
148	C₂²⋊Q₈×C₆₇	—	2	2	no	—
149	C₂²⋊Q₈×C₆₇	—	2	2	no	—
150	C₂²⋊Q₈×C₆₇	—	2	2	no	—
151	C₂²⋊Q₈×C₆₇	—	2	4	no	—
152	C₂²⋊Q₈×C₆₇	—	2	4	no	—
153	C₂²⋊Q₈×C₆₇	—	2	4	no	—
154	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
155	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
156	C₄×Q₈×C₆₇	—	2	2	no	—
157	C₄×Q₈×C₆₇	—	2	2	no	—
158	C₄×Q₈×C₆₇	—	2	2	no	—
159	C₄×Q₈×C₆₇	—	2	2	no	—
160	C₄×Q₈×C₆₇	—	2	2	no	—
161	C₄×Q₈×C₆₇	—	2	2	no	—
162	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
165	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
167	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
169	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
170	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
171	C₄×D₄×C₆₇	—	2	1	no	—
172	C₄×D₄×C₆₇	—	2	1	no	—
173	C₄×D₄×C₆₇	—	2	1	no	—
174	C₄×D₄×C₆₇	—	2	1	no	—
175	C₄×D₄×C₆₇	—	2	4	no	—
176	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₆₇	C₂³	1	4	yes	—
179	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
181	#117×C₆₇	—	2	2	no	—
182	#117×C₆₇	—	2	2	no	—
183	#117×C₆₇	—	2	2	no	—
184	#117×C₆₇	—	2	4	no	—
185	#117×C₆₇	—	2	1	no	—
186	#117×C₆₇	—	2	1	no	—
187	#117×C₆₇	C₂³	1	1	yes	characteristic
188	#117×C₆₇	C₂³	1	1	yes	characteristic
189	#117×C₆₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
194	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
195	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	—	2	1	no	—
197	C₂×C₄²×C₆₇	—	2	1	no	—
198	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
199	#107×C₆₇	C₂³	1	4	yes	—
200	#107×C₆₇	C₂³	1	1	yes	characteristic
201	#107×C₆₇	C₂³	1	1	yes	characteristic
202	#106×C₆₇	C₂³	1	1	yes	characteristic
203	#106×C₆₇	C₂³	1	4	yes	—
204	#106×C₆₇	C₂³	1	1	yes	characteristic
205	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
206	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
207	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
208	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
209	#103×C₆₇	C₂³	1	4	yes	—
210	#103×C₆₇	C₂³	1	4	yes	—
211	#103×C₆₇	C₂³	1	4	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	4	yes	—
214	#103×C₆₇	C₂³	1	1	yes	characteristic
215	#103×C₆₇	C₂³	1	4	yes	—
216	#103×C₆₇	C₂³	1	4	yes	—
217	#103×C₆₇	C₂³	1	1	yes	characteristic
218	#103×C₆₇	C₂³	1	1	yes	characteristic
219	#103×C₆₇	C₂³	1	1	yes	characteristic
220	#102×C₆₇	C₂³	1	4	yes	—
221	#102×C₆₇	C₂³	1	1	yes	characteristic
222	#102×C₆₇	C₂³	1	1	yes	characteristic
223	#102×C₆₇	C₂³	1	1	yes	characteristic
224	#102×C₆₇	C₂³	1	1	yes	characteristic
225	#97×C₆₇	C₂³	1	4	yes	—
226	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×C₈×C₆₇	C₂³	1	4	yes	—
231	#41×C₆₇	—	2	2	no	—
232	#41×C₆₇	—	2	2	no	—
233	#41×C₆₇	—	2	2	no	—
234	#41×C₆₇	#41	1	4	yes	—
235	C₂×Q₈×C₆₇	—	2	2	no	—
236	C₂×Q₈×C₆₇	—	2	2	no	—
237	C₂×Q₈×C₆₇	—	2	4	no	—
238	C₂×Q₈×C₆₇	—	2	2	no	—
239	C₂×Q₈×C₆₇	—	2	4	no	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	8	2	no	—
242	C₂×Q₈×C₆₇	—	8	4	no	—
243	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
244	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₆₇	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₆₇	—	2	1	no	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	—	2	1	no	—
253	C₂²×C₄×C₆₇	—	2	2	no	—
254	C₂²×C₄×C₆₇	—	2	2	no	—
255	C₂²×C₄×C₆₇	—	2	1	no	—
256	C₂²×C₄×C₆₇	—	2	1	no	—
257	C₂²×C₄×C₆₇	—	2	1	no	—
258	C₂²×C₄×C₆₇	—	2	1	no	—
259	C₂²×C₄×C₆₇	—	2	1	no	—
260	C₂²×C₄×C₆₇	—	2	4	no	—
261	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
264	Q₁₆×C₆₇	—	2	2	no	—
265	Q₁₆×C₆₇	—	2	8	no	—
266	SD₁₆×C₆₇	—	2	2	no	—
267	SD₁₆×C₆₇	—	2	2	no	—
268	SD₁₆×C₆₇	—	2	8	no	—
269	D₈×C₆₇	—	2	2	no	—
270	M₁₆×C₆₇	—	2	4	no	—
271	C₂×C₈×C₆₇	—	2	2	no	—
272	C₂×C₈×C₆₇	—	2	2	no	—
273	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
276	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
277	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₆₇	—	2	2	no	—
279	C₄⋊C₄×C₆₇	—	2	2	no	—
280	C₄⋊C₄×C₆₇	—	2	2	no	—
281	C₄⋊C₄×C₆₇	—	2	2	no	—
282	C₄⋊C₄×C₆₇	—	2	4	no	—
283	C₄⋊C₄×C₆₇	—	2	2	no	—
284	C₄⋊C₄×C₆₇	—	2	4	no	—
285	C₄⋊C₄×C₆₇	—	2	2	no	—
286	C₄⋊C₄×C₆₇	—	2	2	no	—
287	C₄⋊C₄×C₆₇	—	2	1	no	—
288	C₄⋊C₄×C₆₇	—	2	1	no	—
289	C₄⋊C₄×C₆₇	—	2	1	no	—
290	C₄⋊C₄×C₆₇	—	2	1	no	—
291	C₄⋊C₄×C₆₇	—	2	4	no	—
292	C₄⋊C₄×C₆₇	—	2	4	no	—
293	C₄⋊C₄×C₆₇	—	2	4	no	—
294	C₄⋊C₄×C₆₇	—	2	4	no	—
295	C₄⋊C₄×C₆₇	—	2	4	no	—
296	C₄⋊C₄×C₆₇	—	2	4	no	—
297	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
302	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
303	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂²⋊C₄×C₆₇	—	2	1	no	—
309	C₂²⋊C₄×C₆₇	—	2	1	no	—
310	C₂²⋊C₄×C₆₇	—	2	1	no	—
311	C₂²⋊C₄×C₆₇	—	2	1	no	—
312	C₂²⋊C₄×C₆₇	—	2	4	no	—
313	C₂²⋊C₄×C₆₇	—	2	1	no	—
314	C₂²⋊C₄×C₆₇	—	2	1	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	4	no	—
317	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
318	C₄²×C₆₇	—	2	1	no	—
319	C₄²×C₆₇	—	2	1	no	—
320	C₄²×C₆₇	—	2	1	no	—
321	C₄²×C₆₇	—	2	1	no	—
322	C₄²×C₆₇	—	2	1	no	—
323	C₄²×C₆₇	—	2	1	no	—
324	C₄²×C₆₇	—	2	4	no	—
325	C₄²×C₆₇	—	2	4	no	—
326	C₄²×C₆₇	—	2	4	no	—
327	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
330	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
331	C₄²×C₆₇	C₂⁴	1	4	yes	—
332	C₂³×C₆₇	—	2	1	no	—
333	C₂³×C₆₇	—	2	1	no	—
334	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
335	Q₈×C₆₇	—	2	4	no	—
336	Q₈×C₆₇	—	2	4	no	—
337	Q₈×C₆₇	—	2	1	no	—
338	Q₈×C₆₇	—	2	4	no	—
339	Q₈×C₆₇	—	2	1	no	—
340	Q₈×C₆₇	—	2	4	no	—
341	Q₈×C₆₇	—	2	1	no	—
342	Q₈×C₆₇	—	4	4	no	—
343	Q₈×C₆₇	—	4	4	no	—
344	Q₈×C₆₇	—	8	2	no	—
345	Q₈×C₆₇	—	8	4	no	—
346	Q₈×C₆₇	C₂×#41	1	2	yes	—
347	D₄×C₆₇	—	2	4	no	—
348	D₄×C₆₇	—	2	1	no	—
349	D₄×C₆₇	—	2	1	no	—
350	D₄×C₆₇	—	2	1	no	—
351	D₄×C₆₇	—	4	2	no	—
352	D₄×C₆₇	C₂×#41	1	2	yes	—
353	C₂×C₄×C₆₇	—	2	1	no	—
354	C₂×C₄×C₆₇	—	2	4	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	1	no	—
358	C₂×C₄×C₆₇	—	2	1	no	—
359	C₂×C₄×C₆₇	—	2	1	no	—
360	C₂×C₄×C₆₇	—	2	4	no	—
361	C₂×C₄×C₆₇	—	2	1	no	—
362	C₂×C₄×C₆₇	—	2	1	no	—
363	C₂×C₄×C₆₇	—	2	4	no	—
364	C₂×C₄×C₆₇	—	4	4	no	—
365	C₂×C₄×C₆₇	—	4	2	no	—
366	C₂×C₄×C₆₇	—	4	2	no	—
367	C₂×C₄×C₆₇	—	4	2	no	—
368	C₂×C₄×C₆₇	—	4	2	no	—
369	C₂×C₄×C₆₇	—	4	2	no	—
370	C₂×C₄×C₆₇	—	8	4	no	—
371	C₂×C₄×C₆₇	—	8	2	no	—
372	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
374	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
380	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
381	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
382	C₈×C₆₇	—	2	1	no	—
383	C₈×C₆₇	—	2	1	no	—
384	C₈×C₆₇	—	2	4	no	—
385	C₈×C₆₇	—	2	1	no	—
386	C₈×C₆₇	—	2	1	no	—
387	C₂²×C₆₇	—	2	1	no	—
388	C₂²×C₆₇	—	2	1	no	—
389	C₂²×C₆₇	—	2	2	no	—
390	C₂²×C₆₇	—	4	1	no	—
391	C₂²×C₆₇	—	4	1	no	—
392	C₂²×C₆₇	—	4	1	no	—
393	C₂²×C₆₇	—	4	1	no	—
394	C₂²×C₆₇	—	4	1	no	—
395	C₂²×C₆₇	#548	1	2	yes	—
396	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
397	C₄×C₆₇	—	2	2	no	—
398	C₄×C₆₇	—	2	1	no	—
399	C₄×C₆₇	—	2	4	no	—
400	C₄×C₆₇	—	2	1	no	—
401	C₄×C₆₇	—	2	4	no	—
402	C₄×C₆₇	—	4	1	no	—
403	C₄×C₆₇	—	4	4	no	—
404	C₄×C₆₇	—	4	1	no	—
405	C₄×C₆₇	—	4	1	no	—
406	C₄×C₆₇	—	4	4	no	—
407	C₄×C₆₇	—	4	1	no	—
408	C₄×C₆₇	—	4	1	no	—
409	C₄×C₆₇	#548	1	2	yes	—
410	C₄×C₆₇	#577	1	2	yes	—
411	C₄×C₆₇	#578	1	2	yes	—
412	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
413	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
414	#61330	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
415	C₂×C₆₇	—	2	2	no	—
416	C₂×C₆₇	—	4	2	no	—
417	C₂×C₆₇	—	8	1	no	—
418	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
419	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
420	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
421	#3509	C₂×C₆₇	1	1	yes	characteristic, complemented
422	#3503	C₂×C₆₇	1	1	yes	characteristic, complemented
423	#3374	C₂×C₆₇	1	2	yes	complemented
424	#3372	C₂×C₆₇	1	2	yes	complemented
425	#3369	C₂×C₆₇	1	2	yes	complemented
426	#3367	C₂×C₆₇	1	2	yes	complemented
427	#3364	C₂×C₆₇	1	2	yes	complemented
428	#3363	C₂×C₆₇	1	2	yes	complemented
429	#3360	C₂×C₆₇	1	2	yes	complemented
430	#3359	C₂×C₆₇	1	2	yes	complemented
431	#3137	C₂×C₆₇	1	2	yes	complemented
432	C₂×#487	C₂×C₆₇	1	1	yes	characteristic, complemented
433	#3082	C₂×C₆₇	1	2	yes	complemented
434	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
435	#3046	C₂×C₆₇	1	2	yes	—
436	#3039	C₂×C₆₇	1	1	yes	characteristic, complemented
437	#2960	C₂×C₆₇	1	1	yes	characteristic, complemented
438	#2947	C₂×C₆₇	1	2	yes	complemented
439	C₄×#135	C₂×C₆₇	1	1	yes	characteristic
440	C₆₇	#61330	1	1	yes	characteristic, direct product factor, Sylow
441	C₂×#137	C₂²×C₆₇	1	2	yes	—
442	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
443	Q₈²	C₂²×C₆₇	1	2	yes	—
444	#557	C₂²×C₆₇	1	2	yes	—
445	#557	C₂²×C₆₇	1	2	yes	—
446	#557	C₂²×C₆₇	1	2	yes	—
447	#556	C₂²×C₆₇	1	2	yes	—
448	#556	C₂²×C₆₇	1	2	yes	—
449	#554	—	2	2	no	—
450	#554	C₂²×C₆₇	1	2	yes	—
451	#552	—	2	2	no	—
452	#552	—	2	2	no	—
453	D₄×Q₈	—	2	2	no	—
454	D₄×Q₈	C₂²×C₆₇	1	2	yes	—
455	#544	—	2	2	no	—
456	#544	C₂²×C₆₇	1	2	yes	—
457	#541	—	2	2	no	—
458	#536	C₂²×C₆₇	1	2	yes	—
459	#533	—	2	1	no	—
460	#533	—	2	1	no	—
461	#533	—	2	1	no	—
462	#533	C₂²×C₆₇	1	1	yes	characteristic
463	C₂×C₄⋊Q₈	—	2	1	no	—
464	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
465	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
466	#520	C₂²×C₆₇	1	2	yes	—
467	#519	C₂²×C₆₇	1	2	yes	—
468	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
469	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
470	#491	C₂²×C₆₇	1	4	yes	—
471	#489	C₂²×C₆₇	1	4	yes	—
472	#488	C₂²×C₆₇	1	4	yes	—
473	#487	C₂²×C₆₇	1	4	yes	—
474	#487	C₂²×C₆₇	1	2	yes	—
475	#487	C₂²×C₆₇	1	2	yes	—
476	#487	C₂²×C₆₇	1	2	yes	—
477	#487	C₂²×C₆₇	1	2	yes	—
478	#479	C₂²×C₆₇	1	4	yes	—
479	#479	C₂²×C₆₇	1	4	yes	—
480	#477	C₂²×C₆₇	1	2	yes	—
481	#477	C₂²×C₆₇	1	4	yes	—
482	#476	C₂²×C₆₇	1	2	yes	—
483	#475	C₂²×C₆₇	1	2	yes	—
484	#475	C₂²×C₆₇	1	4	yes	—
485	#474	C₂²×C₆₇	1	2	yes	—
486	#464	C₂²×C₆₇	1	4	yes	—
487	#463	C₂²×C₆₇	1	4	yes	—
488	#462	C₂²×C₆₇	1	2	yes	—
489	#462	C₂²×C₆₇	1	4	yes	—
490	#462	C₂²×C₆₇	1	2	yes	—
491	#461	C₂²×C₆₇	1	2	yes	—
492	#461	C₂²×C₆₇	1	4	yes	—
493	#461	C₂²×C₆₇	1	2	yes	—
494	#446	C₂²×C₆₇	1	2	yes	—
495	#446	C₂²×C₆₇	1	2	yes	—
496	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
497	C₈×Q₈	C₂²×C₆₇	1	2	yes	—
498	#441	C₂²×C₆₇	1	4	yes	—
499	#440	C₂²×C₆₇	1	4	yes	—
500	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
501	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	—
502	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
503	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
504	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	—
505	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
506	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
507	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
508	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
509	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
510	#428	C₂²×C₆₇	1	2	yes	—
511	#427	C₂²×C₆₇	1	1	yes	characteristic
512	#424	C₂²×C₆₇	1	2	yes	—
513	#423	C₂²×C₆₇	1	1	yes	characteristic
514	#419	C₂²×C₆₇	1	2	yes	—
515	#417	C₂²×C₆₇	1	2	yes	—
516	#416	C₂²×C₆₇	1	1	yes	characteristic
517	#416	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×#103	C₂²×C₆₇	1	2	yes	—
519	C₂×#103	C₂²×C₆₇	1	2	yes	—
520	#405	C₂²×C₆₇	1	2	yes	—
521	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
522	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
523	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
524	C₂²×Q₈	—	2	2	no	—
525	C₂²×Q₈	—	2	1	no	—
526	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
527	#137	—	2	8	no	—
528	#135	—	2	4	no	—
529	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
530	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
531	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
532	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
533	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
534	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
535	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
536	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
537	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
538	C₄⋊Q₈	—	2	2	no	—
539	C₄⋊Q₈	—	2	2	no	—
540	C₄⋊Q₈	—	2	2	no	—
541	C₄⋊Q₈	—	2	4	no	—
542	C₄⋊Q₈	—	2	1	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	—	2	1	no	—
546	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
547	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
550	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
551	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
553	C₄⋊Q₈	C₂³×C₆₇	1	4	yes	—
554	#126	—	2	4	no	—
555	#126	—	2	4	no	—
556	#125	—	2	2	no	—
557	#125	—	2	2	no	—
558	#125	—	2	2	no	—
559	#125	—	2	4	no	—
560	#125	—	2	4	no	—
561	#125	—	2	4	no	—
562	#125	D₄×C₆₇	1	2	yes	—
563	#125	C₂³×C₆₇	1	4	yes	—
564	#124	C₂³×C₆₇	1	4	yes	—
565	#123	—	2	4	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	2	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	4	no	—
574	C₂²⋊Q₈	—	2	4	no	—
575	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
576	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
584	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
585	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
586	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
588	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
589	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
590	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
591	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	4	no	—
597	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
599	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
600	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₆₇	1	4	yes	—
602	#117	—	2	2	no	—
603	#117	—	2	2	no	—
604	#117	—	2	2	no	—
605	#117	—	2	4	no	—
606	#117	—	2	1	no	—
607	#117	—	2	1	no	—
608	#117	C₂³×C₆₇	1	1	yes	characteristic
609	#117	C₂³×C₆₇	1	1	yes	characteristic
610	#117	C₂³×C₆₇	1	2	yes	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	—	2	1	no	—
619	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
620	#107	C₂³×C₆₇	1	1	yes	characteristic
621	#107	C₂³×C₆₇	1	1	yes	characteristic
622	#107	C₂³×C₆₇	1	4	yes	—
623	#106	C₂³×C₆₇	1	1	yes	characteristic
624	#106	C₂³×C₆₇	1	1	yes	characteristic
625	#106	C₂³×C₆₇	1	4	yes	—
626	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
627	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
628	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
629	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
630	#103	C₂³×C₆₇	1	4	yes	—
631	#103	C₂³×C₆₇	1	4	yes	—
632	#103	C₂³×C₆₇	1	4	yes	—
633	#103	C₂³×C₆₇	1	4	yes	—
634	#103	C₂³×C₆₇	1	1	yes	characteristic
635	#103	C₂³×C₆₇	1	1	yes	characteristic
636	#103	C₂³×C₆₇	1	1	yes	characteristic
637	#103	C₂³×C₆₇	1	1	yes	characteristic
638	#103	C₂³×C₆₇	1	4	yes	—
639	#103	C₂³×C₆₇	1	4	yes	—
640	#103	C₂³×C₆₇	1	4	yes	—
641	#102	C₂³×C₆₇	1	1	yes	characteristic
642	#102	C₂³×C₆₇	1	1	yes	characteristic
643	#102	C₂³×C₆₇	1	1	yes	characteristic
644	#102	C₂³×C₆₇	1	1	yes	characteristic
645	#102	C₂³×C₆₇	1	4	yes	—
646	#97	C₂³×C₆₇	1	4	yes	—
647	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
648	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
649	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
650	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
651	C₄×C₈	C₂³×C₆₇	1	4	yes	—
652	#41	—	2	2	no	—
653	#41	—	2	2	no	—
654	#41	—	2	2	no	—
655	#41	#41×C₆₇	1	4	yes	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	4	no	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	8	2	no	—
663	C₂×Q₈	—	8	4	no	—
664	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
665	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
666	C₂×Q₈	C₂⁴×C₆₇	1	4	yes	—
667	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
668	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
672	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
683	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
685	Q₁₆	—	2	2	no	—
686	Q₁₆	—	2	8	no	—
687	SD₁₆	—	2	2	no	—
688	SD₁₆	—	2	2	no	—
689	SD₁₆	—	2	8	no	—
690	D₈	—	2	2	no	—
691	M₁₆	—	2	4	no	—
692	C₂×C₈	—	2	2	no	—
693	C₂×C₈	—	2	2	no	—
694	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
695	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
696	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
697	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
698	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
721	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
723	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
725	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
727	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	1	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	1	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	4	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	4	no	—
748	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
749	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
750	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
752	C₄²	C₂⁴×C₆₇	1	4	yes	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	4	no	—
758	Q₈	—	2	1	no	—
759	Q₈	—	2	4	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	2	1	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	4	no	—
765	Q₈	—	8	2	no	—
766	Q₈	—	8	4	no	—
767	Q₈	C₂×#41×C₆₇	1	2	yes	—
768	D₄	—	2	4	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	4	2	no	—
773	D₄	C₂×#41×C₆₇	1	2	yes	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	4	4	no	—
786	C₂×C₄	—	4	2	no	—
787	C₂×C₄	—	4	2	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	4	no	—
792	C₂×C₄	—	8	2	no	—
793	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
794	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
795	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
799	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
800	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
801	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
802	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	4	no	—
806	C₈	—	2	1	no	—
807	C₈	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	—	4	1	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	#548×C₆₇	1	2	yes	—
817	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
818	C₄	—	2	1	no	—
819	C₄	—	2	4	no	—
820	C₄	—	2	1	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	4	no	—
826	C₄	—	4	1	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	4	no	—
830	C₄	#548×C₆₇	1	2	yes	—
831	C₄	#577×C₆₇	1	2	yes	—
832	C₄	#578×C₆₇	1	2	yes	—
833	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
834	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
835	C₂	—	2	2	no	—
836	C₂	—	4	2	no	—
837	C₂	—	8	1	no	—
838	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
839	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
840	C₂	C₂×#578×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₂×#135×C₆₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #533×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3509	C₂	semidirect
2. C₆₇×#3503	C₂	semidirect
3. C₆₇×#3374	C₂	semidirect
4. C₆₇×#3372	C₂	semidirect
5. C₆₇×#3369	C₂	semidirect
6. C₆₇×#3367	C₂	semidirect
7. C₆₇×#3364	C₂	semidirect
8. C₆₇×#3363	C₂	semidirect
9. C₆₇×#3360	C₂	semidirect
10. C₆₇×#3359	C₂	semidirect
11. C₆₇×#3137	C₂	semidirect
12. C₂×#487×C₆₇	C₂	semidirect
13. C₆₇×#3082	C₂	semidirect
14. C₆₇×#3079	C₂	semidirect
16. C₆₇×#3039	C₂	semidirect
17. C₆₇×#2960	C₂	semidirect
18. C₆₇×#2947	C₂	semidirect
414. #61330	C₆₇	direct (N × H)
421. #3509	C₂×C₆₇	semidirect
422. #3503	C₂×C₆₇	semidirect
423. #3374	C₂×C₆₇	semidirect
424. #3372	C₂×C₆₇	semidirect
425. #3369	C₂×C₆₇	semidirect
426. #3367	C₂×C₆₇	semidirect
427. #3364	C₂×C₆₇	semidirect
428. #3363	C₂×C₆₇	semidirect
429. #3360	C₂×C₆₇	semidirect
430. #3359	C₂×C₆₇	semidirect
431. #3137	C₂×C₆₇	semidirect
432. C₂×#487	C₂×C₆₇	semidirect
433. #3082	C₂×C₆₇	semidirect
434. #3079	C₂×C₆₇	semidirect
436. #3039	C₂×C₆₇	semidirect
437. #2960	C₂×C₆₇	semidirect
438. #2947	C₂×C₆₇	semidirect
440. C₆₇	#61330	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×#3509	2
C₆₇×#3503	2
C₆₇×#3374	2
C₆₇×#3372	2
C₆₇×#3369	2
C₆₇×#3367	2
C₆₇×#3364	2
C₆₇×#3363	2
C₆₇×#3360	2
C₆₇×#3359	2
C₆₇×#3137	2
C₂×#487×C₆₇	2
C₆₇×#3082	2
C₆₇×#3079	2
C₆₇×#3046	2
C₆₇×#3039	2
C₆₇×#2960	2
C₆₇×#2947	2
C₄×#135×C₆₇	2
#61330	67

Subgroups — C67×#61330 #30740581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61330 #30740581