Subgroups — C₆₇×#61596 #30740847

Order 17152.

2168 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#550×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3332	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3317	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3304	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3284	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3278	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3271	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3194	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3187	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3007	C₂	1	2	yes	maximal, complemented
16	C₆₇×#3002	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂×#137×C₆₇	C₂²	1	4	yes	complemented
20	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
21	#556×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	#554×C₆₇	—	2	1	no	—
23	#552×C₆₇	C₂²	1	2	yes	complemented
24	#551×C₆₇	—	2	2	no	—
25	#550×C₆₇	—	2	1	no	—
26	#550×C₆₇	—	2	2	no	—
27	#550×C₆₇	—	2	1	no	—
28	#550×C₆₇	C₂²	1	4	yes	—
29	#550×C₆₇	C₂²	1	2	yes	—
30	#550×C₆₇	C₂²	1	2	yes	—
31	D₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	#548×C₆₇	C₂²	1	2	yes	complemented
33	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#547×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#546×C₆₇	—	2	1	no	—
36	#542×C₆₇	—	2	1	no	—
37	#539×C₆₇	—	2	2	no	—
38	#533×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#127×C₆₇	—	2	1	no	—
40	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
41	#529×C₆₇	C₂²	1	1	yes	characteristic
42	#525×C₆₇	C₂²	1	2	yes	—
43	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
44	C₂×#121×C₆₇	—	2	2	no	—
45	C₂×#121×C₆₇	C₂²	1	2	yes	—
46	#520×C₆₇	—	2	1	no	—
47	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₆₇	—	2	1	no	—
49	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
50	#496×C₆₇	C₂²	1	2	yes	complemented
51	#492×C₆₇	C₂²	1	2	yes	complemented
52	#490×C₆₇	C₂²	1	2	yes	complemented
53	#486×C₆₇	C₂²	1	2	yes	complemented
54	#483×C₆₇	C₂²	1	1	yes	characteristic
55	#483×C₆₇	C₂²	1	2	yes	—
56	#482×C₆₇	C₂²	1	4	yes	complemented
57	#481×C₆₇	C₂²	1	4	yes	complemented
58	#480×C₆₇	C₂²	1	1	yes	characteristic
59	#479×C₆₇	C₂²	1	2	yes	complemented
60	#475×C₆₇	C₂²	1	2	yes	complemented
61	#469×C₆₇	C₂²	1	4	yes	complemented
62	#468×C₆₇	C₂²	1	4	yes	complemented
63	#465×C₆₇	C₂²	1	4	yes	complemented
64	#465×C₆₇	C₂²	1	4	yes	complemented
65	#464×C₆₇	C₂²	1	2	yes	complemented
66	#462×C₆₇	C₂²	1	2	yes	complemented
67	#460×C₆₇	C₂²	1	4	yes	complemented
68	#460×C₆₇	C₂²	1	2	yes	complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#452×C₆₇	C₂²	1	4	yes	complemented
72	#452×C₆₇	C₂²	1	4	yes	complemented
73	#451×C₆₇	C₂²	1	1	yes	characteristic
74	#451×C₆₇	C₂²	1	2	yes	—
75	#450×C₆₇	C₂²	1	2	yes	—
76	#450×C₆₇	C₂²	1	2	yes	—
77	#450×C₆₇	C₂²	1	2	yes	—
78	#449×C₆₇	C₂²	1	4	yes	complemented
79	#449×C₆₇	C₂²	1	4	yes	complemented
80	#448×C₆₇	C₂²	1	1	yes	characteristic
81	#448×C₆₇	C₂²	1	4	yes	complemented
82	#447×C₆₇	C₂²	1	2	yes	—
83	#441×C₆₇	C₂²	1	4	yes	complemented
84	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
85	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
86	#436×C₆₇	C₂²	1	2	yes	complemented
87	#435×C₆₇	C₂²	1	4	yes	complemented
88	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
89	#432×C₆₇	C₂²	1	1	yes	characteristic
90	#431×C₆₇	C₂²	1	1	yes	characteristic
91	#417×C₆₇	C₂²	1	4	yes	complemented
92	#416×C₆₇	C₂²	1	4	yes	complemented
93	#407×C₆₇	C₂²	1	2	yes	—
94	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
95	C₂×#41×C₆₇	—	2	1	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	2	no	—
98	C₂×#41×C₆₇	—	4	8	no	—
99	C₂×#41×C₆₇	C₂³	1	4	yes	—
100	C₂×#41×C₆₇	C₂³	1	4	yes	—
101	C₂×#41×C₆₇	C₂³	1	2	yes	—
102	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
104	C₂²×D₄×C₆₇	—	2	2	no	—
105	C₂²×D₄×C₆₇	—	2	2	no	—
106	C₂²×D₄×C₆₇	—	2	1	no	—
107	C₂²×D₄×C₆₇	—	2	1	no	—
108	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₆₇	—	2	2	no	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	#137×C₆₇	—	4	8	no	—
113	#135×C₆₇	—	4	8	no	—
114	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
115	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
120	C₂×D₈×C₆₇	C₂³	1	4	yes	—
121	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
122	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
123	C₄⋊Q₈×C₆₇	—	2	1	no	—
124	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
126	#127×C₆₇	—	2	2	no	—
127	#127×C₆₇	—	2	2	no	—
128	#127×C₆₇	—	2	4	no	—
129	#127×C₆₇	—	2	1	no	—
130	#127×C₆₇	—	2	1	no	—
131	#127×C₆₇	C₂³	1	2	yes	—
132	#127×C₆₇	C₂³	1	2	yes	—
133	#126×C₆₇	—	2	2	no	—
134	#126×C₆₇	—	2	2	no	—
135	#126×C₆₇	—	2	1	no	—
136	#125×C₆₇	—	2	2	no	—
137	#125×C₆₇	—	2	1	no	—
138	#125×C₆₇	C₂³	1	1	yes	characteristic
139	#124×C₆₇	—	2	1	no	—
140	#124×C₆₇	—	2	2	no	—
141	#124×C₆₇	C₂³	1	1	yes	characteristic
142	#123×C₆₇	—	2	2	no	—
143	#123×C₆₇	—	2	2	no	—
144	#123×C₆₇	—	2	1	no	—
145	#123×C₆₇	—	2	2	no	—
146	#123×C₆₇	—	2	2	no	—
147	C₂²⋊Q₈×C₆₇	—	2	2	no	—
148	C₂²⋊Q₈×C₆₇	—	2	2	no	—
149	C₂²⋊Q₈×C₆₇	—	2	1	no	—
150	C₂²⋊Q₈×C₆₇	—	2	2	no	—
151	C₂²⋊Q₈×C₆₇	—	2	1	no	—
152	C₂²⋊Q₈×C₆₇	—	2	2	no	—
153	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
156	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
157	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
158	#121×C₆₇	—	2	2	no	—
159	#121×C₆₇	—	2	1	no	—
160	#121×C₆₇	—	2	2	no	—
161	#121×C₆₇	—	2	2	no	—
162	#121×C₆₇	—	2	4	no	—
163	#121×C₆₇	—	2	4	no	—
164	#121×C₆₇	—	2	4	no	—
165	#121×C₆₇	—	2	4	no	—
166	#121×C₆₇	C₂³	1	1	yes	characteristic
167	#121×C₆₇	C₂³	1	4	yes	—
168	#121×C₆₇	C₂³	1	2	yes	—
169	#121×C₆₇	C₂³	1	4	yes	—
170	#120×C₆₇	—	2	2	no	—
171	C₄×Q₈×C₆₇	—	2	1	no	—
172	C₄×Q₈×C₆₇	—	2	1	no	—
173	C₄×Q₈×C₆₇	—	2	1	no	—
174	C₄×Q₈×C₆₇	—	2	1	no	—
175	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
177	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
178	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
179	C₄×D₄×C₆₇	—	2	1	no	—
180	C₄×D₄×C₆₇	—	2	2	no	—
181	C₄×D₄×C₆₇	—	2	2	no	—
182	C₄×D₄×C₆₇	—	2	1	no	—
183	C₄×D₄×C₆₇	—	2	2	no	—
184	C₄×D₄×C₆₇	—	2	4	no	—
185	C₄×D₄×C₆₇	—	2	2	no	—
186	C₄×D₄×C₆₇	—	2	2	no	—
187	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
188	C₄×D₄×C₆₇	D₄	1	2	yes	—
189	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
190	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
191	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₄×D₄×C₆₇	C₂³	1	2	yes	—
194	#117×C₆₇	—	2	1	no	—
195	#117×C₆₇	—	2	2	no	—
196	#117×C₆₇	—	2	1	no	—
197	#117×C₆₇	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
199	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
200	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
201	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
207	C₂×C₄²×C₆₇	—	2	1	no	—
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	#107×C₆₇	C₂³	1	2	yes	—
210	#106×C₆₇	C₂³	1	2	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#103×C₆₇	C₂³	1	2	yes	—
216	#103×C₆₇	C₂³	1	4	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#103×C₆₇	C₂³	1	2	yes	—
219	#102×C₆₇	C₂³	1	2	yes	—
220	#102×C₆₇	C₂³	1	4	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	4	yes	—
223	#102×C₆₇	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
226	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
227	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
229	#97×C₆₇	C₂³	1	2	yes	—
230	C₄×C₈×C₆₇	C₂³	1	2	yes	—
231	C₂⁴×C₆₇	—	2	2	no	—
232	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
233	#41×C₆₇	—	2	8	no	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	4	4	no	—
236	#41×C₆₇	—	4	4	no	—
237	#41×C₆₇	—	4	4	no	—
238	#41×C₆₇	—	4	4	no	—
239	#41×C₆₇	—	4	8	no	—
240	#41×C₆₇	—	4	8	no	—
241	C₂×Q₈×C₆₇	—	2	4	no	—
242	C₂×Q₈×C₆₇	—	2	1	no	—
243	C₂×Q₈×C₆₇	—	2	1	no	—
244	C₂×Q₈×C₆₇	—	2	2	no	—
245	C₂×Q₈×C₆₇	—	4	4	no	—
246	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
248	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
249	C₂×D₄×C₆₇	—	2	1	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	4	no	—
253	C₂×D₄×C₆₇	—	2	2	no	—
254	C₂×D₄×C₆₇	—	2	4	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	2	no	—
257	C₂×D₄×C₆₇	—	2	2	no	—
258	C₂×D₄×C₆₇	—	2	2	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	4	2	no	—
262	C₂×D₄×C₆₇	—	4	4	no	—
263	C₂×D₄×C₆₇	—	4	4	no	—
264	C₂×D₄×C₆₇	—	4	8	no	—
265	C₂×D₄×C₆₇	—	8	2	no	—
266	C₂×D₄×C₆₇	—	8	4	no	—
267	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
268	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
269	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
271	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	—	2	1	no	—
273	C₂²×C₄×C₆₇	—	2	1	no	—
274	C₂²×C₄×C₆₇	—	2	2	no	—
275	C₂²×C₄×C₆₇	—	2	2	no	—
276	C₂²×C₄×C₆₇	—	2	1	no	—
277	C₂²×C₄×C₆₇	—	2	4	no	—
278	C₂²×C₄×C₆₇	—	2	4	no	—
279	C₂²×C₄×C₆₇	—	2	2	no	—
280	C₂²×C₄×C₆₇	—	4	4	no	—
281	C₂²×C₄×C₆₇	—	4	8	no	—
282	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
290	Q₁₆×C₆₇	—	2	8	no	—
291	Q₁₆×C₆₇	—	2	4	no	—
292	SD₁₆×C₆₇	—	2	4	no	—
293	SD₁₆×C₆₇	—	4	4	no	—
294	SD₁₆×C₆₇	—	4	4	no	—
295	SD₁₆×C₆₇	—	4	4	no	—
296	D₈×C₆₇	—	4	4	no	—
297	M₁₆×C₆₇	—	4	4	no	—
298	C₂×C₈×C₆₇	—	4	4	no	—
299	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
300	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
301	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
302	C₄⋊C₄×C₆₇	—	2	1	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	1	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	2	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	1	no	—
312	C₄⋊C₄×C₆₇	—	2	1	no	—
313	C₄⋊C₄×C₆₇	—	2	1	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	1	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	1	no	—
318	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
321	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
323	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
325	C₂²⋊C₄×C₆₇	—	2	1	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	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	1	no	—
334	C₂²⋊C₄×C₆₇	—	2	1	no	—
335	C₂²⋊C₄×C₆₇	—	2	1	no	—
336	C₂²⋊C₄×C₆₇	—	2	2	no	—
337	C₂²⋊C₄×C₆₇	—	2	1	no	—
338	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
339	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
340	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
341	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
342	C₄²×C₆₇	—	2	2	no	—
343	C₄²×C₆₇	—	2	2	no	—
344	C₄²×C₆₇	—	2	2	no	—
345	C₄²×C₆₇	—	2	2	no	—
346	C₄²×C₆₇	—	2	1	no	—
347	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂³×C₆₇	—	2	4	no	—
352	C₂³×C₆₇	—	2	1	no	—
353	C₂³×C₆₇	—	2	4	no	—
354	C₂³×C₆₇	—	4	2	no	—
355	C₂³×C₆₇	—	4	2	no	—
356	C₂³×C₆₇	—	4	4	no	—
357	C₂³×C₆₇	—	4	4	no	—
358	C₂³×C₆₇	—	4	4	no	—
359	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
360	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
361	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
362	Q₈×C₆₇	—	2	4	no	—
363	Q₈×C₆₇	—	2	2	no	—
364	Q₈×C₆₇	—	2	2	no	—
365	Q₈×C₆₇	—	2	4	no	—
366	Q₈×C₆₇	—	4	2	no	—
367	Q₈×C₆₇	—	8	2	no	—
368	Q₈×C₆₇	H(5,𝔽₂)	1	4	yes	—
369	D₄×C₆₇	—	2	2	no	—
370	D₄×C₆₇	—	2	2	no	—
371	D₄×C₆₇	—	2	2	no	—
372	D₄×C₆₇	—	2	4	no	—
373	D₄×C₆₇	—	2	4	no	—
374	D₄×C₆₇	—	4	2	no	—
375	D₄×C₆₇	—	4	8	no	—
376	D₄×C₆₇	—	4	8	no	—
377	D₄×C₆₇	—	4	4	no	—
378	D₄×C₆₇	—	4	4	no	—
379	D₄×C₆₇	—	4	4	no	—
380	D₄×C₆₇	—	4	2	no	—
381	D₄×C₆₇	—	4	4	no	—
382	D₄×C₆₇	—	8	2	no	—
383	D₄×C₆₇	—	8	2	no	—
384	D₄×C₆₇	—	8	4	no	—
385	D₄×C₆₇	—	8	4	no	—
386	D₄×C₆₇	—	8	2	no	—
387	C₂×C₄×C₆₇	—	2	4	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	2	2	no	—
391	C₂×C₄×C₆₇	—	2	4	no	—
392	C₂×C₄×C₆₇	—	2	4	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	1	no	—
395	C₂×C₄×C₆₇	—	2	2	no	—
396	C₂×C₄×C₆₇	—	2	2	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	2	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	4	2	no	—
401	C₂×C₄×C₆₇	—	4	2	no	—
402	C₂×C₄×C₆₇	—	4	2	no	—
403	C₂×C₄×C₆₇	—	4	8	no	—
404	C₂×C₄×C₆₇	—	4	8	no	—
405	C₂×C₄×C₆₇	—	4	4	no	—
406	C₂×C₄×C₆₇	—	4	2	no	—
407	C₂×C₄×C₆₇	—	4	2	no	—
408	C₂×C₄×C₆₇	—	8	2	no	—
409	C₂×C₄×C₆₇	—	8	2	no	—
410	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
418	C₈×C₆₇	—	2	2	no	—
419	C₈×C₆₇	—	2	4	no	—
420	C₈×C₆₇	—	2	2	no	—
421	C₂²×C₆₇	—	2	1	no	—
422	C₂²×C₆₇	—	2	1	no	—
423	C₂²×C₆₇	—	2	2	no	—
424	C₂²×C₆₇	—	2	2	no	—
425	C₂²×C₆₇	—	2	2	no	—
426	C₂²×C₆₇	—	2	2	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	2	no	—
429	C₂²×C₆₇	—	4	4	no	—
430	C₂²×C₆₇	—	4	1	no	—
431	C₂²×C₆₇	—	4	1	no	—
432	C₂²×C₆₇	—	4	4	no	—
433	C₂²×C₆₇	—	4	1	no	—
434	C₂²×C₆₇	—	4	4	no	—
435	C₂²×C₆₇	—	8	4	no	—
436	C₂²×C₆₇	—	8	8	no	—
437	C₂²×C₆₇	#577	1	2	yes	—
438	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
439	C₄×C₆₇	—	2	4	no	—
440	C₄×C₆₇	—	2	2	no	—
441	C₄×C₆₇	—	2	2	no	—
442	C₄×C₆₇	—	2	1	no	—
443	C₄×C₆₇	—	2	1	no	—
444	C₄×C₆₇	—	2	1	no	—
445	C₄×C₆₇	—	2	1	no	—
446	C₄×C₆₇	—	4	2	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	1	no	—
449	C₄×C₆₇	—	4	2	no	—
450	C₄×C₆₇	—	4	2	no	—
451	C₄×C₆₇	—	4	1	no	—
452	C₄×C₆₇	#575	1	2	yes	—
453	C₄×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
454	#61596	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
455	C₂×C₆₇	—	2	2	no	—
456	C₂×C₆₇	—	4	2	no	—
457	C₂×C₆₇	—	4	2	no	—
458	C₂×C₆₇	—	8	1	no	—
459	C₂×C₆₇	—	8	4	no	—
460	C₂×C₆₇	#3484	1	1	yes	characteristic
461	C₂×C₆₇	C₂×#575	1	1	yes	characteristic
462	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
463	#3520	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₂×#550	C₂×C₆₇	1	1	yes	characteristic, complemented
465	#3332	C₂×C₆₇	1	2	yes	complemented
466	#3317	C₂×C₆₇	1	4	yes	complemented
467	#3304	C₂×C₆₇	1	2	yes	complemented
468	#3284	C₂×C₆₇	1	2	yes	complemented
469	#3278	C₂×C₆₇	1	2	yes	complemented
470	#3271	C₂×C₆₇	1	4	yes	complemented
471	#3217	C₂×C₆₇	1	1	yes	characteristic, complemented
472	#3208	C₂×C₆₇	1	1	yes	characteristic, complemented
473	#3194	C₂×C₆₇	1	2	yes	complemented
474	#3187	C₂×C₆₇	1	2	yes	complemented
475	#3113	C₂×C₆₇	1	1	yes	characteristic, complemented
476	#3108	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#3007	C₂×C₆₇	1	2	yes	complemented
478	#3002	C₂×C₆₇	1	2	yes	complemented
479	#2974	C₂×C₆₇	1	1	yes	characteristic, complemented
480	C₆₇	#61596	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²×#41	C₂²×C₆₇	1	2	yes	—
482	C₂×#137	C₂²×C₆₇	1	4	yes	complemented
483	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
484	#556	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	#554	—	2	1	no	—
486	#552	C₂²×C₆₇	1	2	yes	complemented
487	#551	—	2	2	no	—
488	#550	—	2	1	no	—
489	#550	—	2	2	no	—
490	#550	—	2	1	no	—
491	#550	C₂²×C₆₇	1	2	yes	—
492	#550	C₂²×C₆₇	1	4	yes	—
493	#550	C₂²×C₆₇	1	2	yes	—
494	D₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
495	#548	C₂²×C₆₇	1	2	yes	complemented
496	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	#547	C₂²×C₆₇	1	1	yes	characteristic, complemented
498	#546	—	2	1	no	—
499	#542	—	2	1	no	—
500	#539	—	2	2	no	—
501	#533	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#127	—	2	1	no	—
503	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
504	#529	C₂²×C₆₇	1	1	yes	characteristic
505	#525	C₂²×C₆₇	1	2	yes	—
506	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
507	C₂×#121	—	2	2	no	—
508	C₂×#121	C₂²×C₆₇	1	2	yes	—
509	#520	—	2	1	no	—
510	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
511	C₂×C₄×D₄	—	2	1	no	—
512	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
513	#496	C₂²×C₆₇	1	2	yes	complemented
514	#492	C₂²×C₆₇	1	2	yes	complemented
515	#490	C₂²×C₆₇	1	2	yes	complemented
516	#486	C₂²×C₆₇	1	2	yes	complemented
517	#483	C₂²×C₆₇	1	1	yes	characteristic
518	#483	C₂²×C₆₇	1	2	yes	—
519	#482	C₂²×C₆₇	1	4	yes	complemented
520	#481	C₂²×C₆₇	1	4	yes	complemented
521	#480	C₂²×C₆₇	1	1	yes	characteristic
522	#479	C₂²×C₆₇	1	2	yes	complemented
523	#475	C₂²×C₆₇	1	2	yes	complemented
524	#469	C₂²×C₆₇	1	4	yes	complemented
525	#468	C₂²×C₆₇	1	4	yes	complemented
526	#465	C₂²×C₆₇	1	4	yes	complemented
527	#465	C₂²×C₆₇	1	4	yes	complemented
528	#464	C₂²×C₆₇	1	2	yes	complemented
529	#462	C₂²×C₆₇	1	2	yes	complemented
530	#460	C₂²×C₆₇	1	4	yes	complemented
531	#460	C₂²×C₆₇	1	2	yes	complemented
532	#459	C₂²×C₆₇	1	2	yes	complemented
533	#452	C₂²×C₆₇	1	4	yes	complemented
534	#452	C₂²×C₆₇	1	4	yes	complemented
535	#452	C₂²×C₆₇	1	4	yes	complemented
536	#451	C₂²×C₆₇	1	1	yes	characteristic
537	#451	C₂²×C₆₇	1	2	yes	—
538	#450	C₂²×C₆₇	1	2	yes	—
539	#450	C₂²×C₆₇	1	2	yes	—
540	#450	C₂²×C₆₇	1	2	yes	—
541	#449	C₂²×C₆₇	1	4	yes	complemented
542	#449	C₂²×C₆₇	1	4	yes	complemented
543	#448	C₂²×C₆₇	1	1	yes	characteristic
544	#448	C₂²×C₆₇	1	4	yes	complemented
545	#447	C₂²×C₆₇	1	2	yes	—
546	#441	C₂²×C₆₇	1	4	yes	complemented
547	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
548	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
549	#436	C₂²×C₆₇	1	2	yes	complemented
550	#435	C₂²×C₆₇	1	4	yes	complemented
551	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
552	#432	C₂²×C₆₇	1	1	yes	characteristic
553	#431	C₂²×C₆₇	1	1	yes	characteristic
554	#417	C₂²×C₆₇	1	4	yes	complemented
555	#416	C₂²×C₆₇	1	4	yes	complemented
556	#407	C₂²×C₆₇	1	2	yes	—
557	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
558	C₂×#41	—	2	1	no	—
559	C₂×#41	—	2	2	no	—
560	C₂×#41	—	2	2	no	—
561	C₂×#41	—	4	8	no	—
562	C₂×#41	C₂³×C₆₇	1	4	yes	—
563	C₂×#41	C₂³×C₆₇	1	4	yes	—
564	C₂×#41	C₂³×C₆₇	1	2	yes	—
565	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
567	C₂²×D₄	—	2	2	no	—
568	C₂²×D₄	—	2	2	no	—
569	C₂²×D₄	—	2	1	no	—
570	C₂²×D₄	—	2	1	no	—
571	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
573	C₂³×C₄	—	2	2	no	—
574	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
575	#137	—	4	8	no	—
576	#135	—	4	8	no	—
577	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
578	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
579	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
581	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
582	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
583	C₂×D₈	C₂³×C₆₇	1	4	yes	—
584	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
585	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
586	C₄⋊Q₈	—	2	1	no	—
587	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
588	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
589	#127	—	2	2	no	—
590	#127	—	2	2	no	—
591	#127	—	2	4	no	—
592	#127	—	2	1	no	—
593	#127	—	2	1	no	—
594	#127	C₂³×C₆₇	1	2	yes	—
595	#127	C₂³×C₆₇	1	2	yes	—
596	#126	—	2	2	no	—
597	#126	—	2	2	no	—
598	#126	—	2	1	no	—
599	#125	—	2	2	no	—
600	#125	—	2	1	no	—
601	#125	C₂³×C₆₇	1	1	yes	characteristic
602	#124	—	2	1	no	—
603	#124	—	2	2	no	—
604	#124	C₂³×C₆₇	1	1	yes	characteristic
605	#123	—	2	2	no	—
606	#123	—	2	2	no	—
607	#123	—	2	1	no	—
608	#123	—	2	2	no	—
609	#123	—	2	2	no	—
610	C₂²⋊Q₈	—	2	2	no	—
611	C₂²⋊Q₈	—	2	2	no	—
612	C₂²⋊Q₈	—	2	1	no	—
613	C₂²⋊Q₈	—	2	2	no	—
614	C₂²⋊Q₈	—	2	1	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
617	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
618	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
619	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
620	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
621	#121	—	2	2	no	—
622	#121	—	2	1	no	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	4	no	—
626	#121	—	2	4	no	—
627	#121	—	2	4	no	—
628	#121	—	2	4	no	—
629	#121	C₂³×C₆₇	1	4	yes	—
630	#121	C₂³×C₆₇	1	4	yes	—
631	#121	C₂³×C₆₇	1	1	yes	characteristic
632	#121	C₂³×C₆₇	1	2	yes	—
633	#120	—	2	2	no	—
634	C₄×Q₈	—	2	1	no	—
635	C₄×Q₈	—	2	1	no	—
636	C₄×Q₈	—	2	1	no	—
637	C₄×Q₈	—	2	1	no	—
638	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
639	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
640	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
641	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	2	no	—
647	C₄×D₄	—	2	4	no	—
648	C₄×D₄	—	2	2	no	—
649	C₄×D₄	—	2	2	no	—
650	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
651	C₄×D₄	D₄×C₆₇	1	2	yes	—
652	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₄×D₄	C₂³×C₆₇	1	2	yes	—
657	#117	—	2	1	no	—
658	#117	—	2	2	no	—
659	#117	—	2	1	no	—
660	#117	C₂³×C₆₇	1	2	yes	—
661	C₂×C₄⋊C₄	—	2	1	no	—
662	C₂×C₄⋊C₄	—	2	2	no	—
663	C₂×C₄⋊C₄	—	2	1	no	—
664	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
667	C₂×C₂²⋊C₄	—	2	2	no	—
668	C₂×C₂²⋊C₄	—	2	2	no	—
669	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
670	C₂×C₄²	—	2	1	no	—
671	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
672	#107	C₂³×C₆₇	1	2	yes	—
673	#106	C₂³×C₆₇	1	2	yes	—
674	#106	C₂³×C₆₇	1	4	yes	—
675	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
676	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
677	#103	C₂³×C₆₇	1	2	yes	—
678	#103	C₂³×C₆₇	1	4	yes	—
679	#103	C₂³×C₆₇	1	2	yes	—
680	#103	C₂³×C₆₇	1	2	yes	—
681	#103	C₂³×C₆₇	1	4	yes	—
682	#102	C₂³×C₆₇	1	4	yes	—
683	#102	C₂³×C₆₇	1	4	yes	—
684	#102	C₂³×C₆₇	1	4	yes	—
685	#102	C₂³×C₆₇	1	4	yes	—
686	#102	C₂³×C₆₇	1	2	yes	—
687	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
688	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
689	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
690	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
691	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
692	#97	C₂³×C₆₇	1	2	yes	—
693	C₄×C₈	C₂³×C₆₇	1	2	yes	—
694	C₂⁴	—	2	2	no	—
695	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
696	#41	—	2	8	no	—
697	#41	—	2	8	no	—
698	#41	—	4	4	no	—
699	#41	—	4	4	no	—
700	#41	—	4	4	no	—
701	#41	—	4	4	no	—
702	#41	—	4	8	no	—
703	#41	—	4	8	no	—
704	C₂×Q₈	—	2	4	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	2	no	—
708	C₂×Q₈	—	4	4	no	—
709	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
711	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	4	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	2	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	4	no	—
726	C₂×D₄	—	4	8	no	—
727	C₂×D₄	—	4	4	no	—
728	C₂×D₄	—	8	2	no	—
729	C₂×D₄	—	8	4	no	—
730	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
731	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
732	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
733	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
734	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₂²×C₄	—	2	1	no	—
736	C₂²×C₄	—	2	1	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	4	no	—
741	C₂²×C₄	—	2	4	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	4	4	no	—
744	C₂²×C₄	—	4	8	no	—
745	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
746	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
747	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
748	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
749	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
753	Q₁₆	—	2	8	no	—
754	Q₁₆	—	2	4	no	—
755	SD₁₆	—	2	4	no	—
756	SD₁₆	—	4	4	no	—
757	SD₁₆	—	4	4	no	—
758	SD₁₆	—	4	4	no	—
759	D₈	—	4	4	no	—
760	M₁₆	—	4	4	no	—
761	C₂×C₈	—	4	4	no	—
762	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
763	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
764	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	1	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	1	no	—
776	C₄⋊C₄	—	2	1	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	1	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
783	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
785	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
786	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
787	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
788	C₂²⋊C₄	—	2	1	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
802	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
803	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
804	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	2	1	no	—
810	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
811	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
812	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
814	C₂³	—	2	4	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	4	no	—
817	C₂³	—	4	2	no	—
818	C₂³	—	4	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
823	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
824	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
825	Q₈	—	2	4	no	—
826	Q₈	—	2	2	no	—
827	Q₈	—	2	2	no	—
828	Q₈	—	2	4	no	—
829	Q₈	—	4	2	no	—
830	Q₈	—	8	2	no	—
831	Q₈	H(5,𝔽₂)×C₆₇	1	4	yes	—
832	D₄	—	2	2	no	—
833	D₄	—	2	2	no	—
834	D₄	—	2	2	no	—
835	D₄	—	2	4	no	—
836	D₄	—	2	4	no	—
837	D₄	—	4	2	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	8	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	4	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	8	2	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	4	no	—
848	D₄	—	8	4	no	—
849	D₄	—	8	2	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	4	2	no	—
864	C₂×C₄	—	4	2	no	—
865	C₂×C₄	—	4	2	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	—	4	4	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
874	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
875	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
876	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
877	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
879	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
880	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
881	C₈	—	2	2	no	—
882	C₈	—	2	4	no	—
883	C₈	—	2	2	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	1	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	4	1	no	—
895	C₂²	—	4	4	no	—
896	C₂²	—	4	4	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	8	4	no	—
899	C₂²	—	8	8	no	—
900	C₂²	#577×C₆₇	1	2	yes	—
901	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	1	no	—
909	C₄	—	4	1	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	2	no	—
914	C₄	—	4	1	no	—
915	C₄	#575×C₆₇	1	2	yes	—
916	C₄	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
917	C₂	—	2	2	no	—
918	C₂	—	4	2	no	—
919	C₂	—	4	2	no	—
920	C₂	—	8	4	no	—
921	C₂	—	8	1	no	—
922	C₂	C₆₇×#3484	1	1	yes	characteristic
923	C₂	C₂×#575×C₆₇	1	1	yes	characteristic
924	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3520	C₂	semidirect
2. C₂×#550×C₆₇	C₂	semidirect
3. C₆₇×#3332	C₂	semidirect
4. C₆₇×#3317	C₂	semidirect
5. C₆₇×#3304	C₂	semidirect
6. C₆₇×#3284	C₂	semidirect
7. C₆₇×#3278	C₂	semidirect
8. C₆₇×#3271	C₂	semidirect
9. C₆₇×#3217	C₂	semidirect
10. C₆₇×#3208	C₂	semidirect
11. C₆₇×#3194	C₂	semidirect
12. C₆₇×#3187	C₂	semidirect
13. C₆₇×#3113	C₂	semidirect
14. C₆₇×#3108	C₂	semidirect
15. C₆₇×#3007	C₂	semidirect
16. C₆₇×#3002	C₂	semidirect
17. C₆₇×#2974	C₂	semidirect
19. C₂×#137×C₆₇	C₂²	semidirect
20. C₂×#135×C₆₇	C₂²	semidirect
21. #556×C₆₇	C₂²	semidirect
23. #552×C₆₇	C₂²	semidirect
31. D₄×Q₈×C₆₇	C₂²	semidirect
32. #548×C₆₇	C₂²	semidirect
33. #547×C₆₇	C₂²	semidirect
34. #547×C₆₇	C₂²	semidirect
50. #496×C₆₇	C₂²	semidirect
51. #492×C₆₇	C₂²	semidirect
52. #490×C₆₇	C₂²	semidirect
53. #486×C₆₇	C₂²	semidirect
56. #482×C₆₇	C₂²	semidirect
57. #481×C₆₇	C₂²	semidirect
59. #479×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #469×C₆₇	C₂²	semidirect
62. #468×C₆₇	C₂²	semidirect
63. #465×C₆₇	C₂²	semidirect
64. #465×C₆₇	C₂²	semidirect
65. #464×C₆₇	C₂²	semidirect
66. #462×C₆₇	C₂²	semidirect
67. #460×C₆₇	C₂²	semidirect
68. #460×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
71. #452×C₆₇	C₂²	semidirect
72. #452×C₆₇	C₂²	semidirect
78. #449×C₆₇	C₂²	semidirect
79. #449×C₆₇	C₂²	semidirect
81. #448×C₆₇	C₂²	semidirect
83. #441×C₆₇	C₂²	semidirect
84. C₄×Q₁₆×C₆₇	C₂²	semidirect
85. C₄×SD₁₆×C₆₇	C₂²	semidirect
86. #436×C₆₇	C₂²	semidirect
87. #435×C₆₇	C₂²	semidirect
88. C₈×D₄×C₆₇	C₂²	semidirect
91. #417×C₆₇	C₂²	semidirect
92. #416×C₆₇	C₂²	semidirect
454. #61596	C₆₇	direct (N × H)
463. #3520	C₂×C₆₇	semidirect
464. C₂×#550	C₂×C₆₇	semidirect
465. #3332	C₂×C₆₇	semidirect
466. #3317	C₂×C₆₇	semidirect
467. #3304	C₂×C₆₇	semidirect
468. #3284	C₂×C₆₇	semidirect
469. #3278	C₂×C₆₇	semidirect
470. #3271	C₂×C₆₇	semidirect
471. #3217	C₂×C₆₇	semidirect
472. #3208	C₂×C₆₇	semidirect
473. #3194	C₂×C₆₇	semidirect
474. #3187	C₂×C₆₇	semidirect
475. #3113	C₂×C₆₇	semidirect
476. #3108	C₂×C₆₇	semidirect
477. #3007	C₂×C₆₇	semidirect
478. #3002	C₂×C₆₇	semidirect
479. #2974	C₂×C₆₇	semidirect
480. C₆₇	#61596	direct (N × H)
482. C₂×#137	C₂²×C₆₇	semidirect
483. C₂×#135	C₂²×C₆₇	semidirect
484. #556	C₂²×C₆₇	semidirect
486. #552	C₂²×C₆₇	semidirect
494. D₄×Q₈	C₂²×C₆₇	semidirect
495. #548	C₂²×C₆₇	semidirect
496. #547	C₂²×C₆₇	semidirect
497. #547	C₂²×C₆₇	semidirect
513. #496	C₂²×C₆₇	semidirect
514. #492	C₂²×C₆₇	semidirect
515. #490	C₂²×C₆₇	semidirect
516. #486	C₂²×C₆₇	semidirect
519. #482	C₂²×C₆₇	semidirect
520. #481	C₂²×C₆₇	semidirect
522. #479	C₂²×C₆₇	semidirect
523. #475	C₂²×C₆₇	semidirect
524. #469	C₂²×C₆₇	semidirect
525. #468	C₂²×C₆₇	semidirect
526. #465	C₂²×C₆₇	semidirect
527. #465	C₂²×C₆₇	semidirect
528. #464	C₂²×C₆₇	semidirect
529. #462	C₂²×C₆₇	semidirect
530. #460	C₂²×C₆₇	semidirect
531. #460	C₂²×C₆₇	semidirect
532. #459	C₂²×C₆₇	semidirect
533. #452	C₂²×C₆₇	semidirect
534. #452	C₂²×C₆₇	semidirect
535. #452	C₂²×C₆₇	semidirect
541. #449	C₂²×C₆₇	semidirect
542. #449	C₂²×C₆₇	semidirect
544. #448	C₂²×C₆₇	semidirect
546. #441	C₂²×C₆₇	semidirect
547. C₄×Q₁₆	C₂²×C₆₇	semidirect
548. C₄×SD₁₆	C₂²×C₆₇	semidirect
549. #436	C₂²×C₆₇	semidirect
550. #435	C₂²×C₆₇	semidirect
551. C₈×D₄	C₂²×C₆₇	semidirect
554. #417	C₂²×C₆₇	semidirect
555. #416	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×#3520	2
C₂×#550×C₆₇	2
C₆₇×#3332	2
C₆₇×#3317	2
C₆₇×#3304	2
C₆₇×#3284	2
C₆₇×#3278	2
C₆₇×#3271	2
C₆₇×#3217	2
C₆₇×#3208	2
C₆₇×#3194	2
C₆₇×#3187	2
C₆₇×#3113	2
C₆₇×#3108	2
C₆₇×#3007	2
C₆₇×#3002	2
C₆₇×#2974	2
#61596	67

Subgroups — C67×#61596 #30740847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61596 #30740847