Subgroups — C₆₇×#35063 #30714314

Order 17152.

2994 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2853	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2849	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2638	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2635	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2600	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2564	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2543	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2484	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2482	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2412	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2410	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2406	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2404	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2325	C₂	1	4	yes	maximal, complemented
17	C₂×#381×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	#525×C₆₇	—	2	8	no	—
23	C₂×#123×C₆₇	C₂²	1	2	yes	—
24	C₂×#123×C₆₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×#121×C₆₇	C₂²	1	4	yes	—
28	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#120×C₆₇	C₂²	1	2	yes	—
31	C₂×#120×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	—	2	8	no	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
39	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
45	#400×C₆₇	C₂²	1	2	yes	complemented
46	#399×C₆₇	C₂²	1	2	yes	complemented
47	#398×C₆₇	C₂²	1	2	yes	complemented
48	#397×C₆₇	C₂²	1	2	yes	complemented
49	#397×C₆₇	C₂²	1	4	yes	complemented
50	#395×C₆₇	C₂²	1	2	yes	complemented
51	#394×C₆₇	C₂²	1	4	yes	—
52	#394×C₆₇	C₂²	1	2	yes	complemented
53	#394×C₆₇	C₂²	1	4	yes	complemented
54	#393×C₆₇	C₂²	1	2	yes	complemented
55	#392×C₆₇	C₂²	1	4	yes	—
56	#392×C₆₇	C₂²	1	2	yes	complemented
57	#388×C₆₇	C₂²	1	4	yes	complemented
58	#388×C₆₇	C₂²	1	4	yes	complemented
59	#388×C₆₇	C₂²	1	4	yes	complemented
60	#387×C₆₇	C₂²	1	4	yes	complemented
61	#387×C₆₇	C₂²	1	4	yes	complemented
62	#387×C₆₇	C₂²	1	4	yes	complemented
63	#386×C₆₇	C₂²	1	4	yes	—
64	#386×C₆₇	C₂²	1	2	yes	—
65	#386×C₆₇	C₂²	1	2	yes	—
66	#386×C₆₇	C₂²	1	4	yes	complemented
67	#386×C₆₇	C₂²	1	4	yes	complemented
68	#386×C₆₇	C₂²	1	4	yes	complemented
69	#386×C₆₇	C₂²	1	4	yes	complemented
70	#385×C₆₇	C₂²	1	2	yes	—
71	#385×C₆₇	C₂²	1	2	yes	—
72	#385×C₆₇	C₂²	1	4	yes	complemented
73	#385×C₆₇	C₂²	1	4	yes	complemented
74	#385×C₆₇	C₂²	1	4	yes	complemented
75	#381×C₆₇	C₂²	1	2	yes	—
76	#381×C₆₇	C₂²	1	1	yes	characteristic
77	#381×C₆₇	C₂²	1	1	yes	characteristic
78	#381×C₆₇	C₂²	1	2	yes	—
79	#381×C₆₇	C₂²	1	2	yes	complemented
80	#381×C₆₇	C₂²	1	2	yes	complemented
81	#380×C₆₇	C₂²	1	4	yes	complemented
82	#379×C₆₇	C₂²	1	2	yes	—
83	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
84	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
85	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
86	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
87	C₂×#41×C₆₇	—	2	4	no	—
88	C₂×#41×C₆₇	—	4	4	no	—
89	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₆₇	—	2	4	no	—
91	C₂²×D₄×C₆₇	—	2	8	no	—
92	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
93	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
94	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
95	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
97	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
98	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	—	2	4	no	—
100	C₂³×C₄×C₆₇	—	4	4	no	—
101	C₂³×C₄×C₆₇	—	4	4	no	—
102	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
109	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
111	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
112	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
116	#123×C₆₇	—	2	8	no	—
117	#123×C₆₇	—	4	4	no	—
118	C₂²⋊Q₈×C₆₇	—	2	4	no	—
119	C₂²⋊Q₈×C₆₇	—	2	4	no	—
120	#121×C₆₇	—	2	16	no	—
121	#121×C₆₇	—	2	4	no	—
122	#121×C₆₇	—	2	4	no	—
123	#120×C₆₇	—	2	8	no	—
124	#120×C₆₇	—	4	4	no	—
125	C₄×D₄×C₆₇	—	2	8	no	—
126	C₄×D₄×C₆₇	—	2	8	no	—
127	C₄×D₄×C₆₇	—	2	8	no	—
128	C₄×D₄×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	2	8	no	—
130	C₄×D₄×C₆₇	—	2	8	no	—
131	#117×C₆₇	—	2	4	no	—
132	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
133	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
143	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
144	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
163	C₂×C₄²×C₆₇	—	2	4	no	—
164	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
167	#95×C₆₇	C₂³	1	2	yes	—
168	#95×C₆₇	C₂³	1	4	yes	—
169	#95×C₆₇	C₂³	1	4	yes	—
170	#95×C₆₇	C₂³	1	2	yes	—
171	#95×C₆₇	C₂³	1	2	yes	—
172	#95×C₆₇	C₂³	1	2	yes	—
173	#95×C₆₇	C₂³	1	4	yes	—
174	#95×C₆₇	C₂³	1	4	yes	—
175	#95×C₆₇	C₂³	1	4	yes	—
176	#95×C₆₇	C₂³	1	4	yes	—
177	#95×C₆₇	C₂³	1	4	yes	—
178	#95×C₆₇	C₂³	1	4	yes	—
179	C₂⁴×C₆₇	—	2	2	no	—
180	C₂⁴×C₆₇	—	2	4	no	—
181	C₂⁴×C₆₇	—	2	4	no	—
182	C₂⁴×C₆₇	—	2	4	no	—
183	C₂⁴×C₆₇	—	2	4	no	—
184	C₂⁴×C₆₇	—	4	2	no	—
185	C₂⁴×C₆₇	—	4	2	no	—
186	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
187	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
188	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
189	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
190	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
192	#41×C₆₇	—	4	16	no	—
193	C₂×Q₈×C₆₇	—	2	2	no	—
194	C₂×Q₈×C₆₇	—	4	2	no	—
195	C₂×D₄×C₆₇	—	2	32	no	—
196	C₂×D₄×C₆₇	—	2	4	no	—
197	C₂×D₄×C₆₇	—	2	4	no	—
198	C₂×D₄×C₆₇	—	2	4	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	4	no	—
201	C₂×D₄×C₆₇	—	2	4	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	8	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	4	no	—
206	C₂×D₄×C₆₇	—	2	8	no	—
207	C₂×D₄×C₆₇	—	2	2	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	4	4	no	—
210	C₂×D₄×C₆₇	—	4	2	no	—
211	C₂×D₄×C₆₇	—	4	4	no	—
212	C₂×D₄×C₆₇	—	4	4	no	—
213	C₂×D₄×C₆₇	#41	1	8	yes	complemented
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	4	no	—
216	C₂²×C₄×C₆₇	—	2	4	no	—
217	C₂²×C₄×C₆₇	—	2	4	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	4	no	—
221	C₂²×C₄×C₆₇	—	2	8	no	—
222	C₂²×C₄×C₆₇	—	2	4	no	—
223	C₂²×C₄×C₆₇	—	2	4	no	—
224	C₂²×C₄×C₆₇	—	2	4	no	—
225	C₂²×C₄×C₆₇	—	4	16	no	—
226	C₂²×C₄×C₆₇	—	4	2	no	—
227	C₂²×C₄×C₆₇	—	4	2	no	—
228	C₂²×C₄×C₆₇	—	4	2	no	—
229	C₂²×C₄×C₆₇	—	4	2	no	—
230	C₂²×C₄×C₆₇	—	4	4	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	—	4	2	no	—
233	C₂²×C₄×C₆₇	—	4	2	no	—
234	C₂²×C₄×C₆₇	—	4	2	no	—
235	C₂²×C₄×C₆₇	—	4	4	no	—
236	C₂²×C₄×C₆₇	—	4	4	no	—
237	C₂²×C₄×C₆₇	—	4	16	no	—
238	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₆₇	—	2	4	no	—
257	C₄⋊C₄×C₆₇	—	2	4	no	—
258	C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₄⋊C₄×C₆₇	—	2	4	no	—
261	C₄⋊C₄×C₆₇	—	2	4	no	—
262	C₄⋊C₄×C₆₇	—	2	8	no	—
263	C₄⋊C₄×C₆₇	—	4	4	no	—
264	C₄⋊C₄×C₆₇	—	4	4	no	—
265	C₂²⋊C₄×C₆₇	—	2	4	no	—
266	C₂²⋊C₄×C₆₇	—	2	4	no	—
267	C₂²⋊C₄×C₆₇	—	2	4	no	—
268	C₂²⋊C₄×C₆₇	—	2	4	no	—
269	C₂²⋊C₄×C₆₇	—	2	4	no	—
270	C₂²⋊C₄×C₆₇	—	2	8	no	—
271	C₂²⋊C₄×C₆₇	—	2	4	no	—
272	C₂²⋊C₄×C₆₇	—	2	4	no	—
273	C₂²⋊C₄×C₆₇	—	2	4	no	—
274	C₂²⋊C₄×C₆₇	—	2	4	no	—
275	C₂²⋊C₄×C₆₇	—	2	4	no	—
276	C₂²⋊C₄×C₆₇	—	2	4	no	—
277	C₂²⋊C₄×C₆₇	—	2	8	no	—
278	C₂²⋊C₄×C₆₇	—	4	4	no	—
279	C₂²⋊C₄×C₆₇	—	4	4	no	—
280	C₂²⋊C₄×C₆₇	—	4	4	no	—
281	C₂²⋊C₄×C₆₇	—	4	4	no	—
282	C₂²⋊C₄×C₆₇	—	4	4	no	—
283	C₄²×C₆₇	—	2	4	no	—
284	C₄²×C₆₇	—	2	4	no	—
285	C₄²×C₆₇	—	2	4	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	8	no	—
291	C₂³×C₆₇	—	2	8	no	—
292	C₂³×C₆₇	—	2	8	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	4	no	—
298	C₂³×C₆₇	—	2	4	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	4	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	4	4	no	—
306	C₂³×C₆₇	—	4	16	no	—
307	C₂³×C₆₇	—	4	16	no	—
308	C₂³×C₆₇	—	4	4	no	—
309	C₂³×C₆₇	—	4	4	no	—
310	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
311	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
312	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
313	C₂³×C₆₇	C₂×#41	1	4	yes	—
314	C₂³×C₆₇	C₂×#41	1	4	yes	—
315	C₂³×C₆₇	H(5,𝔽₂)	1	4	yes	—
316	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
317	Q₈×C₆₇	—	4	4	no	—
318	D₄×C₆₇	—	2	16	no	—
319	D₄×C₆₇	—	2	16	no	—
320	D₄×C₆₇	—	4	4	no	—
321	D₄×C₆₇	—	4	8	no	—
322	D₄×C₆₇	—	4	8	no	—
323	D₄×C₆₇	—	4	8	no	—
324	D₄×C₆₇	—	8	8	no	—
325	C₂×C₄×C₆₇	—	2	8	no	—
326	C₂×C₄×C₆₇	—	2	8	no	—
327	C₂×C₄×C₆₇	—	2	8	no	—
328	C₂×C₄×C₆₇	—	2	2	no	—
329	C₂×C₄×C₆₇	—	2	2	no	—
330	C₂×C₄×C₆₇	—	2	2	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	4	no	—
340	C₂×C₄×C₆₇	—	2	4	no	—
341	C₂×C₄×C₆₇	—	2	4	no	—
342	C₂×C₄×C₆₇	—	2	4	no	—
343	C₂×C₄×C₆₇	—	2	4	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	4	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	4	no	—
348	C₂×C₄×C₆₇	—	2	4	no	—
349	C₂×C₄×C₆₇	—	2	4	no	—
350	C₂×C₄×C₆₇	—	2	4	no	—
351	C₂×C₄×C₆₇	—	4	4	no	—
352	C₂×C₄×C₆₇	—	4	4	no	—
353	C₂×C₄×C₆₇	—	4	4	no	—
354	C₂×C₄×C₆₇	—	4	4	no	—
355	C₂×C₄×C₆₇	—	4	8	no	—
356	C₂×C₄×C₆₇	—	4	8	no	—
357	C₂×C₄×C₆₇	—	4	8	no	—
358	C₂×C₄×C₆₇	—	4	4	no	—
359	C₂×C₄×C₆₇	—	4	4	no	—
360	C₂×C₄×C₆₇	—	8	8	no	—
361	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
362	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
363	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
366	C₂²×C₆₇	—	2	2	no	—
367	C₂²×C₆₇	—	2	2	no	—
368	C₂²×C₆₇	—	2	2	no	—
369	C₂²×C₆₇	—	2	2	no	—
370	C₂²×C₆₇	—	2	8	no	—
371	C₂²×C₆₇	—	2	8	no	—
372	C₂²×C₆₇	—	2	2	no	—
373	C₂²×C₆₇	—	2	4	no	—
374	C₂²×C₆₇	—	2	2	no	—
375	C₂²×C₆₇	—	2	2	no	—
376	C₂²×C₆₇	—	2	8	no	—
377	C₂²×C₆₇	—	4	16	no	—
378	C₂²×C₆₇	—	4	16	no	—
379	C₂²×C₆₇	—	4	2	no	—
380	C₂²×C₆₇	—	4	2	no	—
381	C₂²×C₆₇	—	4	4	no	—
382	C₂²×C₆₇	—	4	4	no	—
383	C₂²×C₆₇	—	4	2	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	4	no	—
387	C₂²×C₆₇	—	4	4	no	—
388	C₂²×C₆₇	#525	1	4	yes	—
389	C₂²×C₆₇	#534	1	4	yes	—
390	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
391	C₂²×C₆₇	C₂²×#41	1	2	yes	—
392	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
393	C₂²×C₆₇	#585	1	2	yes	—
394	C₄×C₆₇	—	2	4	no	—
395	C₄×C₆₇	—	2	2	no	—
396	C₄×C₆₇	—	2	2	no	—
397	C₄×C₆₇	—	2	2	no	—
398	C₄×C₆₇	—	2	2	no	—
399	C₄×C₆₇	—	4	2	no	—
400	C₄×C₆₇	—	4	2	no	—
401	C₄×C₆₇	—	4	2	no	—
402	C₄×C₆₇	—	4	2	no	—
403	C₄×C₆₇	—	4	2	no	—
404	C₄×C₆₇	—	4	4	no	—
405	C₄×C₆₇	—	4	4	no	—
406	#35063	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
407	C₂×C₆₇	—	2	4	no	—
408	C₂×C₆₇	—	2	4	no	—
409	C₂×C₆₇	—	4	2	no	—
410	C₂×C₆₇	—	4	4	no	—
411	C₂×C₆₇	—	8	2	no	—
412	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
413	C₂×C₆₇	C₂×#534	1	1	yes	characteristic
414	C₂×C₆₇	#3449	1	1	yes	characteristic
415	C₂×C₆₇	#3513	1	4	yes	—
416	C₂×#525	C₂×C₆₇	1	1	yes	characteristic, complemented
417	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
418	#2853	C₂×C₆₇	1	2	yes	complemented
419	#2849	C₂×C₆₇	1	2	yes	complemented
420	#2638	C₂×C₆₇	1	2	yes	complemented
421	#2635	C₂×C₆₇	1	2	yes	complemented
422	#2600	C₂×C₆₇	1	4	yes	complemented
423	#2564	C₂×C₆₇	1	2	yes	complemented
424	#2543	C₂×C₆₇	1	2	yes	complemented
425	#2484	C₂×C₆₇	1	1	yes	characteristic, complemented
426	#2482	C₂×C₆₇	1	1	yes	characteristic, complemented
427	#2412	C₂×C₆₇	1	2	yes	complemented
428	#2410	C₂×C₆₇	1	2	yes	complemented
429	#2406	C₂×C₆₇	1	1	yes	characteristic, complemented
430	#2404	C₂×C₆₇	1	1	yes	characteristic, complemented
431	#2325	C₂×C₆₇	1	4	yes	complemented
432	C₂×#381	C₂×C₆₇	1	1	yes	characteristic, complemented
433	C₆₇	#35063	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
435	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
436	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
437	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
438	#525	—	2	8	no	—
439	C₂×#123	C₂²×C₆₇	1	2	yes	—
440	C₂×#123	C₂²×C₆₇	1	2	yes	—
441	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
442	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
443	C₂×#121	C₂²×C₆₇	1	4	yes	—
444	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
445	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	C₂×#120	C₂²×C₆₇	1	2	yes	—
447	C₂×#120	C₂²×C₆₇	1	2	yes	—
448	C₂×C₄×D₄	—	2	8	no	—
449	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
450	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
451	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
452	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
453	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
454	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
455	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
456	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
457	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
458	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
459	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
460	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
461	#400	C₂²×C₆₇	1	2	yes	complemented
462	#399	C₂²×C₆₇	1	2	yes	complemented
463	#398	C₂²×C₆₇	1	2	yes	complemented
464	#397	C₂²×C₆₇	1	4	yes	complemented
465	#397	C₂²×C₆₇	1	2	yes	complemented
466	#395	C₂²×C₆₇	1	2	yes	complemented
467	#394	C₂²×C₆₇	1	4	yes	—
468	#394	C₂²×C₆₇	1	4	yes	complemented
469	#394	C₂²×C₆₇	1	2	yes	complemented
470	#393	C₂²×C₆₇	1	2	yes	complemented
471	#392	C₂²×C₆₇	1	4	yes	—
472	#392	C₂²×C₆₇	1	2	yes	complemented
473	#388	C₂²×C₆₇	1	4	yes	complemented
474	#388	C₂²×C₆₇	1	4	yes	complemented
475	#388	C₂²×C₆₇	1	4	yes	complemented
476	#387	C₂²×C₆₇	1	4	yes	complemented
477	#387	C₂²×C₆₇	1	4	yes	complemented
478	#387	C₂²×C₆₇	1	4	yes	complemented
479	#386	C₂²×C₆₇	1	4	yes	—
480	#386	C₂²×C₆₇	1	2	yes	—
481	#386	C₂²×C₆₇	1	2	yes	—
482	#386	C₂²×C₆₇	1	4	yes	complemented
483	#386	C₂²×C₆₇	1	4	yes	complemented
484	#386	C₂²×C₆₇	1	4	yes	complemented
485	#386	C₂²×C₆₇	1	4	yes	complemented
486	#385	C₂²×C₆₇	1	2	yes	—
487	#385	C₂²×C₆₇	1	2	yes	—
488	#385	C₂²×C₆₇	1	4	yes	complemented
489	#385	C₂²×C₆₇	1	4	yes	complemented
490	#385	C₂²×C₆₇	1	4	yes	complemented
491	#381	C₂²×C₆₇	1	2	yes	—
492	#381	C₂²×C₆₇	1	2	yes	—
493	#381	C₂²×C₆₇	1	1	yes	characteristic
494	#381	C₂²×C₆₇	1	1	yes	characteristic
495	#381	C₂²×C₆₇	1	2	yes	complemented
496	#381	C₂²×C₆₇	1	2	yes	complemented
497	#380	C₂²×C₆₇	1	4	yes	complemented
498	#379	C₂²×C₆₇	1	2	yes	—
499	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
500	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
501	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
502	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
503	C₂×#41	—	2	4	no	—
504	C₂×#41	—	4	4	no	—
505	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
506	C₂²×D₄	—	2	4	no	—
507	C₂²×D₄	—	2	8	no	—
508	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
509	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
510	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
511	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
512	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
513	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
514	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
515	C₂³×C₄	—	2	4	no	—
516	C₂³×C₄	—	4	4	no	—
517	C₂³×C₄	—	4	4	no	—
518	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
519	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
521	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
523	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
524	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
525	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
526	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
527	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
528	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
532	#123	—	2	8	no	—
533	#123	—	4	4	no	—
534	C₂²⋊Q₈	—	2	4	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	#121	—	2	16	no	—
537	#121	—	2	4	no	—
538	#121	—	2	4	no	—
539	#120	—	2	8	no	—
540	#120	—	4	4	no	—
541	C₄×D₄	—	2	8	no	—
542	C₄×D₄	—	2	8	no	—
543	C₄×D₄	—	2	8	no	—
544	C₄×D₄	—	2	8	no	—
545	C₄×D₄	—	2	8	no	—
546	C₄×D₄	—	2	8	no	—
547	#117	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	4	no	—
549	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
556	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
557	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	4	4	no	—
561	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
579	C₂×C₄²	—	2	4	no	—
580	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
583	#95	C₂³×C₆₇	1	2	yes	—
584	#95	C₂³×C₆₇	1	4	yes	—
585	#95	C₂³×C₆₇	1	4	yes	—
586	#95	C₂³×C₆₇	1	2	yes	—
587	#95	C₂³×C₆₇	1	2	yes	—
588	#95	C₂³×C₆₇	1	2	yes	—
589	#95	C₂³×C₆₇	1	4	yes	—
590	#95	C₂³×C₆₇	1	4	yes	—
591	#95	C₂³×C₆₇	1	4	yes	—
592	#95	C₂³×C₆₇	1	4	yes	—
593	#95	C₂³×C₆₇	1	4	yes	—
594	#95	C₂³×C₆₇	1	4	yes	—
595	C₂⁴	—	2	2	no	—
596	C₂⁴	—	2	4	no	—
597	C₂⁴	—	2	4	no	—
598	C₂⁴	—	2	4	no	—
599	C₂⁴	—	2	4	no	—
600	C₂⁴	—	4	2	no	—
601	C₂⁴	—	4	2	no	—
602	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
603	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
604	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
605	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
606	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
607	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
608	#41	—	4	16	no	—
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×D₄	—	2	32	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	4	no	—
615	C₂×D₄	—	2	4	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	4	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	8	no	—
620	C₂×D₄	—	2	4	no	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	4	no	—
625	C₂×D₄	—	4	2	no	—
626	C₂×D₄	—	4	4	no	—
627	C₂×D₄	—	4	4	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	#41×C₆₇	1	8	yes	complemented
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	4	no	—
632	C₂²×C₄	—	2	4	no	—
633	C₂²×C₄	—	2	4	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	4	no	—
637	C₂²×C₄	—	2	8	no	—
638	C₂²×C₄	—	2	4	no	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	4	16	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	2	no	—
644	C₂²×C₄	—	4	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	4	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	—	4	4	no	—
652	C₂²×C₄	—	4	4	no	—
653	C₂²×C₄	—	4	16	no	—
654	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
655	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
656	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
657	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
658	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
659	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
660	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
661	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	2	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	8	no	—
679	C₄⋊C₄	—	4	4	no	—
680	C₄⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	2	4	no	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	8	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	8	no	—
694	C₂²⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	4	4	no	—
696	C₂²⋊C₄	—	4	4	no	—
697	C₂²⋊C₄	—	4	4	no	—
698	C₂²⋊C₄	—	4	4	no	—
699	C₄²	—	2	4	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	4	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	8	no	—
707	C₂³	—	2	8	no	—
708	C₂³	—	2	8	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	2	no	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	2	no	—
717	C₂³	—	2	4	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	4	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	16	no	—
723	C₂³	—	4	16	no	—
724	C₂³	—	4	4	no	—
725	C₂³	—	4	4	no	—
726	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
727	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
728	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
729	C₂³	C₂×#41×C₆₇	1	4	yes	—
730	C₂³	C₂×#41×C₆₇	1	4	yes	—
731	C₂³	H(5,𝔽₂)×C₆₇	1	4	yes	—
732	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
733	Q₈	—	4	4	no	—
734	D₄	—	2	16	no	—
735	D₄	—	2	16	no	—
736	D₄	—	4	4	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	8	no	—
739	D₄	—	4	8	no	—
740	D₄	—	8	8	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	4	no	—
756	C₂×C₄	—	2	4	no	—
757	C₂×C₄	—	2	4	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	4	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	4	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	4	4	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	8	no	—
772	C₂×C₄	—	4	8	no	—
773	C₂×C₄	—	4	8	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	8	8	no	—
777	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
778	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
779	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
780	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
781	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	8	no	—
787	C₂²	—	2	8	no	—
788	C₂²	—	2	2	no	—
789	C₂²	—	2	4	no	—
790	C₂²	—	2	2	no	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	8	no	—
793	C₂²	—	4	16	no	—
794	C₂²	—	4	16	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	4	no	—
798	C₂²	—	4	4	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	4	no	—
803	C₂²	—	4	4	no	—
804	C₂²	#525×C₆₇	1	4	yes	—
805	C₂²	#534×C₆₇	1	4	yes	—
806	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
807	C₂²	C₂²×#41×C₆₇	1	2	yes	—
808	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
809	C₂²	#585×C₆₇	1	2	yes	—
810	C₄	—	2	4	no	—
811	C₄	—	2	2	no	—
812	C₄	—	2	2	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	4	no	—
821	C₄	—	4	4	no	—
822	C₂	—	2	4	no	—
823	C₂	—	2	4	no	—
824	C₂	—	4	2	no	—
825	C₂	—	4	4	no	—
826	C₂	—	8	2	no	—
827	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
828	C₂	C₂×#534×C₆₇	1	1	yes	characteristic
829	C₂	C₆₇×#3449	1	1	yes	characteristic
830	C₂	C₆₇×#3513	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×#525×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2853	C₂	semidirect
4. C₆₇×#2849	C₂	semidirect
5. C₆₇×#2638	C₂	semidirect
6. C₆₇×#2635	C₂	semidirect
7. C₆₇×#2600	C₂	semidirect
8. C₆₇×#2564	C₂	semidirect
9. C₆₇×#2543	C₂	semidirect
10. C₆₇×#2484	C₂	semidirect
11. C₆₇×#2482	C₂	semidirect
12. C₆₇×#2412	C₂	semidirect
13. C₆₇×#2410	C₂	semidirect
14. C₆₇×#2406	C₂	semidirect
15. C₆₇×#2404	C₂	semidirect
16. C₆₇×#2325	C₂	semidirect
17. C₂×#381×C₆₇	C₂	semidirect
25. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
28. C₂×#121×C₆₇	C₂²	semidirect
29. C₂×#121×C₆₇	C₂²	semidirect
37. C₂×C₄×D₄×C₆₇	C₂²	semidirect
38. C₂×C₄×D₄×C₆₇	C₂²	semidirect
45. #400×C₆₇	C₂²	semidirect
46. #399×C₆₇	C₂²	semidirect
47. #398×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
50. #395×C₆₇	C₂²	semidirect
52. #394×C₆₇	C₂²	semidirect
53. #394×C₆₇	C₂²	semidirect
54. #393×C₆₇	C₂²	semidirect
56. #392×C₆₇	C₂²	semidirect
57. #388×C₆₇	C₂²	semidirect
58. #388×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #387×C₆₇	C₂²	semidirect
61. #387×C₆₇	C₂²	semidirect
62. #387×C₆₇	C₂²	semidirect
66. #386×C₆₇	C₂²	semidirect
67. #386×C₆₇	C₂²	semidirect
68. #386×C₆₇	C₂²	semidirect
69. #386×C₆₇	C₂²	semidirect
72. #385×C₆₇	C₂²	semidirect
73. #385×C₆₇	C₂²	semidirect
74. #385×C₆₇	C₂²	semidirect
79. #381×C₆₇	C₂²	semidirect
80. #381×C₆₇	C₂²	semidirect
81. #380×C₆₇	C₂²	semidirect
83. C₂×#95×C₆₇	C₂²	semidirect
84. C₂×#95×C₆₇	C₂²	semidirect
102. C₂³×C₄×C₆₇	D₄	semidirect
213. C₂×D₄×C₆₇	#41	semidirect
406. #35063	C₆₇	direct (N × H)
416. C₂×#525	C₂×C₆₇	semidirect
417. C₂²×C₄×D₄	C₂×C₆₇	semidirect
418. #2853	C₂×C₆₇	semidirect
419. #2849	C₂×C₆₇	semidirect
420. #2638	C₂×C₆₇	semidirect
421. #2635	C₂×C₆₇	semidirect
422. #2600	C₂×C₆₇	semidirect
423. #2564	C₂×C₆₇	semidirect
424. #2543	C₂×C₆₇	semidirect
425. #2484	C₂×C₆₇	semidirect
426. #2482	C₂×C₆₇	semidirect
427. #2412	C₂×C₆₇	semidirect
428. #2410	C₂×C₆₇	semidirect
429. #2406	C₂×C₆₇	semidirect
430. #2404	C₂×C₆₇	semidirect
431. #2325	C₂×C₆₇	semidirect
432. C₂×#381	C₂×C₆₇	semidirect
433. C₆₇	#35063	direct (N × H)
441. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
442. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
444. C₂×#121	C₂²×C₆₇	semidirect
445. C₂×#121	C₂²×C₆₇	semidirect
453. C₂×C₄×D₄	C₂²×C₆₇	semidirect
454. C₂×C₄×D₄	C₂²×C₆₇	semidirect
461. #400	C₂²×C₆₇	semidirect
462. #399	C₂²×C₆₇	semidirect
463. #398	C₂²×C₆₇	semidirect
464. #397	C₂²×C₆₇	semidirect
465. #397	C₂²×C₆₇	semidirect
466. #395	C₂²×C₆₇	semidirect
468. #394	C₂²×C₆₇	semidirect
469. #394	C₂²×C₆₇	semidirect
470. #393	C₂²×C₆₇	semidirect
472. #392	C₂²×C₆₇	semidirect
473. #388	C₂²×C₆₇	semidirect
474. #388	C₂²×C₆₇	semidirect
475. #388	C₂²×C₆₇	semidirect
476. #387	C₂²×C₆₇	semidirect
477. #387	C₂²×C₆₇	semidirect
478. #387	C₂²×C₆₇	semidirect
482. #386	C₂²×C₆₇	semidirect
483. #386	C₂²×C₆₇	semidirect
484. #386	C₂²×C₆₇	semidirect
485. #386	C₂²×C₆₇	semidirect
488. #385	C₂²×C₆₇	semidirect
489. #385	C₂²×C₆₇	semidirect
490. #385	C₂²×C₆₇	semidirect
495. #381	C₂²×C₆₇	semidirect
496. #381	C₂²×C₆₇	semidirect
497. #380	C₂²×C₆₇	semidirect
499. C₂×#95	C₂²×C₆₇	semidirect
500. C₂×#95	C₂²×C₆₇	semidirect
518. C₂³×C₄	D₄×C₆₇	semidirect
629. C₂×D₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2853	2
C₆₇×#2849	2
C₆₇×#2638	2
C₆₇×#2635	2
C₆₇×#2600	2
C₆₇×#2564	2
C₆₇×#2543	2
C₆₇×#2484	2
C₆₇×#2482	2
C₆₇×#2412	2
C₆₇×#2410	2
C₆₇×#2406	2
C₆₇×#2404	2
C₆₇×#2325	2
C₂×#381×C₆₇	2
#35063	67

Subgroups — C67×#35063 #30714314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#35063 #30714314