Subgroups — C₆₇×#59370 #30738621

Order 17152.

2536 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2749	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2748	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2684	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2603	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2578	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2557	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2534	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2480	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2467	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2435	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2403	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2372	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2358	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
17	D₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂×#386×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×#126×C₆₇	C₂²	1	2	yes	complemented
24	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
27	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	C₂×#120×C₆₇	C₂²	1	2	yes	—
29	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#120×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#400×C₆₇	C₂²	1	2	yes	complemented
39	#399×C₆₇	C₂²	1	2	yes	complemented
40	#398×C₆₇	C₂²	1	2	yes	complemented
41	#397×C₆₇	C₂²	1	2	yes	complemented
42	#397×C₆₇	C₂²	1	2	yes	complemented
43	#397×C₆₇	C₂²	1	2	yes	complemented
44	#397×C₆₇	C₂²	1	2	yes	complemented
45	#396×C₆₇	C₂²	1	2	yes	complemented
46	#396×C₆₇	C₂²	1	2	yes	complemented
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	2	yes	complemented
49	#394×C₆₇	C₂²	1	2	yes	complemented
50	#394×C₆₇	C₂²	1	2	yes	complemented
51	#393×C₆₇	C₂²	1	2	yes	complemented
52	#392×C₆₇	C₂²	1	2	yes	—
53	#392×C₆₇	C₂²	1	2	yes	—
54	#391×C₆₇	C₂²	1	2	yes	complemented
55	#390×C₆₇	C₂²	1	1	yes	characteristic
56	#390×C₆₇	C₂²	1	2	yes	complemented
57	#390×C₆₇	C₂²	1	2	yes	complemented
58	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
59	#388×C₆₇	C₂²	1	2	yes	complemented
60	#388×C₆₇	C₂²	1	2	yes	complemented
61	#388×C₆₇	C₂²	1	2	yes	complemented
62	#388×C₆₇	C₂²	1	2	yes	complemented
63	#388×C₆₇	C₂²	1	2	yes	complemented
64	#388×C₆₇	C₂²	1	2	yes	complemented
65	#388×C₆₇	C₂²	1	2	yes	complemented
66	#387×C₆₇	C₂²	1	2	yes	complemented
67	#387×C₆₇	C₂²	1	2	yes	complemented
68	#387×C₆₇	C₂²	1	2	yes	complemented
69	#386×C₆₇	C₂²	1	2	yes	—
70	#386×C₆₇	C₂²	1	1	yes	characteristic
71	#386×C₆₇	C₂²	1	1	yes	characteristic
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	1	yes	characteristic
74	#386×C₆₇	C₂²	1	2	yes	—
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	1	yes	characteristic
77	#386×C₆₇	C₂²	1	2	yes	complemented
78	#386×C₆₇	C₂²	1	2	yes	complemented
79	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#386×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#386×C₆₇	C₂²	1	2	yes	complemented
82	#386×C₆₇	C₂²	1	2	yes	complemented
83	#386×C₆₇	C₂²	1	2	yes	complemented
84	#386×C₆₇	C₂²	1	2	yes	complemented
85	#385×C₆₇	C₂²	1	2	yes	complemented
86	#385×C₆₇	C₂²	1	2	yes	complemented
87	#385×C₆₇	C₂²	1	2	yes	complemented
88	#385×C₆₇	C₂²	1	2	yes	complemented
89	#385×C₆₇	C₂²	1	2	yes	complemented
90	#383×C₆₇	C₂²	1	2	yes	complemented
91	#381×C₆₇	C₂²	1	2	yes	complemented
92	#380×C₆₇	C₂²	1	2	yes	complemented
93	#380×C₆₇	C₂²	1	2	yes	complemented
94	#380×C₆₇	C₂²	1	2	yes	complemented
95	#379×C₆₇	C₂²	1	2	yes	—
96	#379×C₆₇	C₂²	1	1	yes	characteristic
97	#379×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	#376×C₆₇	C₂²	1	2	yes	complemented
106	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
109	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₆₇	—	2	8	no	—
112	C₂²×D₄×C₆₇	—	2	4	no	—
113	C₂²×D₄×C₆₇	—	4	2	no	—
114	C₂²×D₄×C₆₇	—	4	2	no	—
115	C₂²×D₄×C₆₇	—	4	2	no	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
118	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
121	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
122	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
123	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₆₇	—	4	4	no	—
125	C₂³×C₄×C₆₇	—	4	2	no	—
126	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
135	#126×C₆₇	—	4	4	no	—
136	#124×C₆₇	—	2	4	no	—
137	#124×C₆₇	—	4	2	no	—
138	#123×C₆₇	—	4	4	no	—
139	C₂²⋊Q₈×C₆₇	—	4	2	no	—
140	#120×C₆₇	—	2	8	no	—
141	#120×C₆₇	—	2	4	no	—
142	#120×C₆₇	—	4	2	no	—
143	C₄×D₄×C₆₇	—	2	8	no	—
144	C₄×D₄×C₆₇	—	4	4	no	—
145	C₄×D₄×C₆₇	—	4	4	no	—
146	C₄×D₄×C₆₇	—	4	4	no	—
147	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
158	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
159	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
192	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
193	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
195	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
196	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
197	#95×C₆₇	C₂³	1	2	yes	—
198	#95×C₆₇	C₂³	1	2	yes	—
199	#95×C₆₇	C₂³	1	2	yes	—
200	#95×C₆₇	C₂³	1	2	yes	—
201	#95×C₆₇	C₂³	1	2	yes	—
202	#95×C₆₇	C₂³	1	2	yes	—
203	#95×C₆₇	C₂³	1	2	yes	—
204	#95×C₆₇	C₂³	1	2	yes	—
205	#95×C₆₇	C₂³	1	2	yes	—
206	#95×C₆₇	C₂³	1	2	yes	—
207	#95×C₆₇	C₂³	1	2	yes	—
208	#95×C₆₇	C₂³	1	2	yes	—
209	#95×C₆₇	C₂³	1	2	yes	—
210	#95×C₆₇	C₂³	1	2	yes	—
211	#95×C₆₇	C₂³	1	2	yes	—
212	#95×C₆₇	C₂³	1	2	yes	—
213	#95×C₆₇	C₂³	1	2	yes	—
214	#95×C₆₇	C₂³	1	2	yes	—
215	#95×C₆₇	C₂³	1	2	yes	—
216	C₂⁴×C₆₇	—	2	2	no	—
217	C₂⁴×C₆₇	—	2	2	no	—
218	C₂⁴×C₆₇	—	2	2	no	—
219	C₂⁴×C₆₇	—	2	4	no	—
220	C₂⁴×C₆₇	—	2	2	no	—
221	C₂⁴×C₆₇	—	2	2	no	—
222	C₂⁴×C₆₇	—	2	4	no	—
223	C₂⁴×C₆₇	—	2	4	no	—
224	C₂⁴×C₆₇	—	2	2	no	—
225	C₂⁴×C₆₇	—	4	2	no	—
226	C₂⁴×C₆₇	—	4	2	no	—
227	C₂⁴×C₆₇	—	4	2	no	—
228	C₂⁴×C₆₇	—	4	1	no	—
229	C₂⁴×C₆₇	—	4	1	no	—
230	C₂⁴×C₆₇	—	4	1	no	—
231	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
232	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₆₇	—	2	2	no	—
238	C₂×Q₈×C₆₇	—	4	1	no	—
239	C₂×Q₈×C₆₇	—	4	1	no	—
240	C₂×D₄×C₆₇	—	2	4	no	—
241	C₂×D₄×C₆₇	—	2	4	no	—
242	C₂×D₄×C₆₇	—	2	4	no	—
243	C₂×D₄×C₆₇	—	2	4	no	—
244	C₂×D₄×C₆₇	—	2	4	no	—
245	C₂×D₄×C₆₇	—	2	4	no	—
246	C₂×D₄×C₆₇	—	2	2	no	—
247	C₂×D₄×C₆₇	—	2	2	no	—
248	C₂×D₄×C₆₇	—	2	4	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	2	no	—
253	C₂×D₄×C₆₇	—	4	2	no	—
254	C₂×D₄×C₆₇	—	4	2	no	—
255	C₂×D₄×C₆₇	—	4	2	no	—
256	C₂×D₄×C₆₇	—	4	1	no	—
257	C₂×D₄×C₆₇	—	4	1	no	—
258	C₂×D₄×C₆₇	—	4	1	no	—
259	C₂×D₄×C₆₇	—	4	1	no	—
260	C₂×D₄×C₆₇	—	4	1	no	—
261	C₂×D₄×C₆₇	—	4	1	no	—
262	C₂×D₄×C₆₇	—	4	16	no	—
263	C₂×D₄×C₆₇	—	4	16	no	—
264	C₂×D₄×C₆₇	#41	1	8	yes	—
265	C₂×D₄×C₆₇	#41	1	4	yes	—
266	C₂²×C₄×C₆₇	—	2	4	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	2	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	—	4	1	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	1	no	—
282	C₂²×C₄×C₆₇	—	4	1	no	—
283	C₂²×C₄×C₆₇	—	4	1	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	—	4	2	no	—
289	C₂²×C₄×C₆₇	—	4	2	no	—
290	C₂²×C₄×C₆₇	—	4	16	no	—
291	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₆₇	—	2	4	no	—
305	C₄⋊C₄×C₆₇	—	2	4	no	—
306	C₄⋊C₄×C₆₇	—	4	2	no	—
307	C₄⋊C₄×C₆₇	—	4	2	no	—
308	C₄⋊C₄×C₆₇	—	4	1	no	—
309	C₄⋊C₄×C₆₇	—	4	2	no	—
310	C₄⋊C₄×C₆₇	—	4	2	no	—
311	C₄⋊C₄×C₆₇	—	4	2	no	—
312	C₄⋊C₄×C₆₇	—	4	2	no	—
313	C₄⋊C₄×C₆₇	—	4	2	no	—
314	C₂²⋊C₄×C₆₇	—	2	4	no	—
315	C₂²⋊C₄×C₆₇	—	2	4	no	—
316	C₂²⋊C₄×C₆₇	—	2	2	no	—
317	C₂²⋊C₄×C₆₇	—	2	4	no	—
318	C₂²⋊C₄×C₆₇	—	2	4	no	—
319	C₂²⋊C₄×C₆₇	—	2	4	no	—
320	C₂²⋊C₄×C₆₇	—	2	4	no	—
321	C₂²⋊C₄×C₆₇	—	2	4	no	—
322	C₂²⋊C₄×C₆₇	—	2	4	no	—
323	C₂²⋊C₄×C₆₇	—	2	4	no	—
324	C₂²⋊C₄×C₆₇	—	2	4	no	—
325	C₂²⋊C₄×C₆₇	—	2	4	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	4	2	no	—
330	C₂²⋊C₄×C₆₇	—	4	1	no	—
331	C₂²⋊C₄×C₆₇	—	4	2	no	—
332	C₂²⋊C₄×C₆₇	—	4	2	no	—
333	C₂²⋊C₄×C₆₇	—	4	2	no	—
334	C₂²⋊C₄×C₆₇	—	4	1	no	—
335	C₂²⋊C₄×C₆₇	—	4	2	no	—
336	C₂²⋊C₄×C₆₇	—	4	2	no	—
337	C₂²⋊C₄×C₆₇	—	4	2	no	—
338	C₂²⋊C₄×C₆₇	—	4	2	no	—
339	C₂²⋊C₄×C₆₇	—	4	1	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	no	—
341	C₂²⋊C₄×C₆₇	—	4	2	no	—
342	C₂²⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	—	4	2	no	—
344	C₂²⋊C₄×C₆₇	—	4	2	no	—
345	C₄²×C₆₇	—	2	4	no	—
346	C₄²×C₆₇	—	2	2	no	—
347	C₄²×C₆₇	—	2	4	no	—
348	C₄²×C₆₇	—	4	2	no	—
349	C₄²×C₆₇	—	4	2	no	—
350	C₄²×C₆₇	—	4	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	2	no	—
353	C₂³×C₆₇	—	2	1	no	—
354	C₂³×C₆₇	—	2	8	no	—
355	C₂³×C₆₇	—	2	2	no	—
356	C₂³×C₆₇	—	2	2	no	—
357	C₂³×C₆₇	—	2	2	no	—
358	C₂³×C₆₇	—	2	2	no	—
359	C₂³×C₆₇	—	2	2	no	—
360	C₂³×C₆₇	—	2	1	no	—
361	C₂³×C₆₇	—	2	2	no	—
362	C₂³×C₆₇	—	2	2	no	—
363	C₂³×C₆₇	—	2	2	no	—
364	C₂³×C₆₇	—	2	1	no	—
365	C₂³×C₆₇	—	2	2	no	—
366	C₂³×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	2	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	1	no	—
370	C₂³×C₆₇	—	2	1	no	—
371	C₂³×C₆₇	—	2	1	no	—
372	C₂³×C₆₇	—	2	1	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	2	1	no	—
375	C₂³×C₆₇	—	2	2	no	—
376	C₂³×C₆₇	—	2	1	no	—
377	C₂³×C₆₇	—	2	1	no	—
378	C₂³×C₆₇	—	4	8	no	—
379	C₂³×C₆₇	—	4	8	no	—
380	C₂³×C₆₇	—	4	4	no	—
381	C₂³×C₆₇	—	4	4	no	—
382	C₂³×C₆₇	—	4	8	no	—
383	C₂³×C₆₇	—	4	8	no	—
384	C₂³×C₆₇	—	4	4	no	—
385	C₂³×C₆₇	—	4	4	no	—
386	C₂³×C₆₇	—	4	4	no	—
387	C₂³×C₆₇	—	8	4	no	—
388	C₂³×C₆₇	—	8	2	no	—
389	C₂³×C₆₇	—	8	2	no	—
390	C₂³×C₆₇	—	8	4	no	—
391	C₂³×C₆₇	—	8	2	no	—
392	C₂³×C₆₇	C₂×#41	1	2	yes	—
393	C₂³×C₆₇	C₂×#41	1	2	yes	—
394	C₂³×C₆₇	C₂×#41	1	4	yes	—
395	C₂³×C₆₇	C₂×#41	1	4	yes	—
396	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
397	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
398	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
399	Q₈×C₆₇	—	8	2	no	—
400	D₄×C₆₇	—	2	16	no	—
401	D₄×C₆₇	—	4	4	no	—
402	D₄×C₆₇	—	4	8	no	—
403	D₄×C₆₇	—	4	4	no	—
404	D₄×C₆₇	—	4	8	no	—
405	D₄×C₆₇	—	4	8	no	—
406	D₄×C₆₇	—	4	4	no	—
407	D₄×C₆₇	—	4	4	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	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	2	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	2	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	2	no	—
419	C₂×C₄×C₆₇	—	2	2	no	—
420	C₂×C₄×C₆₇	—	2	2	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	2	no	—
423	C₂×C₄×C₆₇	—	2	1	no	—
424	C₂×C₄×C₆₇	—	2	2	no	—
425	C₂×C₄×C₆₇	—	2	2	no	—
426	C₂×C₄×C₆₇	—	2	2	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	2	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	2	no	—
436	C₂×C₄×C₆₇	—	2	2	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	2	no	—
442	C₂×C₄×C₆₇	—	2	2	no	—
443	C₂×C₄×C₆₇	—	2	1	no	—
444	C₂×C₄×C₆₇	—	4	4	no	—
445	C₂×C₄×C₆₇	—	4	4	no	—
446	C₂×C₄×C₆₇	—	4	8	no	—
447	C₂×C₄×C₆₇	—	4	4	no	—
448	C₂×C₄×C₆₇	—	4	8	no	—
449	C₂×C₄×C₆₇	—	4	4	no	—
450	C₂×C₄×C₆₇	—	8	4	no	—
451	C₂×C₄×C₆₇	—	8	4	no	—
452	C₂×C₄×C₆₇	—	8	4	no	—
453	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
454	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
455	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
456	C₂²×C₆₇	—	2	4	no	—
457	C₂²×C₆₇	—	2	2	no	—
458	C₂²×C₆₇	—	2	4	no	—
459	C₂²×C₆₇	—	2	2	no	—
460	C₂²×C₆₇	—	2	4	no	—
461	C₂²×C₆₇	—	2	4	no	—
462	C₂²×C₆₇	—	2	4	no	—
463	C₂²×C₆₇	—	2	4	no	—
464	C₂²×C₆₇	—	2	2	no	—
465	C₂²×C₆₇	—	2	2	no	—
466	C₂²×C₆₇	—	2	2	no	—
467	C₂²×C₆₇	—	2	4	no	—
468	C₂²×C₆₇	—	2	4	no	—
469	C₂²×C₆₇	—	4	16	no	—
470	C₂²×C₆₇	—	4	1	no	—
471	C₂²×C₆₇	—	4	1	no	—
472	C₂²×C₆₇	—	4	1	no	—
473	C₂²×C₆₇	—	4	2	no	—
474	C₂²×C₆₇	—	4	2	no	—
475	C₂²×C₆₇	—	4	2	no	—
476	C₂²×C₆₇	—	4	2	no	—
477	C₂²×C₆₇	—	4	2	no	—
478	C₂²×C₆₇	—	4	2	no	—
479	C₂²×C₆₇	—	4	1	no	—
480	C₂²×C₆₇	—	4	1	no	—
481	C₂²×C₆₇	—	4	2	no	—
482	C₂²×C₆₇	—	4	1	no	—
483	C₂²×C₆₇	—	4	1	no	—
484	C₂²×C₆₇	—	4	2	no	—
485	C₂²×C₆₇	—	4	1	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	—	4	1	no	—
488	C₂²×C₆₇	—	8	8	no	—
489	C₂²×C₆₇	—	8	8	no	—
490	C₂²×C₆₇	#551	1	4	yes	—
491	C₂²×C₆₇	C₂²×#41	1	2	yes	—
492	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
493	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	2	yes	—
495	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
496	C₄×C₆₇	—	2	4	no	—
497	C₄×C₆₇	—	2	2	no	—
498	C₄×C₆₇	—	2	4	no	—
499	C₄×C₆₇	—	4	2	no	—
500	C₄×C₆₇	—	4	2	no	—
501	C₄×C₆₇	—	4	1	no	—
502	C₄×C₆₇	—	4	2	no	—
503	C₄×C₆₇	—	4	2	no	—
504	C₄×C₆₇	—	4	2	no	—
505	C₄×C₆₇	—	4	2	no	—
506	C₄×C₆₇	—	4	2	no	—
507	C₄×C₆₇	—	4	2	no	—
508	C₄×C₆₇	—	4	2	no	—
509	#59370	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
510	C₂×C₆₇	—	2	4	no	—
511	C₂×C₆₇	—	4	2	no	—
512	C₂×C₆₇	—	4	2	no	—
513	C₂×C₆₇	—	4	4	no	—
514	C₂×C₆₇	—	4	2	no	—
515	C₂×C₆₇	—	8	1	no	—
516	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
517	C₂×C₆₇	#3481	1	2	yes	—
518	C₂×C₆₇	#3490	1	1	yes	characteristic
519	C₂×C₆₇	#3519	1	2	yes	—
520	C₂×C₆₇	#3532	1	1	yes	characteristic
521	#2749	C₂×C₆₇	1	2	yes	complemented
522	#2748	C₂×C₆₇	1	1	yes	characteristic, complemented
523	#2684	C₂×C₆₇	1	1	yes	characteristic, complemented
524	#2603	C₂×C₆₇	1	2	yes	complemented
525	#2578	C₂×C₆₇	1	2	yes	complemented
526	#2557	C₂×C₆₇	1	2	yes	complemented
527	#2534	C₂×C₆₇	1	2	yes	complemented
528	#2480	C₂×C₆₇	1	2	yes	complemented
529	#2467	C₂×C₆₇	1	2	yes	complemented
530	#2450	C₂×C₆₇	1	2	yes	complemented
531	#2435	C₂×C₆₇	1	1	yes	characteristic, complemented
532	#2418	C₂×C₆₇	1	2	yes	complemented
533	#2403	C₂×C₆₇	1	1	yes	characteristic
534	#2372	C₂×C₆₇	1	1	yes	characteristic, complemented
535	#2358	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#2353	C₂×C₆₇	1	2	yes	complemented
537	D₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
538	C₄×#120	C₂×C₆₇	1	2	yes	complemented
539	C₂×#386	C₂×C₆₇	1	1	yes	characteristic, complemented
540	C₆₇	#59370	1	1	yes	characteristic, direct product factor, Sylow
541	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
542	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
543	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₂×#126	C₂²×C₆₇	1	2	yes	complemented
545	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
546	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic, complemented
547	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
548	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
549	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
550	C₂×#120	C₂²×C₆₇	1	2	yes	—
551	C₂×#120	C₂²×C₆₇	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
553	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
554	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
555	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
556	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
557	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
558	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	#400	C₂²×C₆₇	1	2	yes	complemented
560	#399	C₂²×C₆₇	1	2	yes	complemented
561	#398	C₂²×C₆₇	1	2	yes	complemented
562	#397	C₂²×C₆₇	1	2	yes	complemented
563	#397	C₂²×C₆₇	1	2	yes	complemented
564	#397	C₂²×C₆₇	1	2	yes	complemented
565	#397	C₂²×C₆₇	1	2	yes	complemented
566	#396	C₂²×C₆₇	1	2	yes	complemented
567	#396	C₂²×C₆₇	1	2	yes	complemented
568	#394	C₂²×C₆₇	1	2	yes	—
569	#394	C₂²×C₆₇	1	2	yes	complemented
570	#394	C₂²×C₆₇	1	2	yes	complemented
571	#394	C₂²×C₆₇	1	2	yes	complemented
572	#393	C₂²×C₆₇	1	2	yes	complemented
573	#392	C₂²×C₆₇	1	2	yes	—
574	#392	C₂²×C₆₇	1	2	yes	—
575	#391	C₂²×C₆₇	1	2	yes	complemented
576	#390	C₂²×C₆₇	1	1	yes	characteristic
577	#390	C₂²×C₆₇	1	2	yes	complemented
578	#390	C₂²×C₆₇	1	2	yes	complemented
579	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
580	#388	C₂²×C₆₇	1	2	yes	complemented
581	#388	C₂²×C₆₇	1	2	yes	complemented
582	#388	C₂²×C₆₇	1	2	yes	complemented
583	#388	C₂²×C₆₇	1	2	yes	complemented
584	#388	C₂²×C₆₇	1	2	yes	complemented
585	#388	C₂²×C₆₇	1	2	yes	complemented
586	#388	C₂²×C₆₇	1	2	yes	complemented
587	#387	C₂²×C₆₇	1	2	yes	complemented
588	#387	C₂²×C₆₇	1	2	yes	complemented
589	#387	C₂²×C₆₇	1	2	yes	complemented
590	#386	C₂²×C₆₇	1	1	yes	characteristic
591	#386	C₂²×C₆₇	1	2	yes	—
592	#386	C₂²×C₆₇	1	2	yes	—
593	#386	C₂²×C₆₇	1	2	yes	—
594	#386	C₂²×C₆₇	1	2	yes	—
595	#386	C₂²×C₆₇	1	1	yes	characteristic
596	#386	C₂²×C₆₇	1	1	yes	characteristic
597	#386	C₂²×C₆₇	1	1	yes	characteristic
598	#386	C₂²×C₆₇	1	2	yes	complemented
599	#386	C₂²×C₆₇	1	2	yes	complemented
600	#386	C₂²×C₆₇	1	2	yes	complemented
601	#386	C₂²×C₆₇	1	2	yes	complemented
602	#386	C₂²×C₆₇	1	2	yes	complemented
603	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
604	#386	C₂²×C₆₇	1	1	yes	characteristic, complemented
605	#386	C₂²×C₆₇	1	2	yes	complemented
606	#385	C₂²×C₆₇	1	2	yes	complemented
607	#385	C₂²×C₆₇	1	2	yes	complemented
608	#385	C₂²×C₆₇	1	2	yes	complemented
609	#385	C₂²×C₆₇	1	2	yes	complemented
610	#385	C₂²×C₆₇	1	2	yes	complemented
611	#383	C₂²×C₆₇	1	2	yes	complemented
612	#381	C₂²×C₆₇	1	2	yes	complemented
613	#380	C₂²×C₆₇	1	2	yes	complemented
614	#380	C₂²×C₆₇	1	2	yes	complemented
615	#380	C₂²×C₆₇	1	2	yes	complemented
616	#379	C₂²×C₆₇	1	2	yes	—
617	#379	C₂²×C₆₇	1	1	yes	characteristic
618	#379	C₂²×C₆₇	1	2	yes	complemented
619	#379	C₂²×C₆₇	1	2	yes	complemented
620	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
621	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
622	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
624	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
625	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
626	#376	C₂²×C₆₇	1	2	yes	complemented
627	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
628	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
629	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
630	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
631	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
632	C₂²×D₄	—	2	8	no	—
633	C₂²×D₄	—	2	4	no	—
634	C₂²×D₄	—	4	2	no	—
635	C₂²×D₄	—	4	2	no	—
636	C₂²×D₄	—	4	2	no	—
637	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
638	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
639	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
640	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
641	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
642	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
643	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
645	C₂³×C₄	—	4	4	no	—
646	C₂³×C₄	—	4	2	no	—
647	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
648	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
649	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
652	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
653	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
654	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
655	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
656	#126	—	4	4	no	—
657	#124	—	2	4	no	—
658	#124	—	4	2	no	—
659	#123	—	4	4	no	—
660	C₂²⋊Q₈	—	4	2	no	—
661	#120	—	2	8	no	—
662	#120	—	2	4	no	—
663	#120	—	4	2	no	—
664	C₄×D₄	—	2	8	no	—
665	C₄×D₄	—	4	4	no	—
666	C₄×D₄	—	4	4	no	—
667	C₄×D₄	—	4	4	no	—
668	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
669	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
671	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
672	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
675	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
676	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
677	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
678	C₂×C₂²⋊C₄	—	4	4	no	—
679	C₂×C₂²⋊C₄	—	4	4	no	—
680	C₂×C₂²⋊C₄	—	4	2	no	—
681	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
682	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
683	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
694	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
695	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
709	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
712	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
713	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
714	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
715	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
716	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
717	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
718	#95	C₂³×C₆₇	1	2	yes	—
719	#95	C₂³×C₆₇	1	2	yes	—
720	#95	C₂³×C₆₇	1	2	yes	—
721	#95	C₂³×C₆₇	1	2	yes	—
722	#95	C₂³×C₆₇	1	2	yes	—
723	#95	C₂³×C₆₇	1	2	yes	—
724	#95	C₂³×C₆₇	1	2	yes	—
725	#95	C₂³×C₆₇	1	2	yes	—
726	#95	C₂³×C₆₇	1	2	yes	—
727	#95	C₂³×C₆₇	1	2	yes	—
728	#95	C₂³×C₆₇	1	2	yes	—
729	#95	C₂³×C₆₇	1	2	yes	—
730	#95	C₂³×C₆₇	1	2	yes	—
731	#95	C₂³×C₆₇	1	2	yes	—
732	#95	C₂³×C₆₇	1	2	yes	—
733	#95	C₂³×C₆₇	1	2	yes	—
734	#95	C₂³×C₆₇	1	2	yes	—
735	#95	C₂³×C₆₇	1	2	yes	—
736	#95	C₂³×C₆₇	1	2	yes	—
737	C₂⁴	—	2	2	no	—
738	C₂⁴	—	2	2	no	—
739	C₂⁴	—	2	2	no	—
740	C₂⁴	—	2	4	no	—
741	C₂⁴	—	2	2	no	—
742	C₂⁴	—	2	2	no	—
743	C₂⁴	—	2	4	no	—
744	C₂⁴	—	2	4	no	—
745	C₂⁴	—	2	2	no	—
746	C₂⁴	—	4	2	no	—
747	C₂⁴	—	4	2	no	—
748	C₂⁴	—	4	2	no	—
749	C₂⁴	—	4	1	no	—
750	C₂⁴	—	4	1	no	—
751	C₂⁴	—	4	1	no	—
752	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
753	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
754	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
755	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
756	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
757	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
758	C₂×Q₈	—	2	2	no	—
759	C₂×Q₈	—	4	1	no	—
760	C₂×Q₈	—	4	1	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	4	no	—
765	C₂×D₄	—	2	4	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	4	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	1	no	—
778	C₂×D₄	—	4	1	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	—	4	1	no	—
781	C₂×D₄	—	4	1	no	—
782	C₂×D₄	—	4	1	no	—
783	C₂×D₄	—	4	16	no	—
784	C₂×D₄	—	4	16	no	—
785	C₂×D₄	#41×C₆₇	1	8	yes	—
786	C₂×D₄	#41×C₆₇	1	4	yes	—
787	C₂²×C₄	—	2	4	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	4	no	—
790	C₂²×C₄	—	2	4	no	—
791	C₂²×C₄	—	2	4	no	—
792	C₂²×C₄	—	2	2	no	—
793	C₂²×C₄	—	2	4	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	4	no	—
796	C₂²×C₄	—	2	4	no	—
797	C₂²×C₄	—	4	1	no	—
798	C₂²×C₄	—	4	2	no	—
799	C₂²×C₄	—	4	2	no	—
800	C₂²×C₄	—	4	2	no	—
801	C₂²×C₄	—	4	2	no	—
802	C₂²×C₄	—	4	1	no	—
803	C₂²×C₄	—	4	1	no	—
804	C₂²×C₄	—	4	1	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	16	no	—
812	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
813	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
814	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
816	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
818	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
819	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
820	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
821	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
822	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
825	C₄⋊C₄	—	2	4	no	—
826	C₄⋊C₄	—	2	4	no	—
827	C₄⋊C₄	—	4	2	no	—
828	C₄⋊C₄	—	4	2	no	—
829	C₄⋊C₄	—	4	1	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	2	4	no	—
836	C₂²⋊C₄	—	2	4	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	4	no	—
839	C₂²⋊C₄	—	2	4	no	—
840	C₂²⋊C₄	—	2	4	no	—
841	C₂²⋊C₄	—	2	4	no	—
842	C₂²⋊C₄	—	2	4	no	—
843	C₂²⋊C₄	—	2	4	no	—
844	C₂²⋊C₄	—	2	4	no	—
845	C₂²⋊C₄	—	2	4	no	—
846	C₂²⋊C₄	—	2	4	no	—
847	C₂²⋊C₄	—	2	4	no	—
848	C₂²⋊C₄	—	2	4	no	—
849	C₂²⋊C₄	—	2	4	no	—
850	C₂²⋊C₄	—	4	2	no	—
851	C₂²⋊C₄	—	4	1	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	2	no	—
855	C₂²⋊C₄	—	4	1	no	—
856	C₂²⋊C₄	—	4	2	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	2	no	—
860	C₂²⋊C₄	—	4	1	no	—
861	C₂²⋊C₄	—	4	2	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	2	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₄²	—	2	4	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	4	no	—
869	C₄²	—	4	2	no	—
870	C₄²	—	4	2	no	—
871	C₄²	—	4	1	no	—
872	C₂³	—	2	1	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	1	no	—
875	C₂³	—	2	8	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	2	2	no	—
878	C₂³	—	2	2	no	—
879	C₂³	—	2	2	no	—
880	C₂³	—	2	2	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	2	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	4	8	no	—
900	C₂³	—	4	8	no	—
901	C₂³	—	4	4	no	—
902	C₂³	—	4	4	no	—
903	C₂³	—	4	8	no	—
904	C₂³	—	4	8	no	—
905	C₂³	—	4	4	no	—
906	C₂³	—	4	4	no	—
907	C₂³	—	4	4	no	—
908	C₂³	—	8	2	no	—
909	C₂³	—	8	4	no	—
910	C₂³	—	8	2	no	—
911	C₂³	—	8	4	no	—
912	C₂³	—	8	2	no	—
913	C₂³	C₂×#41×C₆₇	1	2	yes	—
914	C₂³	C₂×#41×C₆₇	1	2	yes	—
915	C₂³	C₂×#41×C₆₇	1	4	yes	—
916	C₂³	C₂×#41×C₆₇	1	4	yes	—
917	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
918	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
919	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
920	Q₈	—	8	2	no	—
921	D₄	—	2	16	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	8	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	4	no	—
926	D₄	—	4	8	no	—
927	D₄	—	4	8	no	—
928	D₄	—	4	4	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	2	1	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	4	4	no	—
966	C₂×C₄	—	4	4	no	—
967	C₂×C₄	—	4	8	no	—
968	C₂×C₄	—	4	4	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	4	4	no	—
971	C₂×C₄	—	8	4	no	—
972	C₂×C₄	—	8	4	no	—
973	C₂×C₄	—	8	4	no	—
974	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
975	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
976	C₂×C₄	H(5,𝔽₂)×C₆₇	1	4	yes	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	4	no	—
979	C₂²	—	2	2	no	—
980	C₂²	—	2	4	no	—
981	C₂²	—	2	4	no	—
982	C₂²	—	2	4	no	—
983	C₂²	—	2	4	no	—
984	C₂²	—	2	4	no	—
985	C₂²	—	2	2	no	—
986	C₂²	—	2	2	no	—
987	C₂²	—	2	2	no	—
988	C₂²	—	2	4	no	—
989	C₂²	—	2	4	no	—
990	C₂²	—	4	16	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	1	no	—
993	C₂²	—	4	2	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	4	2	no	—
1004	C₂²	—	4	1	no	—
1005	C₂²	—	4	1	no	—
1006	C₂²	—	4	2	no	—
1007	C₂²	—	4	1	no	—
1008	C₂²	—	4	2	no	—
1009	C₂²	—	8	8	no	—
1010	C₂²	—	8	8	no	—
1011	C₂²	#551×C₆₇	1	4	yes	—
1012	C₂²	C₂²×#41×C₆₇	1	2	yes	—
1013	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1014	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1015	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	2	yes	—
1016	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1017	C₄	—	2	4	no	—
1018	C₄	—	2	4	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	—	4	2	no	—
1022	C₄	—	4	2	no	—
1023	C₄	—	4	2	no	—
1024	C₄	—	4	1	no	—
1025	C₄	—	4	2	no	—
1026	C₄	—	4	2	no	—
1027	C₄	—	4	2	no	—
1028	C₄	—	4	2	no	—
1029	C₄	—	4	2	no	—
1030	C₂	—	2	4	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	2	no	—
1034	C₂	—	4	4	no	—
1035	C₂	—	8	1	no	—
1036	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
1037	C₂	C₆₇×#3481	1	2	yes	—
1038	C₂	C₆₇×#3490	1	1	yes	characteristic
1039	C₂	C₆₇×#3519	1	2	yes	—
1040	C₂	C₆₇×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2403	C₂
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. C₆₇×#2749	C₂	semidirect
2. C₆₇×#2748	C₂	semidirect
3. C₆₇×#2684	C₂	semidirect
4. C₆₇×#2603	C₂	semidirect
5. C₆₇×#2578	C₂	semidirect
6. C₆₇×#2557	C₂	semidirect
7. C₆₇×#2534	C₂	semidirect
8. C₆₇×#2480	C₂	semidirect
9. C₆₇×#2467	C₂	semidirect
10. C₆₇×#2450	C₂	semidirect
11. C₆₇×#2435	C₂	semidirect
12. C₆₇×#2418	C₂	semidirect
14. C₆₇×#2372	C₂	semidirect
15. C₆₇×#2358	C₂	semidirect
16. C₆₇×#2353	C₂	semidirect
17. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂×#386×C₆₇	C₂	semidirect
22. C₂⁴×C₄×C₆₇	C₂²	semidirect
23. C₂×#126×C₆₇	C₂²	semidirect
25. C₂×#124×C₆₇	C₂²	semidirect
26. C₂×#123×C₆₇	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
33. C₂×C₄×D₄×C₆₇	C₂²	semidirect
34. C₂×C₄×D₄×C₆₇	C₂²	semidirect
36. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
37. C₂²×C₂²⋊C₄×C₆₇	C₂²	semidirect
38. #400×C₆₇	C₂²	semidirect
39. #399×C₆₇	C₂²	semidirect
40. #398×C₆₇	C₂²	semidirect
41. #397×C₆₇	C₂²	semidirect
42. #397×C₆₇	C₂²	semidirect
43. #397×C₆₇	C₂²	semidirect
44. #397×C₆₇	C₂²	semidirect
45. #396×C₆₇	C₂²	semidirect
46. #396×C₆₇	C₂²	semidirect
48. #394×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #394×C₆₇	C₂²	semidirect
51. #393×C₆₇	C₂²	semidirect
54. #391×C₆₇	C₂²	semidirect
56. #390×C₆₇	C₂²	semidirect
57. #390×C₆₇	C₂²	semidirect
58. #390×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #388×C₆₇	C₂²	semidirect
64. #388×C₆₇	C₂²	semidirect
65. #388×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
77. #386×C₆₇	C₂²	semidirect
78. #386×C₆₇	C₂²	semidirect
79. #386×C₆₇	C₂²	semidirect
80. #386×C₆₇	C₂²	semidirect
81. #386×C₆₇	C₂²	semidirect
82. #386×C₆₇	C₂²	semidirect
83. #386×C₆₇	C₂²	semidirect
84. #386×C₆₇	C₂²	semidirect
85. #385×C₆₇	C₂²	semidirect
86. #385×C₆₇	C₂²	semidirect
87. #385×C₆₇	C₂²	semidirect
88. #385×C₆₇	C₂²	semidirect
89. #385×C₆₇	C₂²	semidirect
90. #383×C₆₇	C₂²	semidirect
91. #381×C₆₇	C₂²	semidirect
92. #380×C₆₇	C₂²	semidirect
93. #380×C₆₇	C₂²	semidirect
94. #380×C₆₇	C₂²	semidirect
97. #379×C₆₇	C₂²	semidirect
98. #379×C₆₇	C₂²	semidirect
99. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
105. #376×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
509. #59370	C₆₇	direct (N × H)
521. #2749	C₂×C₆₇	semidirect
522. #2748	C₂×C₆₇	semidirect
523. #2684	C₂×C₆₇	semidirect
524. #2603	C₂×C₆₇	semidirect
525. #2578	C₂×C₆₇	semidirect
526. #2557	C₂×C₆₇	semidirect
527. #2534	C₂×C₆₇	semidirect
528. #2480	C₂×C₆₇	semidirect
529. #2467	C₂×C₆₇	semidirect
530. #2450	C₂×C₆₇	semidirect
531. #2435	C₂×C₆₇	semidirect
532. #2418	C₂×C₆₇	semidirect
534. #2372	C₂×C₆₇	semidirect
535. #2358	C₂×C₆₇	semidirect
536. #2353	C₂×C₆₇	semidirect
537. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
538. C₄×#120	C₂×C₆₇	semidirect
539. C₂×#386	C₂×C₆₇	semidirect
540. C₆₇	#59370	direct (N × H)
543. C₂⁴×C₄	C₂²×C₆₇	semidirect
544. C₂×#126	C₂²×C₆₇	semidirect
546. C₂×#124	C₂²×C₆₇	semidirect
547. C₂×#123	C₂²×C₆₇	semidirect
548. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
554. C₂×C₄×D₄	C₂²×C₆₇	semidirect
555. C₂×C₄×D₄	C₂²×C₆₇	semidirect
557. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
558. C₂²×C₂²⋊C₄	C₂²×C₆₇	semidirect
559. #400	C₂²×C₆₇	semidirect
560. #399	C₂²×C₆₇	semidirect
561. #398	C₂²×C₆₇	semidirect
562. #397	C₂²×C₆₇	semidirect
563. #397	C₂²×C₆₇	semidirect
564. #397	C₂²×C₆₇	semidirect
565. #397	C₂²×C₆₇	semidirect
566. #396	C₂²×C₆₇	semidirect
567. #396	C₂²×C₆₇	semidirect
569. #394	C₂²×C₆₇	semidirect
570. #394	C₂²×C₆₇	semidirect
571. #394	C₂²×C₆₇	semidirect
572. #393	C₂²×C₆₇	semidirect
575. #391	C₂²×C₆₇	semidirect
577. #390	C₂²×C₆₇	semidirect
578. #390	C₂²×C₆₇	semidirect
579. #390	C₂²×C₆₇	semidirect
580. #388	C₂²×C₆₇	semidirect
581. #388	C₂²×C₆₇	semidirect
582. #388	C₂²×C₆₇	semidirect
583. #388	C₂²×C₆₇	semidirect
584. #388	C₂²×C₆₇	semidirect
585. #388	C₂²×C₆₇	semidirect
586. #388	C₂²×C₆₇	semidirect
587. #387	C₂²×C₆₇	semidirect
588. #387	C₂²×C₆₇	semidirect
589. #387	C₂²×C₆₇	semidirect
598. #386	C₂²×C₆₇	semidirect
599. #386	C₂²×C₆₇	semidirect
600. #386	C₂²×C₆₇	semidirect
601. #386	C₂²×C₆₇	semidirect
602. #386	C₂²×C₆₇	semidirect
603. #386	C₂²×C₆₇	semidirect
604. #386	C₂²×C₆₇	semidirect
605. #386	C₂²×C₆₇	semidirect
606. #385	C₂²×C₆₇	semidirect
607. #385	C₂²×C₆₇	semidirect
608. #385	C₂²×C₆₇	semidirect
609. #385	C₂²×C₆₇	semidirect
610. #385	C₂²×C₆₇	semidirect
611. #383	C₂²×C₆₇	semidirect
612. #381	C₂²×C₆₇	semidirect
613. #380	C₂²×C₆₇	semidirect
614. #380	C₂²×C₆₇	semidirect
615. #380	C₂²×C₆₇	semidirect
618. #379	C₂²×C₆₇	semidirect
619. #379	C₂²×C₆₇	semidirect
620. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
621. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
622. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
623. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
624. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
625. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
626. #376	C₂²×C₆₇	semidirect
627. C₂×#95	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×#2749	2
C₆₇×#2748	2
C₆₇×#2684	2
C₆₇×#2603	2
C₆₇×#2578	2
C₆₇×#2557	2
C₆₇×#2534	2
C₆₇×#2480	2
C₆₇×#2467	2
C₆₇×#2450	2
C₆₇×#2435	2
C₆₇×#2418	2
C₆₇×#2403	2
C₆₇×#2372	2
C₆₇×#2358	2
C₆₇×#2353	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×#120×C₆₇	2
C₂×#386×C₆₇	2
#59370	67

Subgroups — C67×#59370 #30738621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59370 #30738621