Subgroups — C₆₇×#59357 #30738608

Order 17152.

2062 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2735	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2684	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2668	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#2611	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2600	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2598	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2578	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2530	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2523	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2477	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2460	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2427	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2372	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2364	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×#124×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
24	C₂×#121×C₆₇	C₂²	1	2	yes	—
25	C₂×#120×C₆₇	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
32	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	#400×C₆₇	C₂²	1	2	yes	complemented
34	#400×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	#399×C₆₇	C₂²	1	1	yes	characteristic
36	#399×C₆₇	C₂²	1	1	yes	characteristic
37	#398×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#397×C₆₇	C₂²	1	2	yes	—
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	2	yes	—
41	#397×C₆₇	C₂²	1	2	yes	—
42	#397×C₆₇	C₂²	1	1	yes	characteristic
43	#397×C₆₇	C₂²	1	2	yes	complemented
44	#396×C₆₇	C₂²	1	2	yes	—
45	#394×C₆₇	C₂²	1	2	yes	—
46	#394×C₆₇	C₂²	1	2	yes	—
47	#394×C₆₇	C₂²	1	2	yes	—
48	#394×C₆₇	C₂²	1	1	yes	characteristic, complemented
49	#393×C₆₇	C₂²	1	2	yes	—
50	#393×C₆₇	C₂²	1	2	yes	—
51	#392×C₆₇	C₂²	1	1	yes	characteristic
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#391×C₆₇	C₂²	1	2	yes	complemented
54	#391×C₆₇	C₂²	1	2	yes	complemented
55	#389×C₆₇	C₂²	1	2	yes	complemented
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	—
59	#388×C₆₇	C₂²	1	2	yes	—
60	#388×C₆₇	C₂²	1	2	yes	—
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	#387×C₆₇	C₂²	1	2	yes	complemented
65	#387×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	#387×C₆₇	C₂²	1	2	yes	complemented
70	#387×C₆₇	C₂²	1	2	yes	complemented
71	#387×C₆₇	C₂²	1	2	yes	complemented
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	—
75	#386×C₆₇	C₂²	1	2	yes	—
76	#386×C₆₇	C₂²	1	2	yes	—
77	#386×C₆₇	C₂²	1	2	yes	—
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	complemented
81	#385×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	—
83	#385×C₆₇	C₂²	1	2	yes	—
84	#385×C₆₇	C₂²	1	2	yes	complemented
85	#385×C₆₇	C₂²	1	2	yes	complemented
86	#383×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#383×C₆₇	C₂²	1	2	yes	complemented
88	#381×C₆₇	C₂²	1	1	yes	characteristic
89	#381×C₆₇	C₂²	1	1	yes	characteristic
90	#380×C₆₇	C₂²	1	2	yes	—
91	#380×C₆₇	C₂²	1	2	yes	—
92	#380×C₆₇	C₂²	1	2	yes	complemented
93	#379×C₆₇	C₂²	1	1	yes	characteristic
94	#379×C₆₇	C₂²	1	1	yes	characteristic
95	#379×C₆₇	C₂²	1	2	yes	—
96	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
97	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
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	#376×C₆₇	C₂²	1	2	yes	complemented
105	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
109	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
110	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
111	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	—	2	4	no	—
114	C₂³×C₄×C₆₇	—	4	2	no	—
115	C₂³×C₄×C₆₇	—	4	2	no	—
116	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
123	#125×C₆₇	—	4	2	no	—
124	#124×C₆₇	—	2	8	no	—
125	C₂²⋊Q₈×C₆₇	—	4	4	no	—
126	#121×C₆₇	—	2	8	no	—
127	#120×C₆₇	—	2	8	no	—
128	C₄×D₄×C₆₇	—	2	8	no	—
129	C₄×D₄×C₆₇	—	4	2	no	—
130	C₄×D₄×C₆₇	—	4	4	no	—
131	C₄×D₄×C₆₇	—	4	4	no	—
132	#117×C₆₇	—	4	2	no	—
133	#117×C₆₇	—	4	2	no	—
134	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
147	C₂×C₄⋊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	2	yes	—
157	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	2	yes	—
172	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
181	#95×C₆₇	C₂³	1	2	yes	—
182	#95×C₆₇	C₂³	1	2	yes	—
183	#95×C₆₇	C₂³	1	2	yes	—
184	#95×C₆₇	C₂³	1	2	yes	—
185	#95×C₆₇	C₂³	1	2	yes	—
186	#95×C₆₇	C₂³	1	2	yes	—
187	#95×C₆₇	C₂³	1	2	yes	—
188	#95×C₆₇	C₂³	1	1	yes	characteristic
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	1	yes	characteristic
191	#95×C₆₇	C₂³	1	2	yes	—
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	2	yes	—
195	#95×C₆₇	C₂³	1	2	yes	—
196	#95×C₆₇	C₂³	1	2	yes	—
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	1	yes	characteristic
203	#95×C₆₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₆₇	—	2	4	no	—
209	C₂⁴×C₆₇	—	2	2	no	—
210	C₂⁴×C₆₇	—	4	1	no	—
211	C₂⁴×C₆₇	—	4	1	no	—
212	C₂⁴×C₆₇	—	4	2	no	—
213	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
215	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₆₇	—	2	4	no	—
217	C₂×Q₈×C₆₇	—	4	2	no	—
218	C₂×Q₈×C₆₇	—	4	2	no	—
219	C₂×D₄×C₆₇	—	2	4	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	4	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	4	2	no	—
225	C₂×D₄×C₆₇	—	4	1	no	—
226	C₂×D₄×C₆₇	—	4	2	no	—
227	C₂×D₄×C₆₇	—	4	2	no	—
228	C₂×D₄×C₆₇	—	4	2	no	—
229	C₂×D₄×C₆₇	#41	1	8	yes	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	4	2	no	—
240	C₂²×C₄×C₆₇	—	4	1	no	—
241	C₂²×C₄×C₆₇	—	4	1	no	—
242	C₂²×C₄×C₆₇	—	4	2	no	—
243	C₂²×C₄×C₆₇	—	4	2	no	—
244	C₂²×C₄×C₆₇	—	4	2	no	—
245	C₂²×C₄×C₆₇	—	4	2	no	—
246	C₂²×C₄×C₆₇	—	4	2	no	—
247	C₂²×C₄×C₆₇	—	4	2	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	16	no	—
251	C₂²×C₄×C₆₇	#41	1	4	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
268	C₄⋊C₄×C₆₇	—	2	4	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	4	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	4	no	—
273	C₄⋊C₄×C₆₇	—	4	2	no	—
274	C₄⋊C₄×C₆₇	—	4	2	no	—
275	C₄⋊C₄×C₆₇	—	4	1	no	—
276	C₄⋊C₄×C₆₇	—	4	1	no	—
277	C₄⋊C₄×C₆₇	—	4	1	no	—
278	C₄⋊C₄×C₆₇	—	4	2	no	—
279	C₄⋊C₄×C₆₇	—	4	1	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	1	no	—
282	C₂²⋊C₄×C₆₇	—	2	4	no	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	4	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	4	no	—
289	C₂²⋊C₄×C₆₇	—	2	4	no	—
290	C₂²⋊C₄×C₆₇	—	2	4	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	4	no	—
293	C₂²⋊C₄×C₆₇	—	2	4	no	—
294	C₂²⋊C₄×C₆₇	—	2	4	no	—
295	C₂²⋊C₄×C₆₇	—	4	2	no	—
296	C₂²⋊C₄×C₆₇	—	4	2	no	—
297	C₂²⋊C₄×C₆₇	—	4	2	no	—
298	C₂²⋊C₄×C₆₇	—	4	2	no	—
299	C₂²⋊C₄×C₆₇	—	4	2	no	—
300	C₂²⋊C₄×C₆₇	—	4	1	no	—
301	C₂²⋊C₄×C₆₇	—	4	1	no	—
302	C₂²⋊C₄×C₆₇	—	4	1	no	—
303	C₂²⋊C₄×C₆₇	—	4	1	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	2	no	—
307	C₄²×C₆₇	—	2	4	no	—
308	C₄²×C₆₇	—	2	4	no	—
309	C₄²×C₆₇	—	2	2	no	—
310	C₄²×C₆₇	—	2	2	no	—
311	C₄²×C₆₇	—	4	2	no	—
312	C₄²×C₆₇	—	4	2	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	2	no	—
315	C₂³×C₆₇	—	2	2	no	—
316	C₂³×C₆₇	—	2	2	no	—
317	C₂³×C₆₇	—	2	2	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	2	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	1	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	2	no	—
327	C₂³×C₆₇	—	2	2	no	—
328	C₂³×C₆₇	—	2	2	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	4	8	no	—
332	C₂³×C₆₇	—	4	4	no	—
333	C₂³×C₆₇	—	4	4	no	—
334	C₂³×C₆₇	—	4	8	no	—
335	C₂³×C₆₇	—	4	4	no	—
336	C₂³×C₆₇	C₂×#41	1	4	yes	—
337	C₂³×C₆₇	C₂×#41	1	4	yes	—
338	C₂³×C₆₇	C₂×#41	1	2	yes	—
339	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
340	Q₈×C₆₇	—	8	4	no	—
341	D₄×C₆₇	—	4	8	no	—
342	D₄×C₆₇	—	4	8	no	—
343	D₄×C₆₇	—	4	4	no	—
344	D₄×C₆₇	—	4	8	no	—
345	C₂×C₄×C₆₇	—	2	8	no	—
346	C₂×C₄×C₆₇	—	2	1	no	—
347	C₂×C₄×C₆₇	—	2	1	no	—
348	C₂×C₄×C₆₇	—	2	1	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	1	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	1	no	—
367	C₂×C₄×C₆₇	—	2	1	no	—
368	C₂×C₄×C₆₇	—	2	1	no	—
369	C₂×C₄×C₆₇	—	2	1	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	2	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	2	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	2	no	—
385	C₂×C₄×C₆₇	—	2	2	no	—
386	C₂×C₄×C₆₇	—	4	4	no	—
387	C₂×C₄×C₆₇	—	4	8	no	—
388	C₂×C₄×C₆₇	—	4	8	no	—
389	C₂×C₄×C₆₇	—	8	4	no	—
390	C₂×C₄×C₆₇	—	8	4	no	—
391	C₂×C₄×C₆₇	—	8	4	no	—
392	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
393	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
394	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
396	C₂²×C₆₇	—	2	4	no	—
397	C₂²×C₆₇	—	2	4	no	—
398	C₂²×C₆₇	—	2	4	no	—
399	C₂²×C₆₇	—	2	4	no	—
400	C₂²×C₆₇	—	2	4	no	—
401	C₂²×C₆₇	—	2	2	no	—
402	C₂²×C₆₇	—	2	4	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	4	16	no	—
405	C₂²×C₆₇	—	4	2	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	1	no	—
408	C₂²×C₆₇	—	4	2	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	2	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	4	2	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
417	C₂²×C₆₇	C₂²×#41	1	2	yes	—
418	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂²×C₆₇	#585	1	2	yes	—
421	C₄×C₆₇	—	2	2	no	—
422	C₄×C₆₇	—	2	2	no	—
423	C₄×C₆₇	—	2	4	no	—
424	C₄×C₆₇	—	2	4	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₄×C₆₇	—	4	2	no	—
427	C₄×C₆₇	—	4	1	no	—
428	C₄×C₆₇	—	4	2	no	—
429	C₄×C₆₇	—	4	1	no	—
430	C₄×C₆₇	—	4	2	no	—
431	C₄×C₆₇	—	4	2	no	—
432	C₄×C₆₇	—	4	2	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	—	4	1	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	1	no	—
437	#59357	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
438	C₂×C₆₇	—	4	4	no	—
439	C₂×C₆₇	—	4	2	no	—
440	C₂×C₆₇	—	4	4	no	—
441	C₂×C₆₇	#3475	1	2	yes	—
442	C₂×C₆₇	#3481	1	1	yes	characteristic
443	C₂×C₆₇	#3490	1	1	yes	characteristic
444	C₂×C₆₇	#3505	1	2	yes	—
445	C₂×C₆₇	#3540	1	1	yes	characteristic
446	#2735	C₂×C₆₇	1	1	yes	characteristic, complemented
447	#2684	C₂×C₆₇	1	2	yes	complemented
448	#2668	C₂×C₆₇	1	1	yes	characteristic
449	#2611	C₂×C₆₇	1	1	yes	characteristic, complemented
450	#2607	C₂×C₆₇	1	1	yes	characteristic, complemented
451	#2600	C₂×C₆₇	1	1	yes	characteristic, complemented
452	#2598	C₂×C₆₇	1	1	yes	characteristic, complemented
453	#2578	C₂×C₆₇	1	2	yes	complemented
454	#2530	C₂×C₆₇	1	2	yes	complemented
455	#2523	C₂×C₆₇	1	2	yes	complemented
456	#2477	C₂×C₆₇	1	2	yes	complemented
457	#2460	C₂×C₆₇	1	2	yes	complemented
458	#2450	C₂×C₆₇	1	2	yes	complemented
459	#2427	C₂×C₆₇	1	2	yes	complemented
460	#2372	C₂×C₆₇	1	2	yes	complemented
461	#2364	C₂×C₆₇	1	2	yes	complemented
462	#2353	C₂×C₆₇	1	2	yes	complemented
463	C₄×#120	C₂×C₆₇	1	2	yes	complemented
464	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
465	C₆₇	#59357	1	1	yes	characteristic, direct product factor, Sylow
466	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
467	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
468	C₂×#124	C₂²×C₆₇	1	2	yes	—
469	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
470	C₂×#121	C₂²×C₆₇	1	2	yes	—
471	C₂×#120	C₂²×C₆₇	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
473	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
476	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
477	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
478	#400	C₂²×C₆₇	1	1	yes	characteristic, complemented
479	#400	C₂²×C₆₇	1	1	yes	characteristic, complemented
480	#400	C₂²×C₆₇	1	2	yes	complemented
481	#399	C₂²×C₆₇	1	1	yes	characteristic
482	#399	C₂²×C₆₇	1	1	yes	characteristic
483	#398	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	#397	C₂²×C₆₇	1	2	yes	—
485	#397	C₂²×C₆₇	1	1	yes	characteristic
486	#397	C₂²×C₆₇	1	2	yes	—
487	#397	C₂²×C₆₇	1	2	yes	—
488	#397	C₂²×C₆₇	1	2	yes	—
489	#397	C₂²×C₆₇	1	2	yes	complemented
490	#396	C₂²×C₆₇	1	2	yes	—
491	#394	C₂²×C₆₇	1	2	yes	—
492	#394	C₂²×C₆₇	1	2	yes	—
493	#394	C₂²×C₆₇	1	2	yes	—
494	#394	C₂²×C₆₇	1	1	yes	characteristic, complemented
495	#393	C₂²×C₆₇	1	2	yes	—
496	#393	C₂²×C₆₇	1	2	yes	—
497	#392	C₂²×C₆₇	1	1	yes	characteristic
498	#391	C₂²×C₆₇	1	2	yes	complemented
499	#391	C₂²×C₆₇	1	2	yes	complemented
500	#391	C₂²×C₆₇	1	2	yes	complemented
501	#389	C₂²×C₆₇	1	2	yes	complemented
502	#388	C₂²×C₆₇	1	2	yes	—
503	#388	C₂²×C₆₇	1	2	yes	—
504	#388	C₂²×C₆₇	1	2	yes	—
505	#388	C₂²×C₆₇	1	2	yes	—
506	#388	C₂²×C₆₇	1	2	yes	—
507	#388	C₂²×C₆₇	1	2	yes	complemented
508	#388	C₂²×C₆₇	1	2	yes	complemented
509	#388	C₂²×C₆₇	1	2	yes	complemented
510	#387	C₂²×C₆₇	1	2	yes	complemented
511	#387	C₂²×C₆₇	1	2	yes	complemented
512	#387	C₂²×C₆₇	1	2	yes	complemented
513	#387	C₂²×C₆₇	1	2	yes	complemented
514	#387	C₂²×C₆₇	1	2	yes	complemented
515	#387	C₂²×C₆₇	1	2	yes	complemented
516	#387	C₂²×C₆₇	1	2	yes	complemented
517	#387	C₂²×C₆₇	1	2	yes	complemented
518	#386	C₂²×C₆₇	1	2	yes	—
519	#386	C₂²×C₆₇	1	2	yes	—
520	#386	C₂²×C₆₇	1	2	yes	—
521	#386	C₂²×C₆₇	1	2	yes	—
522	#386	C₂²×C₆₇	1	2	yes	—
523	#386	C₂²×C₆₇	1	2	yes	—
524	#386	C₂²×C₆₇	1	2	yes	—
525	#386	C₂²×C₆₇	1	2	yes	—
526	#386	C₂²×C₆₇	1	2	yes	complemented
527	#385	C₂²×C₆₇	1	2	yes	—
528	#385	C₂²×C₆₇	1	2	yes	—
529	#385	C₂²×C₆₇	1	2	yes	—
530	#385	C₂²×C₆₇	1	2	yes	complemented
531	#385	C₂²×C₆₇	1	2	yes	complemented
532	#383	C₂²×C₆₇	1	2	yes	complemented
533	#383	C₂²×C₆₇	1	1	yes	characteristic, complemented
534	#381	C₂²×C₆₇	1	1	yes	characteristic
535	#381	C₂²×C₆₇	1	1	yes	characteristic
536	#380	C₂²×C₆₇	1	2	yes	—
537	#380	C₂²×C₆₇	1	2	yes	—
538	#380	C₂²×C₆₇	1	2	yes	complemented
539	#379	C₂²×C₆₇	1	1	yes	characteristic
540	#379	C₂²×C₆₇	1	1	yes	characteristic
541	#379	C₂²×C₆₇	1	2	yes	—
542	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
543	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
544	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
545	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
546	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
547	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
548	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
549	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
550	#376	C₂²×C₆₇	1	2	yes	complemented
551	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
552	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
553	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
555	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
556	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
557	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
558	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
559	C₂³×C₄	—	2	4	no	—
560	C₂³×C₄	—	4	2	no	—
561	C₂³×C₄	—	4	2	no	—
562	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
564	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
565	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
566	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
567	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
568	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
569	#125	—	4	2	no	—
570	#124	—	2	8	no	—
571	C₂²⋊Q₈	—	4	4	no	—
572	#121	—	2	8	no	—
573	#120	—	2	8	no	—
574	C₄×D₄	—	2	8	no	—
575	C₄×D₄	—	4	2	no	—
576	C₄×D₄	—	4	4	no	—
577	C₄×D₄	—	4	4	no	—
578	#117	—	4	2	no	—
579	#117	—	4	2	no	—
580	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
620	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
622	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
623	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
624	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
625	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
627	#95	C₂³×C₆₇	1	2	yes	—
628	#95	C₂³×C₆₇	1	2	yes	—
629	#95	C₂³×C₆₇	1	2	yes	—
630	#95	C₂³×C₆₇	1	2	yes	—
631	#95	C₂³×C₆₇	1	2	yes	—
632	#95	C₂³×C₆₇	1	2	yes	—
633	#95	C₂³×C₆₇	1	2	yes	—
634	#95	C₂³×C₆₇	1	1	yes	characteristic
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	1	yes	characteristic
637	#95	C₂³×C₆₇	1	2	yes	—
638	#95	C₂³×C₆₇	1	2	yes	—
639	#95	C₂³×C₆₇	1	2	yes	—
640	#95	C₂³×C₆₇	1	2	yes	—
641	#95	C₂³×C₆₇	1	2	yes	—
642	#95	C₂³×C₆₇	1	2	yes	—
643	#95	C₂³×C₆₇	1	2	yes	—
644	#95	C₂³×C₆₇	1	2	yes	—
645	#95	C₂³×C₆₇	1	2	yes	—
646	#95	C₂³×C₆₇	1	2	yes	—
647	#95	C₂³×C₆₇	1	2	yes	—
648	#95	C₂³×C₆₇	1	1	yes	characteristic
649	#95	C₂³×C₆₇	1	1	yes	characteristic
650	#95	C₂³×C₆₇	1	2	yes	—
651	#95	C₂³×C₆₇	1	2	yes	—
652	#95	C₂³×C₆₇	1	2	yes	—
653	#95	C₂³×C₆₇	1	2	yes	—
654	C₂⁴	—	2	4	no	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	4	1	no	—
657	C₂⁴	—	4	1	no	—
658	C₂⁴	—	4	2	no	—
659	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
660	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
661	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
662	C₂×Q₈	—	2	4	no	—
663	C₂×Q₈	—	4	2	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	4	2	no	—
671	C₂×D₄	—	4	1	no	—
672	C₂×D₄	—	4	2	no	—
673	C₂×D₄	—	4	2	no	—
674	C₂×D₄	—	4	2	no	—
675	C₂×D₄	#41×C₆₇	1	8	yes	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	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	—	4	2	no	—
686	C₂²×C₄	—	4	1	no	—
687	C₂²×C₄	—	4	1	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	2	no	—
693	C₂²×C₄	—	4	2	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	2	no	—
696	C₂²×C₄	—	4	16	no	—
697	C₂²×C₄	#41×C₆₇	1	4	yes	—
698	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
708	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
713	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	4	1	no	—
720	C₄⋊C₄	—	4	1	no	—
721	C₄⋊C₄	—	4	1	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	1	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	4	1	no	—
742	C₂²⋊C₄	—	4	1	no	—
743	C₂²⋊C₄	—	4	1	no	—
744	C₂²⋊C₄	—	4	1	no	—
745	C₂²⋊C₄	—	4	2	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₄²	—	2	4	no	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	4	2	no	—
758	C₄²	—	4	2	no	—
759	C₄²	—	4	2	no	—
760	C₄²	—	4	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	2	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	1	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	2	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	4	8	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	8	no	—
781	C₂³	—	4	4	no	—
782	C₂³	C₂×#41×C₆₇	1	4	yes	—
783	C₂³	C₂×#41×C₆₇	1	4	yes	—
784	C₂³	C₂×#41×C₆₇	1	2	yes	—
785	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
786	Q₈	—	8	4	no	—
787	D₄	—	4	8	no	—
788	D₄	—	4	8	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	8	no	—
791	C₂×C₄	—	2	8	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	1	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	8	no	—
835	C₂×C₄	—	8	4	no	—
836	C₂×C₄	—	8	4	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
839	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
840	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
841	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	4	no	—
849	C₂²	—	2	4	no	—
850	C₂²	—	4	16	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	1	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	1	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
863	C₂²	C₂²×#41×C₆₇	1	2	yes	—
864	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
865	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
866	C₂²	#585×C₆₇	1	2	yes	—
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	4	no	—
871	C₄	—	4	1	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	1	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₂	—	4	2	no	—
884	C₂	—	4	4	no	—
885	C₂	—	4	4	no	—
886	C₂	C₆₇×#3475	1	2	yes	—
887	C₂	C₆₇×#3481	1	1	yes	characteristic
888	C₂	C₆₇×#3490	1	1	yes	characteristic
889	C₂	C₆₇×#3505	1	2	yes	—
890	C₂	C₆₇×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2668	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×#2735	C₂	semidirect
2. C₆₇×#2684	C₂	semidirect
4. C₆₇×#2611	C₂	semidirect
5. C₆₇×#2607	C₂	semidirect
6. C₆₇×#2600	C₂	semidirect
7. C₆₇×#2598	C₂	semidirect
8. C₆₇×#2578	C₂	semidirect
9. C₆₇×#2530	C₂	semidirect
10. C₆₇×#2523	C₂	semidirect
11. C₆₇×#2477	C₂	semidirect
12. C₆₇×#2460	C₂	semidirect
13. C₆₇×#2450	C₂	semidirect
14. C₆₇×#2427	C₂	semidirect
15. C₆₇×#2372	C₂	semidirect
16. C₆₇×#2364	C₂	semidirect
17. C₆₇×#2353	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₆₇×#2280	C₂	semidirect
21. C₂×#125×C₆₇	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
29. C₂×C₄×D₄×C₆₇	C₂²	semidirect
32. #400×C₆₇	C₂²	semidirect
33. #400×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
37. #398×C₆₇	C₂²	semidirect
43. #397×C₆₇	C₂²	semidirect
48. #394×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
53. #391×C₆₇	C₂²	semidirect
54. #391×C₆₇	C₂²	semidirect
55. #389×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #388×C₆₇	C₂²	semidirect
63. #388×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
66. #387×C₆₇	C₂²	semidirect
67. #387×C₆₇	C₂²	semidirect
68. #387×C₆₇	C₂²	semidirect
69. #387×C₆₇	C₂²	semidirect
70. #387×C₆₇	C₂²	semidirect
71. #387×C₆₇	C₂²	semidirect
80. #386×C₆₇	C₂²	semidirect
84. #385×C₆₇	C₂²	semidirect
85. #385×C₆₇	C₂²	semidirect
86. #383×C₆₇	C₂²	semidirect
87. #383×C₆₇	C₂²	semidirect
92. #380×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. #376×C₆₇	C₂²	semidirect
105. #376×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
437. #59357	C₆₇	direct (N × H)
446. #2735	C₂×C₆₇	semidirect
447. #2684	C₂×C₆₇	semidirect
449. #2611	C₂×C₆₇	semidirect
450. #2607	C₂×C₆₇	semidirect
451. #2600	C₂×C₆₇	semidirect
452. #2598	C₂×C₆₇	semidirect
453. #2578	C₂×C₆₇	semidirect
454. #2530	C₂×C₆₇	semidirect
455. #2523	C₂×C₆₇	semidirect
456. #2477	C₂×C₆₇	semidirect
457. #2460	C₂×C₆₇	semidirect
458. #2450	C₂×C₆₇	semidirect
459. #2427	C₂×C₆₇	semidirect
460. #2372	C₂×C₆₇	semidirect
461. #2364	C₂×C₆₇	semidirect
462. #2353	C₂×C₆₇	semidirect
463. C₄×#120	C₂×C₆₇	semidirect
464. #2280	C₂×C₆₇	semidirect
465. C₆₇	#59357	direct (N × H)
467. C₂×#125	C₂²×C₆₇	semidirect
469. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
475. C₂×C₄×D₄	C₂²×C₆₇	semidirect
478. #400	C₂²×C₆₇	semidirect
479. #400	C₂²×C₆₇	semidirect
480. #400	C₂²×C₆₇	semidirect
483. #398	C₂²×C₆₇	semidirect
489. #397	C₂²×C₆₇	semidirect
494. #394	C₂²×C₆₇	semidirect
498. #391	C₂²×C₆₇	semidirect
499. #391	C₂²×C₆₇	semidirect
500. #391	C₂²×C₆₇	semidirect
501. #389	C₂²×C₆₇	semidirect
507. #388	C₂²×C₆₇	semidirect
508. #388	C₂²×C₆₇	semidirect
509. #388	C₂²×C₆₇	semidirect
510. #387	C₂²×C₆₇	semidirect
511. #387	C₂²×C₆₇	semidirect
512. #387	C₂²×C₆₇	semidirect
513. #387	C₂²×C₆₇	semidirect
514. #387	C₂²×C₆₇	semidirect
515. #387	C₂²×C₆₇	semidirect
516. #387	C₂²×C₆₇	semidirect
517. #387	C₂²×C₆₇	semidirect
526. #386	C₂²×C₆₇	semidirect
530. #385	C₂²×C₆₇	semidirect
531. #385	C₂²×C₆₇	semidirect
532. #383	C₂²×C₆₇	semidirect
533. #383	C₂²×C₆₇	semidirect
538. #380	C₂²×C₆₇	semidirect
547. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
548. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
549. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
550. #376	C₂²×C₆₇	semidirect
551. #376	C₂²×C₆₇	semidirect
552. 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×#2735	2
C₆₇×#2684	2
C₆₇×#2668	2
C₆₇×#2611	2
C₆₇×#2607	2
C₆₇×#2600	2
C₆₇×#2598	2
C₆₇×#2578	2
C₆₇×#2530	2
C₆₇×#2523	2
C₆₇×#2477	2
C₆₇×#2460	2
C₆₇×#2450	2
C₆₇×#2427	2
C₆₇×#2372	2
C₆₇×#2364	2
C₆₇×#2353	2
C₄×#120×C₆₇	2
C₆₇×#2280	2
#59357	67

Subgroups — C67×#59357 #30738608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59357 #30738608