Subgroups — C₆₇×#59369 #30738620

Order 17152.

2154 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2764	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#2760	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2743	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2607	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2600	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#2572	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2561	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2527	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2493	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2457	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2450	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2419	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
14	C₆₇×#2404	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2339	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₆₇	C₂	1	2	yes	maximal, complemented
19	C₂×#381×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×#120×C₆₇	C₂²	1	2	yes	—
25	C₂×C₄×D₄×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	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	#401×C₆₇	C₂²	1	2	yes	complemented
32	#400×C₆₇	C₂²	1	2	yes	complemented
33	#400×C₆₇	C₂²	1	2	yes	complemented
34	#400×C₆₇	C₂²	1	2	yes	complemented
35	#400×C₆₇	C₂²	1	2	yes	complemented
36	#399×C₆₇	C₂²	1	2	yes	—
37	#398×C₆₇	C₂²	1	2	yes	complemented
38	#397×C₆₇	C₂²	1	1	yes	characteristic
39	#397×C₆₇	C₂²	1	2	yes	—
40	#397×C₆₇	C₂²	1	1	yes	characteristic
41	#396×C₆₇	C₂²	1	2	yes	complemented
42	#394×C₆₇	C₂²	1	2	yes	—
43	#394×C₆₇	C₂²	1	2	yes	—
44	#393×C₆₇	C₂²	1	1	yes	characteristic
45	#393×C₆₇	C₂²	1	1	yes	characteristic
46	#393×C₆₇	C₂²	1	1	yes	characteristic
47	#393×C₆₇	C₂²	1	1	yes	characteristic
48	#393×C₆₇	C₂²	1	2	yes	complemented
49	#392×C₆₇	C₂²	1	1	yes	characteristic
50	#392×C₆₇	C₂²	1	1	yes	characteristic
51	#391×C₆₇	C₂²	1	2	yes	complemented
52	#391×C₆₇	C₂²	1	2	yes	complemented
53	#391×C₆₇	C₂²	1	2	yes	complemented
54	#388×C₆₇	C₂²	1	2	yes	—
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	2	yes	complemented
59	#388×C₆₇	C₂²	1	2	yes	complemented
60	#387×C₆₇	C₂²	1	2	yes	complemented
61	#387×C₆₇	C₂²	1	2	yes	complemented
62	#387×C₆₇	C₂²	1	2	yes	complemented
63	#387×C₆₇	C₂²	1	2	yes	complemented
64	#387×C₆₇	C₂²	1	2	yes	complemented
65	#387×C₆₇	C₂²	1	2	yes	complemented
66	#386×C₆₇	C₂²	1	2	yes	—
67	#386×C₆₇	C₂²	1	2	yes	—
68	#386×C₆₇	C₂²	1	2	yes	—
69	#386×C₆₇	C₂²	1	2	yes	—
70	#386×C₆₇	C₂²	1	2	yes	—
71	#386×C₆₇	C₂²	1	2	yes	—
72	#386×C₆₇	C₂²	1	2	yes	—
73	#386×C₆₇	C₂²	1	2	yes	—
74	#386×C₆₇	C₂²	1	2	yes	complemented
75	#386×C₆₇	C₂²	1	2	yes	complemented
76	#385×C₆₇	C₂²	1	2	yes	—
77	#385×C₆₇	C₂²	1	2	yes	—
78	#385×C₆₇	C₂²	1	2	yes	—
79	#385×C₆₇	C₂²	1	2	yes	—
80	#385×C₆₇	C₂²	1	2	yes	complemented
81	#383×C₆₇	C₂²	1	2	yes	complemented
82	#383×C₆₇	C₂²	1	2	yes	complemented
83	#381×C₆₇	C₂²	1	1	yes	characteristic
84	#381×C₆₇	C₂²	1	2	yes	—
85	#381×C₆₇	C₂²	1	2	yes	—
86	#381×C₆₇	C₂²	1	1	yes	characteristic
87	#381×C₆₇	C₂²	1	1	yes	characteristic
88	#381×C₆₇	C₂²	1	1	yes	characteristic
89	#381×C₆₇	C₂²	1	2	yes	—
90	#381×C₆₇	C₂²	1	1	yes	characteristic
91	#381×C₆₇	C₂²	1	2	yes	complemented
92	#381×C₆₇	C₂²	1	2	yes	complemented
93	#380×C₆₇	C₂²	1	2	yes	—
94	#380×C₆₇	C₂²	1	2	yes	complemented
95	#380×C₆₇	C₂²	1	2	yes	complemented
96	#379×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	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
103	#376×C₆₇	C₂²	1	2	yes	complemented
104	C₂×#95×C₆₇	C₂²	1	2	yes	—
105	C₂×#95×C₆₇	C₂²	1	2	yes	—
106	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
107	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×#41×C₆₇	—	2	8	no	—
109	C₂×#41×C₆₇	—	4	2	no	—
110	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
111	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
113	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
114	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₆₇	—	2	4	no	—
117	C₂³×C₄×C₆₇	—	4	2	no	—
118	C₂³×C₄×C₆₇	—	4	2	no	—
119	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
121	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
123	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
124	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
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	#123×C₆₇	—	4	4	no	—
130	C₂²⋊Q₈×C₆₇	—	4	2	no	—
131	#120×C₆₇	—	2	8	no	—
132	C₄×D₄×C₆₇	—	2	8	no	—
133	C₄×D₄×C₆₇	—	2	8	no	—
134	C₄×D₄×C₆₇	—	4	4	no	—
135	C₄×D₄×C₆₇	—	4	4	no	—
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	2	yes	—
140	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
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	2	yes	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
147	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
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	1	yes	characteristic
159	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
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	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	2	yes	—
172	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
176	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
177	#95×C₆₇	C₂³	1	2	yes	—
178	#95×C₆₇	C₂³	1	2	yes	—
179	#95×C₆₇	C₂³	1	2	yes	—
180	#95×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	2	yes	—
189	#95×C₆₇	C₂³	1	2	yes	—
190	#95×C₆₇	C₂³	1	2	yes	—
191	#95×C₆₇	C₂³	1	1	yes	characteristic
192	#95×C₆₇	C₂³	1	2	yes	—
193	#95×C₆₇	C₂³	1	2	yes	—
194	#95×C₆₇	C₂³	1	1	yes	characteristic
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	2	no	—
209	C₂⁴×C₆₇	—	2	2	no	—
210	C₂⁴×C₆₇	—	2	2	no	—
211	C₂⁴×C₆₇	—	2	4	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	1	yes	characteristic
216	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
217	#41×C₆₇	—	4	16	no	—
218	C₂×Q₈×C₆₇	—	2	4	no	—
219	C₂×Q₈×C₆₇	—	4	1	no	—
220	C₂×Q₈×C₆₇	—	4	1	no	—
221	C₂×Q₈×C₆₇	—	4	2	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	4	no	—
224	C₂×D₄×C₆₇	—	2	4	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	4	no	—
227	C₂×D₄×C₆₇	—	2	4	no	—
228	C₂×D₄×C₆₇	—	2	4	no	—
229	C₂×D₄×C₆₇	—	4	2	no	—
230	C₂×D₄×C₆₇	—	4	2	no	—
231	C₂×D₄×C₆₇	—	4	1	no	—
232	C₂×D₄×C₆₇	#41	1	8	yes	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	4	no	—
235	C₂²×C₄×C₆₇	—	2	4	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	2	4	no	—
239	C₂²×C₄×C₆₇	—	2	4	no	—
240	C₂²×C₄×C₆₇	—	2	4	no	—
241	C₂²×C₄×C₆₇	—	2	2	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	4	no	—
245	C₂²×C₄×C₆₇	—	2	4	no	—
246	C₂²×C₄×C₆₇	—	4	1	no	—
247	C₂²×C₄×C₆₇	—	4	1	no	—
248	C₂²×C₄×C₆₇	—	4	2	no	—
249	C₂²×C₄×C₆₇	—	4	2	no	—
250	C₂²×C₄×C₆₇	—	4	1	no	—
251	C₂²×C₄×C₆₇	—	4	1	no	—
252	C₂²×C₄×C₆₇	—	4	2	no	—
253	C₂²×C₄×C₆₇	—	4	2	no	—
254	C₂²×C₄×C₆₇	—	4	2	no	—
255	C₂²×C₄×C₆₇	—	4	2	no	—
256	C₂²×C₄×C₆₇	—	4	2	no	—
257	C₂²×C₄×C₆₇	—	4	2	no	—
258	C₂²×C₄×C₆₇	—	4	2	no	—
259	C₂²×C₄×C₆₇	—	4	2	no	—
260	C₂²×C₄×C₆₇	—	4	16	no	—
261	C₂²×C₄×C₆₇	#41	1	4	yes	complemented
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₆₇	—	2	4	no	—
278	C₄⋊C₄×C₆₇	—	2	4	no	—
279	C₄⋊C₄×C₆₇	—	4	2	no	—
280	C₄⋊C₄×C₆₇	—	4	2	no	—
281	C₄⋊C₄×C₆₇	—	4	2	no	—
282	C₄⋊C₄×C₆₇	—	4	2	no	—
283	C₄⋊C₄×C₆₇	—	4	2	no	—
284	C₄⋊C₄×C₆₇	—	4	1	no	—
285	C₄⋊C₄×C₆₇	—	4	2	no	—
286	C₄⋊C₄×C₆₇	—	4	2	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	—	2	4	no	—
296	C₂²⋊C₄×C₆₇	—	2	4	no	—
297	C₂²⋊C₄×C₆₇	—	4	1	no	—
298	C₂²⋊C₄×C₆₇	—	4	1	no	—
299	C₂²⋊C₄×C₆₇	—	4	1	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	2	no	—
304	C₂²⋊C₄×C₆₇	—	4	2	no	—
305	C₂²⋊C₄×C₆₇	—	4	2	no	—
306	C₂²⋊C₄×C₆₇	—	4	2	no	—
307	C₂²⋊C₄×C₆₇	—	4	2	no	—
308	C₂²⋊C₄×C₆₇	—	4	2	no	—
309	C₂²⋊C₄×C₆₇	—	4	2	no	—
310	C₂²⋊C₄×C₆₇	—	4	2	no	—
311	C₄²×C₆₇	—	2	4	no	—
312	C₄²×C₆₇	—	2	4	no	—
313	C₄²×C₆₇	—	4	2	no	—
314	C₄²×C₆₇	—	4	2	no	—
315	C₄²×C₆₇	—	4	2	no	—
316	C₂³×C₆₇	—	2	1	no	—
317	C₂³×C₆₇	—	2	1	no	—
318	C₂³×C₆₇	—	2	2	no	—
319	C₂³×C₆₇	—	2	8	no	—
320	C₂³×C₆₇	—	2	2	no	—
321	C₂³×C₆₇	—	2	2	no	—
322	C₂³×C₆₇	—	2	2	no	—
323	C₂³×C₆₇	—	2	1	no	—
324	C₂³×C₆₇	—	2	2	no	—
325	C₂³×C₆₇	—	2	2	no	—
326	C₂³×C₆₇	—	2	1	no	—
327	C₂³×C₆₇	—	2	1	no	—
328	C₂³×C₆₇	—	2	1	no	—
329	C₂³×C₆₇	—	2	2	no	—
330	C₂³×C₆₇	—	2	2	no	—
331	C₂³×C₆₇	—	2	2	no	—
332	C₂³×C₆₇	—	2	2	no	—
333	C₂³×C₆₇	—	2	2	no	—
334	C₂³×C₆₇	—	4	8	no	—
335	C₂³×C₆₇	—	4	8	no	—
336	C₂³×C₆₇	—	4	4	no	—
337	C₂³×C₆₇	—	4	4	no	—
338	C₂³×C₆₇	C₂×#41	1	2	yes	—
339	C₂³×C₆₇	C₂×#41	1	4	yes	—
340	C₂³×C₆₇	C₂×#41	1	4	yes	—
341	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
342	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
343	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
344	Q₈×C₆₇	—	4	4	no	—
345	Q₈×C₆₇	—	8	2	no	—
346	D₄×C₆₇	—	2	16	no	—
347	D₄×C₆₇	—	4	8	no	—
348	D₄×C₆₇	—	4	8	no	—
349	D₄×C₆₇	—	4	4	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	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	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	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	1	no	—
374	C₂×C₄×C₆₇	—	2	1	no	—
375	C₂×C₄×C₆₇	—	2	1	no	—
376	C₂×C₄×C₆₇	—	2	1	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	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	2	no	—
388	C₂×C₄×C₆₇	—	2	2	no	—
389	C₂×C₄×C₆₇	—	4	4	no	—
390	C₂×C₄×C₆₇	—	4	8	no	—
391	C₂×C₄×C₆₇	—	4	8	no	—
392	C₂×C₄×C₆₇	—	4	8	no	—
393	C₂×C₄×C₆₇	—	4	4	no	—
394	C₂×C₄×C₆₇	—	4	4	no	—
395	C₂×C₄×C₆₇	—	8	4	no	—
396	C₂×C₄×C₆₇	—	8	4	no	—
397	C₂×C₄×C₆₇	—	8	4	no	—
398	C₂×C₄×C₆₇	—	8	2	no	—
399	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
400	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
401	C₂²×C₆₇	—	2	4	no	—
402	C₂²×C₆₇	—	2	2	no	—
403	C₂²×C₆₇	—	2	4	no	—
404	C₂²×C₆₇	—	2	2	no	—
405	C₂²×C₆₇	—	2	4	no	—
406	C₂²×C₆₇	—	2	4	no	—
407	C₂²×C₆₇	—	2	4	no	—
408	C₂²×C₆₇	—	2	2	no	—
409	C₂²×C₆₇	—	2	2	no	—
410	C₂²×C₆₇	—	2	4	no	—
411	C₂²×C₆₇	—	2	4	no	—
412	C₂²×C₆₇	—	4	16	no	—
413	C₂²×C₆₇	—	4	1	no	—
414	C₂²×C₆₇	—	4	1	no	—
415	C₂²×C₆₇	—	4	2	no	—
416	C₂²×C₆₇	—	4	2	no	—
417	C₂²×C₆₇	—	4	2	no	—
418	C₂²×C₆₇	—	4	2	no	—
419	C₂²×C₆₇	—	4	2	no	—
420	C₂²×C₆₇	—	4	2	no	—
421	C₂²×C₆₇	—	4	1	no	—
422	C₂²×C₆₇	—	4	1	no	—
423	C₂²×C₆₇	#551	1	4	yes	—
424	C₂²×C₆₇	C₂²×#41	1	2	yes	—
425	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂²×C₆₇	#585	1	2	yes	—
429	C₄×C₆₇	—	2	4	no	—
430	C₄×C₆₇	—	2	4	no	—
431	C₄×C₆₇	—	4	1	no	—
432	C₄×C₆₇	—	4	1	no	—
433	C₄×C₆₇	—	4	2	no	—
434	C₄×C₆₇	—	4	2	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	2	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	2	no	—
439	C₄×C₆₇	—	4	2	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	1	no	—
442	C₄×C₆₇	—	4	1	no	—
443	C₄×C₆₇	—	4	2	no	—
444	#59369	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂×C₆₇	—	2	4	no	—
446	C₂×C₆₇	—	4	4	no	—
447	C₂×C₆₇	—	4	2	no	—
448	C₂×C₆₇	—	4	2	no	—
449	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
450	C₂×C₆₇	#3475	1	2	yes	—
451	C₂×C₆₇	#3490	1	1	yes	characteristic
452	C₂×C₆₇	#3513	1	2	yes	—
453	C₂×C₆₇	#3533	1	1	yes	characteristic
454	#2764	C₂×C₆₇	1	1	yes	characteristic, complemented
455	#2760	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2743	C₂×C₆₇	1	2	yes	complemented
457	#2607	C₂×C₆₇	1	1	yes	characteristic, complemented
458	#2600	C₂×C₆₇	1	1	yes	characteristic, complemented
459	#2572	C₂×C₆₇	1	2	yes	complemented
460	#2561	C₂×C₆₇	1	1	yes	characteristic, complemented
461	#2527	C₂×C₆₇	1	2	yes	complemented
462	#2493	C₂×C₆₇	1	2	yes	complemented
463	#2457	C₂×C₆₇	1	2	yes	complemented
464	#2450	C₂×C₆₇	1	2	yes	complemented
465	#2419	C₂×C₆₇	1	2	yes	complemented
466	#2418	C₂×C₆₇	1	2	yes	complemented
467	#2404	C₂×C₆₇	1	1	yes	characteristic
468	#2353	C₂×C₆₇	1	2	yes	complemented
469	#2353	C₂×C₆₇	1	2	yes	complemented
470	#2339	C₂×C₆₇	1	2	yes	complemented
471	C₄×#120	C₂×C₆₇	1	2	yes	complemented
472	C₂×#381	C₂×C₆₇	1	1	yes	characteristic, complemented
473	C₆₇	#59369	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
475	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
476	C₂×#123	C₂²×C₆₇	1	2	yes	—
477	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
478	C₂×#120	C₂²×C₆₇	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
480	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
481	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
482	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
483	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
484	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
485	#401	C₂²×C₆₇	1	2	yes	complemented
486	#400	C₂²×C₆₇	1	2	yes	complemented
487	#400	C₂²×C₆₇	1	2	yes	complemented
488	#400	C₂²×C₆₇	1	2	yes	complemented
489	#400	C₂²×C₆₇	1	2	yes	complemented
490	#399	C₂²×C₆₇	1	2	yes	—
491	#398	C₂²×C₆₇	1	2	yes	complemented
492	#397	C₂²×C₆₇	1	1	yes	characteristic
493	#397	C₂²×C₆₇	1	1	yes	characteristic
494	#397	C₂²×C₆₇	1	2	yes	—
495	#396	C₂²×C₆₇	1	2	yes	complemented
496	#394	C₂²×C₆₇	1	2	yes	—
497	#394	C₂²×C₆₇	1	2	yes	—
498	#393	C₂²×C₆₇	1	1	yes	characteristic
499	#393	C₂²×C₆₇	1	1	yes	characteristic
500	#393	C₂²×C₆₇	1	1	yes	characteristic
501	#393	C₂²×C₆₇	1	1	yes	characteristic
502	#393	C₂²×C₆₇	1	2	yes	complemented
503	#392	C₂²×C₆₇	1	1	yes	characteristic
504	#392	C₂²×C₆₇	1	1	yes	characteristic
505	#391	C₂²×C₆₇	1	2	yes	complemented
506	#391	C₂²×C₆₇	1	2	yes	complemented
507	#391	C₂²×C₆₇	1	2	yes	complemented
508	#388	C₂²×C₆₇	1	2	yes	—
509	#388	C₂²×C₆₇	1	2	yes	—
510	#388	C₂²×C₆₇	1	2	yes	—
511	#388	C₂²×C₆₇	1	2	yes	—
512	#388	C₂²×C₆₇	1	2	yes	complemented
513	#388	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	#387	C₂²×C₆₇	1	2	yes	complemented
519	#387	C₂²×C₆₇	1	2	yes	complemented
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	—
527	#386	C₂²×C₆₇	1	2	yes	—
528	#386	C₂²×C₆₇	1	2	yes	complemented
529	#386	C₂²×C₆₇	1	2	yes	complemented
530	#385	C₂²×C₆₇	1	2	yes	—
531	#385	C₂²×C₆₇	1	2	yes	—
532	#385	C₂²×C₆₇	1	2	yes	—
533	#385	C₂²×C₆₇	1	2	yes	—
534	#385	C₂²×C₆₇	1	2	yes	complemented
535	#383	C₂²×C₆₇	1	2	yes	complemented
536	#383	C₂²×C₆₇	1	2	yes	complemented
537	#381	C₂²×C₆₇	1	2	yes	—
538	#381	C₂²×C₆₇	1	2	yes	—
539	#381	C₂²×C₆₇	1	1	yes	characteristic
540	#381	C₂²×C₆₇	1	1	yes	characteristic
541	#381	C₂²×C₆₇	1	1	yes	characteristic
542	#381	C₂²×C₆₇	1	2	yes	—
543	#381	C₂²×C₆₇	1	1	yes	characteristic
544	#381	C₂²×C₆₇	1	1	yes	characteristic
545	#381	C₂²×C₆₇	1	2	yes	complemented
546	#381	C₂²×C₆₇	1	2	yes	complemented
547	#380	C₂²×C₆₇	1	2	yes	—
548	#380	C₂²×C₆₇	1	2	yes	complemented
549	#380	C₂²×C₆₇	1	2	yes	complemented
550	#379	C₂²×C₆₇	1	2	yes	—
551	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
552	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
553	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
554	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
556	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
557	#376	C₂²×C₆₇	1	2	yes	complemented
558	C₂×#95	C₂²×C₆₇	1	2	yes	—
559	C₂×#95	C₂²×C₆₇	1	2	yes	—
560	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
561	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
562	C₂×#41	—	2	8	no	—
563	C₂×#41	—	4	2	no	—
564	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
565	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
567	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
568	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
569	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
570	C₂³×C₄	—	2	4	no	—
571	C₂³×C₄	—	4	2	no	—
572	C₂³×C₄	—	4	2	no	—
573	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
576	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
577	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
578	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
580	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
581	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
583	#123	—	4	4	no	—
584	C₂²⋊Q₈	—	4	2	no	—
585	#120	—	2	8	no	—
586	C₄×D₄	—	2	8	no	—
587	C₄×D₄	—	2	8	no	—
588	C₄×D₄	—	4	4	no	—
589	C₄×D₄	—	4	4	no	—
590	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
600	C₂×C₂²⋊C₄	—	4	2	no	—
601	C₂×C₂²⋊C₄	—	4	2	no	—
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	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
613	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
616	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
626	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
627	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
629	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
630	C₂×C₄²	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	2	yes	—
635	#95	C₂³×C₆₇	1	2	yes	—
636	#95	C₂³×C₆₇	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
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	#95	C₂³×C₆₇	1	2	yes	—
655	#95	C₂³×C₆₇	1	2	yes	—
656	#95	C₂³×C₆₇	1	1	yes	characteristic
657	#95	C₂³×C₆₇	1	1	yes	characteristic
658	#95	C₂³×C₆₇	1	2	yes	—
659	#95	C₂³×C₆₇	1	2	yes	—
660	#95	C₂³×C₆₇	1	2	yes	—
661	#95	C₂³×C₆₇	1	2	yes	—
662	C₂⁴	—	2	2	no	—
663	C₂⁴	—	2	2	no	—
664	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	4	no	—
666	C₂⁴	—	4	2	no	—
667	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
668	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
669	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
670	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
671	#41	—	4	16	no	—
672	C₂×Q₈	—	2	4	no	—
673	C₂×Q₈	—	4	1	no	—
674	C₂×Q₈	—	4	1	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	4	1	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	#41×C₆₇	1	8	yes	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	2	4	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	4	1	no	—
701	C₂²×C₄	—	4	1	no	—
702	C₂²×C₄	—	4	2	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	1	no	—
705	C₂²×C₄	—	4	1	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	2	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	16	no	—
715	C₂²×C₄	#41×C₆₇	1	4	yes	complemented
716	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	2	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	1	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	1	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₄²	—	2	4	no	—
766	C₄²	—	2	4	no	—
767	C₄²	—	4	2	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	2	8	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	4	8	no	—
789	C₂³	—	4	8	no	—
790	C₂³	—	4	4	no	—
791	C₂³	—	4	4	no	—
792	C₂³	C₂×#41×C₆₇	1	2	yes	—
793	C₂³	C₂×#41×C₆₇	1	4	yes	—
794	C₂³	C₂×#41×C₆₇	1	4	yes	—
795	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
796	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
797	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
798	Q₈	—	4	4	no	—
799	Q₈	—	8	2	no	—
800	D₄	—	2	16	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	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	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	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	1	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	—	8	4	no	—
852	C₂×C₄	—	8	4	no	—
853	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
854	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
855	C₂²	—	2	2	no	—
856	C₂²	—	2	4	no	—
857	C₂²	—	2	2	no	—
858	C₂²	—	2	4	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	2	4	no	—
861	C₂²	—	2	4	no	—
862	C₂²	—	2	2	no	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	4	16	no	—
867	C₂²	—	4	1	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	1	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	#551×C₆₇	1	4	yes	—
878	C₂²	C₂²×#41×C₆₇	1	2	yes	—
879	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
880	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
881	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
882	C₂²	#585×C₆₇	1	2	yes	—
883	C₄	—	2	4	no	—
884	C₄	—	2	4	no	—
885	C₄	—	4	1	no	—
886	C₄	—	4	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	1	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₂	—	2	4	no	—
899	C₂	—	4	2	no	—
900	C₂	—	4	2	no	—
901	C₂	—	4	4	no	—
902	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
903	C₂	C₆₇×#3475	1	2	yes	—
904	C₂	C₆₇×#3490	1	1	yes	characteristic
905	C₂	C₆₇×#3513	1	2	yes	—
906	C₂	C₆₇×#3533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2404	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×#2764	C₂	semidirect
2. C₆₇×#2760	C₂	semidirect
3. C₆₇×#2743	C₂	semidirect
4. C₆₇×#2607	C₂	semidirect
5. C₆₇×#2600	C₂	semidirect
6. C₆₇×#2572	C₂	semidirect
7. C₆₇×#2561	C₂	semidirect
8. C₆₇×#2527	C₂	semidirect
9. C₆₇×#2493	C₂	semidirect
10. C₆₇×#2457	C₂	semidirect
11. C₆₇×#2450	C₂	semidirect
12. C₆₇×#2419	C₂	semidirect
13. C₆₇×#2418	C₂	semidirect
15. C₆₇×#2353	C₂	semidirect
16. C₆₇×#2353	C₂	semidirect
17. C₆₇×#2339	C₂	semidirect
18. C₄×#120×C₆₇	C₂	semidirect
19. C₂×#381×C₆₇	C₂	semidirect
31. #401×C₆₇	C₂²	semidirect
32. #400×C₆₇	C₂²	semidirect
33. #400×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
35. #400×C₆₇	C₂²	semidirect
37. #398×C₆₇	C₂²	semidirect
41. #396×C₆₇	C₂²	semidirect
48. #393×C₆₇	C₂²	semidirect
51. #391×C₆₇	C₂²	semidirect
52. #391×C₆₇	C₂²	semidirect
53. #391×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
63. #387×C₆₇	C₂²	semidirect
64. #387×C₆₇	C₂²	semidirect
65. #387×C₆₇	C₂²	semidirect
74. #386×C₆₇	C₂²	semidirect
75. #386×C₆₇	C₂²	semidirect
80. #385×C₆₇	C₂²	semidirect
81. #383×C₆₇	C₂²	semidirect
82. #383×C₆₇	C₂²	semidirect
91. #381×C₆₇	C₂²	semidirect
92. #381×C₆₇	C₂²	semidirect
94. #380×C₆₇	C₂²	semidirect
95. #380×C₆₇	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
103. #376×C₆₇	C₂²	semidirect
106. C₂×#95×C₆₇	C₂²	semidirect
261. C₂²×C₄×C₆₇	#41	semidirect
444. #59369	C₆₇	direct (N × H)
454. #2764	C₂×C₆₇	semidirect
455. #2760	C₂×C₆₇	semidirect
456. #2743	C₂×C₆₇	semidirect
457. #2607	C₂×C₆₇	semidirect
458. #2600	C₂×C₆₇	semidirect
459. #2572	C₂×C₆₇	semidirect
460. #2561	C₂×C₆₇	semidirect
461. #2527	C₂×C₆₇	semidirect
462. #2493	C₂×C₆₇	semidirect
463. #2457	C₂×C₆₇	semidirect
464. #2450	C₂×C₆₇	semidirect
465. #2419	C₂×C₆₇	semidirect
466. #2418	C₂×C₆₇	semidirect
468. #2353	C₂×C₆₇	semidirect
469. #2353	C₂×C₆₇	semidirect
470. #2339	C₂×C₆₇	semidirect
471. C₄×#120	C₂×C₆₇	semidirect
472. C₂×#381	C₂×C₆₇	semidirect
473. C₆₇	#59369	direct (N × H)
485. #401	C₂²×C₆₇	semidirect
486. #400	C₂²×C₆₇	semidirect
487. #400	C₂²×C₆₇	semidirect
488. #400	C₂²×C₆₇	semidirect
489. #400	C₂²×C₆₇	semidirect
491. #398	C₂²×C₆₇	semidirect
495. #396	C₂²×C₆₇	semidirect
502. #393	C₂²×C₆₇	semidirect
505. #391	C₂²×C₆₇	semidirect
506. #391	C₂²×C₆₇	semidirect
507. #391	C₂²×C₆₇	semidirect
512. #388	C₂²×C₆₇	semidirect
513. #388	C₂²×C₆₇	semidirect
514. #387	C₂²×C₆₇	semidirect
515. #387	C₂²×C₆₇	semidirect
516. #387	C₂²×C₆₇	semidirect
517. #387	C₂²×C₆₇	semidirect
518. #387	C₂²×C₆₇	semidirect
519. #387	C₂²×C₆₇	semidirect
528. #386	C₂²×C₆₇	semidirect
529. #386	C₂²×C₆₇	semidirect
534. #385	C₂²×C₆₇	semidirect
535. #383	C₂²×C₆₇	semidirect
536. #383	C₂²×C₆₇	semidirect
545. #381	C₂²×C₆₇	semidirect
546. #381	C₂²×C₆₇	semidirect
548. #380	C₂²×C₆₇	semidirect
549. #380	C₂²×C₆₇	semidirect
555. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
556. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
557. #376	C₂²×C₆₇	semidirect
560. C₂×#95	C₂²×C₆₇	semidirect
715. C₂²×C₄	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2764	2
C₆₇×#2760	2
C₆₇×#2743	2
C₆₇×#2607	2
C₆₇×#2600	2
C₆₇×#2572	2
C₆₇×#2561	2
C₆₇×#2527	2
C₆₇×#2493	2
C₆₇×#2457	2
C₆₇×#2450	2
C₆₇×#2419	2
C₆₇×#2418	2
C₆₇×#2404	2
C₆₇×#2353	2
C₆₇×#2339	2
C₄×#120×C₆₇	2
C₂×#381×C₆₇	2
#59369	67

Subgroups — C67×#59369 #30738620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59369 #30738620