Subgroups — C₆₇×#21420 #30700671

Order 17152.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2280	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1996	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1964	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1898	C₂	1	4	yes	maximal, complemented
7	C₄×#99×C₆₇	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₆₇	C₄	1	1	yes	characteristic, complemented
9	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
10	#525×C₆₇	—	2	1	no	—
11	#525×C₆₇	—	2	1	no	—
12	#525×C₆₇	—	2	1	no	—
13	#525×C₆₇	—	2	1	no	—
14	#525×C₆₇	—	2	1	no	—
15	#525×C₆₇	—	2	1	no	—
16	#525×C₆₇	—	2	1	no	—
17	#525×C₆₇	—	2	1	no	—
18	C₂×#123×C₆₇	C₄	1	2	yes	complemented
19	C₂×C₂²⋊Q₈×C₆₇	C₄	1	1	yes	characteristic, complemented
20	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂×#121×C₆₇	C₄	1	1	yes	characteristic, complemented
22	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#120×C₆₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₆₇	C₄	1	2	yes	complemented
25	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
26	C₂×#117×C₆₇	—	2	1	no	—
27	C₂×#117×C₆₇	C₄	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
29	C₂²×C₄²×C₆₇	—	2	1	no	—
30	C₂×#99×C₆₇	C₂²	1	8	yes	—
31	#381×C₆₇	—	2	1	no	—
32	#380×C₆₇	—	2	1	no	—
33	#380×C₆₇	C₂²	1	2	yes	—
34	#379×C₆₇	C₂²	1	2	yes	—
35	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
36	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
37	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
39	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
41	C₂×#95×C₆₇	—	2	1	no	—
42	#342×C₆₇	C₂²	1	8	yes	—
43	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
44	C₂×#41×C₆₇	—	2	1	no	—
45	C₂×#41×C₆₇	—	2	1	no	—
46	C₂×#41×C₆₇	—	2	1	no	—
47	C₂×#41×C₆₇	—	2	1	no	—
48	C₂×#41×C₆₇	—	4	4	no	—
49	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₆₇	C₂×C₄	1	2	yes	—
52	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
54	C₂³×C₄×C₆₇	—	2	2	no	—
55	C₂³×C₄×C₆₇	—	4	4	no	—
56	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₆₇	C₂×C₄	1	2	yes	complemented
61	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
67	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
71	#123×C₆₇	—	2	2	no	—
72	#123×C₆₇	—	2	2	no	—
73	#123×C₆₇	—	2	2	no	—
74	#123×C₆₇	—	2	2	no	—
75	C₂²⋊Q₈×C₆₇	—	2	1	no	—
76	C₂²⋊Q₈×C₆₇	—	2	1	no	—
77	C₂²⋊Q₈×C₆₇	—	2	1	no	—
78	C₂²⋊Q₈×C₆₇	—	2	1	no	—
79	C₂²⋊Q₈×C₆₇	—	2	1	no	—
80	C₂²⋊Q₈×C₆₇	—	2	1	no	—
81	C₂²⋊Q₈×C₆₇	—	2	1	no	—
82	C₂²⋊Q₈×C₆₇	—	2	1	no	—
83	#121×C₆₇	—	2	1	no	—
84	#121×C₆₇	—	2	1	no	—
85	#121×C₆₇	—	2	1	no	—
86	#121×C₆₇	—	2	1	no	—
87	#121×C₆₇	—	2	1	no	—
88	#121×C₆₇	—	2	1	no	—
89	#121×C₆₇	—	2	1	no	—
90	#121×C₆₇	—	2	1	no	—
91	#120×C₆₇	—	2	2	no	—
92	#120×C₆₇	—	2	2	no	—
93	#120×C₆₇	—	2	2	no	—
94	#120×C₆₇	—	2	2	no	—
95	C₄×D₄×C₆₇	—	2	2	no	—
96	C₄×D₄×C₆₇	—	2	2	no	—
97	C₄×D₄×C₆₇	—	2	2	no	—
98	C₄×D₄×C₆₇	—	2	2	no	—
99	C₄×D₄×C₆₇	—	2	2	no	—
100	C₄×D₄×C₆₇	—	2	2	no	—
101	C₄×D₄×C₆₇	—	2	2	no	—
102	C₄×D₄×C₆₇	—	2	2	no	—
103	#117×C₆₇	—	2	1	no	—
104	#117×C₆₇	—	2	1	no	—
105	#117×C₆₇	—	2	1	no	—
106	#117×C₆₇	—	2	1	no	—
107	#117×C₆₇	—	4	4	no	—
108	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
109	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
110	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic, complemented
111	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	complemented
112	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	complemented
113	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
114	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
115	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
116	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
117	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
119	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	complemented
120	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	complemented
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄²×C₆₇	—	2	2	no	—
125	C₂×C₄²×C₆₇	—	2	2	no	—
126	C₂×C₄²×C₆₇	—	2	2	no	—
127	C₂×C₄²×C₆₇	—	4	4	no	—
128	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	complemented
129	#99×C₆₇	—	2	16	no	—
130	#95×C₆₇	—	2	2	no	—
131	#95×C₆₇	—	2	2	no	—
132	#95×C₆₇	—	2	2	no	—
133	#95×C₆₇	—	2	2	no	—
134	C₂⁴×C₆₇	—	2	4	no	—
135	C₂⁴×C₆₇	—	4	2	no	—
136	C₂⁴×C₆₇	—	4	2	no	—
137	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×C₆₇	C₂²×C₄	1	2	yes	—
140	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
143	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
145	#41×C₆₇	—	4	4	no	—
146	#41×C₆₇	—	4	4	no	—
147	#41×C₆₇	—	4	4	no	—
148	#41×C₆₇	—	4	4	no	—
149	C₂×Q₈×C₆₇	—	2	1	no	—
150	C₂×Q₈×C₆₇	—	2	1	no	—
151	C₂×Q₈×C₆₇	—	4	2	no	—
152	C₂×D₄×C₆₇	—	2	2	no	—
153	C₂×D₄×C₆₇	—	2	2	no	—
154	C₂×D₄×C₆₇	—	2	2	no	—
155	C₂×D₄×C₆₇	—	2	2	no	—
156	C₂×D₄×C₆₇	—	2	2	no	—
157	C₂×D₄×C₆₇	—	2	2	no	—
158	C₂×D₄×C₆₇	—	2	8	no	—
159	C₂×D₄×C₆₇	—	2	1	no	—
160	C₂×D₄×C₆₇	—	2	1	no	—
161	C₂×D₄×C₆₇	—	4	2	no	—
162	C₂×D₄×C₆₇	—	4	4	no	—
163	C₂×D₄×C₆₇	—	4	4	no	—
164	C₂²×C₄×C₆₇	—	2	4	no	—
165	C₂²×C₄×C₆₇	—	2	4	no	—
166	C₂²×C₄×C₆₇	—	2	4	no	—
167	C₂²×C₄×C₆₇	—	2	8	no	—
168	C₂²×C₄×C₆₇	—	2	4	no	—
169	C₂²×C₄×C₆₇	—	2	2	no	—
170	C₂²×C₄×C₆₇	—	2	2	no	—
171	C₂²×C₄×C₆₇	—	2	4	no	—
172	C₂²×C₄×C₆₇	—	4	2	no	—
173	C₂²×C₄×C₆₇	—	4	2	no	—
174	C₂²×C₄×C₆₇	—	4	2	no	—
175	C₂²×C₄×C₆₇	—	4	2	no	—
176	C₂²×C₄×C₆₇	—	4	2	no	—
177	C₂²×C₄×C₆₇	—	4	2	no	—
178	C₂²×C₄×C₆₇	—	4	2	no	—
179	C₂²×C₄×C₆₇	—	4	2	no	—
180	C₂²×C₄×C₆₇	—	4	2	no	—
181	C₂²×C₄×C₆₇	—	4	2	no	—
182	C₂²×C₄×C₆₇	—	4	2	no	—
183	C₂²×C₄×C₆₇	—	4	4	no	—
184	C₂²×C₄×C₆₇	—	4	4	no	—
185	C₂²×C₄×C₆₇	—	4	4	no	—
186	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
203	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
206	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
207	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₆₇	—	2	1	no	—
218	C₄⋊C₄×C₆₇	—	2	1	no	—
219	C₄⋊C₄×C₆₇	—	2	1	no	—
220	C₄⋊C₄×C₆₇	—	2	1	no	—
221	C₄⋊C₄×C₆₇	—	2	2	no	—
222	C₄⋊C₄×C₆₇	—	2	2	no	—
223	C₄⋊C₄×C₆₇	—	2	2	no	—
224	C₄⋊C₄×C₆₇	—	2	2	no	—
225	C₄⋊C₄×C₆₇	—	4	4	no	—
226	C₂²⋊C₄×C₆₇	—	2	8	no	—
227	C₂²⋊C₄×C₆₇	—	2	2	no	—
228	C₂²⋊C₄×C₆₇	—	2	2	no	—
229	C₂²⋊C₄×C₆₇	—	2	2	no	—
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	2	no	—
235	C₂²⋊C₄×C₆₇	—	2	2	no	—
236	C₂²⋊C₄×C₆₇	—	2	2	no	—
237	C₂²⋊C₄×C₆₇	—	2	2	no	—
238	C₂²⋊C₄×C₆₇	—	2	8	no	—
239	C₂²⋊C₄×C₆₇	—	4	4	no	—
240	C₂²⋊C₄×C₆₇	—	4	4	no	—
241	C₂²⋊C₄×C₆₇	#41	1	8	yes	complemented
242	C₄²×C₆₇	—	2	2	no	—
243	C₄²×C₆₇	—	2	2	no	—
244	C₄²×C₆₇	—	4	4	no	—
245	C₄²×C₆₇	—	4	4	no	—
246	C₄²×C₆₇	—	4	4	no	—
247	C₂³×C₆₇	—	2	2	no	—
248	C₂³×C₆₇	—	2	2	no	—
249	C₂³×C₆₇	—	2	2	no	—
250	C₂³×C₆₇	—	2	2	no	—
251	C₂³×C₆₇	—	2	2	no	—
252	C₂³×C₆₇	—	2	2	no	—
253	C₂³×C₆₇	—	2	2	no	—
254	C₂³×C₆₇	—	2	2	no	—
255	C₂³×C₆₇	—	2	2	no	—
256	C₂³×C₆₇	—	2	2	no	—
257	C₂³×C₆₇	—	2	2	no	—
258	C₂³×C₆₇	—	2	2	no	—
259	C₂³×C₆₇	—	2	2	no	—
260	C₂³×C₆₇	—	2	4	no	—
261	C₂³×C₆₇	—	4	1	no	—
262	C₂³×C₆₇	—	4	1	no	—
263	C₂³×C₆₇	—	4	1	no	—
264	C₂³×C₆₇	—	4	1	no	—
265	C₂³×C₆₇	—	4	1	no	—
266	C₂³×C₆₇	—	4	1	no	—
267	C₂³×C₆₇	—	4	1	no	—
268	C₂³×C₆₇	—	4	1	no	—
269	C₂³×C₆₇	—	4	16	no	—
270	C₂³×C₆₇	—	4	2	no	—
271	C₂³×C₆₇	—	4	2	no	—
272	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
277	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
278	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
279	C₂³×C₆₇	C₂×#41	1	4	yes	—
280	Q₈×C₆₇	—	4	2	no	—
281	Q₈×C₆₇	—	4	2	no	—
282	D₄×C₆₇	—	4	2	no	—
283	D₄×C₆₇	—	4	4	no	—
284	D₄×C₆₇	—	4	4	no	—
285	D₄×C₆₇	—	4	4	no	—
286	D₄×C₆₇	—	4	4	no	—
287	D₄×C₆₇	—	4	4	no	—
288	D₄×C₆₇	—	4	4	no	—
289	D₄×C₆₇	—	4	2	no	—
290	C₂×C₄×C₆₇	—	2	2	no	—
291	C₂×C₄×C₆₇	—	2	2	no	—
292	C₂×C₄×C₆₇	—	2	2	no	—
293	C₂×C₄×C₆₇	—	2	2	no	—
294	C₂×C₄×C₆₇	—	2	2	no	—
295	C₂×C₄×C₆₇	—	2	2	no	—
296	C₂×C₄×C₆₇	—	2	2	no	—
297	C₂×C₄×C₆₇	—	2	2	no	—
298	C₂×C₄×C₆₇	—	2	2	no	—
299	C₂×C₄×C₆₇	—	2	2	no	—
300	C₂×C₄×C₆₇	—	2	2	no	—
301	C₂×C₄×C₆₇	—	2	2	no	—
302	C₂×C₄×C₆₇	—	2	2	no	—
303	C₂×C₄×C₆₇	—	2	2	no	—
304	C₂×C₄×C₆₇	—	2	2	no	—
305	C₂×C₄×C₆₇	—	2	2	no	—
306	C₂×C₄×C₆₇	—	2	2	no	—
307	C₂×C₄×C₆₇	—	2	2	no	—
308	C₂×C₄×C₆₇	—	2	4	no	—
309	C₂×C₄×C₆₇	—	2	8	no	—
310	C₂×C₄×C₆₇	—	4	1	no	—
311	C₂×C₄×C₆₇	—	4	1	no	—
312	C₂×C₄×C₆₇	—	4	1	no	—
313	C₂×C₄×C₆₇	—	4	1	no	—
314	C₂×C₄×C₆₇	—	4	1	no	—
315	C₂×C₄×C₆₇	—	4	1	no	—
316	C₂×C₄×C₆₇	—	4	1	no	—
317	C₂×C₄×C₆₇	—	4	1	no	—
318	C₂×C₄×C₆₇	—	4	1	no	—
319	C₂×C₄×C₆₇	—	4	1	no	—
320	C₂×C₄×C₆₇	—	4	1	no	—
321	C₂×C₄×C₆₇	—	4	1	no	—
322	C₂×C₄×C₆₇	—	4	4	no	—
323	C₂×C₄×C₆₇	—	4	4	no	—
324	C₂×C₄×C₆₇	—	4	16	no	—
325	C₂×C₄×C₆₇	—	4	4	no	—
326	C₂×C₄×C₆₇	—	4	4	no	—
327	C₂×C₄×C₆₇	—	4	2	no	—
328	C₂×C₄×C₆₇	—	4	2	no	—
329	C₂×C₄×C₆₇	—	4	4	no	—
330	C₂×C₄×C₆₇	—	4	4	no	—
331	C₂×C₄×C₆₇	—	4	4	no	—
332	C₂×C₄×C₆₇	#99	1	4	yes	complemented
333	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
335	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
336	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
337	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
339	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₆₇	—	2	8	no	—
342	C₂²×C₆₇	—	2	1	no	—
343	C₂²×C₆₇	—	2	1	no	—
344	C₂²×C₆₇	—	2	1	no	—
345	C₂²×C₆₇	—	2	1	no	—
346	C₂²×C₆₇	—	2	1	no	—
347	C₂²×C₆₇	—	2	1	no	—
348	C₂²×C₆₇	—	2	1	no	—
349	C₂²×C₆₇	—	2	1	no	—
350	C₂²×C₆₇	—	2	1	no	—
351	C₂²×C₆₇	—	2	1	no	—
352	C₂²×C₆₇	—	2	1	no	—
353	C₂²×C₆₇	—	2	1	no	—
354	C₂²×C₆₇	—	2	1	no	—
355	C₂²×C₆₇	—	2	1	no	—
356	C₂²×C₆₇	—	2	1	no	—
357	C₂²×C₆₇	—	2	1	no	—
358	C₂²×C₆₇	—	4	4	no	—
359	C₂²×C₆₇	—	4	4	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	4	no	—
362	C₂²×C₆₇	—	4	4	no	—
363	C₂²×C₆₇	—	4	4	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	8	4	no	—
368	C₂²×C₆₇	C₂×#99	1	2	yes	—
369	C₂²×C₆₇	#410	1	2	yes	—
370	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×C₆₇	C₄×#41	1	2	yes	—
372	C₂²×C₆₇	#525	1	2	yes	—
373	C₂²×C₆₇	#532	1	2	yes	—
374	C₄×C₆₇	—	2	1	no	—
375	C₄×C₆₇	—	2	1	no	—
376	C₄×C₆₇	—	2	1	no	—
377	C₄×C₆₇	—	2	1	no	—
378	C₄×C₆₇	—	2	1	no	—
379	C₄×C₆₇	—	2	1	no	—
380	C₄×C₆₇	—	4	8	no	—
381	C₄×C₆₇	—	4	2	no	—
382	C₄×C₆₇	—	4	2	no	—
383	C₄×C₆₇	—	4	2	no	—
384	C₄×C₆₇	—	8	4	no	—
385	C₄×C₆₇	C₂×#99	1	2	yes	—
386	C₄×C₆₇	C₂×#99	1	2	yes	—
387	#21420	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
388	C₂×C₆₇	—	2	2	no	—
389	C₂×C₆₇	—	2	2	no	—
390	C₂×C₆₇	—	2	2	no	—
391	C₂×C₆₇	—	2	2	no	—
392	C₂×C₆₇	—	2	2	no	—
393	C₂×C₆₇	—	4	1	no	—
394	C₂×C₆₇	—	4	1	no	—
395	C₂×C₆₇	—	8	2	no	—
396	C₂×C₆₇	#2297	1	1	yes	characteristic
397	C₂×C₆₇	C₂²×#99	1	1	yes	characteristic
398	C₂×C₆₇	C₂×#410	1	1	yes	characteristic
399	C₂×#525	C₂×C₆₇	1	1	yes	characteristic
400	#2280	C₂×C₆₇	1	1	yes	characteristic, complemented
401	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
402	#1996	C₂×C₆₇	1	2	yes	complemented
403	#1964	C₂×C₆₇	1	2	yes	complemented
404	#1898	C₂×C₆₇	1	4	yes	complemented
405	C₄×#99	C₂×C₆₇	1	4	yes	complemented
406	C₆₇	#21420	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²×#41	C₄×C₆₇	1	1	yes	characteristic, complemented
408	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
409	#525	—	2	1	no	—
410	#525	—	2	1	no	—
411	#525	—	2	1	no	—
412	#525	—	2	1	no	—
413	#525	—	2	1	no	—
414	#525	—	2	1	no	—
415	#525	—	2	1	no	—
416	#525	—	2	1	no	—
417	C₂×#123	C₄×C₆₇	1	2	yes	complemented
418	C₂×C₂²⋊Q₈	C₄×C₆₇	1	1	yes	characteristic, complemented
419	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
420	C₂×#121	C₄×C₆₇	1	1	yes	characteristic, complemented
421	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#120	C₂²×C₆₇	1	2	yes	—
423	C₂×C₄×D₄	C₄×C₆₇	1	2	yes	complemented
424	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
425	C₂×#117	—	2	1	no	—
426	C₂×#117	C₄×C₆₇	1	1	yes	characteristic, complemented
427	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
428	C₂²×C₄²	—	2	1	no	—
429	C₂×#99	C₂²×C₆₇	1	8	yes	—
430	#381	—	2	1	no	—
431	#380	—	2	1	no	—
432	#380	C₂²×C₆₇	1	2	yes	—
433	#379	C₂²×C₆₇	1	2	yes	—
434	C₄×C₂²⋊C₄	—	2	1	no	—
435	C₄×C₂²⋊C₄	—	2	1	no	—
436	C₄×C₂²⋊C₄	—	2	1	no	—
437	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
438	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
439	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
440	C₂×#95	—	2	1	no	—
441	#342	C₂²×C₆₇	1	8	yes	—
442	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
443	C₂×#41	—	2	1	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	4	4	no	—
448	C₂²×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
449	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
450	C₂²×D₄	C₂×C₄×C₆₇	1	2	yes	—
451	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
452	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
453	C₂³×C₄	—	2	2	no	—
454	C₂³×C₄	—	4	4	no	—
455	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
456	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
457	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
458	C₂³×C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
459	C₂³×C₄	C₂×C₄×C₆₇	1	2	yes	complemented
460	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
461	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
462	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
463	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
464	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
465	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
466	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
467	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
470	#123	—	2	2	no	—
471	#123	—	2	2	no	—
472	#123	—	2	2	no	—
473	#123	—	2	2	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	1	no	—
479	C₂²⋊Q₈	—	2	1	no	—
480	C₂²⋊Q₈	—	2	1	no	—
481	C₂²⋊Q₈	—	2	1	no	—
482	#121	—	2	1	no	—
483	#121	—	2	1	no	—
484	#121	—	2	1	no	—
485	#121	—	2	1	no	—
486	#121	—	2	1	no	—
487	#121	—	2	1	no	—
488	#121	—	2	1	no	—
489	#121	—	2	1	no	—
490	#120	—	2	2	no	—
491	#120	—	2	2	no	—
492	#120	—	2	2	no	—
493	#120	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	C₄×D₄	—	2	2	no	—
502	#117	—	2	1	no	—
503	#117	—	2	1	no	—
504	#117	—	2	1	no	—
505	#117	—	2	1	no	—
506	#117	—	4	4	no	—
507	C₂×C₄⋊C₄	—	2	2	no	—
508	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
509	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic, complemented
510	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	complemented
511	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	2	yes	complemented
512	C₂×C₂²⋊C₄	—	2	2	no	—
513	C₂×C₂²⋊C₄	—	2	8	no	—
514	C₂×C₂²⋊C₄	—	2	2	no	—
515	C₂×C₂²⋊C₄	—	2	2	no	—
516	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	complemented
519	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	complemented
520	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
523	C₂×C₄²	—	2	2	no	—
524	C₂×C₄²	—	2	2	no	—
525	C₂×C₄²	—	2	2	no	—
526	C₂×C₄²	—	4	4	no	—
527	C₂×C₄²	C₂×C₄×C₆₇	1	2	yes	complemented
528	#99	—	2	16	no	—
529	#95	—	2	2	no	—
530	#95	—	2	2	no	—
531	#95	—	2	2	no	—
532	#95	—	2	2	no	—
533	C₂⁴	—	2	4	no	—
534	C₂⁴	—	4	2	no	—
535	C₂⁴	—	4	2	no	—
536	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
537	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
538	C₂⁴	C₂²×C₄×C₆₇	1	2	yes	—
539	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
540	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
541	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
542	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
543	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
544	#41	—	4	4	no	—
545	#41	—	4	4	no	—
546	#41	—	4	4	no	—
547	#41	—	4	4	no	—
548	C₂×Q₈	—	2	1	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	4	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	8	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	2	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	2	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	4	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
586	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
587	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
588	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
589	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
590	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
591	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
592	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
593	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
594	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
595	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
596	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
597	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
598	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
599	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
600	C₂²×C₄	C₂²⋊C₄×C₆₇	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
602	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
603	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
604	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
605	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
606	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
607	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
609	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
610	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
611	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
613	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
614	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
615	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	2	8	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	8	no	—
638	C₂²⋊C₄	—	4	4	no	—
639	C₂²⋊C₄	—	4	4	no	—
640	C₂²⋊C₄	#41×C₆₇	1	8	yes	complemented
641	C₄²	—	2	2	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	4	4	no	—
644	C₄²	—	4	4	no	—
645	C₄²	—	4	4	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	4	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	—	4	1	no	—
665	C₂³	—	4	1	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	16	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
672	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
673	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
674	C₂³	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
675	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
676	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
677	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
678	C₂³	C₂×#41×C₆₇	1	4	yes	—
679	Q₈	—	4	2	no	—
680	Q₈	—	4	2	no	—
681	D₄	—	4	2	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	4	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	4	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	16	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	4	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	4	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	4	no	—
731	C₂×C₄	#99×C₆₇	1	4	yes	complemented
732	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
733	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
734	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
735	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
736	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
737	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
738	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
739	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
740	C₂²	—	2	8	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	1	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	1	no	—
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	1	no	—
755	C₂²	—	2	1	no	—
756	C₂²	—	2	1	no	—
757	C₂²	—	4	4	no	—
758	C₂²	—	4	4	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	4	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	2	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	8	4	no	—
767	C₂²	C₂×#99×C₆₇	1	2	yes	—
768	C₂²	#410×C₆₇	1	2	yes	—
769	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
770	C₂²	C₄×#41×C₆₇	1	2	yes	—
771	C₂²	#525×C₆₇	1	2	yes	—
772	C₂²	#532×C₆₇	1	2	yes	—
773	C₄	—	2	1	no	—
774	C₄	—	2	1	no	—
775	C₄	—	2	1	no	—
776	C₄	—	2	1	no	—
777	C₄	—	2	1	no	—
778	C₄	—	2	1	no	—
779	C₄	—	4	8	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	8	4	no	—
784	C₄	C₂×#99×C₆₇	1	2	yes	—
785	C₄	C₂×#99×C₆₇	1	2	yes	—
786	C₂	—	2	2	no	—
787	C₂	—	2	2	no	—
788	C₂	—	2	2	no	—
789	C₂	—	2	2	no	—
790	C₂	—	2	2	no	—
791	C₂	—	4	1	no	—
792	C₂	—	4	1	no	—
793	C₂	—	8	2	no	—
794	C₂	C₆₇×#2297	1	1	yes	characteristic
795	C₂	C₂²×#99×C₆₇	1	1	yes	characteristic
796	C₂	C₂×#410×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₆₇
Frattini, cosocle	C₂⁴	C₂⁴×C₆₇
socle	C₂²×C₆₇	C₂²×C₂²⋊C₄
prime radical	C₂×#525×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂⁴×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2280	C₂	semidirect
3. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
4. C₆₇×#1996	C₂	semidirect
5. C₆₇×#1964	C₂	semidirect
6. C₆₇×#1898	C₂	semidirect
7. C₄×#99×C₆₇	C₂	semidirect
8. C₂²×#41×C₆₇	C₄	semidirect
18. C₂×#123×C₆₇	C₄	semidirect
19. C₂×C₂²⋊Q₈×C₆₇	C₄	semidirect
21. C₂×#121×C₆₇	C₄	semidirect
24. C₂×C₄×D₄×C₆₇	C₄	semidirect
27. C₂×#117×C₆₇	C₄	semidirect
49. C₂²×Q₈×C₆₇	C₂×C₄	semidirect
52. C₂²×D₄×C₆₇	C₂×C₄	semidirect
60. C₂³×C₄×C₆₇	C₂×C₄	semidirect
109. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
110. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
111. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
112. C₂×C₄⋊C₄×C₆₇	C₂×C₄	semidirect
119. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
120. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
128. C₂×C₄²×C₆₇	C₂×C₄	semidirect
241. C₂²⋊C₄×C₆₇	#41	semidirect
332. C₂×C₄×C₆₇	#99	semidirect
387. #21420	C₆₇	direct (N × H)
400. #2280	C₂×C₆₇	semidirect
401. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
402. #1996	C₂×C₆₇	semidirect
403. #1964	C₂×C₆₇	semidirect
404. #1898	C₂×C₆₇	semidirect
405. C₄×#99	C₂×C₆₇	semidirect
406. C₆₇	#21420	direct (N × H)
407. C₂²×#41	C₄×C₆₇	semidirect
417. C₂×#123	C₄×C₆₇	semidirect
418. C₂×C₂²⋊Q₈	C₄×C₆₇	semidirect
420. C₂×#121	C₄×C₆₇	semidirect
423. C₂×C₄×D₄	C₄×C₆₇	semidirect
426. C₂×#117	C₄×C₆₇	semidirect
448. C₂²×Q₈	C₂×C₄×C₆₇	semidirect
451. C₂²×D₄	C₂×C₄×C₆₇	semidirect
459. C₂³×C₄	C₂×C₄×C₆₇	semidirect
508. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
509. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
510. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
511. C₂×C₄⋊C₄	C₂×C₄×C₆₇	semidirect
518. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
519. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
527. C₂×C₄²	C₂×C₄×C₆₇	semidirect
640. C₂²⋊C₄	#41×C₆₇	semidirect
731. C₂×C₄	#99×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₆₇	2
C₆₇×#2280	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₆₇×#1996	2
C₆₇×#1964	2
C₆₇×#1898	2
C₄×#99×C₆₇	2
#21420	67

Subgroups — C67×#21420 #30700671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21420 #30700671