Subgroups — C₂×C₆₇×#2395 #30713793

Order 17152.

3182 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2395	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#399×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#398×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#397×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#397×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#394×C₆₇	C₂	1	2	yes	maximal
10	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₆₇	—	2	8	no	—
17	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	—
18	C₂×#117×C₆₇	—	2	8	no	—
19	C₂×#117×C₆₇	C₂²	1	8	yes	complemented
20	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×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	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
32	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
33	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
34	#400×C₆₇	C₂²	1	8	yes	complemented
35	#399×C₆₇	C₂²	1	8	yes	complemented
36	#398×C₆₇	C₂²	1	8	yes	complemented
37	#397×C₆₇	C₂²	1	16	yes	complemented
38	#397×C₆₇	C₂²	1	8	yes	complemented
39	#394×C₆₇	C₂²	1	16	yes	—
40	C₄×C₄⋊C₄×C₆₇	C₂²	1	16	yes	complemented
41	C₄×C₂²⋊C₄×C₆₇	C₂²	1	16	yes	complemented
42	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
43	C₂×#95×C₆₇	C₂²	1	2	yes	—
44	C₂×#95×C₆₇	C₂²	1	2	yes	—
45	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
46	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×#95×C₆₇	C₂²	1	2	yes	—
48	C₂×#95×C₆₇	C₂²	1	2	yes	—
49	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
50	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₆₇	—	2	4	no	—
52	C₂²×D₄×C₆₇	—	2	4	no	—
53	C₂²×D₄×C₆₇	—	2	4	no	—
54	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₆₇	—	2	8	no	—
56	C₂³×C₄×C₆₇	—	2	4	no	—
57	C₂³×C₄×C₆₇	—	2	8	no	—
58	C₂³×C₄×C₆₇	D₄	1	8	yes	—
59	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
65	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
67	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₆₇	—	2	32	no	—
71	#117×C₆₇	—	2	32	no	—
72	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
73	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
74	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
75	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
76	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
77	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
81	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
88	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
94	C₂×C₄²×C₆₇	—	2	8	no	—
95	C₂×C₄²×C₆₇	—	2	4	no	—
96	C₂×C₄²×C₆₇	—	2	8	no	—
97	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
98	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
99	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
100	#95×C₆₇	C₂³	1	8	yes	—
101	#95×C₆₇	C₂³	1	8	yes	—
102	#95×C₆₇	C₂³	1	4	yes	—
103	#95×C₆₇	C₂³	1	4	yes	—
104	#95×C₆₇	C₂³	1	8	yes	—
105	#95×C₆₇	C₂³	1	8	yes	—
106	C₂⁴×C₆₇	—	2	2	no	—
107	C₂⁴×C₆₇	—	2	4	no	—
108	C₂⁴×C₆₇	—	2	4	no	—
109	C₂⁴×C₆₇	—	2	4	no	—
110	C₂⁴×C₆₇	—	2	4	no	—
111	C₂⁴×C₆₇	—	2	2	no	—
112	C₂⁴×C₆₇	—	2	2	no	—
113	C₂⁴×C₆₇	—	2	2	no	—
114	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
115	C₂⁴×C₆₇	#41	1	4	yes	—
116	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
117	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
118	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
119	C₂×D₄×C₆₇	—	2	32	no	—
120	C₂×D₄×C₆₇	—	2	8	no	—
121	C₂×D₄×C₆₇	—	2	8	no	—
122	C₂×D₄×C₆₇	—	2	8	no	—
123	C₂²×C₄×C₆₇	—	2	2	no	—
124	C₂²×C₄×C₆₇	—	2	4	no	—
125	C₂²×C₄×C₆₇	—	2	4	no	—
126	C₂²×C₄×C₆₇	—	2	4	no	—
127	C₂²×C₄×C₆₇	—	2	2	no	—
128	C₂²×C₄×C₆₇	—	2	32	no	—
129	C₂²×C₄×C₆₇	—	2	16	no	—
130	C₂²×C₄×C₆₇	—	2	2	no	—
131	C₂²×C₄×C₆₇	—	2	4	no	—
132	C₂²×C₄×C₆₇	—	2	4	no	—
133	C₂²×C₄×C₆₇	—	2	2	no	—
134	C₂²×C₄×C₆₇	—	2	4	no	—
135	C₂²×C₄×C₆₇	—	2	4	no	—
136	C₂²×C₄×C₆₇	—	2	4	no	—
137	C₂²×C₄×C₆₇	—	2	4	no	—
138	C₂²×C₄×C₆₇	—	2	4	no	—
139	C₂²×C₄×C₆₇	—	2	4	no	—
140	C₂²×C₄×C₆₇	—	2	4	no	—
141	C₂²×C₄×C₆₇	—	2	4	no	—
142	C₂²×C₄×C₆₇	—	2	4	no	—
143	C₂²×C₄×C₆₇	—	2	8	no	—
144	C₂²×C₄×C₆₇	—	2	16	no	—
145	C₂²×C₄×C₆₇	—	4	16	no	—
146	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₆₇	C₂×D₄	1	16	yes	—
148	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₆₇	#41	1	8	yes	—
150	C₂²×C₄×C₆₇	#41	1	4	yes	—
151	C₂²×C₄×C₆₇	#41	1	8	yes	—
152	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
161	C₄⋊C₄×C₆₇	—	2	8	no	—
162	C₄⋊C₄×C₆₇	—	2	8	no	—
163	C₄⋊C₄×C₆₇	—	2	8	no	—
164	C₄⋊C₄×C₆₇	—	2	16	no	—
165	C₄⋊C₄×C₆₇	—	2	16	no	—
166	C₂²⋊C₄×C₆₇	—	2	16	no	—
167	C₂²⋊C₄×C₆₇	—	2	8	no	—
168	C₂²⋊C₄×C₆₇	—	2	16	no	—
169	C₂²⋊C₄×C₆₇	—	2	8	no	—
170	C₂²⋊C₄×C₆₇	—	2	16	no	—
171	C₂²⋊C₄×C₆₇	—	2	16	no	—
172	C₄²×C₆₇	—	2	16	no	—
173	C₄²×C₆₇	—	2	8	no	—
174	C₄²×C₆₇	—	2	16	no	—
175	C₂³×C₆₇	—	2	8	no	—
176	C₂³×C₆₇	—	2	8	no	—
177	C₂³×C₆₇	—	2	8	no	—
178	C₂³×C₆₇	—	2	16	no	—
179	C₂³×C₆₇	—	2	8	no	—
180	C₂³×C₆₇	—	2	2	no	—
181	C₂³×C₆₇	—	2	4	no	—
182	C₂³×C₆₇	—	2	4	no	—
183	C₂³×C₆₇	—	2	4	no	—
184	C₂³×C₆₇	—	2	4	no	—
185	C₂³×C₆₇	—	2	2	no	—
186	C₂³×C₆₇	—	2	2	no	—
187	C₂³×C₆₇	—	2	2	no	—
188	C₂³×C₆₇	—	4	4	no	—
189	C₂³×C₆₇	—	4	8	no	—
190	C₂³×C₆₇	—	4	8	no	—
191	C₂³×C₆₇	—	4	8	no	—
192	C₂³×C₆₇	—	4	4	no	—
193	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
194	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
195	C₂³×C₆₇	C₂×#41	1	4	yes	—
196	C₂³×C₆₇	C₂×#41	1	4	yes	—
197	C₂³×C₆₇	C₂×#41	1	2	yes	—
198	C₂³×C₆₇	C₂×#41	1	2	yes	—
199	C₂³×C₆₇	C₂×#41	1	4	yes	—
200	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
201	D₄×C₆₇	—	2	32	no	—
202	C₂×C₄×C₆₇	—	2	8	no	—
203	C₂×C₄×C₆₇	—	2	8	no	—
204	C₂×C₄×C₆₇	—	2	16	no	—
205	C₂×C₄×C₆₇	—	2	2	no	—
206	C₂×C₄×C₆₇	—	2	4	no	—
207	C₂×C₄×C₆₇	—	2	4	no	—
208	C₂×C₄×C₆₇	—	2	4	no	—
209	C₂×C₄×C₆₇	—	2	2	no	—
210	C₂×C₄×C₆₇	—	2	32	no	—
211	C₂×C₄×C₆₇	—	2	2	no	—
212	C₂×C₄×C₆₇	—	2	4	no	—
213	C₂×C₄×C₆₇	—	2	4	no	—
214	C₂×C₄×C₆₇	—	2	2	no	—
215	C₂×C₄×C₆₇	—	2	4	no	—
216	C₂×C₄×C₆₇	—	2	4	no	—
217	C₂×C₄×C₆₇	—	2	4	no	—
218	C₂×C₄×C₆₇	—	2	4	no	—
219	C₂×C₄×C₆₇	—	2	4	no	—
220	C₂×C₄×C₆₇	—	2	4	no	—
221	C₂×C₄×C₆₇	—	2	4	no	—
222	C₂×C₄×C₆₇	—	2	4	no	—
223	C₂×C₄×C₆₇	—	2	4	no	—
224	C₂×C₄×C₆₇	—	4	4	no	—
225	C₂×C₄×C₆₇	—	4	8	no	—
226	C₂×C₄×C₆₇	—	4	8	no	—
227	C₂×C₄×C₆₇	—	4	4	no	—
228	C₂×C₄×C₆₇	—	4	8	no	—
229	C₂×C₄×C₆₇	—	4	16	no	—
230	C₂×C₄×C₆₇	#123	1	16	yes	—
231	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
232	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
234	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
235	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
236	C₂²×C₆₇	—	2	4	no	—
237	C₂²×C₆₇	—	2	4	no	—
238	C₂²×C₆₇	—	2	4	no	—
239	C₂²×C₆₇	—	2	8	no	—
240	C₂²×C₆₇	—	2	4	no	—
241	C₂²×C₆₇	—	4	16	no	—
242	C₂²×C₆₇	—	4	16	no	—
243	C₂²×C₆₇	—	4	2	no	—
244	C₂²×C₆₇	—	4	4	no	—
245	C₂²×C₆₇	—	4	4	no	—
246	C₂²×C₆₇	—	4	4	no	—
247	C₂²×C₆₇	—	4	2	no	—
248	C₂²×C₆₇	C₂×#123	1	4	yes	—
249	C₂²×C₆₇	#525	1	4	yes	—
250	C₂²×C₆₇	#529	1	8	yes	—
251	C₂²×C₆₇	#529	1	8	yes	—
252	C₂²×C₆₇	#532	1	4	yes	—
253	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
254	C₂²×C₆₇	C₂²×#41	1	2	yes	—
255	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
256	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
257	C₂²×C₆₇	C₂²×#41	1	2	yes	—
258	C₄×C₆₇	—	2	4	no	—
259	C₄×C₆₇	—	2	4	no	—
260	C₄×C₆₇	—	2	8	no	—
261	C₄×C₆₇	—	4	2	no	—
262	C₄×C₆₇	—	4	4	no	—
263	C₄×C₆₇	—	4	4	no	—
264	C₄×C₆₇	—	4	2	no	—
265	C₄×C₆₇	—	4	4	no	—
266	C₄×C₆₇	C₂×#123	1	8	yes	—
267	C₂×#2395	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂×C₆₇	—	4	4	no	—
269	C₂×C₆₇	—	4	4	no	—
270	C₂×C₆₇	#2395	1	8	yes	direct product factor
271	C₂×C₆₇	C₂²×#123	1	1	yes	characteristic
272	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
273	C₂×C₆₇	C₂×#529	1	2	yes	—
274	C₂×C₆₇	C₂×#529	1	2	yes	—
275	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
276	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic
277	C₂²×#117	C₂×C₆₇	1	1	yes	characteristic, complemented
278	#2395	C₂×C₆₇	1	16	yes	direct product factor
279	C₂×#400	C₂×C₆₇	1	1	yes	characteristic, complemented
280	C₂×#399	C₂×C₆₇	1	1	yes	characteristic, complemented
281	C₂×#398	C₂×C₆₇	1	1	yes	characteristic, complemented
282	C₂×#397	C₂×C₆₇	1	2	yes	complemented
283	C₂×#397	C₂×C₆₇	1	1	yes	characteristic, complemented
284	C₂×#394	C₂×C₆₇	1	2	yes	—
285	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	2	yes	complemented
286	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
287	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	complemented
288	C₆₇	C₂×#2395	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
290	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
291	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
292	C₂×C₄×D₄	—	2	8	no	—
293	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	—
294	C₂×#117	—	2	8	no	—
295	C₂×#117	C₂²×C₆₇	1	8	yes	complemented
296	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
297	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
299	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
300	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
302	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
304	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
305	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
306	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
307	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
308	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
310	#400	C₂²×C₆₇	1	8	yes	complemented
311	#399	C₂²×C₆₇	1	8	yes	complemented
312	#398	C₂²×C₆₇	1	8	yes	complemented
313	#397	C₂²×C₆₇	1	16	yes	complemented
314	#397	C₂²×C₆₇	1	8	yes	complemented
315	#394	C₂²×C₆₇	1	16	yes	—
316	C₄×C₄⋊C₄	C₂²×C₆₇	1	16	yes	complemented
317	C₄×C₂²⋊C₄	C₂²×C₆₇	1	16	yes	complemented
318	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
319	C₂×#95	C₂²×C₆₇	1	2	yes	—
320	C₂×#95	C₂²×C₆₇	1	2	yes	—
321	C₂×#95	C₂²×C₆₇	1	2	yes	—
322	C₂×#95	C₂²×C₆₇	1	2	yes	—
323	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
324	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
325	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
326	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	—	2	4	no	—
330	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
331	C₂³×C₄	—	2	8	no	—
332	C₂³×C₄	—	2	4	no	—
333	C₂³×C₄	—	2	8	no	—
334	C₂³×C₄	D₄×C₆₇	1	8	yes	—
335	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
337	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
338	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
339	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
341	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
343	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
344	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
346	C₄×D₄	—	2	32	no	—
347	#117	—	2	32	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	4	no	—
351	C₂×C₄⋊C₄	—	2	8	no	—
352	C₂×C₄⋊C₄	—	2	8	no	—
353	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
356	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
357	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
358	C₂×C₂²⋊C₄	—	2	8	no	—
359	C₂×C₂²⋊C₄	—	2	4	no	—
360	C₂×C₂²⋊C₄	—	2	8	no	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	—	2	8	no	—
363	C₂×C₂²⋊C₄	—	2	8	no	—
364	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
370	C₂×C₄²	—	2	8	no	—
371	C₂×C₄²	—	2	4	no	—
372	C₂×C₄²	—	2	8	no	—
373	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
374	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
375	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
376	#95	C₂³×C₆₇	1	8	yes	—
377	#95	C₂³×C₆₇	1	4	yes	—
378	#95	C₂³×C₆₇	1	8	yes	—
379	#95	C₂³×C₆₇	1	4	yes	—
380	#95	C₂³×C₆₇	1	8	yes	—
381	#95	C₂³×C₆₇	1	8	yes	—
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
391	C₂⁴	#41×C₆₇	1	4	yes	—
392	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
393	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
394	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
395	C₂×D₄	—	2	32	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	32	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	2	16	no	—
421	C₂²×C₄	—	4	16	no	—
422	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₆₇	1	16	yes	—
424	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
425	C₂²×C₄	#41×C₆₇	1	8	yes	—
426	C₂²×C₄	#41×C₆₇	1	4	yes	—
427	C₂²×C₄	#41×C₆₇	1	8	yes	—
428	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	16	no	—
441	C₄⋊C₄	—	2	16	no	—
442	C₂²⋊C₄	—	2	16	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	2	16	no	—
448	C₄²	—	2	16	no	—
449	C₄²	—	2	8	no	—
450	C₄²	—	2	16	no	—
451	C₂³	—	2	8	no	—
452	C₂³	—	2	8	no	—
453	C₂³	—	2	8	no	—
454	C₂³	—	2	16	no	—
455	C₂³	—	2	8	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	4	no	—
469	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
470	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
471	C₂³	C₂×#41×C₆₇	1	4	yes	—
472	C₂³	C₂×#41×C₆₇	1	4	yes	—
473	C₂³	C₂×#41×C₆₇	1	2	yes	—
474	C₂³	C₂×#41×C₆₇	1	2	yes	—
475	C₂³	C₂×#41×C₆₇	1	4	yes	—
476	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
477	D₄	—	2	32	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	16	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	32	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	16	no	—
506	C₂×C₄	#123×C₆₇	1	16	yes	—
507	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
509	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
510	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
511	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	8	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	16	no	—
518	C₂²	—	4	16	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	2	no	—
524	C₂²	C₂×#123×C₆₇	1	4	yes	—
525	C₂²	#525×C₆₇	1	4	yes	—
526	C₂²	#529×C₆₇	1	8	yes	—
527	C₂²	#529×C₆₇	1	8	yes	—
528	C₂²	#532×C₆₇	1	4	yes	—
529	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
530	C₂²	C₂²×#41×C₆₇	1	2	yes	—
531	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
532	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
533	C₂²	C₂²×#41×C₆₇	1	2	yes	—
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	8	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	4	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	4	no	—
542	C₄	C₂×#123×C₆₇	1	8	yes	—
543	C₂	—	4	4	no	—
544	C₂	—	4	4	no	—
545	C₂	C₆₇×#2395	1	8	yes	direct product factor
546	C₂	C₂²×#123×C₆₇	1	1	yes	characteristic
547	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
548	C₂	C₂×#529×C₆₇	1	2	yes	—
549	C₂	C₂×#529×C₆₇	1	2	yes	—
550	C₂	C₂×#532×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₆₇	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
socle	C₂⁴×C₆₇	C₂⁴
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₆₇	C₂	semidirect
3. C₆₇×#2395	C₂	direct (N × H)
4. C₂×#400×C₆₇	C₂	semidirect
5. C₂×#399×C₆₇	C₂	semidirect
6. C₂×#398×C₆₇	C₂	semidirect
7. C₂×#397×C₆₇	C₂	semidirect
8. C₂×#397×C₆₇	C₂	semidirect
10. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
11. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
19. C₂×#117×C₆₇	C₂²	semidirect
34. #400×C₆₇	C₂²	semidirect
35. #399×C₆₇	C₂²	semidirect
36. #398×C₆₇	C₂²	semidirect
37. #397×C₆₇	C₂²	semidirect
38. #397×C₆₇	C₂²	semidirect
40. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
41. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
42. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
267. C₂×#2395	C₆₇	direct (N × H)
270. C₂×C₆₇	#2395	direct (N × H)
277. C₂²×#117	C₂×C₆₇	semidirect
278. #2395	C₂×C₆₇	direct (N × H)
279. C₂×#400	C₂×C₆₇	semidirect
280. C₂×#399	C₂×C₆₇	semidirect
281. C₂×#398	C₂×C₆₇	semidirect
282. C₂×#397	C₂×C₆₇	semidirect
283. C₂×#397	C₂×C₆₇	semidirect
285. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
286. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
287. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
288. C₆₇	C₂×#2395	direct (N × H)
295. C₂×#117	C₂²×C₆₇	semidirect
310. #400	C₂²×C₆₇	semidirect
311. #399	C₂²×C₆₇	semidirect
312. #398	C₂²×C₆₇	semidirect
313. #397	C₂²×C₆₇	semidirect
314. #397	C₂²×C₆₇	semidirect
316. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
317. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
318. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
545. C₂	C₆₇×#2395	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₆₇	2
C₂²×#117×C₆₇	2
C₆₇×#2395	2
C₂×#400×C₆₇	2
C₂×#399×C₆₇	2
C₂×#398×C₆₇	2
C₂×#397×C₆₇	2
C₂×#394×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₂×#2395	67

Subgroups — C2×C67×#2395 #30713793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2395 #30713793