Subgroups — C₂×C₆₇×#2517 #30714002

Order 17152.

2182 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2517	C₂	1	16	yes	maximal, direct product factor
2	C₂×#399×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#397×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#397×C₆₇	C₂	1	2	yes	maximal
5	C₂×#387×C₆₇	C₂	1	2	yes	maximal, complemented
6	C₂×#387×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#387×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#385×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#382×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
23	#399×C₆₇	C₂²	1	8	yes	—
24	#397×C₆₇	C₂²	1	8	yes	—
25	#397×C₆₇	C₂²	1	16	yes	—
26	#387×C₆₇	C₂²	1	16	yes	complemented
27	#387×C₆₇	C₂²	1	16	yes	complemented
28	#387×C₆₇	C₂²	1	16	yes	complemented
29	#385×C₆₇	C₂²	1	8	yes	—
30	#382×C₆₇	C₂²	1	16	yes	complemented
31	C₄×C₂²⋊C₄×C₆₇	C₂²	1	16	yes	—
32	C₂×#95×C₆₇	C₂²	1	2	yes	—
33	C₂×#95×C₆₇	C₂²	1	2	yes	—
34	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
35	C₂×#95×C₆₇	C₂²	1	2	yes	—
36	C₂×#95×C₆₇	C₂²	1	2	yes	—
37	C₂×#95×C₆₇	C₂²	1	2	yes	—
38	C₂×#95×C₆₇	C₂²	1	2	yes	—
39	C₂×#95×C₆₇	C₂²	1	2	yes	—
40	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
41	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	—	2	8	no	—
43	C₂³×C₄×C₆₇	—	4	2	no	—
44	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
51	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
57	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
67	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
71	C₂×C₄²×C₆₇	—	2	8	no	—
72	C₂×C₄²×C₆₇	—	4	4	no	—
73	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
74	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
75	#95×C₆₇	C₂³	1	8	yes	—
76	#95×C₆₇	C₂³	1	8	yes	—
77	#95×C₆₇	C₂³	1	4	yes	—
78	#95×C₆₇	C₂³	1	8	yes	—
79	#95×C₆₇	C₂³	1	8	yes	—
80	#95×C₆₇	C₂³	1	8	yes	—
81	#95×C₆₇	C₂³	1	8	yes	—
82	#95×C₆₇	C₂³	1	8	yes	—
83	#95×C₆₇	C₂³	1	4	yes	—
84	C₂⁴×C₆₇	—	2	4	no	—
85	C₂⁴×C₆₇	—	2	4	no	—
86	C₂⁴×C₆₇	—	2	2	no	—
87	C₂⁴×C₆₇	—	2	2	no	—
88	C₂⁴×C₆₇	#41	1	4	yes	—
89	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
90	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	—	2	4	no	—
92	C₂²×C₄×C₆₇	—	2	4	no	—
93	C₂²×C₄×C₆₇	—	2	4	no	—
94	C₂²×C₄×C₆₇	—	2	4	no	—
95	C₂²×C₄×C₆₇	—	2	4	no	—
96	C₂²×C₄×C₆₇	—	2	4	no	—
97	C₂²×C₄×C₆₇	—	2	4	no	—
98	C₂²×C₄×C₆₇	—	2	4	no	—
99	C₂²×C₄×C₆₇	—	2	4	no	—
100	C₂²×C₄×C₆₇	—	2	4	no	—
101	C₂²×C₄×C₆₇	—	2	4	no	—
102	C₂²×C₄×C₆₇	—	2	4	no	—
103	C₂²×C₄×C₆₇	—	2	4	no	—
104	C₂²×C₄×C₆₇	—	2	4	no	—
105	C₂²×C₄×C₆₇	—	2	4	no	—
106	C₂²×C₄×C₆₇	—	2	4	no	—
107	C₂²×C₄×C₆₇	—	2	4	no	—
108	C₂²×C₄×C₆₇	—	2	2	no	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	—	2	4	no	—
111	C₂²×C₄×C₆₇	—	2	16	no	—
112	C₂²×C₄×C₆₇	—	4	4	no	—
113	C₂²×C₄×C₆₇	—	4	16	no	—
114	C₂²×C₄×C₆₇	#41	1	8	yes	—
115	C₂²×C₄×C₆₇	#41	1	8	yes	—
116	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
124	C₄⋊C₄×C₆₇	—	2	16	no	—
125	C₄⋊C₄×C₆₇	—	2	16	no	—
126	C₄⋊C₄×C₆₇	—	2	16	no	—
127	C₄⋊C₄×C₆₇	—	4	4	no	—
128	C₄⋊C₄×C₆₇	—	4	4	no	—
129	C₂²⋊C₄×C₆₇	—	2	16	no	—
130	C₂²⋊C₄×C₆₇	—	2	8	no	—
131	C₂²⋊C₄×C₆₇	—	2	16	no	—
132	C₂²⋊C₄×C₆₇	—	4	4	no	—
133	C₄²×C₆₇	—	2	16	no	—
134	C₄²×C₆₇	—	4	8	no	—
135	C₂³×C₆₇	—	2	16	no	—
136	C₂³×C₆₇	—	2	8	no	—
137	C₂³×C₆₇	—	2	4	no	—
138	C₂³×C₆₇	—	2	4	no	—
139	C₂³×C₆₇	—	2	2	no	—
140	C₂³×C₆₇	—	2	2	no	—
141	C₂³×C₆₇	—	4	4	no	—
142	C₂³×C₆₇	—	4	8	no	—
143	C₂³×C₆₇	—	4	4	no	—
144	C₂³×C₆₇	C₂×#41	1	4	yes	—
145	C₂³×C₆₇	C₂×#41	1	2	yes	—
146	C₂³×C₆₇	C₂×#41	1	4	yes	—
147	C₂³×C₆₇	C₂×#41	1	4	yes	—
148	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
149	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
150	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
151	C₂×C₄×C₆₇	—	2	16	no	—
152	C₂×C₄×C₆₇	—	2	16	no	—
153	C₂×C₄×C₆₇	—	2	4	no	—
154	C₂×C₄×C₆₇	—	2	4	no	—
155	C₂×C₄×C₆₇	—	2	4	no	—
156	C₂×C₄×C₆₇	—	2	4	no	—
157	C₂×C₄×C₆₇	—	2	4	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	4	no	—
161	C₂×C₄×C₆₇	—	2	4	no	—
162	C₂×C₄×C₆₇	—	2	4	no	—
163	C₂×C₄×C₆₇	—	2	4	no	—
164	C₂×C₄×C₆₇	—	2	4	no	—
165	C₂×C₄×C₆₇	—	2	4	no	—
166	C₂×C₄×C₆₇	—	2	4	no	—
167	C₂×C₄×C₆₇	—	2	4	no	—
168	C₂×C₄×C₆₇	—	2	4	no	—
169	C₂×C₄×C₆₇	—	2	4	no	—
170	C₂×C₄×C₆₇	—	2	2	no	—
171	C₂×C₄×C₆₇	—	2	2	no	—
172	C₂×C₄×C₆₇	—	2	4	no	—
173	C₂×C₄×C₆₇	—	4	16	no	—
174	C₂×C₄×C₆₇	—	4	8	no	—
175	C₂×C₄×C₆₇	—	4	8	no	—
176	C₂×C₄×C₆₇	—	4	8	no	—
177	C₂×C₄×C₆₇	—	4	4	no	—
178	C₂×C₄×C₆₇	—	4	8	no	—
179	C₂×C₄×C₆₇	—	4	4	no	—
180	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
181	C₂×C₄×C₆₇	C₂×#41	1	8	yes	—
182	C₂²×C₆₇	—	2	8	no	—
183	C₂²×C₆₇	—	2	4	no	—
184	C₂²×C₆₇	—	4	2	no	—
185	C₂²×C₆₇	—	4	4	no	—
186	C₂²×C₆₇	—	4	2	no	—
187	C₂²×C₆₇	—	4	16	no	—
188	C₂²×C₆₇	#529	1	8	yes	—
189	C₂²×C₆₇	#539	1	4	yes	—
190	C₂²×C₆₇	#551	1	4	yes	—
191	C₂²×C₆₇	#552	1	8	yes	—
192	C₂²×C₆₇	#559	1	4	yes	—
193	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
194	C₂²×C₆₇	C₂²×#41	1	2	yes	—
195	C₂²×C₆₇	C₂²×#41	1	2	yes	—
196	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
197	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
198	C₄×C₆₇	—	2	8	no	—
199	C₄×C₆₇	—	2	8	no	—
200	C₄×C₆₇	—	4	4	no	—
201	C₄×C₆₇	—	4	4	no	—
202	C₄×C₆₇	—	4	4	no	—
203	C₄×C₆₇	—	4	2	no	—
204	C₄×C₆₇	—	4	4	no	—
205	C₄×C₆₇	—	4	2	no	—
206	C₂×#2517	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₆₇	—	4	4	no	—
208	C₂×C₆₇	#2517	1	8	yes	direct product factor
209	C₂×C₆₇	C₂×#529	1	2	yes	—
210	C₂×C₆₇	C₂×#539	1	1	yes	characteristic
211	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
212	C₂×C₆₇	C₂×#552	1	2	yes	—
213	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
214	#2517	C₂×C₆₇	1	16	yes	direct product factor
215	C₂×#399	C₂×C₆₇	1	1	yes	characteristic
216	C₂×#397	C₂×C₆₇	1	1	yes	characteristic
217	C₂×#397	C₂×C₆₇	1	2	yes	—
218	C₂×#387	C₂×C₆₇	1	2	yes	complemented
219	C₂×#387	C₂×C₆₇	1	2	yes	complemented
220	C₂×#387	C₂×C₆₇	1	2	yes	complemented
221	C₂×#385	C₂×C₆₇	1	1	yes	characteristic
222	C₂×#382	C₂×C₆₇	1	2	yes	complemented
223	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	2	yes	—
224	C₆₇	C₂×#2517	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
230	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
231	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
236	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
237	#399	C₂²×C₆₇	1	8	yes	—
238	#397	C₂²×C₆₇	1	8	yes	—
239	#397	C₂²×C₆₇	1	16	yes	—
240	#387	C₂²×C₆₇	1	16	yes	complemented
241	#387	C₂²×C₆₇	1	16	yes	complemented
242	#387	C₂²×C₆₇	1	16	yes	complemented
243	#385	C₂²×C₆₇	1	8	yes	—
244	#382	C₂²×C₆₇	1	16	yes	complemented
245	C₄×C₂²⋊C₄	C₂²×C₆₇	1	16	yes	—
246	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
247	C₂×#95	C₂²×C₆₇	1	2	yes	—
248	C₂×#95	C₂²×C₆₇	1	2	yes	—
249	C₂×#95	C₂²×C₆₇	1	2	yes	—
250	C₂×#95	C₂²×C₆₇	1	2	yes	—
251	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
252	C₂×#95	C₂²×C₆₇	1	2	yes	—
253	C₂×#95	C₂²×C₆₇	1	2	yes	—
254	C₂×#95	C₂²×C₆₇	1	2	yes	—
255	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
256	C₂³×C₄	—	2	8	no	—
257	C₂³×C₄	—	4	2	no	—
258	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
261	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
262	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
263	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
264	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
265	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
266	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	8	no	—
268	C₂×C₄⋊C₄	—	2	8	no	—
269	C₂×C₄⋊C₄	—	2	8	no	—
270	C₂×C₄⋊C₄	—	4	2	no	—
271	C₂×C₄⋊C₄	—	4	2	no	—
272	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
273	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
274	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
277	C₂×C₂²⋊C₄	—	2	8	no	—
278	C₂×C₂²⋊C₄	—	2	4	no	—
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	4	2	no	—
281	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
285	C₂×C₄²	—	2	8	no	—
286	C₂×C₄²	—	4	4	no	—
287	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
288	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
289	#95	C₂³×C₆₇	1	8	yes	—
290	#95	C₂³×C₆₇	1	8	yes	—
291	#95	C₂³×C₆₇	1	4	yes	—
292	#95	C₂³×C₆₇	1	8	yes	—
293	#95	C₂³×C₆₇	1	8	yes	—
294	#95	C₂³×C₆₇	1	8	yes	—
295	#95	C₂³×C₆₇	1	8	yes	—
296	#95	C₂³×C₆₇	1	8	yes	—
297	#95	C₂³×C₆₇	1	4	yes	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	2	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	#41×C₆₇	1	4	yes	—
303	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
304	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	16	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	16	no	—
328	C₂²×C₄	#41×C₆₇	1	8	yes	—
329	C₂²×C₄	#41×C₆₇	1	8	yes	—
330	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
334	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
338	C₄⋊C₄	—	2	16	no	—
339	C₄⋊C₄	—	2	16	no	—
340	C₄⋊C₄	—	2	16	no	—
341	C₄⋊C₄	—	4	4	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	2	16	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	16	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₄²	—	2	16	no	—
348	C₄²	—	4	8	no	—
349	C₂³	—	2	16	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	8	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×#41×C₆₇	1	4	yes	—
359	C₂³	C₂×#41×C₆₇	1	2	yes	—
360	C₂³	C₂×#41×C₆₇	1	4	yes	—
361	C₂³	C₂×#41×C₆₇	1	4	yes	—
362	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
363	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
364	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
365	C₂×C₄	—	2	16	no	—
366	C₂×C₄	—	2	16	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	16	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
395	C₂×C₄	C₂×#41×C₆₇	1	8	yes	—
396	C₂²	—	2	8	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	4	16	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	#529×C₆₇	1	8	yes	—
403	C₂²	#539×C₆₇	1	4	yes	—
404	C₂²	#551×C₆₇	1	4	yes	—
405	C₂²	#552×C₆₇	1	8	yes	—
406	C₂²	#559×C₆₇	1	4	yes	—
407	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
408	C₂²	C₂²×#41×C₆₇	1	2	yes	—
409	C₂²	C₂²×#41×C₆₇	1	2	yes	—
410	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
411	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
412	C₄	—	2	8	no	—
413	C₄	—	2	8	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	4	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	2	no	—
420	C₂	—	4	4	no	—
421	C₂	C₆₇×#2517	1	8	yes	direct product factor
422	C₂	C₂×#529×C₆₇	1	2	yes	—
423	C₂	C₂×#539×C₆₇	1	1	yes	characteristic
424	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
425	C₂	C₂×#552×C₆₇	1	2	yes	—
426	C₂	C₂×#559×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2517	C₂	direct (N × H)
5. C₂×#387×C₆₇	C₂	semidirect
6. C₂×#387×C₆₇	C₂	semidirect
7. C₂×#387×C₆₇	C₂	semidirect
9. C₂×#382×C₆₇	C₂	semidirect
26. #387×C₆₇	C₂²	semidirect
27. #387×C₆₇	C₂²	semidirect
28. #387×C₆₇	C₂²	semidirect
30. #382×C₆₇	C₂²	semidirect
206. C₂×#2517	C₆₇	direct (N × H)
208. C₂×C₆₇	#2517	direct (N × H)
214. #2517	C₂×C₆₇	direct (N × H)
218. C₂×#387	C₂×C₆₇	semidirect
219. C₂×#387	C₂×C₆₇	semidirect
220. C₂×#387	C₂×C₆₇	semidirect
222. C₂×#382	C₂×C₆₇	semidirect
224. C₆₇	C₂×#2517	direct (N × H)
240. #387	C₂²×C₆₇	semidirect
241. #387	C₂²×C₆₇	semidirect
242. #387	C₂²×C₆₇	semidirect
244. #382	C₂²×C₆₇	semidirect
421. C₂	C₆₇×#2517	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#2517	2
C₂×#399×C₆₇	2
C₂×#397×C₆₇	2
C₂×#387×C₆₇	2
C₂×#385×C₆₇	2
C₂×#382×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₂×#2517	67

Subgroups — C2×C67×#2517 #30714002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2517 #30714002