Subgroups — C₂×C₆₇×#2495 #30714028

Order 17152.

2182 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2495	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#397×C₆₇	C₂	1	2	yes	maximal
4	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#388×C₆₇	C₂	1	2	yes	maximal
7	C₂×#383×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#382×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#380×C₆₇	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
27	#400×C₆₇	C₂²	1	16	yes	complemented
28	#397×C₆₇	C₂²	1	16	yes	—
29	#389×C₆₇	C₂²	1	8	yes	complemented
30	#389×C₆₇	C₂²	1	8	yes	complemented
31	#388×C₆₇	C₂²	1	16	yes	—
32	#383×C₆₇	C₂²	1	16	yes	complemented
33	#382×C₆₇	C₂²	1	8	yes	complemented
34	#380×C₆₇	C₂²	1	8	yes	—
35	#380×C₆₇	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₆₇	C₂²	1	8	yes	complemented
37	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	—
38	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#95×C₆₇	C₂²	1	2	yes	—
41	C₂×#95×C₆₇	C₂²	1	2	yes	—
42	C₂×#95×C₆₇	C₂²	1	2	yes	—
43	C₂×#95×C₆₇	C₂²	1	2	yes	—
44	C₂×#95×C₆₇	C₂²	1	2	yes	—
45	C₂×#95×C₆₇	C₂²	1	2	yes	—
46	C₂×#95×C₆₇	C₂²	1	2	yes	—
47	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	—	2	4	no	—
49	C₂³×C₄×C₆₇	—	2	4	no	—
50	C₂³×C₄×C₆₇	—	2	4	no	—
51	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
52	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
66	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
67	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
68	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₆₇	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
76	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
78	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
81	C₂×C₂²⋊C₄×C₆₇	C₂³	1	8	yes	—
82	C₂×C₄²×C₆₇	—	2	4	no	—
83	C₂×C₄²×C₆₇	—	2	8	no	—
84	C₂×C₄²×C₆₇	—	2	4	no	—
85	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
86	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
87	C₂×C₄²×C₆₇	C₂³	1	8	yes	—
88	#95×C₆₇	C₂³	1	4	yes	—
89	#95×C₆₇	C₂³	1	4	yes	—
90	#95×C₆₇	C₂³	1	8	yes	—
91	#95×C₆₇	C₂³	1	8	yes	—
92	#95×C₆₇	C₂³	1	8	yes	—
93	#95×C₆₇	C₂³	1	8	yes	—
94	#95×C₆₇	C₂³	1	8	yes	—
95	#95×C₆₇	C₂³	1	8	yes	—
96	#95×C₆₇	C₂³	1	8	yes	—
97	C₂⁴×C₆₇	—	2	2	no	—
98	C₂⁴×C₆₇	—	2	2	no	—
99	C₂⁴×C₆₇	—	2	2	no	—
100	C₂⁴×C₆₇	—	2	2	no	—
101	C₂⁴×C₆₇	—	2	2	no	—
102	C₂⁴×C₆₇	—	2	2	no	—
103	C₂⁴×C₆₇	#41	1	4	yes	—
104	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
105	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
106	C₂²×C₄×C₆₇	—	2	2	no	—
107	C₂²×C₄×C₆₇	—	2	2	no	—
108	C₂²×C₄×C₆₇	—	2	4	no	—
109	C₂²×C₄×C₆₇	—	2	2	no	—
110	C₂²×C₄×C₆₇	—	2	2	no	—
111	C₂²×C₄×C₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	4	no	—
113	C₂²×C₄×C₆₇	—	2	4	no	—
114	C₂²×C₄×C₆₇	—	2	2	no	—
115	C₂²×C₄×C₆₇	—	2	2	no	—
116	C₂²×C₄×C₆₇	—	2	4	no	—
117	C₂²×C₄×C₆₇	—	2	2	no	—
118	C₂²×C₄×C₆₇	—	2	4	no	—
119	C₂²×C₄×C₆₇	—	2	4	no	—
120	C₂²×C₄×C₆₇	—	2	4	no	—
121	C₂²×C₄×C₆₇	—	2	4	no	—
122	C₂²×C₄×C₆₇	—	2	2	no	—
123	C₂²×C₄×C₆₇	—	2	2	no	—
124	C₂²×C₄×C₆₇	—	2	2	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	4	no	—
129	C₂²×C₄×C₆₇	—	2	2	no	—
130	C₂²×C₄×C₆₇	—	2	4	no	—
131	C₂²×C₄×C₆₇	—	2	2	no	—
132	C₂²×C₄×C₆₇	—	2	8	no	—
133	C₂²×C₄×C₆₇	—	2	8	no	—
134	C₂²×C₄×C₆₇	—	2	8	no	—
135	C₂²×C₄×C₆₇	—	4	16	no	—
136	C₂²×C₄×C₆₇	#41	1	4	yes	—
137	C₂²×C₄×C₆₇	#41	1	4	yes	—
138	C₂²×C₄×C₆₇	#41	1	4	yes	—
139	C₂²×C₄×C₆₇	#41	1	4	yes	—
140	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
150	C₄⋊C₄×C₆₇	—	2	8	no	—
151	C₄⋊C₄×C₆₇	—	2	8	no	—
152	C₄⋊C₄×C₆₇	—	2	8	no	—
153	C₄⋊C₄×C₆₇	—	2	8	no	—
154	C₄⋊C₄×C₆₇	—	4	8	no	—
155	C₄⋊C₄×C₆₇	—	4	8	no	—
156	C₂²⋊C₄×C₆₇	—	2	8	no	—
157	C₂²⋊C₄×C₆₇	—	2	16	no	—
158	C₂²⋊C₄×C₆₇	—	2	8	no	—
159	C₂²⋊C₄×C₆₇	—	4	8	no	—
160	C₄²×C₆₇	—	2	8	no	—
161	C₄²×C₆₇	—	2	16	no	—
162	C₄²×C₆₇	—	2	8	no	—
163	C₂³×C₆₇	—	2	8	no	—
164	C₂³×C₆₇	—	2	8	no	—
165	C₂³×C₆₇	—	2	8	no	—
166	C₂³×C₆₇	—	2	2	no	—
167	C₂³×C₆₇	—	2	2	no	—
168	C₂³×C₆₇	—	2	2	no	—
169	C₂³×C₆₇	—	2	2	no	—
170	C₂³×C₆₇	—	2	2	no	—
171	C₂³×C₆₇	—	2	2	no	—
172	C₂³×C₆₇	—	4	4	no	—
173	C₂³×C₆₇	—	4	4	no	—
174	C₂³×C₆₇	—	4	4	no	—
175	C₂³×C₆₇	—	4	4	no	—
176	C₂³×C₆₇	C₂×#41	1	4	yes	—
177	C₂³×C₆₇	C₂×#41	1	2	yes	—
178	C₂³×C₆₇	C₂×#41	1	2	yes	—
179	C₂³×C₆₇	C₂×#41	1	2	yes	—
180	C₂³×C₆₇	C₂×#41	1	2	yes	—
181	C₂³×C₆₇	C₂×#41	1	2	yes	—
182	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
183	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
184	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
185	C₂×C₄×C₆₇	—	2	8	no	—
186	C₂×C₄×C₆₇	—	2	2	no	—
187	C₂×C₄×C₆₇	—	2	2	no	—
188	C₂×C₄×C₆₇	—	2	4	no	—
189	C₂×C₄×C₆₇	—	2	2	no	—
190	C₂×C₄×C₆₇	—	2	2	no	—
191	C₂×C₄×C₆₇	—	2	2	no	—
192	C₂×C₄×C₆₇	—	2	4	no	—
193	C₂×C₄×C₆₇	—	2	4	no	—
194	C₂×C₄×C₆₇	—	2	2	no	—
195	C₂×C₄×C₆₇	—	2	2	no	—
196	C₂×C₄×C₆₇	—	2	4	no	—
197	C₂×C₄×C₆₇	—	2	2	no	—
198	C₂×C₄×C₆₇	—	2	4	no	—
199	C₂×C₄×C₆₇	—	2	4	no	—
200	C₂×C₄×C₆₇	—	2	4	no	—
201	C₂×C₄×C₆₇	—	2	4	no	—
202	C₂×C₄×C₆₇	—	2	2	no	—
203	C₂×C₄×C₆₇	—	2	2	no	—
204	C₂×C₄×C₆₇	—	2	2	no	—
205	C₂×C₄×C₆₇	—	2	4	no	—
206	C₂×C₄×C₆₇	—	2	4	no	—
207	C₂×C₄×C₆₇	—	2	2	no	—
208	C₂×C₄×C₆₇	—	2	4	no	—
209	C₂×C₄×C₆₇	—	2	2	no	—
210	C₂×C₄×C₆₇	—	2	4	no	—
211	C₂×C₄×C₆₇	—	2	2	no	—
212	C₂×C₄×C₆₇	—	4	4	no	—
213	C₂×C₄×C₆₇	—	4	8	no	—
214	C₂×C₄×C₆₇	—	4	8	no	—
215	C₂×C₄×C₆₇	—	4	4	no	—
216	C₂×C₄×C₆₇	—	4	4	no	—
217	C₂×C₄×C₆₇	—	4	8	no	—
218	C₂×C₄×C₆₇	—	4	4	no	—
219	C₂×C₄×C₆₇	—	4	8	no	—
220	C₂×C₄×C₆₇	—	4	16	no	—
221	C₂×C₄×C₆₇	#126	1	16	yes	—
222	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
223	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
224	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
225	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
226	C₂²×C₆₇	—	2	4	no	—
227	C₂²×C₆₇	—	2	4	no	—
228	C₂²×C₆₇	—	2	4	no	—
229	C₂²×C₆₇	—	4	2	no	—
230	C₂²×C₆₇	—	4	2	no	—
231	C₂²×C₆₇	—	4	2	no	—
232	C₂²×C₆₇	—	4	2	no	—
233	C₂²×C₆₇	—	4	16	no	—
234	C₂²×C₆₇	C₂×#126	1	4	yes	—
235	C₂²×C₆₇	#529	1	4	yes	—
236	C₂²×C₆₇	#542	1	4	yes	—
237	C₂²×C₆₇	#552	1	4	yes	—
238	C₂²×C₆₇	#552	1	4	yes	—
239	C₂²×C₆₇	#553	1	4	yes	—
240	C₂²×C₆₇	#555	1	4	yes	—
241	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
242	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
243	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
244	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
245	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
246	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
247	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
248	C₄×C₆₇	—	2	4	no	—
249	C₄×C₆₇	—	4	2	no	—
250	C₄×C₆₇	—	4	4	no	—
251	C₄×C₆₇	—	4	4	no	—
252	C₄×C₆₇	—	4	2	no	—
253	C₄×C₆₇	—	4	2	no	—
254	C₄×C₆₇	—	4	4	no	—
255	C₄×C₆₇	—	4	2	no	—
256	C₄×C₆₇	—	4	4	no	—
257	C₄×C₆₇	C₂×#126	1	8	yes	—
258	C₂×#2495	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂×C₆₇	—	4	4	no	—
260	C₂×C₆₇	#2495	1	8	yes	direct product factor
261	C₂×C₆₇	C₂²×#126	1	1	yes	characteristic
262	C₂×C₆₇	C₂×#529	1	1	yes	characteristic
263	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
264	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
265	C₂×C₆₇	C₂×#552	1	1	yes	characteristic
266	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
267	C₂×C₆₇	C₂×#555	1	1	yes	characteristic
268	#2495	C₂×C₆₇	1	16	yes	direct product factor
269	C₂×#400	C₂×C₆₇	1	2	yes	complemented
270	C₂×#397	C₂×C₆₇	1	2	yes	—
271	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
272	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
273	C₂×#388	C₂×C₆₇	1	2	yes	—
274	C₂×#383	C₂×C₆₇	1	2	yes	complemented
275	C₂×#382	C₂×C₆₇	1	1	yes	characteristic, complemented
276	C₂×#380	C₂×C₆₇	1	1	yes	characteristic
277	C₂×#380	C₂×C₆₇	1	1	yes	characteristic
278	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
279	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic
280	C₆₇	C₂×#2495	1	1	yes	characteristic, direct product factor, Sylow
281	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
285	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
288	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
289	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
290	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
291	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
292	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
293	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
294	C₂²×C₄²	C₂²×C₆₇	1	2	yes	—
295	#400	C₂²×C₆₇	1	16	yes	complemented
296	#397	C₂²×C₆₇	1	16	yes	—
297	#389	C₂²×C₆₇	1	8	yes	complemented
298	#389	C₂²×C₆₇	1	8	yes	complemented
299	#388	C₂²×C₆₇	1	16	yes	—
300	#383	C₂²×C₆₇	1	16	yes	complemented
301	#382	C₂²×C₆₇	1	8	yes	complemented
302	#380	C₂²×C₆₇	1	8	yes	—
303	#380	C₂²×C₆₇	1	8	yes	—
304	C₄×C₄⋊C₄	C₂²×C₆₇	1	8	yes	complemented
305	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	—
306	C₂×#95	C₂²×C₆₇	1	2	yes	—
307	C₂×#95	C₂²×C₆₇	1	2	yes	—
308	C₂×#95	C₂²×C₆₇	1	2	yes	—
309	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
310	C₂×#95	C₂²×C₆₇	1	2	yes	—
311	C₂×#95	C₂²×C₆₇	1	2	yes	—
312	C₂×#95	C₂²×C₆₇	1	2	yes	—
313	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
314	C₂×#95	C₂²×C₆₇	1	2	yes	—
315	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	2	4	no	—
318	C₂³×C₄	—	2	4	no	—
319	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
320	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
321	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
324	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
325	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
328	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	4	4	no	—
335	C₂×C₄⋊C₄	—	4	4	no	—
336	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
341	C₂×C₄⋊C₄	C₂³×C₆₇	1	8	yes	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	8	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	4	4	no	—
346	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₆₇	1	8	yes	—
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	—	2	8	no	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
354	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
355	C₂×C₄²	C₂³×C₆₇	1	8	yes	—
356	#95	C₂³×C₆₇	1	4	yes	—
357	#95	C₂³×C₆₇	1	4	yes	—
358	#95	C₂³×C₆₇	1	8	yes	—
359	#95	C₂³×C₆₇	1	8	yes	—
360	#95	C₂³×C₆₇	1	8	yes	—
361	#95	C₂³×C₆₇	1	8	yes	—
362	#95	C₂³×C₆₇	1	8	yes	—
363	#95	C₂³×C₆₇	1	8	yes	—
364	#95	C₂³×C₆₇	1	8	yes	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	2	2	no	—
368	C₂⁴	—	2	2	no	—
369	C₂⁴	—	2	2	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	#41×C₆₇	1	4	yes	—
372	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
373	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	—	4	16	no	—
404	C₂²×C₄	#41×C₆₇	1	4	yes	—
405	C₂²×C₄	#41×C₆₇	1	4	yes	—
406	C₂²×C₄	#41×C₆₇	1	4	yes	—
407	C₂²×C₄	#41×C₆₇	1	4	yes	—
408	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
413	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	4	8	no	—
423	C₄⋊C₄	—	4	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	4	8	no	—
428	C₄²	—	2	8	no	—
429	C₄²	—	2	16	no	—
430	C₄²	—	2	8	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	C₂×#41×C₆₇	1	4	yes	—
445	C₂³	C₂×#41×C₆₇	1	2	yes	—
446	C₂³	C₂×#41×C₆₇	1	2	yes	—
447	C₂³	C₂×#41×C₆₇	1	2	yes	—
448	C₂³	C₂×#41×C₆₇	1	2	yes	—
449	C₂³	C₂×#41×C₆₇	1	2	yes	—
450	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
451	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
452	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	16	no	—
489	C₂×C₄	#126×C₆₇	1	16	yes	—
490	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
491	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
492	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
493	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	16	no	—
502	C₂²	C₂×#126×C₆₇	1	4	yes	—
503	C₂²	#529×C₆₇	1	4	yes	—
504	C₂²	#542×C₆₇	1	4	yes	—
505	C₂²	#552×C₆₇	1	4	yes	—
506	C₂²	#552×C₆₇	1	4	yes	—
507	C₂²	#553×C₆₇	1	4	yes	—
508	C₂²	#555×C₆₇	1	4	yes	—
509	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
510	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
511	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
512	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
513	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
514	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
515	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	4	no	—
525	C₄	C₂×#126×C₆₇	1	8	yes	—
526	C₂	—	4	4	no	—
527	C₂	C₆₇×#2495	1	8	yes	direct product factor
528	C₂	C₂²×#126×C₆₇	1	1	yes	characteristic
529	C₂	C₂×#529×C₆₇	1	1	yes	characteristic
530	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
531	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
532	C₂	C₂×#552×C₆₇	1	1	yes	characteristic
533	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
534	C₂	C₂×#555×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×#2495	C₂	direct (N × H)
2. C₂×#400×C₆₇	C₂	semidirect
4. C₂×#389×C₆₇	C₂	semidirect
5. C₂×#389×C₆₇	C₂	semidirect
7. C₂×#383×C₆₇	C₂	semidirect
8. C₂×#382×C₆₇	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
27. #400×C₆₇	C₂²	semidirect
29. #389×C₆₇	C₂²	semidirect
30. #389×C₆₇	C₂²	semidirect
32. #383×C₆₇	C₂²	semidirect
33. #382×C₆₇	C₂²	semidirect
36. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
258. C₂×#2495	C₆₇	direct (N × H)
260. C₂×C₆₇	#2495	direct (N × H)
268. #2495	C₂×C₆₇	direct (N × H)
269. C₂×#400	C₂×C₆₇	semidirect
271. C₂×#389	C₂×C₆₇	semidirect
272. C₂×#389	C₂×C₆₇	semidirect
274. C₂×#383	C₂×C₆₇	semidirect
275. C₂×#382	C₂×C₆₇	semidirect
278. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
280. C₆₇	C₂×#2495	direct (N × H)
295. #400	C₂²×C₆₇	semidirect
297. #389	C₂²×C₆₇	semidirect
298. #389	C₂²×C₆₇	semidirect
300. #383	C₂²×C₆₇	semidirect
301. #382	C₂²×C₆₇	semidirect
304. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
527. C₂	C₆₇×#2495	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×#2495	2
C₂×#400×C₆₇	2
C₂×#397×C₆₇	2
C₂×#389×C₆₇	2
C₂×#388×C₆₇	2
C₂×#383×C₆₇	2
C₂×#382×C₆₇	2
C₂×#380×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₂×#2495	67

Subgroups — C2×C67×#2495 #30714028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2495 #30714028