Subgroups — C₆₇×#59865 #30739116

Order 17152.

1772 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2794	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2709	C₂	1	2	yes	maximal
3	C₆₇×#2595	C₂	1	4	yes	maximal, complemented
4	C₆₇×#2593	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2562	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2562	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2516	C₂	1	4	yes	maximal, complemented
8	C₆₇×#2487	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2486	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2485	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2374	C₂	1	2	yes	maximal, complemented
12	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
13	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
14	C₄×#127×C₆₇	C₂	1	1	yes	maximal, characteristic
15	C₄×#125×C₆₇	C₂	1	2	yes	maximal, complemented
16	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₇	C₂²	1	2	yes	—
18	C₂×#123×C₆₇	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₇	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
26	#400×C₆₇	C₂²	1	4	yes	—
27	#400×C₆₇	C₂²	1	4	yes	—
28	#400×C₆₇	C₂²	1	2	yes	—
29	#399×C₆₇	C₂²	1	2	yes	—
30	#398×C₆₇	C₂²	1	2	yes	—
31	#397×C₆₇	C₂²	1	4	yes	—
32	#397×C₆₇	C₂²	1	2	yes	—
33	#394×C₆₇	C₂²	1	4	yes	—
34	#394×C₆₇	C₂²	1	4	yes	—
35	#394×C₆₇	C₂²	1	4	yes	—
36	#390×C₆₇	C₂²	1	2	yes	—
37	#390×C₆₇	C₂²	1	1	yes	characteristic
38	#390×C₆₇	C₂²	1	2	yes	—
39	#390×C₆₇	C₂²	1	1	yes	characteristic
40	#389×C₆₇	C₂²	1	2	yes	—
41	#389×C₆₇	C₂²	1	2	yes	—
42	#388×C₆₇	C₂²	1	4	yes	—
43	#388×C₆₇	C₂²	1	4	yes	—
44	#388×C₆₇	C₂²	1	4	yes	—
45	#388×C₆₇	C₂²	1	4	yes	—
46	#388×C₆₇	C₂²	1	4	yes	—
47	#388×C₆₇	C₂²	1	4	yes	—
48	#388×C₆₇	C₂²	1	4	yes	—
49	#387×C₆₇	C₂²	1	4	yes	—
50	#387×C₆₇	C₂²	1	4	yes	—
51	#387×C₆₇	C₂²	1	4	yes	—
52	#387×C₆₇	C₂²	1	4	yes	—
53	#387×C₆₇	C₂²	1	4	yes	—
54	#386×C₆₇	C₂²	1	4	yes	—
55	#386×C₆₇	C₂²	1	4	yes	—
56	#386×C₆₇	C₂²	1	2	yes	—
57	#385×C₆₇	C₂²	1	2	yes	—
58	#384×C₆₇	C₂²	1	1	yes	characteristic
59	#382×C₆₇	C₂²	1	2	yes	—
60	#381×C₆₇	C₂²	1	2	yes	—
61	#380×C₆₇	C₂²	1	2	yes	—
62	#380×C₆₇	C₂²	1	1	yes	characteristic
63	#380×C₆₇	C₂²	1	1	yes	characteristic
64	#380×C₆₇	C₂²	1	2	yes	—
65	#380×C₆₇	C₂²	1	2	yes	—
66	#380×C₆₇	C₂²	1	2	yes	—
67	#380×C₆₇	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
69	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₆₇	C₂²	1	4	yes	—
72	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
73	C₄×C₂²⋊C₄×C₆₇	C₂²	1	4	yes	—
74	C₄³×C₆₇	C₂²	1	1	yes	characteristic
75	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
76	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
77	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
82	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
83	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
84	#127×C₆₇	—	2	4	no	—
85	#125×C₆₇	—	2	8	no	—
86	#123×C₆₇	—	2	8	no	—
87	C₄×D₄×C₆₇	—	2	8	no	—
88	C₄×D₄×C₆₇	—	2	8	no	—
89	C₄×D₄×C₆₇	—	4	2	no	—
90	C₄×D₄×C₆₇	—	4	2	no	—
91	#117×C₆₇	—	4	4	no	—
92	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
93	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
94	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
126	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
129	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
130	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
131	#95×C₆₇	C₂³	1	4	yes	—
132	#95×C₆₇	C₂³	1	4	yes	—
133	#95×C₆₇	C₂³	1	4	yes	—
134	#95×C₆₇	C₂³	1	4	yes	—
135	#95×C₆₇	C₂³	1	4	yes	—
136	#95×C₆₇	C₂³	1	4	yes	—
137	#95×C₆₇	C₂³	1	4	yes	—
138	#95×C₆₇	C₂³	1	4	yes	—
139	#95×C₆₇	C₂³	1	4	yes	—
140	#95×C₆₇	C₂³	1	4	yes	—
141	#95×C₆₇	C₂³	1	4	yes	—
142	#95×C₆₇	C₂³	1	2	yes	—
143	#95×C₆₇	C₂³	1	2	yes	—
144	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
145	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
146	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
147	C₂×D₄×C₆₇	—	2	4	no	—
148	C₂×D₄×C₆₇	—	2	4	no	—
149	C₂×D₄×C₆₇	—	2	4	no	—
150	C₂×D₄×C₆₇	—	2	4	no	—
151	C₂×D₄×C₆₇	—	2	2	no	—
152	C₂×D₄×C₆₇	—	4	1	no	—
153	C₂×D₄×C₆₇	—	4	1	no	—
154	C₂×D₄×C₆₇	—	4	1	no	—
155	C₂×D₄×C₆₇	—	4	2	no	—
156	C₂×D₄×C₆₇	—	4	2	no	—
157	C₂×D₄×C₆₇	—	4	1	no	—
158	C₂×D₄×C₆₇	#41	1	4	yes	—
159	C₂²×C₄×C₆₇	—	2	4	no	—
160	C₂²×C₄×C₆₇	—	2	4	no	—
161	C₂²×C₄×C₆₇	—	2	4	no	—
162	C₂²×C₄×C₆₇	—	2	4	no	—
163	C₂²×C₄×C₆₇	—	2	4	no	—
164	C₂²×C₄×C₆₇	—	2	2	no	—
165	C₂²×C₄×C₆₇	—	2	2	no	—
166	C₂²×C₄×C₆₇	—	2	4	no	—
167	C₂²×C₄×C₆₇	—	4	2	no	—
168	C₂²×C₄×C₆₇	—	4	2	no	—
169	C₂²×C₄×C₆₇	—	4	2	no	—
170	C₂²×C₄×C₆₇	—	4	4	no	—
171	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
183	C₄⋊C₄×C₆₇	—	2	4	no	—
184	C₄⋊C₄×C₆₇	—	2	4	no	—
185	C₄⋊C₄×C₆₇	—	2	8	no	—
186	C₄⋊C₄×C₆₇	—	2	8	no	—
187	C₄⋊C₄×C₆₇	—	2	8	no	—
188	C₄⋊C₄×C₆₇	—	2	4	no	—
189	C₄⋊C₄×C₆₇	—	2	4	no	—
190	C₄⋊C₄×C₆₇	—	2	4	no	—
191	C₄⋊C₄×C₆₇	—	2	4	no	—
192	C₄⋊C₄×C₆₇	—	4	2	no	—
193	C₄⋊C₄×C₆₇	—	4	2	no	—
194	C₄⋊C₄×C₆₇	—	4	4	no	—
195	C₄⋊C₄×C₆₇	—	4	1	no	—
196	C₄⋊C₄×C₆₇	—	4	1	no	—
197	C₂²⋊C₄×C₆₇	—	2	4	no	—
198	C₂²⋊C₄×C₆₇	—	2	8	no	—
199	C₂²⋊C₄×C₆₇	—	2	4	no	—
200	C₂²⋊C₄×C₆₇	—	2	4	no	—
201	C₂²⋊C₄×C₆₇	—	2	4	no	—
202	C₂²⋊C₄×C₆₇	—	2	4	no	—
203	C₂²⋊C₄×C₆₇	—	4	2	no	—
204	C₂²⋊C₄×C₆₇	—	4	4	no	—
205	C₂²⋊C₄×C₆₇	—	4	4	no	—
206	C₂²⋊C₄×C₆₇	—	4	4	no	—
207	C₂²⋊C₄×C₆₇	—	4	4	no	—
208	C₂²⋊C₄×C₆₇	—	4	4	no	—
209	C₂²⋊C₄×C₆₇	—	4	2	no	—
210	C₂²⋊C₄×C₆₇	—	4	1	no	—
211	C₂²⋊C₄×C₆₇	—	4	1	no	—
212	C₄²×C₆₇	—	2	2	no	—
213	C₄²×C₆₇	—	2	2	no	—
214	C₄²×C₆₇	—	4	1	no	—
215	C₄²×C₆₇	—	4	2	no	—
216	C₄²×C₆₇	—	4	4	no	—
217	C₄²×C₆₇	—	4	4	no	—
218	C₄²×C₆₇	—	4	4	no	—
219	C₄²×C₆₇	#41	1	8	yes	—
220	C₂³×C₆₇	—	2	2	no	—
221	C₂³×C₆₇	—	2	2	no	—
222	C₂³×C₆₇	—	2	1	no	—
223	C₂³×C₆₇	—	2	1	no	—
224	C₂³×C₆₇	—	2	2	no	—
225	C₂³×C₆₇	—	2	1	no	—
226	C₂³×C₆₇	—	2	2	no	—
227	C₂³×C₆₇	—	2	1	no	—
228	C₂³×C₆₇	—	2	2	no	—
229	C₂³×C₆₇	—	2	2	no	—
230	C₂³×C₆₇	—	2	2	no	—
231	C₂³×C₆₇	—	2	2	no	—
232	C₂³×C₆₇	—	2	2	no	—
233	C₂³×C₆₇	—	2	2	no	—
234	C₂³×C₆₇	—	2	2	no	—
235	C₂³×C₆₇	C₂×#41	1	2	yes	—
236	C₂³×C₆₇	C₂×#41	1	2	yes	—
237	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
238	D₄×C₆₇	—	4	4	no	—
239	D₄×C₆₇	—	4	8	no	—
240	D₄×C₆₇	—	4	8	no	—
241	D₄×C₆₇	—	4	4	no	—
242	C₂×C₄×C₆₇	—	2	2	no	—
243	C₂×C₄×C₆₇	—	2	1	no	—
244	C₂×C₄×C₆₇	—	2	2	no	—
245	C₂×C₄×C₆₇	—	2	2	no	—
246	C₂×C₄×C₆₇	—	2	2	no	—
247	C₂×C₄×C₆₇	—	2	1	no	—
248	C₂×C₄×C₆₇	—	2	4	no	—
249	C₂×C₄×C₆₇	—	2	2	no	—
250	C₂×C₄×C₆₇	—	2	2	no	—
251	C₂×C₄×C₆₇	—	2	2	no	—
252	C₂×C₄×C₆₇	—	2	2	no	—
253	C₂×C₄×C₆₇	—	2	4	no	—
254	C₂×C₄×C₆₇	—	2	4	no	—
255	C₂×C₄×C₆₇	—	2	4	no	—
256	C₂×C₄×C₆₇	—	2	1	no	—
257	C₂×C₄×C₆₇	—	2	2	no	—
258	C₂×C₄×C₆₇	—	2	4	no	—
259	C₂×C₄×C₆₇	—	2	4	no	—
260	C₂×C₄×C₆₇	—	2	1	no	—
261	C₂×C₄×C₆₇	—	2	1	no	—
262	C₂×C₄×C₆₇	—	2	4	no	—
263	C₂×C₄×C₆₇	—	2	4	no	—
264	C₂×C₄×C₆₇	—	2	4	no	—
265	C₂×C₄×C₆₇	—	2	4	no	—
266	C₂×C₄×C₆₇	—	2	2	no	—
267	C₂×C₄×C₆₇	—	2	4	no	—
268	C₂×C₄×C₆₇	—	2	4	no	—
269	C₂×C₄×C₆₇	—	4	4	no	—
270	C₂×C₄×C₆₇	—	4	4	no	—
271	C₂×C₄×C₆₇	—	4	8	no	—
272	C₂×C₄×C₆₇	—	8	4	no	—
273	C₂×C₄×C₆₇	—	8	4	no	—
274	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
275	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
276	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
277	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
278	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
279	C₂²×C₆₇	—	2	4	no	—
280	C₂²×C₆₇	—	2	4	no	—
281	C₂²×C₆₇	—	2	2	no	—
282	C₂²×C₆₇	—	2	2	no	—
283	C₂²×C₆₇	—	4	1	no	—
284	C₂²×C₆₇	—	4	1	no	—
285	C₂²×C₆₇	—	4	2	no	—
286	C₂²×C₆₇	—	4	2	no	—
287	C₂²×C₆₇	—	4	1	no	—
288	C₂²×C₆₇	—	4	1	no	—
289	C₂²×C₆₇	—	4	2	no	—
290	C₂²×C₆₇	—	4	2	no	—
291	C₂²×C₆₇	—	4	2	no	—
292	C₂²×C₆₇	—	4	2	no	—
293	C₂²×C₆₇	—	4	2	no	—
294	C₂²×C₆₇	—	4	2	no	—
295	C₂²×C₆₇	—	4	2	no	—
296	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
297	C₂²×C₆₇	C₂²×#41	1	2	yes	—
298	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
299	C₂²×C₆₇	#585	1	2	yes	—
300	C₂²×C₆₇	#585	1	1	yes	characteristic
301	C₄×C₆₇	—	2	4	no	—
302	C₄×C₆₇	—	2	2	no	—
303	C₄×C₆₇	—	2	4	no	—
304	C₄×C₆₇	—	4	4	no	—
305	C₄×C₆₇	—	4	2	no	—
306	C₄×C₆₇	—	4	1	no	—
307	C₄×C₆₇	—	4	1	no	—
308	C₄×C₆₇	—	4	4	no	—
309	C₄×C₆₇	—	4	4	no	—
310	C₄×C₆₇	—	4	1	no	—
311	C₄×C₆₇	—	4	4	no	—
312	C₄×C₆₇	#559	1	4	yes	—
313	#59865	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂×C₆₇	—	4	2	no	—
315	C₂×C₆₇	—	4	2	no	—
316	C₂×C₆₇	—	8	2	no	—
317	C₂×C₆₇	#3475	1	2	yes	—
318	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
319	C₂×C₆₇	#3505	1	1	yes	characteristic
320	C₂×C₆₇	#3512	1	2	yes	—
321	C₂×C₆₇	#3551	1	1	yes	characteristic
322	#2794	C₂×C₆₇	1	2	yes	complemented
323	#2709	C₂×C₆₇	1	2	yes	—
324	#2595	C₂×C₆₇	1	4	yes	complemented
325	#2593	C₂×C₆₇	1	2	yes	complemented
326	#2562	C₂×C₆₇	1	2	yes	complemented
327	#2562	C₂×C₆₇	1	2	yes	complemented
328	#2516	C₂×C₆₇	1	4	yes	complemented
329	#2487	C₂×C₆₇	1	1	yes	characteristic, complemented
330	#2486	C₂×C₆₇	1	1	yes	characteristic, complemented
331	#2485	C₂×C₆₇	1	2	yes	complemented
332	#2374	C₂×C₆₇	1	2	yes	complemented
333	#2352	C₂×C₆₇	1	2	yes	complemented
334	#2352	C₂×C₆₇	1	2	yes	complemented
335	C₄×#127	C₂×C₆₇	1	1	yes	characteristic
336	C₄×#125	C₂×C₆₇	1	2	yes	complemented
337	C₆₇	#59865	1	1	yes	characteristic, direct product factor, Sylow
338	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
339	C₂×#125	C₂²×C₆₇	1	2	yes	—
340	C₂×#123	C₂²×C₆₇	1	2	yes	—
341	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
343	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
344	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
345	C₂×#117	C₂²×C₆₇	1	2	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
347	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
348	#400	C₂²×C₆₇	1	4	yes	—
349	#400	C₂²×C₆₇	1	4	yes	—
350	#400	C₂²×C₆₇	1	2	yes	—
351	#399	C₂²×C₆₇	1	2	yes	—
352	#398	C₂²×C₆₇	1	2	yes	—
353	#397	C₂²×C₆₇	1	2	yes	—
354	#397	C₂²×C₆₇	1	4	yes	—
355	#394	C₂²×C₆₇	1	4	yes	—
356	#394	C₂²×C₆₇	1	4	yes	—
357	#394	C₂²×C₆₇	1	4	yes	—
358	#390	C₂²×C₆₇	1	1	yes	characteristic
359	#390	C₂²×C₆₇	1	2	yes	—
360	#390	C₂²×C₆₇	1	1	yes	characteristic
361	#390	C₂²×C₆₇	1	2	yes	—
362	#389	C₂²×C₆₇	1	2	yes	—
363	#389	C₂²×C₆₇	1	2	yes	—
364	#388	C₂²×C₆₇	1	4	yes	—
365	#388	C₂²×C₆₇	1	4	yes	—
366	#388	C₂²×C₆₇	1	4	yes	—
367	#388	C₂²×C₆₇	1	4	yes	—
368	#388	C₂²×C₆₇	1	4	yes	—
369	#388	C₂²×C₆₇	1	4	yes	—
370	#388	C₂²×C₆₇	1	4	yes	—
371	#387	C₂²×C₆₇	1	4	yes	—
372	#387	C₂²×C₆₇	1	4	yes	—
373	#387	C₂²×C₆₇	1	4	yes	—
374	#387	C₂²×C₆₇	1	4	yes	—
375	#387	C₂²×C₆₇	1	4	yes	—
376	#386	C₂²×C₆₇	1	4	yes	—
377	#386	C₂²×C₆₇	1	4	yes	—
378	#386	C₂²×C₆₇	1	2	yes	—
379	#385	C₂²×C₆₇	1	2	yes	—
380	#384	C₂²×C₆₇	1	1	yes	characteristic
381	#382	C₂²×C₆₇	1	2	yes	—
382	#381	C₂²×C₆₇	1	2	yes	—
383	#380	C₂²×C₆₇	1	2	yes	—
384	#380	C₂²×C₆₇	1	1	yes	characteristic
385	#380	C₂²×C₆₇	1	1	yes	characteristic
386	#380	C₂²×C₆₇	1	2	yes	—
387	#380	C₂²×C₆₇	1	2	yes	—
388	#380	C₂²×C₆₇	1	2	yes	—
389	#380	C₂²×C₆₇	1	2	yes	—
390	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
391	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
392	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
393	C₄×C₄⋊C₄	C₂²×C₆₇	1	4	yes	—
394	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
395	C₄×C₂²⋊C₄	C₂²×C₆₇	1	4	yes	—
396	C₄³	C₂²×C₆₇	1	1	yes	characteristic
397	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
398	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
399	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
401	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
403	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
404	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
405	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
406	#127	—	2	4	no	—
407	#125	—	2	8	no	—
408	#123	—	2	8	no	—
409	C₄×D₄	—	2	8	no	—
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	4	2	no	—
412	C₄×D₄	—	4	2	no	—
413	#117	—	4	4	no	—
414	C₂×C₄⋊C₄	—	4	2	no	—
415	C₂×C₄⋊C₄	—	4	2	no	—
416	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
419	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
421	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
423	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
426	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
427	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
443	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
444	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
445	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
448	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
450	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
451	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
452	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
453	#95	C₂³×C₆₇	1	4	yes	—
454	#95	C₂³×C₆₇	1	4	yes	—
455	#95	C₂³×C₆₇	1	4	yes	—
456	#95	C₂³×C₆₇	1	4	yes	—
457	#95	C₂³×C₆₇	1	4	yes	—
458	#95	C₂³×C₆₇	1	4	yes	—
459	#95	C₂³×C₆₇	1	4	yes	—
460	#95	C₂³×C₆₇	1	4	yes	—
461	#95	C₂³×C₆₇	1	4	yes	—
462	#95	C₂³×C₆₇	1	4	yes	—
463	#95	C₂³×C₆₇	1	4	yes	—
464	#95	C₂³×C₆₇	1	2	yes	—
465	#95	C₂³×C₆₇	1	2	yes	—
466	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
467	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
468	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	—	4	1	no	—
476	C₂×D₄	—	4	1	no	—
477	C₂×D₄	—	4	2	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	—	4	1	no	—
480	C₂×D₄	#41×C₆₇	1	4	yes	—
481	C₂²×C₄	—	2	4	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	4	2	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
495	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
501	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₄⋊C₄	—	4	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	2	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	1	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	4	no	—
531	C₂²⋊C₄	—	4	4	no	—
532	C₂²⋊C₄	—	4	4	no	—
533	C₂²⋊C₄	—	4	4	no	—
534	C₄²	—	2	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	4	4	no	—
537	C₄²	—	4	1	no	—
538	C₄²	—	4	2	no	—
539	C₄²	—	4	4	no	—
540	C₄²	—	4	4	no	—
541	C₄²	#41×C₆₇	1	8	yes	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	C₂×#41×C₆₇	1	2	yes	—
558	C₂³	C₂×#41×C₆₇	1	2	yes	—
559	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
560	D₄	—	4	4	no	—
561	D₄	—	4	8	no	—
562	D₄	—	4	8	no	—
563	D₄	—	4	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	8	4	no	—
595	C₂×C₄	—	8	4	no	—
596	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
597	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
598	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
599	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
600	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₆₇	1	2	yes	—
620	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
621	C₂²	#585×C₆₇	1	2	yes	—
622	C₂²	#585×C₆₇	1	1	yes	characteristic
623	C₄	—	2	4	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	4	no	—
626	C₄	—	4	4	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	4	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	4	no	—
633	C₄	—	4	4	no	—
634	C₄	#559×C₆₇	1	4	yes	—
635	C₂	—	4	2	no	—
636	C₂	—	4	2	no	—
637	C₂	—	8	2	no	—
638	C₂	C₆₇×#3475	1	2	yes	—
639	C₂	C₂×#559×C₆₇	1	1	yes	characteristic
640	C₂	C₆₇×#3505	1	1	yes	characteristic
641	C₂	C₆₇×#3512	1	2	yes	—
642	C₂	C₆₇×#3551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#127×C₆₇	C₂²
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×#2794	C₂	semidirect
3. C₆₇×#2595	C₂	semidirect
4. C₆₇×#2593	C₂	semidirect
5. C₆₇×#2562	C₂	semidirect
6. C₆₇×#2562	C₂	semidirect
7. C₆₇×#2516	C₂	semidirect
8. C₆₇×#2487	C₂	semidirect
9. C₆₇×#2486	C₂	semidirect
10. C₆₇×#2485	C₂	semidirect
11. C₆₇×#2374	C₂	semidirect
12. C₆₇×#2352	C₂	semidirect
13. C₆₇×#2352	C₂	semidirect
15. C₄×#125×C₆₇	C₂	semidirect
313. #59865	C₆₇	direct (N × H)
322. #2794	C₂×C₆₇	semidirect
324. #2595	C₂×C₆₇	semidirect
325. #2593	C₂×C₆₇	semidirect
326. #2562	C₂×C₆₇	semidirect
327. #2562	C₂×C₆₇	semidirect
328. #2516	C₂×C₆₇	semidirect
329. #2487	C₂×C₆₇	semidirect
330. #2486	C₂×C₆₇	semidirect
331. #2485	C₂×C₆₇	semidirect
332. #2374	C₂×C₆₇	semidirect
333. #2352	C₂×C₆₇	semidirect
334. #2352	C₂×C₆₇	semidirect
336. C₄×#125	C₂×C₆₇	semidirect
337. C₆₇	#59865	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×#2794	2
C₆₇×#2709	2
C₆₇×#2595	2
C₆₇×#2593	2
C₆₇×#2562	2
C₆₇×#2516	2
C₆₇×#2487	2
C₆₇×#2486	2
C₆₇×#2485	2
C₆₇×#2374	2
C₆₇×#2352	2
C₄×#127×C₆₇	2
C₄×#125×C₆₇	2
#59865	67

Subgroups — C67×#59865 #30739116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59865 #30739116