Subgroups — C₂×#27161664 #38756050

Order 25216.

1336 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27161664	C₂	1	16	yes	maximal, direct product factor
2	C₂×#20263319	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#20263319	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#20263313	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#20263312	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#20263308	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#20263307	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#20263303	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#20263298	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#20263298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#20263297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#20263295	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₄×Dic₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#20263286	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊Dic₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#120×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₃₉₄	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₁₉₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₉₇	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₁₉₇	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₁₉₇	C₂²	1	1	yes	characteristic, complemented
22	C₂³×Dic₁₉₇	C₂²	1	1	yes	characteristic
23	C₂³×Dic₁₉₇	C₂²	1	1	yes	characteristic
24	C₂³×Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₄×D₁₉₇	C₂²	1	1	yes	characteristic, complemented
26	#20263319	C₂²	1	8	yes	complemented
27	#20263319	C₂²	1	8	yes	complemented
28	#20263313	C₂²	1	8	yes	complemented
29	#20263312	C₂²	1	8	yes	complemented
30	#20263308	C₂²	1	8	yes	complemented
31	#20263307	C₂²	1	8	yes	complemented
32	#20263303	C₂²	1	8	yes	complemented
33	#20263298	C₂²	1	8	yes	complemented
34	#20263298	C₂²	1	8	yes	complemented
35	#20263297	C₂²	1	8	yes	complemented
36	#20263295	C₂²	1	8	yes	complemented
37	D₄×Dic₁₉₇	C₂²	1	8	yes	complemented
38	#20263286	C₂²	1	8	yes	complemented
39	C₂×C₄⋊Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄⋊Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#15691337	C₂²	1	1	yes	characteristic, complemented
42	C₂×#15691337	C₂²	1	1	yes	characteristic, complemented
43	C₂×#15691337	C₂²	1	1	yes	characteristic, complemented
44	C₂×#15691337	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₁₉₇	C₂²	1	8	yes	complemented
53	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
55	C₂×#15691335	C₂²	1	1	yes	characteristic, complemented
56	C₂×#15691335	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₄×Dic₁₉₇	C₂²	1	1	yes	characteristic, complemented
59	C₂⁵×C₁₉₇	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₉₇	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₁₉₇	C₂²	1	1	yes	characteristic
62	C₂²×D₄×C₁₉₇	C₂²	1	1	yes	characteristic
63	#120×C₁₉₇	C₂²	1	8	yes	complemented
64	C₂×C₂²⋊C₄×C₁₉₇	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₁₉₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₁₉₇	C₂²	1	1	yes	characteristic
67	C₂³×D₁₉₇	C₂³	1	1	yes	characteristic
68	C₂×Dic₃₉₄	—	4	2	no	—
69	C₂×Dic₃₉₄	C₂³	1	4	yes	complemented
70	C₂×C₂²⋊D₁₉₇	—	2	4	no	—
71	C₂×C₂²⋊D₁₉₇	—	4	2	no	—
72	C₂×C₂²⋊D₁₉₇	—	4	2	no	—
73	C₂×C₂²⋊D₁₉₇	—	4	2	no	—
74	C₂×C₂²⋊D₁₉₇	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₁₉₇	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₁₉₇	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₁₉₇	C₂³	1	4	yes	complemented
78	C₂²×Dic₁₉₇	—	4	2	no	—
79	C₂²×Dic₁₉₇	—	4	2	no	—
80	C₂²×Dic₁₉₇	—	4	2	no	—
81	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
83	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
84	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
85	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
86	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₉₇	C₂³	1	1	yes	characteristic
88	C₂²×Dic₁₉₇	C₂³	1	4	yes	—
89	C₂²×Dic₁₉₇	C₂³	1	4	yes	—
90	C₂²×Dic₁₉₇	C₂³	1	4	yes	complemented
91	C₂×C₄×D₁₉₇	—	4	2	no	—
92	C₂×C₄×D₁₉₇	C₂³	1	4	yes	complemented
93	C₄⋊Dic₁₉₇	C₂³	1	4	yes	complemented
94	C₄⋊Dic₁₉₇	C₂³	1	4	yes	complemented
95	#15691337	C₂³	1	4	yes	complemented
96	#15691337	C₂³	1	4	yes	complemented
97	#15691337	C₂³	1	4	yes	complemented
98	#15691337	C₂³	1	4	yes	complemented
99	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
100	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
101	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
102	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
103	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
104	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
105	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	—
106	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	complemented
107	C₂²⋊Dic₁₉₇	C₂³	1	4	yes	complemented
108	#15691335	C₂³	1	4	yes	complemented
109	#15691335	C₂³	1	4	yes	complemented
110	C₄×Dic₁₉₇	C₂³	1	4	yes	complemented
111	C₄×Dic₁₉₇	C₂³	1	4	yes	complemented
112	C₂⁴×C₁₉₇	—	2	4	no	—
113	C₂⁴×C₁₉₇	—	4	2	no	—
114	C₂⁴×C₁₉₇	—	4	2	no	—
115	C₂⁴×C₁₉₇	C₂³	1	1	yes	characteristic
116	C₂⁴×C₁₉₇	C₂³	1	1	yes	characteristic
117	C₂⁴×C₁₉₇	C₂³	1	1	yes	characteristic
118	C₂⁴×C₁₉₇	C₂³	1	1	yes	characteristic
119	C₂⁴×C₁₉₇	C₂³	1	4	yes	—
120	C₂×D₄×C₁₉₇	—	2	4	no	—
121	C₂×D₄×C₁₉₇	—	4	2	no	—
122	C₂×D₄×C₁₉₇	—	4	2	no	—
123	C₂×D₄×C₁₉₇	C₂³	1	4	yes	—
124	C₂×D₄×C₁₉₇	C₂³	1	4	yes	—
125	C₂×D₄×C₁₉₇	C₂³	1	4	yes	—
126	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
129	C₂²⋊C₄×C₁₉₇	C₂³	1	4	yes	—
130	C₂²⋊C₄×C₁₉₇	C₂³	1	4	yes	—
131	C₂²⋊C₄×C₁₉₇	C₂³	1	4	yes	—
132	C₂²×D₁₉₇	—	2	2	no	—
133	C₂²×D₁₉₇	—	2	2	no	—
134	C₂²×D₁₉₇	—	2	2	no	—
135	C₂²×D₁₉₇	C₂⁴	1	2	yes	—
136	Dic₃₉₄	—	4	4	no	—
137	C₂²⋊D₁₉₇	—	2	8	no	—
138	C₂²⋊D₁₉₇	—	4	4	no	—
139	C₂²⋊D₁₉₇	—	4	4	no	—
140	C₂²⋊D₁₉₇	—	4	4	no	—
141	C₂×Dic₁₉₇	—	2	2	no	—
142	C₂×Dic₁₉₇	—	2	2	no	—
143	C₂×Dic₁₉₇	—	2	2	no	—
144	C₂×Dic₁₉₇	—	2	2	no	—
145	C₂×Dic₁₉₇	—	2	2	no	—
146	C₂×Dic₁₉₇	—	2	2	no	—
147	C₂×Dic₁₉₇	—	2	2	no	—
148	C₂×Dic₁₉₇	—	4	4	no	—
149	C₂×Dic₁₉₇	—	4	4	no	—
150	C₂×Dic₁₉₇	—	4	4	no	—
151	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
152	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
153	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
154	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
155	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
156	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
157	C₂×Dic₁₉₇	C₂⁴	1	2	yes	—
158	C₄×D₁₉₇	—	4	4	no	—
159	C₂³×C₁₉₇	—	2	2	no	—
160	C₂³×C₁₉₇	—	2	2	no	—
161	C₂³×C₁₉₇	—	2	2	no	—
162	C₂³×C₁₉₇	—	2	8	no	—
163	C₂³×C₁₉₇	—	2	2	no	—
164	C₂³×C₁₉₇	—	2	2	no	—
165	C₂³×C₁₉₇	—	2	2	no	—
166	C₂³×C₁₉₇	—	2	2	no	—
167	C₂³×C₁₉₇	—	2	2	no	—
168	C₂³×C₁₉₇	—	2	2	no	—
169	C₂³×C₁₉₇	—	2	2	no	—
170	C₂³×C₁₉₇	—	2	2	no	—
171	C₂³×C₁₉₇	—	4	4	no	—
172	C₂³×C₁₉₇	—	4	4	no	—
173	C₂³×C₁₉₇	—	4	16	no	—
174	C₂³×C₁₉₇	#41	1	4	yes	—
175	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
176	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
177	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
178	C₂³×C₁₉₇	C₂⁴	1	2	yes	—
179	C₂³×C₁₉₇	C₂⁴	1	1	yes	characteristic
180	D₄×C₁₉₇	—	2	8	no	—
181	D₄×C₁₉₇	—	4	4	no	—
182	D₄×C₁₉₇	—	4	4	no	—
183	C₂×C₄×C₁₉₇	—	2	2	no	—
184	C₂×C₄×C₁₉₇	—	2	2	no	—
185	C₂×C₄×C₁₉₇	—	2	2	no	—
186	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
187	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
188	C₂×C₄×C₁₉₇	C₂⁴	1	2	yes	—
189	C₂²×C₁₉₇	—	2	8	no	—
190	C₂²×C₁₉₇	—	2	2	no	—
191	C₂²×C₁₉₇	—	2	2	no	—
192	C₂²×C₁₉₇	—	2	2	no	—
193	C₂²×C₁₉₇	—	2	2	no	—
194	C₂²×C₁₉₇	—	2	2	no	—
195	C₂²×C₁₉₇	—	2	2	no	—
196	C₂²×C₁₉₇	—	2	2	no	—
197	C₂²×C₁₉₇	—	2	2	no	—
198	C₂²×C₁₉₇	—	2	2	no	—
199	C₂²×C₁₉₇	—	2	2	no	—
200	C₂²×C₁₉₇	—	2	2	no	—
201	C₂²×C₁₉₇	—	4	16	no	—
202	C₂²×C₁₉₇	—	4	4	no	—
203	C₂²×C₁₉₇	—	4	4	no	—
204	C₂²×C₁₉₇	—	4	4	no	—
205	C₂²×C₁₉₇	C₂×#41	1	4	yes	—
206	C₂²×C₁₉₇	C₂×#41	1	2	yes	—
207	C₂²×C₁₉₇	H(5,𝔽₂)	1	2	yes	—
208	C₂²×C₁₉₇	H(5,𝔽₂)	1	2	yes	—
209	C₂²×C₁₉₇	C₂⁵	1	1	yes	characteristic
210	C₂×D₁₉₇	—	2	2	no	—
211	C₂×D₁₉₇	—	2	2	no	—
212	C₂×D₁₉₇	—	2	2	no	—
213	C₂×D₁₉₇	—	4	4	no	—
214	C₄×C₁₉₇	—	2	2	no	—
215	C₄×C₁₉₇	—	2	2	no	—
216	C₄×C₁₉₇	—	2	2	no	—
217	Dic₁₉₇	—	2	2	no	—
218	Dic₁₉₇	—	2	2	no	—
219	Dic₁₉₇	—	2	2	no	—
220	Dic₁₉₇	—	2	2	no	—
221	Dic₁₉₇	—	2	2	no	—
222	Dic₁₉₇	—	2	2	no	—
223	Dic₁₉₇	—	2	2	no	—
224	C₂×C₁₉₇	—	2	4	no	—
225	C₂×C₁₉₇	—	4	2	no	—
226	C₂×C₁₉₇	—	4	2	no	—
227	C₂×C₁₉₇	—	4	2	no	—
228	C₂×C₁₉₇	#538	1	4	yes	complemented
229	C₂×C₁₉₇	C₂²×#41	1	1	yes	characteristic
230	C₂×C₁₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₁₉₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
232	D₁₉₇	—	4	2	no	—
233	C₁₉₇	C₂×#538	1	1	yes	characteristic, complemented, Sylow
234	C₂×#538	—	197	1	no	maximal, Sylow
235	#538	—	197	16	no	—
236	C₂×#126	—	197	1	no	—
237	C₂×#126	—	197	1	no	—
238	C₂×#124	—	197	1	no	—
239	C₂×#124	—	197	1	no	—
240	C₂×#123	—	197	1	no	—
241	C₂×#123	—	197	1	no	—
242	C₂×C₂²⋊Q₈	—	197	1	no	—
243	C₂×#121	—	197	1	no	—
244	C₂×#121	—	197	1	no	—
245	C₂×#121	—	197	1	no	—
246	C₂×#120	—	197	1	no	—
247	C₂×#120	D₁₉₇	1	1	yes	characteristic, complemented
248	C₂×C₄×D₄	—	197	1	no	—
249	C₂×C₄×D₄	—	197	1	no	—
250	C₂²×C₂²⋊C₄	—	197	1	no	—
251	C₂⁵	C₂×D₁₉₇	1	1	yes	characteristic
252	C₂²×Q₈	—	197	1	no	—
253	C₂²×D₄	—	197	1	no	—
254	C₂²×D₄	—	197	1	no	—
255	C₂²×D₄	—	197	1	no	—
256	C₂²×D₄	—	197	1	no	—
257	C₂²×D₄	C₂×D₁₉₇	1	1	yes	characteristic
258	C₂²×D₄	C₂×D₁₉₇	1	1	yes	characteristic
259	C₂²×D₄	C₂×D₁₉₇	1	1	yes	characteristic
260	C₂³×C₄	—	197	1	no	—
261	C₂³×C₄	—	197	1	no	—
262	C₂³×C₄	—	197	1	no	—
263	C₂³×C₄	—	197	1	no	—
264	#126	—	197	8	no	—
265	#126	—	197	8	no	—
266	#124	—	197	8	no	—
267	#124	—	197	8	no	—
268	#123	—	197	8	no	—
269	#123	—	197	8	no	—
270	C₂²⋊Q₈	—	197	8	no	—
271	#121	—	197	8	no	—
272	#121	—	197	8	no	—
273	#121	—	197	8	no	—
274	#120	—	197	8	no	—
275	#120	C₂×D₁₉₇	1	8	yes	complemented
276	C₄×D₄	—	197	8	no	—
277	C₄×D₄	—	197	8	no	—
278	C₂×C₄⋊C₄	—	197	1	no	—
279	C₂×C₄⋊C₄	—	197	1	no	—
280	C₂×C₄⋊C₄	—	197	1	no	—
281	C₂×C₄⋊C₄	—	197	1	no	—
282	C₂×C₄⋊C₄	—	197	1	no	—
283	C₂×C₄⋊C₄	—	197	1	no	—
284	C₂×C₂²⋊C₄	—	197	1	no	—
285	C₂×C₂²⋊C₄	—	197	1	no	—
286	C₂×C₂²⋊C₄	—	197	1	no	—
287	C₂×C₂²⋊C₄	—	197	1	no	—
288	C₂×C₂²⋊C₄	—	197	8	no	—
289	C₂×C₂²⋊C₄	—	197	1	no	—
290	C₂×C₂²⋊C₄	—	197	1	no	—
291	C₂×C₂²⋊C₄	—	197	1	no	—
292	C₂×C₂²⋊C₄	—	197	1	no	—
293	C₂×C₂²⋊C₄	—	197	1	no	—
294	C₂×C₂²⋊C₄	—	197	1	no	—
295	C₂×C₂²⋊C₄	—	197	1	no	—
296	C₂×C₂²⋊C₄	C₂×D₁₉₇	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	C₂×D₁₉₇	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	C₂×D₁₉₇	1	1	yes	characteristic
299	C₂×C₄²	—	197	1	no	—
300	C₂×C₄²	—	197	1	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	4	2	no	—
303	C₂⁴	—	4	2	no	—
304	C₂⁴	—	197	1	no	—
305	C₂⁴	C₂²×D₁₉₇	1	1	yes	characteristic
306	C₂⁴	C₂²×D₁₉₇	1	1	yes	characteristic
307	C₂⁴	C₂²×D₁₉₇	1	1	yes	characteristic
308	C₂⁴	C₂²×D₁₉₇	1	1	yes	characteristic
309	C₂⁴	C₂²×D₁₉₇	1	4	yes	—
310	C₂×Q₈	—	788	2	no	—
311	C₂×Q₈	—	197	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	788	2	no	—
316	C₂×D₄	—	788	2	no	—
317	C₂×D₄	—	788	2	no	—
318	C₂×D₄	—	394	4	no	—
319	C₂×D₄	—	197	4	no	—
320	C₂×D₄	—	197	4	no	—
321	C₂×D₄	—	197	4	no	—
322	C₂×D₄	—	197	4	no	—
323	C₂×D₄	C₂²×D₁₉₇	1	4	yes	—
324	C₂×D₄	C₂²×D₁₉₇	1	4	yes	—
325	C₂×D₄	C₂²×D₁₉₇	1	4	yes	—
326	C₂²×C₄	—	788	2	no	—
327	C₂²×C₄	—	788	2	no	—
328	C₂²×C₄	—	788	2	no	—
329	C₂²×C₄	—	788	2	no	—
330	C₂²×C₄	—	197	4	no	—
331	C₂²×C₄	—	197	4	no	—
332	C₂²×C₄	—	197	4	no	—
333	C₂²×C₄	—	197	4	no	—
334	C₂²×C₄	—	197	1	no	—
335	C₂²×C₄	—	197	1	no	—
336	C₂²×C₄	—	197	1	no	—
337	C₂²×C₄	—	197	1	no	—
338	C₂²×C₄	—	197	1	no	—
339	C₂²×C₄	—	197	1	no	—
340	C₂²×C₄	—	197	1	no	—
341	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
343	C₂²×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
344	C₄⋊C₄	—	197	4	no	—
345	C₄⋊C₄	—	197	4	no	—
346	C₄⋊C₄	—	197	4	no	—
347	C₄⋊C₄	—	197	4	no	—
348	C₄⋊C₄	—	197	4	no	—
349	C₄⋊C₄	—	197	4	no	—
350	C₂²⋊C₄	—	197	4	no	—
351	C₂²⋊C₄	—	197	4	no	—
352	C₂²⋊C₄	—	197	4	no	—
353	C₂²⋊C₄	—	197	4	no	—
354	C₂²⋊C₄	—	197	4	no	—
355	C₂²⋊C₄	—	197	4	no	—
356	C₂²⋊C₄	—	197	4	no	—
357	C₂²⋊C₄	—	197	4	no	—
358	C₂²⋊C₄	—	197	4	no	—
359	C₂²⋊C₄	—	197	4	no	—
360	C₂²⋊C₄	—	197	4	no	—
361	C₂²⋊C₄	C₂²×D₁₉₇	1	4	yes	—
362	C₂²⋊C₄	C₂²×D₁₉₇	1	4	yes	—
363	C₂²⋊C₄	C₂²×D₁₉₇	1	4	yes	—
364	C₄²	—	197	4	no	—
365	C₄²	—	197	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	16	no	—
381	C₂³	—	394	2	no	—
382	C₂³	—	394	2	no	—
383	C₂³	—	394	2	no	—
384	C₂³	—	197	2	no	—
385	C₂³	#15691357	1	4	yes	—
386	C₂³	C₂³×D₁₉₇	1	2	yes	—
387	C₂³	C₂³×D₁₉₇	1	2	yes	—
388	C₂³	C₂³×D₁₉₇	1	2	yes	—
389	C₂³	C₂³×D₁₉₇	1	2	yes	—
390	C₂³	C₂³×D₁₉₇	1	1	yes	characteristic
391	Q₈	—	788	4	no	—
392	D₄	—	2	8	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	788	4	no	—
396	D₄	—	788	4	no	—
397	D₄	—	788	4	no	—
398	D₄	—	394	8	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	788	4	no	—
403	C₂×C₄	—	788	4	no	—
404	C₂×C₄	—	788	4	no	—
405	C₂×C₄	—	788	4	no	—
406	C₂×C₄	—	394	2	no	—
407	C₂×C₄	—	394	2	no	—
408	C₂×C₄	—	394	2	no	—
409	C₂×C₄	—	394	2	no	—
410	C₂×C₄	—	394	2	no	—
411	C₂×C₄	—	394	2	no	—
412	C₂×C₄	—	394	2	no	—
413	C₂×C₄	—	197	2	no	—
414	C₂×C₄	—	197	2	no	—
415	C₂×C₄	—	197	2	no	—
416	C₂×C₄	—	197	2	no	—
417	C₂×C₄	—	197	2	no	—
418	C₂×C₄	—	197	2	no	—
419	C₂×C₄	—	197	2	no	—
420	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
421	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
422	C₂×C₄	C₂³×D₁₉₇	1	2	yes	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	16	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	788	4	no	—
440	C₂²	—	394	2	no	—
441	C₂²	—	394	2	no	—
442	C₂²	—	394	2	no	—
443	C₂²	C₂×#15691357	1	4	yes	—
444	C₂²	C₂×#15691357	1	2	yes	—
445	C₂²	#20263371	1	2	yes	—
446	C₂²	#20263371	1	2	yes	—
447	C₂²	C₂⁴×D₁₉₇	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	394	2	no	—
452	C₄	—	394	2	no	—
453	C₄	—	394	2	no	—
454	C₄	—	394	2	no	—
455	C₄	—	394	2	no	—
456	C₄	—	394	2	no	—
457	C₄	—	394	2	no	—
458	C₂	—	2	4	no	—
459	C₂	—	4	2	no	—
460	C₂	—	4	2	no	—
461	C₂	—	4	2	no	—
462	C₂	—	788	2	no	—
463	C₂	#27161664	1	4	yes	direct product factor
464	C₂	C₂²×#15691357	1	1	yes	characteristic
465	C₂	C₂×#20263371	1	1	yes	characteristic
466	C₂	C₂×#20263371	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₉₇
commutator, cosocle	C₂²×C₁₉₇	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉₇
Fitting	C₂×#120×C₁₉₇	C₂
socle	C₂³×C₁₉₇	C₂⁴
hypercenter	C₂×#120	D₁₉₇
hypocenter	C₁₉₇	C₂×#538
LCS	G ▷ C₂²×C₁₉₇ ▷ C₁₉₇
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. #27161664	C₂	direct (N × H)
2. C₂×#20263319	C₂	semidirect
3. C₂×#20263319	C₂	semidirect
4. C₂×#20263313	C₂	semidirect
5. C₂×#20263312	C₂	semidirect
6. C₂×#20263308	C₂	semidirect
7. C₂×#20263307	C₂	semidirect
8. C₂×#20263303	C₂	semidirect
9. C₂×#20263298	C₂	semidirect
10. C₂×#20263298	C₂	semidirect
11. C₂×#20263297	C₂	semidirect
12. C₂×#20263295	C₂	semidirect
13. C₂×D₄×Dic₁₉₇	C₂	semidirect
14. C₂×#20263286	C₂	semidirect
15. C₂²×C₂²⋊Dic₁₉₇	C₂	semidirect
16. C₂×#120×C₁₉₇	C₂	semidirect
17. C₂²×Dic₃₉₄	C₂²	semidirect
21. C₂²×C₂²⋊D₁₉₇	C₂²	semidirect
24. C₂³×Dic₁₉₇	C₂²	semidirect
25. C₂²×C₄×D₁₉₇	C₂²	semidirect
26. #20263319	C₂²	semidirect
27. #20263319	C₂²	semidirect
28. #20263313	C₂²	semidirect
29. #20263312	C₂²	semidirect
30. #20263308	C₂²	semidirect
31. #20263307	C₂²	semidirect
32. #20263303	C₂²	semidirect
33. #20263298	C₂²	semidirect
34. #20263298	C₂²	semidirect
35. #20263297	C₂²	semidirect
36. #20263295	C₂²	semidirect
37. D₄×Dic₁₉₇	C₂²	semidirect
38. #20263286	C₂²	semidirect
39. C₂×C₄⋊Dic₁₉₇	C₂²	semidirect
40. C₂×C₄⋊Dic₁₉₇	C₂²	semidirect
41. C₂×#15691337	C₂²	semidirect
42. C₂×#15691337	C₂²	semidirect
43. C₂×#15691337	C₂²	semidirect
44. C₂×#15691337	C₂²	semidirect
52. C₂×C₂²⋊Dic₁₉₇	C₂²	semidirect
53. C₂×C₂²⋊Dic₁₉₇	C₂²	semidirect
54. C₂×C₂²⋊Dic₁₉₇	C₂²	semidirect
55. C₂×#15691335	C₂²	semidirect
56. C₂×#15691335	C₂²	semidirect
57. C₂×C₄×Dic₁₉₇	C₂²	semidirect
58. C₂×C₄×Dic₁₉₇	C₂²	semidirect
63. #120×C₁₉₇	C₂²	semidirect
69. C₂×Dic₃₉₄	C₂³	semidirect
77. C₂×C₂²⋊D₁₉₇	C₂³	semidirect
90. C₂²×Dic₁₉₇	C₂³	semidirect
92. C₂×C₄×D₁₉₇	C₂³	semidirect
93. C₄⋊Dic₁₉₇	C₂³	semidirect
94. C₄⋊Dic₁₉₇	C₂³	semidirect
95. #15691337	C₂³	semidirect
96. #15691337	C₂³	semidirect
97. #15691337	C₂³	semidirect
98. #15691337	C₂³	semidirect
106. C₂²⋊Dic₁₉₇	C₂³	semidirect
107. C₂²⋊Dic₁₉₇	C₂³	semidirect
108. #15691335	C₂³	semidirect
109. #15691335	C₂³	semidirect
110. C₄×Dic₁₉₇	C₂³	semidirect
111. C₄×Dic₁₉₇	C₂³	semidirect
228. C₂×C₁₉₇	#538	semidirect
233. C₁₉₇	C₂×#538	semidirect
247. C₂×#120	D₁₉₇	semidirect
275. #120	C₂×D₁₉₇	semidirect
463. C₂	#27161664	direct (N × H)

Maximal subgroups

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

subgroup	index
#27161664	2
C₂×#20263319	2
C₂×#20263313	2
C₂×#20263312	2
C₂×#20263308	2
C₂×#20263307	2
C₂×#20263303	2
C₂×#20263298	2
C₂×#20263297	2
C₂×#20263295	2
C₂×D₄×Dic₁₉₇	2
C₂×#20263286	2
C₂²×C₂²⋊Dic₁₉₇	2
C₂×#120×C₁₉₇	2
C₂×#538	197

Subgroups — C2×#27161664 #38756050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27161664 #38756050