Subgroups — C₂×#20265737 #27184433

Order 12928.

1984 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265737	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15692239	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15692237	C₂	1	2	yes	maximal, complemented
6	C₂×#15692236	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15692228	C₂	1	2	yes	maximal, complemented
8	C₂×#15692226	C₂	1	2	yes	maximal, complemented
9	C₂×#15692224	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15692223	C₂	1	2	yes	maximal, complemented
11	C₂×C₂²⋊C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#120×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₀₁	C₂²	1	1	yes	characteristic
14	C₂⁴×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
15	C₂²×D₄₀₄	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₂²⋊D₁₀₁	—	2	8	no	—
17	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
22	C₂²×C₂²⋊D₁₀₁	C₂²	1	8	yes	complemented
23	C₂×D₄×D₁₀₁	—	2	8	no	—
24	C₂×D₄×D₁₀₁	C₂²	1	8	yes	complemented
25	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	complemented
28	#15692239	C₂²	1	8	yes	complemented
29	#15692237	C₂²	1	16	yes	complemented
30	#15692236	C₂²	1	8	yes	complemented
31	#15692228	C₂²	1	16	yes	complemented
32	#15692226	C₂²	1	16	yes	complemented
33	#15692224	C₂²	1	8	yes	complemented
34	#15692223	C₂²	1	16	yes	complemented
35	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	yes	complemented
36	C₂×#13108053	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
40	C₂×#13108051	C₂²	1	2	yes	complemented
41	C₂×#13108051	C₂²	1	2	yes	complemented
42	C₂²⋊C₄×D₁₀₁	C₂²	1	8	yes	complemented
43	C₂⁵×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
44	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
45	C₂²×D₄×C₁₀₁	C₂²	1	2	yes	complemented
46	#120×C₁₀₁	C₂²	1	8	yes	complemented
47	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	2	yes	complemented
49	C₂³×D₁₀₁	—	2	4	no	—
50	C₂³×D₁₀₁	—	4	4	no	—
51	C₂³×D₁₀₁	—	4	4	no	—
52	C₂³×D₁₀₁	D₄	1	8	yes	complemented
53	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
54	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
55	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
56	C₂³×D₁₀₁	C₂³	1	4	yes	—
57	C₂³×D₁₀₁	C₂³	1	4	yes	complemented
58	C₂×D₄₀₄	—	2	4	no	—
59	C₂×D₄₀₄	C₂³	1	4	yes	complemented
60	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
61	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
62	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
63	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
64	C₂×C₂²⋊D₁₀₁	—	2	32	no	—
65	C₂×C₂²⋊D₁₀₁	—	4	4	no	—
66	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
67	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
68	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	complemented
69	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	complemented
70	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	complemented
71	D₄×D₁₀₁	—	2	32	no	—
72	C₂²×Dic₁₀₁	—	2	4	no	—
73	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
74	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
75	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
76	C₂²×Dic₁₀₁	C₂³	1	4	yes	complemented
77	C₂×C₄×D₁₀₁	—	2	4	no	—
78	C₂×C₄×D₁₀₁	—	4	4	no	—
79	C₂×C₄×D₁₀₁	C₂³	1	4	yes	complemented
80	C₂×C₄×D₁₀₁	C₂³	1	8	yes	complemented
81	C₄⋊Dic₁₀₁	C₂³	1	8	yes	complemented
82	#13108053	C₂³	1	8	yes	complemented
83	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	complemented
84	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	complemented
85	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	complemented
86	#13108051	C₂³	1	8	yes	complemented
87	#13108051	C₂³	1	8	yes	complemented
88	C₂⁴×C₁₀₁	—	2	4	no	—
89	C₂⁴×C₁₀₁	—	4	4	no	—
90	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
91	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
92	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
93	C₂⁴×C₁₀₁	C₂³	1	4	yes	complemented
94	C₂×D₄×C₁₀₁	—	2	4	no	—
95	C₂×D₄×C₁₀₁	—	4	4	no	—
96	C₂×D₄×C₁₀₁	C₂³	1	4	yes	—
97	C₂×D₄×C₁₀₁	C₂³	1	8	yes	complemented
98	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
100	C₂²⋊C₄×C₁₀₁	C₂³	1	4	yes	complemented
101	C₂²⋊C₄×C₁₀₁	C₂³	1	8	yes	complemented
102	C₂³×C₁₀₁	—	2	4	no	—
103	C₂³×C₁₀₁	—	2	2	no	—
104	C₂³×C₁₀₁	—	2	4	no	—
105	C₂³×C₁₀₁	—	2	8	no	—
106	C₂³×C₁₀₁	—	2	4	no	—
107	C₂³×C₁₀₁	—	2	4	no	—
108	C₂³×C₁₀₁	—	2	4	no	—
109	C₂³×C₁₀₁	—	4	8	no	—
110	C₂³×C₁₀₁	—	4	16	no	—
111	C₂³×C₁₀₁	C₂×D₄	1	4	yes	—
112	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
113	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
114	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
115	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
116	C₂²×D₁₀₁	—	2	4	no	—
117	C₂²×D₁₀₁	—	2	4	no	—
118	C₂²×D₁₀₁	—	2	2	no	—
119	C₂²×D₁₀₁	—	2	4	no	—
120	C₂²×D₁₀₁	—	2	8	no	—
121	C₂²×D₁₀₁	—	4	16	no	—
122	C₂²×D₁₀₁	—	4	8	no	—
123	C₂²×D₁₀₁	—	4	8	no	—
124	C₂²×D₁₀₁	—	4	16	no	—
125	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
126	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
127	C₂²×D₁₀₁	C₂×D₄	1	16	yes	complemented
128	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
129	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
130	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
131	D₄×C₁₀₁	—	2	8	no	—
132	D₄×C₁₀₁	—	4	8	no	—
133	C₂×C₄×C₁₀₁	—	2	2	no	—
134	C₂×C₄×C₁₀₁	—	2	4	no	—
135	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
136	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
137	C₂²⋊D₁₀₁	—	2	8	no	—
138	C₂²⋊D₁₀₁	—	2	8	no	—
139	C₂²⋊D₁₀₁	—	2	16	no	—
140	C₂²⋊D₁₀₁	—	2	16	no	—
141	C₂²⋊D₁₀₁	—	4	8	no	—
142	C₂×Dic₁₀₁	—	2	2	no	—
143	C₂×Dic₁₀₁	—	2	4	no	—
144	C₂×Dic₁₀₁	—	2	8	no	—
145	C₂×Dic₁₀₁	—	2	4	no	—
146	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
147	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
148	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
149	D₄₀₄	—	2	8	no	—
150	C₄×D₁₀₁	—	2	8	no	—
151	C₄×D₁₀₁	—	4	8	no	—
152	C₂²×C₁₀₁	—	2	8	no	—
153	C₂²×C₁₀₁	—	2	4	no	—
154	C₂²×C₁₀₁	—	2	4	no	—
155	C₂²×C₁₀₁	—	2	2	no	—
156	C₂²×C₁₀₁	—	2	4	no	—
157	C₂²×C₁₀₁	—	2	4	no	—
158	C₂²×C₁₀₁	—	2	4	no	—
159	C₂²×C₁₀₁	—	4	16	no	—
160	C₂²×C₁₀₁	—	4	4	no	—
161	C₂²×C₁₀₁	—	4	8	no	—
162	C₂²×C₁₀₁	C₂²×D₄	1	4	yes	—
163	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
164	C₂²×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
165	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
166	C₂×D₁₀₁	—	2	8	no	—
167	C₂×D₁₀₁	—	2	8	no	—
168	C₂×D₁₀₁	—	2	4	no	—
169	C₂×D₁₀₁	—	2	4	no	—
170	C₂×D₁₀₁	—	2	2	no	—
171	C₂×D₁₀₁	—	2	4	no	—
172	C₂×D₁₀₁	—	4	16	no	—
173	C₂×D₁₀₁	—	4	16	no	—
174	C₂×D₁₀₁	—	4	4	no	—
175	C₂×D₁₀₁	C₂²×D₄	1	4	yes	—
176	C₂×D₁₀₁	C₂²×D₄	1	4	yes	—
177	C₄×C₁₀₁	—	2	2	no	—
178	C₄×C₁₀₁	—	2	4	no	—
179	Dic₁₀₁	—	2	2	no	—
180	Dic₁₀₁	—	2	4	no	—
181	Dic₁₀₁	—	2	4	no	—
182	C₂×C₁₀₁	—	2	4	no	—
183	C₂×C₁₀₁	—	4	2	no	—
184	C₂×C₁₀₁	—	4	4	no	—
185	C₂×C₁₀₁	#534	1	4	yes	complemented
186	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
187	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	2	yes	—
188	D₁₀₁	—	2	4	no	—
189	D₁₀₁	—	2	4	no	—
190	D₁₀₁	—	4	2	no	—
191	C₂×#534	—	101	1	no	maximal, Sylow
192	C₁₀₁	C₂×#534	1	1	yes	characteristic, complemented, Sylow
193	C₂³×D₄	—	101	1	no	—
194	C₂³×D₄	—	101	1	no	—
195	#534	—	101	16	no	—
196	C₂×#123	—	101	1	no	—
197	C₂×#123	—	101	2	no	—
198	C₂×#123	—	101	1	no	—
199	C₂×#121	—	101	2	no	—
200	C₂×#121	—	101	2	no	—
201	C₂×#120	—	101	1	no	—
202	C₂×#120	—	101	2	no	—
203	C₂×#120	D₁₀₁	1	1	yes	characteristic, complemented
204	C₂²×C₂²⋊C₄	—	101	1	no	—
205	C₂⁵	—	101	1	no	—
206	C₂⁵	—	101	1	no	—
207	C₂⁵	C₂×D₁₀₁	1	1	yes	characteristic, complemented
208	C₂²×D₄	—	101	2	no	—
209	C₂²×D₄	—	101	2	no	—
210	C₂²×D₄	—	101	1	no	—
211	C₂²×D₄	—	101	1	no	—
212	C₂²×D₄	—	101	2	no	—
213	C₂²×D₄	—	101	8	no	—
214	C₂²×D₄	—	101	8	no	—
215	C₂²×D₄	—	101	1	no	—
216	C₂²×D₄	—	202	8	no	—
217	C₂²×D₄	—	202	8	no	—
218	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
219	C₂²×D₄	C₂×D₁₀₁	1	2	yes	complemented
220	C₂³×C₄	—	101	1	no	—
221	C₂³×C₄	—	101	2	no	—
222	C₂³×C₄	—	101	1	no	—
223	#123	—	101	8	no	—
224	#123	—	101	16	no	—
225	#123	—	101	8	no	—
226	#121	—	101	16	no	—
227	#121	—	101	16	no	—
228	#120	—	101	8	no	—
229	#120	—	101	16	no	—
230	#120	C₂×D₁₀₁	1	8	yes	complemented
231	C₂×C₄⋊C₄	—	101	2	no	—
232	C₂×C₄⋊C₄	—	101	2	no	—
233	C₂×C₂²⋊C₄	—	101	1	no	—
234	C₂×C₂²⋊C₄	—	101	2	no	—
235	C₂×C₂²⋊C₄	—	101	2	no	—
236	C₂×C₂²⋊C₄	—	101	2	no	—
237	C₂×C₂²⋊C₄	—	101	2	no	—
238	C₂×C₂²⋊C₄	—	101	8	no	—
239	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
240	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	4	4	no	—
243	C₂⁴	—	101	8	no	—
244	C₂⁴	—	101	4	no	—
245	C₂⁴	—	101	1	no	—
246	C₂⁴	—	101	1	no	—
247	C₂⁴	—	101	4	no	—
248	C₂⁴	—	101	1	no	—
249	C₂⁴	—	404	4	no	—
250	C₂⁴	—	404	4	no	—
251	C₂⁴	—	202	4	no	—
252	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
253	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
254	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
255	C₂⁴	C₂²×D₁₀₁	1	4	yes	complemented
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	4	4	no	—
258	C₂×D₄	—	101	8	no	—
259	C₂×D₄	—	101	8	no	—
260	C₂×D₄	—	101	4	no	—
261	C₂×D₄	—	101	4	no	—
262	C₂×D₄	—	101	8	no	—
263	C₂×D₄	—	101	4	no	—
264	C₂×D₄	—	404	4	no	—
265	C₂×D₄	—	202	4	no	—
266	C₂×D₄	—	202	32	no	—
267	C₂×D₄	—	202	4	no	—
268	C₂×D₄	—	202	8	no	—
269	C₂×D₄	—	202	8	no	—
270	C₂×D₄	—	202	32	no	—
271	C₂×D₄	—	202	4	no	—
272	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
273	C₂×D₄	C₂²×D₁₀₁	1	8	yes	complemented
274	C₂²×C₄	—	101	4	no	—
275	C₂²×C₄	—	101	2	no	—
276	C₂²×C₄	—	101	1	no	—
277	C₂²×C₄	—	101	2	no	—
278	C₂²×C₄	—	101	8	no	—
279	C₂²×C₄	—	101	4	no	—
280	C₂²×C₄	—	404	4	no	—
281	C₂²×C₄	—	202	4	no	—
282	C₂²×C₄	—	202	4	no	—
283	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
284	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
285	C₄⋊C₄	—	101	8	no	—
286	C₄⋊C₄	—	101	8	no	—
287	C₂²⋊C₄	—	101	4	no	—
288	C₂²⋊C₄	—	101	8	no	—
289	C₂²⋊C₄	—	101	8	no	—
290	C₂²⋊C₄	—	101	8	no	—
291	C₂²⋊C₄	—	101	8	no	—
292	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	complemented
293	C₂²⋊C₄	C₂²×D₁₀₁	1	8	yes	complemented
294	C₂³	—	2	4	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	2	8	no	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	4	8	no	—
302	C₂³	—	4	16	no	—
303	C₂³	—	101	16	no	—
304	C₂³	—	101	4	no	—
305	C₂³	—	101	4	no	—
306	C₂³	—	101	2	no	—
307	C₂³	—	101	2	no	—
308	C₂³	—	101	2	no	—
309	C₂³	—	404	16	no	—
310	C₂³	—	404	8	no	—
311	C₂³	—	404	8	no	—
312	C₂³	—	404	16	no	—
313	C₂³	—	202	8	no	—
314	C₂³	—	202	2	no	—
315	C₂³	—	202	4	no	—
316	C₂³	—	202	4	no	—
317	C₂³	—	202	4	no	—
318	C₂³	D₄×D₁₀₁	1	4	yes	—
319	C₂³	C₂³×D₁₀₁	1	2	yes	—
320	C₂³	C₂³×D₁₀₁	1	4	yes	—
321	C₂³	C₂³×D₁₀₁	1	2	yes	—
322	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
323	D₄	—	2	8	no	—
324	D₄	—	4	8	no	—
325	D₄	—	404	8	no	—
326	D₄	—	202	8	no	—
327	D₄	—	202	8	no	—
328	D₄	—	202	16	no	—
329	D₄	—	202	16	no	—
330	D₄	—	202	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	101	4	no	—
334	C₂×C₄	—	101	2	no	—
335	C₂×C₄	—	101	4	no	—
336	C₂×C₄	—	404	8	no	—
337	C₂×C₄	—	202	8	no	—
338	C₂×C₄	—	202	8	no	—
339	C₂×C₄	—	202	2	no	—
340	C₂×C₄	—	202	4	no	—
341	C₂×C₄	—	202	4	no	—
342	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
343	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
344	C₂²	—	2	8	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	4	no	—
351	C₂²	—	4	16	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	4	4	no	—
354	C₂²	—	101	4	no	—
355	C₂²	—	101	4	no	—
356	C₂²	—	404	16	no	—
357	C₂²	—	404	16	no	—
358	C₂²	—	404	4	no	—
359	C₂²	—	202	2	no	—
360	C₂²	—	202	4	no	—
361	C₂²	—	202	8	no	—
362	C₂²	—	202	8	no	—
363	C₂²	—	202	4	no	—
364	C₂²	—	202	4	no	—
365	C₂²	C₂×D₄×D₁₀₁	1	4	yes	—
366	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
367	C₂²	#15692300	1	4	yes	—
368	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	2	4	no	—
371	C₄	—	202	2	no	—
372	C₄	—	202	4	no	—
373	C₄	—	202	4	no	—
374	C₂	—	2	4	no	—
375	C₂	—	4	4	no	—
376	C₂	—	4	2	no	—
377	C₂	—	404	2	no	—
378	C₂	—	202	4	no	—
379	C₂	—	202	4	no	—
380	C₂	#20265737	1	4	yes	direct product factor
381	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
382	C₂	C₂×#15692300	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₁₀₁
commutator, cosocle	C₂²×C₁₀₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	C₂×#120×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂⁴
hypercenter	C₂×#120	D₁₀₁
hypocenter	C₁₀₁	C₂×#534
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₂²⋊D₁₀₁	C₂	semidirect
2. C₂²×D₄×D₁₀₁	C₂	semidirect
3. #20265737	C₂	direct (N × H)
4. C₂×#15692239	C₂	semidirect
5. C₂×#15692237	C₂	semidirect
6. C₂×#15692236	C₂	semidirect
7. C₂×#15692228	C₂	semidirect
8. C₂×#15692226	C₂	semidirect
9. C₂×#15692224	C₂	semidirect
10. C₂×#15692223	C₂	semidirect
11. C₂×C₂²⋊C₄×D₁₀₁	C₂	semidirect
12. C₂×#120×C₁₀₁	C₂	semidirect
14. C₂⁴×D₁₀₁	C₂²	semidirect
15. C₂²×D₄₀₄	C₂²	semidirect
19. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
20. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
21. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
22. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
24. C₂×D₄×D₁₀₁	C₂²	semidirect
25. C₂³×Dic₁₀₁	C₂²	semidirect
26. C₂²×C₄×D₁₀₁	C₂²	semidirect
27. C₂²×C₄×D₁₀₁	C₂²	semidirect
28. #15692239	C₂²	semidirect
29. #15692237	C₂²	semidirect
30. #15692236	C₂²	semidirect
31. #15692228	C₂²	semidirect
32. #15692226	C₂²	semidirect
33. #15692224	C₂²	semidirect
34. #15692223	C₂²	semidirect
35. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
36. C₂×#13108053	C₂²	semidirect
37. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
38. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
40. C₂×#13108051	C₂²	semidirect
41. C₂×#13108051	C₂²	semidirect
42. C₂²⋊C₄×D₁₀₁	C₂²	semidirect
43. C₂⁵×C₁₀₁	C₂²	semidirect
45. C₂²×D₄×C₁₀₁	C₂²	semidirect
46. #120×C₁₀₁	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
52. C₂³×D₁₀₁	D₄	semidirect
57. C₂³×D₁₀₁	C₂³	semidirect
59. C₂×D₄₀₄	C₂³	semidirect
68. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
69. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
70. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
76. C₂²×Dic₁₀₁	C₂³	semidirect
79. C₂×C₄×D₁₀₁	C₂³	semidirect
80. C₂×C₄×D₁₀₁	C₂³	semidirect
81. C₄⋊Dic₁₀₁	C₂³	semidirect
82. #13108053	C₂³	semidirect
83. C₂²⋊Dic₁₀₁	C₂³	semidirect
84. C₂²⋊Dic₁₀₁	C₂³	semidirect
85. C₂²⋊Dic₁₀₁	C₂³	semidirect
86. #13108051	C₂³	semidirect
87. #13108051	C₂³	semidirect
93. C₂⁴×C₁₀₁	C₂³	semidirect
97. C₂×D₄×C₁₀₁	C₂³	semidirect
100. C₂²⋊C₄×C₁₀₁	C₂³	semidirect
101. C₂²⋊C₄×C₁₀₁	C₂³	semidirect
127. C₂²×D₁₀₁	C₂×D₄	semidirect
185. C₂×C₁₀₁	#534	semidirect
192. C₁₀₁	C₂×#534	semidirect
203. C₂×#120	D₁₀₁	semidirect
207. C₂⁵	C₂×D₁₀₁	semidirect
219. C₂²×D₄	C₂×D₁₀₁	semidirect
230. #120	C₂×D₁₀₁	semidirect
239. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
240. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
255. C₂⁴	C₂²×D₁₀₁	semidirect
273. C₂×D₄	C₂²×D₁₀₁	semidirect
292. C₂²⋊C₄	C₂²×D₁₀₁	semidirect
293. C₂²⋊C₄	C₂²×D₁₀₁	semidirect
380. C₂	#20265737	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₂²⋊D₁₀₁	2
C₂²×D₄×D₁₀₁	2
#20265737	2
C₂×#15692239	2
C₂×#15692237	2
C₂×#15692236	2
C₂×#15692228	2
C₂×#15692226	2
C₂×#15692224	2
C₂×#15692223	2
C₂×C₂²⋊C₄×D₁₀₁	2
C₂×#120×C₁₀₁	2
C₂×#534	101

Subgroups — C2×#20265737 #27184433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265737 #27184433