Subgroups — C₂×#20265742 #27184439

Order 12928.

1896 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13108073	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₂²⋊D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265742	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15692251	C₂	1	2	yes	maximal, complemented
5	C₂×#15692241	C₂	1	2	yes	maximal, complemented
6	C₂×#15692228	C₂	1	2	yes	maximal, complemented
7	C₂×#15692227	C₂	1	2	yes	maximal, complemented
8	C₂×#15692225	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15692224	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15692223	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15692211	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	C₂×#13108073	—	2	8	no	—
15	C₂×#13108073	C₂²	1	8	yes	complemented
16	C₂²×Dic₂₀₂	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄₀₄	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊D₁₀₁	—	2	8	no	—
19	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
20	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
21	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₁₀₁	C₂²	1	8	yes	complemented
23	C₂²×C₂²⋊D₁₀₁	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	complemented
26	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
27	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic, complemented
29	#15692251	C₂²	1	16	yes	complemented
30	#15692241	C₂²	1	16	yes	complemented
31	#15692228	C₂²	1	16	yes	complemented
32	#15692227	C₂²	1	16	yes	complemented
33	#15692225	C₂²	1	8	yes	complemented
34	#15692224	C₂²	1	8	yes	complemented
35	#15692223	C₂²	1	8	yes	complemented
36	#15692211	C₂²	1	8	yes	complemented
37	C₂×#13108053	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
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	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
43	C₂⁵×C₁₀₁	C₂²	1	1	yes	characteristic
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
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	C₂³	1	1	yes	characteristic
52	C₂³×D₁₀₁	C₂³	1	2	yes	—
53	C₂³×D₁₀₁	C₂³	1	4	yes	—
54	#13108073	—	2	32	no	—
55	C₂×Dic₂₀₂	—	2	4	no	—
56	C₂×Dic₂₀₂	C₂³	1	4	yes	complemented
57	C₂×D₄₀₄	—	4	4	no	—
58	C₂×D₄₀₄	C₂³	1	8	yes	complemented
59	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
60	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
61	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
62	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
63	C₂×C₂²⋊D₁₀₁	—	2	32	no	—
64	C₂×C₂²⋊D₁₀₁	—	4	4	no	—
65	C₂×C₂²⋊D₁₀₁	—	4	4	no	—
66	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
67	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
68	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	—
69	C₂×C₂²⋊D₁₀₁	C₂³	1	4	yes	complemented
70	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	complemented
71	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	complemented
72	C₂²×Dic₁₀₁	—	2	4	no	—
73	C₂²×Dic₁₀₁	D₄	1	8	yes	complemented
74	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
75	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
76	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
78	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
79	C₂²×Dic₁₀₁	C₂³	1	4	yes	complemented
80	C₂×C₄×D₁₀₁	—	2	4	no	—
81	C₂×C₄×D₁₀₁	C₂³	1	4	yes	complemented
82	#13108053	C₂³	1	8	yes	complemented
83	C₂²⋊Dic₁₀₁	C₂³	1	4	yes	—
84	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	complemented
85	#13108051	C₂³	1	8	yes	complemented
86	#13108051	C₂³	1	8	yes	complemented
87	C₄×Dic₁₀₁	C₂³	1	8	yes	complemented
88	C₂⁴×C₁₀₁	—	2	4	no	—
89	C₂⁴×C₁₀₁	—	4	4	no	—
90	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
91	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
92	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
93	C₂⁴×C₁₀₁	C₂³	1	4	yes	—
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	—
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	8	no	—
105	C₂³×C₁₀₁	—	2	4	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	2	no	—
117	C₂²×D₁₀₁	—	2	8	no	—
118	C₂²×D₁₀₁	—	2	4	no	—
119	C₂²×D₁₀₁	—	2	4	no	—
120	C₂²×D₁₀₁	—	2	4	no	—
121	C₂²×D₁₀₁	—	2	4	no	—
122	C₂²×D₁₀₁	—	4	8	no	—
123	C₂²×D₁₀₁	—	4	16	no	—
124	C₂²×D₁₀₁	C₂⁴	1	4	yes	—
125	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
126	D₄×C₁₀₁	—	2	8	no	—
127	D₄×C₁₀₁	—	4	8	no	—
128	C₂×C₄×C₁₀₁	—	2	2	no	—
129	C₂×C₄×C₁₀₁	—	2	4	no	—
130	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
131	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
132	C₂²⋊D₁₀₁	—	2	8	no	—
133	C₂²⋊D₁₀₁	—	2	16	no	—
134	C₂²⋊D₁₀₁	—	2	16	no	—
135	C₂²⋊D₁₀₁	—	2	8	no	—
136	C₂²⋊D₁₀₁	—	4	8	no	—
137	C₂²⋊D₁₀₁	—	4	8	no	—
138	C₂×Dic₁₀₁	—	2	2	no	—
139	C₂×Dic₁₀₁	—	2	4	no	—
140	C₂×Dic₁₀₁	—	2	8	no	—
141	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
142	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
143	C₂×Dic₁₀₁	C₂×D₄	1	16	yes	complemented
144	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
145	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
146	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
147	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
148	D₄₀₄	—	4	8	no	—
149	C₄×D₁₀₁	—	2	8	no	—
150	Dic₂₀₂	—	2	8	no	—
151	C₂²×C₁₀₁	—	2	8	no	—
152	C₂²×C₁₀₁	—	2	4	no	—
153	C₂²×C₁₀₁	—	2	2	no	—
154	C₂²×C₁₀₁	—	2	4	no	—
155	C₂²×C₁₀₁	—	2	4	no	—
156	C₂²×C₁₀₁	—	2	4	no	—
157	C₂²×C₁₀₁	—	2	4	no	—
158	C₂²×C₁₀₁	—	4	16	no	—
159	C₂²×C₁₀₁	—	4	4	no	—
160	C₂²×C₁₀₁	—	4	8	no	—
161	C₂²×C₁₀₁	C₂²×D₄	1	4	yes	—
162	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
163	C₂²×C₁₀₁	H(5,𝔽₂)	1	4	yes	—
164	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
165	C₂×D₁₀₁	—	2	2	no	—
166	C₂×D₁₀₁	—	2	4	no	—
167	C₂×D₁₀₁	—	2	4	no	—
168	C₂×D₁₀₁	—	2	4	no	—
169	C₂×D₁₀₁	—	2	4	no	—
170	C₂×D₁₀₁	—	4	16	no	—
171	C₂×D₁₀₁	—	4	4	no	—
172	C₂×D₁₀₁	—	4	8	no	—
173	C₄×C₁₀₁	—	2	2	no	—
174	C₄×C₁₀₁	—	2	4	no	—
175	Dic₁₀₁	—	2	2	no	—
176	Dic₁₀₁	—	2	4	no	—
177	Dic₁₀₁	C₂²×D₄	1	4	yes	—
178	Dic₁₀₁	C₂²×D₄	1	4	yes	—
179	C₂×C₁₀₁	—	2	4	no	—
180	C₂×C₁₀₁	—	4	2	no	—
181	C₂×C₁₀₁	—	4	4	no	—
182	C₂×C₁₀₁	#535	1	4	yes	complemented
183	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
184	C₂×C₁₀₁	C₂×H(5,𝔽₂)	1	2	yes	—
185	D₁₀₁	—	4	2	no	—
186	D₁₀₁	—	4	4	no	—
187	C₂×#535	—	101	1	no	maximal, Sylow
188	C₁₀₁	C₂×#535	1	1	yes	characteristic, complemented, Sylow
189	C₂²×#41	—	101	1	no	—
190	C₂³×D₄	—	101	1	no	—
191	#535	—	101	16	no	—
192	C₂×#127	—	101	2	no	—
193	C₂×#124	—	101	2	no	—
194	C₂×#121	—	101	2	no	—
195	C₂×#121	—	101	2	no	—
196	C₂×#120	—	101	1	no	—
197	C₂×#120	—	101	1	no	—
198	C₂×#120	—	101	1	no	—
199	C₂×#120	D₁₀₁	1	1	yes	characteristic, complemented
200	C₂×#117	—	101	1	no	—
201	C₂⁵	—	101	1	no	—
202	C₂⁵	C₂×D₁₀₁	1	1	yes	characteristic
203	C₂×#41	—	101	8	no	—
204	C₂×#41	—	202	8	no	—
205	C₂²×Q₈	—	101	1	no	—
206	C₂²×D₄	—	101	2	no	—
207	C₂²×D₄	—	101	2	no	—
208	C₂²×D₄	—	101	1	no	—
209	C₂²×D₄	—	101	2	no	—
210	C₂²×D₄	—	101	2	no	—
211	C₂²×D₄	—	101	1	no	—
212	C₂²×D₄	—	101	8	no	—
213	C₂²×D₄	—	101	2	no	—
214	C₂²×D₄	—	202	8	no	—
215	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
216	C₂²×D₄	C₂×D₁₀₁	1	2	yes	complemented
217	C₂³×C₄	—	101	1	no	—
218	C₂³×C₄	—	101	1	no	—
219	C₂³×C₄	—	101	1	no	—
220	#127	—	101	16	no	—
221	#124	—	101	16	no	—
222	#121	—	101	16	no	—
223	#121	—	101	16	no	—
224	#120	—	101	8	no	—
225	#120	—	101	8	no	—
226	#120	—	101	8	no	—
227	#120	C₂×D₁₀₁	1	8	yes	complemented
228	#117	—	101	8	no	—
229	C₂×C₄⋊C₄	—	101	2	no	—
230	C₂×C₂²⋊C₄	—	101	1	no	—
231	C₂×C₂²⋊C₄	—	101	2	no	—
232	C₂×C₂²⋊C₄	—	101	2	no	—
233	C₂×C₂²⋊C₄	—	101	2	no	—
234	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
236	C₂×C₄²	—	101	2	no	—
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	4	4	no	—
239	C₂⁴	—	101	4	no	—
240	C₂⁴	—	101	2	no	—
241	C₂⁴	—	101	1	no	—
242	C₂⁴	—	404	4	no	—
243	C₂⁴	—	202	4	no	—
244	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
245	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
246	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
247	C₂⁴	C₂²×D₁₀₁	1	4	yes	—
248	#41	—	202	32	no	—
249	C₂×Q₈	—	101	4	no	—
250	C₂×Q₈	—	202	4	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	4	4	no	—
253	C₂×D₄	—	101	8	no	—
254	C₂×D₄	—	101	8	no	—
255	C₂×D₄	—	101	4	no	—
256	C₂×D₄	—	101	8	no	—
257	C₂×D₄	—	101	8	no	—
258	C₂×D₄	—	101	4	no	—
259	C₂×D₄	—	101	8	no	—
260	C₂×D₄	—	404	4	no	—
261	C₂×D₄	—	404	4	no	—
262	C₂×D₄	—	404	4	no	—
263	C₂×D₄	—	202	8	no	—
264	C₂×D₄	—	202	8	no	—
265	C₂×D₄	—	202	32	no	—
266	C₂×D₄	—	202	4	no	—
267	C₂×D₄	—	202	4	no	—
268	C₂×D₄	C₂²×D₁₀₁	1	4	yes	—
269	C₂×D₄	C₂²×D₁₀₁	1	8	yes	complemented
270	C₂²×C₄	—	101	8	no	—
271	C₂²×C₄	—	101	4	no	—
272	C₂²×C₄	—	101	1	no	—
273	C₂²×C₄	—	101	1	no	—
274	C₂²×C₄	—	101	4	no	—
275	C₂²×C₄	—	101	2	no	—
276	C₂²×C₄	—	101	1	no	—
277	C₂²×C₄	—	101	4	no	—
278	C₂²×C₄	—	202	4	no	—
279	C₂²×C₄	—	202	4	no	—
280	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
281	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
282	C₄⋊C₄	—	101	8	no	—
283	C₂²⋊C₄	—	101	4	no	—
284	C₂²⋊C₄	—	101	8	no	—
285	C₂²⋊C₄	—	101	8	no	—
286	C₂²⋊C₄	—	101	8	no	—
287	C₂²⋊C₄	C₂²×D₁₀₁	1	4	yes	—
288	C₂²⋊C₄	C₂²×D₁₀₁	1	8	yes	complemented
289	C₄²	—	101	8	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	4	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	8	no	—
298	C₂³	—	4	16	no	—
299	C₂³	—	101	4	no	—
300	C₂³	—	101	2	no	—
301	C₂³	—	404	16	no	—
302	C₂³	—	404	8	no	—
303	C₂³	—	202	2	no	—
304	C₂³	—	202	8	no	—
305	C₂³	—	202	4	no	—
306	C₂³	—	202	4	no	—
307	C₂³	—	202	4	no	—
308	C₂³	—	202	4	no	—
309	C₂³	D₄×D₁₀₁	1	4	yes	—
310	C₂³	C₂³×D₁₀₁	1	4	yes	—
311	C₂³	C₂³×D₁₀₁	1	2	yes	—
312	C₂³	C₂³×D₁₀₁	1	2	yes	—
313	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
314	Q₈	—	202	8	no	—
315	D₄	—	2	8	no	—
316	D₄	—	4	8	no	—
317	D₄	—	404	8	no	—
318	D₄	—	404	8	no	—
319	D₄	—	404	8	no	—
320	D₄	—	202	16	no	—
321	D₄	—	202	16	no	—
322	D₄	—	202	8	no	—
323	D₄	—	202	8	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	101	4	no	—
327	C₂×C₄	—	101	4	no	—
328	C₂×C₄	—	101	16	no	—
329	C₂×C₄	—	101	2	no	—
330	C₂×C₄	—	101	2	no	—
331	C₂×C₄	—	101	4	no	—
332	C₂×C₄	—	101	2	no	—
333	C₂×C₄	—	202	8	no	—
334	C₂×C₄	—	202	8	no	—
335	C₂×C₄	—	202	2	no	—
336	C₂×C₄	—	202	4	no	—
337	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
338	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
339	C₂²	—	2	8	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	4	16	no	—
347	C₂²	—	4	8	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	404	16	no	—
350	C₂²	—	404	8	no	—
351	C₂²	—	404	4	no	—
352	C₂²	—	202	2	no	—
353	C₂²	—	202	4	no	—
354	C₂²	—	202	4	no	—
355	C₂²	—	202	4	no	—
356	C₂²	—	202	4	no	—
357	C₂²	C₂×D₄×D₁₀₁	1	4	yes	—
358	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
359	C₂²	#15692300	1	4	yes	—
360	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
361	C₄	—	2	2	no	—
362	C₄	—	2	4	no	—
363	C₄	—	101	4	no	—
364	C₄	—	101	4	no	—
365	C₄	—	202	2	no	—
366	C₄	—	202	4	no	—
367	C₂	—	2	4	no	—
368	C₂	—	4	4	no	—
369	C₂	—	4	2	no	—
370	C₂	—	404	4	no	—
371	C₂	—	404	2	no	—
372	C₂	#20265742	1	4	yes	direct product factor
373	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
374	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×#535
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. C₂²×#13108073	C₂	semidirect
2. C₂³×C₂²⋊D₁₀₁	C₂	semidirect
3. #20265742	C₂	direct (N × H)
4. C₂×#15692251	C₂	semidirect
5. C₂×#15692241	C₂	semidirect
6. C₂×#15692228	C₂	semidirect
7. C₂×#15692227	C₂	semidirect
8. C₂×#15692225	C₂	semidirect
9. C₂×#15692224	C₂	semidirect
10. C₂×#15692223	C₂	semidirect
11. C₂×#15692211	C₂	semidirect
12. C₂×#120×C₁₀₁	C₂	semidirect
15. C₂×#13108073	C₂²	semidirect
16. C₂²×Dic₂₀₂	C₂²	semidirect
17. C₂²×D₄₀₄	C₂²	semidirect
22. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
23. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
24. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
25. C₂²×C₂²⋊D₁₀₁	C₂²	semidirect
27. C₂³×Dic₁₀₁	C₂²	semidirect
28. C₂²×C₄×D₁₀₁	C₂²	semidirect
29. #15692251	C₂²	semidirect
30. #15692241	C₂²	semidirect
31. #15692228	C₂²	semidirect
32. #15692227	C₂²	semidirect
33. #15692225	C₂²	semidirect
34. #15692224	C₂²	semidirect
35. #15692223	C₂²	semidirect
36. #15692211	C₂²	semidirect
37. C₂×#13108053	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
40. C₂×#13108051	C₂²	semidirect
41. C₂×#13108051	C₂²	semidirect
42. C₂×C₄×Dic₁₀₁	C₂²	semidirect
45. C₂²×D₄×C₁₀₁	C₂²	semidirect
46. #120×C₁₀₁	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
56. C₂×Dic₂₀₂	C₂³	semidirect
58. C₂×D₄₀₄	C₂³	semidirect
69. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
70. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
71. C₂×C₂²⋊D₁₀₁	C₂³	semidirect
73. C₂²×Dic₁₀₁	D₄	semidirect
79. C₂²×Dic₁₀₁	C₂³	semidirect
81. C₂×C₄×D₁₀₁	C₂³	semidirect
82. #13108053	C₂³	semidirect
84. C₂²⋊Dic₁₀₁	C₂³	semidirect
85. #13108051	C₂³	semidirect
86. #13108051	C₂³	semidirect
87. C₄×Dic₁₀₁	C₂³	semidirect
97. C₂×D₄×C₁₀₁	C₂³	semidirect
101. C₂²⋊C₄×C₁₀₁	C₂³	semidirect
143. C₂×Dic₁₀₁	C₂×D₄	semidirect
182. C₂×C₁₀₁	#535	semidirect
188. C₁₀₁	C₂×#535	semidirect
199. C₂×#120	D₁₀₁	semidirect
216. C₂²×D₄	C₂×D₁₀₁	semidirect
227. #120	C₂×D₁₀₁	semidirect
235. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
269. C₂×D₄	C₂²×D₁₀₁	semidirect
288. C₂²⋊C₄	C₂²×D₁₀₁	semidirect
372. C₂	#20265742	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13108073	2
C₂³×C₂²⋊D₁₀₁	2
#20265742	2
C₂×#15692251	2
C₂×#15692241	2
C₂×#15692228	2
C₂×#15692227	2
C₂×#15692225	2
C₂×#15692224	2
C₂×#15692223	2
C₂×#15692211	2
C₂×#120×C₁₀₁	2
C₂×#535	101

Subgroups — C2×#20265742 #27184439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265742 #27184439