Subgroups — C₂×#20265687 #27184373

Order 12928.

1880 conjugacy classes of subgroups.

The subgroup lattice has 368 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×C₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#20265687	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15692237	C₂	1	2	yes	maximal, complemented
5	C₂×#15692235	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15692234	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15692226	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15692223	C₂	1	2	yes	maximal, complemented
9	C₂×D₄×Dic₁₀₁	C₂	1	2	yes	maximal, complemented
10	C₂×#15692215	C₂	1	2	yes	maximal, complemented
11	C₂×#15692213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×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×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
19	C₂³×Dic₁₀₁	C₂²	1	1	yes	characteristic
20	C₂³×Dic₁₀₁	C₂²	1	2	yes	complemented
21	C₂²×C₄×D₁₀₁	—	2	8	no	—
22	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₀₁	C₂²	1	8	yes	complemented
27	#15692237	C₂²	1	16	yes	complemented
28	#15692235	C₂²	1	8	yes	complemented
29	#15692234	C₂²	1	8	yes	complemented
30	#15692226	C₂²	1	8	yes	complemented
31	#15692223	C₂²	1	16	yes	complemented
32	D₄×Dic₁₀₁	C₂²	1	16	yes	complemented
33	#15692215	C₂²	1	16	yes	complemented
34	#15692213	C₂²	1	8	yes	complemented
35	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄⋊Dic₁₀₁	C₂²	1	2	yes	complemented
37	C₂×#13108053	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	complemented
40	C₂×#13108051	C₂²	1	2	yes	—
41	C₂×#13108051	C₂²	1	2	yes	—
42	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	complemented
43	C₂²×D₄×C₁₀₁	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic, complemented
45	C₂³×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
46	#121×C₁₀₁	C₂²	1	8	yes	complemented
47	C₂×C₄⋊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	—	2	4	no	—
51	C₂³×D₁₀₁	—	2	4	no	—
52	C₂³×D₁₀₁	C₂³	1	4	yes	—
53	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
54	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
55	#13108073	—	2	32	no	—
56	C₂×Dic₂₀₂	—	2	4	no	—
57	C₂×Dic₂₀₂	C₂³	1	4	yes	complemented
58	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
59	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
60	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
61	C₂×C₂²⋊D₁₀₁	C₂³	1	8	yes	—
62	C₂²×Dic₁₀₁	—	2	4	no	—
63	C₂²×Dic₁₀₁	—	2	8	no	—
64	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
65	C₂²×Dic₁₀₁	C₂³	1	4	yes	—
66	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
67	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
68	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₀₁	C₂³	1	8	yes	complemented
70	C₂×C₄×D₁₀₁	—	2	4	no	—
71	C₂×C₄×D₁₀₁	—	2	4	no	—
72	C₂×C₄×D₁₀₁	—	2	4	no	—
73	C₂×C₄×D₁₀₁	—	2	32	no	—
74	C₂×C₄×D₁₀₁	D₄	1	8	yes	complemented
75	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
76	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
77	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
78	C₂×C₄×D₁₀₁	C₂³	1	4	yes	—
79	C₄⋊Dic₁₀₁	C₂³	1	4	yes	complemented
80	C₄⋊Dic₁₀₁	C₂³	1	8	yes	complemented
81	#13108053	C₂³	1	8	yes	complemented
82	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	—
83	C₂²⋊Dic₁₀₁	C₂³	1	8	yes	complemented
84	#13108051	C₂³	1	8	yes	—
85	#13108051	C₂³	1	8	yes	—
86	C₄×Dic₁₀₁	C₂³	1	8	yes	complemented
87	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
88	C₂⁴×C₁₀₁	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₀₁	—	2	8	no	—
90	C₂×D₄×C₁₀₁	—	2	4	no	—
91	C₂×D₄×C₁₀₁	C₂³	1	8	yes	—
92	C₂×D₄×C₁₀₁	C₂³	1	4	yes	complemented
93	C₂²×C₄×C₁₀₁	—	2	4	no	—
94	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₁	C₂³	1	4	yes	—
96	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
97	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₁₀₁	C₂³	1	4	yes	complemented
99	C₂²⋊C₄×C₁₀₁	C₂³	1	8	yes	complemented
100	C₂³×C₁₀₁	—	2	2	no	—
101	C₂³×C₁₀₁	—	2	2	no	—
102	C₂³×C₁₀₁	—	2	4	no	—
103	C₂³×C₁₀₁	—	2	4	no	—
104	C₂³×C₁₀₁	—	2	4	no	—
105	C₂³×C₁₀₁	#41	1	4	yes	complemented
106	C₂³×C₁₀₁	C₂⁴	1	4	yes	—
107	C₂³×C₁₀₁	C₂⁴	1	2	yes	—
108	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
109	C₂²×D₁₀₁	—	2	32	no	—
110	C₂²×D₁₀₁	—	2	2	no	—
111	C₂²×D₁₀₁	—	2	2	no	—
112	C₂²×D₁₀₁	—	2	2	no	—
113	C₂²×D₁₀₁	—	2	2	no	—
114	C₂²×D₁₀₁	—	2	8	no	—
115	C₂²×D₁₀₁	—	2	8	no	—
116	C₂²×D₁₀₁	—	2	8	no	—
117	C₂²×D₁₀₁	C₂×D₄	1	4	yes	—
118	C₂²×D₁₀₁	#41	1	4	yes	complemented
119	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
120	C₂²×D₁₀₁	C₂⁴	1	2	yes	—
121	D₄×C₁₀₁	—	2	16	no	—
122	D₄×C₁₀₁	—	2	8	no	—
123	C₂×C₄×C₁₀₁	—	2	2	no	—
124	C₂×C₄×C₁₀₁	—	2	4	no	—
125	C₂×C₄×C₁₀₁	—	2	8	no	—
126	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
127	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
128	C₂×C₄×C₁₀₁	C₂⁴	1	4	yes	—
129	C₂×C₄×C₁₀₁	C₂⁴	1	2	yes	—
130	C₂²⋊D₁₀₁	—	2	16	no	—
131	C₂²⋊D₁₀₁	—	2	16	no	—
132	C₂×Dic₁₀₁	—	2	2	no	—
133	C₂×Dic₁₀₁	—	2	4	no	—
134	C₂×Dic₁₀₁	—	2	4	no	—
135	C₂×Dic₁₀₁	—	2	8	no	—
136	C₂×Dic₁₀₁	—	2	16	no	—
137	C₂×Dic₁₀₁	C₂×D₄	1	4	yes	—
138	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
139	C₂×Dic₁₀₁	C₂⁴	1	4	yes	—
140	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
141	C₂×Dic₁₀₁	C₂⁴	1	2	yes	—
142	C₄×D₁₀₁	—	2	8	no	—
143	C₄×D₁₀₁	—	2	8	no	—
144	C₄×D₁₀₁	—	2	8	no	—
145	C₄×D₁₀₁	C₂×D₄	1	16	yes	complemented
146	Dic₂₀₂	—	2	8	no	—
147	C₂²×C₁₀₁	—	2	8	no	—
148	C₂²×C₁₀₁	—	2	2	no	—
149	C₂²×C₁₀₁	—	2	2	no	—
150	C₂²×C₁₀₁	—	2	4	no	—
151	C₂²×C₁₀₁	—	2	4	no	—
152	C₂²×C₁₀₁	—	2	4	no	—
153	C₂²×C₁₀₁	—	4	8	no	—
154	C₂²×C₁₀₁	C₂²×D₄	1	2	yes	—
155	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
156	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
157	C₂²×C₁₀₁	C₂×#41	1	4	yes	complemented
158	C₂²×C₁₀₁	C₂⁵	1	1	yes	characteristic
159	C₂×D₁₀₁	—	2	32	no	—
160	C₂×D₁₀₁	—	2	8	no	—
161	C₂×D₁₀₁	—	2	8	no	—
162	C₂×D₁₀₁	—	2	2	no	—
163	C₂×D₁₀₁	—	2	2	no	—
164	C₂×D₁₀₁	—	2	2	no	—
165	C₂×D₁₀₁	—	2	2	no	—
166	C₂×D₁₀₁	C₂²×D₄	1	4	yes	—
167	C₂×D₁₀₁	C₂×#41	1	4	yes	complemented
168	C₄×C₁₀₁	—	2	2	no	—
169	C₄×C₁₀₁	—	2	4	no	—
170	C₄×C₁₀₁	C₂²×D₄	1	4	yes	—
171	Dic₁₀₁	—	2	4	no	—
172	Dic₁₀₁	—	2	2	no	—
173	Dic₁₀₁	—	2	4	no	—
174	Dic₁₀₁	C₂²×D₄	1	4	yes	—
175	C₂×C₁₀₁	—	2	4	no	—
176	C₂×C₁₀₁	—	4	4	no	—
177	C₂×C₁₀₁	#525	1	4	yes	complemented
178	C₂×C₁₀₁	C₂³×D₄	1	1	yes	characteristic
179	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
180	C₂×C₁₀₁	C₂²×#41	1	1	yes	characteristic
181	D₁₀₁	—	2	4	no	—
182	D₁₀₁	—	2	4	no	—
183	C₂×#525	—	101	1	no	maximal, Sylow
184	C₁₀₁	C₂×#525	1	1	yes	characteristic, complemented, Sylow
185	C₂²×#41	—	101	1	no	—
186	C₂⁴×C₄	—	101	1	no	—
187	#525	—	101	16	no	—
188	C₂×#123	—	101	2	no	—
189	C₂×C₂²⋊Q₈	—	101	1	no	—
190	C₂×C₂²⋊Q₈	—	101	1	no	—
191	C₂×#121	—	101	1	no	—
192	C₂×#121	D₁₀₁	1	1	yes	characteristic, complemented
193	C₂×#120	—	101	2	no	—
194	C₂×C₄×D₄	—	101	2	no	—
195	C₂×C₄×D₄	—	101	2	no	—
196	C₂×#117	—	101	1	no	—
197	C₂⁵	—	101	1	no	—
198	C₂×#41	—	101	8	no	—
199	C₂×#41	—	202	8	no	—
200	C₂²×Q₈	—	101	1	no	—
201	C₂²×D₄	—	101	2	no	—
202	C₂²×D₄	—	101	2	no	—
203	C₂²×D₄	C₂×D₁₀₁	1	2	yes	—
204	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
205	C₂³×C₄	—	101	1	no	—
206	C₂³×C₄	—	101	1	no	—
207	C₂³×C₄	—	101	2	no	—
208	C₂³×C₄	—	101	1	no	—
209	C₂³×C₄	—	101	1	no	—
210	C₂³×C₄	—	101	1	no	—
211	C₂³×C₄	—	101	8	no	—
212	C₂³×C₄	—	202	8	no	—
213	C₂³×C₄	C₂×D₁₀₁	1	1	yes	characteristic
214	#123	—	101	16	no	—
215	C₂²⋊Q₈	—	101	8	no	—
216	C₂²⋊Q₈	—	101	8	no	—
217	#121	—	101	8	no	—
218	#121	C₂×D₁₀₁	1	8	yes	complemented
219	#120	—	101	16	no	—
220	C₄×D₄	—	101	16	no	—
221	C₄×D₄	—	101	16	no	—
222	#117	—	101	8	no	—
223	C₂×C₄⋊C₄	—	101	1	no	—
224	C₂×C₄⋊C₄	—	101	2	no	—
225	C₂×C₄⋊C₄	—	101	2	no	—
226	C₂×C₄⋊C₄	C₂×D₁₀₁	1	1	yes	characteristic, complemented
227	C₂×C₂²⋊C₄	—	101	2	no	—
228	C₂×C₂²⋊C₄	—	101	2	no	—
229	C₂×C₂²⋊C₄	—	101	2	no	—
230	C₂×C₂²⋊C₄	—	101	2	no	—
231	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	2	yes	complemented
232	C₂×C₄²	—	101	2	no	—
233	C₂⁴	—	101	1	no	—
234	C₂⁴	—	101	1	no	—
235	C₂⁴	—	101	4	no	—
236	C₂⁴	—	202	4	no	—
237	C₂⁴	—	202	4	no	—
238	C₂⁴	—	202	4	no	—
239	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
240	C₂⁴	C₂²×D₁₀₁	1	1	yes	characteristic
241	#41	—	202	32	no	—
242	C₂×Q₈	—	101	4	no	—
243	C₂×Q₈	—	202	4	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	101	8	no	—
247	C₂×D₄	—	101	8	no	—
248	C₂×D₄	—	202	8	no	—
249	C₂×D₄	—	202	8	no	—
250	C₂×D₄	C₂²×D₁₀₁	1	8	yes	—
251	C₂×D₄	C₂²×D₁₀₁	1	4	yes	complemented
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	101	1	no	—
254	C₂²×C₄	—	101	8	no	—
255	C₂²×C₄	—	101	4	no	—
256	C₂²×C₄	—	101	4	no	—
257	C₂²×C₄	—	101	8	no	—
258	C₂²×C₄	—	101	2	no	—
259	C₂²×C₄	—	101	1	no	—
260	C₂²×C₄	—	101	2	no	—
261	C₂²×C₄	—	101	4	no	—
262	C₂²×C₄	—	101	4	no	—
263	C₂²×C₄	—	101	4	no	—
264	C₂²×C₄	—	202	4	no	—
265	C₂²×C₄	—	202	32	no	—
266	C₂²×C₄	—	202	4	no	—
267	C₂²×C₄	—	202	4	no	—
268	C₂²×C₄	—	202	8	no	—
269	C₂²×C₄	—	202	4	no	—
270	C₂²×C₄	C₂²×D₁₀₁	1	4	yes	—
271	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
272	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
274	C₄⋊C₄	—	101	8	no	—
275	C₄⋊C₄	—	101	4	no	—
276	C₄⋊C₄	—	101	8	no	—
277	C₄⋊C₄	C₂²×D₁₀₁	1	4	yes	complemented
278	C₂²⋊C₄	—	101	8	no	—
279	C₂²⋊C₄	—	101	8	no	—
280	C₂²⋊C₄	—	101	8	no	—
281	C₂²⋊C₄	—	101	8	no	—
282	C₂²⋊C₄	C₂²×D₁₀₁	1	8	yes	complemented
283	C₄²	—	101	8	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	101	4	no	—
290	C₂³	—	101	4	no	—
291	C₂³	—	101	2	no	—
292	C₂³	—	101	2	no	—
293	C₂³	—	202	8	no	—
294	C₂³	—	202	8	no	—
295	C₂³	—	202	32	no	—
296	C₂³	—	202	2	no	—
297	C₂³	—	202	2	no	—
298	C₂³	—	202	2	no	—
299	C₂³	—	202	2	no	—
300	C₂³	—	202	8	no	—
301	C₂³	#13108073	1	4	yes	complemented
302	C₂³	C₂³×D₁₀₁	1	4	yes	—
303	C₂³	C₂³×D₁₀₁	1	2	yes	—
304	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
305	Q₈	—	202	8	no	—
306	D₄	—	2	16	no	—
307	D₄	—	2	8	no	—
308	D₄	—	202	16	no	—
309	D₄	—	202	16	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	101	4	no	—
314	C₂×C₄	—	101	2	no	—
315	C₂×C₄	—	101	16	no	—
316	C₂×C₄	—	101	4	no	—
317	C₂×C₄	—	101	2	no	—
318	C₂×C₄	—	101	4	no	—
319	C₂×C₄	—	202	8	no	—
320	C₂×C₄	—	202	8	no	—
321	C₂×C₄	—	202	8	no	—
322	C₂×C₄	—	202	16	no	—
323	C₂×C₄	—	202	2	no	—
324	C₂×C₄	—	202	4	no	—
325	C₂×C₄	—	202	4	no	—
326	C₂×C₄	—	202	8	no	—
327	C₂×C₄	D₄×D₁₀₁	1	4	yes	—
328	C₂×C₄	C₂³×D₁₀₁	1	4	yes	—
329	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
330	C₂×C₄	C₂³×D₁₀₁	1	2	yes	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	101	4	no	—
339	C₂²	—	101	4	no	—
340	C₂²	—	202	32	no	—
341	C₂²	—	202	2	no	—
342	C₂²	—	202	2	no	—
343	C₂²	—	202	2	no	—
344	C₂²	—	202	2	no	—
345	C₂²	—	202	8	no	—
346	C₂²	—	202	8	no	—
347	C₂²	C₂×D₄×D₁₀₁	1	2	yes	—
348	C₂²	#41×D₁₀₁	1	2	yes	—
349	C₂²	C₂×#13108073	1	2	yes	—
350	C₂²	C₂×#13108073	1	4	yes	complemented
351	C₂²	C₂⁴×D₁₀₁	1	1	yes	characteristic
352	C₄	—	2	2	no	—
353	C₄	—	2	4	no	—
354	C₄	—	101	4	no	—
355	C₄	—	202	2	no	—
356	C₄	—	202	4	no	—
357	C₄	—	202	4	no	—
358	C₄	C₂×D₄×D₁₀₁	1	4	yes	—
359	C₂	—	2	4	no	—
360	C₂	—	4	4	no	—
361	C₂	—	202	4	no	—
362	C₂	—	202	4	no	—
363	C₂	#20265687	1	4	yes	direct product factor
364	C₂	C₂²×D₄×D₁₀₁	1	1	yes	characteristic
365	C₂	C₂×#41×D₁₀₁	1	1	yes	characteristic
366	C₂	C₂²×#13108073	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₀₁
commutator, cosocle	C₂²×C₁₀₁	C₂⁵
Frattini	C₂²	C₂⁴×D₁₀₁
Fitting	C₂×#121×C₁₀₁	C₂
socle	C₂³×C₁₀₁	C₂⁴
hypercenter	C₂×#121	D₁₀₁
hypocenter	C₁₀₁	C₂×#525
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×#13108073	C₂	semidirect
2. C₂³×C₄×D₁₀₁	C₂	semidirect
3. #20265687	C₂	direct (N × H)
4. C₂×#15692237	C₂	semidirect
5. C₂×#15692235	C₂	semidirect
6. C₂×#15692234	C₂	semidirect
7. C₂×#15692226	C₂	semidirect
8. C₂×#15692223	C₂	semidirect
9. C₂×D₄×Dic₁₀₁	C₂	semidirect
10. C₂×#15692215	C₂	semidirect
11. C₂×#15692213	C₂	semidirect
12. C₂×#121×C₁₀₁	C₂	semidirect
15. C₂×#13108073	C₂²	semidirect
16. C₂²×Dic₂₀₂	C₂²	semidirect
20. C₂³×Dic₁₀₁	C₂²	semidirect
26. C₂²×C₄×D₁₀₁	C₂²	semidirect
27. #15692237	C₂²	semidirect
28. #15692235	C₂²	semidirect
29. #15692234	C₂²	semidirect
30. #15692226	C₂²	semidirect
31. #15692223	C₂²	semidirect
32. D₄×Dic₁₀₁	C₂²	semidirect
33. #15692215	C₂²	semidirect
34. #15692213	C₂²	semidirect
35. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
36. C₂×C₄⋊Dic₁₀₁	C₂²	semidirect
37. C₂×#13108053	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₀₁	C₂²	semidirect
42. C₂×C₄×Dic₁₀₁	C₂²	semidirect
44. C₂²×D₄×C₁₀₁	C₂²	semidirect
46. #121×C₁₀₁	C₂²	semidirect
47. C₂×C₄⋊C₄×C₁₀₁	C₂²	semidirect
48. C₂×C₂²⋊C₄×C₁₀₁	C₂²	semidirect
57. C₂×Dic₂₀₂	C₂³	semidirect
69. C₂²×Dic₁₀₁	C₂³	semidirect
74. C₂×C₄×D₁₀₁	D₄	semidirect
79. C₄⋊Dic₁₀₁	C₂³	semidirect
80. C₄⋊Dic₁₀₁	C₂³	semidirect
81. #13108053	C₂³	semidirect
83. C₂²⋊Dic₁₀₁	C₂³	semidirect
86. C₄×Dic₁₀₁	C₂³	semidirect
92. C₂×D₄×C₁₀₁	C₂³	semidirect
98. C₄⋊C₄×C₁₀₁	C₂³	semidirect
99. C₂²⋊C₄×C₁₀₁	C₂³	semidirect
105. C₂³×C₁₀₁	#41	semidirect
118. C₂²×D₁₀₁	#41	semidirect
145. C₄×D₁₀₁	C₂×D₄	semidirect
157. C₂²×C₁₀₁	C₂×#41	semidirect
167. C₂×D₁₀₁	C₂×#41	semidirect
177. C₂×C₁₀₁	#525	semidirect
184. C₁₀₁	C₂×#525	semidirect
192. C₂×#121	D₁₀₁	semidirect
204. C₂²×D₄	C₂×D₁₀₁	semidirect
218. #121	C₂×D₁₀₁	semidirect
226. C₂×C₄⋊C₄	C₂×D₁₀₁	semidirect
231. C₂×C₂²⋊C₄	C₂×D₁₀₁	semidirect
251. C₂×D₄	C₂²×D₁₀₁	semidirect
277. C₄⋊C₄	C₂²×D₁₀₁	semidirect
282. C₂²⋊C₄	C₂²×D₁₀₁	semidirect
301. C₂³	#13108073	semidirect
350. C₂²	C₂×#13108073	semidirect
363. C₂	#20265687	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×C₄×D₁₀₁	2
#20265687	2
C₂×#15692237	2
C₂×#15692235	2
C₂×#15692234	2
C₂×#15692226	2
C₂×#15692223	2
C₂×D₄×Dic₁₀₁	2
C₂×#15692215	2
C₂×#15692213	2
C₂×#121×C₁₀₁	2
C₂×#525	101

Subgroups — C2×#20265687 #27184373

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20265687 #27184373