Subgroups — C₂×#13093099 #15686901

Order 2944.

1124 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093099	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625069	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10625069	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10625060	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625065	C₂	1	1	yes	maximal, characteristic
7	C₂×#10625065	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625067	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10625067	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#10625058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#10625064	C₂	1	1	yes	maximal, characteristic
12	C₂×#10625063	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#10625043	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10625043	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄⋊C₄×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×D₉₂	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
22	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
23	C₂₃×#125	C₂²	1	8	yes	complemented
24	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×(C₂×D₂₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
41	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×Dic₂₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
53	#10625069	C₂²	1	8	yes	complemented
54	#10625069	C₂²	1	8	yes	complemented
55	#10625067	C₂²	1	8	yes	complemented
56	#10625067	C₂²	1	8	yes	complemented
57	#10625065	C₂²	1	8	yes	—
58	#10625065	C₂²	1	8	yes	—
59	#10625064	C₂²	1	8	yes	—
60	#10625063	C₂²	1	8	yes	complemented
61	C₄⋊C₄×D₂₃	C₂²	1	8	yes	complemented
62	#10625060	C₂²	1	8	yes	complemented
63	#10625060	C₂²	1	8	yes	complemented
64	#10625058	C₂²	1	8	yes	complemented
65	#10625043	C₂²	1	8	yes	complemented
66	#10625043	C₂²	1	8	yes	complemented
67	C₂³×D₂₃	C₂³	1	1	yes	characteristic
68	C₂³×D₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
77	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
78	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
79	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₂₃	C₂³	1	1	yes	characteristic
82	C₂×D₉₂	—	2	4	no	—
83	C₂×D₉₂	C₂³	1	4	yes	—
84	C₂×C₄×D₂₃	—	2	4	no	—
85	C₂×C₄×D₂₃	—	2	4	no	—
86	C₂×C₄×D₂₃	—	2	4	no	—
87	C₂×C₄×D₂₃	—	2	4	no	—
88	C₂×C₄×D₂₃	C₂³	1	4	yes	—
89	C₂×C₄×D₂₃	C₂³	1	4	yes	—
90	C₂×C₄×D₂₃	C₂³	1	4	yes	—
91	C₂×C₄×D₂₃	C₂³	1	4	yes	—
92	C₂×Dic₄₆	—	2	4	no	—
93	C₂×Dic₄₆	C₂³	1	4	yes	—
94	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
95	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
96	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
97	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
98	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
99	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
100	C₄²×C₂₃	C₂³	1	4	yes	—
101	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
102	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
103	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
104	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
105	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
106	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
107	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
108	(C₂×D₂₃)⋊C₄	C₂³	1	4	yes	—
109	C₄⋊Dic₂₃	C₂³	1	4	yes	—
110	C₄⋊Dic₂₃	C₂³	1	4	yes	—
111	Dic₂₃⋊C₄	C₂³	1	4	yes	—
112	Dic₂₃⋊C₄	C₂³	1	4	yes	—
113	Dic₂₃⋊C₄	C₂³	1	4	yes	—
114	Dic₂₃⋊C₄	C₂³	1	4	yes	—
115	Dic₂₃⋊C₄	C₂³	1	4	yes	—
116	Dic₂₃⋊C₄	C₂³	1	4	yes	—
117	Dic₂₃⋊C₄	C₂³	1	4	yes	—
118	Dic₂₃⋊C₄	C₂³	1	4	yes	—
119	C₄×Dic₂₃	C₂³	1	4	yes	—
120	C₄×Dic₂₃	C₂³	1	4	yes	—
121	C₄×Dic₂₃	C₂³	1	4	yes	—
122	C₄×Dic₂₃	C₂³	1	4	yes	—
123	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
124	C₂²×D₂₃	—	2	2	no	—
125	C₂²×D₂₃	—	2	2	no	—
126	C₂²×D₂₃	—	2	2	no	—
127	C₂²×D₂₃	—	2	2	no	—
128	C₂²×D₂₃	—	2	2	no	—
129	C₂²×D₂₃	#41	1	4	yes	—
130	C₂²×D₂₃	C₂⁴	1	2	yes	—
131	C₂²×D₂₃	C₂⁴	1	2	yes	—
132	C₂×C₄×C₂₃	—	2	2	no	—
133	C₂×C₄×C₂₃	—	2	2	no	—
134	C₂×C₄×C₂₃	—	2	2	no	—
135	C₂×C₄×C₂₃	—	2	2	no	—
136	C₂×C₄×C₂₃	—	2	2	no	—
137	C₂×C₄×C₂₃	—	2	2	no	—
138	C₂×C₄×C₂₃	—	2	2	no	—
139	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
140	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
141	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
143	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
144	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
145	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
146	C₂×Dic₂₃	—	2	2	no	—
147	C₂×Dic₂₃	—	2	2	no	—
148	C₂×Dic₂₃	—	2	2	no	—
149	C₂×Dic₂₃	—	2	2	no	—
150	C₂×Dic₂₃	—	2	2	no	—
151	C₂×Dic₂₃	#41	1	4	yes	—
152	C₂×Dic₂₃	C₂⁴	1	2	yes	—
153	C₂×Dic₂₃	C₂⁴	1	2	yes	—
154	C₂×Dic₂₃	C₂⁴	1	2	yes	—
155	C₂×Dic₂₃	C₂⁴	1	2	yes	—
156	C₂×Dic₂₃	C₂⁴	1	2	yes	—
157	C₂×Dic₂₃	C₂⁴	1	2	yes	—
158	D₉₂	—	2	8	no	—
159	C₄×D₂₃	—	2	8	no	—
160	C₄×D₂₃	—	2	8	no	—
161	C₄×D₂₃	—	2	8	no	—
162	C₄×D₂₃	—	2	8	no	—
163	Dic₄₆	—	2	8	no	—
164	C₂×#552	—	23	1	no	maximal, Sylow
165	C₂²×C₂₃	C₂×#41	1	2	yes	—
166	C₂²×C₂₃	C₂×#41	1	2	yes	—
167	C₂²×C₂₃	2₋¹⁺⁴	1	2	yes	—
168	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
169	C₂×D₂₃	—	2	8	no	—
170	C₂×D₂₃	—	2	2	no	—
171	C₂×D₂₃	—	2	2	no	—
172	C₂×D₂₃	—	2	2	no	—
173	C₂×D₂₃	—	2	2	no	—
174	C₂×D₂₃	—	2	2	no	—
175	C₂×D₂₃	—	4	4	no	—
176	C₂×D₂₃	C₂×#41	1	4	yes	—
177	C₄×C₂₃	—	2	2	no	—
178	C₄×C₂₃	—	2	2	no	—
179	C₄×C₂₃	—	2	2	no	—
180	C₄×C₂₃	—	2	2	no	—
181	C₄×C₂₃	—	2	2	no	—
182	C₄×C₂₃	—	2	2	no	—
183	C₄×C₂₃	—	2	2	no	—
184	Dic₂₃	—	2	2	no	—
185	Dic₂₃	—	2	2	no	—
186	Dic₂₃	—	2	2	no	—
187	Dic₂₃	—	2	2	no	—
188	Dic₂₃	—	2	2	no	—
189	Dic₂₃	C₂×#41	1	4	yes	—
190	#552	—	23	16	no	—
191	C₂×#126	—	23	1	no	—
192	C₂×#126	—	23	1	no	—
193	C₂×#125	—	23	1	no	—
194	C₂×#125	—	23	1	no	—
195	C₂×#125	D₂₃	1	1	yes	characteristic, complemented
196	C₂×#123	—	23	1	no	—
197	C₂×#123	—	23	1	no	—
198	C₂×C₂²⋊Q₈	—	23	1	no	—
199	C₂×C₂²⋊Q₈	—	23	1	no	—
200	C₂×C₄×Q₈	—	23	1	no	—
201	C₂×C₄×D₄	—	23	1	no	—
202	C₂×#117	—	23	1	no	—
203	C₂×#117	—	23	1	no	—
204	C₂×#117	—	23	1	no	—
205	C₂²×C₄⋊C₄	—	23	1	no	—
206	C₂×C₂₃	#552	1	4	yes	complemented
207	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
208	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
209	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	D₂₃	—	2	4	no	—
211	D₂₃	—	4	2	no	—
212	C₂²×Q₈	—	23	1	no	—
213	C₂²×D₄	—	23	1	no	—
214	C₂³×C₄	—	23	1	no	—
215	C₂³×C₄	—	23	1	no	—
216	C₂³×C₄	—	23	1	no	—
217	C₂³×C₄	—	23	1	no	—
218	#126	—	23	8	no	—
219	#126	—	23	8	no	—
220	#125	—	23	8	no	—
221	#125	—	23	8	no	—
222	#125	C₂×D₂₃	1	8	yes	complemented
223	#123	—	23	8	no	—
224	#123	—	23	8	no	—
225	C₂²⋊Q₈	—	23	8	no	—
226	C₂²⋊Q₈	—	23	8	no	—
227	C₄×Q₈	—	23	8	no	—
228	C₄×D₄	—	23	8	no	—
229	#117	—	23	8	no	—
230	#117	—	23	8	no	—
231	#117	—	23	8	no	—
232	C₂×C₄⋊C₄	—	23	1	no	—
233	C₂×C₄⋊C₄	—	23	1	no	—
234	C₂×C₄⋊C₄	—	23	1	no	—
235	C₂×C₄⋊C₄	—	23	1	no	—
236	C₂×C₄⋊C₄	—	23	1	no	—
237	C₂×C₄⋊C₄	—	23	1	no	—
238	C₂×C₄⋊C₄	—	23	1	no	—
239	C₂×C₄⋊C₄	—	23	1	no	—
240	C₂×C₄⋊C₄	—	23	1	no	—
241	C₂×C₄⋊C₄	—	23	1	no	—
242	C₂×C₄⋊C₄	—	23	8	no	—
243	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	23	1	no	—
250	C₂×C₂²⋊C₄	—	23	1	no	—
251	C₂×C₂²⋊C₄	—	23	1	no	—
252	C₂×C₂²⋊C₄	—	23	1	no	—
253	C₂×C₂²⋊C₄	—	23	1	no	—
254	C₂×C₂²⋊C₄	—	23	1	no	—
255	C₂×C₂²⋊C₄	—	23	1	no	—
256	C₂×C₂²⋊C₄	—	23	1	no	—
257	C₂×C₄²	—	23	1	no	—
258	C₂×C₄²	—	23	1	no	—
259	C₂×C₄²	—	23	1	no	—
260	C₂×C₄²	—	23	1	no	—
261	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
262	C₂₃	C₂×#552	1	1	yes	characteristic, complemented, Sylow
263	C₂⁴	—	23	1	no	—
264	C₂⁴	—	23	1	no	—
265	C₂×Q₈	—	23	4	no	—
266	C₂×Q₈	—	46	4	no	—
267	C₂×D₄	—	23	4	no	—
268	C₂×D₄	—	46	4	no	—
269	C₂²×C₄	—	23	1	no	—
270	C₂²×C₄	—	23	1	no	—
271	C₂²×C₄	—	23	1	no	—
272	C₂²×C₄	—	23	1	no	—
273	C₂²×C₄	—	23	1	no	—
274	C₂²×C₄	—	23	1	no	—
275	C₂²×C₄	—	23	4	no	—
276	C₂²×C₄	—	23	4	no	—
277	C₂²×C₄	—	23	4	no	—
278	C₂²×C₄	—	23	4	no	—
279	C₂²×C₄	—	46	4	no	—
280	C₂²×C₄	—	46	4	no	—
281	C₂²×C₄	—	46	4	no	—
282	C₂²×C₄	—	46	4	no	—
283	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
284	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
286	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
290	C₄⋊C₄	—	23	4	no	—
291	C₄⋊C₄	—	23	4	no	—
292	C₄⋊C₄	—	23	4	no	—
293	C₄⋊C₄	—	23	4	no	—
294	C₄⋊C₄	—	23	4	no	—
295	C₄⋊C₄	—	23	4	no	—
296	C₄⋊C₄	—	23	4	no	—
297	C₄⋊C₄	—	23	4	no	—
298	C₄⋊C₄	—	23	4	no	—
299	C₄⋊C₄	—	23	4	no	—
300	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
301	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
302	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
303	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
304	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
305	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
306	C₂²⋊C₄	—	23	4	no	—
307	C₂²⋊C₄	—	23	4	no	—
308	C₂²⋊C₄	—	23	4	no	—
309	C₂²⋊C₄	—	23	4	no	—
310	C₂²⋊C₄	—	23	4	no	—
311	C₂²⋊C₄	—	23	4	no	—
312	C₂²⋊C₄	—	23	4	no	—
313	C₂²⋊C₄	—	23	4	no	—
314	C₄²	—	23	4	no	—
315	C₄²	—	23	4	no	—
316	C₄²	—	23	4	no	—
317	C₄²	—	23	4	no	—
318	C₄²	C₂²×D₂₃	1	4	yes	—
319	C₂³	—	23	4	no	—
320	C₂³	—	23	2	no	—
321	C₂³	—	23	2	no	—
322	C₂³	—	46	2	no	—
323	C₂³	—	46	2	no	—
324	C₂³	—	46	2	no	—
325	C₂³	—	46	2	no	—
326	C₂³	—	46	2	no	—
327	C₂³	C₂³×D₂₃	1	1	yes	characteristic
328	Q₈	—	46	8	no	—
329	D₄	—	46	8	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	23	4	no	—
338	C₂×C₄	—	23	2	no	—
339	C₂×C₄	—	23	2	no	—
340	C₂×C₄	—	23	2	no	—
341	C₂×C₄	—	23	2	no	—
342	C₂×C₄	—	23	2	no	—
343	C₂×C₄	—	23	2	no	—
344	C₂×C₄	—	46	8	no	—
345	C₂×C₄	—	46	8	no	—
346	C₂×C₄	—	46	8	no	—
347	C₂×C₄	—	46	8	no	—
348	C₂×C₄	—	46	2	no	—
349	C₂×C₄	—	46	2	no	—
350	C₂×C₄	—	46	2	no	—
351	C₂×C₄	—	46	2	no	—
352	C₂×C₄	—	46	2	no	—
353	C₂×C₄	C₂³×D₂₃	1	2	yes	—
354	C₂×C₄	C₂³×D₂₃	1	2	yes	—
355	C₂×C₄	C₂³×D₂₃	1	2	yes	—
356	C₂×C₄	C₂³×D₂₃	1	2	yes	—
357	C₂×C₄	C₂³×D₂₃	1	2	yes	—
358	C₂×C₄	C₂³×D₂₃	1	2	yes	—
359	C₂×C₄	C₂³×D₂₃	1	2	yes	—
360	C₂²	—	23	4	no	—
361	C₂²	—	46	2	no	—
362	C₂²	—	46	2	no	—
363	C₂²	—	46	8	no	—
364	C₂²	—	46	2	no	—
365	C₂²	—	46	2	no	—
366	C₂²	—	46	2	no	—
367	C₂²	—	92	4	no	—
368	C₂²	#10625158	1	2	yes	—
369	C₂²	#41×D₂₃	1	2	yes	—
370	C₂²	#41×D₂₃	1	2	yes	—
371	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	23	4	no	—
380	C₄	—	46	2	no	—
381	C₄	—	46	2	no	—
382	C₄	—	46	2	no	—
383	C₄	—	46	2	no	—
384	C₄	—	46	2	no	—
385	C₂	—	46	4	no	—
386	C₂	—	92	2	no	—
387	C₂	#13093099	1	4	yes	direct product factor
388	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
389	C₂	C₂×#41×D₂₃	1	1	yes	characteristic
390	C₂	C₂×#10625158	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₂₃×#125	C₂
socle	C₂³×C₂₃	C₂⁴
prime radical	C₂²×D₉₂	C₂²
hypercenter	C₂×#125	D₂₃
hypocenter	C₂₃	C₂×#552
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. #13093099	C₂	direct (N × H)
2. C₂×#10625069	C₂	semidirect
3. C₂×#10625069	C₂	semidirect
4. C₂×#10625060	C₂	semidirect
5. C₂×#10625060	C₂	semidirect
8. C₂×#10625067	C₂	semidirect
9. C₂×#10625067	C₂	semidirect
10. C₂×#10625058	C₂	semidirect
12. C₂×#10625063	C₂	semidirect
13. C₂×#10625043	C₂	semidirect
14. C₂×#10625043	C₂	semidirect
15. C₂×C₄⋊C₄×D₂₃	C₂	semidirect
16. C₂×C₂₃×#125	C₂	semidirect
23. C₂₃×#125	C₂²	semidirect
53. #10625069	C₂²	semidirect
54. #10625069	C₂²	semidirect
55. #10625067	C₂²	semidirect
56. #10625067	C₂²	semidirect
60. #10625063	C₂²	semidirect
61. C₄⋊C₄×D₂₃	C₂²	semidirect
62. #10625060	C₂²	semidirect
63. #10625060	C₂²	semidirect
64. #10625058	C₂²	semidirect
65. #10625043	C₂²	semidirect
66. #10625043	C₂²	semidirect
195. C₂×#125	D₂₃	semidirect
206. C₂×C₂₃	#552	semidirect
222. #125	C₂×D₂₃	semidirect
262. C₂₃	C₂×#552	semidirect
387. C₂	#13093099	direct (N × H)

Maximal subgroups

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

subgroup	index
#13093099	2
C₂×#10625069	2
C₂×#10625060	2
C₂×#10625065	2
C₂×#10625067	2
C₂×#10625058	2
C₂×#10625064	2
C₂×#10625063	2
C₂×#10625043	2
C₂×C₄⋊C₄×D₂₃	2
C₂×C₂₃×#125	2
C₂×#552	23

Subgroups — C2×#13093099 #15686901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093099 #15686901