Subgroups — C₂×C₂₃×#3140 #19208241

Order 5888.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3140	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#489	C₂	1	4	yes	maximal, complemented
5	C₂×C₂₃×#488	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#419	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#418	C₂	1	2	yes	maximal
8	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
12	C₂₃×#533	—	2	4	no	—
13	C₂₃×#533	C₂²	1	8	yes	complemented
14	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
15	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
16	C₂×C₂₃×#124	—	2	2	no	—
17	C₂×C₂₃×#124	—	2	4	no	—
18	C₂×C₂₃×#124	C₂²	1	2	yes	—
19	C₂×C₂₃×#124	C₂²	1	2	yes	—
20	C₂×C₂₃×#124	C₂²	1	8	yes	—
21	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
23	C₂×C₂₃×#117	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₂₃	—	2	2	no	—
25	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#489	C₂²	1	32	yes	complemented
27	C₂₃×#488	C₂²	1	32	yes	complemented
28	C₂₃×#419	C₂²	1	16	yes	complemented
29	C₂₃×#418	C₂²	1	16	yes	—
30	C₂×C₂₃×#103	C₂²	1	8	yes	complemented
31	C₂×C₂₃×#102	C₂²	1	8	yes	—
32	C₄×M₁₆×C₂₃	C₂²	1	8	yes	complemented
33	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
34	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
35	C₂⁵×C₂₃	—	2	1	no	—
36	C₂²×Q₈×C₂₃	—	2	2	no	—
37	C₂²×Q₈×C₂₃	—	2	1	no	—
38	C₂²×Q₈×C₂₃	—	2	2	no	—
39	C₂²×Q₈×C₂₃	—	2	8	no	—
40	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
41	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
42	C₂²×D₄×C₂₃	—	2	2	no	—
43	C₂²×D₄×C₂₃	—	2	1	no	—
44	C₂²×D₄×C₂₃	—	2	8	no	—
45	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	D₄	1	2	yes	—
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₂₃	—	2	8	no	—
51	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
52	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
53	C₂₃×C₄⋊Q₈	—	2	4	no	—
54	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
55	C₂₃×#125	—	2	4	no	—
56	C₂₃×#125	C₂³	1	8	yes	complemented
57	C₂₃×#124	—	2	16	no	—
58	C₂₃×#124	—	2	4	no	—
59	C₂₃×#124	—	2	4	no	—
60	C₂₃×#124	C₂³	1	8	yes	—
61	C₂₃×#124	C₂³	1	8	yes	—
62	C₂₃×C₂²⋊Q₈	—	2	16	no	—
63	C₄×Q₈×C₂₃	—	2	16	no	—
64	C₂₃×#117	—	2	4	no	—
65	C₂₃×#117	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₂₃	—	2	16	no	—
71	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
73	C₂×C₄²×C₂₃	—	2	2	no	—
74	C₂×C₄²×C₂₃	D₄	1	2	yes	—
75	C₂×C₄²×C₂₃	D₄	1	4	yes	—
76	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
79	C₂₃×#103	C₂³	1	32	yes	complemented
80	C₂₃×#102	C₂³	1	32	yes	—
81	C₂₃×#97	C₂³	1	8	yes	complemented
82	C₄×C₈×C₂₃	C₂³	1	8	yes	complemented
83	C₂⁴×C₂₃	—	2	4	no	—
84	C₂⁴×C₂₃	—	2	2	no	—
85	C₂⁴×C₂₃	—	4	8	no	—
86	C₂⁴×C₂₃	—	4	4	no	—
87	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₂₃	—	2	8	no	—
89	C₂×Q₈×C₂₃	—	2	4	no	—
90	C₂×Q₈×C₂₃	—	2	2	no	—
91	C₂×Q₈×C₂₃	—	2	8	no	—
92	C₂×Q₈×C₂₃	—	2	16	no	—
93	C₂×Q₈×C₂₃	—	4	8	no	—
94	C₂×Q₈×C₂₃	—	4	8	no	—
95	C₂×Q₈×C₂₃	—	4	4	no	—
96	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
97	C₂×D₄×C₂₃	—	2	4	no	—
98	C₂×D₄×C₂₃	—	2	2	no	—
99	C₂×D₄×C₂₃	—	2	8	no	—
100	C₂×D₄×C₂₃	—	2	16	no	—
101	C₂×D₄×C₂₃	—	4	8	no	—
102	C₂×D₄×C₂₃	—	4	4	no	—
103	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₂₃	—	2	4	no	—
105	C₂²×C₄×C₂₃	—	2	4	no	—
106	C₂²×C₄×C₂₃	—	2	2	no	—
107	C₂²×C₄×C₂₃	—	4	4	no	—
108	C₂²×C₄×C₂₃	—	4	4	no	—
109	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₂₃	#41	1	8	yes	—
115	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
117	M₁₆×C₂₃	—	2	16	no	—
118	C₂×C₈×C₂₃	—	2	8	no	—
119	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
120	C₄⋊C₄×C₂₃	—	2	16	no	—
121	C₄⋊C₄×C₂₃	—	2	8	no	—
122	C₄⋊C₄×C₂₃	—	2	4	no	—
123	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
124	C₂²⋊C₄×C₂₃	—	2	8	no	—
125	C₂²⋊C₄×C₂₃	—	2	16	no	—
126	C₂²⋊C₄×C₂₃	—	2	16	no	—
127	C₄²×C₂₃	—	2	8	no	—
128	C₄²×C₂₃	C₂×D₄	1	8	yes	—
129	C₄²×C₂₃	C₂×D₄	1	2	yes	—
130	C₄²×C₂₃	C₂×D₄	1	2	yes	—
131	C₄²×C₂₃	C₂⁴	1	2	yes	—
132	C₄²×C₂₃	C₂⁴	1	2	yes	—
133	C₂×#3140	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂³×C₂₃	—	2	4	no	—
135	C₂³×C₂₃	—	2	4	no	—
136	C₂³×C₂₃	—	4	16	no	—
137	C₂³×C₂₃	—	4	8	no	—
138	C₂³×C₂₃	—	4	4	no	—
139	C₂³×C₂₃	—	4	8	no	—
140	C₂³×C₂₃	—	8	16	no	—
141	C₂³×C₂₃	#124	1	4	yes	—
142	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
143	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₂₃	—	2	8	no	—
145	Q₈×C₂₃	—	4	16	no	—
146	Q₈×C₂₃	—	4	8	no	—
147	Q₈×C₂₃	—	4	4	no	—
148	D₄×C₂₃	—	2	8	no	—
149	D₄×C₂₃	—	4	8	no	—
150	D₄×C₂₃	—	4	4	no	—
151	C₂×C₄×C₂₃	—	2	4	no	—
152	C₂×C₄×C₂₃	—	2	4	no	—
153	C₂×C₄×C₂₃	—	2	8	no	—
154	C₂×C₄×C₂₃	—	2	4	no	—
155	C₂×C₄×C₂₃	—	4	8	no	—
156	C₂×C₄×C₂₃	—	4	8	no	—
157	C₂×C₄×C₂₃	—	4	4	no	—
158	C₂×C₄×C₂₃	—	4	8	no	—
159	C₂×C₄×C₂₃	#124	1	8	yes	—
160	C₂×C₄×C₂₃	#124	1	4	yes	—
161	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
162	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
163	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
166	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
167	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
168	C₈×C₂₃	—	2	8	no	—
169	C₂×#533	C₂×C₂₃	1	1	yes	characteristic, complemented
170	C₂²×#124	C₂×C₂₃	1	1	yes	characteristic
171	#3140	C₂×C₂₃	1	16	yes	direct product factor
172	C₂×#489	C₂×C₂₃	1	4	yes	complemented
173	C₂×#488	C₂×C₂₃	1	4	yes	complemented
174	C₂×#419	C₂×C₂₃	1	2	yes	complemented
175	C₂×#418	C₂×C₂₃	1	2	yes	—
176	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
177	C₂²×C₂₃	—	2	8	no	—
178	C₂²×C₂₃	—	2	4	no	—
179	C₂²×C₂₃	—	4	4	no	—
180	C₂²×C₂₃	—	4	8	no	—
181	C₂²×C₂₃	—	8	16	no	—
182	C₂²×C₂₃	—	8	8	no	—
183	C₂²×C₂₃	C₂×#124	1	4	yes	—
184	C₂²×C₂₃	C₂×#124	1	2	yes	—
185	C₂²×C₂₃	#575	1	4	yes	—
186	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
187	C₄×C₂₃	—	2	4	no	—
188	C₄×C₂₃	—	2	4	no	—
189	C₄×C₂₃	—	4	4	no	—
190	C₄×C₂₃	—	4	8	no	—
191	C₄×C₂₃	C₂×#124	1	4	yes	—
192	C₄×C₂₃	C₂×#124	1	2	yes	—
193	C₄×C₂₃	C₂²×#41	1	2	yes	—
194	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
195	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
196	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
197	#533	—	2	4	no	—
198	#533	C₂²×C₂₃	1	8	yes	complemented
199	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
200	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
201	C₂×#124	—	2	2	no	—
202	C₂×#124	—	2	4	no	—
203	C₂×#124	C₂²×C₂₃	1	2	yes	—
204	C₂×#124	C₂²×C₂₃	1	2	yes	—
205	C₂×#124	C₂²×C₂₃	1	8	yes	—
206	C₂×C₂²⋊Q₈	—	2	2	no	—
207	C₂×C₄×Q₈	—	2	2	no	—
208	C₂×#117	C₂²×C₂₃	1	2	yes	—
209	C₂²×C₂²⋊C₄	—	2	2	no	—
210	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
211	#489	C₂²×C₂₃	1	32	yes	complemented
212	#488	C₂²×C₂₃	1	32	yes	complemented
213	#419	C₂²×C₂₃	1	16	yes	complemented
214	#418	C₂²×C₂₃	1	16	yes	—
215	C₂×#103	C₂²×C₂₃	1	8	yes	complemented
216	C₂×#102	C₂²×C₂₃	1	8	yes	—
217	C₄×M₁₆	C₂²×C₂₃	1	8	yes	complemented
218	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
219	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
220	C₂×C₂₃	—	2	4	no	—
221	C₂×C₂₃	—	8	4	no	—
222	C₂×C₂₃	#3140	1	4	yes	direct product factor
223	C₂×C₂₃	C₂²×#124	1	1	yes	characteristic
224	C₂×C₂₃	C₂×#575	1	2	yes	—
225	C₂⁵	—	2	1	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×Q₈	—	2	8	no	—
230	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
231	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
236	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
237	C₂³×C₄	—	2	1	no	—
238	C₂³×C₄	D₄×C₂₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
242	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
243	C₄⋊Q₈	—	2	4	no	—
244	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
245	#125	—	2	4	no	—
246	#125	C₂³×C₂₃	1	8	yes	complemented
247	#124	—	2	16	no	—
248	#124	—	2	4	no	—
249	#124	—	2	4	no	—
250	#124	C₂³×C₂₃	1	8	yes	—
251	#124	C₂³×C₂₃	1	8	yes	—
252	C₂²⋊Q₈	—	2	16	no	—
253	C₄×Q₈	—	2	16	no	—
254	#117	—	2	4	no	—
255	#117	C₂³×C₂₃	1	8	yes	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	16	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	D₄×C₂₃	1	2	yes	—
265	C₂×C₄²	D₄×C₂₃	1	4	yes	—
266	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
269	#103	C₂³×C₂₃	1	32	yes	complemented
270	#102	C₂³×C₂₃	1	32	yes	—
271	#97	C₂³×C₂₃	1	8	yes	complemented
272	C₄×C₈	C₂³×C₂₃	1	8	yes	complemented
273	C₂₃	C₂×#3140	1	1	yes	characteristic, direct product factor, Sylow
274	C₂⁴	—	2	4	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	—	4	8	no	—
277	C₂⁴	—	4	4	no	—
278	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	16	no	—
284	C₂×Q₈	—	4	8	no	—
285	C₂×Q₈	—	4	8	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	16	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
303	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
305	C₂²×C₄	#41×C₂₃	1	8	yes	—
306	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
308	M₁₆	—	2	16	no	—
309	C₂×C₈	—	2	8	no	—
310	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
311	C₄⋊C₄	—	2	16	no	—
312	C₄⋊C₄	—	2	8	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	16	no	—
317	C₂²⋊C₄	—	2	16	no	—
318	C₄²	—	2	8	no	—
319	C₄²	C₂×D₄×C₂₃	1	8	yes	—
320	C₄²	C₂×D₄×C₂₃	1	2	yes	—
321	C₄²	C₂×D₄×C₂₃	1	2	yes	—
322	C₄²	C₂⁴×C₂₃	1	2	yes	—
323	C₄²	C₂⁴×C₂₃	1	2	yes	—
324	C₂³	—	2	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	4	16	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	8	no	—
329	C₂³	—	4	4	no	—
330	C₂³	—	8	16	no	—
331	C₂³	C₂₃×#124	1	4	yes	—
332	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
333	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	16	no	—
336	Q₈	—	4	8	no	—
337	Q₈	—	4	4	no	—
338	D₄	—	2	8	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	C₂₃×#124	1	8	yes	—
350	C₂×C₄	C₂₃×#124	1	4	yes	—
351	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
352	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
354	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
356	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
357	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
358	C₈	—	2	8	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	8	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	8	no	—
363	C₂²	—	8	16	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₂×C₂₃×#124	1	4	yes	—
366	C₂²	C₂×C₂₃×#124	1	2	yes	—
367	C₂²	C₂₃×#575	1	4	yes	—
368	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	8	no	—
373	C₄	C₂×C₂₃×#124	1	4	yes	—
374	C₄	C₂×C₂₃×#124	1	2	yes	—
375	C₄	C₂²×#41×C₂₃	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₂₃×#3140	1	4	yes	direct product factor
379	C₂	C₂²×C₂₃×#124	1	1	yes	characteristic
380	C₂	C₂×C₂₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#533	C₂	semidirect
3. C₂₃×#3140	C₂	direct (N × H)
4. C₂×C₂₃×#489	C₂	semidirect
5. C₂×C₂₃×#488	C₂	semidirect
6. C₂×C₂₃×#419	C₂	semidirect
8. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
13. C₂₃×#533	C₂²	semidirect
14. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
15. C₂×C₂₃×#125	C₂²	semidirect
26. C₂₃×#489	C₂²	semidirect
27. C₂₃×#488	C₂²	semidirect
28. C₂₃×#419	C₂²	semidirect
30. C₂×C₂₃×#103	C₂²	semidirect
32. C₄×M₁₆×C₂₃	C₂²	semidirect
33. C₂×C₂₃×#97	C₂²	semidirect
34. C₂×C₄×C₈×C₂₃	C₂²	semidirect
54. C₂₃×C₄⋊Q₈	C₂³	semidirect
56. C₂₃×#125	C₂³	semidirect
79. C₂₃×#103	C₂³	semidirect
81. C₂₃×#97	C₂³	semidirect
82. C₄×C₈×C₂₃	C₂³	semidirect
133. C₂×#3140	C₂₃	direct (N × H)
169. C₂×#533	C₂×C₂₃	semidirect
171. #3140	C₂×C₂₃	direct (N × H)
172. C₂×#489	C₂×C₂₃	semidirect
173. C₂×#488	C₂×C₂₃	semidirect
174. C₂×#419	C₂×C₂₃	semidirect
176. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
198. #533	C₂²×C₂₃	semidirect
199. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
200. C₂×#125	C₂²×C₂₃	semidirect
211. #489	C₂²×C₂₃	semidirect
212. #488	C₂²×C₂₃	semidirect
213. #419	C₂²×C₂₃	semidirect
215. C₂×#103	C₂²×C₂₃	semidirect
217. C₄×M₁₆	C₂²×C₂₃	semidirect
218. C₂×#97	C₂²×C₂₃	semidirect
219. C₂×C₄×C₈	C₂²×C₂₃	semidirect
222. C₂×C₂₃	#3140	direct (N × H)
244. C₄⋊Q₈	C₂³×C₂₃	semidirect
246. #125	C₂³×C₂₃	semidirect
269. #103	C₂³×C₂₃	semidirect
271. #97	C₂³×C₂₃	semidirect
272. C₄×C₈	C₂³×C₂₃	semidirect
273. C₂₃	C₂×#3140	direct (N × H)
378. C₂	C₂₃×#3140	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#533	2
C₂²×C₂₃×#124	2
C₂₃×#3140	2
C₂×C₂₃×#489	2
C₂×C₂₃×#488	2
C₂×C₂₃×#419	2
C₂×C₂₃×#418	2
C₂×C₄×M₁₆×C₂₃	2
C₂×#3140	23

Subgroups — C2×C23×#3140 #19208241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3140 #19208241