Subgroups — C₄×C₂₃×#488 #19169268

Order 5888.

858 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	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂₃×#124	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1958	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1934	C₂	1	2	yes	maximal
7	C₂₃×#1933	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂₃×#103	C₂	1	2	yes	maximal, complemented
10	C₄×C₂₃×#102	C₂	1	2	yes	maximal
11	C₄²×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
13	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#488	C₄	1	8	yes	direct product factor
17	C₂×C₂₃×#103	C₂²	1	2	yes	—
18	C₂×C₂₃×#103	C₂²	1	2	yes	—
19	C₂×C₂₃×#102	C₂²	1	2	yes	—
20	C₂×C₂₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#391	C₂²	1	1	yes	characteristic
26	C₂₃×#390	C₂²	1	1	yes	characteristic
27	C₂₃×#389	C₂²	1	2	yes	—
28	C₂₃×#388	—	2	2	no	—
29	C₂₃×#387	—	2	2	no	—
30	C₂₃×#382	C₂²	1	1	yes	characteristic
31	C₂₃×#382	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₂₃	—	2	2	no	—
33	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
34	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
35	C₄³×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#340	C₂²	1	2	yes	—
37	C₂₃×#340	C₂²	1	2	yes	—
38	C₂₃×#340	C₂²	1	2	yes	—
39	C₂₃×#340	C₂²	1	2	yes	—
40	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₂₃	—	2	1	no	—
43	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
45	C₂₃×#125	—	2	2	no	—
46	C₂₃×#125	C₂×C₄	1	4	yes	complemented
47	C₂₃×#124	—	2	2	no	—
48	C₂₃×#124	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₂₃	—	2	4	no	—
50	C₄×D₄×C₂₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
53	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
61	C₂×C₄²×C₂₃	—	2	1	no	—
62	C₂×C₄²×C₂₃	—	2	2	no	—
63	C₂×C₄²×C₂₃	D₄	1	2	yes	—
64	C₂×C₄²×C₂₃	D₄	1	2	yes	—
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
68	C₂₃×#103	—	2	4	no	—
69	C₂₃×#103	C₂×C₄	1	8	yes	complemented
70	C₂₃×#102	—	2	4	no	—
71	C₂₃×#102	C₂×C₄	1	8	yes	—
72	C₄×C₈×C₂₃	—	2	4	no	—
73	C₄×C₈×C₂₃	—	2	2	no	—
74	C₄×C₈×C₂₃	—	2	4	no	—
75	C₄×C₈×C₂₃	C₂×C₄	1	4	yes	complemented
76	C₂₃×#95	—	2	2	no	—
77	C₂₃×#95	—	2	2	no	—
78	C₂₃×#95	—	2	2	no	—
79	C₂₃×#95	—	2	2	no	—
80	C₂₃×#95	—	2	2	no	—
81	C₂⁴×C₂₃	—	2	1	no	—
82	C₂×Q₈×C₂₃	—	2	1	no	—
83	C₂×Q₈×C₂₃	—	2	2	no	—
84	C₂×Q₈×C₂₃	—	2	2	no	—
85	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
86	C₂×D₄×C₂₃	—	2	2	no	—
87	C₂×D₄×C₂₃	—	2	2	no	—
88	C₂×D₄×C₂₃	—	2	1	no	—
89	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₂₃	—	2	1	no	—
91	C₂²×C₄×C₂₃	—	2	2	no	—
92	C₂²×C₄×C₂₃	—	2	1	no	—
93	C₂²×C₄×C₂₃	—	2	2	no	—
94	C₂²×C₄×C₂₃	—	2	1	no	—
95	C₂²×C₄×C₂₃	—	4	2	no	—
96	C₂²×C₄×C₂₃	—	4	4	no	—
97	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₂₃	—	2	2	no	—
103	C₂×C₈×C₂₃	—	2	2	no	—
104	C₂×C₈×C₂₃	—	2	2	no	—
105	C₂×C₈×C₂₃	—	2	2	no	—
106	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₂₃	#41	1	4	yes	—
108	C₄⋊C₄×C₂₃	—	2	8	no	—
109	C₄⋊C₄×C₂₃	—	2	2	no	—
110	C₄⋊C₄×C₂₃	—	2	2	no	—
111	C₄⋊C₄×C₂₃	—	2	2	no	—
112	C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₄⋊C₄×C₂₃	—	2	2	no	—
114	C₄⋊C₄×C₂₃	—	4	2	no	—
115	C₄⋊C₄×C₂₃	—	4	4	no	—
116	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
117	C₂²⋊C₄×C₂₃	—	2	8	no	—
118	C₂²⋊C₄×C₂₃	—	4	2	no	—
119	C₂²⋊C₄×C₂₃	—	4	4	no	—
120	C₄²×C₂₃	—	2	4	no	—
121	C₄²×C₂₃	—	2	4	no	—
122	C₄²×C₂₃	—	2	2	no	—
123	C₄²×C₂₃	—	4	2	no	—
124	C₄²×C₂₃	—	4	4	no	—
125	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₂₃	#41	1	2	yes	—
127	C₄²×C₂₃	#41	1	4	yes	—
128	C₄×#488	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂³×C₂₃	—	2	2	no	—
130	C₂³×C₂₃	—	4	1	no	—
131	C₂³×C₂₃	—	4	1	no	—
132	C₂³×C₂₃	—	4	2	no	—
133	C₂³×C₂₃	—	4	2	no	—
134	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₂₃	—	2	4	no	—
136	Q₈×C₂₃	—	4	2	no	—
137	D₄×C₂₃	—	2	4	no	—
138	D₄×C₂₃	—	4	2	no	—
139	C₂×C₄×C₂₃	—	2	2	no	—
140	C₂×C₄×C₂₃	—	2	2	no	—
141	C₂×C₄×C₂₃	—	2	2	no	—
142	C₂×C₄×C₂₃	—	2	2	no	—
143	C₂×C₄×C₂₃	—	2	2	no	—
144	C₂×C₄×C₂₃	—	2	2	no	—
145	C₂×C₄×C₂₃	—	2	4	no	—
146	C₂×C₄×C₂₃	—	4	1	no	—
147	C₂×C₄×C₂₃	—	4	1	no	—
148	C₂×C₄×C₂₃	—	4	2	no	—
149	C₂×C₄×C₂₃	—	4	2	no	—
150	C₂×C₄×C₂₃	—	4	1	no	—
151	C₂×C₄×C₂₃	—	4	1	no	—
152	C₂×C₄×C₂₃	—	4	2	no	—
153	C₂×C₄×C₂₃	—	4	2	no	—
154	C₂×C₄×C₂₃	—	4	2	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	—	8	4	no	—
158	C₂×C₄×C₂₃	C₄×D₄	1	4	yes	—
159	C₂×C₄×C₂₃	#124	1	2	yes	—
160	C₂×C₄×C₂₃	#124	1	2	yes	—
161	C₂×C₄×C₂₃	#135	1	4	yes	—
162	C₂×C₄×C₂₃	#135	1	4	yes	—
163	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
165	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
166	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
167	C₈×C₂₃	—	2	4	no	—
168	C₈×C₂₃	—	2	4	no	—
169	C₂×#488	C₂×C₂₃	1	1	yes	characteristic
170	C₄×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
171	C₄×#124	C₂×C₂₃	1	1	yes	characteristic
172	#1991	C₂×C₂₃	1	1	yes	characteristic, complemented
173	#1958	C₂×C₂₃	1	1	yes	characteristic
174	#1934	C₂×C₂₃	1	2	yes	—
175	#1933	C₂×C₂₃	1	2	yes	complemented
176	#1835	C₂×C₂₃	1	1	yes	characteristic, complemented
177	C₄×#103	C₂×C₂₃	1	2	yes	complemented
178	C₄×#102	C₂×C₂₃	1	2	yes	—
179	C₄²×C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
180	C₂²×C₂₃	—	4	4	no	—
181	C₂²×C₂₃	—	4	2	no	—
182	C₂²×C₂₃	—	8	1	no	—
183	C₂²×C₂₃	—	8	1	no	—
184	C₂²×C₂₃	—	8	2	no	—
185	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₂₃	C₂×#124	1	1	yes	characteristic
187	C₂²×C₂₃	#532	1	1	yes	characteristic
188	C₂²×C₂₃	C₂×#135	1	2	yes	—
189	C₂²×C₂₃	C₂×#135	1	2	yes	—
190	C₄×C₂₃	—	2	2	no	—
191	C₄×C₂₃	—	2	4	no	—
192	C₄×C₂₃	—	2	4	no	—
193	C₄×C₂₃	—	4	4	no	—
194	C₄×C₂₃	—	4	2	no	—
195	C₄×C₂₃	—	8	1	no	—
196	C₄×C₂₃	—	8	1	no	—
197	C₄×C₂₃	—	8	2	no	—
198	C₄×C₂₃	#488	1	4	yes	direct product factor
199	C₄×C₂₃	C₄×#41	1	2	yes	—
200	C₄×C₂₃	#529	1	2	yes	—
201	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
202	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
203	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
204	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
205	#488	C₄×C₂₃	1	8	yes	direct product factor
206	C₂×#103	C₂²×C₂₃	1	2	yes	—
207	C₂×#103	C₂²×C₂₃	1	2	yes	—
208	C₂×#102	C₂²×C₂₃	1	2	yes	—
209	C₂×#102	C₂²×C₂₃	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
211	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	—
213	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
214	#391	C₂²×C₂₃	1	1	yes	characteristic
215	#390	C₂²×C₂₃	1	1	yes	characteristic
216	#389	C₂²×C₂₃	1	2	yes	—
217	#388	—	2	2	no	—
218	#387	—	2	2	no	—
219	#382	C₂²×C₂₃	1	1	yes	characteristic
220	#382	C₂²×C₂₃	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	2	2	no	—
222	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
223	C₄×C₂²⋊C₄	—	2	2	no	—
224	C₄³	C₂²×C₂₃	1	1	yes	characteristic
225	#340	C₂²×C₂₃	1	2	yes	—
226	#340	C₂²×C₂₃	1	2	yes	—
227	#340	C₂²×C₂₃	1	2	yes	—
228	#340	C₂²×C₂₃	1	2	yes	—
229	C₂×C₂₃	—	8	2	no	—
230	C₂×C₂₃	C₄×#124	1	1	yes	characteristic
231	C₂×C₂₃	C₄×#135	1	2	yes	—
232	C₂×C₂₃	C₂×#488	1	1	yes	characteristic
233	C₂×C₂₃	#3131	1	1	yes	characteristic
234	C₂×C₂₃	#3168	1	2	yes	—
235	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
236	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
237	C₂³×C₄	—	2	1	no	—
238	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
239	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
240	#125	—	2	2	no	—
241	#125	C₂×C₄×C₂₃	1	4	yes	complemented
242	#124	—	2	2	no	—
243	#124	C₂×C₄×C₂₃	1	4	yes	—
244	C₄×Q₈	—	2	4	no	—
245	C₄×D₄	—	2	4	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	D₄×C₂₃	1	2	yes	—
259	C₂×C₄²	D₄×C₂₃	1	2	yes	—
260	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
263	#103	—	2	4	no	—
264	#103	C₂×C₄×C₂₃	1	8	yes	complemented
265	#102	—	2	4	no	—
266	#102	C₂×C₄×C₂₃	1	8	yes	—
267	C₄×C₈	—	2	4	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	—	2	4	no	—
270	C₄×C₈	C₂×C₄×C₂₃	1	4	yes	complemented
271	#95	—	2	2	no	—
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	C₂₃	C₄×#488	1	1	yes	characteristic, direct product factor, Sylow
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
303	C₂×C₈	#41×C₂₃	1	4	yes	—
304	C₄⋊C₄	—	2	8	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	4	no	—
312	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
313	C₂²⋊C₄	—	2	8	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	4	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	4	no	—
321	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
322	C₄²	#41×C₂₃	1	2	yes	—
323	C₄²	#41×C₂₃	1	4	yes	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	4	2	no	—
332	D₄	—	2	4	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	4	no	—
353	C₂×C₄	C₄×D₄×C₂₃	1	4	yes	—
354	C₂×C₄	C₂₃×#124	1	2	yes	—
355	C₂×C₄	C₂₃×#124	1	2	yes	—
356	C₂×C₄	C₂₃×#135	1	4	yes	—
357	C₂×C₄	C₂₃×#135	1	4	yes	—
358	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
360	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
361	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
362	C₈	—	2	4	no	—
363	C₈	—	2	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
370	C₂²	C₂×C₂₃×#124	1	1	yes	characteristic
371	C₂²	C₂₃×#532	1	1	yes	characteristic
372	C₂²	C₂×C₂₃×#135	1	2	yes	—
373	C₂²	C₂×C₂₃×#135	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	4	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	1	no	—
381	C₄	—	8	1	no	—
382	C₄	C₂₃×#488	1	4	yes	direct product factor
383	C₄	C₄×#41×C₂₃	1	2	yes	—
384	C₄	C₂₃×#529	1	2	yes	—
385	C₂	—	8	2	no	—
386	C₂	C₄×C₂₃×#124	1	1	yes	characteristic
387	C₂	C₄×C₂₃×#135	1	2	yes	—
388	C₂	C₂×C₂₃×#488	1	1	yes	characteristic
389	C₂	C₂₃×#3131	1	1	yes	characteristic
390	C₂	C₂₃×#3168	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂²×D₄
prime radical	C₂²×D₄×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₄³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₂₃×#125	C₂	semidirect
4. C₂₃×#1991	C₂	semidirect
7. C₂₃×#1933	C₂	semidirect
8. C₂₃×#1835	C₂	semidirect
9. C₄×C₂₃×#103	C₂	semidirect
11. C₄²×C₈×C₂₃	C₂	semidirect
16. C₂₃×#488	C₄	direct (N × H)
46. C₂₃×#125	C₂×C₄	semidirect
69. C₂₃×#103	C₂×C₄	semidirect
75. C₄×C₈×C₂₃	C₂×C₄	semidirect
128. C₄×#488	C₂₃	direct (N × H)
170. C₄×#125	C₂×C₂₃	semidirect
172. #1991	C₂×C₂₃	semidirect
175. #1933	C₂×C₂₃	semidirect
176. #1835	C₂×C₂₃	semidirect
177. C₄×#103	C₂×C₂₃	semidirect
179. C₄²×C₈	C₂×C₂₃	semidirect
198. C₄×C₂₃	#488	direct (N × H)
205. #488	C₄×C₂₃	direct (N × H)
241. #125	C₂×C₄×C₂₃	semidirect
264. #103	C₂×C₄×C₂₃	semidirect
270. C₄×C₈	C₂×C₄×C₂₃	semidirect
276. C₂₃	C₄×#488	direct (N × H)
382. C₄	C₂₃×#488	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×#488	2
C₄×C₂₃×#125	2
C₄×C₂₃×#124	2
C₂₃×#1991	2
C₂₃×#1958	2
C₂₃×#1934	2
C₂₃×#1933	2
C₂₃×#1835	2
C₄×C₂₃×#103	2
C₄×C₂₃×#102	2
C₄²×C₈×C₂₃	2
C₄×#488	23

Subgroups — C4×C23×#488 #19169268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₃×#488 #19169268