Subgroups — C₂₃×#17959 #19165585

Order 5888.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2966	C₂	1	2	yes	maximal, complemented
3	C₂₃×#1591	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1590	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×SD₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
8	C₈×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1494	C₂	1	2	yes	maximal, complemented
11	C₂×C₈²×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#529	C₂²	1	2	yes	—
13	C₂₃×#499	C₄	1	1	yes	characteristic
14	C₂₃×#495	C₄	1	1	yes	characteristic
15	C₂₃×#488	C₄	1	2	yes	—
16	C₂₃×#467	C₄	1	1	yes	characteristic
17	C₂₃×#466	C₄	1	1	yes	characteristic
18	C₂₃×#465	C₄	1	2	yes	—
19	C₂₃×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
21	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
23	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#436	C₂²	1	2	yes	—
25	C₂₃×#435	—	2	2	no	—
26	C₈×D₄×C₂₃	—	2	2	no	—
27	C₈×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂₃×#433	—	2	2	no	—
29	C₂₃×#432	C₂²	1	2	yes	—
30	C₂₃×#405	—	2	2	no	—
31	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#335	C₂²	1	1	yes	characteristic
35	C₂₃×#335	C₂²	1	1	yes	characteristic
36	C₂₃×#334	C₂²	1	2	yes	—
37	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₂₃×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
40	C₂₃×D₄⋊C₈	C₂²	1	2	yes	—
41	C₈²×C₂₃	C₂²	1	1	yes	characteristic
42	C₈²×C₂₃	C₂²	1	1	yes	characteristic
43	C₈²×C₂₃	C₂²	1	1	yes	characteristic
44	C₈²×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₂₃	C₂×C₄	1	2	yes	—
47	C₂×D₈×C₂₃	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₂₃	—	2	2	no	—
49	C₂²×C₈×C₂₃	—	2	1	no	—
50	C₂²×C₈×C₂₃	—	2	2	no	—
51	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₂₃	D₄	1	1	yes	characteristic
55	C₂₃×#126	—	2	2	no	—
56	C₂₃×#125	C₂×C₄	1	2	yes	—
57	C₂₃×#124	C₂×C₄	1	2	yes	—
58	C₂₃×#123	—	2	2	no	—
59	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
60	C₂₃×#121	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
62	C₄×D₄×C₂₃	—	2	2	no	—
63	C₄×D₄×C₂₃	C₂³	1	2	yes	—
64	C₂₃×#117	—	2	2	no	—
65	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
66	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
67	C₂₃×#107	C₂×C₄	1	1	yes	characteristic
68	C₂₃×#106	C₂×C₄	1	2	yes	—
69	C₂₃×C₄⋊C₈	—	2	2	no	—
70	C₂₃×C₄⋊C₈	—	2	2	no	—
71	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
72	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
73	C₂₃×#103	C₂×C₄	1	2	yes	—
74	C₂₃×#103	C₂×C₄	1	2	yes	—
75	C₂₃×#102	C₂×C₄	1	2	yes	—
76	C₂₃×#102	C₂×C₄	1	2	yes	—
77	C₂₃×C₂²⋊C₈	—	2	2	no	—
78	C₂₃×C₂²⋊C₈	—	2	2	no	—
79	C₂₃×C₂²⋊C₈	—	2	2	no	—
80	C₂₃×#97	—	2	2	no	—
81	C₂₃×#97	—	2	2	no	—
82	C₄×C₈×C₂₃	—	2	2	no	—
83	C₄×C₈×C₂₃	—	2	1	no	—
84	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
86	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₂₃	D₄	1	1	yes	characteristic
88	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₂₃	—	2	2	no	—
96	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₂₃	—	2	2	no	—
98	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
101	Q₁₆×C₂₃	—	2	2	no	—
102	SD₁₆×C₂₃	—	2	4	no	—
103	D₈×C₂₃	—	2	2	no	—
104	M₁₆×C₂₃	—	4	4	no	—
105	C₂×C₈×C₂₃	—	2	4	no	—
106	C₂×C₈×C₂₃	—	2	1	no	—
107	C₂×C₈×C₂₃	—	2	1	no	—
108	C₂×C₈×C₂₃	—	2	2	no	—
109	C₂×C₈×C₂₃	—	2	2	no	—
110	C₂×C₈×C₂₃	—	2	2	no	—
111	C₂×C₈×C₂₃	—	2	2	no	—
112	C₂×C₈×C₂₃	—	2	2	no	—
113	C₂×C₈×C₂₃	—	2	2	no	—
114	C₂×C₈×C₂₃	—	4	4	no	—
115	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₄⋊C₄×C₂₃	—	2	2	no	—
124	C₄⋊C₄×C₂₃	—	2	2	no	—
125	C₄⋊C₄×C₂₃	—	2	2	no	—
126	C₄⋊C₄×C₂₃	—	2	2	no	—
127	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
129	C₂²⋊C₄×C₂₃	—	2	2	no	—
130	C₂²⋊C₄×C₂₃	—	2	2	no	—
131	C₂²⋊C₄×C₂₃	—	2	2	no	—
132	C₂²⋊C₄×C₂₃	—	2	2	no	—
133	C₂²⋊C₄×C₂₃	—	2	2	no	—
134	C₄²×C₂₃	—	2	2	no	—
135	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₂₃	#41	1	1	yes	characteristic
138	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
139	#17959	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₂₃	—	2	2	no	—
141	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₂₃	—	2	2	no	—
143	Q₈×C₂₃	—	2	2	no	—
144	D₄×C₂₃	—	2	2	no	—
145	D₄×C₂₃	—	2	2	no	—
146	D₄×C₂₃	—	4	4	no	—
147	C₂×C₄×C₂₃	—	2	2	no	—
148	C₂×C₄×C₂₃	—	2	1	no	—
149	C₂×C₄×C₂₃	—	2	1	no	—
150	C₂×C₄×C₂₃	—	2	1	no	—
151	C₂×C₄×C₂₃	—	2	1	no	—
152	C₂×C₄×C₂₃	—	2	2	no	—
153	C₂×C₄×C₂₃	—	2	2	no	—
154	C₂×C₄×C₂₃	—	2	2	no	—
155	C₂×C₄×C₂₃	—	4	2	no	—
156	C₂×C₄×C₂₃	—	4	2	no	—
157	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
163	C₈×C₂₃	—	2	2	no	—
164	C₈×C₂₃	—	2	2	no	—
165	C₈×C₂₃	—	2	1	no	—
166	C₈×C₂₃	—	2	1	no	—
167	C₈×C₂₃	—	2	1	no	—
168	C₈×C₂₃	—	2	1	no	—
169	C₈×C₂₃	—	4	2	no	—
170	C₈×C₂₃	—	4	2	no	—
171	C₈×C₂₃	#131	1	2	yes	—
172	C₈×C₂₃	#131	1	2	yes	—
173	C₈×C₂₃	#135	1	2	yes	—
174	C₈×C₂₃	#135	1	2	yes	—
175	#3168	C₂×C₂₃	1	1	yes	characteristic
176	#2966	C₂×C₂₃	1	2	yes	complemented
177	#1591	C₂×C₂₃	1	1	yes	characteristic, complemented
178	#1590	C₂×C₂₃	1	2	yes	complemented
179	#1589	C₂×C₂₃	1	1	yes	characteristic, complemented
180	C₈×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
181	C₈×SD₁₆	C₂×C₂₃	1	2	yes	complemented
182	C₈×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
183	#1568	C₂×C₂₃	1	1	yes	characteristic, complemented
184	#1494	C₂×C₂₃	1	2	yes	complemented
185	C₂×C₈²	C₂×C₂₃	1	1	yes	characteristic, complemented
186	C₂²×C₂₃	—	2	1	no	—
187	C₂²×C₂₃	—	2	1	no	—
188	C₂²×C₂₃	—	4	2	no	—
189	C₂²×C₂₃	—	4	2	no	—
190	C₂²×C₂₃	—	4	2	no	—
191	C₂²×C₂₃	#443	1	2	yes	—
192	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₂₃	—	2	1	no	—
194	C₄×C₂₃	—	2	1	no	—
195	C₄×C₂₃	—	2	1	no	—
196	C₄×C₂₃	—	2	1	no	—
197	C₄×C₂₃	—	4	2	no	—
198	C₄×C₂₃	—	4	2	no	—
199	C₄×C₂₃	—	4	2	no	—
200	C₄×C₂₃	C₂×#131	1	1	yes	characteristic
201	C₄×C₂₃	C₂×#131	1	1	yes	characteristic
202	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
203	C₄×C₂₃	C₂×#135	1	1	yes	characteristic
204	#529	C₂²×C₂₃	1	2	yes	—
205	#499	C₄×C₂₃	1	1	yes	characteristic
206	#495	C₄×C₂₃	1	1	yes	characteristic
207	#488	C₄×C₂₃	1	2	yes	—
208	#467	C₄×C₂₃	1	1	yes	characteristic
209	#466	C₄×C₂₃	1	1	yes	characteristic
210	#465	C₄×C₂₃	1	2	yes	—
211	#446	C₂²×C₂₃	1	2	yes	—
212	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
213	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
214	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
215	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
216	#436	C₂²×C₂₃	1	2	yes	—
217	#435	—	2	2	no	—
218	C₈×D₄	—	2	2	no	—
219	C₈×D₄	C₂²×C₂₃	1	2	yes	—
220	#433	—	2	2	no	—
221	#432	C₂²×C₂₃	1	2	yes	—
222	#405	—	2	2	no	—
223	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
226	#335	C₂²×C₂₃	1	1	yes	characteristic
227	#335	C₂²×C₂₃	1	1	yes	characteristic
228	#334	C₂²×C₂₃	1	2	yes	—
229	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
230	Q₈⋊C₈	C₂²×C₂₃	1	2	yes	—
231	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
232	D₄⋊C₈	C₂²×C₂₃	1	2	yes	—
233	C₈²	C₂²×C₂₃	1	1	yes	characteristic
234	C₈²	C₂²×C₂₃	1	1	yes	characteristic
235	C₈²	C₂²×C₂₃	1	1	yes	characteristic
236	C₈²	C₂²×C₂₃	1	1	yes	characteristic
237	C₂×C₂₃	—	2	2	no	—
238	C₂×C₂₃	—	8	2	no	—
239	C₂×C₂₃	#2931	1	1	yes	characteristic
240	C₂×C₂₃	C₄×#135	1	1	yes	characteristic
241	C₂×C₂₃	C₂×#443	1	1	yes	characteristic
242	C₂×Q₁₆	C₂×C₄×C₂₃	1	1	yes	characteristic
243	C₂×SD₁₆	C₂×C₄×C₂₃	1	2	yes	—
244	C₂×D₈	C₂×C₄×C₂₃	1	1	yes	characteristic
245	C₂×M₁₆	—	2	2	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
249	C₂²×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
250	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₂₃	1	1	yes	characteristic
252	#126	—	2	2	no	—
253	#125	C₂×C₄×C₂₃	1	2	yes	—
254	#124	C₂×C₄×C₂₃	1	2	yes	—
255	#123	—	2	2	no	—
256	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
257	#121	C₂×C₄×C₂₃	1	2	yes	—
258	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	C₂³×C₂₃	1	2	yes	—
261	#117	—	2	2	no	—
262	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
263	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
264	#107	C₂×C₄×C₂₃	1	1	yes	characteristic
265	#106	C₂×C₄×C₂₃	1	2	yes	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
269	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
270	#103	C₂×C₄×C₂₃	1	2	yes	—
271	#103	C₂×C₄×C₂₃	1	2	yes	—
272	#102	C₂×C₄×C₂₃	1	2	yes	—
273	#102	C₂×C₄×C₂₃	1	2	yes	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₂²⋊C₈	—	2	2	no	—
277	#97	—	2	2	no	—
278	#97	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
282	C₄×C₈	C₂×C₄×C₂₃	1	1	yes	characteristic
283	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
284	C₄×C₈	D₄×C₂₃	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
291	C₂₃	#17959	1	1	yes	characteristic, direct product factor, Sylow
292	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
298	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
299	Q₁₆	—	2	2	no	—
300	SD₁₆	—	2	4	no	—
301	D₈	—	2	2	no	—
302	M₁₆	—	4	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
314	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
315	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
316	C₂×C₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
326	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
335	C₄²	#41×C₂₃	1	1	yes	characteristic
336	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	D₄	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	4	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
355	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
356	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
357	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	4	2	no	—
367	C₈	—	4	2	no	—
368	C₈	C₂₃×#131	1	2	yes	—
369	C₈	C₂₃×#131	1	2	yes	—
370	C₈	C₂₃×#135	1	2	yes	—
371	C₈	C₂₃×#135	1	2	yes	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	4	2	no	—
377	C₂²	C₂₃×#443	1	2	yes	—
378	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	C₂×C₂₃×#131	1	1	yes	characteristic
387	C₄	C₂×C₂₃×#131	1	1	yes	characteristic
388	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
389	C₄	C₂×C₂₃×#135	1	1	yes	characteristic
390	C₂	—	2	2	no	—
391	C₂	—	8	2	no	—
392	C₂	C₂₃×#2931	1	1	yes	characteristic
393	C₂	C₄×C₂₃×#135	1	1	yes	characteristic
394	C₂	C₂×C₂₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₂₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₄²	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂₃×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂×C₄×C₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2966	C₂	semidirect
3. C₂₃×#1591	C₂	semidirect
4. C₂₃×#1590	C₂	semidirect
5. C₂₃×#1589	C₂	semidirect
6. C₈×Q₁₆×C₂₃	C₂	semidirect
7. C₈×SD₁₆×C₂₃	C₂	semidirect
8. C₈×D₈×C₂₃	C₂	semidirect
9. C₂₃×#1568	C₂	semidirect
10. C₂₃×#1494	C₂	semidirect
11. C₂×C₈²×C₂₃	C₂	semidirect
139. #17959	C₂₃	direct (N × H)
176. #2966	C₂×C₂₃	semidirect
177. #1591	C₂×C₂₃	semidirect
178. #1590	C₂×C₂₃	semidirect
179. #1589	C₂×C₂₃	semidirect
180. C₈×Q₁₆	C₂×C₂₃	semidirect
181. C₈×SD₁₆	C₂×C₂₃	semidirect
182. C₈×D₈	C₂×C₂₃	semidirect
183. #1568	C₂×C₂₃	semidirect
184. #1494	C₂×C₂₃	semidirect
185. C₂×C₈²	C₂×C₂₃	semidirect
291. C₂₃	#17959	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3168	2
C₂₃×#2966	2
C₂₃×#1591	2
C₂₃×#1590	2
C₂₃×#1589	2
C₈×Q₁₆×C₂₃	2
C₈×SD₁₆×C₂₃	2
C₈×D₈×C₂₃	2
C₂₃×#1568	2
C₂₃×#1494	2
C₂×C₈²×C₂₃	2
#17959	23

Subgroups — C23×#17959 #19165585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17959 #19165585