Subgroups — C₂₃×#21556 #19169182

Order 5888.

874 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#473	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂₃×#137	C₂	1	2	yes	maximal
3	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2875	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1930	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1908	C₂	1	2	yes	maximal
9	C₂₃×#1815	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂₃×#101	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×#137	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
16	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
18	C₂₃×#473	C₄	1	8	yes	complemented
19	C₂₃×#441	—	2	1	no	—
20	C₂₃×#441	—	2	1	no	—
21	C₂₃×#441	—	2	1	no	—
22	C₂₃×#441	—	2	1	no	—
23	C₂₃×#441	—	2	2	no	—
24	C₂₃×#440	—	2	2	no	—
25	C₄×Q₁₆×C₂₃	—	2	2	no	—
26	C₄×SD₁₆×C₂₃	—	2	2	no	—
27	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
29	C₂₃×#428	C₂²	1	2	yes	—
30	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
31	C₂₃×#419	C₂²	1	2	yes	—
32	C₂₃×#417	C₂²	1	2	yes	—
33	C₂×C₂₃×#103	C₂²	1	2	yes	—
34	C₂×C₂₃×#101	C₂²	1	2	yes	—
35	C₂×C₂₃×#101	C₂²	1	2	yes	—
36	C₂₃×#405	—	2	1	no	—
37	C₂₃×#405	—	2	1	no	—
38	C₂₃×#405	C₂²	1	1	yes	characteristic
39	C₂₃×#405	C₂²	1	1	yes	characteristic
40	C₄×M₁₆×C₂₃	—	2	1	no	—
41	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
42	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#97	—	2	1	no	—
44	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
45	C₂₃×#343	C₂²	1	2	yes	—
46	C₂₃×#343	C₂²	1	2	yes	—
47	C₂₃×#341	C₂²	1	2	yes	—
48	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
50	C₂₃×#137	—	2	4	no	—
51	C₂₃×#137	C₂×C₄	1	8	yes	—
52	C₂×Q₁₆×C₂₃	—	2	2	no	—
53	C₂×Q₁₆×C₂₃	—	2	1	no	—
54	C₂×Q₁₆×C₂₃	—	2	1	no	—
55	C₂×Q₁₆×C₂₃	—	2	2	no	—
56	C₂×Q₁₆×C₂₃	C₂×C₄	1	4	yes	complemented
57	C₂×SD₁₆×C₂₃	—	2	2	no	—
58	C₂₃×#131	—	2	2	no	—
59	C₂₃×#131	—	2	2	no	—
60	C₂₃×#131	—	2	2	no	—
61	C₂₃×#131	C₂×C₄	1	4	yes	—
62	C₂×M₁₆×C₂₃	—	2	1	no	—
63	C₂×M₁₆×C₂₃	—	2	1	no	—
64	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
65	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
67	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₂₃	—	2	1	no	—
69	C₂²×C₈×C₂₃	—	2	1	no	—
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₄×Q₈×C₂₃	—	2	2	no	—
73	C₄×Q₈×C₂₃	—	2	2	no	—
74	C₄×Q₈×C₂₃	—	2	2	no	—
75	C₄×Q₈×C₂₃	—	2	2	no	—
76	C₄×Q₈×C₂₃	D₄	1	2	yes	—
77	C₄×D₄×C₂₃	—	2	2	no	—
78	C₄×D₄×C₂₃	D₄	1	2	yes	—
79	C₂₃×#117	—	2	1	no	—
80	C₂₃×#117	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₂₃	—	2	1	no	—
84	C₂×C₄²×C₂₃	—	2	2	no	—
85	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
86	C₂₃×#108	—	2	2	no	—
87	C₂₃×#108	C₂×C₄	1	4	yes	complemented
88	C₂₃×#107	—	2	2	no	—
89	C₂₃×#106	—	2	1	no	—
90	C₂₃×#106	—	2	1	no	—
91	C₂₃×#106	—	2	2	no	—
92	C₂₃×#103	—	2	2	no	—
93	C₂₃×#103	—	2	2	no	—
94	C₂₃×#103	—	2	2	no	—
95	C₂₃×#103	—	2	2	no	—
96	C₂₃×#103	—	2	2	no	—
97	C₂₃×#102	—	2	2	no	—
98	C₂₃×#101	—	2	4	no	—
99	C₂₃×#101	C₂×C₄	1	8	yes	complemented
100	C₂₃×#97	—	2	1	no	—
101	C₂₃×#97	—	2	1	no	—
102	C₂₃×#97	—	2	1	no	—
103	C₂₃×#97	—	2	2	no	—
104	C₂₃×#97	D₄	1	1	yes	characteristic
105	C₂₃×#97	D₄	1	1	yes	characteristic
106	C₂₃×#97	D₄	1	1	yes	characteristic
107	C₂₃×#97	D₄	1	1	yes	characteristic
108	C₄×C₈×C₂₃	—	2	1	no	—
109	C₄×C₈×C₂₃	—	2	1	no	—
110	C₄×C₈×C₂₃	—	2	1	no	—
111	C₄×C₈×C₂₃	—	2	2	no	—
112	#41×C₂₃	—	2	1	no	—
113	#41×C₂₃	—	2	1	no	—
114	#41×C₂₃	C₂²×C₄	1	2	yes	—
115	#41×C₂₃	#41	1	2	yes	—
116	C₂×Q₈×C₂₃	—	2	2	no	—
117	C₂×Q₈×C₂₃	—	2	2	no	—
118	C₂×Q₈×C₂₃	—	2	2	no	—
119	C₂×Q₈×C₂₃	—	2	2	no	—
120	C₂×Q₈×C₂₃	—	2	2	no	—
121	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
122	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₂₃	—	2	1	no	—
124	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	—	2	1	no	—
126	C₂²×C₄×C₂₃	—	2	2	no	—
127	C₂²×C₄×C₂₃	—	2	2	no	—
128	C₂²×C₄×C₂₃	—	2	2	no	—
129	C₂²×C₄×C₂₃	#41	1	2	yes	—
130	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₂₃	—	2	8	no	—
132	Q₁₆×C₂₃	—	2	4	no	—
133	Q₁₆×C₂₃	—	2	4	no	—
134	SD₁₆×C₂₃	—	2	8	no	—
135	M₁₆×C₂₃	—	2	4	no	—
136	M₁₆×C₂₃	—	2	1	no	—
137	M₁₆×C₂₃	—	2	1	no	—
138	M₁₆×C₂₃	—	2	2	no	—
139	M₁₆×C₂₃	—	2	4	no	—
140	M₁₆×C₂₃	—	2	2	no	—
141	M₁₆×C₂₃	—	2	2	no	—
142	M₁₆×C₂₃	C₂²×C₄	1	2	yes	—
143	M₁₆×C₂₃	C₂²×C₄	1	4	yes	—
144	M₁₆×C₂₃	#41	1	2	yes	—
145	C₂×C₈×C₂₃	—	2	4	no	—
146	C₂×C₈×C₂₃	—	2	2	no	—
147	C₂×C₈×C₂₃	—	2	1	no	—
148	C₂×C₈×C₂₃	—	2	1	no	—
149	C₂×C₈×C₂₃	—	2	1	no	—
150	C₂×C₈×C₂₃	—	2	1	no	—
151	C₂×C₈×C₂₃	—	2	4	no	—
152	C₂×C₈×C₂₃	—	2	2	no	—
153	C₂×C₈×C₂₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₂₃	#41	1	2	yes	—
159	C₄⋊C₄×C₂₃	—	2	2	no	—
160	C₄⋊C₄×C₂₃	—	2	2	no	—
161	C₄⋊C₄×C₂₃	—	2	2	no	—
162	C₄⋊C₄×C₂₃	—	4	2	no	—
163	C₄⋊C₄×C₂₃	—	4	2	no	—
164	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₂₃	—	2	1	no	—
166	C₂²⋊C₄×C₂₃	—	2	2	no	—
167	C₄²×C₂₃	—	2	2	no	—
168	C₄²×C₂₃	—	2	1	no	—
169	C₄²×C₂₃	—	4	2	no	—
170	C₄²×C₂₃	—	4	2	no	—
171	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₂₃	C₂×D₄	1	2	yes	—
174	#21556	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂³×C₂₃	—	2	1	no	—
176	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
177	Q₈×C₂₃	—	2	1	no	—
178	Q₈×C₂₃	—	2	4	no	—
179	Q₈×C₂₃	—	2	4	no	—
180	Q₈×C₂₃	—	4	2	no	—
181	Q₈×C₂₃	—	4	2	no	—
182	Q₈×C₂₃	C₄×D₄	1	2	yes	—
183	D₄×C₂₃	—	2	2	no	—
184	D₄×C₂₃	—	2	2	no	—
185	D₄×C₂₃	—	2	1	no	—
186	D₄×C₂₃	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₂₃	—	2	1	no	—
188	C₂×C₄×C₂₃	—	2	2	no	—
189	C₂×C₄×C₂₃	—	2	2	no	—
190	C₂×C₄×C₂₃	—	2	4	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	4	2	no	—
193	C₂×C₄×C₂₃	—	4	2	no	—
194	C₂×C₄×C₂₃	—	4	2	no	—
195	C₂×C₄×C₂₃	—	4	2	no	—
196	C₂×C₄×C₂₃	—	8	2	no	—
197	C₂×C₄×C₂₃	—	8	2	no	—
198	C₂×C₄×C₂₃	#121	1	2	yes	—
199	C₂×C₄×C₂₃	#121	1	2	yes	—
200	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
206	C₈×C₂₃	—	2	2	no	—
207	C₈×C₂₃	—	2	4	no	—
208	C₈×C₂₃	—	2	1	no	—
209	C₈×C₂₃	—	2	2	no	—
210	C₈×C₂₃	—	2	1	no	—
211	C₈×C₂₃	—	4	2	no	—
212	C₈×C₂₃	C₄×D₄	1	2	yes	—
213	C₈×C₂₃	C₄×D₄	1	2	yes	—
214	C₂×#473	C₂×C₂₃	1	1	yes	characteristic
215	C₄×#137	C₂×C₂₃	1	2	yes	—
216	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
217	#2875	C₂×C₂₃	1	1	yes	characteristic
218	#1979	C₂×C₂₃	1	1	yes	characteristic, complemented
219	#1951	C₂×C₂₃	1	1	yes	characteristic, complemented
220	#1930	C₂×C₂₃	1	2	yes	complemented
221	#1908	C₂×C₂₃	1	2	yes	—
222	#1815	C₂×C₂₃	1	1	yes	characteristic
223	#1778	C₂×C₂₃	1	1	yes	characteristic, complemented
224	C₄×#101	C₂×C₂₃	1	2	yes	complemented
225	C₂²×C₂₃	—	2	2	no	—
226	C₂²×C₂₃	—	2	2	no	—
227	C₂²×C₂₃	—	4	2	no	—
228	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
229	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
230	C₂²×C₂₃	#529	1	1	yes	characteristic
231	C₄×C₂₃	—	2	2	no	—
232	C₄×C₂₃	—	2	2	no	—
233	C₄×C₂₃	—	2	2	no	—
234	C₄×C₂₃	—	4	4	no	—
235	C₄×C₂₃	—	4	2	no	—
236	C₄×C₂₃	—	8	2	no	—
237	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₂₃	#525	1	1	yes	characteristic
240	C₄×C₂₃	#532	1	1	yes	characteristic
241	C₂×#137	C₂²×C₂₃	1	2	yes	—
242	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
243	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
244	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
245	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
247	#473	C₄×C₂₃	1	8	yes	complemented
248	#441	—	2	2	no	—
249	#441	—	2	1	no	—
250	#441	—	2	1	no	—
251	#441	—	2	1	no	—
252	#441	—	2	1	no	—
253	#440	—	2	2	no	—
254	C₄×Q₁₆	—	2	2	no	—
255	C₄×SD₁₆	—	2	2	no	—
256	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
257	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
258	#428	C₂²×C₂₃	1	2	yes	—
259	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
260	#419	C₂²×C₂₃	1	2	yes	—
261	#417	C₂²×C₂₃	1	2	yes	—
262	C₂×#103	C₂²×C₂₃	1	2	yes	—
263	C₂×#101	C₂²×C₂₃	1	2	yes	—
264	C₂×#101	C₂²×C₂₃	1	2	yes	—
265	#405	—	2	1	no	—
266	#405	—	2	1	no	—
267	#405	C₂²×C₂₃	1	1	yes	characteristic
268	#405	C₂²×C₂₃	1	1	yes	characteristic
269	C₄×M₁₆	—	2	1	no	—
270	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
271	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
272	C₂×#97	—	2	1	no	—
273	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
274	#343	C₂²×C₂₃	1	2	yes	—
275	#343	C₂²×C₂₃	1	2	yes	—
276	#341	C₂²×C₂₃	1	2	yes	—
277	C₂×C₂₃	—	2	1	no	—
278	C₂×C₂₃	—	2	1	no	—
279	C₂×C₂₃	—	4	2	no	—
280	C₂×C₂₃	C₄×#121	1	1	yes	characteristic
281	C₂×C₂₃	#3069	1	2	yes	—
282	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
283	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
284	#137	—	2	4	no	—
285	#137	C₂×C₄×C₂₃	1	8	yes	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	2	1	no	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×Q₁₆	C₂×C₄×C₂₃	1	4	yes	complemented
291	C₂×SD₁₆	—	2	2	no	—
292	#131	—	2	2	no	—
293	#131	—	2	2	no	—
294	#131	—	2	2	no	—
295	#131	C₂×C₄×C₂₃	1	4	yes	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
299	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
300	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
301	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	D₄×C₂₃	1	2	yes	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	D₄×C₂₃	1	2	yes	—
313	#117	—	2	1	no	—
314	#117	C₂³×C₂₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
320	#108	—	2	2	no	—
321	#108	C₂×C₄×C₂₃	1	4	yes	complemented
322	#107	—	2	2	no	—
323	#106	—	2	1	no	—
324	#106	—	2	1	no	—
325	#106	—	2	2	no	—
326	#103	—	2	2	no	—
327	#103	—	2	2	no	—
328	#103	—	2	2	no	—
329	#103	—	2	2	no	—
330	#103	—	2	2	no	—
331	#102	—	2	2	no	—
332	#101	—	2	4	no	—
333	#101	C₂×C₄×C₂₃	1	8	yes	complemented
334	#97	—	2	1	no	—
335	#97	—	2	1	no	—
336	#97	—	2	1	no	—
337	#97	—	2	2	no	—
338	#97	D₄×C₂₃	1	1	yes	characteristic
339	#97	D₄×C₂₃	1	1	yes	characteristic
340	#97	D₄×C₂₃	1	1	yes	characteristic
341	#97	D₄×C₂₃	1	1	yes	characteristic
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	2	2	no	—
346	C₂₃	#21556	1	1	yes	characteristic, direct product factor, Sylow
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	C₂²×C₄×C₂₃	1	2	yes	—
350	#41	#41×C₂₃	1	2	yes	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
357	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	#41×C₂₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
366	Q₁₆	—	2	8	no	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	—	2	4	no	—
369	SD₁₆	—	2	8	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	C₂²×C₄×C₂₃	1	2	yes	—
378	M₁₆	C₂²×C₄×C₂₃	1	4	yes	—
379	M₁₆	#41×C₂₃	1	2	yes	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	C₂²×C₄×C₂₃	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
392	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
393	C₂×C₈	#41×C₂₃	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	4	2	no	—
405	C₄²	—	4	2	no	—
406	C₄²	C₂×D₄×C₂₃	1	2	yes	—
407	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
408	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
411	Q₈	—	2	1	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	C₄×D₄×C₂₃	1	2	yes	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	1	no	—
420	D₄	C₄×D₄×C₂₃	1	2	yes	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	C₂₃×#121	1	2	yes	—
433	C₂×C₄	C₂₃×#121	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	2	4	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	1	no	—
445	C₈	—	4	2	no	—
446	C₈	C₄×D₄×C₂₃	1	2	yes	—
447	C₈	C₄×D₄×C₂₃	1	2	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
452	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
453	C₂²	C₂₃×#529	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
461	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
462	C₄	C₂₃×#525	1	1	yes	characteristic
463	C₄	C₂₃×#532	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	4	2	no	—
467	C₂	C₄×C₂₃×#121	1	1	yes	characteristic
468	C₂	C₂₃×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×#41×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₂₃×#441	C₂	semidirect
5. C₂₃×#1979	C₂	semidirect
6. C₂₃×#1951	C₂	semidirect
7. C₂₃×#1930	C₂	semidirect
10. C₂₃×#1778	C₂	semidirect
11. C₄×C₂₃×#101	C₂	semidirect
18. C₂₃×#473	C₄	semidirect
56. C₂×Q₁₆×C₂₃	C₂×C₄	semidirect
87. C₂₃×#108	C₂×C₄	semidirect
99. C₂₃×#101	C₂×C₄	semidirect
174. #21556	C₂₃	direct (N × H)
216. C₂×#441	C₂×C₂₃	semidirect
218. #1979	C₂×C₂₃	semidirect
219. #1951	C₂×C₂₃	semidirect
220. #1930	C₂×C₂₃	semidirect
223. #1778	C₂×C₂₃	semidirect
224. C₄×#101	C₂×C₂₃	semidirect
247. #473	C₄×C₂₃	semidirect
290. C₂×Q₁₆	C₂×C₄×C₂₃	semidirect
321. #108	C₂×C₄×C₂₃	semidirect
333. #101	C₂×C₄×C₂₃	semidirect
346. C₂₃	#21556	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×#473	2
C₄×C₂₃×#137	2
C₂×C₂₃×#441	2
C₂₃×#2875	2
C₂₃×#1979	2
C₂₃×#1951	2
C₂₃×#1930	2
C₂₃×#1908	2
C₂₃×#1815	2
C₂₃×#1778	2
C₄×C₂₃×#101	2
#21556	23

Subgroups — C23×#21556 #19169182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21556 #19169182