Subgroups — C₂₃×#21099 #19168725

Order 5888.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#104	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2879	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1938	C₂	1	4	yes	maximal, complemented
7	C₂₃×#1937	C₂	1	4	yes	maximal, complemented
8	C₂₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
17	C₂₃×#424	—	2	2	no	—
18	C₂₃×#424	C₂²	1	4	yes	complemented
19	C₂₃×#423	—	2	2	no	—
20	C₂×C₂₃×#104	—	2	4	no	—
21	C₂×C₂₃×#104	C₂²	1	2	yes	—
22	C₂×C₂₃×#104	C₂²	1	2	yes	—
23	C₂₃×#419	C₄	1	2	yes	complemented
24	C₂₃×#418	C₄	1	2	yes	complemented
25	C₂₃×#417	C₄	1	4	yes	complemented
26	C₂₃×#416	C₂²	1	4	yes	—
27	C₂₃×#408	—	2	2	no	—
28	C₂₃×#408	C₂²	1	4	yes	—
29	C₂₃×#407	—	2	2	no	—
30	C₄×M₁₆×C₂₃	—	2	4	no	—
31	C₂×C₂₃×#97	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
33	C₂₃×#341	C₂²	1	4	yes	complemented
34	C₂₃×#339	C₂²	1	2	yes	complemented
35	C₂₃×#339	C₂²	1	2	yes	complemented
36	C₂×#41×C₂₃	—	2	1	no	—
37	C₂×#41×C₂₃	—	2	1	no	—
38	C₂×#41×C₂₃	—	2	2	no	—
39	C₂×#41×C₂₃	—	2	2	no	—
40	C₂×#41×C₂₃	—	2	2	no	—
41	C₂×#41×C₂₃	—	2	2	no	—
42	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
43	C₂×#41×C₂₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₂₃	—	2	1	no	—
46	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₂₃	—	2	1	no	—
48	C₂³×C₄×C₂₃	—	2	1	no	—
49	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₂₃	—	2	2	no	—
51	C₂×M₁₆×C₂₃	—	2	2	no	—
52	C₂×M₁₆×C₂₃	—	2	2	no	—
53	C₂×M₁₆×C₂₃	—	2	2	no	—
54	C₂×M₁₆×C₂₃	—	2	1	no	—
55	C₂×M₁₆×C₂₃	—	2	1	no	—
56	C₂×M₁₆×C₂₃	—	2	2	no	—
57	C₂×M₁₆×C₂₃	—	2	2	no	—
58	C₂×M₁₆×C₂₃	—	2	2	no	—
59	C₂×M₁₆×C₂₃	—	2	2	no	—
60	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₂₃	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
63	C₂×M₁₆×C₂₃	D₄	1	2	yes	—
64	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
65	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₂₃	—	2	1	no	—
67	C₂²×C₈×C₂₃	—	2	1	no	—
68	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
69	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
70	C₂₃×#117	—	2	1	no	—
71	C₂₃×#117	—	2	1	no	—
72	C₂₃×#117	C₂×C₄	1	2	yes	—
73	C₂₃×#117	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
76	C₂×C₄²×C₂₃	—	2	1	no	—
77	C₂×C₄²×C₂₃	—	2	1	no	—
78	C₂×C₄²×C₂₃	—	2	2	no	—
79	C₂×C₄²×C₂₃	D₄	1	4	yes	—
80	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
82	C₂₃×C₄⋊C₈	—	2	8	no	—
83	C₂₃×#104	—	2	4	no	—
84	C₂₃×#104	—	2	4	no	—
85	C₂₃×#103	C₂×C₄	1	8	yes	complemented
86	C₂₃×#102	C₂×C₄	1	8	yes	complemented
87	C₂₃×C₂²⋊C₈	—	2	8	no	—
88	C₂₃×#97	—	2	4	no	—
89	C₄×C₈×C₂₃	—	2	4	no	—
90	C₂⁴×C₂₃	—	2	1	no	—
91	C₂⁴×C₂₃	#41	1	1	yes	characteristic
92	#41×C₂₃	—	2	4	no	—
93	#41×C₂₃	—	2	4	no	—
94	#41×C₂₃	—	2	2	no	—
95	#41×C₂₃	—	2	2	no	—
96	#41×C₂₃	—	2	2	no	—
97	#41×C₂₃	—	2	2	no	—
98	#41×C₂₃	—	4	2	no	—
99	#41×C₂₃	—	4	2	no	—
100	#41×C₂₃	—	4	2	no	—
101	#41×C₂₃	—	4	2	no	—
102	C₂×Q₈×C₂₃	—	2	1	no	—
103	C₂×Q₈×C₂₃	—	2	2	no	—
104	C₂×Q₈×C₂₃	—	2	2	no	—
105	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₂₃	—	2	2	no	—
107	C₂×D₄×C₂₃	—	2	2	no	—
108	C₂×D₄×C₂₃	—	2	2	no	—
109	C₂×D₄×C₂₃	—	2	2	no	—
110	C₂×D₄×C₂₃	—	2	1	no	—
111	C₂×D₄×C₂₃	—	4	2	no	—
112	C₂×D₄×C₂₃	—	4	2	no	—
113	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₂₃	—	2	1	no	—
115	C₂²×C₄×C₂₃	—	2	1	no	—
116	C₂²×C₄×C₂₃	—	2	4	no	—
117	C₂²×C₄×C₂₃	—	2	1	no	—
118	C₂²×C₄×C₂₃	—	2	2	no	—
119	C₂²×C₄×C₂₃	—	2	2	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	4	4	no	—
122	C₂²×C₄×C₂₃	—	4	2	no	—
123	C₂²×C₄×C₂₃	—	4	2	no	—
124	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₂₃	#41	1	2	yes	—
130	C₂²×C₄×C₂₃	#41	1	2	yes	—
131	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	#41	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₂₃	—	2	4	no	—
135	M₁₆×C₂₃	—	2	4	no	—
136	M₁₆×C₂₃	—	2	4	no	—
137	M₁₆×C₂₃	—	2	4	no	—
138	M₁₆×C₂₃	—	2	2	no	—
139	M₁₆×C₂₃	—	2	2	no	—
140	M₁₆×C₂₃	—	2	2	no	—
141	M₁₆×C₂₃	—	2	2	no	—
142	M₁₆×C₂₃	—	4	2	no	—
143	M₁₆×C₂₃	—	4	2	no	—
144	C₂×C₈×C₂₃	—	2	2	no	—
145	C₂×C₈×C₂₃	—	2	2	no	—
146	C₂×C₈×C₂₃	—	2	2	no	—
147	C₂×C₈×C₂₃	—	2	2	no	—
148	C₂×C₈×C₂₃	—	2	2	no	—
149	C₂×C₈×C₂₃	—	2	2	no	—
150	C₂×C₈×C₂₃	—	4	2	no	—
151	C₂×C₈×C₂₃	—	4	2	no	—
152	C₂×C₈×C₂₃	C₂²×C₄	1	4	yes	—
153	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₂₃	—	2	2	no	—
155	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
156	C₂²⋊C₄×C₂₃	—	2	2	no	—
157	C₂²⋊C₄×C₂₃	—	2	2	no	—
158	C₄²×C₂₃	—	2	2	no	—
159	C₄²×C₂₃	—	2	4	no	—
160	C₄²×C₂₃	—	2	2	no	—
161	C₄²×C₂₃	—	2	1	no	—
162	C₄²×C₂₃	—	2	1	no	—
163	C₄²×C₂₃	C₂×D₄	1	2	yes	—
164	C₄²×C₂₃	C₂×D₄	1	2	yes	—
165	#21099	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂³×C₂₃	—	2	2	no	—
167	C₂³×C₂₃	—	4	2	no	—
168	C₂³×C₂₃	—	4	2	no	—
169	C₂³×C₂₃	—	8	2	no	—
170	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₂₃	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₂₃	#123	1	2	yes	—
173	C₂³×C₂₃	#126	1	2	yes	—
174	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
175	Q₈×C₂₃	—	2	2	no	—
176	Q₈×C₂₃	—	2	2	no	—
177	Q₈×C₂₃	—	4	2	no	—
178	D₄×C₂₃	—	2	2	no	—
179	D₄×C₂₃	—	2	2	no	—
180	D₄×C₂₃	—	4	2	no	—
181	D₄×C₂₃	—	4	2	no	—
182	D₄×C₂₃	—	4	4	no	—
183	D₄×C₂₃	—	4	2	no	—
184	C₂×C₄×C₂₃	—	2	4	no	—
185	C₂×C₄×C₂₃	—	2	2	no	—
186	C₂×C₄×C₂₃	—	2	4	no	—
187	C₂×C₄×C₂₃	—	2	2	no	—
188	C₂×C₄×C₂₃	—	2	2	no	—
189	C₂×C₄×C₂₃	—	4	8	no	—
190	C₂×C₄×C₂₃	—	4	2	no	—
191	C₂×C₄×C₂₃	—	4	2	no	—
192	C₂×C₄×C₂₃	—	4	2	no	—
193	C₂×C₄×C₂₃	—	4	2	no	—
194	C₂×C₄×C₂₃	—	4	4	no	—
195	C₂×C₄×C₂₃	—	8	2	no	—
196	C₂×C₄×C₂₃	#117	1	2	yes	—
197	C₂×C₄×C₂₃	#117	1	2	yes	—
198	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₂₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₂₃	#121	1	2	yes	—
203	C₂×C₄×C₂₃	#121	1	2	yes	—
204	C₂×C₄×C₂₃	#123	1	2	yes	—
205	C₂×C₄×C₂₃	#124	1	2	yes	—
206	C₂×C₄×C₂₃	#124	1	2	yes	—
207	C₂×C₄×C₂₃	#126	1	2	yes	—
208	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
214	C₈×C₂₃	—	2	4	no	—
215	C₈×C₂₃	—	2	4	no	—
216	C₈×C₂₃	—	4	2	no	—
217	C₈×C₂₃	—	4	2	no	—
218	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
219	C₂²×#104	C₂×C₂₃	1	1	yes	characteristic
220	#2896	C₂×C₂₃	1	1	yes	characteristic
221	#2879	C₂×C₂₃	1	1	yes	characteristic
222	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
223	#1938	C₂×C₂₃	1	4	yes	complemented
224	#1937	C₂×C₂₃	1	4	yes	complemented
225	#1738	C₂×C₂₃	1	1	yes	characteristic, complemented
226	C₂×#339	C₂×C₂₃	1	1	yes	characteristic, complemented
227	C₂²×C₂₃	—	2	2	no	—
228	C₂²×C₂₃	—	2	2	no	—
229	C₂²×C₂₃	—	2	2	no	—
230	C₂²×C₂₃	—	4	2	no	—
231	C₂²×C₂₃	—	4	2	no	—
232	C₂²×C₂₃	—	4	4	no	—
233	C₂²×C₂₃	—	4	2	no	—
234	C₂²×C₂₃	—	8	4	no	—
235	C₂²×C₂₃	#388	1	2	yes	—
236	C₂²×C₂₃	#388	1	2	yes	—
237	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
238	C₂²×C₂₃	C₂×#123	1	1	yes	characteristic
239	C₂²×C₂₃	C₂×#126	1	1	yes	characteristic
240	C₄×C₂₃	—	2	4	no	—
241	C₄×C₂₃	—	4	2	no	—
242	C₄×C₂₃	—	4	4	no	—
243	C₄×C₂₃	—	4	2	no	—
244	C₄×C₂₃	#388	1	2	yes	—
245	C₄×C₂₃	#388	1	2	yes	—
246	C₄×C₂₃	C₂×#117	1	1	yes	characteristic
247	C₄×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
249	C₄×C₂₃	C₂×#124	1	1	yes	characteristic
250	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
252	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
253	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
254	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
255	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
257	#424	—	2	2	no	—
258	#424	C₂²×C₂₃	1	4	yes	complemented
259	#423	—	2	2	no	—
260	C₂×#104	—	2	4	no	—
261	C₂×#104	C₂²×C₂₃	1	2	yes	—
262	C₂×#104	C₂²×C₂₃	1	2	yes	—
263	#419	C₄×C₂₃	1	2	yes	complemented
264	#418	C₄×C₂₃	1	2	yes	complemented
265	#417	C₄×C₂₃	1	4	yes	complemented
266	#416	C₂²×C₂₃	1	4	yes	—
267	#408	—	2	2	no	—
268	#408	C₂²×C₂₃	1	4	yes	—
269	#407	—	2	2	no	—
270	C₄×M₁₆	—	2	4	no	—
271	C₂×#97	C₂²×C₂₃	1	2	yes	complemented
272	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
273	#341	C₂²×C₂₃	1	4	yes	complemented
274	#339	C₂²×C₂₃	1	2	yes	complemented
275	#339	C₂²×C₂₃	1	2	yes	complemented
276	C₂×C₂₃	—	2	1	no	—
277	C₂×C₂₃	—	2	2	no	—
278	C₂×C₂₃	—	2	1	no	—
279	C₂×C₂₃	—	2	2	no	—
280	C₂×C₂₃	—	8	2	no	—
281	C₂×C₂₃	C₂×#388	1	1	yes	characteristic
282	C₂×C₂₃	#2956	1	2	yes	—
283	C₂×#41	—	2	1	no	—
284	C₂×#41	—	2	1	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	2	no	—
289	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
290	C₂×#41	C₂³×C₂₃	1	2	yes	—
291	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	—	2	2	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
308	C₂×M₁₆	C₂×C₄×C₂₃	1	2	yes	—
309	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
310	C₂×M₁₆	D₄×C₂₃	1	2	yes	—
311	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
312	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
313	C₂²×C₈	—	2	1	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
316	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
317	#117	—	2	1	no	—
318	#117	—	2	1	no	—
319	#117	C₂×C₄×C₂₃	1	2	yes	—
320	#117	C₂³×C₂₃	1	2	yes	—
321	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	D₄×C₂₃	1	4	yes	—
327	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
329	C₄⋊C₈	—	2	8	no	—
330	#104	—	2	4	no	—
331	#104	—	2	4	no	—
332	#103	C₂×C₄×C₂₃	1	8	yes	complemented
333	#102	C₂×C₄×C₂₃	1	8	yes	complemented
334	C₂²⋊C₈	—	2	8	no	—
335	#97	—	2	4	no	—
336	C₄×C₈	—	2	4	no	—
337	C₂₃	#21099	1	1	yes	characteristic, direct product factor, Sylow
338	C₂⁴	—	2	1	no	—
339	C₂⁴	#41×C₂₃	1	1	yes	characteristic
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	—	2	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
377	C₂²×C₄	#41×C₂₃	1	2	yes	—
378	C₂²×C₄	#41×C₂₃	1	2	yes	—
379	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
380	C₂²×C₄	#41×C₂₃	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	4	no	—
385	M₁₆	—	2	4	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	4	2	no	—
391	M₁₆	—	4	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₂×C₈	C₂²×C₄×C₂₃	1	4	yes	—
401	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	C₂×D₄×C₂₃	1	2	yes	—
412	C₄²	C₂×D₄×C₂₃	1	2	yes	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
418	C₂³	C₄×D₄×C₂₃	1	1	yes	characteristic
419	C₂³	C₂₃×#123	1	2	yes	—
420	C₂³	C₂₃×#126	1	2	yes	—
421	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	4	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	C₂₃×#117	1	2	yes	—
444	C₂×C₄	C₂₃×#117	1	2	yes	—
445	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
446	C₂×C₄	C₄×D₄×C₂₃	1	1	yes	characteristic
447	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
448	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
449	C₂×C₄	C₂₃×#121	1	2	yes	—
450	C₂×C₄	C₂₃×#121	1	2	yes	—
451	C₂×C₄	C₂₃×#123	1	2	yes	—
452	C₂×C₄	C₂₃×#124	1	2	yes	—
453	C₂×C₄	C₂₃×#124	1	2	yes	—
454	C₂×C₄	C₂₃×#126	1	2	yes	—
455	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
461	C₈	—	2	4	no	—
462	C₈	—	2	4	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	8	4	no	—
473	C₂²	C₂₃×#388	1	2	yes	—
474	C₂²	C₂₃×#388	1	2	yes	—
475	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
476	C₂²	C₂×C₂₃×#123	1	1	yes	characteristic
477	C₂²	C₂×C₂₃×#126	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	C₂₃×#388	1	2	yes	—
483	C₄	C₂₃×#388	1	2	yes	—
484	C₄	C₂×C₂₃×#117	1	1	yes	characteristic
485	C₄	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
486	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
487	C₄	C₂×C₂₃×#124	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	2	1	no	—
492	C₂	—	8	2	no	—
493	C₂	C₂×C₂₃×#388	1	1	yes	characteristic
494	C₂	C₂₃×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂×C₄×D₄
prime radical	C₂²×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×M₁₆×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2905	C₂	semidirect
5. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
6. C₂₃×#1938	C₂	semidirect
7. C₂₃×#1937	C₂	semidirect
8. C₂₃×#1738	C₂	semidirect
9. C₂×C₂₃×#339	C₂	semidirect
18. C₂₃×#424	C₂²	semidirect
23. C₂₃×#419	C₄	semidirect
24. C₂₃×#418	C₄	semidirect
25. C₂₃×#417	C₄	semidirect
31. C₂×C₂₃×#97	C₂²	semidirect
32. C₂×C₄×C₈×C₂₃	C₂²	semidirect
33. C₂₃×#341	C₂²	semidirect
34. C₂₃×#339	C₂²	semidirect
35. C₂₃×#339	C₂²	semidirect
85. C₂₃×#103	C₂×C₄	semidirect
86. C₂₃×#102	C₂×C₄	semidirect
165. #21099	C₂₃	direct (N × H)
218. #2905	C₂×C₂₃	semidirect
222. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
223. #1938	C₂×C₂₃	semidirect
224. #1937	C₂×C₂₃	semidirect
225. #1738	C₂×C₂₃	semidirect
226. C₂×#339	C₂×C₂₃	semidirect
258. #424	C₂²×C₂₃	semidirect
263. #419	C₄×C₂₃	semidirect
264. #418	C₄×C₂₃	semidirect
265. #417	C₄×C₂₃	semidirect
271. C₂×#97	C₂²×C₂₃	semidirect
272. C₂×C₄×C₈	C₂²×C₂₃	semidirect
273. #341	C₂²×C₂₃	semidirect
274. #339	C₂²×C₂₃	semidirect
275. #339	C₂²×C₂₃	semidirect
332. #103	C₂×C₄×C₂₃	semidirect
333. #102	C₂×C₄×C₂₃	semidirect
337. C₂₃	#21099	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×#2905	2
C₂²×C₂₃×#104	2
C₂₃×#2896	2
C₂₃×#2879	2
C₂×C₄×M₁₆×C₂₃	2
C₂₃×#1938	2
C₂₃×#1937	2
C₂₃×#1738	2
C₂×C₂₃×#339	2
#21099	23

Subgroups — C23×#21099 #19168725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21099 #19168725