Subgroups — C₂₃×#26972 #19174598

Order 5888.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2429	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2421	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2036	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2001	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1935	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1894	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#470	—	2	4	no	—
26	C₄×Q₁₆×C₂₃	—	2	4	no	—
27	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
40	C₂₃×#400	—	2	1	no	—
41	C₂₃×#398	—	2	1	no	—
42	C₂₃×#397	—	2	1	no	—
43	C₂₃×#396	—	2	1	no	—
44	C₂₃×#391	C₂²	1	1	yes	characteristic
45	C₂₃×#391	C₂²	1	1	yes	characteristic
46	C₂₃×#389	—	2	1	no	—
47	C₂₃×#389	C₂²	1	1	yes	characteristic
48	C₂₃×#389	C₂²	1	1	yes	characteristic
49	C₂₃×#388	—	2	1	no	—
50	C₂₃×#388	—	2	1	no	—
51	C₂₃×#387	—	2	1	no	—
52	C₂₃×#382	C₂²	1	1	yes	characteristic
53	C₂₃×#380	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₂₃	—	2	2	no	—
66	C₂×Q₁₆×C₂₃	—	2	2	no	—
67	C₂×Q₁₆×C₂₃	—	2	2	no	—
68	C₂×Q₁₆×C₂₃	—	2	2	no	—
69	C₂×Q₁₆×C₂₃	—	2	2	no	—
70	C₂×Q₁₆×C₂₃	—	4	1	no	—
71	C₂×M₁₆×C₂₃	—	2	2	no	—
72	C₂×M₁₆×C₂₃	—	2	2	no	—
73	C₂×M₁₆×C₂₃	—	4	1	no	—
74	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₂₃×C₄⋊Q₈	—	2	2	no	—
79	C₂₃×C₄⋊Q₈	—	4	1	no	—
80	C₂₃×C₂²⋊Q₈	—	2	2	no	—
81	C₂₃×C₂²⋊Q₈	—	2	2	no	—
82	C₂₃×C₂²⋊Q₈	—	2	2	no	—
83	C₂₃×C₂²⋊Q₈	—	4	1	no	—
84	C₂₃×C₂²⋊Q₈	—	4	1	no	—
85	C₂₃×C₂²⋊Q₈	—	4	1	no	—
86	C₄×Q₈×C₂₃	—	2	2	no	—
87	C₄×Q₈×C₂₃	—	2	2	no	—
88	C₄×Q₈×C₂₃	—	4	1	no	—
89	C₄×Q₈×C₂₃	—	4	1	no	—
90	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
91	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₂₃	—	2	1	no	—
111	C₂×C₄²×C₂₃	—	2	1	no	—
112	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
114	C₂₃×#107	—	2	2	no	—
115	C₂₃×#106	—	2	2	no	—
116	C₂₃×#103	—	2	2	no	—
117	C₂₃×#103	—	2	2	no	—
118	C₂₃×#103	—	2	2	no	—
119	C₂₃×#103	—	2	2	no	—
120	C₂₃×#103	—	4	1	no	—
121	C₂₃×#103	—	4	1	no	—
122	C₂₃×#103	—	4	1	no	—
123	C₂₃×#103	D₄	1	4	yes	—
124	C₂₃×C₂²⋊C₈	—	2	2	no	—
125	C₂₃×#97	—	4	1	no	—
126	C₄×C₈×C₂₃	—	2	2	no	—
127	C₂₃×#95	—	2	1	no	—
128	C₂₃×#95	—	2	1	no	—
129	C₂₃×#95	—	2	1	no	—
130	C₂₃×#95	—	2	1	no	—
131	C₂₃×#95	—	2	1	no	—
132	C₂₃×#95	—	2	1	no	—
133	C₂₃×#95	—	2	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	D₄	1	1	yes	characteristic
137	C₂₃×#95	D₄	1	1	yes	characteristic
138	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₂₃	—	2	1	no	—
140	C₂×Q₈×C₂₃	—	2	1	no	—
141	C₂×Q₈×C₂₃	—	2	1	no	—
142	C₂×Q₈×C₂₃	—	2	1	no	—
143	C₂×Q₈×C₂₃	—	2	1	no	—
144	C₂×Q₈×C₂₃	—	2	1	no	—
145	C₂×Q₈×C₂₃	—	2	1	no	—
146	C₂×Q₈×C₂₃	—	2	1	no	—
147	C₂×Q₈×C₂₃	—	2	1	no	—
148	C₂×Q₈×C₂₃	—	2	1	no	—
149	C₂×Q₈×C₂₃	—	2	1	no	—
150	C₂×Q₈×C₂₃	—	2	1	no	—
151	C₂×Q₈×C₂₃	—	2	1	no	—
152	C₂×Q₈×C₂₃	—	2	1	no	—
153	C₂×Q₈×C₂₃	—	2	1	no	—
154	C₂×Q₈×C₂₃	—	2	1	no	—
155	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₂₃	#41	1	2	yes	—
157	C₂²×C₄×C₂₃	—	2	1	no	—
158	C₂²×C₄×C₂₃	—	2	1	no	—
159	C₂²×C₄×C₂₃	—	2	1	no	—
160	C₂²×C₄×C₂₃	—	2	1	no	—
161	C₂²×C₄×C₂₃	—	2	1	no	—
162	C₂²×C₄×C₂₃	—	2	1	no	—
163	C₂²×C₄×C₂₃	—	2	1	no	—
164	C₂²×C₄×C₂₃	—	2	1	no	—
165	C₂²×C₄×C₂₃	—	2	1	no	—
166	C₂²×C₄×C₂₃	—	2	1	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	—	2	1	no	—
169	C₂²×C₄×C₂₃	—	2	1	no	—
170	C₂²×C₄×C₂₃	—	2	1	no	—
171	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
177	Q₁₆×C₂₃	—	2	8	no	—
178	Q₁₆×C₂₃	—	4	4	no	—
179	M₁₆×C₂₃	—	4	4	no	—
180	C₂×C₈×C₂₃	—	2	1	no	—
181	C₂×C₈×C₂₃	—	2	1	no	—
182	C₂×C₈×C₂₃	—	2	1	no	—
183	C₂×C₈×C₂₃	—	2	1	no	—
184	C₂×C₈×C₂₃	—	2	1	no	—
185	C₂×C₈×C₂₃	—	2	1	no	—
186	C₂×C₈×C₂₃	—	2	1	no	—
187	C₂×C₈×C₂₃	—	2	1	no	—
188	C₂×C₈×C₂₃	—	2	1	no	—
189	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₂₃	#41	1	2	yes	—
191	C₂×C₈×C₂₃	#41	1	2	yes	—
192	C₄⋊C₄×C₂₃	—	2	1	no	—
193	C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₄⋊C₄×C₂₃	—	2	1	no	—
197	C₄⋊C₄×C₂₃	—	2	1	no	—
198	C₄⋊C₄×C₂₃	—	2	1	no	—
199	C₄⋊C₄×C₂₃	—	2	1	no	—
200	C₄⋊C₄×C₂₃	—	2	1	no	—
201	C₄⋊C₄×C₂₃	—	4	2	no	—
202	C₄⋊C₄×C₂₃	—	4	2	no	—
203	C₄⋊C₄×C₂₃	—	4	2	no	—
204	C₄⋊C₄×C₂₃	—	4	2	no	—
205	C₄⋊C₄×C₂₃	—	4	2	no	—
206	C₄⋊C₄×C₂₃	—	4	2	no	—
207	C₄⋊C₄×C₂₃	—	4	2	no	—
208	C₄⋊C₄×C₂₃	—	4	2	no	—
209	C₄⋊C₄×C₂₃	—	4	2	no	—
210	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂²⋊C₄×C₂₃	—	2	2	no	—
212	C₂²⋊C₄×C₂₃	—	4	1	no	—
213	C₂²⋊C₄×C₂₃	—	4	2	no	—
214	C₂²⋊C₄×C₂₃	—	4	2	no	—
215	C₂²⋊C₄×C₂₃	—	4	2	no	—
216	C₂²⋊C₄×C₂₃	—	4	2	no	—
217	C₄²×C₂₃	—	2	1	no	—
218	C₄²×C₂₃	—	2	1	no	—
219	C₄²×C₂₃	—	2	1	no	—
220	C₄²×C₂₃	—	2	1	no	—
221	C₄²×C₂₃	—	4	2	no	—
222	C₄²×C₂₃	—	4	2	no	—
223	#26972	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₂₃	—	2	1	no	—
225	C₂³×C₂₃	—	2	1	no	—
226	C₂³×C₂₃	—	2	1	no	—
227	C₂³×C₂₃	—	2	1	no	—
228	C₂³×C₂₃	—	2	1	no	—
229	C₂³×C₂₃	—	2	1	no	—
230	C₂³×C₂₃	—	2	1	no	—
231	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₂₃	—	2	2	no	—
233	Q₈×C₂₃	—	2	2	no	—
234	Q₈×C₂₃	—	2	2	no	—
235	Q₈×C₂₃	—	2	2	no	—
236	Q₈×C₂₃	—	4	1	no	—
237	Q₈×C₂₃	—	4	1	no	—
238	Q₈×C₂₃	—	4	1	no	—
239	Q₈×C₂₃	—	4	1	no	—
240	Q₈×C₂₃	—	4	1	no	—
241	Q₈×C₂₃	—	4	1	no	—
242	Q₈×C₂₃	—	4	1	no	—
243	Q₈×C₂₃	—	4	1	no	—
244	C₂×C₄×C₂₃	—	2	1	no	—
245	C₂×C₄×C₂₃	—	2	1	no	—
246	C₂×C₄×C₂₃	—	2	1	no	—
247	C₂×C₄×C₂₃	—	2	1	no	—
248	C₂×C₄×C₂₃	—	2	2	no	—
249	C₂×C₄×C₂₃	—	2	2	no	—
250	C₂×C₄×C₂₃	—	2	1	no	—
251	C₂×C₄×C₂₃	—	2	1	no	—
252	C₂×C₄×C₂₃	—	2	1	no	—
253	C₂×C₄×C₂₃	—	2	2	no	—
254	C₂×C₄×C₂₃	—	2	1	no	—
255	C₂×C₄×C₂₃	—	2	1	no	—
256	C₂×C₄×C₂₃	—	2	1	no	—
257	C₂×C₄×C₂₃	—	2	1	no	—
258	C₂×C₄×C₂₃	—	2	1	no	—
259	C₂×C₄×C₂₃	—	2	1	no	—
260	C₂×C₄×C₂₃	—	2	1	no	—
261	C₂×C₄×C₂₃	—	4	1	no	—
262	C₂×C₄×C₂₃	—	4	1	no	—
263	C₂×C₄×C₂₃	—	4	1	no	—
264	C₂×C₄×C₂₃	—	4	1	no	—
265	C₂×C₄×C₂₃	—	4	1	no	—
266	C₂×C₄×C₂₃	—	4	1	no	—
267	C₂×C₄×C₂₃	—	4	1	no	—
268	C₂×C₄×C₂₃	—	4	1	no	—
269	C₂×C₄×C₂₃	—	4	1	no	—
270	C₂×C₄×C₂₃	—	4	1	no	—
271	C₂×C₄×C₂₃	—	4	1	no	—
272	C₂×C₄×C₂₃	—	4	1	no	—
273	C₂×C₄×C₂₃	—	4	1	no	—
274	C₂×C₄×C₂₃	—	4	1	no	—
275	C₂×C₄×C₂₃	—	4	1	no	—
276	C₂×C₄×C₂₃	—	4	1	no	—
277	C₂×C₄×C₂₃	—	4	1	no	—
278	C₂×C₄×C₂₃	—	4	1	no	—
279	C₂×C₄×C₂₃	—	4	1	no	—
280	C₂×C₄×C₂₃	—	4	1	no	—
281	C₂×C₄×C₂₃	—	4	1	no	—
282	C₂×C₄×C₂₃	—	4	1	no	—
283	C₂×C₄×C₂₃	—	4	1	no	—
284	C₂×C₄×C₂₃	—	4	1	no	—
285	C₂×C₄×C₂₃	—	4	1	no	—
286	C₂×C₄×C₂₃	#137	1	2	yes	—
287	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
293	C₈×C₂₃	—	2	2	no	—
294	C₈×C₂₃	—	2	2	no	—
295	C₈×C₂₃	—	2	2	no	—
296	C₈×C₂₃	—	4	1	no	—
297	C₂×#470	C₂×C₂₃	1	1	yes	characteristic
298	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
299	#2429	C₂×C₂₃	1	1	yes	characteristic
300	#2421	C₂×C₂₃	1	1	yes	characteristic
301	#2085	C₂×C₂₃	1	1	yes	characteristic, complemented
302	#2036	C₂×C₂₃	1	1	yes	characteristic
303	#2016	C₂×C₂₃	1	1	yes	characteristic, complemented
304	#2001	C₂×C₂₃	1	1	yes	characteristic
305	#1960	C₂×C₂₃	1	1	yes	characteristic, complemented
306	#1935	C₂×C₂₃	1	1	yes	characteristic, complemented
307	#1933	C₂×C₂₃	1	1	yes	characteristic, complemented
308	#1894	C₂×C₂₃	1	1	yes	characteristic
309	#1878	C₂×C₂₃	1	1	yes	characteristic, complemented
310	#1865	C₂×C₂₃	1	1	yes	characteristic, complemented
311	#1753	C₂×C₂₃	1	1	yes	characteristic
312	C₂²×C₂₃	—	4	1	no	—
313	C₂²×C₂₃	—	4	1	no	—
314	C₂²×C₂₃	—	4	1	no	—
315	C₂²×C₂₃	—	4	1	no	—
316	C₂²×C₂₃	—	4	1	no	—
317	C₂²×C₂₃	—	4	1	no	—
318	C₂²×C₂₃	—	4	1	no	—
319	C₂²×C₂₃	#532	1	1	yes	characteristic
320	C₂²×C₂₃	D₄²	1	1	yes	characteristic
321	C₂²×C₂₃	#546	1	1	yes	characteristic
322	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
323	C₂²×C₂₃	#575	1	1	yes	characteristic
324	C₂²×C₂₃	#578	1	1	yes	characteristic
325	C₂²×C₂₃	#578	1	1	yes	characteristic
326	C₄×C₂₃	—	2	2	no	—
327	C₄×C₂₃	—	4	1	no	—
328	C₄×C₂₃	—	4	1	no	—
329	C₄×C₂₃	—	4	2	no	—
330	C₄×C₂₃	—	4	2	no	—
331	C₄×C₂₃	—	4	1	no	—
332	C₄×C₂₃	—	4	2	no	—
333	C₄×C₂₃	—	4	1	no	—
334	C₄×C₂₃	—	8	1	no	—
335	C₄×C₂₃	—	8	1	no	—
336	C₄×C₂₃	—	8	1	no	—
337	C₄×C₂₃	—	8	1	no	—
338	C₄×C₂₃	—	8	1	no	—
339	C₄×C₂₃	#525	1	1	yes	characteristic
340	C₄×C₂₃	#540	1	1	yes	characteristic
341	C₄×C₂₃	#546	1	1	yes	characteristic
342	C₄×C₂₃	#553	1	1	yes	characteristic
343	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
344	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
345	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
346	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
347	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
348	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
351	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
352	#470	—	2	4	no	—
353	C₄×Q₁₆	—	2	4	no	—
354	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
355	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
356	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
357	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
358	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
359	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
360	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
361	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
362	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
363	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
366	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
367	#400	—	2	1	no	—
368	#398	—	2	1	no	—
369	#397	—	2	1	no	—
370	#396	—	2	1	no	—
371	#391	C₂²×C₂₃	1	1	yes	characteristic
372	#391	C₂²×C₂₃	1	1	yes	characteristic
373	#389	—	2	1	no	—
374	#389	C₂²×C₂₃	1	1	yes	characteristic
375	#389	C₂²×C₂₃	1	1	yes	characteristic
376	#388	—	2	1	no	—
377	#388	—	2	1	no	—
378	#387	—	2	1	no	—
379	#382	C₂²×C₂₃	1	1	yes	characteristic
380	#380	C₂²×C₂₃	1	1	yes	characteristic
381	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
382	#340	C₂²×C₂₃	1	1	yes	characteristic
383	#340	C₂²×C₂₃	1	1	yes	characteristic
384	#340	C₂²×C₂₃	1	1	yes	characteristic
385	#340	C₂²×C₂₃	1	1	yes	characteristic
386	#336	C₂²×C₂₃	1	1	yes	characteristic
387	#336	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×C₂₃	—	8	1	no	—
389	C₂×C₂₃	#2464	1	1	yes	characteristic
390	C₂×C₂₃	#3172	1	1	yes	characteristic
391	C₂×C₂₃	#3177	1	1	yes	characteristic
392	C₂×C₂₃	#3269	1	1	yes	characteristic
393	C₂×C₂₃	#3270	1	1	yes	characteristic
394	C₂×C₂₃	#3327	1	1	yes	characteristic
395	C₂×C₂₃	#3328	1	1	yes	characteristic
396	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
397	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
399	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂×Q₁₆	—	2	2	no	—
401	C₂×Q₁₆	—	2	2	no	—
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×Q₁₆	—	2	2	no	—
405	C₂×Q₁₆	—	4	1	no	—
406	C₂×M₁₆	—	2	2	no	—
407	C₂×M₁₆	—	2	2	no	—
408	C₂×M₁₆	—	4	1	no	—
409	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
413	C₄⋊Q₈	—	2	2	no	—
414	C₄⋊Q₈	—	4	1	no	—
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	—	2	2	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	4	1	no	—
419	C₂²⋊Q₈	—	4	1	no	—
420	C₂²⋊Q₈	—	4	1	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	2	no	—
423	C₄×Q₈	—	4	1	no	—
424	C₄×Q₈	—	4	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
449	#107	—	2	2	no	—
450	#106	—	2	2	no	—
451	#103	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	—	2	2	no	—
454	#103	—	2	2	no	—
455	#103	—	4	1	no	—
456	#103	—	4	1	no	—
457	#103	—	4	1	no	—
458	#103	D₄×C₂₃	1	4	yes	—
459	C₂²⋊C₈	—	2	2	no	—
460	#97	—	4	1	no	—
461	C₄×C₈	—	2	2	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	D₄×C₂₃	1	1	yes	characteristic
472	#95	D₄×C₂₃	1	1	yes	characteristic
473	C₂₃	#26972	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
492	C₂×Q₈	#41×C₂₃	1	2	yes	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
512	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
513	Q₁₆	—	2	8	no	—
514	Q₁₆	—	4	4	no	—
515	M₁₆	—	4	4	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
526	C₂×C₈	#41×C₂₃	1	2	yes	—
527	C₂×C₈	#41×C₂₃	1	2	yes	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	4	2	no	—
551	C₂²⋊C₄	—	4	2	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	4	2	no	—
558	C₄²	—	4	2	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	C₂₃×#137	1	2	yes	—
622	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
624	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
625	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
626	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
628	C₈	—	2	2	no	—
629	C₈	—	2	2	no	—
630	C₈	—	2	2	no	—
631	C₈	—	4	1	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	1	no	—
637	C₂²	—	4	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	C₂₃×#532	1	1	yes	characteristic
640	C₂²	D₄²×C₂₃	1	1	yes	characteristic
641	C₂²	C₂₃×#546	1	1	yes	characteristic
642	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
643	C₂²	C₂₃×#575	1	1	yes	characteristic
644	C₂²	C₂₃×#578	1	1	yes	characteristic
645	C₂²	C₂₃×#578	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	—	8	1	no	—
658	C₄	—	8	1	no	—
659	C₄	C₂₃×#525	1	1	yes	characteristic
660	C₄	C₂₃×#540	1	1	yes	characteristic
661	C₄	C₂₃×#546	1	1	yes	characteristic
662	C₄	C₂₃×#553	1	1	yes	characteristic
663	C₂	—	8	1	no	—
664	C₂	C₂₃×#2464	1	1	yes	characteristic
665	C₂	C₂₃×#3172	1	1	yes	characteristic
666	C₂	C₂₃×#3177	1	1	yes	characteristic
667	C₂	C₂₃×#3269	1	1	yes	characteristic
668	C₂	C₂₃×#3270	1	1	yes	characteristic
669	C₂	C₂₃×#3327	1	1	yes	characteristic
670	C₂	C₂₃×#3328	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
5. C₂₃×#2085	C₂	semidirect
7. C₂₃×#2016	C₂	semidirect
9. C₂₃×#1960	C₂	semidirect
10. C₂₃×#1935	C₂	semidirect
11. C₂₃×#1933	C₂	semidirect
13. C₂₃×#1878	C₂	semidirect
14. C₂₃×#1865	C₂	semidirect
223. #26972	C₂₃	direct (N × H)
298. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
301. #2085	C₂×C₂₃	semidirect
303. #2016	C₂×C₂₃	semidirect
305. #1960	C₂×C₂₃	semidirect
306. #1935	C₂×C₂₃	semidirect
307. #1933	C₂×C₂₃	semidirect
309. #1878	C₂×C₂₃	semidirect
310. #1865	C₂×C₂₃	semidirect
473. C₂₃	#26972	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×#470	2
C₂×C₄×Q₁₆×C₂₃	2
C₂₃×#2429	2
C₂₃×#2421	2
C₂₃×#2085	2
C₂₃×#2036	2
C₂₃×#2016	2
C₂₃×#2001	2
C₂₃×#1960	2
C₂₃×#1935	2
C₂₃×#1933	2
C₂₃×#1894	2
C₂₃×#1878	2
C₂₃×#1865	2
C₂₃×#1753	2
#26972	23

Subgroups — C23×#26972 #19174598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26972 #19174598