Subgroups — C₂₃×#27069 #19174695

Order 5888.

734 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2513	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2097	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2055	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2013	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#1968	C₂	1	1	yes	maximal, characteristic
8	C₂₃×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1925	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#397	—	2	1	no	—
34	C₂₃×#397	—	2	1	no	—
35	C₂₃×#391	C₂²	1	1	yes	characteristic
36	C₂₃×#391	C₂²	1	1	yes	characteristic
37	C₂₃×#390	C₂²	1	1	yes	characteristic
38	C₂₃×#390	C₂²	1	1	yes	characteristic
39	C₂₃×#390	C₂²	1	1	yes	characteristic
40	C₂₃×#389	—	2	1	no	—
41	C₂₃×#389	C₂²	1	1	yes	characteristic
42	C₂₃×#388	—	2	1	no	—
43	C₂₃×#388	—	2	1	no	—
44	C₂₃×#387	—	2	1	no	—
45	C₂₃×#387	—	2	1	no	—
46	C₂₃×#382	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₂₃	—	2	1	no	—
48	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#340	C₂²	1	1	yes	characteristic
52	C₂₃×#340	C₂²	1	1	yes	characteristic
53	C₂₃×#340	C₂²	1	1	yes	characteristic
54	C₂₃×#340	C₂²	1	1	yes	characteristic
55	C₂₃×#336	C₂²	1	1	yes	characteristic
56	C₂₃×#336	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic
58	C₂₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
60	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₂₃	—	2	2	no	—
63	C₂×SD₁₆×C₂₃	—	2	2	no	—
64	C₂×SD₁₆×C₂₃	—	2	2	no	—
65	C₂×SD₁₆×C₂₃	—	4	1	no	—
66	C₂×SD₁₆×C₂₃	—	4	1	no	—
67	C₂×SD₁₆×C₂₃	—	4	1	no	—
68	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂₃×C₄⋊Q₈	—	2	2	no	—
73	C₂₃×C₄⋊Q₈	—	2	2	no	—
74	C₄×Q₈×C₂₃	—	2	2	no	—
75	C₄×Q₈×C₂₃	—	2	2	no	—
76	C₄×Q₈×C₂₃	—	4	1	no	—
77	C₄×Q₈×C₂₃	—	4	1	no	—
78	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₄²×C₂₃	—	2	1	no	—
97	C₂×C₄²×C₂₃	—	2	1	no	—
98	C₂×C₄²×C₂₃	—	2	1	no	—
99	C₂×C₄²×C₂₃	—	2	1	no	—
100	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×#107	—	4	1	no	—
104	C₂₃×#106	—	2	2	no	—
105	C₂₃×C₄⋊C₈	—	4	1	no	—
106	C₂₃×#103	—	2	2	no	—
107	C₂₃×#103	—	2	2	no	—
108	C₂₃×#103	—	2	2	no	—
109	C₂₃×#103	—	4	1	no	—
110	C₂₃×#103	—	4	1	no	—
111	C₂₃×#103	—	4	1	no	—
112	C₂₃×#102	—	2	2	no	—
113	C₂₃×#102	—	4	1	no	—
114	C₄×C₈×C₂₃	—	4	1	no	—
115	C₂₃×#95	—	2	1	no	—
116	C₂₃×#95	—	2	1	no	—
117	C₂₃×#95	—	2	1	no	—
118	C₂₃×#95	—	2	1	no	—
119	C₂₃×#95	—	2	1	no	—
120	C₂₃×#95	—	2	1	no	—
121	C₂₃×#95	—	2	1	no	—
122	C₂₃×#95	—	2	1	no	—
123	C₂₃×#95	—	2	1	no	—
124	C₂₃×#95	D₄	1	1	yes	characteristic
125	C₂₃×#95	D₄	1	1	yes	characteristic
126	C₂⁴×C₂₃	—	2	1	no	—
127	C₂×Q₈×C₂₃	—	2	1	no	—
128	C₂×Q₈×C₂₃	—	2	1	no	—
129	C₂×Q₈×C₂₃	—	2	1	no	—
130	C₂×Q₈×C₂₃	—	2	1	no	—
131	C₂×Q₈×C₂₃	—	2	1	no	—
132	C₂×Q₈×C₂₃	—	2	1	no	—
133	C₂×Q₈×C₂₃	—	2	1	no	—
134	C₂×Q₈×C₂₃	—	2	1	no	—
135	C₂×Q₈×C₂₃	—	2	1	no	—
136	C₂×Q₈×C₂₃	—	2	1	no	—
137	C₂×Q₈×C₂₃	#41	1	2	yes	—
138	C₂×Q₈×C₂₃	#41	1	2	yes	—
139	C₂×D₄×C₂₃	—	2	1	no	—
140	C₂×D₄×C₂₃	—	2	1	no	—
141	C₂×D₄×C₂₃	—	2	1	no	—
142	C₂×D₄×C₂₃	—	2	1	no	—
143	C₂×D₄×C₂₃	—	2	1	no	—
144	C₂×D₄×C₂₃	—	2	1	no	—
145	C₂²×C₄×C₂₃	—	2	1	no	—
146	C₂²×C₄×C₂₃	—	2	1	no	—
147	C₂²×C₄×C₂₃	—	2	1	no	—
148	C₂²×C₄×C₂₃	—	2	1	no	—
149	C₂²×C₄×C₂₃	—	2	1	no	—
150	C₂²×C₄×C₂₃	—	2	1	no	—
151	C₂²×C₄×C₂₃	—	2	1	no	—
152	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
159	SD₁₆×C₂₃	—	4	4	no	—
160	SD₁₆×C₂₃	—	4	4	no	—
161	C₂×C₈×C₂₃	—	2	1	no	—
162	C₂×C₈×C₂₃	—	2	1	no	—
163	C₂×C₈×C₂₃	—	2	1	no	—
164	C₂×C₈×C₂₃	—	2	1	no	—
165	C₂×C₈×C₂₃	—	2	1	no	—
166	C₂×C₈×C₂₃	—	2	1	no	—
167	C₂×C₈×C₂₃	—	2	1	no	—
168	C₂×C₈×C₂₃	—	2	1	no	—
169	C₂×C₈×C₂₃	—	2	1	no	—
170	C₂×C₈×C₂₃	—	2	1	no	—
171	C₂×C₈×C₂₃	—	2	1	no	—
172	C₂×C₈×C₂₃	#41	1	2	yes	—
173	C₄⋊C₄×C₂₃	—	2	4	no	—
174	C₄⋊C₄×C₂₃	—	2	4	no	—
175	C₄⋊C₄×C₂₃	—	2	2	no	—
176	C₄⋊C₄×C₂₃	—	2	2	no	—
177	C₄⋊C₄×C₂₃	—	2	1	no	—
178	C₄⋊C₄×C₂₃	—	2	1	no	—
179	C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₄⋊C₄×C₂₃	—	2	1	no	—
182	C₄⋊C₄×C₂₃	—	2	1	no	—
183	C₄⋊C₄×C₂₃	—	2	1	no	—
184	C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₄⋊C₄×C₂₃	—	2	1	no	—
186	C₄⋊C₄×C₂₃	—	4	2	no	—
187	C₄⋊C₄×C₂₃	—	4	2	no	—
188	C₄⋊C₄×C₂₃	—	8	1	no	—
189	C₄⋊C₄×C₂₃	#41	1	2	yes	—
190	C₂²⋊C₄×C₂₃	—	4	2	no	—
191	C₂²⋊C₄×C₂₃	—	4	2	no	—
192	C₂²⋊C₄×C₂₃	—	8	1	no	—
193	C₂²⋊C₄×C₂₃	—	8	1	no	—
194	C₂²⋊C₄×C₂₃	—	8	1	no	—
195	C₂²⋊C₄×C₂₃	—	8	1	no	—
196	C₄²×C₂₃	—	2	1	no	—
197	C₄²×C₂₃	—	2	1	no	—
198	C₄²×C₂₃	—	2	1	no	—
199	C₄²×C₂₃	—	2	1	no	—
200	C₄²×C₂₃	—	2	1	no	—
201	C₄²×C₂₃	—	2	1	no	—
202	C₄²×C₂₃	—	4	2	no	—
203	C₄²×C₂₃	—	4	2	no	—
204	C₄²×C₂₃	—	4	2	no	—
205	C₄²×C₂₃	—	8	1	no	—
206	#27069	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂³×C₂₃	—	4	1	no	—
208	C₂³×C₂₃	—	4	1	no	—
209	C₂³×C₂₃	—	4	1	no	—
210	C₂³×C₂₃	—	4	1	no	—
211	C₂³×C₂₃	—	4	1	no	—
212	C₂³×C₂₃	—	4	1	no	—
213	C₂³×C₂₃	—	4	1	no	—
214	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
215	Q₈×C₂₃	—	2	2	no	—
216	Q₈×C₂₃	—	2	2	no	—
217	Q₈×C₂₃	—	2	2	no	—
218	Q₈×C₂₃	—	2	2	no	—
219	Q₈×C₂₃	—	4	1	no	—
220	Q₈×C₂₃	—	4	1	no	—
221	Q₈×C₂₃	—	4	1	no	—
222	Q₈×C₂₃	—	4	1	no	—
223	D₄×C₂₃	—	4	1	no	—
224	D₄×C₂₃	—	4	1	no	—
225	D₄×C₂₃	—	4	1	no	—
226	D₄×C₂₃	—	4	1	no	—
227	C₂×C₄×C₂₃	—	2	1	no	—
228	C₂×C₄×C₂₃	—	2	1	no	—
229	C₂×C₄×C₂₃	—	2	1	no	—
230	C₂×C₄×C₂₃	—	2	1	no	—
231	C₂×C₄×C₂₃	—	2	1	no	—
232	C₂×C₄×C₂₃	—	2	2	no	—
233	C₂×C₄×C₂₃	—	2	2	no	—
234	C₂×C₄×C₂₃	—	2	1	no	—
235	C₂×C₄×C₂₃	—	2	1	no	—
236	C₂×C₄×C₂₃	—	2	1	no	—
237	C₂×C₄×C₂₃	—	2	2	no	—
238	C₂×C₄×C₂₃	—	2	1	no	—
239	C₂×C₄×C₂₃	—	2	1	no	—
240	C₂×C₄×C₂₃	—	2	1	no	—
241	C₂×C₄×C₂₃	—	2	1	no	—
242	C₂×C₄×C₂₃	—	2	1	no	—
243	C₂×C₄×C₂₃	—	2	1	no	—
244	C₂×C₄×C₂₃	—	2	1	no	—
245	C₂×C₄×C₂₃	—	2	1	no	—
246	C₂×C₄×C₂₃	—	4	1	no	—
247	C₂×C₄×C₂₃	—	4	1	no	—
248	C₂×C₄×C₂₃	—	4	1	no	—
249	C₂×C₄×C₂₃	—	4	1	no	—
250	C₂×C₄×C₂₃	—	4	1	no	—
251	C₂×C₄×C₂₃	—	4	1	no	—
252	C₂×C₄×C₂₃	—	4	1	no	—
253	C₂×C₄×C₂₃	—	4	1	no	—
254	C₂×C₄×C₂₃	—	4	1	no	—
255	C₂×C₄×C₂₃	—	4	1	no	—
256	C₂×C₄×C₂₃	—	4	1	no	—
257	C₂×C₄×C₂₃	—	4	1	no	—
258	C₂×C₄×C₂₃	—	4	1	no	—
259	C₂×C₄×C₂₃	—	4	1	no	—
260	C₂×C₄×C₂₃	—	4	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	#135	1	2	yes	—
265	C₂×C₄×C₂₃	#137	1	2	yes	—
266	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
271	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
272	C₈×C₂₃	—	2	2	no	—
273	C₈×C₂₃	—	4	1	no	—
274	C₈×C₂₃	—	4	1	no	—
275	C₈×C₂₃	—	4	1	no	—
276	#2513	C₂×C₂₃	1	1	yes	characteristic
277	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
278	#2097	C₂×C₂₃	1	1	yes	characteristic, complemented
279	#2055	C₂×C₂₃	1	1	yes	characteristic
280	#2043	C₂×C₂₃	1	1	yes	characteristic, complemented
281	#2013	C₂×C₂₃	1	1	yes	characteristic
282	#1968	C₂×C₂₃	1	1	yes	characteristic
283	#1928	C₂×C₂₃	1	1	yes	characteristic, complemented
284	#1925	C₂×C₂₃	1	1	yes	characteristic
285	#1920	C₂×C₂₃	1	1	yes	characteristic, complemented
286	#1916	C₂×C₂₃	1	1	yes	characteristic, complemented
287	#1880	C₂×C₂₃	1	1	yes	characteristic
288	#1880	C₂×C₂₃	1	1	yes	characteristic
289	#1805	C₂×C₂₃	1	1	yes	characteristic, complemented
290	C₄×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
291	C₂²×C₂₃	—	8	1	no	—
292	C₂²×C₂₃	—	8	1	no	—
293	C₂²×C₂₃	—	8	1	no	—
294	C₂²×C₂₃	—	8	1	no	—
295	C₂²×C₂₃	—	8	1	no	—
296	C₂²×C₂₃	—	8	1	no	—
297	C₂²×C₂₃	—	8	1	no	—
298	C₂²×C₂₃	#525	1	1	yes	characteristic
299	C₂²×C₂₃	#546	1	1	yes	characteristic
300	C₂²×C₂₃	#550	1	1	yes	characteristic
301	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
302	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
303	C₂²×C₂₃	#577	1	1	yes	characteristic
304	C₂²×C₂₃	#577	1	1	yes	characteristic
305	C₄×C₂₃	—	2	2	no	—
306	C₄×C₂₃	—	2	2	no	—
307	C₄×C₂₃	—	4	1	no	—
308	C₄×C₂₃	—	4	2	no	—
309	C₄×C₂₃	—	4	2	no	—
310	C₄×C₂₃	—	4	1	no	—
311	C₄×C₂₃	—	4	1	no	—
312	C₄×C₂₃	—	4	2	no	—
313	C₄×C₂₃	—	4	1	no	—
314	C₄×C₂₃	—	8	1	no	—
315	C₄×C₂₃	—	8	1	no	—
316	C₄×C₂₃	—	8	1	no	—
317	C₄×C₂₃	—	8	1	no	—
318	C₄×C₂₃	#529	1	1	yes	characteristic
319	C₄×C₂₃	#538	1	1	yes	characteristic
320	C₄×C₂₃	#551	1	1	yes	characteristic
321	C₄×C₂₃	#553	1	1	yes	characteristic
322	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
323	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
324	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
327	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
328	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
329	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
330	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
331	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
332	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
333	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
334	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
335	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
336	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
337	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
338	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
339	#397	—	2	1	no	—
340	#397	—	2	1	no	—
341	#391	C₂²×C₂₃	1	1	yes	characteristic
342	#391	C₂²×C₂₃	1	1	yes	characteristic
343	#390	C₂²×C₂₃	1	1	yes	characteristic
344	#390	C₂²×C₂₃	1	1	yes	characteristic
345	#390	C₂²×C₂₃	1	1	yes	characteristic
346	#389	—	2	1	no	—
347	#389	C₂²×C₂₃	1	1	yes	characteristic
348	#388	—	2	1	no	—
349	#388	—	2	1	no	—
350	#387	—	2	1	no	—
351	#387	—	2	1	no	—
352	#382	C₂²×C₂₃	1	1	yes	characteristic
353	C₄×C₄⋊C₄	—	2	1	no	—
354	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
355	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
356	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
357	#340	C₂²×C₂₃	1	1	yes	characteristic
358	#340	C₂²×C₂₃	1	1	yes	characteristic
359	#340	C₂²×C₂₃	1	1	yes	characteristic
360	#340	C₂²×C₂₃	1	1	yes	characteristic
361	#336	C₂²×C₂₃	1	1	yes	characteristic
362	#336	C₂²×C₂₃	1	1	yes	characteristic
363	#336	C₂²×C₂₃	1	1	yes	characteristic
364	#336	C₂²×C₂₃	1	1	yes	characteristic
365	C₂×C₂₃	—	16	1	no	—
366	C₂×C₂₃	#2467	1	1	yes	characteristic
367	C₂×C₂₃	#3108	1	1	yes	characteristic
368	C₂×C₂₃	#3126	1	1	yes	characteristic
369	C₂×C₂₃	#3303	1	1	yes	characteristic
370	C₂×C₂₃	#3320	1	1	yes	characteristic
371	C₂×C₂₃	#3394	1	1	yes	characteristic
372	C₂×C₂₃	#3400	1	1	yes	characteristic
373	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
374	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
375	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
376	C₂×SD₁₆	—	2	2	no	—
377	C₂×SD₁₆	—	2	2	no	—
378	C₂×SD₁₆	—	2	2	no	—
379	C₂×SD₁₆	—	4	1	no	—
380	C₂×SD₁₆	—	4	1	no	—
381	C₂×SD₁₆	—	4	1	no	—
382	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
383	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
385	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
386	C₄⋊Q₈	—	2	2	no	—
387	C₄⋊Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	2	no	—
389	C₄×Q₈	—	2	2	no	—
390	C₄×Q₈	—	4	1	no	—
391	C₄×Q₈	—	4	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₂²⋊C₄	—	2	1	no	—
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₄²	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	—	2	1	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
415	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
417	#107	—	4	1	no	—
418	#106	—	2	2	no	—
419	C₄⋊C₈	—	4	1	no	—
420	#103	—	2	2	no	—
421	#103	—	2	2	no	—
422	#103	—	2	2	no	—
423	#103	—	4	1	no	—
424	#103	—	4	1	no	—
425	#103	—	4	1	no	—
426	#102	—	2	2	no	—
427	#102	—	4	1	no	—
428	C₄×C₈	—	4	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	D₄×C₂₃	1	1	yes	characteristic
439	#95	D₄×C₂₃	1	1	yes	characteristic
440	C₂₃	#27069	1	1	yes	characteristic, direct product factor, Sylow
441	C₂⁴	—	2	1	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	#41×C₂₃	1	2	yes	—
453	C₂×Q₈	#41×C₂₃	1	2	yes	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
474	SD₁₆	—	4	4	no	—
475	SD₁₆	—	4	4	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	#41×C₂₃	1	2	yes	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	8	1	no	—
504	C₄⋊C₄	#41×C₂₃	1	2	yes	—
505	C₂²⋊C₄	—	4	2	no	—
506	C₂²⋊C₄	—	4	2	no	—
507	C₂²⋊C₄	—	8	1	no	—
508	C₂²⋊C₄	—	8	1	no	—
509	C₂²⋊C₄	—	8	1	no	—
510	C₂²⋊C₄	—	8	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	4	2	no	—
518	C₄²	—	4	2	no	—
519	C₄²	—	4	2	no	—
520	C₄²	—	8	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
529	Q₈	—	2	2	no	—
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	4	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	C₂₃×#135	1	2	yes	—
579	C₂×C₄	C₂₃×#137	1	2	yes	—
580	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
581	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
582	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
583	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
584	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
585	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
586	C₈	—	2	2	no	—
587	C₈	—	4	1	no	—
588	C₈	—	4	1	no	—
589	C₈	—	4	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	—	8	1	no	—
597	C₂²	C₂₃×#525	1	1	yes	characteristic
598	C₂²	C₂₃×#546	1	1	yes	characteristic
599	C₂²	C₂₃×#550	1	1	yes	characteristic
600	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
601	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
602	C₂²	C₂₃×#577	1	1	yes	characteristic
603	C₂²	C₂₃×#577	1	1	yes	characteristic
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	—	8	1	no	—
616	C₄	—	8	1	no	—
617	C₄	C₂₃×#529	1	1	yes	characteristic
618	C₄	C₂₃×#538	1	1	yes	characteristic
619	C₄	C₂₃×#551	1	1	yes	characteristic
620	C₄	C₂₃×#553	1	1	yes	characteristic
621	C₂	—	16	1	no	—
622	C₂	C₂₃×#2467	1	1	yes	characteristic
623	C₂	C₂₃×#3108	1	1	yes	characteristic
624	C₂	C₂₃×#3126	1	1	yes	characteristic
625	C₂	C₂₃×#3303	1	1	yes	characteristic
626	C₂	C₂₃×#3320	1	1	yes	characteristic
627	C₂	C₂₃×#3394	1	1	yes	characteristic
628	C₂	C₂₃×#3400	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2365	C₂	semidirect
3. C₂₃×#2097	C₂	semidirect
5. C₂₃×#2043	C₂	semidirect
8. C₂₃×#1928	C₂	semidirect
10. C₂₃×#1920	C₂	semidirect
11. C₂₃×#1916	C₂	semidirect
14. C₂₃×#1805	C₂	semidirect
15. C₄×C₂₃×#103	C₂	semidirect
206. #27069	C₂₃	direct (N × H)
277. #2365	C₂×C₂₃	semidirect
278. #2097	C₂×C₂₃	semidirect
280. #2043	C₂×C₂₃	semidirect
283. #1928	C₂×C₂₃	semidirect
285. #1920	C₂×C₂₃	semidirect
286. #1916	C₂×C₂₃	semidirect
289. #1805	C₂×C₂₃	semidirect
290. C₄×#103	C₂×C₂₃	semidirect
440. C₂₃	#27069	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×#2513	2
C₂₃×#2365	2
C₂₃×#2097	2
C₂₃×#2055	2
C₂₃×#2043	2
C₂₃×#2013	2
C₂₃×#1968	2
C₂₃×#1928	2
C₂₃×#1925	2
C₂₃×#1920	2
C₂₃×#1916	2
C₂₃×#1880	2
C₂₃×#1805	2
C₄×C₂₃×#103	2
#27069	23

Subgroups — C23×#27069 #19174695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#27069 #19174695