Subgroups — C₂₃×#25183 #19172809

Order 5888.

1000 conjugacy classes of subgroups.

The subgroup lattice has 792 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, complemented
2	C₂₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#455	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#3009	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2038	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2015	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1929	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1888	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1882	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1866	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
20	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂₃×#536	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
25	C₂₃×#520	C₂²	1	1	yes	characteristic
26	C₂₃×#519	C₂²	1	1	yes	characteristic, complemented
27	C₂₃×#473	—	2	4	no	—
28	C₂₃×#464	—	2	1	no	—
29	C₂₃×#464	—	2	1	no	—
30	C₂₃×#462	—	2	1	no	—
31	C₂₃×#462	—	2	1	no	—
32	C₂₃×#455	—	2	4	no	—
33	C₂₃×#452	—	2	1	no	—
34	C₂₃×#452	—	2	1	no	—
35	C₂₃×#450	—	2	1	no	—
36	C₂₃×#450	—	2	1	no	—
37	C₂₃×#441	—	2	1	no	—
38	C₂₃×#440	—	2	1	no	—
39	C₄×Q₁₆×C₂₃	—	2	1	no	—
40	C₄×SD₁₆×C₂₃	—	2	1	no	—
41	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#104	C₂²	1	1	yes	characteristic
47	C₂₃×#419	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#418	—	2	1	no	—
49	C₂₃×#418	C₂²	1	1	yes	characteristic
50	C₂₃×#418	C₂²	1	1	yes	characteristic
51	C₂₃×#417	—	2	1	no	—
52	C₂₃×#417	C₂²	1	1	yes	characteristic
53	C₂₃×#416	—	2	1	no	—
54	C₂₃×#416	C₂²	1	1	yes	characteristic
55	C₂₃×#416	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₂₃×#102	—	2	1	no	—
58	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
62	C₂₃×#408	C₂²	1	1	yes	characteristic
63	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#343	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#339	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#339	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×H(5,𝔽₂)	—	2	2	no	—
70	C₂₃×H(5,𝔽₂)	—	2	2	no	—
71	C₂₃×H(5,𝔽₂)	—	2	2	no	—
72	C₂₃×H(5,𝔽₂)	—	4	1	no	—
73	C₂×#41×C₂₃	—	2	1	no	—
74	C₂×#41×C₂₃	—	2	1	no	—
75	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
76	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	4	1	no	—
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂₃×#137	—	2	2	no	—
84	C₂₃×#137	—	2	2	no	—
85	C₂₃×#137	—	2	2	no	—
86	C₂₃×#137	—	2	2	no	—
87	C₂₃×#137	—	4	1	no	—
88	C₂₃×#137	D₄	1	4	yes	—
89	C₂×Q₁₆×C₂₃	—	2	1	no	—
90	C₂×Q₁₆×C₂₃	—	2	2	no	—
91	C₂×Q₁₆×C₂₃	—	2	1	no	—
92	C₂×Q₁₆×C₂₃	—	2	1	no	—
93	C₂×Q₁₆×C₂₃	—	2	1	no	—
94	C₂×Q₁₆×C₂₃	—	2	1	no	—
95	C₂×Q₁₆×C₂₃	—	4	1	no	—
96	C₂×SD₁₆×C₂₃	—	2	1	no	—
97	C₂×SD₁₆×C₂₃	—	2	1	no	—
98	C₂×SD₁₆×C₂₃	—	2	1	no	—
99	C₂×SD₁₆×C₂₃	—	2	2	no	—
100	C₂×SD₁₆×C₂₃	—	2	1	no	—
101	C₂×SD₁₆×C₂₃	—	2	1	no	—
102	C₂×SD₁₆×C₂₃	—	4	1	no	—
103	C₂₃×#131	—	2	2	no	—
104	C₂₃×#131	—	4	1	no	—
105	C₂×M₁₆×C₂₃	—	2	1	no	—
106	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₂₃	—	2	1	no	—
111	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	—	2	1	no	—
114	C₂₃×#124	—	2	2	no	—
115	C₂₃×#124	—	2	1	no	—
116	C₂₃×#124	—	2	2	no	—
117	C₂₃×#123	—	4	1	no	—
118	C₂₃×C₂²⋊Q₈	—	2	1	no	—
119	C₂₃×C₂²⋊Q₈	—	2	1	no	—
120	C₄×Q₈×C₂₃	—	2	1	no	—
121	C₄×Q₈×C₂₃	—	2	1	no	—
122	C₄×Q₈×C₂₃	—	2	1	no	—
123	C₄×Q₈×C₂₃	—	2	1	no	—
124	C₄×Q₈×C₂₃	—	2	1	no	—
125	C₄×D₄×C₂₃	—	2	1	no	—
126	C₄×D₄×C₂₃	—	4	1	no	—
127	C₂₃×#117	—	2	1	no	—
128	C₂₃×#117	—	4	1	no	—
129	C₂₃×#117	C₂³	1	1	yes	characteristic
130	C₂₃×#117	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₂₃	—	4	1	no	—
134	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×#108	—	2	2	no	—
136	C₂₃×#108	—	4	1	no	—
137	C₂₃×#107	—	2	1	no	—
138	C₂₃×#106	—	2	1	no	—
139	C₂₃×C₄⋊C₈	—	2	1	no	—
140	C₂₃×C₄⋊C₈	—	2	1	no	—
141	C₂₃×#104	—	2	2	no	—
142	C₂₃×#104	—	2	2	no	—
143	C₂₃×#103	—	2	1	no	—
144	C₂₃×#103	—	2	1	no	—
145	C₂₃×#103	—	2	1	no	—
146	C₂₃×#103	—	2	1	no	—
147	C₂₃×#103	—	2	1	no	—
148	C₂₃×#103	D₄	1	1	yes	characteristic
149	C₂₃×#103	D₄	1	1	yes	characteristic
150	C₂₃×#103	D₄	1	1	yes	characteristic
151	C₂₃×#103	D₄	1	1	yes	characteristic
152	C₂₃×#102	—	2	1	no	—
153	C₂₃×#102	—	2	1	no	—
154	C₂₃×#102	—	2	1	no	—
155	C₂₃×#102	—	2	1	no	—
156	C₂₃×#102	—	2	1	no	—
157	C₂₃×#102	—	2	1	no	—
158	C₂₃×#102	—	2	1	no	—
159	C₂₃×#102	D₄	1	1	yes	characteristic
160	C₂₃×#102	D₄	1	1	yes	characteristic
161	C₂₃×#102	D₄	1	1	yes	characteristic
162	C₂₃×#102	D₄	1	1	yes	characteristic
163	C₂₃×#101	—	2	2	no	—
164	C₂₃×#101	—	2	2	no	—
165	C₂₃×#100	—	2	2	no	—
166	C₂₃×C₂²⋊C₈	—	2	1	no	—
167	C₂₃×C₂²⋊C₈	—	2	1	no	—
168	C₂₃×#97	—	2	1	no	—
169	C₄×C₈×C₂₃	—	2	1	no	—
170	C₂₃×#95	—	4	1	no	—
171	C₂⁴×C₂₃	—	2	1	no	—
172	C₂⁴×C₂₃	—	4	1	no	—
173	#41×C₂₃	—	2	1	no	—
174	#41×C₂₃	—	2	1	no	—
175	#41×C₂₃	—	2	4	no	—
176	#41×C₂₃	—	2	1	no	—
177	#41×C₂₃	—	2	1	no	—
178	#41×C₂₃	—	2	1	no	—
179	#41×C₂₃	—	2	1	no	—
180	#41×C₂₃	—	4	2	no	—
181	#41×C₂₃	—	4	2	no	—
182	#41×C₂₃	—	4	2	no	—
183	#41×C₂₃	C₂×D₄	1	2	yes	—
184	#41×C₂₃	#41	1	2	yes	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	—	2	1	no	—
187	C₂×Q₈×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	—	2	1	no	—
189	C₂×Q₈×C₂₃	—	2	1	no	—
190	C₂×Q₈×C₂₃	—	2	1	no	—
191	C₂×Q₈×C₂₃	—	2	1	no	—
192	C₂×Q₈×C₂₃	—	2	1	no	—
193	C₂×Q₈×C₂₃	—	2	1	no	—
194	C₂×Q₈×C₂₃	—	2	1	no	—
195	C₂×Q₈×C₂₃	—	2	1	no	—
196	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
197	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	4	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	2	1	no	—
204	C₂×D₄×C₂₃	—	2	1	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	2	1	no	—
207	C₂×D₄×C₂₃	—	4	2	no	—
208	C₂×D₄×C₂₃	—	4	1	no	—
209	C₂×D₄×C₂₃	—	4	1	no	—
210	C₂×D₄×C₂₃	—	4	2	no	—
211	C₂×D₄×C₂₃	—	4	4	no	—
212	C₂×D₄×C₂₃	—	4	4	no	—
213	C₂×D₄×C₂₃	—	4	2	no	—
214	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂×D₄×C₂₃	#41	1	2	yes	—
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	1	no	—
222	C₂²×C₄×C₂₃	—	2	1	no	—
223	C₂²×C₄×C₂₃	—	4	1	no	—
224	C₂²×C₄×C₂₃	—	4	1	no	—
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	Q₁₆×C₂₃	—	2	4	no	—
227	Q₁₆×C₂₃	—	4	2	no	—
228	Q₁₆×C₂₃	—	4	2	no	—
229	Q₁₆×C₂₃	—	4	2	no	—
230	Q₁₆×C₂₃	—	4	2	no	—
231	SD₁₆×C₂₃	—	2	4	no	—
232	SD₁₆×C₂₃	—	4	2	no	—
233	SD₁₆×C₂₃	—	4	2	no	—
234	SD₁₆×C₂₃	—	4	2	no	—
235	SD₁₆×C₂₃	—	4	2	no	—
236	M₁₆×C₂₃	—	2	1	no	—
237	M₁₆×C₂₃	—	2	1	no	—
238	M₁₆×C₂₃	—	2	1	no	—
239	M₁₆×C₂₃	—	2	1	no	—
240	M₁₆×C₂₃	—	2	1	no	—
241	M₁₆×C₂₃	—	2	1	no	—
242	M₁₆×C₂₃	—	2	1	no	—
243	M₁₆×C₂₃	—	4	2	no	—
244	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
245	C₂×C₈×C₂₃	—	2	1	no	—
246	C₂×C₈×C₂₃	—	2	1	no	—
247	C₂×C₈×C₂₃	—	2	1	no	—
248	C₂×C₈×C₂₃	—	2	1	no	—
249	C₂×C₈×C₂₃	—	2	1	no	—
250	C₂×C₈×C₂₃	—	2	1	no	—
251	C₂×C₈×C₂₃	—	2	1	no	—
252	C₂×C₈×C₂₃	—	2	1	no	—
253	C₂×C₈×C₂₃	—	4	2	no	—
254	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₄⋊C₄×C₂₃	—	2	1	no	—
259	C₄⋊C₄×C₂₃	—	2	1	no	—
260	C₄⋊C₄×C₂₃	—	4	1	no	—
261	C₄⋊C₄×C₂₃	—	4	1	no	—
262	C₄⋊C₄×C₂₃	—	4	1	no	—
263	C₄⋊C₄×C₂₃	—	4	1	no	—
264	C₄⋊C₄×C₂₃	—	4	1	no	—
265	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
268	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
269	C₂²⋊C₄×C₂₃	—	2	1	no	—
270	C₂²⋊C₄×C₂₃	—	2	1	no	—
271	C₂²⋊C₄×C₂₃	—	4	4	no	—
272	C₂²⋊C₄×C₂₃	—	4	1	no	—
273	C₂²⋊C₄×C₂₃	—	4	1	no	—
274	C₂²⋊C₄×C₂₃	—	4	1	no	—
275	C₄²×C₂₃	—	2	1	no	—
276	C₄²×C₂₃	—	2	1	no	—
277	C₄²×C₂₃	—	2	1	no	—
278	C₄²×C₂₃	—	2	1	no	—
279	C₄²×C₂₃	—	4	1	no	—
280	C₄²×C₂₃	—	4	1	no	—
281	C₄²×C₂₃	—	4	1	no	—
282	#25183	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂³×C₂₃	—	2	1	no	—
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	4	4	no	—
287	C₂³×C₂₃	—	4	1	no	—
288	C₂³×C₂₃	—	4	1	no	—
289	C₂³×C₂₃	—	8	1	no	—
290	C₂³×C₂₃	—	8	1	no	—
291	C₂³×C₂₃	—	16	1	no	—
292	C₂³×C₂₃	—	16	1	no	—
293	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
294	Q₈×C₂₃	—	2	1	no	—
295	Q₈×C₂₃	—	2	2	no	—
296	Q₈×C₂₃	—	2	1	no	—
297	Q₈×C₂₃	—	2	2	no	—
298	Q₈×C₂₃	—	2	1	no	—
299	Q₈×C₂₃	—	4	1	no	—
300	Q₈×C₂₃	—	4	1	no	—
301	Q₈×C₂₃	—	4	1	no	—
302	Q₈×C₂₃	—	4	1	no	—
303	Q₈×C₂₃	—	4	1	no	—
304	Q₈×C₂₃	—	4	1	no	—
305	Q₈×C₂₃	#121	1	2	yes	—
306	D₄×C₂₃	—	2	2	no	—
307	D₄×C₂₃	—	2	2	no	—
308	D₄×C₂₃	—	2	1	no	—
309	D₄×C₂₃	—	2	2	no	—
310	D₄×C₂₃	—	2	1	no	—
311	D₄×C₂₃	—	2	1	no	—
312	D₄×C₂₃	—	2	2	no	—
313	D₄×C₂₃	—	4	4	no	—
314	D₄×C₂₃	—	4	4	no	—
315	D₄×C₂₃	—	4	1	no	—
316	D₄×C₂₃	—	4	1	no	—
317	D₄×C₂₃	—	4	1	no	—
318	D₄×C₂₃	—	4	1	no	—
319	D₄×C₂₃	#121	1	2	yes	—
320	C₂×C₄×C₂₃	—	2	1	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	4	4	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	8	1	no	—
342	C₂×C₄×C₂₃	—	16	1	no	—
343	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
347	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
348	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
349	C₈×C₂₃	—	2	2	no	—
350	C₈×C₂₃	—	2	1	no	—
351	C₈×C₂₃	—	2	1	no	—
352	C₈×C₂₃	—	2	1	no	—
353	C₈×C₂₃	—	2	1	no	—
354	C₈×C₂₃	—	4	1	no	—
355	C₈×C₂₃	—	4	1	no	—
356	C₈×C₂₃	—	4	1	no	—
357	C₂×#473	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#3044	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂×#455	C₂×C₂₃	1	1	yes	characteristic
360	#3009	C₂×C₂₃	1	1	yes	characteristic
361	#2947	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#2897	C₂×C₂₃	1	1	yes	characteristic
363	#2063	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#2052	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2038	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#2015	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#1977	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#1929	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1888	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1882	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1866	C₂×C₂₃	1	1	yes	characteristic, complemented
372	C₂²×C₂₃	—	2	1	no	—
373	C₂²×C₂₃	—	2	1	no	—
374	C₂²×C₂₃	—	2	2	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	8	2	no	—
382	C₂²×C₂₃	—	8	1	no	—
383	C₂²×C₂₃	—	8	1	no	—
384	C₂²×C₂₃	—	16	1	no	—
385	C₂²×C₂₃	—	16	4	no	—
386	C₂²×C₂₃	#538	1	1	yes	characteristic
387	C₂²×C₂₃	D₄²	1	1	yes	characteristic
388	C₂²×C₂₃	#546	1	1	yes	characteristic
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	4	1	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	1	no	—
393	C₄×C₂₃	—	4	1	no	—
394	C₄×C₂₃	—	4	1	no	—
395	C₄×C₂₃	—	4	1	no	—
396	C₄×C₂₃	—	8	1	no	—
397	C₄×C₂₃	—	8	1	no	—
398	C₄×C₂₃	—	8	1	no	—
399	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
400	C₄×C₂₃	#525	1	1	yes	characteristic
401	C₄×C₂₃	D₄²	1	1	yes	characteristic
402	C₄×C₂₃	#546	1	1	yes	characteristic
403	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
408	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
410	#536	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
412	#520	C₂²×C₂₃	1	1	yes	characteristic
413	#519	C₂²×C₂₃	1	1	yes	characteristic, complemented
414	#473	—	2	4	no	—
415	#464	—	2	1	no	—
416	#464	—	2	1	no	—
417	#462	—	2	1	no	—
418	#462	—	2	1	no	—
419	#455	—	2	4	no	—
420	#452	—	2	1	no	—
421	#452	—	2	1	no	—
422	#450	—	2	1	no	—
423	#450	—	2	1	no	—
424	#441	—	2	1	no	—
425	#440	—	2	1	no	—
426	C₄×Q₁₆	—	2	1	no	—
427	C₄×SD₁₆	—	2	1	no	—
428	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
429	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
430	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
431	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#104	C₂²×C₂₃	1	1	yes	characteristic
434	#419	C₂²×C₂₃	1	1	yes	characteristic, complemented
435	#418	—	2	1	no	—
436	#418	C₂²×C₂₃	1	1	yes	characteristic
437	#418	C₂²×C₂₃	1	1	yes	characteristic
438	#417	—	2	1	no	—
439	#417	C₂²×C₂₃	1	1	yes	characteristic
440	#416	—	2	1	no	—
441	#416	C₂²×C₂₃	1	1	yes	characteristic
442	#416	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	C₂×#102	—	2	1	no	—
445	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
449	#408	C₂²×C₂₃	1	1	yes	characteristic
450	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
451	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	#343	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	#339	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#339	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	C₂×C₂₃	—	2	1	no	—
457	C₂×C₂₃	—	2	1	no	—
458	C₂×C₂₃	—	4	2	no	—
459	C₂×C₂₃	—	8	1	no	—
460	C₂×C₂₃	—	8	2	no	—
461	C₂×C₂₃	#2424	1	1	yes	characteristic
462	C₂×C₂₃	#3289	1	1	yes	characteristic
463	C₂×C₂₃	#3290	1	1	yes	characteristic
464	H(5,𝔽₂)	—	2	2	no	—
465	H(5,𝔽₂)	—	2	2	no	—
466	H(5,𝔽₂)	—	2	2	no	—
467	H(5,𝔽₂)	—	4	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	—	2	1	no	—
470	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
471	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
473	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
474	C₂²×D₄	—	2	1	no	—
475	C₂²×D₄	—	2	1	no	—
476	C₂²×D₄	—	4	1	no	—
477	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
478	#137	—	2	2	no	—
479	#137	—	2	2	no	—
480	#137	—	2	2	no	—
481	#137	—	2	2	no	—
482	#137	—	4	1	no	—
483	#137	D₄×C₂₃	1	4	yes	—
484	C₂×Q₁₆	—	2	1	no	—
485	C₂×Q₁₆	—	2	2	no	—
486	C₂×Q₁₆	—	2	1	no	—
487	C₂×Q₁₆	—	2	1	no	—
488	C₂×Q₁₆	—	2	1	no	—
489	C₂×Q₁₆	—	2	1	no	—
490	C₂×Q₁₆	—	4	1	no	—
491	C₂×SD₁₆	—	2	1	no	—
492	C₂×SD₁₆	—	2	1	no	—
493	C₂×SD₁₆	—	2	1	no	—
494	C₂×SD₁₆	—	2	2	no	—
495	C₂×SD₁₆	—	2	1	no	—
496	C₂×SD₁₆	—	2	1	no	—
497	C₂×SD₁₆	—	4	1	no	—
498	#131	—	2	2	no	—
499	#131	—	4	1	no	—
500	C₂×M₁₆	—	2	1	no	—
501	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
505	C₂²×C₈	—	2	1	no	—
506	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
508	C₄⋊Q₈	—	2	1	no	—
509	#124	—	2	2	no	—
510	#124	—	2	1	no	—
511	#124	—	2	2	no	—
512	#123	—	4	1	no	—
513	C₂²⋊Q₈	—	2	1	no	—
514	C₂²⋊Q₈	—	2	1	no	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	—	2	1	no	—
518	C₄×Q₈	—	2	1	no	—
519	C₄×Q₈	—	2	1	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	4	1	no	—
522	#117	—	2	1	no	—
523	#117	—	4	1	no	—
524	#117	C₂³×C₂₃	1	1	yes	characteristic
525	#117	C₂³×C₂₃	1	1	yes	characteristic
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×C₂²⋊C₄	—	4	1	no	—
529	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
530	#108	—	2	2	no	—
531	#108	—	4	1	no	—
532	#107	—	2	1	no	—
533	#106	—	2	1	no	—
534	C₄⋊C₈	—	2	1	no	—
535	C₄⋊C₈	—	2	1	no	—
536	#104	—	2	2	no	—
537	#104	—	2	2	no	—
538	#103	—	2	1	no	—
539	#103	—	2	1	no	—
540	#103	—	2	1	no	—
541	#103	—	2	1	no	—
542	#103	—	2	1	no	—
543	#103	D₄×C₂₃	1	1	yes	characteristic
544	#103	D₄×C₂₃	1	1	yes	characteristic
545	#103	D₄×C₂₃	1	1	yes	characteristic
546	#103	D₄×C₂₃	1	1	yes	characteristic
547	#102	—	2	1	no	—
548	#102	—	2	1	no	—
549	#102	—	2	1	no	—
550	#102	—	2	1	no	—
551	#102	—	2	1	no	—
552	#102	—	2	1	no	—
553	#102	—	2	1	no	—
554	#102	D₄×C₂₃	1	1	yes	characteristic
555	#102	D₄×C₂₃	1	1	yes	characteristic
556	#102	D₄×C₂₃	1	1	yes	characteristic
557	#102	D₄×C₂₃	1	1	yes	characteristic
558	#101	—	2	2	no	—
559	#101	—	2	2	no	—
560	#100	—	2	2	no	—
561	C₂²⋊C₈	—	2	1	no	—
562	C₂²⋊C₈	—	2	1	no	—
563	#97	—	2	1	no	—
564	C₄×C₈	—	2	1	no	—
565	#95	—	4	1	no	—
566	C₂₃	#25183	1	1	yes	characteristic, direct product factor, Sylow
567	C₂⁴	—	2	1	no	—
568	C₂⁴	—	4	1	no	—
569	#41	—	2	1	no	—
570	#41	—	2	1	no	—
571	#41	—	2	4	no	—
572	#41	—	2	1	no	—
573	#41	—	2	1	no	—
574	#41	—	2	1	no	—
575	#41	—	2	1	no	—
576	#41	—	4	2	no	—
577	#41	—	4	2	no	—
578	#41	—	4	2	no	—
579	#41	C₂×D₄×C₂₃	1	2	yes	—
580	#41	#41×C₂₃	1	2	yes	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	2	1	no	—
588	C₂×Q₈	—	2	1	no	—
589	C₂×Q₈	—	2	1	no	—
590	C₂×Q₈	—	2	1	no	—
591	C₂×Q₈	—	2	1	no	—
592	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
593	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
594	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	4	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	4	1	no	—
605	C₂×D₄	—	4	1	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	4	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
612	C₂×D₄	#41×C₂₃	1	2	yes	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	4	1	no	—
620	C₂²×C₄	—	4	1	no	—
621	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
622	Q₁₆	—	2	4	no	—
623	Q₁₆	—	4	2	no	—
624	Q₁₆	—	4	2	no	—
625	Q₁₆	—	4	2	no	—
626	Q₁₆	—	4	2	no	—
627	SD₁₆	—	2	4	no	—
628	SD₁₆	—	4	2	no	—
629	SD₁₆	—	4	2	no	—
630	SD₁₆	—	4	2	no	—
631	SD₁₆	—	4	2	no	—
632	M₁₆	—	2	1	no	—
633	M₁₆	—	2	1	no	—
634	M₁₆	—	2	1	no	—
635	M₁₆	—	2	1	no	—
636	M₁₆	—	2	1	no	—
637	M₁₆	—	2	1	no	—
638	M₁₆	—	2	1	no	—
639	M₁₆	—	4	2	no	—
640	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	4	2	no	—
650	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
652	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
653	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
654	C₄⋊C₄	—	2	1	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	4	1	no	—
657	C₄⋊C₄	—	4	1	no	—
658	C₄⋊C₄	—	4	1	no	—
659	C₄⋊C₄	—	4	1	no	—
660	C₄⋊C₄	—	4	1	no	—
661	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
662	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
665	C₂²⋊C₄	—	2	1	no	—
666	C₂²⋊C₄	—	2	1	no	—
667	C₂²⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	4	1	no	—
669	C₂²⋊C₄	—	4	1	no	—
670	C₂²⋊C₄	—	4	1	no	—
671	C₄²	—	2	1	no	—
672	C₄²	—	2	1	no	—
673	C₄²	—	2	1	no	—
674	C₄²	—	2	1	no	—
675	C₄²	—	4	1	no	—
676	C₄²	—	4	1	no	—
677	C₄²	—	4	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	2	no	—
681	C₂³	—	4	4	no	—
682	C₂³	—	4	1	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	8	1	no	—
685	C₂³	—	8	1	no	—
686	C₂³	—	16	1	no	—
687	C₂³	—	16	1	no	—
688	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
689	Q₈	—	2	1	no	—
690	Q₈	—	2	2	no	—
691	Q₈	—	2	1	no	—
692	Q₈	—	2	2	no	—
693	Q₈	—	2	1	no	—
694	Q₈	—	4	1	no	—
695	Q₈	—	4	1	no	—
696	Q₈	—	4	1	no	—
697	Q₈	—	4	1	no	—
698	Q₈	—	4	1	no	—
699	Q₈	—	4	1	no	—
700	Q₈	C₂₃×#121	1	2	yes	—
701	D₄	—	2	2	no	—
702	D₄	—	2	2	no	—
703	D₄	—	2	1	no	—
704	D₄	—	2	2	no	—
705	D₄	—	2	1	no	—
706	D₄	—	2	1	no	—
707	D₄	—	2	2	no	—
708	D₄	—	4	4	no	—
709	D₄	—	4	4	no	—
710	D₄	—	4	1	no	—
711	D₄	—	4	1	no	—
712	D₄	—	4	1	no	—
713	D₄	—	4	1	no	—
714	D₄	C₂₃×#121	1	2	yes	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	4	4	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	8	1	no	—
737	C₂×C₄	—	16	1	no	—
738	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
739	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
740	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
743	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
744	C₈	—	2	2	no	—
745	C₈	—	2	1	no	—
746	C₈	—	2	1	no	—
747	C₈	—	2	1	no	—
748	C₈	—	2	1	no	—
749	C₈	—	4	1	no	—
750	C₈	—	4	1	no	—
751	C₈	—	4	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	2	1	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	8	2	no	—
762	C₂²	—	8	1	no	—
763	C₂²	—	8	1	no	—
764	C₂²	—	16	1	no	—
765	C₂²	—	16	4	no	—
766	C₂²	C₂₃×#538	1	1	yes	characteristic
767	C₂²	D₄²×C₂₃	1	1	yes	characteristic
768	C₂²	C₂₃×#546	1	1	yes	characteristic
769	C₄	—	2	2	no	—
770	C₄	—	4	1	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	1	no	—
776	C₄	—	8	1	no	—
777	C₄	—	8	1	no	—
778	C₄	—	8	1	no	—
779	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
780	C₄	C₂₃×#525	1	1	yes	characteristic
781	C₄	D₄²×C₂₃	1	1	yes	characteristic
782	C₄	C₂₃×#546	1	1	yes	characteristic
783	C₂	—	2	1	no	—
784	C₂	—	2	1	no	—
785	C₂	—	4	2	no	—
786	C₂	—	8	1	no	—
787	C₂	—	8	2	no	—
788	C₂	C₂₃×#2424	1	1	yes	characteristic
789	C₂	C₂₃×#3289	1	1	yes	characteristic
790	C₂	C₂₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#473	C₂	semidirect
2. C₂₃×#3044	C₂	semidirect
5. C₂₃×#2947	C₂	semidirect
7. C₂₃×#2063	C₂	semidirect
8. C₂₃×#2052	C₂	semidirect
9. C₂₃×#2038	C₂	semidirect
10. C₂₃×#2015	C₂	semidirect
11. C₂₃×#1977	C₂	semidirect
12. C₂₃×#1929	C₂	semidirect
13. C₂₃×#1888	C₂	semidirect
14. C₂₃×#1882	C₂	semidirect
15. C₂₃×#1866	C₂	semidirect
20. C₂²×Q₁₆×C₂₃	C₂²	semidirect
26. C₂₃×#519	C₂²	semidirect
41. C₂×C₂₃×#108	C₂²	semidirect
42. C₂×C₂₃×#108	C₂²	semidirect
43. C₂₃×#428	C₂²	semidirect
44. C₂₃×#424	C₂²	semidirect
47. C₂₃×#419	C₂²	semidirect
56. C₂×C₂₃×#103	C₂²	semidirect
59. C₂×C₂₃×#101	C₂²	semidirect
60. C₂×C₂₃×#101	C₂²	semidirect
63. C₂₃×#405	C₂²	semidirect
64. C₂₃×#391	C₂²	semidirect
65. C₂₃×#343	C₂²	semidirect
66. C₂₃×#339	C₂²	semidirect
67. C₂₃×#339	C₂²	semidirect
68. C₂₃×#336	C₂²	semidirect
282. #25183	C₂₃	direct (N × H)
357. C₂×#473	C₂×C₂₃	semidirect
358. #3044	C₂×C₂₃	semidirect
361. #2947	C₂×C₂₃	semidirect
363. #2063	C₂×C₂₃	semidirect
364. #2052	C₂×C₂₃	semidirect
365. #2038	C₂×C₂₃	semidirect
366. #2015	C₂×C₂₃	semidirect
367. #1977	C₂×C₂₃	semidirect
368. #1929	C₂×C₂₃	semidirect
369. #1888	C₂×C₂₃	semidirect
370. #1882	C₂×C₂₃	semidirect
371. #1866	C₂×C₂₃	semidirect
407. C₂²×Q₁₆	C₂²×C₂₃	semidirect
413. #519	C₂²×C₂₃	semidirect
428. C₂×#108	C₂²×C₂₃	semidirect
429. C₂×#108	C₂²×C₂₃	semidirect
430. #428	C₂²×C₂₃	semidirect
431. #424	C₂²×C₂₃	semidirect
434. #419	C₂²×C₂₃	semidirect
443. C₂×#103	C₂²×C₂₃	semidirect
446. C₂×#101	C₂²×C₂₃	semidirect
447. C₂×#101	C₂²×C₂₃	semidirect
450. #405	C₂²×C₂₃	semidirect
451. #391	C₂²×C₂₃	semidirect
452. #343	C₂²×C₂₃	semidirect
453. #339	C₂²×C₂₃	semidirect
454. #339	C₂²×C₂₃	semidirect
455. #336	C₂²×C₂₃	semidirect
566. C₂₃	#25183	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
C₂₃×#3044	2
C₂×C₂₃×#455	2
C₂₃×#3009	2
C₂₃×#2947	2
C₂₃×#2897	2
C₂₃×#2063	2
C₂₃×#2052	2
C₂₃×#2038	2
C₂₃×#2015	2
C₂₃×#1977	2
C₂₃×#1929	2
C₂₃×#1888	2
C₂₃×#1882	2
C₂₃×#1866	2
#25183	23

Subgroups — C23×#25183 #19172809

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25183 #19172809