Subgroups — C₂₃×#60749 #19208375

Order 5888.

2166 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3449	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3204	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3203	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3202	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3201	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3200	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3199	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3198	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3091	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3054	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3050	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3002	C₂	1	4	yes	maximal, complemented
13	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
16	C₂×C₂₃×#135	C₂²	1	2	yes	—
17	C₂×C₂₃×#135	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#537	C₂²	1	4	yes	—
21	C₂₃×#537	C₂²	1	4	yes	complemented
22	C₂₃×#536	—	2	2	no	—
23	C₂₃×#536	C₂²	1	2	yes	—
24	C₂₃×#536	C₂²	1	2	yes	complemented
25	C₂₃×#535	—	2	2	no	—
26	C₂₃×#535	C₂²	1	2	yes	—
27	C₂₃×#535	C₂²	1	2	yes	complemented
28	C₂₃×#534	—	2	2	no	—
29	C₂₃×#534	—	2	2	no	—
30	C₂₃×#532	—	2	2	no	—
31	C₂₃×#532	—	2	2	no	—
32	C₂₃×#525	—	2	2	no	—
33	C₂₃×#525	—	2	2	no	—
34	C₂₃×#525	C₂²	1	4	yes	—
35	C₂₃×#525	C₂²	1	4	yes	complemented
36	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
37	C₂₃×#485	C₂²	1	4	yes	complemented
38	C₂₃×#485	C₂²	1	4	yes	complemented
39	C₂₃×#484	C₂²	1	4	yes	complemented
40	C₂₃×#483	C₂²	1	4	yes	complemented
41	C₂₃×#482	C₂²	1	4	yes	complemented
42	C₂₃×#482	C₂²	1	4	yes	complemented
43	C₂₃×#481	C₂²	1	4	yes	complemented
44	C₂₃×#480	C₂²	1	4	yes	complemented
45	C₂₃×#470	C₂²	1	2	yes	complemented
46	C₂₃×#470	C₂²	1	2	yes	complemented
47	C₂₃×#469	C₂²	1	2	yes	complemented
48	C₂₃×#469	C₂²	1	2	yes	complemented
49	C₂₃×#468	C₂²	1	4	yes	complemented
50	C₂₃×#468	C₂²	1	4	yes	complemented
51	C₂₃×#467	C₂²	1	2	yes	complemented
52	C₂₃×#467	C₂²	1	2	yes	complemented
53	C₂₃×#466	C₂²	1	2	yes	complemented
54	C₂₃×#466	C₂²	1	2	yes	complemented
55	C₂₃×#465	C₂²	1	4	yes	complemented
56	C₂₃×#465	C₂²	1	4	yes	complemented
57	C₂₃×#452	C₂²	1	4	yes	complemented
58	C₂₃×#452	C₂²	1	4	yes	complemented
59	C₂₃×#451	C₂²	1	4	yes	complemented
60	C₂₃×#450	C₂²	1	4	yes	complemented
61	C₂₃×#449	C₂²	1	4	yes	complemented
62	C₂₃×#449	C₂²	1	4	yes	complemented
63	C₂₃×#448	C₂²	1	4	yes	complemented
64	C₂₃×#447	C₂²	1	4	yes	complemented
65	C₂₃×#427	C₂²	1	2	yes	complemented
66	C₂₃×#427	C₂²	1	2	yes	complemented
67	C₂₃×#416	C₂²	1	4	yes	complemented
68	C₂₃×#416	C₂²	1	4	yes	complemented
69	C₂₃×#408	C₂²	1	1	yes	characteristic
70	C₂₃×#408	C₂²	1	1	yes	characteristic
71	C₂₃×#408	C₂²	1	4	yes	complemented
72	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	4	yes	complemented
75	C₂×#41×C₂₃	—	2	2	no	—
76	C₂×#41×C₂₃	—	2	2	no	—
77	C₂×#41×C₂₃	—	4	2	no	—
78	C₂×#41×C₂₃	—	4	2	no	—
79	C₂×#41×C₂₃	—	4	4	no	—
80	C₂×#41×C₂₃	—	4	4	no	—
81	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
82	C₂×#41×C₂₃	D₄	1	2	yes	—
83	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
84	C₂×#41×C₂₃	C₂³	1	4	yes	—
85	C₂×#41×C₂₃	C₂³	1	4	yes	—
86	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
87	C₂×#41×C₂₃	C₂³	1	2	yes	—
88	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
90	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₂₃	—	2	2	no	—
92	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₂₃	D₄	1	2	yes	—
94	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
95	C₂³×C₄×C₂₃	—	2	2	no	—
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
98	C₂₃×#135	—	4	4	no	—
99	C₂₃×#135	—	4	4	no	—
100	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×D₈×C₂₃	C₂³	1	2	yes	—
105	C₂×D₈×C₂₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₂₃	—	4	2	no	—
107	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
110	C₂²×C₈×C₂₃	—	4	2	no	—
111	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
112	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	—	2	2	no	—
117	C₂₃×C₄⋊Q₈	—	2	2	no	—
118	C₂₃×#127	—	2	2	no	—
119	C₂₃×#127	—	2	2	no	—
120	C₂₃×#124	—	2	2	no	—
121	C₂₃×#124	—	2	2	no	—
122	C₂₃×#124	—	2	2	no	—
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#123	—	2	2	no	—
125	C₂₃×#123	—	2	2	no	—
126	C₂₃×#123	—	2	2	no	—
127	C₂₃×#123	—	2	2	no	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	4	no	—
131	C₂₃×C₂²⋊Q₈	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₂₃×#121	—	2	4	no	—
137	C₂₃×#121	—	2	4	no	—
138	C₂₃×#121	—	2	4	no	—
139	C₂₃×#121	—	2	4	no	—
140	C₂₃×#121	—	2	4	no	—
141	C₂₃×#121	—	2	4	no	—
142	C₂₃×#121	C₂³	1	4	yes	—
143	C₂₃×#121	C₂³	1	4	yes	—
144	C₂₃×#121	C₂³	1	4	yes	—
145	C₂₃×#121	C₂³	1	4	yes	—
146	C₂₃×#120	—	2	4	no	—
147	C₂₃×#120	—	2	4	no	—
148	C₂₃×#120	—	2	2	no	—
149	C₂₃×#120	—	2	2	no	—
150	C₂₃×#120	—	2	2	no	—
151	C₂₃×#120	—	2	2	no	—
152	C₄×D₄×C₂₃	—	2	4	no	—
153	C₄×D₄×C₂₃	—	2	4	no	—
154	C₄×D₄×C₂₃	—	2	4	no	—
155	C₄×D₄×C₂₃	—	2	4	no	—
156	C₂₃×#117	—	2	2	no	—
157	C₂₃×#117	—	2	2	no	—
158	C₂₃×#117	C₂³	1	4	yes	—
159	C₂₃×#117	C₂³	1	2	yes	—
160	C₂₃×#117	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
163	C₂×C₄²×C₂₃	—	2	2	no	—
164	C₂₃×#107	C₂³	1	2	yes	—
165	C₂₃×#107	C₂³	1	2	yes	—
166	C₂₃×#107	C₂³	1	4	yes	—
167	C₂₃×#106	C₂³	1	4	yes	—
168	C₂₃×#106	C₂³	1	2	yes	—
169	C₂₃×#106	C₂³	1	2	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#103	C₂³	1	4	yes	—
172	C₂₃×#103	C₂³	1	4	yes	—
173	C₂₃×#103	C₂³	1	4	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×#102	C₂³	1	4	yes	—
176	C₂₃×#102	C₂³	1	4	yes	—
177	C₂₃×#102	C₂³	1	4	yes	—
178	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
179	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
182	C₂⁴×C₂₃	—	2	2	no	—
183	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
184	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
185	#41×C₂₃	—	2	8	no	—
186	#41×C₂₃	—	2	8	no	—
187	#41×C₂₃	—	4	2	no	—
188	#41×C₂₃	—	4	4	no	—
189	#41×C₂₃	—	4	2	no	—
190	#41×C₂₃	—	4	1	no	—
191	#41×C₂₃	—	4	2	no	—
192	#41×C₂₃	—	4	1	no	—
193	#41×C₂₃	—	4	1	no	—
194	#41×C₂₃	—	4	2	no	—
195	#41×C₂₃	—	4	1	no	—
196	#41×C₂₃	—	4	4	no	—
197	#41×C₂₃	—	4	4	no	—
198	#41×C₂₃	—	4	8	no	—
199	#41×C₂₃	—	4	8	no	—
200	C₂×Q₈×C₂₃	—	2	2	no	—
201	C₂×Q₈×C₂₃	—	4	2	no	—
202	C₂×Q₈×C₂₃	—	4	2	no	—
203	C₂×Q₈×C₂₃	—	4	2	no	—
204	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
205	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	4	no	—
212	C₂×D₄×C₂₃	—	2	4	no	—
213	C₂×D₄×C₂₃	—	2	4	no	—
214	C₂×D₄×C₂₃	—	2	2	no	—
215	C₂×D₄×C₂₃	—	4	2	no	—
216	C₂×D₄×C₂₃	—	4	2	no	—
217	C₂×D₄×C₂₃	—	4	2	no	—
218	C₂×D₄×C₂₃	—	4	4	no	—
219	C₂×D₄×C₂₃	—	4	8	no	—
220	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
222	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
228	C₂²×C₄×C₂₃	—	2	2	no	—
229	C₂²×C₄×C₂₃	—	2	2	no	—
230	C₂²×C₄×C₂₃	—	2	4	no	—
231	C₂²×C₄×C₂₃	—	2	4	no	—
232	C₂²×C₄×C₂₃	—	2	2	no	—
233	C₂²×C₄×C₂₃	—	2	4	no	—
234	C₂²×C₄×C₂₃	—	2	4	no	—
235	C₂²×C₄×C₂₃	—	2	4	no	—
236	C₂²×C₄×C₂₃	—	4	8	no	—
237	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
240	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	Q₁₆×C₂₃	—	4	2	no	—
249	Q₁₆×C₂₃	—	4	2	no	—
250	SD₁₆×C₂₃	—	4	4	no	—
251	SD₁₆×C₂₃	—	4	4	no	—
252	D₈×C₂₃	—	4	2	no	—
253	D₈×C₂₃	—	4	2	no	—
254	M₁₆×C₂₃	—	4	1	no	—
255	M₁₆×C₂₃	—	4	2	no	—
256	M₁₆×C₂₃	—	4	1	no	—
257	C₂×C₈×C₂₃	—	2	4	no	—
258	C₂×C₈×C₂₃	—	2	4	no	—
259	C₂×C₈×C₂₃	—	4	1	no	—
260	C₂×C₈×C₂₃	—	4	2	no	—
261	C₂×C₈×C₂₃	—	4	1	no	—
262	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
265	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
272	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
273	C₂²⋊C₄×C₂₃	—	2	2	no	—
274	C₂²⋊C₄×C₂₃	—	2	2	no	—
275	C₂²⋊C₄×C₂₃	—	2	4	no	—
276	C₂²⋊C₄×C₂₃	—	2	4	no	—
277	C₂²⋊C₄×C₂₃	—	2	4	no	—
278	C₂²⋊C₄×C₂₃	—	2	4	no	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₄²×C₂₃	—	2	2	no	—
285	C₄²×C₂₃	—	2	2	no	—
286	C₄²×C₂₃	—	2	4	no	—
287	#60749	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂³×C₂₃	—	2	2	no	—
289	C₂³×C₂₃	—	2	4	no	—
290	C₂³×C₂₃	—	2	4	no	—
291	C₂³×C₂₃	—	4	2	no	—
292	C₂³×C₂₃	—	4	4	no	—
293	C₂³×C₂₃	—	4	4	no	—
294	C₂³×C₂₃	—	8	4	no	—
295	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
296	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
297	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
298	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
299	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
300	Q₈×C₂₃	—	2	4	no	—
301	Q₈×C₂₃	—	2	4	no	—
302	Q₈×C₂₃	—	4	1	no	—
303	Q₈×C₂₃	—	4	2	no	—
304	Q₈×C₂₃	—	4	1	no	—
305	Q₈×C₂₃	—	4	4	no	—
306	D₄×C₂₃	—	2	4	no	—
307	D₄×C₂₃	—	2	4	no	—
308	D₄×C₂₃	—	4	2	no	—
309	D₄×C₂₃	—	4	2	no	—
310	D₄×C₂₃	—	4	2	no	—
311	D₄×C₂₃	—	4	2	no	—
312	D₄×C₂₃	—	4	1	no	—
313	D₄×C₂₃	—	4	2	no	—
314	D₄×C₂₃	—	4	1	no	—
315	D₄×C₂₃	—	4	4	no	—
316	D₄×C₂₃	—	4	8	no	—
317	D₄×C₂₃	—	4	8	no	—
318	D₄×C₂₃	—	8	4	no	—
319	D₄×C₂₃	—	8	4	no	—
320	D₄×C₂₃	—	8	4	no	—
321	D₄×C₂₃	—	8	4	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	4	no	—
324	C₂×C₄×C₂₃	—	2	4	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	4	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	4	no	—
337	C₂×C₄×C₂₃	—	2	4	no	—
338	C₂×C₄×C₂₃	—	2	4	no	—
339	C₂×C₄×C₂₃	—	4	8	no	—
340	C₂×C₄×C₂₃	—	4	4	no	—
341	C₂×C₄×C₂₃	—	4	8	no	—
342	C₂×C₄×C₂₃	—	8	4	no	—
343	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
345	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
347	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
350	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
351	C₈×C₂₃	—	2	2	no	—
352	C₈×C₂₃	—	2	2	no	—
353	C₈×C₂₃	—	2	2	no	—
354	C₈×C₂₃	—	2	2	no	—
355	#3449	C₂×C₂₃	1	2	yes	complemented
356	#3204	C₂×C₂₃	1	2	yes	complemented
357	#3203	C₂×C₂₃	1	2	yes	complemented
358	#3202	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#3201	C₂×C₂₃	1	4	yes	complemented
360	#3200	C₂×C₂₃	1	2	yes	complemented
361	#3199	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#3198	C₂×C₂₃	1	4	yes	complemented
363	#3091	C₂×C₂₃	1	4	yes	complemented
364	#3054	C₂×C₂₃	1	2	yes	complemented
365	#3050	C₂×C₂₃	1	2	yes	complemented
366	#3002	C₂×C₂₃	1	4	yes	complemented
367	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	—	2	4	no	—
370	C₂²×C₂₃	—	2	2	no	—
371	C₂²×C₂₃	—	2	2	no	—
372	C₂²×C₂₃	—	2	4	no	—
373	C₂²×C₂₃	—	2	2	no	—
374	C₂²×C₂₃	—	2	2	no	—
375	C₂²×C₂₃	—	2	1	no	—
376	C₂²×C₂₃	—	2	1	no	—
377	C₂²×C₂₃	—	4	4	no	—
378	C₂²×C₂₃	—	4	4	no	—
379	C₂²×C₂₃	—	4	4	no	—
380	C₂²×C₂₃	—	4	4	no	—
381	C₂²×C₂₃	—	8	4	no	—
382	C₂²×C₂₃	—	8	8	no	—
383	C₂²×C₂₃	#534	1	2	yes	—
384	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
385	C₄×C₂₃	—	2	2	no	—
386	C₄×C₂₃	—	2	2	no	—
387	C₄×C₂₃	—	2	1	no	—
388	C₄×C₂₃	—	2	1	no	—
389	C₄×C₂₃	—	4	4	no	—
390	C₄×C₂₃	—	4	4	no	—
391	C₄×C₂₃	—	4	4	no	—
392	C₄×C₂₃	#534	1	2	yes	—
393	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
396	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
397	C₂×#135	C₂²×C₂₃	1	2	yes	—
398	C₂×#135	C₂²×C₂₃	1	2	yes	—
399	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
400	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
401	#537	C₂²×C₂₃	1	4	yes	—
402	#537	C₂²×C₂₃	1	4	yes	complemented
403	#536	—	2	2	no	—
404	#536	C₂²×C₂₃	1	2	yes	—
405	#536	C₂²×C₂₃	1	2	yes	complemented
406	#535	—	2	2	no	—
407	#535	C₂²×C₂₃	1	2	yes	—
408	#535	C₂²×C₂₃	1	2	yes	complemented
409	#534	—	2	2	no	—
410	#534	—	2	2	no	—
411	#532	—	2	2	no	—
412	#532	—	2	2	no	—
413	#525	—	2	2	no	—
414	#525	—	2	2	no	—
415	#525	C₂²×C₂₃	1	4	yes	—
416	#525	C₂²×C₂₃	1	4	yes	complemented
417	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
418	#485	C₂²×C₂₃	1	4	yes	complemented
419	#485	C₂²×C₂₃	1	4	yes	complemented
420	#484	C₂²×C₂₃	1	4	yes	complemented
421	#483	C₂²×C₂₃	1	4	yes	complemented
422	#482	C₂²×C₂₃	1	4	yes	complemented
423	#482	C₂²×C₂₃	1	4	yes	complemented
424	#481	C₂²×C₂₃	1	4	yes	complemented
425	#480	C₂²×C₂₃	1	4	yes	complemented
426	#470	C₂²×C₂₃	1	2	yes	complemented
427	#470	C₂²×C₂₃	1	2	yes	complemented
428	#469	C₂²×C₂₃	1	2	yes	complemented
429	#469	C₂²×C₂₃	1	2	yes	complemented
430	#468	C₂²×C₂₃	1	4	yes	complemented
431	#468	C₂²×C₂₃	1	4	yes	complemented
432	#467	C₂²×C₂₃	1	2	yes	complemented
433	#467	C₂²×C₂₃	1	2	yes	complemented
434	#466	C₂²×C₂₃	1	2	yes	complemented
435	#466	C₂²×C₂₃	1	2	yes	complemented
436	#465	C₂²×C₂₃	1	4	yes	complemented
437	#465	C₂²×C₂₃	1	4	yes	complemented
438	#452	C₂²×C₂₃	1	4	yes	complemented
439	#452	C₂²×C₂₃	1	4	yes	complemented
440	#451	C₂²×C₂₃	1	4	yes	complemented
441	#450	C₂²×C₂₃	1	4	yes	complemented
442	#449	C₂²×C₂₃	1	4	yes	complemented
443	#449	C₂²×C₂₃	1	4	yes	complemented
444	#448	C₂²×C₂₃	1	4	yes	complemented
445	#447	C₂²×C₂₃	1	4	yes	complemented
446	#427	C₂²×C₂₃	1	2	yes	complemented
447	#427	C₂²×C₂₃	1	2	yes	complemented
448	#416	C₂²×C₂₃	1	4	yes	complemented
449	#416	C₂²×C₂₃	1	4	yes	complemented
450	#408	C₂²×C₂₃	1	1	yes	characteristic
451	#408	C₂²×C₂₃	1	1	yes	characteristic
452	#408	C₂²×C₂₃	1	4	yes	complemented
453	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
454	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	C₂×C₂²⋊C₈	C₂²×C₂₃	1	4	yes	complemented
456	C₂×C₂₃	—	2	2	no	—
457	C₂×C₂₃	—	4	1	no	—
458	C₂×C₂₃	—	4	1	no	—
459	C₂×C₂₃	—	4	2	no	—
460	C₂×C₂₃	—	4	2	no	—
461	C₂×C₂₃	—	8	4	no	—
462	C₂×C₂₃	C₂×#534	1	1	yes	characteristic
463	C₂×C₂₃	#3584	1	2	yes	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	2	2	no	—
466	C₂×#41	—	4	2	no	—
467	C₂×#41	—	4	2	no	—
468	C₂×#41	—	4	4	no	—
469	C₂×#41	—	4	4	no	—
470	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
471	C₂×#41	D₄×C₂₃	1	2	yes	—
472	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
473	C₂×#41	C₂³×C₂₃	1	4	yes	—
474	C₂×#41	C₂³×C₂₃	1	4	yes	—
475	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
476	C₂×#41	C₂³×C₂₃	1	2	yes	—
477	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
482	C₂²×D₄	D₄×C₂₃	1	2	yes	—
483	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
484	C₂³×C₄	—	2	2	no	—
485	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
486	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
487	#135	—	4	4	no	—
488	#135	—	4	4	no	—
489	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
490	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
491	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
492	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
493	C₂×D₈	C₂³×C₂₃	1	2	yes	—
494	C₂×D₈	C₂³×C₂₃	1	2	yes	—
495	C₂×M₁₆	—	4	2	no	—
496	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
498	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
499	C₂²×C₈	—	4	2	no	—
500	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
501	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
502	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
505	C₄⋊Q₈	—	2	2	no	—
506	C₄⋊Q₈	—	2	2	no	—
507	#127	—	2	2	no	—
508	#127	—	2	2	no	—
509	#124	—	2	2	no	—
510	#124	—	2	2	no	—
511	#124	—	2	2	no	—
512	#124	—	2	2	no	—
513	#123	—	2	2	no	—
514	#123	—	2	2	no	—
515	#123	—	2	2	no	—
516	#123	—	2	2	no	—
517	#123	—	2	4	no	—
518	#123	—	2	4	no	—
519	C₂²⋊Q₈	—	2	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
522	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
523	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
524	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
525	#121	—	2	4	no	—
526	#121	—	2	4	no	—
527	#121	—	2	4	no	—
528	#121	—	2	4	no	—
529	#121	—	2	4	no	—
530	#121	—	2	4	no	—
531	#121	C₂³×C₂₃	1	4	yes	—
532	#121	C₂³×C₂₃	1	4	yes	—
533	#121	C₂³×C₂₃	1	4	yes	—
534	#121	C₂³×C₂₃	1	4	yes	—
535	#120	—	2	4	no	—
536	#120	—	2	4	no	—
537	#120	—	2	2	no	—
538	#120	—	2	2	no	—
539	#120	—	2	2	no	—
540	#120	—	2	2	no	—
541	C₄×D₄	—	2	4	no	—
542	C₄×D₄	—	2	4	no	—
543	C₄×D₄	—	2	4	no	—
544	C₄×D₄	—	2	4	no	—
545	#117	—	2	2	no	—
546	#117	—	2	2	no	—
547	#117	C₂³×C₂₃	1	4	yes	—
548	#117	C₂³×C₂₃	1	2	yes	—
549	#117	C₂³×C₂₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
551	C₂×C₂²⋊C₄	—	2	2	no	—
552	C₂×C₄²	—	2	2	no	—
553	#107	C₂³×C₂₃	1	2	yes	—
554	#107	C₂³×C₂₃	1	2	yes	—
555	#107	C₂³×C₂₃	1	4	yes	—
556	#106	C₂³×C₂₃	1	4	yes	—
557	#106	C₂³×C₂₃	1	2	yes	—
558	#106	C₂³×C₂₃	1	2	yes	—
559	#103	C₂³×C₂₃	1	4	yes	—
560	#103	C₂³×C₂₃	1	4	yes	—
561	#103	C₂³×C₂₃	1	4	yes	—
562	#103	C₂³×C₂₃	1	4	yes	—
563	#102	C₂³×C₂₃	1	4	yes	—
564	#102	C₂³×C₂₃	1	4	yes	—
565	#102	C₂³×C₂₃	1	4	yes	—
566	#102	C₂³×C₂₃	1	4	yes	—
567	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
569	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
570	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
571	C₂₃	#60749	1	1	yes	characteristic, direct product factor, Sylow
572	C₂⁴	—	2	2	no	—
573	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
574	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
575	#41	—	2	8	no	—
576	#41	—	2	8	no	—
577	#41	—	4	2	no	—
578	#41	—	4	4	no	—
579	#41	—	4	2	no	—
580	#41	—	4	1	no	—
581	#41	—	4	2	no	—
582	#41	—	4	1	no	—
583	#41	—	4	1	no	—
584	#41	—	4	2	no	—
585	#41	—	4	1	no	—
586	#41	—	4	4	no	—
587	#41	—	4	4	no	—
588	#41	—	4	8	no	—
589	#41	—	4	8	no	—
590	C₂×Q₈	—	2	2	no	—
591	C₂×Q₈	—	4	2	no	—
592	C₂×Q₈	—	4	2	no	—
593	C₂×Q₈	—	4	2	no	—
594	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
595	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
596	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
598	C₂×D₄	—	2	4	no	—
599	C₂×D₄	—	2	4	no	—
600	C₂×D₄	—	2	4	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	4	no	—
603	C₂×D₄	—	2	4	no	—
604	C₂×D₄	—	2	2	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	8	no	—
610	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
611	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
612	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
613	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
614	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
615	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
616	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
617	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	4	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	4	8	no	—
627	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
628	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
629	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
630	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
631	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
632	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
638	Q₁₆	—	4	2	no	—
639	Q₁₆	—	4	2	no	—
640	SD₁₆	—	4	4	no	—
641	SD₁₆	—	4	4	no	—
642	D₈	—	4	2	no	—
643	D₈	—	4	2	no	—
644	M₁₆	—	4	1	no	—
645	M₁₆	—	4	2	no	—
646	M₁₆	—	4	1	no	—
647	C₂×C₈	—	2	4	no	—
648	C₂×C₈	—	2	4	no	—
649	C₂×C₈	—	4	1	no	—
650	C₂×C₈	—	4	2	no	—
651	C₂×C₈	—	4	1	no	—
652	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
653	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
654	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
655	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
662	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
663	C₂²⋊C₄	—	2	2	no	—
664	C₂²⋊C₄	—	2	2	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	4	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₄²	—	2	4	no	—
675	C₄²	—	2	2	no	—
676	C₄²	—	2	2	no	—
677	C₂³	—	2	2	no	—
678	C₂³	—	2	4	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	4	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
685	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
686	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
687	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
688	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
689	Q₈	—	2	4	no	—
690	Q₈	—	2	4	no	—
691	Q₈	—	4	1	no	—
692	Q₈	—	4	2	no	—
693	Q₈	—	4	1	no	—
694	Q₈	—	4	4	no	—
695	D₄	—	2	4	no	—
696	D₄	—	2	4	no	—
697	D₄	—	4	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	1	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	1	no	—
704	D₄	—	4	4	no	—
705	D₄	—	4	8	no	—
706	D₄	—	4	8	no	—
707	D₄	—	8	4	no	—
708	D₄	—	8	4	no	—
709	D₄	—	8	4	no	—
710	D₄	—	8	4	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	4	no	—
726	C₂×C₄	—	2	4	no	—
727	C₂×C₄	—	2	4	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	4	no	—
730	C₂×C₄	—	4	8	no	—
731	C₂×C₄	—	8	4	no	—
732	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
735	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
737	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
738	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
739	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
740	C₈	—	2	2	no	—
741	C₈	—	2	2	no	—
742	C₈	—	2	2	no	—
743	C₈	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	1	no	—
748	C₂²	—	2	1	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	4	no	—
757	C₂²	—	8	4	no	—
758	C₂²	—	8	8	no	—
759	C₂²	C₂₃×#534	1	2	yes	—
760	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	1	no	—
764	C₄	—	2	1	no	—
765	C₄	—	4	4	no	—
766	C₄	—	4	4	no	—
767	C₄	—	4	4	no	—
768	C₄	C₂₃×#534	1	2	yes	—
769	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
770	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂	—	2	2	no	—
772	C₂	—	4	1	no	—
773	C₂	—	4	1	no	—
774	C₂	—	4	2	no	—
775	C₂	—	4	2	no	—
776	C₂	—	8	4	no	—
777	C₂	C₂×C₂₃×#534	1	1	yes	characteristic
778	C₂	C₂₃×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3449	C₂	semidirect
2. C₂₃×#3204	C₂	semidirect
3. C₂₃×#3203	C₂	semidirect
4. C₂₃×#3202	C₂	semidirect
5. C₂₃×#3201	C₂	semidirect
6. C₂₃×#3200	C₂	semidirect
7. C₂₃×#3199	C₂	semidirect
8. C₂₃×#3198	C₂	semidirect
9. C₂₃×#3091	C₂	semidirect
10. C₂₃×#3054	C₂	semidirect
11. C₂₃×#3050	C₂	semidirect
12. C₂₃×#3002	C₂	semidirect
13. C₂×C₂₃×#408	C₂	semidirect
15. C₂²×#41×C₂₃	C₂²	semidirect
18. C₂²×M₁₆×C₂₃	C₂²	semidirect
19. C₂³×C₈×C₂₃	C₂²	semidirect
21. C₂₃×#537	C₂²	semidirect
24. C₂₃×#536	C₂²	semidirect
27. C₂₃×#535	C₂²	semidirect
35. C₂₃×#525	C₂²	semidirect
36. C₂×C₂₃×#117	C₂²	semidirect
37. C₂₃×#485	C₂²	semidirect
38. C₂₃×#485	C₂²	semidirect
39. C₂₃×#484	C₂²	semidirect
40. C₂₃×#483	C₂²	semidirect
41. C₂₃×#482	C₂²	semidirect
42. C₂₃×#482	C₂²	semidirect
43. C₂₃×#481	C₂²	semidirect
44. C₂₃×#480	C₂²	semidirect
45. C₂₃×#470	C₂²	semidirect
46. C₂₃×#470	C₂²	semidirect
47. C₂₃×#469	C₂²	semidirect
48. C₂₃×#469	C₂²	semidirect
49. C₂₃×#468	C₂²	semidirect
50. C₂₃×#468	C₂²	semidirect
51. C₂₃×#467	C₂²	semidirect
52. C₂₃×#467	C₂²	semidirect
53. C₂₃×#466	C₂²	semidirect
54. C₂₃×#466	C₂²	semidirect
55. C₂₃×#465	C₂²	semidirect
56. C₂₃×#465	C₂²	semidirect
57. C₂₃×#452	C₂²	semidirect
58. C₂₃×#452	C₂²	semidirect
59. C₂₃×#451	C₂²	semidirect
60. C₂₃×#450	C₂²	semidirect
61. C₂₃×#449	C₂²	semidirect
62. C₂₃×#449	C₂²	semidirect
63. C₂₃×#448	C₂²	semidirect
64. C₂₃×#447	C₂²	semidirect
65. C₂₃×#427	C₂²	semidirect
66. C₂₃×#427	C₂²	semidirect
67. C₂₃×#416	C₂²	semidirect
68. C₂₃×#416	C₂²	semidirect
71. C₂₃×#408	C₂²	semidirect
72. C₂₃×#408	C₂²	semidirect
73. C₂₃×#408	C₂²	semidirect
74. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
287. #60749	C₂₃	direct (N × H)
355. #3449	C₂×C₂₃	semidirect
356. #3204	C₂×C₂₃	semidirect
357. #3203	C₂×C₂₃	semidirect
358. #3202	C₂×C₂₃	semidirect
359. #3201	C₂×C₂₃	semidirect
360. #3200	C₂×C₂₃	semidirect
361. #3199	C₂×C₂₃	semidirect
362. #3198	C₂×C₂₃	semidirect
363. #3091	C₂×C₂₃	semidirect
364. #3054	C₂×C₂₃	semidirect
365. #3050	C₂×C₂₃	semidirect
366. #3002	C₂×C₂₃	semidirect
367. C₂×#408	C₂×C₂₃	semidirect
396. C₂²×#41	C₂²×C₂₃	semidirect
399. C₂²×M₁₆	C₂²×C₂₃	semidirect
400. C₂³×C₈	C₂²×C₂₃	semidirect
402. #537	C₂²×C₂₃	semidirect
405. #536	C₂²×C₂₃	semidirect
408. #535	C₂²×C₂₃	semidirect
416. #525	C₂²×C₂₃	semidirect
417. C₂×#117	C₂²×C₂₃	semidirect
418. #485	C₂²×C₂₃	semidirect
419. #485	C₂²×C₂₃	semidirect
420. #484	C₂²×C₂₃	semidirect
421. #483	C₂²×C₂₃	semidirect
422. #482	C₂²×C₂₃	semidirect
423. #482	C₂²×C₂₃	semidirect
424. #481	C₂²×C₂₃	semidirect
425. #480	C₂²×C₂₃	semidirect
426. #470	C₂²×C₂₃	semidirect
427. #470	C₂²×C₂₃	semidirect
428. #469	C₂²×C₂₃	semidirect
429. #469	C₂²×C₂₃	semidirect
430. #468	C₂²×C₂₃	semidirect
431. #468	C₂²×C₂₃	semidirect
432. #467	C₂²×C₂₃	semidirect
433. #467	C₂²×C₂₃	semidirect
434. #466	C₂²×C₂₃	semidirect
435. #466	C₂²×C₂₃	semidirect
436. #465	C₂²×C₂₃	semidirect
437. #465	C₂²×C₂₃	semidirect
438. #452	C₂²×C₂₃	semidirect
439. #452	C₂²×C₂₃	semidirect
440. #451	C₂²×C₂₃	semidirect
441. #450	C₂²×C₂₃	semidirect
442. #449	C₂²×C₂₃	semidirect
443. #449	C₂²×C₂₃	semidirect
444. #448	C₂²×C₂₃	semidirect
445. #447	C₂²×C₂₃	semidirect
446. #427	C₂²×C₂₃	semidirect
447. #427	C₂²×C₂₃	semidirect
448. #416	C₂²×C₂₃	semidirect
449. #416	C₂²×C₂₃	semidirect
452. #408	C₂²×C₂₃	semidirect
453. #408	C₂²×C₂₃	semidirect
454. #408	C₂²×C₂₃	semidirect
455. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
571. C₂₃	#60749	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×#3449	2
C₂₃×#3204	2
C₂₃×#3203	2
C₂₃×#3202	2
C₂₃×#3201	2
C₂₃×#3200	2
C₂₃×#3199	2
C₂₃×#3198	2
C₂₃×#3091	2
C₂₃×#3054	2
C₂₃×#3050	2
C₂₃×#3002	2
C₂×C₂₃×#408	2
#60749	23

Subgroups — C23×#60749 #19208375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60749 #19208375