Subgroups — C₂₃×#17603 #19165229

Order 5888.

1366 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3488	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1516	C₂	1	2	yes	maximal, complemented
6	C₂₃×#1513	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1510	C₂	1	2	yes	maximal, complemented
8	C₂₃×#1507	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1504	C₂	1	2	yes	maximal, complemented
10	C₂₃×#1501	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#327	C₂	1	2	yes	maximal, complemented
12	C₂×C₂₃×H(5,𝔽₂)	C₄	1	1	yes	characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#131	—	2	1	no	—
15	C₂₃×#550	—	2	1	no	—
16	C₂₃×#548	—	2	1	no	—
17	C₂₃×#546	—	2	1	no	—
18	C₂₃×#546	—	2	2	no	—
19	D₄²×C₂₃	—	2	1	no	—
20	D₄²×C₂₃	—	2	2	no	—
21	C₂₃×#537	C₄	1	2	yes	complemented
22	C₂₃×#537	C₄	1	1	yes	characteristic, complemented
23	C₂₃×#535	C₄	1	1	yes	characteristic, complemented
24	C₂₃×#535	C₄	1	2	yes	complemented
25	C₂₃×#525	C₂²	1	1	yes	characteristic
26	C₂₃×#525	C₂²	1	2	yes	—
27	C₂×C₂₃×#121	C₂²	1	2	yes	—
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂₃×#520	C₄	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₂₃	—	2	1	no	—
31	C₂₃×#408	—	2	1	no	—
32	C₂₃×#408	—	2	2	no	—
33	C₂₃×#407	C₂²	1	2	yes	complemented
34	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#391	—	2	1	no	—
38	C₂₃×#386	—	2	2	no	—
39	C₂₃×#381	C₂²	1	2	yes	complemented
40	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
41	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
43	C₂₃×#328	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#328	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#328	C₂²	1	2	yes	complemented
46	C₂₃×#327	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#327	C₂²	1	2	yes	complemented
48	C₂₃×#327	C₂²	1	2	yes	complemented
49	C₂₃×#327	C₂²	1	2	yes	complemented
50	C₂₃×#327	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#327	C₂²	1	2	yes	complemented
52	C₂₃×#327	C₂²	1	2	yes	complemented
53	C₂₃×H(5,𝔽₂)	—	4	4	no	—
54	C₂×#41×C₂₃	—	2	1	no	—
55	C₂×#41×C₂₃	—	4	4	no	—
56	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
57	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
58	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
59	C₂×#41×C₂₃	C₂×C₄	1	2	yes	complemented
60	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
61	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
62	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
63	C₂×#41×C₂₃	D₄	1	2	yes	—
64	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	1	no	—
67	C₂²×D₄×C₂₃	—	2	2	no	—
68	C₂²×D₄×C₂₃	—	2	1	no	—
69	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	complemented
70	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	D₄	1	2	yes	—
73	C₂³×C₄×C₂₃	—	2	2	no	—
74	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂₃×#131	—	4	4	no	—
77	C₂×M₁₆×C₂₃	—	2	2	no	—
78	C₂×M₁₆×C₂₃	—	2	1	no	—
79	C₂²×C₈×C₂₃	—	2	2	no	—
80	C₂²×C₈×C₂₃	—	2	1	no	—
81	C₂₃×#127	—	2	1	no	—
82	C₂₃×#127	—	2	2	no	—
83	C₂₃×#124	—	2	1	no	—
84	C₂₃×#124	—	2	2	no	—
85	C₂₃×#123	—	2	2	no	—
86	C₂₃×#123	—	2	1	no	—
87	C₂₃×C₂²⋊Q₈	—	2	1	no	—
88	C₂₃×C₂²⋊Q₈	—	2	2	no	—
89	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
90	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	complemented
91	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
92	C₂₃×#121	—	2	1	no	—
93	C₂₃×#121	—	2	2	no	—
94	C₂₃×#121	—	2	2	no	—
95	C₂₃×#121	—	2	2	no	—
96	C₂₃×#121	—	2	2	no	—
97	C₂₃×#121	—	2	1	no	—
98	C₂₃×#121	—	2	2	no	—
99	C₂₃×#121	—	2	1	no	—
100	C₂₃×#121	—	2	2	no	—
101	C₂₃×#121	C₂×C₄	1	2	yes	complemented
102	C₂₃×#121	C₂×C₄	1	2	yes	complemented
103	C₂₃×#121	C₂×C₄	1	2	yes	complemented
104	C₂₃×#121	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂₃×#121	C₂×C₄	1	2	yes	complemented
106	C₂₃×#121	C₂³	1	1	yes	characteristic
107	C₂₃×#121	C₂³	1	2	yes	—
108	C₂₃×#120	—	2	2	no	—
109	C₂₃×#120	—	2	1	no	—
110	C₂₃×#120	—	2	2	no	—
111	C₂₃×#120	—	2	2	no	—
112	C₂₃×#120	—	2	2	no	—
113	C₄×Q₈×C₂₃	—	2	1	no	—
114	C₄×D₄×C₂₃	—	2	2	no	—
115	C₄×D₄×C₂₃	—	2	1	no	—
116	C₄×D₄×C₂₃	—	2	1	no	—
117	C₄×D₄×C₂₃	—	2	2	no	—
118	C₄×D₄×C₂₃	—	2	1	no	—
119	C₄×D₄×C₂₃	—	2	2	no	—
120	C₄×D₄×C₂₃	—	4	4	no	—
121	C₂₃×#117	C₂×C₄	1	1	yes	characteristic, complemented
122	C₂₃×#117	C₂×C₄	1	2	yes	complemented
123	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	complemented
125	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
126	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
127	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄²×C₂₃	—	2	1	no	—
132	C₂₃×C₂²⋊C₈	—	2	1	no	—
133	C₂₃×C₂²⋊C₈	—	2	2	no	—
134	C₂₃×C₂²⋊C₈	—	2	1	no	—
135	C₂₃×C₂²⋊C₈	—	2	2	no	—
136	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
137	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
138	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
139	C₂₃×#95	—	2	2	no	—
140	C₂₃×#95	—	2	2	no	—
141	C₂₃×#95	C₂³	1	1	yes	characteristic
142	C₂₃×#95	C₂³	1	2	yes	—
143	C₂₃×#95	C₂³	1	1	yes	characteristic
144	C₂⁴×C₂₃	—	2	1	no	—
145	C₂⁴×C₂₃	—	2	2	no	—
146	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
147	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
148	#41×C₂₃	—	2	4	no	—
149	#41×C₂₃	—	2	4	no	—
150	#41×C₂₃	—	4	4	no	—
151	#41×C₂₃	—	4	4	no	—
152	#41×C₂₃	—	4	2	no	—
153	#41×C₂₃	—	4	2	no	—
154	#41×C₂₃	—	4	4	no	—
155	#41×C₂₃	—	4	2	no	—
156	#41×C₂₃	—	4	4	no	—
157	C₂×Q₈×C₂₃	—	4	2	no	—
158	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×Q₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×Q₈×C₂₃	C₂²⋊C₄	1	2	yes	—
161	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₂₃	—	2	4	no	—
163	C₂×D₄×C₂₃	—	2	1	no	—
164	C₂×D₄×C₂₃	—	2	2	no	—
165	C₂×D₄×C₂₃	—	2	1	no	—
166	C₂×D₄×C₂₃	—	2	2	no	—
167	C₂×D₄×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	2	2	no	—
169	C₂×D₄×C₂₃	—	2	2	no	—
170	C₂×D₄×C₂₃	—	2	2	no	—
171	C₂×D₄×C₂₃	—	2	2	no	—
172	C₂×D₄×C₂₃	—	2	2	no	—
173	C₂×D₄×C₂₃	—	2	1	no	—
174	C₂×D₄×C₂₃	—	4	4	no	—
175	C₂×D₄×C₂₃	—	4	2	no	—
176	C₂×D₄×C₂₃	—	4	4	no	—
177	C₂×D₄×C₂₃	—	4	8	no	—
178	C₂×D₄×C₂₃	—	4	4	no	—
179	C₂×D₄×C₂₃	—	8	2	no	—
180	C₂×D₄×C₂₃	—	8	1	no	—
181	C₂×D₄×C₂₃	—	8	2	no	—
182	C₂×D₄×C₂₃	—	8	1	no	—
183	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
184	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
185	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
186	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
188	C₂×D₄×C₂₃	C₂²⋊C₄	1	2	yes	—
189	C₂×D₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
190	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
191	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	2	no	—
195	C₂²×C₄×C₂₃	—	2	2	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	2	no	—
199	C₂²×C₄×C₂₃	—	4	2	no	—
200	C₂²×C₄×C₂₃	—	4	4	no	—
201	C₂²×C₄×C₂₃	—	4	4	no	—
202	C₂²×C₄×C₂₃	—	4	4	no	—
203	C₂²×C₄×C₂₃	—	8	2	no	—
204	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
215	M₁₆×C₂₃	—	4	4	no	—
216	M₁₆×C₂₃	—	4	2	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	2	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	4	4	no	—
221	C₂×C₈×C₂₃	—	4	2	no	—
222	C₄⋊C₄×C₂₃	—	2	2	no	—
223	C₄⋊C₄×C₂₃	—	2	1	no	—
224	C₄⋊C₄×C₂₃	—	2	1	no	—
225	C₄⋊C₄×C₂₃	—	2	2	no	—
226	C₄⋊C₄×C₂₃	—	2	1	no	—
227	C₄⋊C₄×C₂₃	—	4	2	no	—
228	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
229	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
230	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
231	C₂²⋊C₄×C₂₃	—	2	1	no	—
232	C₂²⋊C₄×C₂₃	—	2	2	no	—
233	C₂²⋊C₄×C₂₃	—	2	1	no	—
234	C₂²⋊C₄×C₂₃	—	2	2	no	—
235	C₂²⋊C₄×C₂₃	—	2	1	no	—
236	C₂²⋊C₄×C₂₃	—	2	2	no	—
237	C₂²⋊C₄×C₂₃	—	2	2	no	—
238	C₂²⋊C₄×C₂₃	—	2	2	no	—
239	C₂²⋊C₄×C₂₃	—	2	1	no	—
240	C₂²⋊C₄×C₂₃	—	2	2	no	—
241	C₂²⋊C₄×C₂₃	—	2	1	no	—
242	C₂²⋊C₄×C₂₃	—	2	2	no	—
243	C₂²⋊C₄×C₂₃	—	4	2	no	—
244	C₂²⋊C₄×C₂₃	—	4	4	no	—
245	C₂²⋊C₄×C₂₃	—	8	1	no	—
246	C₄²×C₂₃	—	2	2	no	—
247	C₄²×C₂₃	—	2	1	no	—
248	C₄²×C₂₃	—	4	2	no	—
249	#17603	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	4	no	—
253	C₂³×C₂₃	—	2	1	no	—
254	C₂³×C₂₃	—	2	1	no	—
255	C₂³×C₂₃	—	2	2	no	—
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	4	2	no	—
258	C₂³×C₂₃	—	4	1	no	—
259	C₂³×C₂₃	—	4	1	no	—
260	C₂³×C₂₃	—	4	2	no	—
261	C₂³×C₂₃	—	4	4	no	—
262	C₂³×C₂₃	—	8	2	no	—
263	C₂³×C₂₃	—	8	1	no	—
264	C₂³×C₂₃	—	8	2	no	—
265	C₂³×C₂₃	—	8	1	no	—
266	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
271	Q₈×C₂₃	—	2	2	no	—
272	Q₈×C₂₃	—	2	2	no	—
273	Q₈×C₂₃	—	4	2	no	—
274	Q₈×C₂₃	—	4	1	no	—
275	D₄×C₂₃	—	2	4	no	—
276	D₄×C₂₃	—	2	4	no	—
277	D₄×C₂₃	—	2	4	no	—
278	D₄×C₂₃	—	2	2	no	—
279	D₄×C₂₃	—	4	2	no	—
280	D₄×C₂₃	—	4	2	no	—
281	D₄×C₂₃	—	4	1	no	—
282	D₄×C₂₃	—	4	2	no	—
283	D₄×C₂₃	—	4	4	no	—
284	D₄×C₂₃	—	4	2	no	—
285	D₄×C₂₃	—	4	1	no	—
286	D₄×C₂₃	—	4	2	no	—
287	D₄×C₂₃	—	4	1	no	—
288	D₄×C₂₃	—	4	2	no	—
289	D₄×C₂₃	—	4	4	no	—
290	D₄×C₂₃	—	4	2	no	—
291	D₄×C₂₃	—	8	2	no	—
292	D₄×C₂₃	—	8	1	no	—
293	D₄×C₂₃	—	8	2	no	—
294	D₄×C₂₃	—	8	2	no	—
295	D₄×C₂₃	—	8	2	no	—
296	D₄×C₂₃	#99	1	4	yes	—
297	C₂×C₄×C₂₃	—	2	4	no	—
298	C₂×C₄×C₂₃	—	2	4	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	2	no	—
310	C₂×C₄×C₂₃	—	4	2	no	—
311	C₂×C₄×C₂₃	—	4	2	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	4	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	2	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	2	no	—
321	C₂×C₄×C₂₃	—	4	2	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	8	2	no	—
324	C₂×C₄×C₂₃	—	8	1	no	—
325	C₂×C₄×C₂₃	—	8	8	no	—
326	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
330	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₈×C₂₃	—	4	1	no	—
333	C₈×C₂₃	—	4	2	no	—
334	C₈×C₂₃	—	4	1	no	—
335	#3488	C₂×C₂₃	1	1	yes	characteristic
336	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#2339	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#1519	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#1516	C₂×C₂₃	1	2	yes	complemented
340	#1513	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#1510	C₂×C₂₃	1	2	yes	complemented
342	#1507	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1504	C₂×C₂₃	1	2	yes	complemented
344	#1501	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂×#327	C₂×C₂₃	1	2	yes	complemented
346	C₂²×C₂₃	—	2	1	no	—
347	C₂²×C₂₃	—	2	2	no	—
348	C₂²×C₂₃	—	2	1	no	—
349	C₂²×C₂₃	—	2	2	no	—
350	C₂²×C₂₃	—	2	1	no	—
351	C₂²×C₂₃	—	2	1	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	1	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	2	1	no	—
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	1	no	—
358	C₂²×C₂₃	—	2	1	no	—
359	C₂²×C₂₃	—	4	4	no	—
360	C₂²×C₂₃	—	4	4	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	—	4	1	no	—
363	C₂²×C₂₃	—	4	1	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	1	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	8	1	no	—
368	C₂²×C₂₃	—	8	1	no	—
369	C₂²×C₂₃	—	16	4	no	—
370	C₂²×C₂₃	—	16	2	no	—
371	C₂²×C₂₃	C₂×#99	1	4	yes	—
372	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
373	C₂²×C₂₃	#576	1	1	yes	characteristic
374	C₂²×C₂₃	#577	1	1	yes	characteristic
375	C₄×C₂₃	—	2	1	no	—
376	C₄×C₂₃	—	2	1	no	—
377	C₄×C₂₃	—	2	2	no	—
378	C₄×C₂₃	—	2	1	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	1	no	—
382	C₄×C₂₃	—	4	1	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	1	no	—
385	C₄×C₂₃	—	8	1	no	—
386	C₄×C₂₃	—	8	2	no	—
387	C₄×C₂₃	C₂×#99	1	2	yes	—
388	C₂×H(5,𝔽₂)	C₄×C₂₃	1	1	yes	characteristic, complemented
389	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×#131	—	2	1	no	—
391	#550	—	2	1	no	—
392	#548	—	2	1	no	—
393	#546	—	2	1	no	—
394	#546	—	2	2	no	—
395	D₄²	—	2	1	no	—
396	D₄²	—	2	2	no	—
397	#537	C₄×C₂₃	1	2	yes	complemented
398	#537	C₄×C₂₃	1	1	yes	characteristic, complemented
399	#535	C₄×C₂₃	1	1	yes	characteristic, complemented
400	#535	C₄×C₂₃	1	2	yes	complemented
401	#525	C₂²×C₂₃	1	1	yes	characteristic
402	#525	C₂²×C₂₃	1	2	yes	—
403	C₂×#121	C₂²×C₂₃	1	2	yes	—
404	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
405	#520	C₄×C₂₃	1	1	yes	characteristic, complemented
406	C₂×C₄×D₄	—	2	1	no	—
407	#408	—	2	2	no	—
408	#408	—	2	1	no	—
409	#407	C₂²×C₂₃	1	2	yes	complemented
410	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
411	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
412	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
413	#391	—	2	1	no	—
414	#386	—	2	2	no	—
415	#381	C₂²×C₂₃	1	2	yes	complemented
416	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
417	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
418	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
419	#328	C₂²×C₂₃	1	1	yes	characteristic, complemented
420	#328	C₂²×C₂₃	1	1	yes	characteristic, complemented
421	#328	C₂²×C₂₃	1	2	yes	complemented
422	#327	C₂²×C₂₃	1	1	yes	characteristic, complemented
423	#327	C₂²×C₂₃	1	2	yes	complemented
424	#327	C₂²×C₂₃	1	2	yes	complemented
425	#327	C₂²×C₂₃	1	2	yes	complemented
426	#327	C₂²×C₂₃	1	1	yes	characteristic, complemented
427	#327	C₂²×C₂₃	1	2	yes	complemented
428	#327	C₂²×C₂₃	1	2	yes	complemented
429	C₂×C₂₃	—	2	1	no	—
430	C₂×C₂₃	—	2	1	no	—
431	C₂×C₂₃	—	2	4	no	—
432	C₂×C₂₃	—	4	2	no	—
433	C₂×C₂₃	—	4	1	no	—
434	C₂×C₂₃	—	4	1	no	—
435	C₂×C₂₃	—	8	1	no	—
436	C₂×C₂₃	—	8	2	no	—
437	C₂×C₂₃	C₂²×#99	1	1	yes	characteristic
438	C₂×C₂₃	#2897	1	1	yes	characteristic
439	C₂×C₂₃	#2901	1	1	yes	characteristic
440	H(5,𝔽₂)	—	4	4	no	—
441	C₂×#41	—	2	1	no	—
442	C₂×#41	—	4	4	no	—
443	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
444	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
445	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
446	C₂×#41	C₂×C₄×C₂₃	1	2	yes	complemented
447	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
448	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
449	C₂×#41	D₄×C₂₃	1	2	yes	—
450	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
451	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
452	C₂²×D₄	—	2	2	no	—
453	C₂²×D₄	—	2	1	no	—
454	C₂²×D₄	—	2	2	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	complemented
457	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
458	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
459	C₂²×D₄	D₄×C₂₃	1	2	yes	—
460	C₂³×C₄	—	2	2	no	—
461	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
462	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
463	#131	—	4	4	no	—
464	C₂×M₁₆	—	2	2	no	—
465	C₂×M₁₆	—	2	1	no	—
466	C₂²×C₈	—	2	2	no	—
467	C₂²×C₈	—	2	1	no	—
468	#127	—	2	1	no	—
469	#127	—	2	2	no	—
470	#124	—	2	1	no	—
471	#124	—	2	2	no	—
472	#123	—	2	2	no	—
473	#123	—	2	1	no	—
474	C₂²⋊Q₈	—	2	1	no	—
475	C₂²⋊Q₈	—	2	2	no	—
476	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
477	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	complemented
478	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
479	#121	—	2	2	no	—
480	#121	—	2	2	no	—
481	#121	—	2	2	no	—
482	#121	—	2	1	no	—
483	#121	—	2	2	no	—
484	#121	—	2	1	no	—
485	#121	—	2	2	no	—
486	#121	—	2	1	no	—
487	#121	—	2	2	no	—
488	#121	C₂×C₄×C₂₃	1	2	yes	complemented
489	#121	C₂×C₄×C₂₃	1	2	yes	complemented
490	#121	C₂×C₄×C₂₃	1	2	yes	complemented
491	#121	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
492	#121	C₂×C₄×C₂₃	1	2	yes	complemented
493	#121	C₂³×C₂₃	1	1	yes	characteristic
494	#121	C₂³×C₂₃	1	2	yes	—
495	#120	—	2	2	no	—
496	#120	—	2	1	no	—
497	#120	—	2	2	no	—
498	#120	—	2	2	no	—
499	#120	—	2	2	no	—
500	C₄×Q₈	—	2	1	no	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	1	no	—
503	C₄×D₄	—	2	1	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	1	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	4	4	no	—
508	#117	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
509	#117	C₂×C₄×C₂₃	1	2	yes	complemented
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	complemented
512	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	2	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₄²	—	2	1	no	—
519	C₂²⋊C₈	—	2	1	no	—
520	C₂²⋊C₈	—	2	2	no	—
521	C₂²⋊C₈	—	2	1	no	—
522	C₂²⋊C₈	—	2	2	no	—
523	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
524	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
525	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
526	#95	—	2	2	no	—
527	#95	—	2	2	no	—
528	#95	C₂³×C₂₃	1	1	yes	characteristic
529	#95	C₂³×C₂₃	1	2	yes	—
530	#95	C₂³×C₂₃	1	1	yes	characteristic
531	C₂₃	#17603	1	1	yes	characteristic, direct product factor, Sylow
532	C₂⁴	—	2	1	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
535	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
536	#41	—	2	4	no	—
537	#41	—	2	4	no	—
538	#41	—	4	4	no	—
539	#41	—	4	4	no	—
540	#41	—	4	2	no	—
541	#41	—	4	2	no	—
542	#41	—	4	4	no	—
543	#41	—	4	2	no	—
544	#41	—	4	4	no	—
545	C₂×Q₈	—	4	2	no	—
546	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
547	C₂×Q₈	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
548	C₂×Q₈	C₂²⋊C₄×C₂₃	1	2	yes	—
549	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	4	4	no	—
565	C₂×D₄	—	4	8	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	8	2	no	—
568	C₂×D₄	—	8	1	no	—
569	C₂×D₄	—	8	2	no	—
570	C₂×D₄	—	8	1	no	—
571	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
572	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
573	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
574	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
575	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
576	C₂×D₄	C₂²⋊C₄×C₂₃	1	2	yes	—
577	C₂×D₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
578	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
579	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	4	2	no	—
588	C₂²×C₄	—	4	4	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	4	no	—
591	C₂²×C₄	—	8	2	no	—
592	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
593	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
595	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
598	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	M₁₆	—	4	4	no	—
604	M₁₆	—	4	2	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	4	4	no	—
609	C₂×C₈	—	4	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
617	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
618	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	2	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	4	2	no	—
632	C₂²⋊C₄	—	4	4	no	—
633	C₂²⋊C₄	—	8	1	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	4	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	1	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	2	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	8	2	no	—
650	C₂³	—	8	1	no	—
651	C₂³	—	8	2	no	—
652	C₂³	—	8	1	no	—
653	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
654	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
655	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
656	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
657	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	2	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	1	no	—
662	D₄	—	2	4	no	—
663	D₄	—	2	4	no	—
664	D₄	—	2	4	no	—
665	D₄	—	2	2	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	1	no	—
675	D₄	—	4	2	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	2	no	—
678	D₄	—	8	2	no	—
679	D₄	—	8	2	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	2	no	—
682	D₄	—	8	1	no	—
683	D₄	C₂₃×#99	1	4	yes	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	8	2	no	—
711	C₂×C₄	—	8	1	no	—
712	C₂×C₄	—	8	8	no	—
713	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
714	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
715	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
716	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
717	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
718	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
719	C₈	—	4	1	no	—
720	C₈	—	4	2	no	—
721	C₈	—	4	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	1	no	—
734	C₂²	—	2	1	no	—
735	C₂²	—	4	4	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	1	no	—
739	C₂²	—	4	1	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	1	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	2	no	—
747	C₂²	C₂×C₂₃×#99	1	4	yes	—
748	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
749	C₂²	C₂₃×#576	1	1	yes	characteristic
750	C₂²	C₂₃×#577	1	1	yes	characteristic
751	C₄	—	2	1	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	2	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	1	no	—
758	C₄	—	4	1	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	1	no	—
761	C₄	—	8	2	no	—
762	C₄	—	8	1	no	—
763	C₄	C₂×C₂₃×#99	1	2	yes	—
764	C₂	—	2	1	no	—
765	C₂	—	2	1	no	—
766	C₂	—	2	4	no	—
767	C₂	—	4	2	no	—
768	C₂	—	4	1	no	—
769	C₂	—	4	1	no	—
770	C₂	—	8	1	no	—
771	C₂	—	8	2	no	—
772	C₂	C₂²×C₂₃×#99	1	1	yes	characteristic
773	C₂	C₂₃×#2897	1	1	yes	characteristic
774	C₂	C₂₃×#2901	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#3488	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2880	C₂	semidirect
3. C₂₃×#2339	C₂	semidirect
4. C₂₃×#1519	C₂	semidirect
5. C₂₃×#1516	C₂	semidirect
6. C₂₃×#1513	C₂	semidirect
7. C₂₃×#1510	C₂	semidirect
8. C₂₃×#1507	C₂	semidirect
9. C₂₃×#1504	C₂	semidirect
10. C₂₃×#1501	C₂	semidirect
11. C₂×C₂₃×#327	C₂	semidirect
12. C₂×C₂₃×H(5,𝔽₂)	C₄	semidirect
21. C₂₃×#537	C₄	semidirect
22. C₂₃×#537	C₄	semidirect
23. C₂₃×#535	C₄	semidirect
24. C₂₃×#535	C₄	semidirect
29. C₂₃×#520	C₄	semidirect
33. C₂₃×#407	C₂²	semidirect
34. C₂₃×#407	C₂²	semidirect
35. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
36. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
39. C₂₃×#381	C₂²	semidirect
40. C₂₃×#380	C₂²	semidirect
41. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
42. C₂×C₂₃×#95	C₂²	semidirect
43. C₂₃×#328	C₂²	semidirect
44. C₂₃×#328	C₂²	semidirect
45. C₂₃×#328	C₂²	semidirect
46. C₂₃×#327	C₂²	semidirect
47. C₂₃×#327	C₂²	semidirect
48. C₂₃×#327	C₂²	semidirect
49. C₂₃×#327	C₂²	semidirect
50. C₂₃×#327	C₂²	semidirect
51. C₂₃×#327	C₂²	semidirect
52. C₂₃×#327	C₂²	semidirect
59. C₂×#41×C₂₃	C₂×C₄	semidirect
60. C₂×#41×C₂₃	C₂×C₄	semidirect
69. C₂²×D₄×C₂₃	C₂×C₄	semidirect
70. C₂²×D₄×C₂₃	C₂×C₄	semidirect
89. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
90. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
101. C₂₃×#121	C₂×C₄	semidirect
102. C₂₃×#121	C₂×C₄	semidirect
103. C₂₃×#121	C₂×C₄	semidirect
104. C₂₃×#121	C₂×C₄	semidirect
105. C₂₃×#121	C₂×C₄	semidirect
121. C₂₃×#117	C₂×C₄	semidirect
122. C₂₃×#117	C₂×C₄	semidirect
124. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
125. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
249. #17603	C₂₃	direct (N × H)
336. #2880	C₂×C₂₃	semidirect
337. #2339	C₂×C₂₃	semidirect
338. #1519	C₂×C₂₃	semidirect
339. #1516	C₂×C₂₃	semidirect
340. #1513	C₂×C₂₃	semidirect
341. #1510	C₂×C₂₃	semidirect
342. #1507	C₂×C₂₃	semidirect
343. #1504	C₂×C₂₃	semidirect
344. #1501	C₂×C₂₃	semidirect
345. C₂×#327	C₂×C₂₃	semidirect
388. C₂×H(5,𝔽₂)	C₄×C₂₃	semidirect
397. #537	C₄×C₂₃	semidirect
398. #537	C₄×C₂₃	semidirect
399. #535	C₄×C₂₃	semidirect
400. #535	C₄×C₂₃	semidirect
405. #520	C₄×C₂₃	semidirect
409. #407	C₂²×C₂₃	semidirect
410. #407	C₂²×C₂₃	semidirect
411. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
412. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
415. #381	C₂²×C₂₃	semidirect
416. #380	C₂²×C₂₃	semidirect
417. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
418. C₂×#95	C₂²×C₂₃	semidirect
419. #328	C₂²×C₂₃	semidirect
420. #328	C₂²×C₂₃	semidirect
421. #328	C₂²×C₂₃	semidirect
422. #327	C₂²×C₂₃	semidirect
423. #327	C₂²×C₂₃	semidirect
424. #327	C₂²×C₂₃	semidirect
425. #327	C₂²×C₂₃	semidirect
426. #327	C₂²×C₂₃	semidirect
427. #327	C₂²×C₂₃	semidirect
428. #327	C₂²×C₂₃	semidirect
446. C₂×#41	C₂×C₄×C₂₃	semidirect
447. C₂×#41	C₂×C₄×C₂₃	semidirect
456. C₂²×D₄	C₂×C₄×C₂₃	semidirect
457. C₂²×D₄	C₂×C₄×C₂₃	semidirect
476. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
477. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
488. #121	C₂×C₄×C₂₃	semidirect
489. #121	C₂×C₄×C₂₃	semidirect
490. #121	C₂×C₄×C₂₃	semidirect
491. #121	C₂×C₄×C₂₃	semidirect
492. #121	C₂×C₄×C₂₃	semidirect
508. #117	C₂×C₄×C₂₃	semidirect
509. #117	C₂×C₄×C₂₃	semidirect
511. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
512. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
531. C₂₃	#17603	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×#3488	2
C₂₃×#2880	2
C₂₃×#2339	2
C₂₃×#1519	2
C₂₃×#1516	2
C₂₃×#1513	2
C₂₃×#1510	2
C₂₃×#1507	2
C₂₃×#1504	2
C₂₃×#1501	2
C₂×C₂₃×#327	2
#17603	23

Subgroups — C23×#17603 #19165229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#17603 #19165229