Subgroups — C₂₃×#26977 #19174603

Order 5888.

1028 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1936	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#121	—	2	1	no	—
21	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#466	—	2	4	no	—
27	C₂₃×#442	—	2	4	no	—
28	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#106	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×C₂₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
41	C₂₃×#397	—	2	1	no	—
42	C₂₃×#394	—	2	1	no	—
43	C₂₃×#394	—	2	1	no	—
44	C₂₃×#392	—	2	1	no	—
45	C₂₃×#390	C₂²	1	1	yes	characteristic
46	C₂₃×#390	C₂²	1	1	yes	characteristic
47	C₂₃×#389	C₂²	1	1	yes	characteristic
48	C₂₃×#389	C₂²	1	1	yes	characteristic
49	C₂₃×#386	—	2	1	no	—
50	C₂₃×#386	—	2	1	no	—
51	C₂₃×#382	C₂²	1	1	yes	characteristic
52	C₂₃×#381	—	2	1	no	—
53	C₂₃×#380	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₂₃	—	2	1	no	—
62	C₂²×D₄×C₂₃	—	2	1	no	—
63	C₂²×D₄×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	—	2	1	no	—
65	C₂²×D₄×C₂₃	—	2	1	no	—
66	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	—	2	1	no	—
70	C₂³×C₄×C₂₃	—	2	1	no	—
71	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂×D₈×C₂₃	—	2	2	no	—
73	C₂×D₈×C₂₃	—	2	2	no	—
74	C₂×D₈×C₂₃	—	2	2	no	—
75	C₂×D₈×C₂₃	—	2	2	no	—
76	C₂×D₈×C₂₃	—	2	2	no	—
77	C₂×D₈×C₂₃	—	4	1	no	—
78	C₂²×C₈×C₂₃	—	2	2	no	—
79	C₂²×C₈×C₂₃	—	2	2	no	—
80	C₂²×C₈×C₂₃	—	4	1	no	—
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂₃×#127	—	2	2	no	—
86	C₂₃×#127	—	4	1	no	—
87	C₂₃×#121	—	2	2	no	—
88	C₂₃×#121	—	2	2	no	—
89	C₂₃×#121	—	2	2	no	—
90	C₂₃×#121	—	4	4	no	—
91	C₂₃×#121	—	4	1	no	—
92	C₂₃×#121	—	4	1	no	—
93	C₂₃×#121	—	4	1	no	—
94	C₄×D₄×C₂₃	—	2	2	no	—
95	C₄×D₄×C₂₃	—	2	2	no	—
96	C₄×D₄×C₂₃	—	4	1	no	—
97	C₄×D₄×C₂₃	—	4	1	no	—
98	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
99	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
119	C₂₃×#107	—	2	2	no	—
120	C₂₃×#106	—	2	2	no	—
121	C₂₃×#102	—	2	2	no	—
122	C₂₃×#102	—	2	2	no	—
123	C₂₃×#102	—	2	2	no	—
124	C₂₃×#102	—	2	2	no	—
125	C₂₃×#102	—	4	1	no	—
126	C₂₃×#102	—	4	1	no	—
127	C₂₃×#102	—	4	1	no	—
128	C₂₃×#102	D₄	1	4	yes	complemented
129	C₂₃×C₂²⋊C₈	—	2	2	no	—
130	C₂₃×#97	—	2	2	no	—
131	C₂₃×#97	—	4	1	no	—
132	C₂₃×#95	—	2	1	no	—
133	C₂₃×#95	—	2	1	no	—
134	C₂₃×#95	—	2	1	no	—
135	C₂₃×#95	—	2	1	no	—
136	C₂₃×#95	—	2	1	no	—
137	C₂₃×#95	D₄	1	1	yes	characteristic
138	C₂₃×#95	D₄	1	1	yes	characteristic
139	C₂⁴×C₂₃	—	2	1	no	—
140	C₂⁴×C₂₃	—	2	1	no	—
141	C₂⁴×C₂₃	—	2	1	no	—
142	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
143	C₂×D₄×C₂₃	—	2	1	no	—
144	C₂×D₄×C₂₃	—	2	1	no	—
145	C₂×D₄×C₂₃	—	2	1	no	—
146	C₂×D₄×C₂₃	—	2	1	no	—
147	C₂×D₄×C₂₃	—	2	1	no	—
148	C₂×D₄×C₂₃	—	2	1	no	—
149	C₂×D₄×C₂₃	—	2	1	no	—
150	C₂×D₄×C₂₃	—	2	1	no	—
151	C₂×D₄×C₂₃	—	2	1	no	—
152	C₂×D₄×C₂₃	—	2	1	no	—
153	C₂×D₄×C₂₃	—	2	1	no	—
154	C₂×D₄×C₂₃	—	2	1	no	—
155	C₂×D₄×C₂₃	—	2	1	no	—
156	C₂×D₄×C₂₃	—	2	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	4	2	no	—
160	C₂×D₄×C₂₃	—	4	2	no	—
161	C₂×D₄×C₂₃	—	4	2	no	—
162	C₂×D₄×C₂₃	—	4	2	no	—
163	C₂×D₄×C₂₃	—	4	2	no	—
164	C₂×D₄×C₂₃	—	4	2	no	—
165	C₂×D₄×C₂₃	—	4	2	no	—
166	C₂×D₄×C₂₃	—	4	2	no	—
167	C₂×D₄×C₂₃	—	4	2	no	—
168	C₂×D₄×C₂₃	—	4	2	no	—
169	C₂×D₄×C₂₃	—	8	1	no	—
170	C₂×D₄×C₂₃	—	8	1	no	—
171	C₂×D₄×C₂₃	—	8	1	no	—
172	C₂×D₄×C₂₃	—	8	1	no	—
173	C₂×D₄×C₂₃	—	8	1	no	—
174	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₂₃	#41	1	2	yes	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	4	2	no	—
188	C₂²×C₄×C₂₃	—	4	2	no	—
189	C₂²×C₄×C₂₃	—	4	2	no	—
190	C₂²×C₄×C₂₃	—	4	2	no	—
191	C₂²×C₄×C₂₃	—	8	1	no	—
192	C₂²×C₄×C₂₃	—	8	1	no	—
193	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
199	D₈×C₂₃	—	2	8	no	—
200	D₈×C₂₃	—	4	4	no	—
201	C₂×C₈×C₂₃	—	2	1	no	—
202	C₂×C₈×C₂₃	—	2	1	no	—
203	C₂×C₈×C₂₃	—	2	1	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	—	4	4	no	—
211	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
212	C₂×C₈×C₂₃	#41	1	2	yes	—
213	C₂×C₈×C₂₃	#41	1	2	yes	—
214	C₄⋊C₄×C₂₃	—	2	1	no	—
215	C₄⋊C₄×C₂₃	—	2	1	no	—
216	C₄⋊C₄×C₂₃	—	2	1	no	—
217	C₄⋊C₄×C₂₃	—	2	1	no	—
218	C₄⋊C₄×C₂₃	—	2	1	no	—
219	C₄⋊C₄×C₂₃	—	2	1	no	—
220	C₄⋊C₄×C₂₃	—	2	1	no	—
221	C₄⋊C₄×C₂₃	—	2	1	no	—
222	C₄⋊C₄×C₂₃	—	2	1	no	—
223	C₄⋊C₄×C₂₃	—	4	2	no	—
224	C₄⋊C₄×C₂₃	—	8	1	no	—
225	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
226	C₂²⋊C₄×C₂₃	—	2	2	no	—
227	C₂²⋊C₄×C₂₃	—	4	1	no	—
228	C₂²⋊C₄×C₂₃	—	4	2	no	—
229	C₂²⋊C₄×C₂₃	—	4	2	no	—
230	C₂²⋊C₄×C₂₃	—	4	2	no	—
231	C₂²⋊C₄×C₂₃	—	4	2	no	—
232	C₂²⋊C₄×C₂₃	—	4	2	no	—
233	C₂²⋊C₄×C₂₃	—	4	2	no	—
234	C₂²⋊C₄×C₂₃	—	8	1	no	—
235	C₂²⋊C₄×C₂₃	—	8	1	no	—
236	C₂²⋊C₄×C₂₃	—	8	1	no	—
237	C₂²⋊C₄×C₂₃	—	8	1	no	—
238	C₄²×C₂₃	—	2	1	no	—
239	C₄²×C₂₃	—	2	1	no	—
240	C₄²×C₂₃	—	2	1	no	—
241	C₄²×C₂₃	—	2	1	no	—
242	#26977	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂³×C₂₃	—	2	1	no	—
244	C₂³×C₂₃	—	2	1	no	—
245	C₂³×C₂₃	—	2	1	no	—
246	C₂³×C₂₃	—	2	1	no	—
247	C₂³×C₂₃	—	2	1	no	—
248	C₂³×C₂₃	—	2	1	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	4	1	no	—
252	C₂³×C₂₃	—	4	1	no	—
253	C₂³×C₂₃	—	4	1	no	—
254	C₂³×C₂₃	—	4	1	no	—
255	C₂³×C₂₃	—	4	1	no	—
256	C₂³×C₂₃	—	4	1	no	—
257	C₂³×C₂₃	—	4	1	no	—
258	C₂³×C₂₃	—	4	1	no	—
259	C₂³×C₂₃	—	4	1	no	—
260	C₂³×C₂₃	—	4	1	no	—
261	C₂³×C₂₃	—	4	1	no	—
262	C₂³×C₂₃	—	4	1	no	—
263	C₂³×C₂₃	—	4	1	no	—
264	C₂³×C₂₃	—	4	1	no	—
265	C₂³×C₂₃	—	4	1	no	—
266	C₂³×C₂₃	—	4	1	no	—
267	C₂³×C₂₃	—	4	1	no	—
268	C₂³×C₂₃	—	4	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
271	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
272	D₄×C₂₃	—	2	2	no	—
273	D₄×C₂₃	—	2	2	no	—
274	D₄×C₂₃	—	2	2	no	—
275	D₄×C₂₃	—	2	2	no	—
276	D₄×C₂₃	—	4	1	no	—
277	D₄×C₂₃	—	4	1	no	—
278	D₄×C₂₃	—	4	1	no	—
279	D₄×C₂₃	—	4	1	no	—
280	D₄×C₂₃	—	4	1	no	—
281	D₄×C₂₃	—	4	1	no	—
282	D₄×C₂₃	—	4	1	no	—
283	D₄×C₂₃	—	4	1	no	—
284	D₄×C₂₃	—	8	4	no	—
285	D₄×C₂₃	—	8	4	no	—
286	D₄×C₂₃	—	8	4	no	—
287	D₄×C₂₃	—	8	4	no	—
288	D₄×C₂₃	—	8	4	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	1	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	1	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	4	1	no	—
306	C₂×C₄×C₂₃	—	4	1	no	—
307	C₂×C₄×C₂₃	—	4	1	no	—
308	C₂×C₄×C₂₃	—	4	1	no	—
309	C₂×C₄×C₂₃	—	4	1	no	—
310	C₂×C₄×C₂₃	—	4	1	no	—
311	C₂×C₄×C₂₃	—	4	1	no	—
312	C₂×C₄×C₂₃	—	4	1	no	—
313	C₂×C₄×C₂₃	—	4	1	no	—
314	C₂×C₄×C₂₃	—	4	1	no	—
315	C₂×C₄×C₂₃	—	4	1	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	1	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	8	4	no	—
324	C₂×C₄×C₂₃	—	8	4	no	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
327	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
329	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
331	C₈×C₂₃	—	2	2	no	—
332	C₈×C₂₃	—	2	2	no	—
333	C₈×C₂₃	—	2	2	no	—
334	C₈×C₂₃	—	4	1	no	—
335	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
336	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#2428	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#2420	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#2085	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#2011	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#1999	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#1961	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#1936	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#1936	C₂×C₂₃	1	1	yes	characteristic, complemented
346	#1893	C₂×C₂₃	1	1	yes	characteristic, complemented
347	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#1862	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#1752	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	2	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	4	1	no	—
354	C₂²×C₂₃	—	4	1	no	—
355	C₂²×C₂₃	—	4	1	no	—
356	C₂²×C₂₃	—	4	1	no	—
357	C₂²×C₂₃	—	4	2	no	—
358	C₂²×C₂₃	—	4	2	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	8	1	no	—
364	C₂²×C₂₃	—	8	1	no	—
365	C₂²×C₂₃	—	8	1	no	—
366	C₂²×C₂₃	—	8	1	no	—
367	C₂²×C₂₃	—	8	1	no	—
368	C₂²×C₂₃	—	8	1	no	—
369	C₂²×C₂₃	—	8	1	no	—
370	C₂²×C₂₃	—	8	1	no	—
371	C₂²×C₂₃	—	8	1	no	—
372	C₂²×C₂₃	—	8	1	no	—
373	C₂²×C₂₃	—	8	1	no	—
374	C₂²×C₂₃	—	8	1	no	—
375	C₂²×C₂₃	—	8	1	no	—
376	C₂²×C₂₃	—	8	1	no	—
377	C₂²×C₂₃	—	8	1	no	—
378	C₂²×C₂₃	#532	1	1	yes	characteristic
379	C₂²×C₂₃	D₄²	1	1	yes	characteristic
380	C₂²×C₂₃	#546	1	1	yes	characteristic
381	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
382	C₂²×C₂₃	#575	1	1	yes	characteristic
383	C₂²×C₂₃	#576	1	1	yes	characteristic
384	C₂²×C₂₃	#576	1	1	yes	characteristic
385	C₄×C₂₃	—	4	1	no	—
386	C₄×C₂₃	—	4	1	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	1	no	—
389	C₄×C₂₃	—	4	1	no	—
390	C₄×C₂₃	—	4	1	no	—
391	C₄×C₂₃	—	8	1	no	—
392	C₄×C₂₃	—	8	1	no	—
393	C₄×C₂₃	—	8	1	no	—
394	C₄×C₂₃	—	8	1	no	—
395	C₄×C₂₃	#525	1	1	yes	characteristic
396	C₄×C₂₃	#540	1	1	yes	characteristic
397	C₄×C₂₃	#546	1	1	yes	characteristic
398	C₄×C₂₃	#553	1	1	yes	characteristic
399	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#121	—	2	1	no	—
404	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
409	#466	—	2	4	no	—
410	#442	—	2	4	no	—
411	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
412	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
416	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
417	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
424	#397	—	2	1	no	—
425	#394	—	2	1	no	—
426	#394	—	2	1	no	—
427	#392	—	2	1	no	—
428	#390	C₂²×C₂₃	1	1	yes	characteristic
429	#390	C₂²×C₂₃	1	1	yes	characteristic
430	#389	C₂²×C₂₃	1	1	yes	characteristic
431	#389	C₂²×C₂₃	1	1	yes	characteristic
432	#386	—	2	1	no	—
433	#386	—	2	1	no	—
434	#382	C₂²×C₂₃	1	1	yes	characteristic
435	#381	—	2	1	no	—
436	#380	C₂²×C₂₃	1	1	yes	characteristic
437	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
438	#340	C₂²×C₂₃	1	1	yes	characteristic
439	#340	C₂²×C₂₃	1	1	yes	characteristic
440	#340	C₂²×C₂₃	1	1	yes	characteristic
441	#340	C₂²×C₂₃	1	1	yes	characteristic
442	#336	C₂²×C₂₃	1	1	yes	characteristic
443	#336	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₂₃	—	4	2	no	—
445	C₂×C₂₃	—	8	2	no	—
446	C₂×C₂₃	—	8	2	no	—
447	C₂×C₂₃	—	16	1	no	—
448	C₂×C₂₃	#2464	1	1	yes	characteristic
449	C₂×C₂₃	#3176	1	1	yes	characteristic
450	C₂×C₂₃	#3180	1	1	yes	characteristic
451	C₂×C₂₃	#3264	1	1	yes	characteristic
452	C₂×C₂₃	#3268	1	1	yes	characteristic
453	C₂×C₂₃	#3318	1	1	yes	characteristic
454	C₂×C₂₃	#3319	1	1	yes	characteristic
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
461	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
462	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
463	C₂³×C₄	—	2	1	no	—
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
466	C₂×D₈	—	2	2	no	—
467	C₂×D₈	—	2	2	no	—
468	C₂×D₈	—	2	2	no	—
469	C₂×D₈	—	2	2	no	—
470	C₂×D₈	—	2	2	no	—
471	C₂×D₈	—	4	1	no	—
472	C₂²×C₈	—	2	2	no	—
473	C₂²×C₈	—	2	2	no	—
474	C₂²×C₈	—	4	1	no	—
475	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
479	#127	—	2	2	no	—
480	#127	—	4	1	no	—
481	#121	—	2	2	no	—
482	#121	—	2	2	no	—
483	#121	—	2	2	no	—
484	#121	—	4	4	no	—
485	#121	—	4	1	no	—
486	#121	—	4	1	no	—
487	#121	—	4	1	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	4	1	no	—
491	C₄×D₄	—	4	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	1	no	—
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
510	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
512	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
513	#107	—	2	2	no	—
514	#106	—	2	2	no	—
515	#102	—	2	2	no	—
516	#102	—	2	2	no	—
517	#102	—	2	2	no	—
518	#102	—	2	2	no	—
519	#102	—	4	1	no	—
520	#102	—	4	1	no	—
521	#102	—	4	1	no	—
522	#102	D₄×C₂₃	1	4	yes	complemented
523	C₂²⋊C₈	—	2	2	no	—
524	#97	—	2	2	no	—
525	#97	—	4	1	no	—
526	#95	—	2	1	no	—
527	#95	—	2	1	no	—
528	#95	—	2	1	no	—
529	#95	—	2	1	no	—
530	#95	—	2	1	no	—
531	#95	D₄×C₂₃	1	1	yes	characteristic
532	#95	D₄×C₂₃	1	1	yes	characteristic
533	C₂₃	#26977	1	1	yes	characteristic, direct product factor, Sylow
534	C₂⁴	—	2	1	no	—
535	C₂⁴	—	2	1	no	—
536	C₂⁴	—	2	1	no	—
537	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	4	2	no	—
555	C₂×D₄	—	4	2	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	2	no	—
559	C₂×D₄	—	4	2	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	2	no	—
562	C₂×D₄	—	4	2	no	—
563	C₂×D₄	—	4	2	no	—
564	C₂×D₄	—	8	1	no	—
565	C₂×D₄	—	8	1	no	—
566	C₂×D₄	—	8	1	no	—
567	C₂×D₄	—	8	1	no	—
568	C₂×D₄	—	8	1	no	—
569	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
570	C₂×D₄	#41×C₂₃	1	2	yes	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	8	1	no	—
587	C₂²×C₄	—	8	1	no	—
588	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
594	D₈	—	2	8	no	—
595	D₈	—	4	4	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	2	1	no	—
601	C₂×C₈	—	2	1	no	—
602	C₂×C₈	—	2	1	no	—
603	C₂×C₈	—	2	1	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	4	4	no	—
606	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
607	C₂×C₈	#41×C₂₃	1	2	yes	—
608	C₂×C₈	#41×C₂₃	1	2	yes	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	8	1	no	—
620	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
621	C₂²⋊C₄	—	2	2	no	—
622	C₂²⋊C₄	—	4	1	no	—
623	C₂²⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	4	2	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	2	no	—
629	C₂²⋊C₄	—	8	1	no	—
630	C₂²⋊C₄	—	8	1	no	—
631	C₂²⋊C₄	—	8	1	no	—
632	C₂²⋊C₄	—	8	1	no	—
633	C₄²	—	2	1	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	—	2	1	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	1	no	—
653	C₂³	—	4	1	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	4	1	no	—
662	C₂³	—	4	1	no	—
663	C₂³	—	4	1	no	—
664	C₂³	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
665	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
666	D₄	—	2	2	no	—
667	D₄	—	2	2	no	—
668	D₄	—	2	2	no	—
669	D₄	—	2	2	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	4	1	no	—
673	D₄	—	4	1	no	—
674	D₄	—	4	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	4	no	—
681	D₄	—	8	4	no	—
682	D₄	—	8	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	4	1	no	—
706	C₂×C₄	—	4	1	no	—
707	C₂×C₄	—	4	1	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	1	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	1	no	—
715	C₂×C₄	—	4	1	no	—
716	C₂×C₄	—	4	1	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
720	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
721	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
722	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
723	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
724	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	4	1	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	8	1	no	—
744	C₂²	—	8	1	no	—
745	C₂²	—	8	1	no	—
746	C₂²	—	8	1	no	—
747	C₂²	—	8	1	no	—
748	C₂²	—	8	1	no	—
749	C₂²	—	8	1	no	—
750	C₂²	—	8	1	no	—
751	C₂²	—	8	1	no	—
752	C₂²	—	8	1	no	—
753	C₂²	—	8	1	no	—
754	C₂²	—	8	1	no	—
755	C₂²	—	8	1	no	—
756	C₂²	—	8	1	no	—
757	C₂²	C₂₃×#532	1	1	yes	characteristic
758	C₂²	D₄²×C₂₃	1	1	yes	characteristic
759	C₂²	C₂₃×#546	1	1	yes	characteristic
760	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
761	C₂²	C₂₃×#575	1	1	yes	characteristic
762	C₂²	C₂₃×#576	1	1	yes	characteristic
763	C₂²	C₂₃×#576	1	1	yes	characteristic
764	C₄	—	4	1	no	—
765	C₄	—	4	1	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	1	no	—
768	C₄	—	4	1	no	—
769	C₄	—	4	1	no	—
770	C₄	—	8	1	no	—
771	C₄	—	8	1	no	—
772	C₄	—	8	1	no	—
773	C₄	—	8	1	no	—
774	C₄	C₂₃×#525	1	1	yes	characteristic
775	C₄	C₂₃×#540	1	1	yes	characteristic
776	C₄	C₂₃×#546	1	1	yes	characteristic
777	C₄	C₂₃×#553	1	1	yes	characteristic
778	C₂	—	4	2	no	—
779	C₂	—	8	2	no	—
780	C₂	—	8	2	no	—
781	C₂	—	16	1	no	—
782	C₂	C₂₃×#2464	1	1	yes	characteristic
783	C₂	C₂₃×#3176	1	1	yes	characteristic
784	C₂	C₂₃×#3180	1	1	yes	characteristic
785	C₂	C₂₃×#3264	1	1	yes	characteristic
786	C₂	C₂₃×#3268	1	1	yes	characteristic
787	C₂	C₂₃×#3318	1	1	yes	characteristic
788	C₂	C₂₃×#3319	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#466	C₂	semidirect
2. C₂×C₂₃×#442	C₂	semidirect
3. C₂₃×#2428	C₂	semidirect
4. C₂₃×#2420	C₂	semidirect
5. C₂₃×#2085	C₂	semidirect
6. C₂₃×#2034	C₂	semidirect
7. C₂₃×#2011	C₂	semidirect
8. C₂₃×#1999	C₂	semidirect
9. C₂₃×#1961	C₂	semidirect
10. C₂₃×#1936	C₂	semidirect
11. C₂₃×#1936	C₂	semidirect
12. C₂₃×#1893	C₂	semidirect
13. C₂₃×#1879	C₂	semidirect
14. C₂₃×#1862	C₂	semidirect
15. C₂₃×#1752	C₂	semidirect
128. C₂₃×#102	D₄	semidirect
242. #26977	C₂₃	direct (N × H)
335. C₂×#466	C₂×C₂₃	semidirect
336. C₂×#442	C₂×C₂₃	semidirect
337. #2428	C₂×C₂₃	semidirect
338. #2420	C₂×C₂₃	semidirect
339. #2085	C₂×C₂₃	semidirect
340. #2034	C₂×C₂₃	semidirect
341. #2011	C₂×C₂₃	semidirect
342. #1999	C₂×C₂₃	semidirect
343. #1961	C₂×C₂₃	semidirect
344. #1936	C₂×C₂₃	semidirect
345. #1936	C₂×C₂₃	semidirect
346. #1893	C₂×C₂₃	semidirect
347. #1879	C₂×C₂₃	semidirect
348. #1862	C₂×C₂₃	semidirect
349. #1752	C₂×C₂₃	semidirect
522. #102	D₄×C₂₃	semidirect
533. C₂₃	#26977	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×#466	2
C₂×C₂₃×#442	2
C₂₃×#2428	2
C₂₃×#2420	2
C₂₃×#2085	2
C₂₃×#2034	2
C₂₃×#2011	2
C₂₃×#1999	2
C₂₃×#1961	2
C₂₃×#1936	2
C₂₃×#1893	2
C₂₃×#1879	2
C₂₃×#1862	2
C₂₃×#1752	2
#26977	23

Subgroups — C23×#26977 #19174603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#26977 #19174603