Subgroups — C₂₃×#36829 #19184455

Order 5888.

1462 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2855	C₂	1	2	yes	maximal
2	C₂₃×#2806	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2802	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2776	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2774	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2745	C₂	1	2	yes	maximal
7	C₂₃×#2738	C₂	1	2	yes	maximal
8	C₂₃×#2698	C₂	1	2	yes	maximal
9	C₂₃×#2689	C₂	1	2	yes	maximal
10	C₂₃×#2655	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2611	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2605	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2599	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2588	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2478	C₂	1	2	yes	maximal
17	C₂₃×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2296	C₂	1	1	yes	maximal, characteristic
20	C₂×C₂₃×#126	C₂²	1	2	yes	—
21	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
27	C₂₃×#401	C₂²	1	2	yes	—
28	C₂₃×#400	C₂²	1	2	yes	—
29	C₂₃×#400	C₂²	1	2	yes	—
30	C₂₃×#400	C₂²	1	2	yes	—
31	C₂₃×#400	C₂²	1	2	yes	—
32	C₂₃×#400	C₂²	1	2	yes	—
33	C₂₃×#400	C₂²	1	2	yes	—
34	C₂₃×#400	C₂²	1	2	yes	—
35	C₂₃×#400	C₂²	1	1	yes	characteristic
36	C₂₃×#399	C₂²	1	1	yes	characteristic
37	C₂₃×#398	C₂²	1	2	yes	—
38	C₂₃×#398	C₂²	1	2	yes	—
39	C₂₃×#398	C₂²	1	2	yes	—
40	C₂₃×#398	C₂²	1	2	yes	—
41	C₂₃×#398	C₂²	1	2	yes	—
42	C₂₃×#398	C₂²	1	2	yes	—
43	C₂₃×#398	C₂²	1	2	yes	—
44	C₂₃×#398	C₂²	1	1	yes	characteristic
45	C₂₃×#398	C₂²	1	1	yes	characteristic
46	C₂₃×#397	C₂²	1	1	yes	characteristic
47	C₂₃×#397	C₂²	1	2	yes	—
48	C₂₃×#397	C₂²	1	1	yes	characteristic
49	C₂₃×#397	C₂²	1	2	yes	—
50	C₂₃×#395	C₂²	1	2	yes	—
51	C₂₃×#395	C₂²	1	2	yes	—
52	C₂₃×#395	C₂²	1	2	yes	—
53	C₂₃×#395	C₂²	1	1	yes	characteristic
54	C₂₃×#393	C₂²	1	1	yes	characteristic
55	C₂₃×#391	C₂²	1	2	yes	—
56	C₂₃×#391	C₂²	1	2	yes	—
57	C₂₃×#391	C₂²	1	2	yes	—
58	C₂₃×#391	C₂²	1	2	yes	—
59	C₂₃×#391	C₂²	1	2	yes	—
60	C₂₃×#389	C₂²	1	2	yes	—
61	C₂₃×#389	C₂²	1	2	yes	—
62	C₂₃×#389	C₂²	1	2	yes	—
63	C₂₃×#389	C₂²	1	2	yes	—
64	C₂₃×#389	C₂²	1	2	yes	—
65	C₂₃×#389	C₂²	1	2	yes	—
66	C₂₃×#389	C₂²	1	2	yes	—
67	C₂₃×#389	C₂²	1	2	yes	—
68	C₂₃×#389	C₂²	1	2	yes	—
69	C₂₃×#389	C₂²	1	2	yes	—
70	C₂₃×#389	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
73	C₂₃×#388	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#387	C₂²	1	2	yes	—
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#387	C₂²	1	2	yes	—
88	C₂₃×#387	C₂²	1	2	yes	—
89	C₂₃×#387	C₂²	1	2	yes	—
90	C₂₃×#387	C₂²	1	2	yes	—
91	C₂₃×#385	C₂²	1	2	yes	—
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#385	C₂²	1	2	yes	—
95	C₂₃×#383	C₂²	1	2	yes	—
96	C₂₃×#383	C₂²	1	1	yes	characteristic
97	C₂₃×#382	C₂²	1	2	yes	—
98	C₂₃×#381	C₂²	1	2	yes	—
99	C₂₃×#381	C₂²	1	2	yes	—
100	C₂₃×#380	C₂²	1	2	yes	—
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
106	C₂₃×#376	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
111	C₂₃×#126	—	4	4	no	—
112	C₂₃×#125	—	2	4	no	—
113	C₂₃×C₂²⋊Q₈	—	4	4	no	—
114	C₄×Q₈×C₂₃	—	2	4	no	—
115	C₂₃×#117	—	2	4	no	—
116	C₂₃×#117	—	4	2	no	—
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄²×C₂₃	—	4	2	no	—
153	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
156	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂₃×#95	C₂³	1	1	yes	characteristic
165	C₂₃×#95	C₂³	1	1	yes	characteristic
166	C₂₃×#95	C₂³	1	2	yes	—
167	C₂₃×#95	C₂³	1	2	yes	—
168	C₂₃×#95	C₂³	1	2	yes	—
169	C₂₃×#95	C₂³	1	2	yes	—
170	C₂₃×#95	C₂³	1	2	yes	—
171	C₂₃×#95	C₂³	1	2	yes	—
172	C₂₃×#95	C₂³	1	2	yes	—
173	C₂₃×#95	C₂³	1	2	yes	—
174	C₂₃×#95	C₂³	1	2	yes	—
175	C₂₃×#95	C₂³	1	2	yes	—
176	C₂₃×#95	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	1	yes	characteristic
185	C₂₃×#95	C₂³	1	2	yes	—
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	1	yes	characteristic
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₂₃	—	2	2	no	—
203	C₂×Q₈×C₂₃	—	2	4	no	—
204	C₂×Q₈×C₂₃	—	4	2	no	—
205	C₂×Q₈×C₂₃	—	4	2	no	—
206	C₂×Q₈×C₂₃	—	4	2	no	—
207	C₂²×C₄×C₂₃	—	2	2	no	—
208	C₂²×C₄×C₂₃	—	2	2	no	—
209	C₂²×C₄×C₂₃	—	2	2	no	—
210	C₂²×C₄×C₂₃	—	2	4	no	—
211	C₂²×C₄×C₂₃	—	2	4	no	—
212	C₂²×C₄×C₂₃	—	4	2	no	—
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₄⋊C₄×C₂₃	—	2	2	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₄⋊C₄×C₂₃	—	2	4	no	—
235	C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₄⋊C₄×C₂₃	—	2	2	no	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	4	2	no	—
245	C₄⋊C₄×C₂₃	—	4	2	no	—
246	C₄⋊C₄×C₂₃	—	4	2	no	—
247	C₄⋊C₄×C₂₃	—	4	2	no	—
248	C₄⋊C₄×C₂₃	—	4	2	no	—
249	C₄⋊C₄×C₂₃	—	4	2	no	—
250	C₄⋊C₄×C₂₃	—	4	2	no	—
251	C₄⋊C₄×C₂₃	—	4	2	no	—
252	C₄⋊C₄×C₂₃	—	4	2	no	—
253	C₄⋊C₄×C₂₃	—	4	2	no	—
254	C₄⋊C₄×C₂₃	—	4	2	no	—
255	C₄⋊C₄×C₂₃	—	4	2	no	—
256	C₄⋊C₄×C₂₃	—	4	2	no	—
257	C₄⋊C₄×C₂₃	—	4	2	no	—
258	C₄⋊C₄×C₂₃	—	4	2	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	2	2	no	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	4	2	no	—
265	C₂²⋊C₄×C₂₃	—	4	2	no	—
266	C₄²×C₂₃	—	2	2	no	—
267	C₄²×C₂₃	—	2	4	no	—
268	C₄²×C₂₃	—	4	1	no	—
269	C₄²×C₂₃	—	4	1	no	—
270	C₄²×C₂₃	—	4	2	no	—
271	C₄²×C₂₃	—	4	2	no	—
272	C₄²×C₂₃	—	4	2	no	—
273	C₄²×C₂₃	—	4	1	no	—
274	C₄²×C₂₃	—	4	1	no	—
275	C₄²×C₂₃	—	4	2	no	—
276	C₄²×C₂₃	#41	1	4	yes	—
277	#36829	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
283	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
284	Q₈×C₂₃	—	4	4	no	—
285	Q₈×C₂₃	—	8	4	no	—
286	C₂×C₄×C₂₃	—	2	8	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	2	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	1	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	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	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	4	8	no	—
333	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
334	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
335	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
336	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
337	C₂×C₄×C₂₃	2₋¹⁺⁴	1	4	yes	—
338	#2855	C₂×C₂₃	1	2	yes	—
339	#2806	C₂×C₂₃	1	2	yes	complemented
340	#2802	C₂×C₂₃	1	2	yes	complemented
341	#2776	C₂×C₂₃	1	2	yes	complemented
342	#2774	C₂×C₂₃	1	2	yes	complemented
343	#2745	C₂×C₂₃	1	2	yes	—
344	#2738	C₂×C₂₃	1	2	yes	—
345	#2698	C₂×C₂₃	1	2	yes	—
346	#2689	C₂×C₂₃	1	2	yes	—
347	#2655	C₂×C₂₃	1	2	yes	complemented
348	#2611	C₂×C₂₃	1	1	yes	characteristic
349	#2605	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2599	C₂×C₂₃	1	1	yes	characteristic
351	#2588	C₂×C₂₃	1	2	yes	complemented
352	#2584	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#2478	C₂×C₂₃	1	2	yes	—
354	#2336	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2320	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#2296	C₂×C₂₃	1	1	yes	characteristic
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	4	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	1	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
365	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
366	C₂²×C₂₃	#585	1	2	yes	—
367	C₄×C₂₃	—	2	2	no	—
368	C₄×C₂₃	—	2	2	no	—
369	C₄×C₂₃	—	2	2	no	—
370	C₄×C₂₃	—	2	2	no	—
371	C₄×C₂₃	—	2	4	no	—
372	C₄×C₂₃	—	4	1	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	—	4	2	no	—
375	C₄×C₂₃	—	4	2	no	—
376	C₄×C₂₃	—	4	2	no	—
377	C₄×C₂₃	—	4	1	no	—
378	C₄×C₂₃	—	4	2	no	—
379	C₄×C₂₃	—	4	2	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	2	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₂×#126	C₂²×C₂₃	1	2	yes	—
386	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
388	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
390	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
391	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
392	#401	C₂²×C₂₃	1	2	yes	—
393	#400	C₂²×C₂₃	1	2	yes	—
394	#400	C₂²×C₂₃	1	2	yes	—
395	#400	C₂²×C₂₃	1	2	yes	—
396	#400	C₂²×C₂₃	1	1	yes	characteristic
397	#400	C₂²×C₂₃	1	2	yes	—
398	#400	C₂²×C₂₃	1	2	yes	—
399	#400	C₂²×C₂₃	1	2	yes	—
400	#400	C₂²×C₂₃	1	2	yes	—
401	#399	C₂²×C₂₃	1	1	yes	characteristic
402	#398	C₂²×C₂₃	1	2	yes	—
403	#398	C₂²×C₂₃	1	2	yes	—
404	#398	C₂²×C₂₃	1	1	yes	characteristic
405	#398	C₂²×C₂₃	1	1	yes	characteristic
406	#398	C₂²×C₂₃	1	2	yes	—
407	#398	C₂²×C₂₃	1	2	yes	—
408	#398	C₂²×C₂₃	1	2	yes	—
409	#398	C₂²×C₂₃	1	2	yes	—
410	#398	C₂²×C₂₃	1	2	yes	—
411	#397	C₂²×C₂₃	1	1	yes	characteristic
412	#397	C₂²×C₂₃	1	1	yes	characteristic
413	#397	C₂²×C₂₃	1	2	yes	—
414	#397	C₂²×C₂₃	1	2	yes	—
415	#395	C₂²×C₂₃	1	2	yes	—
416	#395	C₂²×C₂₃	1	2	yes	—
417	#395	C₂²×C₂₃	1	1	yes	characteristic
418	#395	C₂²×C₂₃	1	2	yes	—
419	#393	C₂²×C₂₃	1	1	yes	characteristic
420	#391	C₂²×C₂₃	1	2	yes	—
421	#391	C₂²×C₂₃	1	2	yes	—
422	#391	C₂²×C₂₃	1	2	yes	—
423	#391	C₂²×C₂₃	1	2	yes	—
424	#391	C₂²×C₂₃	1	2	yes	—
425	#389	C₂²×C₂₃	1	2	yes	—
426	#389	C₂²×C₂₃	1	2	yes	—
427	#389	C₂²×C₂₃	1	2	yes	—
428	#389	C₂²×C₂₃	1	2	yes	—
429	#389	C₂²×C₂₃	1	2	yes	—
430	#389	C₂²×C₂₃	1	2	yes	—
431	#389	C₂²×C₂₃	1	2	yes	—
432	#389	C₂²×C₂₃	1	2	yes	—
433	#389	C₂²×C₂₃	1	2	yes	—
434	#389	C₂²×C₂₃	1	2	yes	—
435	#389	C₂²×C₂₃	1	2	yes	—
436	#388	C₂²×C₂₃	1	2	yes	—
437	#388	C₂²×C₂₃	1	2	yes	—
438	#388	C₂²×C₂₃	1	2	yes	—
439	#387	C₂²×C₂₃	1	2	yes	—
440	#387	C₂²×C₂₃	1	2	yes	—
441	#387	C₂²×C₂₃	1	2	yes	—
442	#387	C₂²×C₂₃	1	2	yes	—
443	#387	C₂²×C₂₃	1	2	yes	—
444	#387	C₂²×C₂₃	1	2	yes	—
445	#387	C₂²×C₂₃	1	2	yes	—
446	#387	C₂²×C₂₃	1	2	yes	—
447	#387	C₂²×C₂₃	1	2	yes	—
448	#387	C₂²×C₂₃	1	2	yes	—
449	#387	C₂²×C₂₃	1	2	yes	—
450	#387	C₂²×C₂₃	1	2	yes	—
451	#387	C₂²×C₂₃	1	2	yes	—
452	#387	C₂²×C₂₃	1	2	yes	—
453	#387	C₂²×C₂₃	1	2	yes	—
454	#387	C₂²×C₂₃	1	2	yes	—
455	#387	C₂²×C₂₃	1	2	yes	—
456	#385	C₂²×C₂₃	1	2	yes	—
457	#385	C₂²×C₂₃	1	2	yes	—
458	#385	C₂²×C₂₃	1	2	yes	—
459	#385	C₂²×C₂₃	1	2	yes	—
460	#383	C₂²×C₂₃	1	2	yes	—
461	#383	C₂²×C₂₃	1	1	yes	characteristic
462	#382	C₂²×C₂₃	1	2	yes	—
463	#381	C₂²×C₂₃	1	2	yes	—
464	#381	C₂²×C₂₃	1	2	yes	—
465	#380	C₂²×C₂₃	1	2	yes	—
466	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
468	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
469	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
470	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
471	#376	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₂₃	—	4	2	no	—
473	C₂×C₂₃	#3455	1	1	yes	characteristic
474	C₂×C₂₃	#3492	1	1	yes	characteristic
475	C₂×C₂₃	#3509	1	1	yes	characteristic
476	C₂×C₂₃	#3535	1	2	yes	—
477	C₂×C₂₃	#3555	1	2	yes	—
478	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
481	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
482	#126	—	4	4	no	—
483	#125	—	2	4	no	—
484	C₂²⋊Q₈	—	4	4	no	—
485	C₄×Q₈	—	2	4	no	—
486	#117	—	2	4	no	—
487	#117	—	4	2	no	—
488	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₄²	—	4	2	no	—
524	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
525	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
534	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
535	#95	C₂³×C₂₃	1	1	yes	characteristic
536	#95	C₂³×C₂₃	1	1	yes	characteristic
537	#95	C₂³×C₂₃	1	2	yes	—
538	#95	C₂³×C₂₃	1	2	yes	—
539	#95	C₂³×C₂₃	1	2	yes	—
540	#95	C₂³×C₂₃	1	2	yes	—
541	#95	C₂³×C₂₃	1	2	yes	—
542	#95	C₂³×C₂₃	1	2	yes	—
543	#95	C₂³×C₂₃	1	2	yes	—
544	#95	C₂³×C₂₃	1	2	yes	—
545	#95	C₂³×C₂₃	1	2	yes	—
546	#95	C₂³×C₂₃	1	2	yes	—
547	#95	C₂³×C₂₃	1	2	yes	—
548	#95	C₂³×C₂₃	1	2	yes	—
549	#95	C₂³×C₂₃	1	2	yes	—
550	#95	C₂³×C₂₃	1	2	yes	—
551	#95	C₂³×C₂₃	1	2	yes	—
552	#95	C₂³×C₂₃	1	2	yes	—
553	#95	C₂³×C₂₃	1	2	yes	—
554	#95	C₂³×C₂₃	1	2	yes	—
555	#95	C₂³×C₂₃	1	1	yes	characteristic
556	#95	C₂³×C₂₃	1	2	yes	—
557	#95	C₂³×C₂₃	1	2	yes	—
558	#95	C₂³×C₂₃	1	2	yes	—
559	#95	C₂³×C₂₃	1	1	yes	characteristic
560	#95	C₂³×C₂₃	1	2	yes	—
561	#95	C₂³×C₂₃	1	2	yes	—
562	#95	C₂³×C₂₃	1	2	yes	—
563	#95	C₂³×C₂₃	1	2	yes	—
564	#95	C₂³×C₂₃	1	2	yes	—
565	#95	C₂³×C₂₃	1	2	yes	—
566	#95	C₂³×C₂₃	1	2	yes	—
567	#95	C₂³×C₂₃	1	2	yes	—
568	#95	C₂³×C₂₃	1	2	yes	—
569	#95	C₂³×C₂₃	1	2	yes	—
570	#95	C₂³×C₂₃	1	2	yes	—
571	#95	C₂³×C₂₃	1	2	yes	—
572	C₂₃	#36829	1	1	yes	characteristic, direct product factor, Sylow
573	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
574	C₂×Q₈	—	2	2	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	—	4	2	no	—
577	C₂×Q₈	—	4	2	no	—
578	C₂×Q₈	—	4	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
587	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
593	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
596	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₄⋊C₄	—	4	2	no	—
625	C₄⋊C₄	—	4	2	no	—
626	C₄⋊C₄	—	4	2	no	—
627	C₄⋊C₄	—	4	2	no	—
628	C₄⋊C₄	—	4	2	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	4	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	4	1	no	—
641	C₄²	—	4	1	no	—
642	C₄²	—	4	2	no	—
643	C₄²	—	4	1	no	—
644	C₄²	—	4	1	no	—
645	C₄²	—	4	2	no	—
646	C₄²	—	4	2	no	—
647	C₄²	—	4	2	no	—
648	C₄²	#41×C₂₃	1	4	yes	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
654	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
655	Q₈	—	4	4	no	—
656	Q₈	—	8	4	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	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	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
705	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
706	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
707	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
708	C₂×C₄	C₂₃×2₋¹⁺⁴	1	4	yes	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
715	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
717	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
718	C₂²	C₂₃×#585	1	2	yes	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	4	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₂	—	4	2	no	—
738	C₂	C₂₃×#3455	1	1	yes	characteristic
739	C₂	C₂₃×#3492	1	1	yes	characteristic
740	C₂	C₂₃×#3509	1	1	yes	characteristic
741	C₂	C₂₃×#3535	1	2	yes	—
742	C₂	C₂₃×#3555	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁴×C₂₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2806	C₂	semidirect
3. C₂₃×#2802	C₂	semidirect
4. C₂₃×#2776	C₂	semidirect
5. C₂₃×#2774	C₂	semidirect
10. C₂₃×#2655	C₂	semidirect
12. C₂₃×#2605	C₂	semidirect
14. C₂₃×#2588	C₂	semidirect
15. C₂₃×#2584	C₂	semidirect
17. C₂₃×#2336	C₂	semidirect
18. C₂₃×#2320	C₂	semidirect
277. #36829	C₂₃	direct (N × H)
339. #2806	C₂×C₂₃	semidirect
340. #2802	C₂×C₂₃	semidirect
341. #2776	C₂×C₂₃	semidirect
342. #2774	C₂×C₂₃	semidirect
347. #2655	C₂×C₂₃	semidirect
349. #2605	C₂×C₂₃	semidirect
351. #2588	C₂×C₂₃	semidirect
352. #2584	C₂×C₂₃	semidirect
354. #2336	C₂×C₂₃	semidirect
355. #2320	C₂×C₂₃	semidirect
572. C₂₃	#36829	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×#2855	2
C₂₃×#2806	2
C₂₃×#2802	2
C₂₃×#2776	2
C₂₃×#2774	2
C₂₃×#2745	2
C₂₃×#2738	2
C₂₃×#2698	2
C₂₃×#2689	2
C₂₃×#2655	2
C₂₃×#2611	2
C₂₃×#2605	2
C₂₃×#2599	2
C₂₃×#2588	2
C₂₃×#2584	2
C₂₃×#2478	2
C₂₃×#2336	2
C₂₃×#2320	2
C₂₃×#2296	2
#36829	23

Subgroups — C23×#36829 #19184455

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36829 #19184455