Subgroups — C₂₃×#60937 #19208563

Order 5888.

1878 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3494	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3263	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3259	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3257	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3256	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3253	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3251	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3084	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3081	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3055	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3045	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3041	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
17	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂₃×#555	—	2	2	no	—
22	C₂₃×#553	—	2	2	no	—
23	C₂₃×#553	—	2	2	no	—
24	C₂₃×#551	—	2	4	no	—
25	C₂₃×#547	—	2	2	no	—
26	C₂₃×#546	—	2	4	no	—
27	C₂₃×#544	C₂²	1	2	yes	—
28	C₂₃×#542	C₂²	1	4	yes	complemented
29	C₂₃×#540	C₂²	1	4	yes	complemented
30	C₂₃×#535	C₂²	1	2	yes	—
31	C₂₃×#532	C₂²	1	4	yes	complemented
32	C₂₃×#529	C₂²	1	4	yes	complemented
33	C₂₃×#525	C₂²	1	2	yes	—
34	C₂×C₂₃×#121	C₂²	1	2	yes	—
35	C₂₃×#520	C₂²	1	2	yes	—
36	C₂₃×#518	C₂²	1	2	yes	—
37	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
38	C₂₃×#479	C₂²	1	4	yes	complemented
39	C₂₃×#478	C₂²	1	4	yes	complemented
40	C₂₃×#478	C₂²	1	4	yes	complemented
41	C₂₃×#478	C₂²	1	4	yes	complemented
42	C₂₃×#476	C₂²	1	4	yes	complemented
43	C₂₃×#476	C₂²	1	4	yes	complemented
44	C₂₃×#475	C₂²	1	4	yes	complemented
45	C₂₃×#474	C₂²	1	4	yes	complemented
46	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#470	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#469	C₂²	1	2	yes	—
49	C₂₃×#469	C₂²	1	2	yes	—
50	C₂₃×#469	C₂²	1	2	yes	—
51	C₂₃×#469	C₂²	1	2	yes	—
52	C₂₃×#469	C₂²	1	4	yes	complemented
53	C₂₃×#469	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#469	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#468	C₂²	1	2	yes	complemented
56	C₂₃×#468	C₂²	1	4	yes	complemented
57	C₂₃×#468	C₂²	1	2	yes	complemented
58	C₂₃×#466	C₂²	1	4	yes	complemented
59	C₂₃×#465	C₂²	1	4	yes	complemented
60	C₂₃×#464	C₂²	1	4	yes	complemented
61	C₂₃×#463	C₂²	1	4	yes	complemented
62	C₂₃×#463	C₂²	1	4	yes	complemented
63	C₂₃×#463	C₂²	1	4	yes	complemented
64	C₂₃×#460	C₂²	1	4	yes	complemented
65	C₂₃×#459	C₂²	1	4	yes	complemented
66	C₂₃×#459	C₂²	1	4	yes	complemented
67	C₂₃×#459	C₂²	1	4	yes	complemented
68	C₂₃×#428	C₂²	1	2	yes	—
69	C₂₃×#427	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
71	C₂₃×#424	C₂²	1	2	yes	—
72	C₂₃×#424	C₂²	1	2	yes	—
73	C₂₃×#424	C₂²	1	2	yes	complemented
74	C₂₃×#424	C₂²	1	2	yes	complemented
75	C₂₃×#423	C₂²	1	2	yes	complemented
76	C₂₃×#423	C₂²	1	2	yes	complemented
77	C₂₃×#418	C₂²	1	2	yes	—
78	C₂₃×#417	C₂²	1	2	yes	—
79	C₂₃×#416	C₂²	1	2	yes	—
80	C₂×C₂₃×#102	C₂²	1	2	yes	—
81	C₂×#41×C₂₃	—	2	4	no	—
82	C₂×#41×C₂₃	C₂³	1	2	yes	—
83	C₂²×D₄×C₂₃	—	2	2	no	—
84	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
87	C₂₃×#135	—	4	2	no	—
88	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
89	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
91	C₂×D₈×C₂₃	—	4	2	no	—
92	C₂×D₈×C₂₃	C₂³	1	2	yes	—
93	C₂×D₈×C₂₃	C₂³	1	2	yes	—
94	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂×D₈×C₂₃	C₂³	1	4	yes	—
96	C₂×M₁₆×C₂₃	—	4	2	no	—
97	C₂×M₁₆×C₂₃	—	4	2	no	—
98	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
99	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₂₃×#127	C₂³	1	4	yes	—
110	C₂₃×#126	—	2	4	no	—
111	C₂₃×#126	—	2	4	no	—
112	C₂₃×#125	—	2	2	no	—
113	C₂₃×#125	C₂³	1	4	yes	—
114	C₂₃×#124	—	2	4	no	—
115	C₂₃×#124	—	2	4	no	—
116	C₂₃×#124	C₂³	1	4	yes	—
117	C₂₃×#123	—	2	4	no	—
118	C₂₃×#123	—	2	2	no	—
119	C₂₃×#123	—	2	4	no	—
120	C₂₃×#123	—	2	4	no	—
121	C₂₃×#123	—	2	4	no	—
122	C₂₃×C₂²⋊Q₈	—	2	4	no	—
123	C₂₃×C₂²⋊Q₈	—	2	4	no	—
124	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
126	C₂₃×#121	—	2	2	no	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	4	no	—
129	C₂₃×#121	—	2	2	no	—
130	C₂₃×#121	—	2	2	no	—
131	C₂₃×#121	—	2	4	no	—
132	C₂₃×#121	—	2	4	no	—
133	C₂₃×#121	C₂³	1	4	yes	—
134	C₂₃×#121	C₂³	1	2	yes	—
135	C₂₃×#121	C₂³	1	4	yes	—
136	C₂₃×#121	C₂³	1	2	yes	—
137	C₂₃×#120	—	2	2	no	—
138	C₂₃×#120	—	2	4	no	—
139	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
140	C₄×D₄×C₂₃	—	2	2	no	—
141	C₄×D₄×C₂₃	—	2	2	no	—
142	C₄×D₄×C₂₃	—	2	4	no	—
143	C₄×D₄×C₂₃	—	2	2	no	—
144	C₄×D₄×C₂₃	—	2	2	no	—
145	C₄×D₄×C₂₃	—	2	4	no	—
146	C₄×D₄×C₂₃	—	2	4	no	—
147	C₄×D₄×C₂₃	C₂³	1	4	yes	—
148	C₄×D₄×C₂₃	C₂³	1	4	yes	—
149	C₄×D₄×C₂₃	C₂³	1	4	yes	—
150	C₂₃×#117	—	2	2	no	—
151	C₂₃×#117	—	2	4	no	—
152	C₂₃×#117	D₄	1	2	yes	—
153	C₂₃×#117	D₄	1	1	yes	characteristic
154	C₂₃×#117	D₄	1	1	yes	characteristic
155	C₂₃×#117	C₂³	1	2	yes	—
156	C₂₃×#117	C₂³	1	2	yes	—
157	C₂₃×#117	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
159	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
162	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
163	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
164	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
165	C₂₃×#107	C₂³	1	2	yes	—
166	C₂₃×#107	C₂³	1	4	yes	—
167	C₂₃×#106	C₂³	1	2	yes	—
168	C₂₃×#106	C₂³	1	2	yes	—
169	C₂₃×#106	C₂³	1	1	yes	characteristic
170	C₂₃×#106	C₂³	1	1	yes	characteristic
171	C₂₃×#106	C₂³	1	4	yes	—
172	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
175	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
176	C₂₃×#103	C₂³	1	2	yes	—
177	C₂₃×#103	C₂³	1	2	yes	—
178	C₂₃×#103	C₂³	1	4	yes	—
179	C₂₃×#102	C₂³	1	4	yes	—
180	C₂₃×#102	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	2	yes	—
182	C₂₃×#102	C₂³	1	2	yes	—
183	C₂₃×#102	C₂³	1	4	yes	—
184	C₂₃×#102	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	4	yes	—
186	C₂⁴×C₂₃	—	2	2	no	—
187	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
188	#41×C₂₃	—	2	4	no	—
189	#41×C₂₃	—	2	4	no	—
190	#41×C₂₃	—	8	8	no	—
191	C₂×Q₈×C₂₃	—	2	4	no	—
192	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂×D₄×C₂₃	—	2	4	no	—
196	C₂×D₄×C₂₃	—	2	2	no	—
197	C₂×D₄×C₂₃	—	2	4	no	—
198	C₂×D₄×C₂₃	—	2	2	no	—
199	C₂×D₄×C₂₃	—	2	4	no	—
200	C₂×D₄×C₂₃	—	2	4	no	—
201	C₂×D₄×C₂₃	—	2	4	no	—
202	C₂×D₄×C₂₃	—	2	4	no	—
203	C₂×D₄×C₂₃	—	8	4	no	—
204	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
205	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₂₃	—	2	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	—	2	4	no	—
213	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
220	Q₁₆×C₂₃	—	4	1	no	—
221	SD₁₆×C₂₃	—	4	2	no	—
222	SD₁₆×C₂₃	—	4	4	no	—
223	D₈×C₂₃	—	4	2	no	—
224	D₈×C₂₃	—	4	2	no	—
225	D₈×C₂₃	—	4	1	no	—
226	D₈×C₂₃	—	4	4	no	—
227	M₁₆×C₂₃	—	2	4	no	—
228	M₁₆×C₂₃	—	4	1	no	—
229	M₁₆×C₂₃	—	4	1	no	—
230	M₁₆×C₂₃	—	4	1	no	—
231	M₁₆×C₂₃	—	4	1	no	—
232	M₁₆×C₂₃	—	4	2	no	—
233	C₂×C₈×C₂₃	—	2	2	no	—
234	C₂×C₈×C₂₃	—	2	2	no	—
235	C₂×C₈×C₂₃	—	4	2	no	—
236	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
239	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₄⋊C₄×C₂₃	—	2	2	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	2	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	2	no	—
248	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
252	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂²⋊C₄×C₂₃	—	2	2	no	—
255	C₂²⋊C₄×C₂₃	—	2	2	no	—
256	C₂²⋊C₄×C₂₃	—	2	2	no	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	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	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	2	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	2	no	—
266	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
267	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
269	C₄²×C₂₃	—	2	4	no	—
270	C₄²×C₂₃	—	2	2	no	—
271	C₄²×C₂₃	C₂×D₄	1	2	yes	—
272	C₄²×C₂₃	C₂×D₄	1	2	yes	—
273	C₄²×C₂₃	C₂⁴	1	4	yes	—
274	#60937	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	4	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	4	2	no	—
279	C₂³×C₂₃	—	4	4	no	—
280	C₂³×C₂₃	—	8	2	no	—
281	C₂³×C₂₃	—	8	2	no	—
282	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
283	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
284	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
285	Q₈×C₂₃	—	2	2	no	—
286	Q₈×C₂₃	—	2	2	no	—
287	Q₈×C₂₃	—	8	4	no	—
288	D₄×C₂₃	—	2	4	no	—
289	D₄×C₂₃	—	2	2	no	—
290	D₄×C₂₃	—	2	4	no	—
291	D₄×C₂₃	—	2	2	no	—
292	D₄×C₂₃	—	4	8	no	—
293	D₄×C₂₃	—	4	4	no	—
294	D₄×C₂₃	—	4	4	no	—
295	D₄×C₂₃	—	4	4	no	—
296	D₄×C₂₃	—	8	4	no	—
297	D₄×C₂₃	—	8	4	no	—
298	D₄×C₂₃	—	8	2	no	—
299	D₄×C₂₃	—	8	4	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	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	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	4	no	—
311	C₂×C₄×C₂₃	—	4	4	no	—
312	C₂×C₄×C₂₃	—	4	4	no	—
313	C₂×C₄×C₂₃	—	8	4	no	—
314	C₂×C₄×C₂₃	—	8	4	no	—
315	C₂×C₄×C₂₃	—	8	4	no	—
316	C₂×C₄×C₂₃	—	8	2	no	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
318	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
323	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
324	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
325	C₈×C₂₃	—	2	1	no	—
326	C₈×C₂₃	—	2	1	no	—
327	C₈×C₂₃	—	2	1	no	—
328	C₈×C₂₃	—	2	1	no	—
329	C₈×C₂₃	—	2	4	no	—
330	#3494	C₂×C₂₃	1	2	yes	complemented
331	#3263	C₂×C₂₃	1	2	yes	complemented
332	#3259	C₂×C₂₃	1	2	yes	complemented
333	#3257	C₂×C₂₃	1	4	yes	complemented
334	#3256	C₂×C₂₃	1	2	yes	complemented
335	#3253	C₂×C₂₃	1	2	yes	complemented
336	#3251	C₂×C₂₃	1	4	yes	complemented
337	#3084	C₂×C₂₃	1	2	yes	complemented
338	#3081	C₂×C₂₃	1	2	yes	complemented
339	#3055	C₂×C₂₃	1	2	yes	complemented
340	#3054	C₂×C₂₃	1	1	yes	characteristic, complemented
341	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#3045	C₂×C₂₃	1	2	yes	complemented
343	#3041	C₂×C₂₃	1	2	yes	complemented
344	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂²×C₂₃	—	2	2	no	—
346	C₂²×C₂₃	—	2	2	no	—
347	C₂²×C₂₃	—	2	2	no	—
348	C₂²×C₂₃	—	2	1	no	—
349	C₂²×C₂₃	—	2	1	no	—
350	C₂²×C₂₃	—	4	2	no	—
351	C₂²×C₂₃	—	4	4	no	—
352	C₂²×C₂₃	—	4	4	no	—
353	C₂²×C₂₃	—	4	2	no	—
354	C₂²×C₂₃	—	4	2	no	—
355	C₂²×C₂₃	—	4	4	no	—
356	C₂²×C₂₃	—	8	2	no	—
357	C₂²×C₂₃	—	16	4	no	—
358	C₂²×C₂₃	#537	1	2	yes	—
359	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₂₃	—	2	4	no	—
361	C₄×C₂₃	—	2	4	no	—
362	C₄×C₂₃	—	2	1	no	—
363	C₄×C₂₃	—	2	1	no	—
364	C₄×C₂₃	—	4	4	no	—
365	C₄×C₂₃	—	4	2	no	—
366	C₄×C₂₃	—	4	2	no	—
367	C₄×C₂₃	—	4	2	no	—
368	C₄×C₂₃	#537	1	2	yes	—
369	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
370	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
371	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
372	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
373	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
374	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
375	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
376	#555	—	2	2	no	—
377	#553	—	2	2	no	—
378	#553	—	2	2	no	—
379	#551	—	2	4	no	—
380	#547	—	2	2	no	—
381	#546	—	2	4	no	—
382	#544	C₂²×C₂₃	1	2	yes	—
383	#542	C₂²×C₂₃	1	4	yes	complemented
384	#540	C₂²×C₂₃	1	4	yes	complemented
385	#535	C₂²×C₂₃	1	2	yes	—
386	#532	C₂²×C₂₃	1	4	yes	complemented
387	#529	C₂²×C₂₃	1	4	yes	complemented
388	#525	C₂²×C₂₃	1	2	yes	—
389	C₂×#121	C₂²×C₂₃	1	2	yes	—
390	#520	C₂²×C₂₃	1	2	yes	—
391	#518	C₂²×C₂₃	1	2	yes	—
392	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
393	#479	C₂²×C₂₃	1	4	yes	complemented
394	#478	C₂²×C₂₃	1	4	yes	complemented
395	#478	C₂²×C₂₃	1	4	yes	complemented
396	#478	C₂²×C₂₃	1	4	yes	complemented
397	#476	C₂²×C₂₃	1	4	yes	complemented
398	#476	C₂²×C₂₃	1	4	yes	complemented
399	#475	C₂²×C₂₃	1	4	yes	complemented
400	#474	C₂²×C₂₃	1	4	yes	complemented
401	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
402	#470	C₂²×C₂₃	1	1	yes	characteristic, complemented
403	#469	C₂²×C₂₃	1	2	yes	—
404	#469	C₂²×C₂₃	1	2	yes	—
405	#469	C₂²×C₂₃	1	2	yes	—
406	#469	C₂²×C₂₃	1	2	yes	—
407	#469	C₂²×C₂₃	1	4	yes	complemented
408	#469	C₂²×C₂₃	1	1	yes	characteristic, complemented
409	#469	C₂²×C₂₃	1	1	yes	characteristic, complemented
410	#468	C₂²×C₂₃	1	2	yes	complemented
411	#468	C₂²×C₂₃	1	4	yes	complemented
412	#468	C₂²×C₂₃	1	2	yes	complemented
413	#466	C₂²×C₂₃	1	4	yes	complemented
414	#465	C₂²×C₂₃	1	4	yes	complemented
415	#464	C₂²×C₂₃	1	4	yes	complemented
416	#463	C₂²×C₂₃	1	4	yes	complemented
417	#463	C₂²×C₂₃	1	4	yes	complemented
418	#463	C₂²×C₂₃	1	4	yes	complemented
419	#460	C₂²×C₂₃	1	4	yes	complemented
420	#459	C₂²×C₂₃	1	4	yes	complemented
421	#459	C₂²×C₂₃	1	4	yes	complemented
422	#459	C₂²×C₂₃	1	4	yes	complemented
423	#428	C₂²×C₂₃	1	2	yes	—
424	#427	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
426	#424	C₂²×C₂₃	1	2	yes	—
427	#424	C₂²×C₂₃	1	2	yes	—
428	#424	C₂²×C₂₃	1	2	yes	complemented
429	#424	C₂²×C₂₃	1	2	yes	complemented
430	#423	C₂²×C₂₃	1	2	yes	complemented
431	#423	C₂²×C₂₃	1	2	yes	complemented
432	#418	C₂²×C₂₃	1	2	yes	—
433	#417	C₂²×C₂₃	1	2	yes	—
434	#416	C₂²×C₂₃	1	2	yes	—
435	C₂×#102	C₂²×C₂₃	1	2	yes	—
436	C₂×C₂₃	—	2	2	no	—
437	C₂×C₂₃	—	4	1	no	—
438	C₂×C₂₃	—	4	1	no	—
439	C₂×C₂₃	—	8	2	no	—
440	C₂×C₂₃	—	8	4	no	—
441	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
442	C₂×C₂₃	#3585	1	2	yes	—
443	C₂×#41	—	2	4	no	—
444	C₂×#41	C₂³×C₂₃	1	2	yes	—
445	C₂²×D₄	—	2	2	no	—
446	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
447	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
448	AGL(1,ℤ/8)	—	4	4	no	—
449	#135	—	4	2	no	—
450	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
451	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
452	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
453	C₂×D₈	—	4	2	no	—
454	C₂×D₈	C₂³×C₂₃	1	2	yes	—
455	C₂×D₈	C₂³×C₂₃	1	2	yes	—
456	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
457	C₂×D₈	C₂³×C₂₃	1	4	yes	—
458	C₂×M₁₆	—	4	2	no	—
459	C₂×M₁₆	—	4	2	no	—
460	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
461	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
462	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
463	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
464	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
465	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
471	#127	C₂³×C₂₃	1	4	yes	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#125	—	2	2	no	—
475	#125	C₂³×C₂₃	1	4	yes	—
476	#124	—	2	4	no	—
477	#124	—	2	4	no	—
478	#124	C₂³×C₂₃	1	4	yes	—
479	#123	—	2	2	no	—
480	#123	—	2	4	no	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	#123	—	2	4	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	C₂²⋊Q₈	—	2	4	no	—
486	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
487	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
488	#121	—	2	2	no	—
489	#121	—	2	2	no	—
490	#121	—	2	4	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	—	2	4	no	—
494	#121	—	2	4	no	—
495	#121	C₂³×C₂₃	1	4	yes	—
496	#121	C₂³×C₂₃	1	4	yes	—
497	#121	C₂³×C₂₃	1	2	yes	—
498	#121	C₂³×C₂₃	1	2	yes	—
499	#120	—	2	2	no	—
500	#120	—	2	4	no	—
501	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	2	no	—
504	C₄×D₄	—	2	4	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	4	no	—
508	C₄×D₄	—	2	4	no	—
509	C₄×D₄	C₂³×C₂₃	1	4	yes	—
510	C₄×D₄	C₂³×C₂₃	1	4	yes	—
511	C₄×D₄	C₂³×C₂₃	1	4	yes	—
512	#117	—	2	2	no	—
513	#117	—	2	4	no	—
514	#117	D₄×C₂₃	1	2	yes	—
515	#117	D₄×C₂₃	1	1	yes	characteristic
516	#117	D₄×C₂₃	1	1	yes	characteristic
517	#117	C₂³×C₂₃	1	2	yes	—
518	#117	C₂³×C₂₃	1	2	yes	—
519	#117	C₂³×C₂₃	1	2	yes	—
520	C₂×C₄⋊C₄	—	2	2	no	—
521	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₂²⋊C₄	—	2	2	no	—
524	C₂×C₂²⋊C₄	—	2	4	no	—
525	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
527	#107	C₂³×C₂₃	1	2	yes	—
528	#107	C₂³×C₂₃	1	4	yes	—
529	#106	C₂³×C₂₃	1	2	yes	—
530	#106	C₂³×C₂₃	1	2	yes	—
531	#106	C₂³×C₂₃	1	1	yes	characteristic
532	#106	C₂³×C₂₃	1	1	yes	characteristic
533	#106	C₂³×C₂₃	1	4	yes	—
534	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
535	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
536	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
538	#103	C₂³×C₂₃	1	2	yes	—
539	#103	C₂³×C₂₃	1	2	yes	—
540	#103	C₂³×C₂₃	1	4	yes	—
541	#102	C₂³×C₂₃	1	4	yes	—
542	#102	C₂³×C₂₃	1	4	yes	—
543	#102	C₂³×C₂₃	1	2	yes	—
544	#102	C₂³×C₂₃	1	2	yes	—
545	#102	C₂³×C₂₃	1	4	yes	—
546	#102	C₂³×C₂₃	1	4	yes	—
547	#102	C₂³×C₂₃	1	4	yes	—
548	C₂₃	#60937	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁴	—	2	2	no	—
550	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
551	#41	—	2	4	no	—
552	#41	—	2	4	no	—
553	#41	—	8	8	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	4	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	4	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	4	no	—
563	C₂×D₄	—	2	4	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	8	4	no	—
567	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
568	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
579	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
583	Q₁₆	—	4	1	no	—
584	SD₁₆	—	4	2	no	—
585	SD₁₆	—	4	4	no	—
586	D₈	—	4	2	no	—
587	D₈	—	4	2	no	—
588	D₈	—	4	1	no	—
589	D₈	—	4	4	no	—
590	M₁₆	—	2	4	no	—
591	M₁₆	—	4	1	no	—
592	M₁₆	—	4	1	no	—
593	M₁₆	—	4	1	no	—
594	M₁₆	—	4	1	no	—
595	M₁₆	—	4	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	2	no	—
598	C₂×C₈	—	4	2	no	—
599	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
600	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
601	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
602	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
603	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	2	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
612	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
613	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
614	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
615	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
616	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
617	C₂²⋊C₄	—	2	2	no	—
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	4	no	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
630	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	2	no	—
634	C₄²	C₂×D₄×C₂₃	1	2	yes	—
635	C₄²	C₂×D₄×C₂₃	1	2	yes	—
636	C₄²	C₂⁴×C₂₃	1	4	yes	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	4	no	—
639	C₂³	—	2	2	no	—
640	C₂³	—	4	2	no	—
641	C₂³	—	4	4	no	—
642	C₂³	—	8	2	no	—
643	C₂³	—	8	2	no	—
644	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
645	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
646	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
647	Q₈	—	2	2	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	8	4	no	—
650	D₄	—	2	4	no	—
651	D₄	—	2	2	no	—
652	D₄	—	2	4	no	—
653	D₄	—	2	2	no	—
654	D₄	—	4	8	no	—
655	D₄	—	4	4	no	—
656	D₄	—	4	4	no	—
657	D₄	—	4	4	no	—
658	D₄	—	8	4	no	—
659	D₄	—	8	4	no	—
660	D₄	—	8	4	no	—
661	D₄	—	8	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	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	4	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	4	no	—
675	C₂×C₄	—	8	4	no	—
676	C₂×C₄	—	8	4	no	—
677	C₂×C₄	—	8	4	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
680	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
681	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
684	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
685	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
686	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
687	C₈	—	2	1	no	—
688	C₈	—	2	1	no	—
689	C₈	—	2	1	no	—
690	C₈	—	2	1	no	—
691	C₈	—	2	4	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	4	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	2	no	—
704	C₂²	—	16	4	no	—
705	C₂²	C₂₃×#537	1	2	yes	—
706	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	4	no	—
710	C₄	—	2	4	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	4	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	C₂₃×#537	1	2	yes	—
716	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
717	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
718	C₂	—	2	2	no	—
719	C₂	—	4	1	no	—
720	C₂	—	4	1	no	—
721	C₂	—	8	4	no	—
722	C₂	—	8	2	no	—
723	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
724	C₂	C₂₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3494	C₂	semidirect
2. C₂₃×#3263	C₂	semidirect
3. C₂₃×#3259	C₂	semidirect
4. C₂₃×#3257	C₂	semidirect
5. C₂₃×#3256	C₂	semidirect
6. C₂₃×#3253	C₂	semidirect
7. C₂₃×#3251	C₂	semidirect
8. C₂₃×#3084	C₂	semidirect
9. C₂₃×#3081	C₂	semidirect
10. C₂₃×#3055	C₂	semidirect
11. C₂₃×#3054	C₂	semidirect
12. C₂×C₂₃×#469	C₂	semidirect
13. C₂₃×#3045	C₂	semidirect
14. C₂₃×#3041	C₂	semidirect
15. C₂₃×#2905	C₂	semidirect
28. C₂₃×#542	C₂²	semidirect
29. C₂₃×#540	C₂²	semidirect
31. C₂₃×#532	C₂²	semidirect
32. C₂₃×#529	C₂²	semidirect
38. C₂₃×#479	C₂²	semidirect
39. C₂₃×#478	C₂²	semidirect
40. C₂₃×#478	C₂²	semidirect
41. C₂₃×#478	C₂²	semidirect
42. C₂₃×#476	C₂²	semidirect
43. C₂₃×#476	C₂²	semidirect
44. C₂₃×#475	C₂²	semidirect
45. C₂₃×#474	C₂²	semidirect
46. C₂₃×#470	C₂²	semidirect
47. C₂₃×#470	C₂²	semidirect
52. C₂₃×#469	C₂²	semidirect
53. C₂₃×#469	C₂²	semidirect
54. C₂₃×#469	C₂²	semidirect
55. C₂₃×#468	C₂²	semidirect
56. C₂₃×#468	C₂²	semidirect
57. C₂₃×#468	C₂²	semidirect
58. C₂₃×#466	C₂²	semidirect
59. C₂₃×#465	C₂²	semidirect
60. C₂₃×#464	C₂²	semidirect
61. C₂₃×#463	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#463	C₂²	semidirect
64. C₂₃×#460	C₂²	semidirect
65. C₂₃×#459	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
67. C₂₃×#459	C₂²	semidirect
73. C₂₃×#424	C₂²	semidirect
74. C₂₃×#424	C₂²	semidirect
75. C₂₃×#423	C₂²	semidirect
76. C₂₃×#423	C₂²	semidirect
274. #60937	C₂₃	direct (N × H)
330. #3494	C₂×C₂₃	semidirect
331. #3263	C₂×C₂₃	semidirect
332. #3259	C₂×C₂₃	semidirect
333. #3257	C₂×C₂₃	semidirect
334. #3256	C₂×C₂₃	semidirect
335. #3253	C₂×C₂₃	semidirect
336. #3251	C₂×C₂₃	semidirect
337. #3084	C₂×C₂₃	semidirect
338. #3081	C₂×C₂₃	semidirect
339. #3055	C₂×C₂₃	semidirect
340. #3054	C₂×C₂₃	semidirect
341. C₂×#469	C₂×C₂₃	semidirect
342. #3045	C₂×C₂₃	semidirect
343. #3041	C₂×C₂₃	semidirect
344. #2905	C₂×C₂₃	semidirect
383. #542	C₂²×C₂₃	semidirect
384. #540	C₂²×C₂₃	semidirect
386. #532	C₂²×C₂₃	semidirect
387. #529	C₂²×C₂₃	semidirect
393. #479	C₂²×C₂₃	semidirect
394. #478	C₂²×C₂₃	semidirect
395. #478	C₂²×C₂₃	semidirect
396. #478	C₂²×C₂₃	semidirect
397. #476	C₂²×C₂₃	semidirect
398. #476	C₂²×C₂₃	semidirect
399. #475	C₂²×C₂₃	semidirect
400. #474	C₂²×C₂₃	semidirect
401. #470	C₂²×C₂₃	semidirect
402. #470	C₂²×C₂₃	semidirect
407. #469	C₂²×C₂₃	semidirect
408. #469	C₂²×C₂₃	semidirect
409. #469	C₂²×C₂₃	semidirect
410. #468	C₂²×C₂₃	semidirect
411. #468	C₂²×C₂₃	semidirect
412. #468	C₂²×C₂₃	semidirect
413. #466	C₂²×C₂₃	semidirect
414. #465	C₂²×C₂₃	semidirect
415. #464	C₂²×C₂₃	semidirect
416. #463	C₂²×C₂₃	semidirect
417. #463	C₂²×C₂₃	semidirect
418. #463	C₂²×C₂₃	semidirect
419. #460	C₂²×C₂₃	semidirect
420. #459	C₂²×C₂₃	semidirect
421. #459	C₂²×C₂₃	semidirect
422. #459	C₂²×C₂₃	semidirect
428. #424	C₂²×C₂₃	semidirect
429. #424	C₂²×C₂₃	semidirect
430. #423	C₂²×C₂₃	semidirect
431. #423	C₂²×C₂₃	semidirect
548. C₂₃	#60937	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×#3494	2
C₂₃×#3263	2
C₂₃×#3259	2
C₂₃×#3257	2
C₂₃×#3256	2
C₂₃×#3253	2
C₂₃×#3251	2
C₂₃×#3084	2
C₂₃×#3081	2
C₂₃×#3055	2
C₂₃×#3054	2
C₂×C₂₃×#469	2
C₂₃×#3045	2
C₂₃×#3041	2
C₂₃×#2905	2
#60937	23

Subgroups — C23×#60937 #19208563

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60937 #19208563