Subgroups — C₂₃×#60430 #19208056

Order 5888.

2762 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₂₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3046	C₂	1	3	yes	maximal, complemented
6	C₂₃×#3045	C₂	1	3	yes	maximal, complemented
7	C₂₃×#3042	C₂	1	3	yes	maximal, complemented
8	C₂₃×#3041	C₂	1	3	yes	maximal, complemented
9	C₂₃×#3040	C₂	1	3	yes	maximal, complemented
10	C₂₃×#3036	C₂	1	3	yes	maximal, complemented
11	C₂₃×#3035	C₂	1	3	yes	maximal, complemented
12	C₂×C₂₃×#463	C₂	1	3	yes	maximal, complemented
13	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂₃×#577	—	2	8	no	—
20	C₂₃×#576	—	2	8	no	—
21	C₂×C₂₃×#137	C₂²	1	3	yes	complemented
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	3	yes	—
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	3	yes	—
24	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
25	C₂×C₂₃×#135	C₂²	1	3	yes	—
26	C₂×C₂₃×#135	C₂²	1	3	yes	complemented
27	C₂²×SD₁₆×C₂₃	C₂²	1	3	yes	complemented
28	C₂²×D₈×C₂₃	C₂²	1	3	yes	—
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
31	C₂₃×#548	—	2	1	no	—
32	C₂₃×#548	—	2	1	no	—
33	C₂₃×#546	—	2	3	no	—
34	C₂₃×#546	—	2	3	no	—
35	C₂₃×#536	C₂²	1	3	yes	complemented
36	C₂₃×#535	C₂²	1	3	yes	complemented
37	C₂₃×#532	C₂²	1	3	yes	complemented
38	C₂×C₂₃×#124	C₂²	1	3	yes	complemented
39	C₂₃×#520	—	2	1	no	—
40	C₂₃×#520	C₂²	1	1	yes	characteristic
41	C₂₃×#520	C₂²	1	3	yes	complemented
42	C₂₃×#518	—	2	3	no	—
43	C₂₃×#518	C₂²	1	3	yes	complemented
44	C₄×#41×C₂₃	—	2	1	no	—
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₂₃	C₂²	1	3	yes	complemented
47	C₂×C₄×D₄×C₂₃	—	2	3	no	—
48	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	complemented
49	C₂₃×#464	C₂²	1	1	yes	characteristic, complemented
50	C₂₃×#464	C₂²	1	3	yes	complemented
51	C₂₃×#464	C₂²	1	6	yes	complemented
52	C₂₃×#463	C₂²	1	3	yes	complemented
53	C₂₃×#463	C₂²	1	6	yes	complemented
54	C₂₃×#463	C₂²	1	6	yes	complemented
55	C₂₃×#463	C₂²	1	6	yes	complemented
56	C₂₃×#463	C₂²	1	3	yes	complemented
57	C₂₃×#463	C₂²	1	6	yes	complemented
58	C₂₃×#462	C₂²	1	3	yes	complemented
59	C₂₃×#461	C₂²	1	3	yes	complemented
60	C₂₃×#461	C₂²	1	6	yes	complemented
61	C₂₃×#460	C₂²	1	3	yes	complemented
62	C₂₃×#459	C₂²	1	3	yes	complemented
63	C₂₃×#459	C₂²	1	6	yes	complemented
64	C₂₃×#424	C₂²	1	3	yes	complemented
65	C₂₃×#424	C₂²	1	3	yes	complemented
66	C₂₃×#423	C₂²	1	3	yes	complemented
67	C₂×C₂₃×C₄⋊C₈	C₂²	1	3	yes	complemented
68	C₂₃×#419	C₂²	1	3	yes	complemented
69	C₂₃×#418	C₂²	1	3	yes	complemented
70	C₂₃×#417	C₂²	1	3	yes	complemented
71	C₂₃×#417	C₂²	1	3	yes	complemented
72	C₂₃×#416	C₂²	1	3	yes	complemented
73	C₂₃×#416	C₂²	1	3	yes	complemented
74	C₂×C₂₃×#103	C₂²	1	3	yes	complemented
75	C₂×C₂₃×#102	C₂²	1	3	yes	complemented
76	C₂₃×2₋¹⁺⁴	—	2	4	no	—
77	C₂₃×2₋¹⁺⁴	—	2	4	no	—
78	C₂₃×H(5,𝔽₂)	—	2	4	no	—
79	C₂₃×H(5,𝔽₂)	—	2	4	no	—
80	C₂₃×H(5,𝔽₂)	—	2	4	no	—
81	C₂₃×H(5,𝔽₂)	D₄	1	8	yes	complemented
82	C₂×#41×C₂₃	—	2	1	no	—
83	C₂×#41×C₂₃	—	2	1	no	—
84	C₂×#41×C₂₃	—	2	3	no	—
85	C₂×#41×C₂₃	C₂³	1	3	yes	—
86	C₂×#41×C₂₃	C₂³	1	3	yes	—
87	C₂×#41×C₂₃	C₂³	1	3	yes	—
88	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×Q₈×C₂₃	—	2	1	no	—
90	C₂²×Q₈×C₂₃	C₂³	1	3	yes	—
91	C₂²×D₄×C₂₃	—	2	3	no	—
92	C₂²×D₄×C₂₃	—	2	3	no	—
93	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
94	C₂²×D₄×C₂₃	C₂³	1	3	yes	—
95	C₂³×C₄×C₂₃	—	2	3	no	—
96	C₂₃×#137	—	2	12	no	—
97	C₂₃×AGL(1,ℤ/8)	—	2	12	no	—
98	C₂₃×AGL(1,ℤ/8)	—	2	12	no	—
99	C₂₃×AGL(1,ℤ/8)	—	2	12	no	—
100	C₂₃×#135	—	2	12	no	—
101	C₂₃×#135	—	2	12	no	—
102	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×Q₁₆×C₂₃	C₂³	1	3	yes	—
104	C₂×SD₁₆×C₂₃	—	2	12	no	—
105	C₂×SD₁₆×C₂₃	C₂³	1	3	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	6	yes	—
107	C₂×SD₁₆×C₂₃	C₂³	1	3	yes	—
108	C₂×SD₁₆×C₂₃	C₂³	1	3	yes	—
109	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×D₈×C₂₃	—	2	12	no	—
111	C₂×D₈×C₂₃	C₂³	1	3	yes	—
112	C₂×D₈×C₂₃	C₂³	1	6	yes	—
113	C₂×D₈×C₂₃	C₂³	1	3	yes	—
114	C₂₃×#131	—	2	4	no	—
115	C₂₃×#131	—	2	4	no	—
116	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
117	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
118	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
120	C₂₃×C₄⋊Q₈	C₂³	1	3	yes	—
121	C₂₃×#127	C₂³	1	3	yes	—
122	C₂₃×#124	—	2	3	no	—
123	C₂₃×#124	—	2	3	no	—
124	C₂₃×#124	C₂³	1	3	yes	—
125	C₂₃×#124	C₂³	1	6	yes	—
126	C₂₃×#124	C₂³	1	1	yes	characteristic
127	C₂₃×#123	—	2	6	no	—
128	C₂₃×C₂²⋊Q₈	—	2	3	no	—
129	C₂₃×C₂²⋊Q₈	—	2	3	no	—
130	C₂₃×#121	—	2	3	no	—
131	C₂₃×#121	—	2	3	no	—
132	C₂₃×#121	—	2	3	no	—
133	C₂₃×#121	—	2	3	no	—
134	C₂₃×#120	—	2	6	no	—
135	C₄×Q₈×C₂₃	—	2	1	no	—
136	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
137	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
138	C₄×Q₈×C₂₃	C₂³	1	3	yes	—
139	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₄×D₄×C₂₃	—	2	3	no	—
141	C₄×D₄×C₂₃	—	2	3	no	—
142	C₄×D₄×C₂₃	—	2	3	no	—
143	C₄×D₄×C₂₃	—	2	3	no	—
144	C₄×D₄×C₂₃	—	2	3	no	—
145	C₄×D₄×C₂₃	—	2	6	no	—
146	C₄×D₄×C₂₃	—	2	3	no	—
147	C₄×D₄×C₂₃	—	2	3	no	—
148	C₄×D₄×C₂₃	—	2	3	no	—
149	C₄×D₄×C₂₃	—	2	3	no	—
150	C₄×D₄×C₂₃	D₄	1	3	yes	—
151	C₄×D₄×C₂₃	D₄	1	3	yes	—
152	C₄×D₄×C₂₃	C₂³	1	6	yes	—
153	C₄×D₄×C₂₃	C₂³	1	3	yes	—
154	C₄×D₄×C₂₃	C₂³	1	3	yes	—
155	C₂₃×#117	—	2	3	no	—
156	C₂₃×#117	—	2	3	no	—
157	C₂₃×#117	C₂³	1	3	yes	—
158	C₂₃×#117	C₂³	1	3	yes	—
159	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	3	yes	—
161	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
162	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
163	C₂×C₂²⋊C₄×C₂₃	—	2	3	no	—
164	C₂×C₂²⋊C₄×C₂₃	—	2	6	no	—
165	C₂×C₄²×C₂₃	—	2	3	no	—
166	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
167	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
168	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
169	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
170	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
172	C₂₃×#103	C₂³	1	3	yes	—
173	C₂₃×#103	C₂³	1	6	yes	—
174	C₂₃×#103	C₂³	1	1	yes	characteristic
175	C₂₃×#103	C₂³	1	3	yes	—
176	C₂₃×#103	C₂³	1	3	yes	—
177	C₂₃×#102	C₂³	1	3	yes	—
178	C₂₃×#102	C₂³	1	6	yes	—
179	C₂₃×#102	C₂³	1	1	yes	characteristic
180	C₂₃×#102	C₂³	1	3	yes	—
181	C₂₃×#102	C₂³	1	3	yes	—
182	C₂⁴×C₂₃	—	2	3	no	—
183	C₂⁴×C₂₃	—	2	3	no	—
184	#41×C₂₃	—	2	8	no	—
185	#41×C₂₃	—	2	6	no	—
186	#41×C₂₃	—	2	6	no	—
187	#41×C₂₃	—	2	6	no	—
188	#41×C₂₃	—	2	6	no	—
189	#41×C₂₃	—	2	6	no	—
190	#41×C₂₃	—	4	4	no	—
191	#41×C₂₃	—	4	12	no	—
192	#41×C₂₃	C₂×D₄	1	12	yes	—
193	#41×C₂₃	C₂×D₄	1	4	yes	—
194	#41×C₂₃	#41	1	4	yes	—
195	C₂×Q₈×C₂₃	—	2	3	no	—
196	C₂×Q₈×C₂₃	—	2	6	no	—
197	C₂×Q₈×C₂₃	—	2	6	no	—
198	C₂×Q₈×C₂₃	—	4	4	no	—
199	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
200	C₂×Q₈×C₂₃	C₂⁴	1	3	yes	—
201	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
202	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
203	C₂×D₄×C₂₃	—	2	3	no	—
204	C₂×D₄×C₂₃	—	2	24	no	—
205	C₂×D₄×C₂₃	—	2	3	no	—
206	C₂×D₄×C₂₃	—	2	3	no	—
207	C₂×D₄×C₂₃	—	2	3	no	—
208	C₂×D₄×C₂₃	—	2	6	no	—
209	C₂×D₄×C₂₃	—	2	3	no	—
210	C₂×D₄×C₂₃	—	2	3	no	—
211	C₂×D₄×C₂₃	—	2	3	no	—
212	C₂×D₄×C₂₃	—	2	6	no	—
213	C₂×D₄×C₂₃	—	2	6	no	—
214	C₂×D₄×C₂₃	—	4	12	no	—
215	C₂×D₄×C₂₃	C₂×D₄	1	12	yes	—
216	C₂×D₄×C₂₃	C₂×D₄	1	3	yes	—
217	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
218	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂×D₄×C₂₃	C₂⁴	1	3	yes	—
220	C₂²×C₄×C₂₃	—	2	3	no	—
221	C₂²×C₄×C₂₃	—	2	3	no	—
222	C₂²×C₄×C₂₃	—	2	3	no	—
223	C₂²×C₄×C₂₃	—	2	3	no	—
224	C₂²×C₄×C₂₃	—	2	3	no	—
225	C₂²×C₄×C₂₃	—	2	3	no	—
226	C₂²×C₄×C₂₃	—	2	3	no	—
227	C₂²×C₄×C₂₃	—	2	6	no	—
228	C₂²×C₄×C₂₃	—	8	6	no	—
229	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
230	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
232	Q₁₆×C₂₃	—	2	2	no	—
233	Q₁₆×C₂₃	—	2	6	no	—
234	SD₁₆×C₂₃	—	2	2	no	—
235	SD₁₆×C₂₃	—	2	6	no	—
236	SD₁₆×C₂₃	—	2	6	no	—
237	SD₁₆×C₂₃	—	2	12	no	—
238	SD₁₆×C₂₃	—	2	6	no	—
239	D₈×C₂₃	—	2	6	no	—
240	D₈×C₂₃	—	2	12	no	—
241	D₈×C₂₃	—	2	6	no	—
242	M₁₆×C₂₃	—	2	6	no	—
243	M₁₆×C₂₃	—	2	6	no	—
244	C₂×C₈×C₂₃	—	2	6	no	—
245	C₂×C₈×C₂₃	—	2	6	no	—
246	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
248	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
250	C₄⋊C₄×C₂₃	—	2	3	no	—
251	C₄⋊C₄×C₂₃	—	2	3	no	—
252	C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₄⋊C₄×C₂₃	—	2	3	no	—
254	C₄⋊C₄×C₂₃	—	2	3	no	—
255	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
256	C₄⋊C₄×C₂₃	C₂×D₄	1	3	yes	—
257	C₄⋊C₄×C₂₃	C₂⁴	1	3	yes	—
258	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²⋊C₄×C₂₃	—	2	3	no	—
260	C₂²⋊C₄×C₂₃	—	2	3	no	—
261	C₂²⋊C₄×C₂₃	—	2	6	no	—
262	C₂²⋊C₄×C₂₃	—	2	3	no	—
263	C₂²⋊C₄×C₂₃	—	2	3	no	—
264	C₂²⋊C₄×C₂₃	—	2	3	no	—
265	C₂²⋊C₄×C₂₃	—	2	6	no	—
266	C₂²⋊C₄×C₂₃	—	2	6	no	—
267	C₂²⋊C₄×C₂₃	—	2	1	no	—
268	C₂²⋊C₄×C₂₃	—	2	1	no	—
269	C₂²⋊C₄×C₂₃	C₂×D₄	1	6	yes	—
270	C₄²×C₂₃	—	2	1	no	—
271	C₄²×C₂₃	—	2	3	no	—
272	C₄²×C₂₃	—	2	3	no	—
273	C₄²×C₂₃	C₂×D₄	1	3	yes	—
274	C₄²×C₂₃	C₂×D₄	1	3	yes	—
275	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₄²×C₂₃	C₂⁴	1	3	yes	—
277	#60430	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂³×C₂₃	—	2	3	no	—
279	C₂³×C₂₃	—	2	12	no	—
280	C₂³×C₂₃	—	2	3	no	—
281	C₂³×C₂₃	—	2	1	no	—
282	C₂³×C₂₃	—	4	6	no	—
283	C₂³×C₂₃	—	8	3	no	—
284	C₂³×C₂₃	—	8	3	no	—
285	C₂³×C₂₃	—	8	3	no	—
286	C₂³×C₂₃	—	8	3	no	—
287	C₂³×C₂₃	C₂²×D₄	1	3	yes	—
288	Q₈×C₂₃	—	2	1	no	—
289	Q₈×C₂₃	—	2	3	no	—
290	Q₈×C₂₃	—	2	1	no	—
291	Q₈×C₂₃	—	2	3	no	—
292	Q₈×C₂₃	—	2	1	no	—
293	Q₈×C₂₃	—	4	6	no	—
294	Q₈×C₂₃	#121	1	4	yes	—
295	Q₈×C₂₃	C₂²×D₄	1	2	yes	—
296	D₄×C₂₃	—	2	12	no	—
297	D₄×C₂₃	—	2	12	no	—
298	D₄×C₂₃	—	2	3	no	—
299	D₄×C₂₃	—	2	1	no	—
300	D₄×C₂₃	—	2	3	no	—
301	D₄×C₂₃	—	2	3	no	—
302	D₄×C₂₃	—	2	1	no	—
303	D₄×C₂₃	—	4	6	no	—
304	D₄×C₂₃	—	4	6	no	—
305	D₄×C₂₃	—	4	6	no	—
306	D₄×C₂₃	—	8	3	no	—
307	D₄×C₂₃	—	8	3	no	—
308	D₄×C₂₃	#121	1	12	yes	—
309	D₄×C₂₃	C₂²×D₄	1	6	yes	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	12	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	3	no	—
314	C₂×C₄×C₂₃	—	2	3	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	4	3	no	—
317	C₂×C₄×C₂₃	—	4	3	no	—
318	C₂×C₄×C₂₃	—	4	6	no	—
319	C₂×C₄×C₂₃	—	4	6	no	—
320	C₂×C₄×C₂₃	—	4	6	no	—
321	C₂×C₄×C₂₃	—	4	6	no	—
322	C₂×C₄×C₂₃	—	8	3	no	—
323	C₂×C₄×C₂₃	—	8	6	no	—
324	C₂×C₄×C₂₃	—	8	3	no	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
329	C₂×C₄×C₂₃	C₂²×D₄	1	3	yes	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
331	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
332	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
333	C₈×C₂₃	—	2	1	no	—
334	C₈×C₂₃	—	2	1	no	—
335	C₈×C₂₃	—	2	3	no	—
336	C₈×C₂₃	—	2	3	no	—
337	C₂×#577	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#3500	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₄×H(5,𝔽₂)	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#3046	C₂×C₂₃	1	3	yes	complemented
342	#3045	C₂×C₂₃	1	3	yes	complemented
343	#3042	C₂×C₂₃	1	3	yes	complemented
344	#3041	C₂×C₂₃	1	3	yes	complemented
345	#3040	C₂×C₂₃	1	3	yes	complemented
346	#3036	C₂×C₂₃	1	3	yes	complemented
347	#3035	C₂×C₂₃	1	3	yes	complemented
348	C₂×#463	C₂×C₂₃	1	3	yes	complemented
349	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2898	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#2897	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂²×C₂₃	—	2	3	no	—
353	C₂²×C₂₃	—	2	3	no	—
354	C₂²×C₂₃	—	2	6	no	—
355	C₂²×C₂₃	—	4	3	no	—
356	C₂²×C₂₃	—	4	3	no	—
357	C₂²×C₂₃	—	4	1	no	—
358	C₂²×C₂₃	—	4	3	no	—
359	C₂²×C₂₃	—	4	1	no	—
360	C₂²×C₂₃	—	4	3	no	—
361	C₂²×C₂₃	—	4	1	no	—
362	C₂²×C₂₃	—	4	3	no	—
363	C₂²×C₂₃	—	8	12	no	—
364	C₂²×C₂₃	—	16	6	no	—
365	C₂²×C₂₃	C₂×#121	1	6	yes	—
366	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
367	C₄×C₂₃	—	2	1	no	—
368	C₄×C₂₃	—	2	3	no	—
369	C₄×C₂₃	—	2	1	no	—
370	C₄×C₂₃	—	2	3	no	—
371	C₄×C₂₃	—	2	2	no	—
372	C₄×C₂₃	—	4	1	no	—
373	C₄×C₂₃	—	4	3	no	—
374	C₄×C₂₃	—	4	1	no	—
375	C₄×C₂₃	—	4	3	no	—
376	C₄×C₂₃	C₂×#121	1	6	yes	—
377	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
379	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
380	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
381	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	1	yes	characteristic
382	#577	—	2	8	no	—
383	#576	—	2	8	no	—
384	C₂×#137	C₂²×C₂₃	1	3	yes	complemented
385	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	3	yes	—
386	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	3	yes	—
387	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	3	yes	complemented
388	C₂×#135	C₂²×C₂₃	1	3	yes	—
389	C₂×#135	C₂²×C₂₃	1	3	yes	complemented
390	C₂²×SD₁₆	C₂²×C₂₃	1	3	yes	complemented
391	C₂²×D₈	C₂²×C₂₃	1	3	yes	—
392	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
393	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
394	#548	—	2	1	no	—
395	#548	—	2	1	no	—
396	#546	—	2	3	no	—
397	#546	—	2	3	no	—
398	#536	C₂²×C₂₃	1	3	yes	complemented
399	#535	C₂²×C₂₃	1	3	yes	complemented
400	#532	C₂²×C₂₃	1	3	yes	complemented
401	C₂×#124	C₂²×C₂₃	1	3	yes	complemented
402	#520	—	2	1	no	—
403	#520	C₂²×C₂₃	1	1	yes	characteristic
404	#520	C₂²×C₂₃	1	3	yes	complemented
405	#518	—	2	3	no	—
406	#518	C₂²×C₂₃	1	3	yes	complemented
407	C₄×#41	—	2	1	no	—
408	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
409	C₄×#41	C₂²×C₂₃	1	3	yes	complemented
410	C₂×C₄×D₄	—	2	3	no	—
411	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	complemented
412	#464	C₂²×C₂₃	1	1	yes	characteristic, complemented
413	#464	C₂²×C₂₃	1	3	yes	complemented
414	#464	C₂²×C₂₃	1	6	yes	complemented
415	#463	C₂²×C₂₃	1	3	yes	complemented
416	#463	C₂²×C₂₃	1	6	yes	complemented
417	#463	C₂²×C₂₃	1	6	yes	complemented
418	#463	C₂²×C₂₃	1	6	yes	complemented
419	#463	C₂²×C₂₃	1	3	yes	complemented
420	#463	C₂²×C₂₃	1	6	yes	complemented
421	#462	C₂²×C₂₃	1	3	yes	complemented
422	#461	C₂²×C₂₃	1	3	yes	complemented
423	#461	C₂²×C₂₃	1	6	yes	complemented
424	#460	C₂²×C₂₃	1	3	yes	complemented
425	#459	C₂²×C₂₃	1	3	yes	complemented
426	#459	C₂²×C₂₃	1	6	yes	complemented
427	#424	C₂²×C₂₃	1	3	yes	complemented
428	#424	C₂²×C₂₃	1	3	yes	complemented
429	#423	C₂²×C₂₃	1	3	yes	complemented
430	C₂×C₄⋊C₈	C₂²×C₂₃	1	3	yes	complemented
431	#419	C₂²×C₂₃	1	3	yes	complemented
432	#418	C₂²×C₂₃	1	3	yes	complemented
433	#417	C₂²×C₂₃	1	3	yes	complemented
434	#417	C₂²×C₂₃	1	3	yes	complemented
435	#416	C₂²×C₂₃	1	3	yes	complemented
436	#416	C₂²×C₂₃	1	3	yes	complemented
437	C₂×#103	C₂²×C₂₃	1	3	yes	complemented
438	C₂×#102	C₂²×C₂₃	1	3	yes	complemented
439	C₂×C₂₃	—	2	6	no	—
440	C₂×C₂₃	—	4	6	no	—
441	C₂×C₂₃	—	8	1	no	—
442	C₂×C₂₃	—	8	3	no	—
443	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
444	C₂×C₂₃	#3584	1	1	yes	characteristic
445	C₂×C₂₃	#3585	1	1	yes	characteristic
446	2₋¹⁺⁴	—	2	4	no	—
447	2₋¹⁺⁴	—	2	4	no	—
448	H(5,𝔽₂)	—	2	4	no	—
449	H(5,𝔽₂)	—	2	4	no	—
450	H(5,𝔽₂)	—	2	4	no	—
451	H(5,𝔽₂)	D₄×C₂₃	1	8	yes	complemented
452	C₂×#41	—	2	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	3	no	—
455	C₂×#41	C₂³×C₂₃	1	3	yes	—
456	C₂×#41	C₂³×C₂₃	1	3	yes	—
457	C₂×#41	C₂³×C₂₃	1	3	yes	—
458	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
459	C₂²×Q₈	—	2	1	no	—
460	C₂²×Q₈	C₂³×C₂₃	1	3	yes	—
461	C₂²×D₄	—	2	3	no	—
462	C₂²×D₄	—	2	3	no	—
463	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
464	C₂²×D₄	C₂³×C₂₃	1	3	yes	—
465	C₂³×C₄	—	2	3	no	—
466	#137	—	2	12	no	—
467	AGL(1,ℤ/8)	—	2	12	no	—
468	AGL(1,ℤ/8)	—	2	12	no	—
469	AGL(1,ℤ/8)	—	2	12	no	—
470	#135	—	2	12	no	—
471	#135	—	2	12	no	—
472	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
473	C₂×Q₁₆	C₂³×C₂₃	1	3	yes	—
474	C₂×SD₁₆	—	2	12	no	—
475	C₂×SD₁₆	C₂³×C₂₃	1	3	yes	—
476	C₂×SD₁₆	C₂³×C₂₃	1	6	yes	—
477	C₂×SD₁₆	C₂³×C₂₃	1	3	yes	—
478	C₂×SD₁₆	C₂³×C₂₃	1	3	yes	—
479	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
480	C₂×D₈	—	2	12	no	—
481	C₂×D₈	C₂³×C₂₃	1	3	yes	—
482	C₂×D₈	C₂³×C₂₃	1	6	yes	—
483	C₂×D₈	C₂³×C₂₃	1	3	yes	—
484	#131	—	2	4	no	—
485	#131	—	2	4	no	—
486	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
487	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
488	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
489	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
490	C₄⋊Q₈	C₂³×C₂₃	1	3	yes	—
491	#127	C₂³×C₂₃	1	3	yes	—
492	#124	—	2	3	no	—
493	#124	—	2	3	no	—
494	#124	C₂³×C₂₃	1	3	yes	—
495	#124	C₂³×C₂₃	1	6	yes	—
496	#124	C₂³×C₂₃	1	1	yes	characteristic
497	#123	—	2	6	no	—
498	C₂²⋊Q₈	—	2	3	no	—
499	C₂²⋊Q₈	—	2	3	no	—
500	#121	—	2	3	no	—
501	#121	—	2	3	no	—
502	#121	—	2	3	no	—
503	#121	—	2	3	no	—
504	#120	—	2	6	no	—
505	C₄×Q₈	—	2	1	no	—
506	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
507	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
508	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
509	C₄×Q₈	C₂³×C₂₃	1	3	yes	—
510	C₄×D₄	—	2	3	no	—
511	C₄×D₄	—	2	3	no	—
512	C₄×D₄	—	2	3	no	—
513	C₄×D₄	—	2	3	no	—
514	C₄×D₄	—	2	3	no	—
515	C₄×D₄	—	2	6	no	—
516	C₄×D₄	—	2	3	no	—
517	C₄×D₄	—	2	3	no	—
518	C₄×D₄	—	2	3	no	—
519	C₄×D₄	—	2	3	no	—
520	C₄×D₄	D₄×C₂₃	1	3	yes	—
521	C₄×D₄	D₄×C₂₃	1	3	yes	—
522	C₄×D₄	C₂³×C₂₃	1	3	yes	—
523	C₄×D₄	C₂³×C₂₃	1	6	yes	—
524	C₄×D₄	C₂³×C₂₃	1	3	yes	—
525	#117	—	2	3	no	—
526	#117	—	2	3	no	—
527	#117	C₂³×C₂₃	1	3	yes	—
528	#117	C₂³×C₂₃	1	3	yes	—
529	C₂×C₄⋊C₄	—	2	3	no	—
530	C₂×C₄⋊C₄	C₂³×C₂₃	1	3	yes	—
531	C₂×C₂²⋊C₄	—	2	3	no	—
532	C₂×C₂²⋊C₄	—	2	3	no	—
533	C₂×C₂²⋊C₄	—	2	3	no	—
534	C₂×C₂²⋊C₄	—	2	6	no	—
535	C₂×C₄²	—	2	3	no	—
536	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
537	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
539	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
540	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
541	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
542	#103	C₂³×C₂₃	1	3	yes	—
543	#103	C₂³×C₂₃	1	6	yes	—
544	#103	C₂³×C₂₃	1	1	yes	characteristic
545	#103	C₂³×C₂₃	1	3	yes	—
546	#103	C₂³×C₂₃	1	3	yes	—
547	#102	C₂³×C₂₃	1	3	yes	—
548	#102	C₂³×C₂₃	1	6	yes	—
549	#102	C₂³×C₂₃	1	1	yes	characteristic
550	#102	C₂³×C₂₃	1	3	yes	—
551	#102	C₂³×C₂₃	1	3	yes	—
552	C₂₃	#60430	1	1	yes	characteristic, direct product factor, Sylow
553	C₂⁴	—	2	3	no	—
554	C₂⁴	—	2	3	no	—
555	#41	—	2	8	no	—
556	#41	—	2	6	no	—
557	#41	—	2	6	no	—
558	#41	—	2	6	no	—
559	#41	—	2	6	no	—
560	#41	—	2	6	no	—
561	#41	—	4	4	no	—
562	#41	—	4	12	no	—
563	#41	C₂×D₄×C₂₃	1	12	yes	—
564	#41	C₂×D₄×C₂₃	1	4	yes	—
565	#41	#41×C₂₃	1	4	yes	—
566	C₂×Q₈	—	2	3	no	—
567	C₂×Q₈	—	2	6	no	—
568	C₂×Q₈	—	2	6	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
571	C₂×Q₈	C₂⁴×C₂₃	1	3	yes	—
572	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
573	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
574	C₂×D₄	—	2	3	no	—
575	C₂×D₄	—	2	24	no	—
576	C₂×D₄	—	2	3	no	—
577	C₂×D₄	—	2	3	no	—
578	C₂×D₄	—	2	3	no	—
579	C₂×D₄	—	2	6	no	—
580	C₂×D₄	—	2	3	no	—
581	C₂×D₄	—	2	3	no	—
582	C₂×D₄	—	2	3	no	—
583	C₂×D₄	—	2	6	no	—
584	C₂×D₄	—	2	6	no	—
585	C₂×D₄	—	4	12	no	—
586	C₂×D₄	C₂×D₄×C₂₃	1	12	yes	—
587	C₂×D₄	C₂×D₄×C₂₃	1	3	yes	—
588	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
589	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
590	C₂×D₄	C₂⁴×C₂₃	1	3	yes	—
591	C₂²×C₄	—	2	3	no	—
592	C₂²×C₄	—	2	3	no	—
593	C₂²×C₄	—	2	3	no	—
594	C₂²×C₄	—	2	3	no	—
595	C₂²×C₄	—	2	3	no	—
596	C₂²×C₄	—	2	3	no	—
597	C₂²×C₄	—	2	3	no	—
598	C₂²×C₄	—	2	6	no	—
599	C₂²×C₄	—	8	6	no	—
600	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
601	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
603	Q₁₆	—	2	2	no	—
604	Q₁₆	—	2	6	no	—
605	SD₁₆	—	2	2	no	—
606	SD₁₆	—	2	6	no	—
607	SD₁₆	—	2	6	no	—
608	SD₁₆	—	2	12	no	—
609	SD₁₆	—	2	6	no	—
610	D₈	—	2	6	no	—
611	D₈	—	2	12	no	—
612	D₈	—	2	6	no	—
613	M₁₆	—	2	6	no	—
614	M₁₆	—	2	6	no	—
615	C₂×C₈	—	2	6	no	—
616	C₂×C₈	—	2	6	no	—
617	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
618	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
619	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
621	C₄⋊C₄	—	2	3	no	—
622	C₄⋊C₄	—	2	3	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	3	no	—
625	C₄⋊C₄	—	2	3	no	—
626	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
627	C₄⋊C₄	C₂×D₄×C₂₃	1	3	yes	—
628	C₄⋊C₄	C₂⁴×C₂₃	1	3	yes	—
629	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
630	C₂²⋊C₄	—	2	3	no	—
631	C₂²⋊C₄	—	2	3	no	—
632	C₂²⋊C₄	—	2	6	no	—
633	C₂²⋊C₄	—	2	3	no	—
634	C₂²⋊C₄	—	2	3	no	—
635	C₂²⋊C₄	—	2	3	no	—
636	C₂²⋊C₄	—	2	6	no	—
637	C₂²⋊C₄	—	2	6	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	1	no	—
640	C₂²⋊C₄	C₂×D₄×C₂₃	1	6	yes	—
641	C₄²	—	2	1	no	—
642	C₄²	—	2	3	no	—
643	C₄²	—	2	3	no	—
644	C₄²	C₂×D₄×C₂₃	1	3	yes	—
645	C₄²	C₂×D₄×C₂₃	1	3	yes	—
646	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
647	C₄²	C₂⁴×C₂₃	1	3	yes	—
648	C₂³	—	2	3	no	—
649	C₂³	—	2	12	no	—
650	C₂³	—	2	3	no	—
651	C₂³	—	2	1	no	—
652	C₂³	—	4	6	no	—
653	C₂³	—	8	3	no	—
654	C₂³	—	8	3	no	—
655	C₂³	—	8	3	no	—
656	C₂³	—	8	3	no	—
657	C₂³	C₂²×D₄×C₂₃	1	3	yes	—
658	Q₈	—	2	1	no	—
659	Q₈	—	2	3	no	—
660	Q₈	—	2	1	no	—
661	Q₈	—	2	3	no	—
662	Q₈	—	2	1	no	—
663	Q₈	—	4	6	no	—
664	Q₈	C₂₃×#121	1	4	yes	—
665	Q₈	C₂²×D₄×C₂₃	1	2	yes	—
666	D₄	—	2	12	no	—
667	D₄	—	2	3	no	—
668	D₄	—	2	1	no	—
669	D₄	—	2	3	no	—
670	D₄	—	2	3	no	—
671	D₄	—	2	1	no	—
672	D₄	—	2	12	no	—
673	D₄	—	4	6	no	—
674	D₄	—	4	6	no	—
675	D₄	—	4	6	no	—
676	D₄	—	8	3	no	—
677	D₄	—	8	3	no	—
678	D₄	C₂₃×#121	1	12	yes	—
679	D₄	C₂²×D₄×C₂₃	1	6	yes	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	12	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	3	no	—
684	C₂×C₄	—	2	3	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	4	3	no	—
687	C₂×C₄	—	4	3	no	—
688	C₂×C₄	—	4	6	no	—
689	C₂×C₄	—	4	6	no	—
690	C₂×C₄	—	4	6	no	—
691	C₂×C₄	—	4	6	no	—
692	C₂×C₄	—	8	6	no	—
693	C₂×C₄	—	8	3	no	—
694	C₂×C₄	—	8	3	no	—
695	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
697	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
698	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
699	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
700	C₂×C₄	C₂²×D₄×C₂₃	1	3	yes	—
701	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
702	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
703	C₈	—	2	1	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	3	no	—
706	C₈	—	2	3	no	—
707	C₂²	—	2	3	no	—
708	C₂²	—	2	3	no	—
709	C₂²	—	2	6	no	—
710	C₂²	—	4	3	no	—
711	C₂²	—	4	3	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	3	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	3	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	3	no	—
718	C₂²	—	8	12	no	—
719	C₂²	—	16	6	no	—
720	C₂²	C₂×C₂₃×#121	1	6	yes	—
721	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
722	C₄	—	2	2	no	—
723	C₄	—	2	1	no	—
724	C₄	—	2	3	no	—
725	C₄	—	2	1	no	—
726	C₄	—	2	3	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	3	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	3	no	—
731	C₄	C₂×C₂₃×#121	1	6	yes	—
732	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
733	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
734	C₂	—	2	6	no	—
735	C₂	—	4	6	no	—
736	C₂	—	8	3	no	—
737	C₂	—	8	1	no	—
738	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
739	C₂	C₂₃×#3584	1	1	yes	characteristic
740	C₂	C₂₃×#3585	1	1	yes	characteristic

	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 ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#577	C₂	semidirect
2. C₂×C₂₃×#576	C₂	semidirect
3. C₂₃×#3500	C₂	semidirect
4. C₄×C₂₃×H(5,𝔽₂)	C₂	semidirect
5. C₂₃×#3046	C₂	semidirect
6. C₂₃×#3045	C₂	semidirect
7. C₂₃×#3042	C₂	semidirect
8. C₂₃×#3041	C₂	semidirect
9. C₂₃×#3040	C₂	semidirect
10. C₂₃×#3036	C₂	semidirect
11. C₂₃×#3035	C₂	semidirect
12. C₂×C₂₃×#463	C₂	semidirect
13. C₂₃×#2906	C₂	semidirect
14. C₂₃×#2898	C₂	semidirect
15. C₂₃×#2897	C₂	semidirect
21. C₂×C₂₃×#137	C₂²	semidirect
24. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₂₃×#135	C₂²	semidirect
27. C₂²×SD₁₆×C₂₃	C₂²	semidirect
35. C₂₃×#536	C₂²	semidirect
36. C₂₃×#535	C₂²	semidirect
37. C₂₃×#532	C₂²	semidirect
38. C₂×C₂₃×#124	C₂²	semidirect
41. C₂₃×#520	C₂²	semidirect
43. C₂₃×#518	C₂²	semidirect
46. C₄×#41×C₂₃	C₂²	semidirect
48. C₂×C₄×D₄×C₂₃	C₂²	semidirect
49. C₂₃×#464	C₂²	semidirect
50. C₂₃×#464	C₂²	semidirect
51. C₂₃×#464	C₂²	semidirect
52. C₂₃×#463	C₂²	semidirect
53. C₂₃×#463	C₂²	semidirect
54. C₂₃×#463	C₂²	semidirect
55. C₂₃×#463	C₂²	semidirect
56. C₂₃×#463	C₂²	semidirect
57. C₂₃×#463	C₂²	semidirect
58. C₂₃×#462	C₂²	semidirect
59. C₂₃×#461	C₂²	semidirect
60. C₂₃×#461	C₂²	semidirect
61. C₂₃×#460	C₂²	semidirect
62. C₂₃×#459	C₂²	semidirect
63. C₂₃×#459	C₂²	semidirect
64. C₂₃×#424	C₂²	semidirect
65. C₂₃×#424	C₂²	semidirect
66. C₂₃×#423	C₂²	semidirect
67. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
68. C₂₃×#419	C₂²	semidirect
69. C₂₃×#418	C₂²	semidirect
70. C₂₃×#417	C₂²	semidirect
71. C₂₃×#417	C₂²	semidirect
72. C₂₃×#416	C₂²	semidirect
73. C₂₃×#416	C₂²	semidirect
74. C₂×C₂₃×#103	C₂²	semidirect
75. C₂×C₂₃×#102	C₂²	semidirect
81. C₂₃×H(5,𝔽₂)	D₄	semidirect
277. #60430	C₂₃	direct (N × H)
337. C₂×#577	C₂×C₂₃	semidirect
338. C₂×#576	C₂×C₂₃	semidirect
339. #3500	C₂×C₂₃	semidirect
340. C₄×H(5,𝔽₂)	C₂×C₂₃	semidirect
341. #3046	C₂×C₂₃	semidirect
342. #3045	C₂×C₂₃	semidirect
343. #3042	C₂×C₂₃	semidirect
344. #3041	C₂×C₂₃	semidirect
345. #3040	C₂×C₂₃	semidirect
346. #3036	C₂×C₂₃	semidirect
347. #3035	C₂×C₂₃	semidirect
348. C₂×#463	C₂×C₂₃	semidirect
349. #2906	C₂×C₂₃	semidirect
350. #2898	C₂×C₂₃	semidirect
351. #2897	C₂×C₂₃	semidirect
384. C₂×#137	C₂²×C₂₃	semidirect
387. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
389. C₂×#135	C₂²×C₂₃	semidirect
390. C₂²×SD₁₆	C₂²×C₂₃	semidirect
398. #536	C₂²×C₂₃	semidirect
399. #535	C₂²×C₂₃	semidirect
400. #532	C₂²×C₂₃	semidirect
401. C₂×#124	C₂²×C₂₃	semidirect
404. #520	C₂²×C₂₃	semidirect
406. #518	C₂²×C₂₃	semidirect
409. C₄×#41	C₂²×C₂₃	semidirect
411. C₂×C₄×D₄	C₂²×C₂₃	semidirect
412. #464	C₂²×C₂₃	semidirect
413. #464	C₂²×C₂₃	semidirect
414. #464	C₂²×C₂₃	semidirect
415. #463	C₂²×C₂₃	semidirect
416. #463	C₂²×C₂₃	semidirect
417. #463	C₂²×C₂₃	semidirect
418. #463	C₂²×C₂₃	semidirect
419. #463	C₂²×C₂₃	semidirect
420. #463	C₂²×C₂₃	semidirect
421. #462	C₂²×C₂₃	semidirect
422. #461	C₂²×C₂₃	semidirect
423. #461	C₂²×C₂₃	semidirect
424. #460	C₂²×C₂₃	semidirect
425. #459	C₂²×C₂₃	semidirect
426. #459	C₂²×C₂₃	semidirect
427. #424	C₂²×C₂₃	semidirect
428. #424	C₂²×C₂₃	semidirect
429. #423	C₂²×C₂₃	semidirect
430. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
431. #419	C₂²×C₂₃	semidirect
432. #418	C₂²×C₂₃	semidirect
433. #417	C₂²×C₂₃	semidirect
434. #417	C₂²×C₂₃	semidirect
435. #416	C₂²×C₂₃	semidirect
436. #416	C₂²×C₂₃	semidirect
437. C₂×#103	C₂²×C₂₃	semidirect
438. C₂×#102	C₂²×C₂₃	semidirect
451. H(5,𝔽₂)	D₄×C₂₃	semidirect
552. C₂₃	#60430	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×#577	2
C₂×C₂₃×#576	2
C₂₃×#3500	2
C₄×C₂₃×H(5,𝔽₂)	2
C₂₃×#3046	2
C₂₃×#3045	2
C₂₃×#3042	2
C₂₃×#3041	2
C₂₃×#3040	2
C₂₃×#3036	2
C₂₃×#3035	2
C₂×C₂₃×#463	2
C₂₃×#2906	2
C₂₃×#2898	2
C₂₃×#2897	2
#60430	23

Subgroups — C23×#60430 #19208056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60430 #19208056