Subgroups — C₂₃×#61090 #19208716

Order 5888.

2714 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3500	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3285	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3280	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3275	C₂	1	8	yes	maximal, complemented
7	C₂×C₂₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3040	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3010	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3009	C₂	1	2	yes	maximal, complemented
13	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂₃×#578	—	2	8	no	—
18	C₂₃×#576	—	2	8	no	—
19	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
20	C₂×C₂₃×#137	C₂²	1	4	yes	complemented
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
23	C₂×C₂₃×#135	C₂²	1	2	yes	—
24	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
26	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
27	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
29	C₂²×D₈×C₂₃	C₂²	1	2	yes	—
30	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#548	C₂²	1	8	yes	complemented
34	C₂₃×#546	—	2	8	no	—
35	C₂₃×#546	C₂²	1	8	yes	complemented
36	C₂₃×#536	—	2	2	no	—
37	C₂₃×#536	C₂²	1	2	yes	—
38	C₂₃×#535	—	2	2	no	—
39	C₂₃×#535	C₂²	1	2	yes	complemented
40	C₂₃×#532	—	2	2	no	—
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#124	—	2	2	no	—
43	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
44	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
45	C₂₃×#495	C₂²	1	4	yes	complemented
46	C₂₃×#495	C₂²	1	4	yes	complemented
47	C₂₃×#470	C₂²	1	4	yes	complemented
48	C₂₃×#469	C₂²	1	4	yes	complemented
49	C₂₃×#467	C₂²	1	4	yes	complemented
50	C₂₃×#466	C₂²	1	4	yes	complemented
51	C₂₃×#464	C₂²	1	8	yes	complemented
52	C₂₃×#463	C₂²	1	8	yes	complemented
53	C₂₃×#452	C₂²	1	8	yes	complemented
54	C₂₃×#450	C₂²	1	8	yes	complemented
55	C₂₃×#449	C₂²	1	8	yes	complemented
56	C₂₃×#448	C₂²	1	8	yes	complemented
57	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
58	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
59	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
60	C₂₃×#436	C₂²	1	4	yes	complemented
61	C₈×D₄×C₂₃	C₂²	1	4	yes	complemented
62	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#419	C₂²	1	2	yes	complemented
65	C₂₃×#418	C₂²	1	2	yes	complemented
66	C₂₃×#416	C₂²	1	2	yes	complemented
67	C₂₃×#408	C₂²	1	1	yes	characteristic
68	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×2₋¹⁺⁴	—	2	8	no	—
71	C₂₃×2₋¹⁺⁴	—	4	4	no	—
72	C₂₃×H(5,𝔽₂)	—	2	8	no	—
73	C₂₃×H(5,𝔽₂)	—	4	4	no	—
74	C₂×#41×C₂₃	—	2	2	no	—
75	C₂×#41×C₂₃	—	2	2	no	—
76	C₂×#41×C₂₃	—	2	4	no	—
77	C₂×#41×C₂₃	C₂³	1	4	yes	—
78	C₂×#41×C₂₃	C₂³	1	4	yes	—
79	C₂×#41×C₂₃	C₂³	1	2	yes	—
80	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₂₃	—	2	2	no	—
83	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
84	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
85	C₂²×D₄×C₂₃	—	2	2	no	—
86	C₂²×D₄×C₂₃	—	2	4	no	—
87	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
88	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
89	C₂₃×#137	—	2	8	no	—
90	C₂₃×#137	—	2	16	no	—
91	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
92	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
93	C₂₃×#135	—	2	8	no	—
94	C₂₃×#135	—	2	8	no	—
95	C₂₃×#135	D₄	1	8	yes	complemented
96	C₂×Q₁₆×C₂₃	—	2	8	no	—
97	C₂×Q₁₆×C₂₃	—	2	4	no	—
98	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
99	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
100	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
102	C₂×SD₁₆×C₂₃	—	4	4	no	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×D₈×C₂₃	—	2	8	no	—
108	C₂×D₈×C₂₃	—	2	4	no	—
109	C₂×D₈×C₂₃	C₂³	1	2	yes	—
110	C₂×D₈×C₂₃	C₂³	1	4	yes	—
111	C₂×D₈×C₂₃	C₂³	1	2	yes	—
112	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂₃×#131	—	2	4	no	—
114	C₂₃×#131	—	2	4	no	—
115	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
123	C₂₃×C₄⋊Q₈	—	2	2	no	—
124	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
125	C₂₃×#127	—	2	2	no	—
126	C₂₃×#127	D₄	1	1	yes	characteristic
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	8	no	—
130	C₂₃×#124	—	2	2	no	—
131	C₂₃×#124	—	2	2	no	—
132	C₂₃×#124	D₄	1	1	yes	characteristic
133	C₂₃×#124	D₄	1	1	yes	characteristic
134	C₂₃×#124	C₂³	1	8	yes	—
135	C₂₃×#123	—	2	4	no	—
136	C₂₃×#123	—	2	8	no	—
137	C₂₃×C₂²⋊Q₈	—	2	8	no	—
138	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
139	C₂₃×#121	—	2	8	no	—
140	C₂₃×#121	—	2	8	no	—
141	C₂₃×#121	D₄	1	4	yes	—
142	C₂₃×#121	C₂³	1	8	yes	—
143	C₂₃×#120	—	2	8	no	—
144	C₂₃×#120	—	2	4	no	—
145	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
146	C₄×D₄×C₂₃	—	2	4	no	—
147	C₄×D₄×C₂₃	—	2	8	no	—
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	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
154	C₂×C₄²×C₂₃	—	2	2	no	—
155	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
156	C₂₃×#107	C₂³	1	2	yes	—
157	C₂₃×#106	C₂³	1	2	yes	—
158	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
159	C₂₃×#103	C₂³	1	4	yes	—
160	C₂₃×#103	C₂³	1	8	yes	—
161	C₂₃×#102	C₂³	1	4	yes	—
162	C₂₃×#102	C₂³	1	8	yes	—
163	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
164	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
165	C₄×C₈×C₂₃	C₂³	1	2	yes	—
166	C₄×C₈×C₂₃	C₂³	1	2	yes	—
167	C₂⁴×C₂₃	—	2	4	no	—
168	C₂⁴×C₂₃	—	2	2	no	—
169	#41×C₂₃	—	2	2	no	—
170	#41×C₂₃	—	2	2	no	—
171	#41×C₂₃	—	2	2	no	—
172	#41×C₂₃	—	2	4	no	—
173	#41×C₂₃	—	2	2	no	—
174	#41×C₂₃	—	2	8	no	—
175	#41×C₂₃	—	2	8	no	—
176	#41×C₂₃	—	4	4	no	—
177	#41×C₂₃	—	4	4	no	—
178	#41×C₂₃	—	4	8	no	—
179	#41×C₂₃	—	4	8	no	—
180	#41×C₂₃	—	4	16	no	—
181	#41×C₂₃	C₂×D₄	1	8	yes	—
182	C₂×Q₈×C₂₃	—	2	4	no	—
183	C₂×Q₈×C₂₃	—	2	2	no	—
184	C₂×Q₈×C₂₃	—	2	8	no	—
185	C₂×Q₈×C₂₃	—	2	4	no	—
186	C₂×Q₈×C₂₃	—	2	4	no	—
187	C₂×Q₈×C₂₃	—	4	4	no	—
188	C₂×Q₈×C₂₃	—	4	8	no	—
189	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
190	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
191	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
192	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	8	no	—
195	C₂×D₄×C₂₃	—	2	4	no	—
196	C₂×D₄×C₂₃	—	2	4	no	—
197	C₂×D₄×C₂₃	—	2	8	no	—
198	C₂×D₄×C₂₃	—	2	4	no	—
199	C₂×D₄×C₂₃	—	2	4	no	—
200	C₂×D₄×C₂₃	—	2	2	no	—
201	C₂×D₄×C₂₃	—	2	4	no	—
202	C₂×D₄×C₂₃	—	4	4	no	—
203	C₂×D₄×C₂₃	—	4	8	no	—
204	C₂×D₄×C₂₃	—	4	16	no	—
205	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
207	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
208	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
210	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
211	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	2	4	no	—
216	C₂²×C₄×C₂₃	—	2	4	no	—
217	C₂²×C₄×C₂₃	—	2	4	no	—
218	C₂²×C₄×C₂₃	C₂×D₄	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	1	yes	characteristic
222	Q₁₆×C₂₃	—	2	8	no	—
223	Q₁₆×C₂₃	—	2	4	no	—
224	Q₁₆×C₂₃	—	2	4	no	—
225	Q₁₆×C₂₃	C₂×D₄	1	4	yes	—
226	SD₁₆×C₂₃	—	2	8	no	—
227	SD₁₆×C₂₃	—	2	8	no	—
228	SD₁₆×C₂₃	—	4	8	no	—
229	SD₁₆×C₂₃	C₂×D₄	1	8	yes	—
230	D₈×C₂₃	—	2	8	no	—
231	D₈×C₂₃	—	2	4	no	—
232	D₈×C₂₃	—	2	4	no	—
233	D₈×C₂₃	C₂×D₄	1	4	yes	—
234	M₁₆×C₂₃	—	2	2	no	—
235	M₁₆×C₂₃	—	2	2	no	—
236	M₁₆×C₂₃	—	2	4	no	—
237	M₁₆×C₂₃	—	2	4	no	—
238	C₂×C₈×C₂₃	—	2	2	no	—
239	C₂×C₈×C₂₃	—	2	4	no	—
240	C₂×C₈×C₂₃	—	2	4	no	—
241	C₂×C₈×C₂₃	C₂×D₄	1	4	yes	—
242	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
244	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
245	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	8	no	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
251	C₂²⋊C₄×C₂₃	—	2	8	no	—
252	C₂²⋊C₄×C₂₃	—	2	2	no	—
253	C₂²⋊C₄×C₂₃	—	2	8	no	—
254	C₂²⋊C₄×C₂₃	—	2	8	no	—
255	C₂²⋊C₄×C₂₃	—	2	8	no	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
258	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
259	C₄²×C₂₃	—	2	2	no	—
260	C₄²×C₂₃	—	2	4	no	—
261	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₂₃	C₂⁴	1	2	yes	—
264	#61090	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	4	no	—
267	C₂³×C₂₃	—	4	8	no	—
268	C₂³×C₂₃	—	4	4	no	—
269	C₂³×C₂₃	—	8	4	no	—
270	C₂³×C₂₃	—	8	8	no	—
271	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
272	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
274	Q₈×C₂₃	—	2	2	no	—
275	Q₈×C₂₃	—	2	2	no	—
276	Q₈×C₂₃	—	2	2	no	—
277	Q₈×C₂₃	—	2	4	no	—
278	Q₈×C₂₃	—	2	4	no	—
279	Q₈×C₂₃	—	4	8	no	—
280	Q₈×C₂₃	—	4	4	no	—
281	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
282	D₄×C₂₃	—	2	8	no	—
283	D₄×C₂₃	—	2	4	no	—
284	D₄×C₂₃	—	2	4	no	—
285	D₄×C₂₃	—	2	2	no	—
286	D₄×C₂₃	—	2	2	no	—
287	D₄×C₂₃	—	2	4	no	—
288	D₄×C₂₃	—	2	2	no	—
289	D₄×C₂₃	—	2	4	no	—
290	D₄×C₂₃	—	4	4	no	—
291	D₄×C₂₃	—	4	8	no	—
292	D₄×C₂₃	—	4	8	no	—
293	D₄×C₂₃	—	4	8	no	—
294	D₄×C₂₃	—	4	4	no	—
295	D₄×C₂₃	—	8	8	no	—
296	D₄×C₂₃	C₂²×D₄	1	4	yes	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	8	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	4	no	—
304	C₂×C₄×C₂₃	—	2	4	no	—
305	C₂×C₄×C₂₃	—	4	2	no	—
306	C₂×C₄×C₂₃	—	4	8	no	—
307	C₂×C₄×C₂₃	—	4	8	no	—
308	C₂×C₄×C₂₃	—	4	8	no	—
309	C₂×C₄×C₂₃	—	4	4	no	—
310	C₂×C₄×C₂₃	—	8	4	no	—
311	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
318	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
319	C₈×C₂₃	—	2	2	no	—
320	C₈×C₂₃	—	2	2	no	—
321	C₈×C₂₃	—	2	2	no	—
322	C₈×C₂₃	C₂²×D₄	1	2	yes	—
323	C₈×C₂₃	C₂²×D₄	1	2	yes	—
324	C₂×#578	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₂×#576	C₂×C₂₃	1	1	yes	characteristic, complemented
326	#3500	C₂×C₂₃	1	2	yes	complemented
327	#3285	C₂×C₂₃	1	4	yes	complemented
328	#3280	C₂×C₂₃	1	4	yes	complemented
329	#3275	C₂×C₂₃	1	8	yes	complemented
330	C₂×#495	C₂×C₂₃	1	1	yes	characteristic, complemented
331	#3059	C₂×C₂₃	1	1	yes	characteristic, complemented
332	#3058	C₂×C₂₃	1	1	yes	characteristic, complemented
333	#3040	C₂×C₂₃	1	2	yes	complemented
334	#3010	C₂×C₂₃	1	2	yes	complemented
335	#3009	C₂×C₂₃	1	2	yes	complemented
336	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
337	#2931	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂²×C₂₃	—	2	2	no	—
339	C₂²×C₂₃	—	2	4	no	—
340	C₂²×C₂₃	—	2	4	no	—
341	C₂²×C₂₃	—	2	2	no	—
342	C₂²×C₂₃	—	2	4	no	—
343	C₂²×C₂₃	—	2	2	no	—
344	C₂²×C₂₃	—	4	4	no	—
345	C₂²×C₂₃	—	4	8	no	—
346	C₂²×C₂₃	—	4	4	no	—
347	C₂²×C₂₃	—	16	4	no	—
348	C₂²×C₂₃	—	16	8	no	—
349	C₂²×C₂₃	D₄²	1	2	yes	—
350	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
351	C₄×C₂₃	—	2	2	no	—
352	C₄×C₂₃	—	2	2	no	—
353	C₄×C₂₃	—	2	4	no	—
354	C₄×C₂₃	—	2	2	no	—
355	C₄×C₂₃	—	2	2	no	—
356	C₄×C₂₃	—	4	4	no	—
357	C₄×C₂₃	—	4	4	no	—
358	C₄×C₂₃	D₄²	1	2	yes	—
359	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
360	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
361	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	complemented
362	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
363	#578	—	2	8	no	—
364	#576	—	2	8	no	—
365	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
366	C₂×#137	C₂²×C₂₃	1	4	yes	complemented
367	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
368	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	—
369	C₂×#135	C₂²×C₂₃	1	2	yes	—
370	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
371	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
372	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
373	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
374	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
375	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
376	C₂²×D₈	C₂²×C₂₃	1	2	yes	—
377	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
378	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
379	#548	C₂²×C₂₃	1	8	yes	complemented
380	#546	—	2	8	no	—
381	#546	C₂²×C₂₃	1	8	yes	complemented
382	#536	—	2	2	no	—
383	#536	C₂²×C₂₃	1	2	yes	—
384	#535	—	2	2	no	—
385	#535	C₂²×C₂₃	1	2	yes	complemented
386	#532	—	2	2	no	—
387	#532	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×#124	—	2	2	no	—
389	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
390	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
391	#495	C₂²×C₂₃	1	4	yes	complemented
392	#495	C₂²×C₂₃	1	4	yes	complemented
393	#470	C₂²×C₂₃	1	4	yes	complemented
394	#469	C₂²×C₂₃	1	4	yes	complemented
395	#467	C₂²×C₂₃	1	4	yes	complemented
396	#466	C₂²×C₂₃	1	4	yes	complemented
397	#464	C₂²×C₂₃	1	8	yes	complemented
398	#463	C₂²×C₂₃	1	8	yes	complemented
399	#452	C₂²×C₂₃	1	8	yes	complemented
400	#450	C₂²×C₂₃	1	8	yes	complemented
401	#449	C₂²×C₂₃	1	8	yes	complemented
402	#448	C₂²×C₂₃	1	8	yes	complemented
403	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
404	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
405	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
406	#436	C₂²×C₂₃	1	4	yes	complemented
407	C₈×D₄	C₂²×C₂₃	1	4	yes	complemented
408	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
409	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
410	#419	C₂²×C₂₃	1	2	yes	complemented
411	#418	C₂²×C₂₃	1	2	yes	complemented
412	#416	C₂²×C₂₃	1	2	yes	complemented
413	#408	C₂²×C₂₃	1	1	yes	characteristic
414	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
415	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
416	C₂×C₂₃	—	2	2	no	—
417	C₂×C₂₃	—	4	2	no	—
418	C₂×C₂₃	—	4	2	no	—
419	C₂×C₂₃	—	4	4	no	—
420	C₂×C₂₃	—	8	4	no	—
421	C₂×C₂₃	C₂×D₄²	1	1	yes	characteristic
422	C₂×C₂₃	#3584	1	2	yes	—
423	2₋¹⁺⁴	—	2	8	no	—
424	2₋¹⁺⁴	—	4	4	no	—
425	H(5,𝔽₂)	—	2	8	no	—
426	H(5,𝔽₂)	—	4	4	no	—
427	C₂×#41	—	2	2	no	—
428	C₂×#41	—	2	2	no	—
429	C₂×#41	—	2	4	no	—
430	C₂×#41	C₂³×C₂₃	1	4	yes	—
431	C₂×#41	C₂³×C₂₃	1	4	yes	—
432	C₂×#41	C₂³×C₂₃	1	2	yes	—
433	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
434	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
435	C₂²×Q₈	—	2	2	no	—
436	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
437	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
438	C₂²×D₄	—	2	2	no	—
439	C₂²×D₄	—	2	4	no	—
440	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
441	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
442	#137	—	2	8	no	—
443	#137	—	2	16	no	—
444	AGL(1,ℤ/8)	—	2	8	no	—
445	AGL(1,ℤ/8)	—	2	16	no	—
446	#135	—	2	8	no	—
447	#135	—	2	8	no	—
448	#135	D₄×C₂₃	1	8	yes	complemented
449	C₂×Q₁₆	—	2	8	no	—
450	C₂×Q₁₆	—	2	4	no	—
451	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
452	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
453	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
454	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
455	C₂×SD₁₆	—	4	4	no	—
456	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
457	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
459	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
460	C₂×D₈	—	2	8	no	—
461	C₂×D₈	—	2	4	no	—
462	C₂×D₈	C₂³×C₂₃	1	2	yes	—
463	C₂×D₈	C₂³×C₂₃	1	4	yes	—
464	C₂×D₈	C₂³×C₂₃	1	2	yes	—
465	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
466	#131	—	2	4	no	—
467	#131	—	2	4	no	—
468	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
470	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
471	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
472	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
473	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
476	C₄⋊Q₈	—	2	2	no	—
477	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
478	#127	—	2	2	no	—
479	#127	D₄×C₂₃	1	1	yes	characteristic
480	#124	—	2	2	no	—
481	#124	—	2	2	no	—
482	#124	—	2	8	no	—
483	#124	—	2	2	no	—
484	#124	—	2	2	no	—
485	#124	D₄×C₂₃	1	1	yes	characteristic
486	#124	D₄×C₂₃	1	1	yes	characteristic
487	#124	C₂³×C₂₃	1	8	yes	—
488	#123	—	2	4	no	—
489	#123	—	2	8	no	—
490	C₂²⋊Q₈	—	2	8	no	—
491	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
492	#121	—	2	8	no	—
493	#121	—	2	8	no	—
494	#121	D₄×C₂₃	1	4	yes	—
495	#121	C₂³×C₂₃	1	8	yes	—
496	#120	—	2	8	no	—
497	#120	—	2	4	no	—
498	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
499	C₄×D₄	—	2	4	no	—
500	C₄×D₄	—	2	8	no	—
501	C₄×D₄	C₂³×C₂₃	1	4	yes	—
502	C₄×D₄	C₂³×C₂₃	1	4	yes	—
503	#117	—	2	2	no	—
504	#117	C₂³×C₂₃	1	2	yes	—
505	C₂×C₂²⋊C₄	—	2	4	no	—
506	C₂×C₂²⋊C₄	—	2	8	no	—
507	C₂×C₄²	—	2	2	no	—
508	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
509	#107	C₂³×C₂₃	1	2	yes	—
510	#106	C₂³×C₂₃	1	2	yes	—
511	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
512	#103	C₂³×C₂₃	1	4	yes	—
513	#103	C₂³×C₂₃	1	8	yes	—
514	#102	C₂³×C₂₃	1	4	yes	—
515	#102	C₂³×C₂₃	1	8	yes	—
516	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
517	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
518	C₄×C₈	C₂³×C₂₃	1	2	yes	—
519	C₄×C₈	C₂³×C₂₃	1	2	yes	—
520	C₂₃	#61090	1	1	yes	characteristic, direct product factor, Sylow
521	C₂⁴	—	2	4	no	—
522	C₂⁴	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	2	4	no	—
527	#41	—	2	2	no	—
528	#41	—	2	8	no	—
529	#41	—	2	8	no	—
530	#41	—	4	4	no	—
531	#41	—	4	4	no	—
532	#41	—	4	8	no	—
533	#41	—	4	8	no	—
534	#41	—	4	16	no	—
535	#41	C₂×D₄×C₂₃	1	8	yes	—
536	C₂×Q₈	—	2	4	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	8	no	—
539	C₂×Q₈	—	2	4	no	—
540	C₂×Q₈	—	2	4	no	—
541	C₂×Q₈	—	4	4	no	—
542	C₂×Q₈	—	4	8	no	—
543	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
544	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
545	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
546	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	8	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	4	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	4	4	no	—
557	C₂×D₄	—	4	8	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
560	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
561	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
562	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
563	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
564	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
565	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	4	no	—
572	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
573	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
576	Q₁₆	—	2	8	no	—
577	Q₁₆	—	2	4	no	—
578	Q₁₆	—	2	4	no	—
579	Q₁₆	C₂×D₄×C₂₃	1	4	yes	—
580	SD₁₆	—	2	8	no	—
581	SD₁₆	—	2	8	no	—
582	SD₁₆	—	4	8	no	—
583	SD₁₆	C₂×D₄×C₂₃	1	8	yes	—
584	D₈	—	2	8	no	—
585	D₈	—	2	4	no	—
586	D₈	—	2	4	no	—
587	D₈	C₂×D₄×C₂₃	1	4	yes	—
588	M₁₆	—	2	2	no	—
589	M₁₆	—	2	2	no	—
590	M₁₆	—	2	4	no	—
591	M₁₆	—	2	4	no	—
592	C₂×C₈	—	2	2	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	—	2	4	no	—
595	C₂×C₈	C₂×D₄×C₂₃	1	4	yes	—
596	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
597	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
598	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
599	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
600	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
604	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
612	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
613	C₄²	—	2	2	no	—
614	C₄²	—	2	4	no	—
615	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
616	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
617	C₄²	C₂⁴×C₂₃	1	2	yes	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	4	8	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	8	4	no	—
623	C₂³	—	8	8	no	—
624	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
625	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
626	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	4	no	—
631	Q₈	—	2	4	no	—
632	Q₈	—	4	8	no	—
633	Q₈	—	4	4	no	—
634	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
635	D₄	—	2	8	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	4	no	—
639	D₄	—	2	2	no	—
640	D₄	—	2	4	no	—
641	D₄	—	2	2	no	—
642	D₄	—	2	2	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	8	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	8	no	—
649	D₄	C₂²×D₄×C₂₃	1	4	yes	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	—	4	8	no	—
661	C₂×C₄	—	4	8	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	8	4	no	—
664	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
666	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
668	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
670	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
671	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₈	—	2	2	no	—
675	C₈	C₂²×D₄×C₂₃	1	2	yes	—
676	C₈	C₂²×D₄×C₂₃	1	2	yes	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	2	4	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	4	4	no	—
685	C₂²	—	4	8	no	—
686	C₂²	—	16	4	no	—
687	C₂²	—	16	8	no	—
688	C₂²	D₄²×C₂₃	1	2	yes	—
689	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
690	C₄	—	2	4	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	4	no	—
697	C₄	D₄²×C₂₃	1	2	yes	—
698	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
699	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	4	2	no	—
702	C₂	—	4	2	no	—
703	C₂	—	4	4	no	—
704	C₂	—	8	4	no	—
705	C₂	C₂×D₄²×C₂₃	1	1	yes	characteristic
706	C₂	C₂₃×#3584	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 ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#578	C₂	semidirect
2. C₂×C₂₃×#576	C₂	semidirect
3. C₂₃×#3500	C₂	semidirect
4. C₂₃×#3285	C₂	semidirect
5. C₂₃×#3280	C₂	semidirect
6. C₂₃×#3275	C₂	semidirect
7. C₂×C₂₃×#495	C₂	semidirect
8. C₂₃×#3059	C₂	semidirect
9. C₂₃×#3058	C₂	semidirect
10. C₂₃×#3040	C₂	semidirect
11. C₂₃×#3010	C₂	semidirect
12. C₂₃×#3009	C₂	semidirect
13. C₄×C₂₃×#135	C₂	semidirect
14. C₂₃×#2931	C₂	semidirect
15. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
19. C₂×C₂₃×#137	C₂²	semidirect
20. C₂×C₂₃×#137	C₂²	semidirect
25. C₂×C₂₃×#135	C₂²	semidirect
26. C₂²×Q₁₆×C₂₃	C₂²	semidirect
27. C₂²×Q₁₆×C₂₃	C₂²	semidirect
28. C₂²×SD₁₆×C₂₃	C₂²	semidirect
32. C₂×C₂₃×#131	C₂²	semidirect
33. C₂₃×#548	C₂²	semidirect
35. C₂₃×#546	C₂²	semidirect
39. C₂₃×#535	C₂²	semidirect
43. C₂×C₂₃×#124	C₂²	semidirect
44. C₄×#41×C₂₃	C₂²	semidirect
45. C₂₃×#495	C₂²	semidirect
46. C₂₃×#495	C₂²	semidirect
47. C₂₃×#470	C₂²	semidirect
48. C₂₃×#469	C₂²	semidirect
49. C₂₃×#467	C₂²	semidirect
50. C₂₃×#466	C₂²	semidirect
51. C₂₃×#464	C₂²	semidirect
52. C₂₃×#463	C₂²	semidirect
53. C₂₃×#452	C₂²	semidirect
54. C₂₃×#450	C₂²	semidirect
55. C₂₃×#449	C₂²	semidirect
56. C₂₃×#448	C₂²	semidirect
57. C₄×Q₁₆×C₂₃	C₂²	semidirect
58. C₄×SD₁₆×C₂₃	C₂²	semidirect
59. C₄×D₈×C₂₃	C₂²	semidirect
60. C₂₃×#436	C₂²	semidirect
61. C₈×D₄×C₂₃	C₂²	semidirect
62. C₂₃×#427	C₂²	semidirect
63. C₂₃×#423	C₂²	semidirect
64. C₂₃×#419	C₂²	semidirect
65. C₂₃×#418	C₂²	semidirect
66. C₂₃×#416	C₂²	semidirect
68. C₂₃×#408	C₂²	semidirect
69. C₂×C₄×C₈×C₂₃	C₂²	semidirect
95. C₂₃×#135	D₄	semidirect
264. #61090	C₂₃	direct (N × H)
324. C₂×#578	C₂×C₂₃	semidirect
325. C₂×#576	C₂×C₂₃	semidirect
326. #3500	C₂×C₂₃	semidirect
327. #3285	C₂×C₂₃	semidirect
328. #3280	C₂×C₂₃	semidirect
329. #3275	C₂×C₂₃	semidirect
330. C₂×#495	C₂×C₂₃	semidirect
331. #3059	C₂×C₂₃	semidirect
332. #3058	C₂×C₂₃	semidirect
333. #3040	C₂×C₂₃	semidirect
334. #3010	C₂×C₂₃	semidirect
335. #3009	C₂×C₂₃	semidirect
336. C₄×#135	C₂×C₂₃	semidirect
337. #2931	C₂×C₂₃	semidirect
361. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
365. C₂×#137	C₂²×C₂₃	semidirect
366. C₂×#137	C₂²×C₂₃	semidirect
371. C₂×#135	C₂²×C₂₃	semidirect
372. C₂²×Q₁₆	C₂²×C₂₃	semidirect
373. C₂²×Q₁₆	C₂²×C₂₃	semidirect
374. C₂²×SD₁₆	C₂²×C₂₃	semidirect
378. C₂×#131	C₂²×C₂₃	semidirect
379. #548	C₂²×C₂₃	semidirect
381. #546	C₂²×C₂₃	semidirect
385. #535	C₂²×C₂₃	semidirect
389. C₂×#124	C₂²×C₂₃	semidirect
390. C₄×#41	C₂²×C₂₃	semidirect
391. #495	C₂²×C₂₃	semidirect
392. #495	C₂²×C₂₃	semidirect
393. #470	C₂²×C₂₃	semidirect
394. #469	C₂²×C₂₃	semidirect
395. #467	C₂²×C₂₃	semidirect
396. #466	C₂²×C₂₃	semidirect
397. #464	C₂²×C₂₃	semidirect
398. #463	C₂²×C₂₃	semidirect
399. #452	C₂²×C₂₃	semidirect
400. #450	C₂²×C₂₃	semidirect
401. #449	C₂²×C₂₃	semidirect
402. #448	C₂²×C₂₃	semidirect
403. C₄×Q₁₆	C₂²×C₂₃	semidirect
404. C₄×SD₁₆	C₂²×C₂₃	semidirect
405. C₄×D₈	C₂²×C₂₃	semidirect
406. #436	C₂²×C₂₃	semidirect
407. C₈×D₄	C₂²×C₂₃	semidirect
408. #427	C₂²×C₂₃	semidirect
409. #423	C₂²×C₂₃	semidirect
410. #419	C₂²×C₂₃	semidirect
411. #418	C₂²×C₂₃	semidirect
412. #416	C₂²×C₂₃	semidirect
414. #408	C₂²×C₂₃	semidirect
415. C₂×C₄×C₈	C₂²×C₂₃	semidirect
448. #135	D₄×C₂₃	semidirect
520. C₂₃	#61090	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×#578	2
C₂×C₂₃×#576	2
C₂₃×#3500	2
C₂₃×#3285	2
C₂₃×#3280	2
C₂₃×#3275	2
C₂×C₂₃×#495	2
C₂₃×#3059	2
C₂₃×#3058	2
C₂₃×#3040	2
C₂₃×#3010	2
C₂₃×#3009	2
C₄×C₂₃×#135	2
C₂₃×#2931	2
#61090	23

Subgroups — C23×#61090 #19208716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61090 #19208716