Subgroups — C₂₃×#60806 #19208432

Order 5888.

2222 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3224	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3222	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3220	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3040	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3038	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3005	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3003	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂₃×#542	C₂²	1	4	yes	complemented
22	C₂₃×#541	C₂²	1	2	yes	complemented
23	C₂₃×#540	C₂²	1	2	yes	complemented
24	C₂₃×#539	—	2	2	no	—
25	C₂₃×#538	—	2	2	no	—
26	C₂₃×#535	—	2	4	no	—
27	C₂₃×#535	C₂²	1	4	yes	—
28	C₂₃×#535	C₂²	1	4	yes	—
29	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
33	C₂₃×#529	—	2	4	no	—
34	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
36	C₂₃×#525	C₂²	1	2	yes	—
37	C₂×C₂₃×#121	—	2	2	no	—
38	C₂×C₂₃×#120	—	2	2	no	—
39	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
40	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
41	C₂₃×#497	C₂²	1	2	yes	complemented
42	C₂₃×#496	C₂²	1	2	yes	complemented
43	C₂₃×#496	C₂²	1	4	yes	complemented
44	C₂₃×#495	C₂²	1	4	yes	complemented
45	C₂₃×#493	C₂²	1	2	yes	complemented
46	C₂₃×#492	C₂²	1	2	yes	complemented
47	C₂₃×#490	C₂²	1	4	yes	complemented
48	C₂₃×#489	C₂²	1	4	yes	complemented
49	C₂₃×#488	C₂²	1	4	yes	complemented
50	C₂₃×#486	C₂²	1	4	yes	complemented
51	C₂₃×#464	C₂²	1	8	yes	complemented
52	C₂₃×#463	C₂²	1	8	yes	complemented
53	C₂₃×#460	C₂²	1	8	yes	complemented
54	C₂₃×#459	C₂²	1	8	yes	complemented
55	C₂₃×#452	C₂²	1	8	yes	complemented
56	C₂₃×#450	C₂²	1	8	yes	complemented
57	C₂₃×#449	C₂²	1	8	yes	complemented
58	C₂₃×#447	C₂²	1	8	yes	complemented
59	C₂₃×#433	C₂²	1	4	yes	complemented
60	C₂₃×#433	C₂²	1	4	yes	complemented
61	C₂₃×#423	C₂²	1	2	yes	complemented
62	C₂₃×#419	C₂²	1	2	yes	complemented
63	C₂₃×#418	C₂²	1	2	yes	—
64	C₂₃×#418	C₂²	1	2	yes	—
65	C₂₃×#418	C₂²	1	2	yes	complemented
66	C₂₃×#407	C₂²	1	2	yes	—
67	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
68	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₂₃	—	2	1	no	—
70	C₂×#41×C₂₃	—	2	2	no	—
71	C₂×#41×C₂₃	—	4	4	no	—
72	C₂×#41×C₂₃	C₂³	1	2	yes	—
73	C₂×#41×C₂₃	C₂³	1	4	yes	—
74	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂²×D₄×C₂₃	—	2	2	no	—
78	C₂²×D₄×C₂₃	—	2	2	no	—
79	C₂²×D₄×C₂₃	—	2	2	no	—
80	C₂²×D₄×C₂₃	—	4	4	no	—
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂₃×#137	—	4	4	no	—
88	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
89	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
90	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
91	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
92	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
93	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
95	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
96	C₂×D₈×C₂₃	C₂³	1	4	yes	—
97	C₂×D₈×C₂₃	C₂³	1	4	yes	—
98	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
99	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
101	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
102	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	complemented
103	C₂₃×#127	—	2	2	no	—
104	C₂₃×#127	—	2	2	no	—
105	C₂₃×#127	C₂³	1	4	yes	—
106	C₂₃×#127	C₂³	1	2	yes	—
107	C₂₃×#127	C₂³	1	2	yes	—
108	C₂₃×#127	C₂³	1	1	yes	characteristic, complemented
109	C₂₃×#126	—	2	4	no	—
110	C₂₃×#126	—	2	4	no	—
111	C₂₃×#125	—	2	4	no	—
112	C₂₃×#125	C₂³	1	2	yes	complemented
113	C₂₃×#124	—	2	4	no	—
114	C₂₃×#124	—	2	2	no	—
115	C₂₃×#124	—	2	2	no	—
116	C₂₃×#124	C₂³	1	4	yes	—
117	C₂₃×#124	C₂³	1	2	yes	—
118	C₂₃×#124	C₂³	1	2	yes	—
119	C₂₃×#124	C₂³	1	2	yes	complemented
120	C₂₃×#123	—	2	2	no	—
121	C₂₃×#123	—	2	4	no	—
122	C₂₃×#123	—	2	4	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	—	2	4	no	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₂₃×#121	—	2	2	no	—
127	C₂₃×#121	—	2	8	no	—
128	C₂₃×#121	—	2	8	no	—
129	C₂₃×#121	—	2	4	no	—
130	C₂₃×#121	C₂³	1	4	yes	—
131	C₂₃×#120	—	2	2	no	—
132	C₂₃×#120	—	2	8	no	—
133	C₂₃×#120	—	2	8	no	—
134	C₄×Q₈×C₂₃	—	2	2	no	—
135	C₄×Q₈×C₂₃	C₂³	1	4	yes	complemented
136	C₄×D₄×C₂₃	—	2	4	no	—
137	C₄×D₄×C₂₃	—	2	4	no	—
138	C₄×D₄×C₂₃	—	2	2	no	—
139	C₄×D₄×C₂₃	C₂³	1	4	yes	complemented
140	C₂₃×#117	—	2	2	no	—
141	C₂₃×#117	D₄	1	4	yes	—
142	C₂₃×#117	C₂³	1	2	yes	—
143	C₂₃×#117	C₂³	1	2	yes	—
144	C₂₃×#117	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
147	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
149	C₂×C₄²×C₂₃	—	2	2	no	—
150	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
152	C₂₃×C₄⋊C₈	C₂³	1	8	yes	complemented
153	C₂₃×#103	C₂³	1	8	yes	complemented
154	C₂₃×#102	C₂³	1	8	yes	—
155	C₂₃×#102	C₂³	1	8	yes	—
156	C₂₃×#102	C₂³	1	8	yes	complemented
157	C₂₃×C₂²⋊C₈	C₂³	1	8	yes	—
158	C₂₃×#97	C₂³	1	2	yes	complemented
159	C₂₃×#97	C₂³	1	2	yes	complemented
160	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
161	C₄×C₈×C₂₃	C₂³	1	2	yes	complemented
162	C₂⁴×C₂₃	—	2	1	no	—
163	C₂⁴×C₂₃	—	2	1	no	—
164	C₂⁴×C₂₃	—	2	1	no	—
165	C₂⁴×C₂₃	—	2	4	no	—
166	C₂⁴×C₂₃	—	4	4	no	—
167	C₂⁴×C₂₃	—	8	4	no	—
168	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
169	#41×C₂₃	—	2	4	no	—
170	#41×C₂₃	—	2	4	no	—
171	#41×C₂₃	—	4	8	no	—
172	#41×C₂₃	—	4	8	no	—
173	C₂×Q₈×C₂₃	—	2	1	no	—
174	C₂×Q₈×C₂₃	—	2	2	no	—
175	C₂×Q₈×C₂₃	—	2	4	no	—
176	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
177	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
178	C₂×D₄×C₂₃	—	2	2	no	—
179	C₂×D₄×C₂₃	—	2	4	no	—
180	C₂×D₄×C₂₃	—	2	4	no	—
181	C₂×D₄×C₂₃	—	2	4	no	—
182	C₂×D₄×C₂₃	—	2	1	no	—
183	C₂×D₄×C₂₃	—	2	1	no	—
184	C₂×D₄×C₂₃	—	2	1	no	—
185	C₂×D₄×C₂₃	—	2	2	no	—
186	C₂×D₄×C₂₃	—	2	8	no	—
187	C₂×D₄×C₂₃	—	2	4	no	—
188	C₂×D₄×C₂₃	—	2	4	no	—
189	C₂×D₄×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	4	no	—
191	C₂×D₄×C₂₃	—	2	4	no	—
192	C₂×D₄×C₂₃	—	4	8	no	—
193	C₂×D₄×C₂₃	—	4	4	no	—
194	C₂×D₄×C₂₃	—	4	8	no	—
195	C₂×D₄×C₂₃	—	4	4	no	—
196	C₂×D₄×C₂₃	—	8	4	no	—
197	C₂×D₄×C₂₃	—	8	4	no	—
198	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
199	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
200	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
201	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₂₃	—	2	4	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	2	no	—
205	C₂²×C₄×C₂₃	—	2	4	no	—
206	C₂²×C₄×C₂₃	—	2	4	no	—
207	C₂²×C₄×C₂₃	—	4	4	no	—
208	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
211	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
212	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
214	Q₁₆×C₂₃	—	4	4	no	—
215	SD₁₆×C₂₃	—	4	4	no	—
216	SD₁₆×C₂₃	—	4	4	no	—
217	SD₁₆×C₂₃	—	4	4	no	—
218	SD₁₆×C₂₃	—	4	4	no	—
219	D₈×C₂₃	—	4	4	no	—
220	D₈×C₂₃	—	4	4	no	—
221	D₈×C₂₃	—	4	4	no	—
222	M₁₆×C₂₃	—	2	4	no	—
223	M₁₆×C₂₃	—	2	4	no	—
224	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
225	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	2	no	—
228	C₄⋊C₄×C₂₃	—	2	4	no	—
229	C₄⋊C₄×C₂₃	—	2	4	no	—
230	C₄⋊C₄×C₂₃	—	2	2	no	—
231	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
232	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
233	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
234	C₂²⋊C₄×C₂₃	—	2	2	no	—
235	C₂²⋊C₄×C₂₃	—	2	4	no	—
236	C₂²⋊C₄×C₂₃	—	2	8	no	—
237	C₂²⋊C₄×C₂₃	—	2	4	no	—
238	C₂²⋊C₄×C₂₃	—	2	4	no	—
239	C₂²⋊C₄×C₂₃	—	2	4	no	—
240	C₂²⋊C₄×C₂₃	—	2	4	no	—
241	C₂²⋊C₄×C₂₃	—	2	4	no	—
242	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
243	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
244	C₄²×C₂₃	—	2	2	no	—
245	C₄²×C₂₃	—	2	4	no	—
246	C₄²×C₂₃	C₂×D₄	1	2	yes	—
247	C₄²×C₂₃	C₂×D₄	1	2	yes	—
248	C₄²×C₂₃	C₂⁴	1	2	yes	—
249	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
251	#60806	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	2	2	no	—
255	C₂³×C₂₃	—	2	2	no	—
256	C₂³×C₂₃	—	2	2	no	—
257	C₂³×C₂₃	—	4	2	no	—
258	C₂³×C₂₃	—	4	8	no	—
259	C₂³×C₂₃	—	4	4	no	—
260	C₂³×C₂₃	—	4	4	no	—
261	C₂³×C₂₃	—	4	4	no	—
262	C₂³×C₂₃	—	4	2	no	—
263	C₂³×C₂₃	—	4	2	no	—
264	C₂³×C₂₃	—	4	2	no	—
265	C₂³×C₂₃	—	8	8	no	—
266	C₂³×C₂₃	—	8	16	no	—
267	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
268	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
269	Q₈×C₂₃	—	2	2	no	—
270	Q₈×C₂₃	—	2	2	no	—
271	Q₈×C₂₃	—	2	4	no	—
272	Q₈×C₂₃	—	4	2	no	—
273	Q₈×C₂₃	—	8	2	no	—
274	D₄×C₂₃	—	2	2	no	—
275	D₄×C₂₃	—	2	2	no	—
276	D₄×C₂₃	—	2	4	no	—
277	D₄×C₂₃	—	2	4	no	—
278	D₄×C₂₃	—	2	4	no	—
279	D₄×C₂₃	—	4	8	no	—
280	D₄×C₂₃	—	4	8	no	—
281	D₄×C₂₃	—	4	4	no	—
282	D₄×C₂₃	—	4	2	no	—
283	D₄×C₂₃	—	4	2	no	—
284	D₄×C₂₃	—	4	2	no	—
285	D₄×C₂₃	—	8	2	no	—
286	D₄×C₂₃	—	8	8	no	—
287	D₄×C₂₃	—	8	4	no	—
288	D₄×C₂₃	—	8	4	no	—
289	D₄×C₂₃	—	8	4	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	4	no	—
292	C₂×C₄×C₂₃	—	2	4	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	4	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	4	2	no	—
297	C₂×C₄×C₂₃	—	4	2	no	—
298	C₂×C₄×C₂₃	—	4	8	no	—
299	C₂×C₄×C₂₃	—	4	2	no	—
300	C₂×C₄×C₂₃	—	4	4	no	—
301	C₂×C₄×C₂₃	—	8	4	no	—
302	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
303	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
304	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
306	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
308	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
309	C₈×C₂₃	—	2	4	no	—
310	C₈×C₂₃	—	2	4	no	—
311	#3455	C₂×C₂₃	1	1	yes	characteristic, complemented
312	C₂×#535	C₂×C₂₃	1	1	yes	characteristic, complemented
313	#3224	C₂×C₂₃	1	8	yes	complemented
314	#3222	C₂×C₂₃	1	4	yes	complemented
315	#3220	C₂×C₂₃	1	4	yes	complemented
316	#3153	C₂×C₂₃	1	1	yes	characteristic, complemented
317	#3151	C₂×C₂₃	1	1	yes	characteristic, complemented
318	#3140	C₂×C₂₃	1	1	yes	characteristic, complemented
319	#3138	C₂×C₂₃	1	1	yes	characteristic, complemented
320	#3040	C₂×C₂₃	1	2	yes	complemented
321	#3038	C₂×C₂₃	1	2	yes	complemented
322	#3005	C₂×C₂₃	1	2	yes	complemented
323	#3003	C₂×C₂₃	1	2	yes	complemented
324	#2921	C₂×C₂₃	1	1	yes	characteristic, complemented
325	C₂²×C₂₃	—	2	2	no	—
326	C₂²×C₂₃	—	2	4	no	—
327	C₂²×C₂₃	—	2	2	no	—
328	C₂²×C₂₃	—	4	4	no	—
329	C₂²×C₂₃	—	4	4	no	—
330	C₂²×C₂₃	—	4	4	no	—
331	C₂²×C₂₃	—	4	4	no	—
332	C₂²×C₂₃	—	4	4	no	—
333	C₂²×C₂₃	—	4	2	no	—
334	C₂²×C₂₃	—	4	2	no	—
335	C₂²×C₂₃	—	4	2	no	—
336	C₂²×C₂₃	—	4	2	no	—
337	C₂²×C₂₃	—	8	4	no	—
338	C₂²×C₂₃	—	8	4	no	—
339	C₂²×C₂₃	—	8	4	no	—
340	C₂²×C₂₃	—	8	16	no	—
341	C₂²×C₂₃	#535	1	2	yes	—
342	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₂₃	—	2	4	no	—
344	C₄×C₂₃	—	2	2	no	—
345	C₄×C₂₃	—	2	2	no	—
346	C₄×C₂₃	—	2	2	no	—
347	C₄×C₂₃	—	4	4	no	—
348	C₄×C₂₃	—	4	2	no	—
349	C₄×C₂₃	—	4	2	no	—
350	C₄×C₂₃	#535	1	2	yes	—
351	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
352	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
353	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
354	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
355	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
356	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
357	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
358	#542	C₂²×C₂₃	1	4	yes	complemented
359	#541	C₂²×C₂₃	1	2	yes	complemented
360	#540	C₂²×C₂₃	1	2	yes	complemented
361	#539	—	2	2	no	—
362	#538	—	2	2	no	—
363	#535	—	2	4	no	—
364	#535	C₂²×C₂₃	1	4	yes	—
365	#535	C₂²×C₂₃	1	4	yes	—
366	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
367	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
368	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
369	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
370	#529	—	2	4	no	—
371	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
372	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
373	#525	C₂²×C₂₃	1	2	yes	—
374	C₂×#121	—	2	2	no	—
375	C₂×#120	—	2	2	no	—
376	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
377	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
378	#497	C₂²×C₂₃	1	2	yes	complemented
379	#496	C₂²×C₂₃	1	2	yes	complemented
380	#496	C₂²×C₂₃	1	4	yes	complemented
381	#495	C₂²×C₂₃	1	4	yes	complemented
382	#493	C₂²×C₂₃	1	2	yes	complemented
383	#492	C₂²×C₂₃	1	2	yes	complemented
384	#490	C₂²×C₂₃	1	4	yes	complemented
385	#489	C₂²×C₂₃	1	4	yes	complemented
386	#488	C₂²×C₂₃	1	4	yes	complemented
387	#486	C₂²×C₂₃	1	4	yes	complemented
388	#464	C₂²×C₂₃	1	8	yes	complemented
389	#463	C₂²×C₂₃	1	8	yes	complemented
390	#460	C₂²×C₂₃	1	8	yes	complemented
391	#459	C₂²×C₂₃	1	8	yes	complemented
392	#452	C₂²×C₂₃	1	8	yes	complemented
393	#450	C₂²×C₂₃	1	8	yes	complemented
394	#449	C₂²×C₂₃	1	8	yes	complemented
395	#447	C₂²×C₂₃	1	8	yes	complemented
396	#433	C₂²×C₂₃	1	4	yes	complemented
397	#433	C₂²×C₂₃	1	4	yes	complemented
398	#423	C₂²×C₂₃	1	2	yes	complemented
399	#419	C₂²×C₂₃	1	2	yes	complemented
400	#418	C₂²×C₂₃	1	2	yes	—
401	#418	C₂²×C₂₃	1	2	yes	—
402	#418	C₂²×C₂₃	1	2	yes	complemented
403	#407	C₂²×C₂₃	1	2	yes	—
404	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
405	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
406	C₂×C₂₃	—	2	2	no	—
407	C₂×C₂₃	—	4	2	no	—
408	C₂×C₂₃	—	8	2	no	—
409	C₂×C₂₃	—	8	2	no	—
410	C₂×C₂₃	—	8	2	no	—
411	C₂×C₂₃	—	8	2	no	—
412	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
413	C₂×C₂₃	#3585	1	2	yes	—
414	C₂⁵	—	2	1	no	—
415	C₂×#41	—	2	2	no	—
416	C₂×#41	—	4	4	no	—
417	C₂×#41	C₂³×C₂₃	1	2	yes	—
418	C₂×#41	C₂³×C₂₃	1	4	yes	—
419	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
420	C₂²×D₄	—	2	1	no	—
421	C₂²×D₄	—	2	1	no	—
422	C₂²×D₄	—	2	2	no	—
423	C₂²×D₄	—	2	2	no	—
424	C₂²×D₄	—	2	2	no	—
425	C₂²×D₄	—	4	4	no	—
426	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
427	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
428	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
429	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
430	C₂³×C₄	—	2	1	no	—
431	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
432	#137	—	4	4	no	—
433	AGL(1,ℤ/8)	—	4	4	no	—
434	AGL(1,ℤ/8)	—	4	4	no	—
435	AGL(1,ℤ/8)	—	4	4	no	—
436	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
437	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
438	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
439	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
440	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
441	C₂×D₈	C₂³×C₂₃	1	4	yes	—
442	C₂×D₈	C₂³×C₂₃	1	4	yes	—
443	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
444	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
445	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
446	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
447	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
448	#127	—	2	2	no	—
449	#127	—	2	2	no	—
450	#127	C₂³×C₂₃	1	4	yes	—
451	#127	C₂³×C₂₃	1	2	yes	—
452	#127	C₂³×C₂₃	1	2	yes	—
453	#127	C₂³×C₂₃	1	1	yes	characteristic, complemented
454	#126	—	2	4	no	—
455	#126	—	2	4	no	—
456	#125	—	2	4	no	—
457	#125	C₂³×C₂₃	1	2	yes	complemented
458	#124	—	2	4	no	—
459	#124	—	2	2	no	—
460	#124	—	2	2	no	—
461	#124	C₂³×C₂₃	1	4	yes	—
462	#124	C₂³×C₂₃	1	2	yes	—
463	#124	C₂³×C₂₃	1	2	yes	—
464	#124	C₂³×C₂₃	1	2	yes	complemented
465	#123	—	2	2	no	—
466	#123	—	2	4	no	—
467	#123	—	2	4	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	4	no	—
470	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	8	no	—
473	#121	—	2	8	no	—
474	#121	—	2	4	no	—
475	#121	C₂³×C₂₃	1	4	yes	—
476	#120	—	2	2	no	—
477	#120	—	2	8	no	—
478	#120	—	2	8	no	—
479	C₄×Q₈	—	2	2	no	—
480	C₄×Q₈	C₂³×C₂₃	1	4	yes	complemented
481	C₄×D₄	—	2	4	no	—
482	C₄×D₄	—	2	4	no	—
483	C₄×D₄	—	2	2	no	—
484	C₄×D₄	C₂³×C₂₃	1	4	yes	complemented
485	#117	—	2	2	no	—
486	#117	D₄×C₂₃	1	4	yes	—
487	#117	C₂³×C₂₃	1	2	yes	—
488	#117	C₂³×C₂₃	1	2	yes	—
489	#117	C₂³×C₂₃	1	2	yes	—
490	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
491	C₂×C₂²⋊C₄	—	2	2	no	—
492	C₂×C₂²⋊C₄	—	2	2	no	—
493	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
494	C₂×C₄²	—	2	2	no	—
495	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
496	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
497	C₄⋊C₈	C₂³×C₂₃	1	8	yes	complemented
498	#103	C₂³×C₂₃	1	8	yes	complemented
499	#102	C₂³×C₂₃	1	8	yes	—
500	#102	C₂³×C₂₃	1	8	yes	—
501	#102	C₂³×C₂₃	1	8	yes	complemented
502	C₂²⋊C₈	C₂³×C₂₃	1	8	yes	—
503	#97	C₂³×C₂₃	1	2	yes	complemented
504	#97	C₂³×C₂₃	1	2	yes	complemented
505	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
506	C₄×C₈	C₂³×C₂₃	1	2	yes	complemented
507	C₂₃	#60806	1	1	yes	characteristic, direct product factor, Sylow
508	C₂⁴	—	2	1	no	—
509	C₂⁴	—	2	1	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	—	2	4	no	—
512	C₂⁴	—	4	4	no	—
513	C₂⁴	—	8	4	no	—
514	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
515	#41	—	2	4	no	—
516	#41	—	2	4	no	—
517	#41	—	4	8	no	—
518	#41	—	4	8	no	—
519	C₂×Q₈	—	2	1	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	2	4	no	—
522	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
523	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
524	C₂×D₄	—	2	2	no	—
525	C₂×D₄	—	2	4	no	—
526	C₂×D₄	—	2	4	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	2	1	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	4	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	4	8	no	—
539	C₂×D₄	—	4	4	no	—
540	C₂×D₄	—	4	8	no	—
541	C₂×D₄	—	4	4	no	—
542	C₂×D₄	—	8	4	no	—
543	C₂×D₄	—	8	4	no	—
544	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
545	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
546	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
547	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	4	no	—
553	C₂²×C₄	—	4	4	no	—
554	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
555	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
556	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
557	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
558	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
559	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
560	Q₁₆	—	4	4	no	—
561	SD₁₆	—	4	4	no	—
562	SD₁₆	—	4	4	no	—
563	SD₁₆	—	4	4	no	—
564	SD₁₆	—	4	4	no	—
565	D₈	—	4	4	no	—
566	D₈	—	4	4	no	—
567	D₈	—	4	4	no	—
568	M₁₆	—	2	4	no	—
569	M₁₆	—	2	4	no	—
570	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
571	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
572	C₄⋊C₄	—	2	4	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	4	no	—
575	C₄⋊C₄	—	2	4	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
578	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
579	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
580	C₂²⋊C₄	—	2	2	no	—
581	C₂²⋊C₄	—	2	4	no	—
582	C₂²⋊C₄	—	2	8	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	2	4	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
589	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
590	C₄²	—	2	2	no	—
591	C₄²	—	2	4	no	—
592	C₄²	C₂×D₄×C₂₃	1	2	yes	—
593	C₄²	C₂×D₄×C₂₃	1	2	yes	—
594	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
595	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
596	C₄²	C₂⁴×C₂₃	1	2	yes	—
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	—	4	8	no	—
604	C₂³	—	4	4	no	—
605	C₂³	—	4	4	no	—
606	C₂³	—	4	4	no	—
607	C₂³	—	4	2	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	—	8	8	no	—
611	C₂³	—	8	16	no	—
612	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
613	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
614	Q₈	—	2	2	no	—
615	Q₈	—	2	2	no	—
616	Q₈	—	2	4	no	—
617	Q₈	—	4	2	no	—
618	Q₈	—	8	2	no	—
619	D₄	—	2	2	no	—
620	D₄	—	2	2	no	—
621	D₄	—	2	4	no	—
622	D₄	—	2	4	no	—
623	D₄	—	2	4	no	—
624	D₄	—	4	8	no	—
625	D₄	—	4	8	no	—
626	D₄	—	4	4	no	—
627	D₄	—	4	2	no	—
628	D₄	—	4	2	no	—
629	D₄	—	4	2	no	—
630	D₄	—	8	8	no	—
631	D₄	—	8	4	no	—
632	D₄	—	8	4	no	—
633	D₄	—	8	2	no	—
634	D₄	—	8	4	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	4	2	no	—
643	C₂×C₄	—	4	8	no	—
644	C₂×C₄	—	4	2	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	8	4	no	—
647	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
648	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
649	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
650	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
651	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
652	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
653	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
654	C₈	—	2	4	no	—
655	C₈	—	2	4	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	4	4	no	—
660	C₂²	—	4	2	no	—
661	C₂²	—	4	2	no	—
662	C₂²	—	4	2	no	—
663	C₂²	—	4	2	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	4	4	no	—
668	C₂²	—	8	4	no	—
669	C₂²	—	8	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	—	8	16	no	—
672	C₂²	C₂₃×#535	1	2	yes	—
673	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	4	2	no	—
679	C₄	—	4	2	no	—
680	C₄	—	4	4	no	—
681	C₄	C₂₃×#535	1	2	yes	—
682	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
683	C₂	—	2	2	no	—
684	C₂	—	4	2	no	—
685	C₂	—	8	2	no	—
686	C₂	—	8	2	no	—
687	C₂	—	8	2	no	—
688	C₂	—	8	2	no	—
689	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
690	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×#3455	C₂	semidirect
2. C₂×C₂₃×#535	C₂	semidirect
3. C₂₃×#3224	C₂	semidirect
4. C₂₃×#3222	C₂	semidirect
5. C₂₃×#3220	C₂	semidirect
6. C₂₃×#3153	C₂	semidirect
7. C₂₃×#3151	C₂	semidirect
8. C₂₃×#3140	C₂	semidirect
9. C₂₃×#3138	C₂	semidirect
10. C₂₃×#3040	C₂	semidirect
11. C₂₃×#3038	C₂	semidirect
12. C₂₃×#3005	C₂	semidirect
13. C₂₃×#3003	C₂	semidirect
14. C₂₃×#2921	C₂	semidirect
17. C₂×C₂₃×#137	C₂²	semidirect
20. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂₃×#542	C₂²	semidirect
22. C₂₃×#541	C₂²	semidirect
23. C₂₃×#540	C₂²	semidirect
29. C₂₃×#533	C₂²	semidirect
30. C₂₃×#532	C₂²	semidirect
39. C₄×#41×C₂₃	C₂²	semidirect
41. C₂₃×#497	C₂²	semidirect
42. C₂₃×#496	C₂²	semidirect
43. C₂₃×#496	C₂²	semidirect
44. C₂₃×#495	C₂²	semidirect
45. C₂₃×#493	C₂²	semidirect
46. C₂₃×#492	C₂²	semidirect
47. C₂₃×#490	C₂²	semidirect
48. C₂₃×#489	C₂²	semidirect
49. C₂₃×#488	C₂²	semidirect
50. C₂₃×#486	C₂²	semidirect
51. C₂₃×#464	C₂²	semidirect
52. C₂₃×#463	C₂²	semidirect
53. C₂₃×#460	C₂²	semidirect
54. C₂₃×#459	C₂²	semidirect
55. C₂₃×#452	C₂²	semidirect
56. C₂₃×#450	C₂²	semidirect
57. C₂₃×#449	C₂²	semidirect
58. C₂₃×#447	C₂²	semidirect
59. C₂₃×#433	C₂²	semidirect
60. C₂₃×#433	C₂²	semidirect
61. C₂₃×#423	C₂²	semidirect
62. C₂₃×#419	C₂²	semidirect
65. C₂₃×#418	C₂²	semidirect
67. C₄×M₁₆×C₂₃	C₂²	semidirect
68. C₄×M₁₆×C₂₃	C₂²	semidirect
91. C₂×Q₁₆×C₂₃	C₂³	semidirect
94. C₂×SD₁₆×C₂₃	C₂³	semidirect
95. C₂×SD₁₆×C₂₃	C₂³	semidirect
98. C₂×D₈×C₂₃	C₂³	semidirect
101. C₂₃×C₄⋊Q₈	C₂³	semidirect
102. C₂₃×C₄⋊Q₈	C₂³	semidirect
108. C₂₃×#127	C₂³	semidirect
112. C₂₃×#125	C₂³	semidirect
119. C₂₃×#124	C₂³	semidirect
135. C₄×Q₈×C₂₃	C₂³	semidirect
139. C₄×D₄×C₂₃	C₂³	semidirect
152. C₂₃×C₄⋊C₈	C₂³	semidirect
153. C₂₃×#103	C₂³	semidirect
156. C₂₃×#102	C₂³	semidirect
158. C₂₃×#97	C₂³	semidirect
159. C₂₃×#97	C₂³	semidirect
160. C₄×C₈×C₂₃	C₂³	semidirect
161. C₄×C₈×C₂₃	C₂³	semidirect
251. #60806	C₂₃	direct (N × H)
311. #3455	C₂×C₂₃	semidirect
312. C₂×#535	C₂×C₂₃	semidirect
313. #3224	C₂×C₂₃	semidirect
314. #3222	C₂×C₂₃	semidirect
315. #3220	C₂×C₂₃	semidirect
316. #3153	C₂×C₂₃	semidirect
317. #3151	C₂×C₂₃	semidirect
318. #3140	C₂×C₂₃	semidirect
319. #3138	C₂×C₂₃	semidirect
320. #3040	C₂×C₂₃	semidirect
321. #3038	C₂×C₂₃	semidirect
322. #3005	C₂×C₂₃	semidirect
323. #3003	C₂×C₂₃	semidirect
324. #2921	C₂×C₂₃	semidirect
354. C₂×#137	C₂²×C₂₃	semidirect
357. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
358. #542	C₂²×C₂₃	semidirect
359. #541	C₂²×C₂₃	semidirect
360. #540	C₂²×C₂₃	semidirect
366. #533	C₂²×C₂₃	semidirect
367. #532	C₂²×C₂₃	semidirect
376. C₄×#41	C₂²×C₂₃	semidirect
378. #497	C₂²×C₂₃	semidirect
379. #496	C₂²×C₂₃	semidirect
380. #496	C₂²×C₂₃	semidirect
381. #495	C₂²×C₂₃	semidirect
382. #493	C₂²×C₂₃	semidirect
383. #492	C₂²×C₂₃	semidirect
384. #490	C₂²×C₂₃	semidirect
385. #489	C₂²×C₂₃	semidirect
386. #488	C₂²×C₂₃	semidirect
387. #486	C₂²×C₂₃	semidirect
388. #464	C₂²×C₂₃	semidirect
389. #463	C₂²×C₂₃	semidirect
390. #460	C₂²×C₂₃	semidirect
391. #459	C₂²×C₂₃	semidirect
392. #452	C₂²×C₂₃	semidirect
393. #450	C₂²×C₂₃	semidirect
394. #449	C₂²×C₂₃	semidirect
395. #447	C₂²×C₂₃	semidirect
396. #433	C₂²×C₂₃	semidirect
397. #433	C₂²×C₂₃	semidirect
398. #423	C₂²×C₂₃	semidirect
399. #419	C₂²×C₂₃	semidirect
402. #418	C₂²×C₂₃	semidirect
404. C₄×M₁₆	C₂²×C₂₃	semidirect
405. C₄×M₁₆	C₂²×C₂₃	semidirect
436. C₂×Q₁₆	C₂³×C₂₃	semidirect
439. C₂×SD₁₆	C₂³×C₂₃	semidirect
440. C₂×SD₁₆	C₂³×C₂₃	semidirect
443. C₂×D₈	C₂³×C₂₃	semidirect
446. C₄⋊Q₈	C₂³×C₂₃	semidirect
447. C₄⋊Q₈	C₂³×C₂₃	semidirect
453. #127	C₂³×C₂₃	semidirect
457. #125	C₂³×C₂₃	semidirect
464. #124	C₂³×C₂₃	semidirect
480. C₄×Q₈	C₂³×C₂₃	semidirect
484. C₄×D₄	C₂³×C₂₃	semidirect
497. C₄⋊C₈	C₂³×C₂₃	semidirect
498. #103	C₂³×C₂₃	semidirect
501. #102	C₂³×C₂₃	semidirect
503. #97	C₂³×C₂₃	semidirect
504. #97	C₂³×C₂₃	semidirect
505. C₄×C₈	C₂³×C₂₃	semidirect
506. C₄×C₈	C₂³×C₂₃	semidirect
507. C₂₃	#60806	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×#3455	2
C₂×C₂₃×#535	2
C₂₃×#3224	2
C₂₃×#3222	2
C₂₃×#3220	2
C₂₃×#3153	2
C₂₃×#3151	2
C₂₃×#3140	2
C₂₃×#3138	2
C₂₃×#3040	2
C₂₃×#3038	2
C₂₃×#3005	2
C₂₃×#3003	2
C₂₃×#2921	2
#60806	23

Subgroups — C23×#60806 #19208432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60806 #19208432