Subgroups — C₂₃×#60426 #19208052

Order 5888.

2870 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#535	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3045	C₂	1	8	yes	maximal, complemented
6	C₂₃×#3043	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3041	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3040	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3038	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#575	—	2	8	no	—
17	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
18	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
19	C₂×C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
21	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
22	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
24	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
25	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
26	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
27	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#535	—	2	2	no	—
30	C₂₃×#535	—	2	2	no	—
31	C₂₃×#535	C₂²	1	4	yes	—
32	C₂₃×#535	C₂²	1	4	yes	complemented
33	C₂×C₂₃×#127	C₂²	1	2	yes	complemented
34	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
35	C₂×C₂₃×#121	—	2	2	no	—
36	C₂×C₂₃×#120	—	2	2	no	—
37	C₂₃×#520	—	2	2	no	—
38	C₂₃×#520	C₂²	1	4	yes	complemented
39	C₂₃×#519	C₂²	1	2	yes	complemented
40	C₂₃×#518	—	2	2	no	—
41	C₂₃×#518	C₂²	1	2	yes	complemented
42	C₄×#41×C₂₃	—	2	2	no	—
43	C₄×#41×C₂₃	C₂²	1	4	yes	complemented
44	C₂×C₂₃×#117	—	2	2	no	—
45	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
47	C₂₃×#464	C₂²	1	16	yes	complemented
48	C₂₃×#463	C₂²	1	16	yes	complemented
49	C₂₃×#460	C₂²	1	16	yes	complemented
50	C₂₃×#459	C₂²	1	16	yes	complemented
51	C₂₃×#424	C₂²	1	4	yes	complemented
52	C₂₃×#424	C₂²	1	4	yes	complemented
53	C₂₃×#423	C₂²	1	4	yes	complemented
54	C₂₃×#419	C₂²	1	2	yes	complemented
55	C₂₃×#418	C₂²	1	4	yes	complemented
56	C₂₃×#418	C₂²	1	4	yes	complemented
57	C₂₃×#418	C₂²	1	2	yes	complemented
58	C₂₃×#417	C₂²	1	4	yes	complemented
59	C₂₃×#416	C₂²	1	4	yes	complemented
60	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
61	C₂⁵×C₂₃	—	2	1	no	—
62	C₂×#41×C₂₃	—	2	1	no	—
63	C₂×#41×C₂₃	—	2	1	no	—
64	C₂×#41×C₂₃	—	2	1	no	—
65	C₂×#41×C₂₃	—	2	1	no	—
66	C₂×#41×C₂₃	—	2	4	no	—
67	C₂×#41×C₂₃	—	2	4	no	—
68	C₂×#41×C₂₃	—	2	4	no	—
69	C₂×#41×C₂₃	D₄	1	8	yes	complemented
70	C₂×#41×C₂₃	C₂³	1	2	yes	—
71	C₂×#41×C₂₃	C₂³	1	2	yes	—
72	C₂×#41×C₂₃	C₂³	1	2	yes	—
73	C₂×#41×C₂₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂²×D₄×C₂₃	—	2	1	no	—
78	C₂²×D₄×C₂₃	—	2	4	no	—
79	C₂²×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	4	no	—
83	C₂²×D₄×C₂₃	—	2	4	no	—
84	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
86	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	—	2	1	no	—
90	C₂³×C₄×C₂₃	—	2	1	no	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂₃×#137	—	2	8	no	—
93	C₂₃×#137	—	2	8	no	—
94	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
95	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
96	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
97	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
98	C₂₃×#135	—	2	16	no	—
99	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
100	C₂×SD₁₆×C₂₃	—	2	8	no	—
101	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
104	C₂×D₈×C₂₃	—	2	8	no	—
105	C₂×D₈×C₂₃	C₂³	1	8	yes	—
106	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
107	C₂×M₁₆×C₂₃	—	2	4	no	—
108	C₂×M₁₆×C₂₃	—	2	4	no	—
109	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
110	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
111	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
114	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
115	C₂₃×#127	—	2	4	no	—
116	C₂₃×#127	C₂³	1	8	yes	—
117	C₂₃×#124	—	2	4	no	—
118	C₂₃×#124	C₂³	1	8	yes	—
119	C₂₃×#121	—	2	8	no	—
120	C₂₃×#121	—	2	8	no	—
121	C₂₃×#120	—	2	8	no	—
122	C₂₃×#120	—	2	8	no	—
123	C₄×Q₈×C₂₃	—	2	4	no	—
124	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
125	C₄×D₄×C₂₃	—	2	8	no	—
126	C₄×D₄×C₂₃	—	2	4	no	—
127	C₄×D₄×C₂₃	—	2	8	no	—
128	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
129	C₂₃×#117	—	2	1	no	—
130	C₂₃×#117	—	2	1	no	—
131	C₂₃×#117	—	2	4	no	—
132	C₂₃×#117	—	2	4	no	—
133	C₂₃×#117	—	2	4	no	—
134	C₂₃×#117	D₄	1	2	yes	—
135	C₂₃×#117	D₄	1	2	yes	—
136	C₂₃×#117	C₂³	1	2	yes	—
137	C₂₃×#117	C₂³	1	2	yes	—
138	C₂₃×#117	C₂³	1	2	yes	—
139	C₂₃×#117	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
141	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
145	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
146	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
147	C₂×C₄²×C₂₃	—	2	1	no	—
148	C₂×C₄²×C₂₃	—	2	4	no	—
149	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
150	C₂₃×C₄⋊C₈	C₂³	1	16	yes	complemented
151	C₂₃×#103	C₂³	1	8	yes	complemented
152	C₂₃×#102	C₂³	1	16	yes	—
153	C₂₃×#102	C₂³	1	8	yes	complemented
154	C₂⁴×C₂₃	—	2	1	no	—
155	C₂⁴×C₂₃	—	2	2	no	—
156	C₂⁴×C₂₃	—	2	1	no	—
157	C₂⁴×C₂₃	—	2	2	no	—
158	C₂⁴×C₂₃	—	2	2	no	—
159	C₂⁴×C₂₃	—	4	4	no	—
160	C₂⁴×C₂₃	—	8	4	no	—
161	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
162	#41×C₂₃	—	2	8	no	—
163	#41×C₂₃	—	2	8	no	—
164	#41×C₂₃	—	2	4	no	—
165	#41×C₂₃	—	2	4	no	—
166	#41×C₂₃	—	2	4	no	—
167	#41×C₂₃	—	2	4	no	—
168	#41×C₂₃	—	2	4	no	—
169	#41×C₂₃	—	2	4	no	—
170	#41×C₂₃	—	4	4	no	—
171	#41×C₂₃	—	4	4	no	—
172	#41×C₂₃	C₂×D₄	1	8	yes	—
173	#41×C₂₃	C₂×D₄	1	8	yes	complemented
174	C₂×Q₈×C₂₃	—	2	1	no	—
175	C₂×Q₈×C₂₃	—	2	1	no	—
176	C₂×Q₈×C₂₃	—	2	2	no	—
177	C₂×Q₈×C₂₃	—	2	2	no	—
178	C₂×Q₈×C₂₃	—	2	2	no	—
179	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	complemented
180	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
181	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
182	C₂×D₄×C₂₃	—	2	8	no	—
183	C₂×D₄×C₂₃	—	2	2	no	—
184	C₂×D₄×C₂₃	—	2	2	no	—
185	C₂×D₄×C₂₃	—	2	2	no	—
186	C₂×D₄×C₂₃	—	2	2	no	—
187	C₂×D₄×C₂₃	—	2	1	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	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	16	no	—
197	C₂×D₄×C₂₃	—	2	2	no	—
198	C₂×D₄×C₂₃	—	2	4	no	—
199	C₂×D₄×C₂₃	—	2	4	no	—
200	C₂×D₄×C₂₃	—	2	4	no	—
201	C₂×D₄×C₂₃	—	2	2	no	—
202	C₂×D₄×C₂₃	—	4	4	no	—
203	C₂×D₄×C₂₃	—	4	4	no	—
204	C₂×D₄×C₂₃	—	4	4	no	—
205	C₂×D₄×C₂₃	—	4	4	no	—
206	C₂×D₄×C₂₃	—	8	8	no	—
207	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	complemented
208	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
209	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
210	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	8	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	2	no	—
217	C₂²×C₄×C₂₃	—	2	2	no	—
218	C₂²×C₄×C₂₃	—	2	2	no	—
219	C₂²×C₄×C₂₃	—	2	8	no	—
220	C₂²×C₄×C₂₃	—	4	4	no	—
221	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
226	C₂²×C₄×C₂₃	#41	1	4	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
230	Q₁₆×C₂₃	—	2	8	no	—
231	SD₁₆×C₂₃	—	2	16	no	—
232	SD₁₆×C₂₃	—	2	8	no	—
233	SD₁₆×C₂₃	—	2	8	no	—
234	D₈×C₂₃	—	2	16	no	—
235	D₈×C₂₃	—	2	8	no	—
236	M₁₆×C₂₃	—	2	4	no	—
237	M₁₆×C₂₃	—	2	4	no	—
238	M₁₆×C₂₃	—	2	4	no	—
239	M₁₆×C₂₃	—	2	4	no	—
240	C₂×C₈×C₂₃	—	2	4	no	—
241	C₂×C₈×C₂₃	—	2	4	no	—
242	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
243	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
244	C₄⋊C₄×C₂₃	—	2	2	no	—
245	C₄⋊C₄×C₂₃	—	2	8	no	—
246	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
247	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
248	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
249	C₂²⋊C₄×C₂₃	—	2	2	no	—
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
251	C₂²⋊C₄×C₂₃	—	2	8	no	—
252	C₂²⋊C₄×C₂₃	—	2	16	no	—
253	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
254	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
255	C₄²×C₂₃	—	2	2	no	—
256	C₄²×C₂₃	—	2	8	no	—
257	C₄²×C₂₃	—	2	2	no	—
258	C₄²×C₂₃	C₂×D₄	1	4	yes	—
259	C₄²×C₂₃	C₂⁴	1	4	yes	—
260	#60426	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	—	2	4	no	—
263	C₂³×C₂₃	—	2	4	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	4	2	no	—
266	C₂³×C₂₃	—	4	4	no	—
267	C₂³×C₂₃	—	4	8	no	—
268	C₂³×C₂₃	—	4	2	no	—
269	C₂³×C₂₃	—	4	4	no	—
270	C₂³×C₂₃	—	4	4	no	—
271	C₂³×C₂₃	—	4	4	no	—
272	C₂³×C₂₃	—	8	2	no	—
273	C₂³×C₂₃	—	8	4	no	—
274	C₂³×C₂₃	—	8	4	no	—
275	C₂³×C₂₃	—	8	16	no	—
276	C₂³×C₂₃	#121	1	4	yes	—
277	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
278	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
279	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₂₃	—	2	4	no	—
281	Q₈×C₂₃	—	2	2	no	—
282	Q₈×C₂₃	—	2	2	no	—
283	Q₈×C₂₃	—	2	2	no	—
284	Q₈×C₂₃	—	4	2	no	—
285	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
286	D₄×C₂₃	—	2	8	no	—
287	D₄×C₂₃	—	2	8	no	—
288	D₄×C₂₃	—	2	4	no	—
289	D₄×C₂₃	—	2	4	no	—
290	D₄×C₂₃	—	2	2	no	—
291	D₄×C₂₃	—	2	2	no	—
292	D₄×C₂₃	—	2	4	no	—
293	D₄×C₂₃	—	2	2	no	—
294	D₄×C₂₃	—	4	4	no	—
295	D₄×C₂₃	—	4	4	no	—
296	D₄×C₂₃	—	4	4	no	—
297	D₄×C₂₃	—	4	4	no	—
298	D₄×C₂₃	—	4	4	no	—
299	D₄×C₂₃	—	4	2	no	—
300	D₄×C₂₃	—	8	16	no	—
301	D₄×C₂₃	C₂²×D₄	1	4	yes	—
302	C₂×C₄×C₂₃	—	2	4	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	8	no	—
305	C₂×C₄×C₂₃	—	2	8	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	4	4	no	—
309	C₂×C₄×C₂₃	—	4	2	no	—
310	C₂×C₄×C₂₃	—	4	4	no	—
311	C₂×C₄×C₂₃	—	4	4	no	—
312	C₂×C₄×C₂₃	—	8	8	no	—
313	C₂×C₄×C₂₃	—	8	2	no	—
314	C₂×C₄×C₂₃	#121	1	4	yes	—
315	C₂×C₄×C₂₃	#121	1	4	yes	—
316	C₂×C₄×C₂₃	#121	1	4	yes	—
317	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
318	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
325	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
326	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
327	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
328	C₈×C₂₃	—	2	4	no	—
329	C₈×C₂₃	—	2	4	no	—
330	C₂×#575	C₂×C₂₃	1	1	yes	characteristic, complemented
331	C₂²×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
332	C₂×#535	C₂×C₂₃	1	1	yes	characteristic, complemented
333	#3428	C₂×C₂₃	1	1	yes	characteristic, complemented
334	#3045	C₂×C₂₃	1	8	yes	complemented
335	#3043	C₂×C₂₃	1	4	yes	complemented
336	#3041	C₂×C₂₃	1	4	yes	complemented
337	#3040	C₂×C₂₃	1	4	yes	complemented
338	#3038	C₂×C₂₃	1	4	yes	complemented
339	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
340	#2896	C₂×C₂₃	1	1	yes	characteristic, complemented
341	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂²×C₂₃	—	2	2	no	—
343	C₂²×C₂₃	—	2	2	no	—
344	C₂²×C₂₃	—	2	2	no	—
345	C₂²×C₂₃	—	2	4	no	—
346	C₂²×C₂₃	—	4	4	no	—
347	C₂²×C₂₃	—	4	4	no	—
348	C₂²×C₂₃	—	4	4	no	—
349	C₂²×C₂₃	—	4	8	no	—
350	C₂²×C₂₃	—	4	2	no	—
351	C₂²×C₂₃	—	4	4	no	—
352	C₂²×C₂₃	—	8	4	no	—
353	C₂²×C₂₃	—	8	4	no	—
354	C₂²×C₂₃	—	8	8	no	—
355	C₂²×C₂₃	—	8	8	no	—
356	C₂²×C₂₃	—	8	8	no	—
357	C₂²×C₂₃	C₂×#121	1	2	yes	—
358	C₂²×C₂₃	C₂×#121	1	2	yes	—
359	C₂²×C₂₃	C₂×#121	1	2	yes	—
360	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₂₃	—	2	8	no	—
362	C₄×C₂₃	—	2	4	no	—
363	C₄×C₂₃	—	4	4	no	—
364	C₄×C₂₃	—	4	2	no	—
365	C₄×C₂₃	C₂×#121	1	2	yes	—
366	C₄×C₂₃	C₂×#121	1	2	yes	—
367	C₄×C₂₃	C₂×#121	1	2	yes	—
368	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
370	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
371	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
372	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
373	#575	—	2	8	no	—
374	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
375	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
376	C₂×AGL(1,ℤ/8)	—	2	8	no	—
377	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	—
378	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
379	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
380	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
381	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
382	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
383	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
384	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
385	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
386	#535	—	2	2	no	—
387	#535	—	2	2	no	—
388	#535	C₂²×C₂₃	1	4	yes	—
389	#535	C₂²×C₂₃	1	4	yes	complemented
390	C₂×#127	C₂²×C₂₃	1	2	yes	complemented
391	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
392	C₂×#121	—	2	2	no	—
393	C₂×#120	—	2	2	no	—
394	#520	—	2	2	no	—
395	#520	C₂²×C₂₃	1	4	yes	complemented
396	#519	C₂²×C₂₃	1	2	yes	complemented
397	#518	—	2	2	no	—
398	#518	C₂²×C₂₃	1	2	yes	complemented
399	C₄×#41	—	2	2	no	—
400	C₄×#41	C₂²×C₂₃	1	4	yes	complemented
401	C₂×#117	—	2	2	no	—
402	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
404	#464	C₂²×C₂₃	1	16	yes	complemented
405	#463	C₂²×C₂₃	1	16	yes	complemented
406	#460	C₂²×C₂₃	1	16	yes	complemented
407	#459	C₂²×C₂₃	1	16	yes	complemented
408	#424	C₂²×C₂₃	1	4	yes	complemented
409	#424	C₂²×C₂₃	1	4	yes	complemented
410	#423	C₂²×C₂₃	1	4	yes	complemented
411	#419	C₂²×C₂₃	1	2	yes	complemented
412	#418	C₂²×C₂₃	1	4	yes	complemented
413	#418	C₂²×C₂₃	1	4	yes	complemented
414	#418	C₂²×C₂₃	1	2	yes	complemented
415	#417	C₂²×C₂₃	1	4	yes	complemented
416	#416	C₂²×C₂₃	1	4	yes	complemented
417	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
418	C₂×C₂₃	—	2	2	no	—
419	C₂×C₂₃	—	2	2	no	—
420	C₂×C₂₃	—	2	2	no	—
421	C₂×C₂₃	—	4	4	no	—
422	C₂×C₂₃	—	8	2	no	—
423	C₂×C₂₃	—	8	4	no	—
424	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
425	C₂×C₂₃	#3585	1	2	yes	—
426	C₂⁵	—	2	1	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	2	1	no	—
431	C₂×#41	—	2	4	no	—
432	C₂×#41	—	2	4	no	—
433	C₂×#41	—	2	4	no	—
434	C₂×#41	D₄×C₂₃	1	8	yes	complemented
435	C₂×#41	C₂³×C₂₃	1	2	yes	—
436	C₂×#41	C₂³×C₂₃	1	2	yes	—
437	C₂×#41	C₂³×C₂₃	1	2	yes	—
438	C₂×#41	C₂³×C₂₃	1	2	yes	—
439	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	—	2	4	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	—	2	4	no	—
448	C₂²×D₄	—	2	4	no	—
449	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
450	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
452	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
453	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
454	C₂³×C₄	—	2	1	no	—
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
457	#137	—	2	8	no	—
458	#137	—	2	8	no	—
459	AGL(1,ℤ/8)	—	2	16	no	—
460	AGL(1,ℤ/8)	—	2	8	no	—
461	AGL(1,ℤ/8)	—	2	16	no	—
462	AGL(1,ℤ/8)	—	2	8	no	—
463	#135	—	2	16	no	—
464	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
465	C₂×SD₁₆	—	2	8	no	—
466	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
467	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
468	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
469	C₂×D₈	—	2	8	no	—
470	C₂×D₈	C₂³×C₂₃	1	8	yes	—
471	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
472	C₂×M₁₆	—	2	4	no	—
473	C₂×M₁₆	—	2	4	no	—
474	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
475	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
476	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
477	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
478	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
479	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
480	#127	—	2	4	no	—
481	#127	C₂³×C₂₃	1	8	yes	—
482	#124	—	2	4	no	—
483	#124	C₂³×C₂₃	1	8	yes	—
484	#121	—	2	8	no	—
485	#121	—	2	8	no	—
486	#120	—	2	8	no	—
487	#120	—	2	8	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	4	no	—
492	C₄×D₄	—	2	8	no	—
493	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
494	#117	—	2	1	no	—
495	#117	—	2	1	no	—
496	#117	—	2	4	no	—
497	#117	—	2	4	no	—
498	#117	—	2	4	no	—
499	#117	D₄×C₂₃	1	2	yes	—
500	#117	D₄×C₂₃	1	2	yes	—
501	#117	C₂³×C₂₃	1	2	yes	—
502	#117	C₂³×C₂₃	1	2	yes	—
503	#117	C₂³×C₂₃	1	2	yes	—
504	#117	C₂³×C₂₃	1	2	yes	—
505	C₂×C₄⋊C₄	—	2	4	no	—
506	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	4	no	—
510	C₂×C₂²⋊C₄	—	2	4	no	—
511	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
512	C₂×C₄²	—	2	1	no	—
513	C₂×C₄²	—	2	4	no	—
514	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
515	C₄⋊C₈	C₂³×C₂₃	1	16	yes	complemented
516	#103	C₂³×C₂₃	1	8	yes	complemented
517	#102	C₂³×C₂₃	1	16	yes	—
518	#102	C₂³×C₂₃	1	8	yes	complemented
519	C₂₃	#60426	1	1	yes	characteristic, direct product factor, Sylow
520	C₂⁴	—	2	1	no	—
521	C₂⁴	—	2	2	no	—
522	C₂⁴	—	2	1	no	—
523	C₂⁴	—	2	2	no	—
524	C₂⁴	—	2	2	no	—
525	C₂⁴	—	4	4	no	—
526	C₂⁴	—	8	4	no	—
527	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
528	#41	—	2	8	no	—
529	#41	—	2	8	no	—
530	#41	—	2	4	no	—
531	#41	—	2	4	no	—
532	#41	—	2	4	no	—
533	#41	—	2	4	no	—
534	#41	—	2	4	no	—
535	#41	—	2	4	no	—
536	#41	—	4	4	no	—
537	#41	—	4	4	no	—
538	#41	C₂×D₄×C₂₃	1	8	yes	—
539	#41	C₂×D₄×C₂₃	1	8	yes	complemented
540	C₂×Q₈	—	2	1	no	—
541	C₂×Q₈	—	2	1	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	complemented
546	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
547	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	16	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	4	4	no	—
569	C₂×D₄	—	4	4	no	—
570	C₂×D₄	—	4	4	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	8	8	no	—
573	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	complemented
574	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
575	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
576	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	8	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	8	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
588	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
592	C₂²×C₄	#41×C₂₃	1	4	yes	—
593	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
596	Q₁₆	—	2	8	no	—
597	SD₁₆	—	2	16	no	—
598	SD₁₆	—	2	8	no	—
599	SD₁₆	—	2	8	no	—
600	D₈	—	2	16	no	—
601	D₈	—	2	8	no	—
602	M₁₆	—	2	4	no	—
603	M₁₆	—	2	4	no	—
604	M₁₆	—	2	4	no	—
605	M₁₆	—	2	4	no	—
606	C₂×C₈	—	2	4	no	—
607	C₂×C₈	—	2	4	no	—
608	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
609	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	8	no	—
612	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
613	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
614	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	8	no	—
618	C₂²⋊C₄	—	2	16	no	—
619	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
620	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
621	C₄²	—	2	2	no	—
622	C₄²	—	2	8	no	—
623	C₄²	—	2	2	no	—
624	C₄²	C₂×D₄×C₂₃	1	4	yes	—
625	C₄²	C₂⁴×C₂₃	1	4	yes	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	4	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	4	2	no	—
631	C₂³	—	4	4	no	—
632	C₂³	—	4	8	no	—
633	C₂³	—	4	2	no	—
634	C₂³	—	4	4	no	—
635	C₂³	—	4	4	no	—
636	C₂³	—	4	4	no	—
637	C₂³	—	8	4	no	—
638	C₂³	—	8	4	no	—
639	C₂³	—	8	2	no	—
640	C₂³	—	8	16	no	—
641	C₂³	C₂₃×#121	1	4	yes	—
642	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
643	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
644	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
645	Q₈	—	2	2	no	—
646	Q₈	—	2	4	no	—
647	Q₈	—	2	2	no	—
648	Q₈	—	2	2	no	—
649	Q₈	—	4	2	no	—
650	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
651	D₄	—	2	8	no	—
652	D₄	—	2	8	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	2	no	—
655	D₄	—	2	2	no	—
656	D₄	—	2	4	no	—
657	D₄	—	2	2	no	—
658	D₄	—	2	4	no	—
659	D₄	—	4	4	no	—
660	D₄	—	4	4	no	—
661	D₄	—	4	4	no	—
662	D₄	—	4	4	no	—
663	D₄	—	4	4	no	—
664	D₄	—	4	2	no	—
665	D₄	—	8	16	no	—
666	D₄	C₂²×D₄×C₂₃	1	4	yes	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	8	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	4	4	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	4	4	no	—
676	C₂×C₄	—	4	4	no	—
677	C₂×C₄	—	8	8	no	—
678	C₂×C₄	—	8	2	no	—
679	C₂×C₄	C₂₃×#121	1	4	yes	—
680	C₂×C₄	C₂₃×#121	1	4	yes	—
681	C₂×C₄	C₂₃×#121	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
683	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
684	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
685	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
686	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
687	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
688	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
689	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
690	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
691	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
692	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
693	C₈	—	2	4	no	—
694	C₈	—	2	4	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	8	no	—
705	C₂²	—	8	4	no	—
706	C₂²	—	8	8	no	—
707	C₂²	—	8	4	no	—
708	C₂²	—	8	8	no	—
709	C₂²	—	8	8	no	—
710	C₂²	C₂×C₂₃×#121	1	2	yes	—
711	C₂²	C₂×C₂₃×#121	1	2	yes	—
712	C₂²	C₂×C₂₃×#121	1	2	yes	—
713	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
714	C₄	—	2	4	no	—
715	C₄	—	2	8	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	4	no	—
718	C₄	C₂×C₂₃×#121	1	2	yes	—
719	C₄	C₂×C₂₃×#121	1	2	yes	—
720	C₄	C₂×C₂₃×#121	1	2	yes	—
721	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
722	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
723	C₂	—	2	2	no	—
724	C₂	—	2	2	no	—
725	C₂	—	2	2	no	—
726	C₂	—	4	4	no	—
727	C₂	—	8	4	no	—
728	C₂	—	8	2	no	—
729	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
730	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. C₂×C₂₃×#575	C₂	semidirect
2. C₂²×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₂₃×#535	C₂	semidirect
4. C₂₃×#3428	C₂	semidirect
5. C₂₃×#3045	C₂	semidirect
6. C₂₃×#3043	C₂	semidirect
7. C₂₃×#3041	C₂	semidirect
8. C₂₃×#3040	C₂	semidirect
9. C₂₃×#3038	C₂	semidirect
10. C₂₃×#2905	C₂	semidirect
11. C₂₃×#2896	C₂	semidirect
12. C₂×C₂₃×#418	C₂	semidirect
17. C₂×C₂₃×#137	C₂²	semidirect
18. C₂×C₂₃×#137	C₂²	semidirect
21. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
23. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
24. C₂×C₂₃×#135	C₂²	semidirect
25. C₂²×SD₁₆×C₂₃	C₂²	semidirect
26. C₂²×D₈×C₂₃	C₂²	semidirect
32. C₂₃×#535	C₂²	semidirect
33. C₂×C₂₃×#127	C₂²	semidirect
34. C₂×C₂₃×#124	C₂²	semidirect
38. C₂₃×#520	C₂²	semidirect
39. C₂₃×#519	C₂²	semidirect
41. C₂₃×#518	C₂²	semidirect
43. C₄×#41×C₂₃	C₂²	semidirect
47. C₂₃×#464	C₂²	semidirect
48. C₂₃×#463	C₂²	semidirect
49. C₂₃×#460	C₂²	semidirect
50. C₂₃×#459	C₂²	semidirect
51. C₂₃×#424	C₂²	semidirect
52. C₂₃×#424	C₂²	semidirect
53. C₂₃×#423	C₂²	semidirect
54. C₂₃×#419	C₂²	semidirect
55. C₂₃×#418	C₂²	semidirect
56. C₂₃×#418	C₂²	semidirect
57. C₂₃×#418	C₂²	semidirect
58. C₂₃×#417	C₂²	semidirect
59. C₂₃×#416	C₂²	semidirect
60. C₂×C₂₃×#102	C₂²	semidirect
69. C₂×#41×C₂₃	D₄	semidirect
99. C₂×Q₁₆×C₂₃	C₂³	semidirect
102. C₂×SD₁₆×C₂₃	C₂³	semidirect
103. C₂×SD₁₆×C₂₃	C₂³	semidirect
106. C₂×D₈×C₂₃	C₂³	semidirect
124. C₄×Q₈×C₂₃	C₂³	semidirect
128. C₄×D₄×C₂₃	C₂³	semidirect
150. C₂₃×C₄⋊C₈	C₂³	semidirect
151. C₂₃×#103	C₂³	semidirect
153. C₂₃×#102	C₂³	semidirect
173. #41×C₂₃	C₂×D₄	semidirect
179. C₂×Q₈×C₂₃	C₂×D₄	semidirect
207. C₂×D₄×C₂₃	C₂×D₄	semidirect
260. #60426	C₂₃	direct (N × H)
330. C₂×#575	C₂×C₂₃	semidirect
331. C₂²×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
332. C₂×#535	C₂×C₂₃	semidirect
333. #3428	C₂×C₂₃	semidirect
334. #3045	C₂×C₂₃	semidirect
335. #3043	C₂×C₂₃	semidirect
336. #3041	C₂×C₂₃	semidirect
337. #3040	C₂×C₂₃	semidirect
338. #3038	C₂×C₂₃	semidirect
339. #2905	C₂×C₂₃	semidirect
340. #2896	C₂×C₂₃	semidirect
341. C₂×#418	C₂×C₂₃	semidirect
374. C₂×#137	C₂²×C₂₃	semidirect
375. C₂×#137	C₂²×C₂₃	semidirect
378. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
379. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
380. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
381. C₂×#135	C₂²×C₂₃	semidirect
382. C₂²×SD₁₆	C₂²×C₂₃	semidirect
383. C₂²×D₈	C₂²×C₂₃	semidirect
389. #535	C₂²×C₂₃	semidirect
390. C₂×#127	C₂²×C₂₃	semidirect
391. C₂×#124	C₂²×C₂₃	semidirect
395. #520	C₂²×C₂₃	semidirect
396. #519	C₂²×C₂₃	semidirect
398. #518	C₂²×C₂₃	semidirect
400. C₄×#41	C₂²×C₂₃	semidirect
404. #464	C₂²×C₂₃	semidirect
405. #463	C₂²×C₂₃	semidirect
406. #460	C₂²×C₂₃	semidirect
407. #459	C₂²×C₂₃	semidirect
408. #424	C₂²×C₂₃	semidirect
409. #424	C₂²×C₂₃	semidirect
410. #423	C₂²×C₂₃	semidirect
411. #419	C₂²×C₂₃	semidirect
412. #418	C₂²×C₂₃	semidirect
413. #418	C₂²×C₂₃	semidirect
414. #418	C₂²×C₂₃	semidirect
415. #417	C₂²×C₂₃	semidirect
416. #416	C₂²×C₂₃	semidirect
417. C₂×#102	C₂²×C₂₃	semidirect
434. C₂×#41	D₄×C₂₃	semidirect
464. C₂×Q₁₆	C₂³×C₂₃	semidirect
467. C₂×SD₁₆	C₂³×C₂₃	semidirect
468. C₂×SD₁₆	C₂³×C₂₃	semidirect
471. C₂×D₈	C₂³×C₂₃	semidirect
489. C₄×Q₈	C₂³×C₂₃	semidirect
493. C₄×D₄	C₂³×C₂₃	semidirect
515. C₄⋊C₈	C₂³×C₂₃	semidirect
516. #103	C₂³×C₂₃	semidirect
518. #102	C₂³×C₂₃	semidirect
519. C₂₃	#60426	direct (N × H)
539. #41	C₂×D₄×C₂₃	semidirect
545. C₂×Q₈	C₂×D₄×C₂₃	semidirect
573. C₂×D₄	C₂×D₄×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#575	2
C₂²×C₂₃×AGL(1,ℤ/8)	2
C₂×C₂₃×#535	2
C₂₃×#3428	2
C₂₃×#3045	2
C₂₃×#3043	2
C₂₃×#3041	2
C₂₃×#3040	2
C₂₃×#3038	2
C₂₃×#2905	2
C₂₃×#2896	2
C₂×C₂₃×#418	2
#60426	23

Subgroups — C23×#60426 #19208052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60426 #19208052