Subgroups — C₂₃×#60146 #19207772

Order 5888.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2935	C₂	1	3	yes	maximal, complemented
5	D₄×M₁₆×C₂₃	C₂	1	3	yes	maximal, complemented
6	C₂₃×#2933	C₂	1	3	yes	maximal, complemented
7	C₂₃×#2933	C₂	1	3	yes	maximal, complemented
8	C₂₃×#2932	C₂	1	3	yes	maximal, complemented
9	C₂₃×#2930	C₂	1	3	yes	maximal, complemented
10	C₂₃×#2929	C₂	1	3	yes	maximal, complemented
11	C₂×C₂₃×#435	C₂	1	3	yes	maximal, complemented
12	C₂₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2875	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#568	—	2	8	no	—
19	C₂×C₂₃×#131	—	2	8	no	—
20	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#131	C₂²	1	3	yes	complemented
25	C₂×C₂₃×#131	C₂²	1	3	yes	complemented
26	C₂×C₂₃×#131	C₂²	1	3	yes	complemented
27	C₂×C₂₃×#131	C₂²	1	3	yes	complemented
28	C₂²×M₁₆×C₂₃	C₂²	1	3	yes	complemented
29	C₂²×M₁₆×C₂₃	C₂²	1	3	yes	complemented
30	C₂²×M₁₆×C₂₃	C₂²	1	3	yes	complemented
31	C₂³×C₈×C₂₃	C₂²	1	3	yes	complemented
32	C₂₃×#550	C₄	1	1	yes	characteristic
33	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
34	C₂₃×#548	C₄	1	1	yes	characteristic
35	C₂₃×#548	C₄	1	1	yes	characteristic
36	C₂₃×#547	C₄	1	3	yes	—
37	C₂₃×#546	C₄	1	3	yes	—
38	C₂₃×#546	C₄	1	3	yes	—
39	D₄²×C₂₃	C₄	1	3	yes	—
40	C₂₃×#532	C₂²	1	3	yes	—
41	C₂₃×#525	C₂²	1	3	yes	—
42	C₂₃×#525	C₂²	1	3	yes	—
43	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₂₃	C₂²	1	3	yes	—
45	C₂₃×#436	C₂²	1	6	yes	complemented
46	C₂₃×#436	C₂²	1	6	yes	complemented
47	C₂₃×#435	C₂²	1	1	yes	characteristic
48	C₂₃×#435	C₂²	1	3	yes	—
49	C₂₃×#435	C₂²	1	3	yes	complemented
50	C₂₃×#435	C₂²	1	3	yes	complemented
51	C₂₃×#435	C₂²	1	3	yes	complemented
52	C₂₃×#435	C₂²	1	3	yes	complemented
53	C₂₃×#435	C₂²	1	3	yes	complemented
54	C₂₃×#435	C₂²	1	3	yes	complemented
55	C₂₃×#435	C₂²	1	6	yes	complemented
56	C₂₃×#435	C₂²	1	6	yes	complemented
57	C₂₃×#435	C₂²	1	6	yes	complemented
58	C₈×D₄×C₂₃	C₂²	1	6	yes	complemented
59	C₈×D₄×C₂₃	C₂²	1	6	yes	complemented
60	C₂₃×#424	C₂²	1	3	yes	complemented
61	C₂₃×#424	C₂²	1	3	yes	complemented
62	C₂₃×#423	C₂²	1	3	yes	complemented
63	C₂×C₂₃×C₄⋊C₈	C₂²	1	3	yes	complemented
64	C₂₃×#408	C₂²	1	3	yes	complemented
65	C₂₃×#408	C₂²	1	3	yes	complemented
66	C₂₃×#408	C₂²	1	3	yes	complemented
67	C₂₃×#408	C₂²	1	3	yes	complemented
68	C₂₃×#407	C₂²	1	3	yes	complemented
69	C₂₃×#407	C₂²	1	3	yes	complemented
70	C₂×C₂₃×C₂²⋊C₈	C₂²	1	3	yes	complemented
71	C₂×C₂₃×C₂²⋊C₈	C₂²	1	3	yes	complemented
72	C₂₃×#405	C₂²	1	3	yes	complemented
73	C₂₃×#405	C₂²	1	3	yes	complemented
74	C₄×M₁₆×C₂₃	C₂²	1	3	yes	complemented
75	C₂×C₂₃×#97	C₂²	1	3	yes	complemented
76	C₂×#41×C₂₃	—	2	4	no	—
77	C₂×#41×C₂₃	—	2	4	no	—
78	C₂×#41×C₂₃	—	2	4	no	—
79	C₂×#41×C₂₃	—	2	4	no	—
80	C₂×#41×C₂₃	C₂×C₄	1	3	yes	—
81	C₂×#41×C₂₃	C₂×C₄	1	3	yes	—
82	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
83	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
84	C₂×#41×C₂₃	C₂³	1	3	yes	—
85	C₂×#41×C₂₃	C₂³	1	3	yes	—
86	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
88	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
89	C₂²×D₄×C₂₃	C₂×C₄	1	3	yes	—
90	C₂²×D₄×C₂₃	C₂×C₄	1	3	yes	—
91	C₂²×D₄×C₂₃	C₂×C₄	1	3	yes	—
92	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
93	C₂³×C₄×C₂₃	C₂³	1	3	yes	—
94	C₂₃×#131	—	2	4	no	—
95	C₂₃×#131	—	2	4	no	—
96	C₂₃×#131	—	2	4	no	—
97	C₂₃×#131	—	2	12	no	—
98	C₂₃×#131	—	2	12	no	—
99	C₂₃×#131	—	2	12	no	—
100	C₂₃×#131	—	2	12	no	—
101	C₂₃×#131	D₄	1	8	yes	complemented
102	C₂×M₁₆×C₂₃	—	2	12	no	—
103	C₂×M₁₆×C₂₃	—	2	12	no	—
104	C₂×M₁₆×C₂₃	—	2	12	no	—
105	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
107	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
108	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
110	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
111	C₂×M₁₆×C₂₃	C₂³	1	6	yes	—
112	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
113	C₂×M₁₆×C₂₃	C₂³	1	3	yes	—
114	C₂²×C₈×C₂₃	—	2	12	no	—
115	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
117	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
118	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
119	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
120	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	6	yes	—
122	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
123	C₂²×C₈×C₂₃	C₂³	1	3	yes	—
124	C₂₃×C₄⋊Q₈	C₂×C₄	1	3	yes	—
125	C₂₃×#127	C₂×C₄	1	3	yes	—
126	C₂₃×#124	C₂×C₄	1	3	yes	—
127	C₂₃×#124	C₂×C₄	1	3	yes	—
128	C₂₃×#123	C₂×C₄	1	6	yes	—
129	C₂₃×#123	C₂×C₄	1	6	yes	—
130	C₂₃×C₂²⋊Q₈	C₂×C₄	1	3	yes	—
131	C₂₃×C₂²⋊Q₈	C₂×C₄	1	3	yes	—
132	C₂₃×C₂²⋊Q₈	C₂×C₄	1	3	yes	—
133	C₂₃×C₂²⋊Q₈	C₂×C₄	1	3	yes	—
134	C₂₃×#121	C₂×C₄	1	6	yes	—
135	C₂₃×#121	C₂×C₄	1	3	yes	—
136	C₂₃×#121	C₂×C₄	1	3	yes	—
137	C₂₃×#121	C₂×C₄	1	3	yes	—
138	C₂₃×#121	C₂×C₄	1	3	yes	—
139	C₂₃×#121	C₂×C₄	1	6	yes	—
140	C₂₃×#120	C₂×C₄	1	6	yes	—
141	C₂₃×#120	C₂×C₄	1	6	yes	—
142	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
143	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
144	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
145	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
146	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
147	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
148	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
149	C₄×D₄×C₂₃	C₂×C₄	1	3	yes	—
150	C₄×D₄×C₂₃	C₂³	1	3	yes	—
151	C₄×D₄×C₂₃	C₂³	1	6	yes	—
152	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₂₃	C₂³	1	3	yes	—
154	C₄×D₄×C₂₃	C₂³	1	3	yes	—
155	C₂₃×#117	C₂³	1	3	yes	—
156	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	3	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	3	yes	—
158	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	3	yes	—
159	C₂×C₄²×C₂₃	C₂³	1	3	yes	—
160	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
162	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
163	C₂₃×C₄⋊C₈	C₂³	1	3	yes	—
164	C₂₃×C₄⋊C₈	C₂³	1	6	yes	—
165	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
166	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
167	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
168	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
169	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
170	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
171	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
172	C₂₃×C₂²⋊C₈	C₂³	1	3	yes	—
173	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	—
174	C₂₃×C₂²⋊C₈	C₂³	1	6	yes	—
175	C₂₃×#97	C₂³	1	1	yes	characteristic
176	C₂₃×#97	C₂³	1	3	yes	—
177	C₂₃×#97	C₂³	1	3	yes	—
178	C₂₃×#97	C₂³	1	3	yes	—
179	C₄×C₈×C₂₃	C₂³	1	6	yes	—
180	C₂⁴×C₂₃	C₂²×C₄	1	3	yes	—
181	C₂⁴×C₂₃	C₂²×C₄	1	3	yes	—
182	#41×C₂₃	—	2	4	no	—
183	#41×C₂₃	—	2	4	no	—
184	#41×C₂₃	—	2	12	no	—
185	#41×C₂₃	—	2	12	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	C₂×D₄	1	4	yes	—
191	#41×C₂₃	#41	1	4	yes	—
192	C₂×Q₈×C₂₃	—	2	4	no	—
193	C₂×Q₈×C₂₃	—	2	4	no	—
194	C₂×Q₈×C₂₃	C₂²×C₄	1	3	yes	—
195	C₂×Q₈×C₂₃	C₂²×C₄	1	3	yes	—
196	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×D₄×C₂₃	—	2	12	no	—
198	C₂×D₄×C₂₃	—	2	12	no	—
199	C₂×D₄×C₂₃	—	4	6	no	—
200	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
202	C₂×D₄×C₂₃	C₂²×C₄	1	6	yes	—
203	C₂×D₄×C₂₃	C₂²×C₄	1	6	yes	—
204	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
205	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
206	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
207	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
208	C₂×D₄×C₂₃	C₂²×C₄	1	6	yes	—
209	C₂×D₄×C₂₃	C₂²×C₄	1	3	yes	—
210	C₂²×C₄×C₂₃	—	2	6	no	—
211	C₂²×C₄×C₂₃	—	2	6	no	—
212	C₂²×C₄×C₂₃	—	2	6	no	—
213	C₂²×C₄×C₂₃	—	2	6	no	—
214	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
215	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
216	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
217	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
218	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
219	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
220	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
221	C₂²×C₄×C₂₃	C₂²×C₄	1	3	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₂₃	C₂⁴	1	3	yes	—
227	M₁₆×C₂₃	—	2	6	no	—
228	M₁₆×C₂₃	—	2	6	no	—
229	M₁₆×C₂₃	—	2	6	no	—
230	M₁₆×C₂₃	—	2	2	no	—
231	M₁₆×C₂₃	—	2	6	no	—
232	M₁₆×C₂₃	—	2	6	no	—
233	M₁₆×C₂₃	—	2	12	no	—
234	M₁₆×C₂₃	—	2	6	no	—
235	M₁₆×C₂₃	C₂×D₄	1	12	yes	complemented
236	C₂×C₈×C₂₃	—	2	6	no	—
237	C₂×C₈×C₂₃	—	2	6	no	—
238	C₂×C₈×C₂₃	—	2	6	no	—
239	C₂×C₈×C₂₃	—	2	2	no	—
240	C₂×C₈×C₂₃	—	2	6	no	—
241	C₂×C₈×C₂₃	—	2	6	no	—
242	C₂×C₈×C₂₃	—	2	6	no	—
243	C₂×C₈×C₂₃	—	2	12	no	—
244	C₂×C₈×C₂₃	C₂×D₄	1	12	yes	complemented
245	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
248	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
249	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
251	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₈×C₂₃	C₂⁴	1	3	yes	—
253	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
254	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
255	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
256	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
257	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
258	C₄⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
259	C₄⋊C₄×C₂₃	C₂²×C₄	1	6	yes	—
260	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
261	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
262	C₂²⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
263	C₂²⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
264	C₂²⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
265	C₂²⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
266	C₂²⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
267	C₂²⋊C₄×C₂₃	C₂²×C₄	1	3	yes	—
268	C₂²⋊C₄×C₂₃	C₂²×C₄	1	6	yes	—
269	C₂²⋊C₄×C₂₃	C₂²×C₄	1	6	yes	—
270	C₂²⋊C₄×C₂₃	C₂²×C₄	1	6	yes	—
271	C₄²×C₂₃	C₂²×C₄	1	3	yes	—
272	C₄²×C₂₃	C₂²×C₄	1	3	yes	—
273	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
274	C₄²×C₂₃	C₂⁴	1	3	yes	—
275	#60146	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₂₃	—	2	6	no	—
277	C₂³×C₂₃	—	2	6	no	—
278	C₂³×C₂₃	—	2	6	no	—
279	C₂³×C₂₃	—	4	3	no	—
280	C₂³×C₂₃	—	4	3	no	—
281	C₂³×C₂₃	—	4	3	no	—
282	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
283	C₂³×C₂₃	C₂³×C₄	1	3	yes	—
284	C₂³×C₂₃	C₂³×C₄	1	3	yes	—
285	C₂³×C₂₃	C₂³×C₄	1	3	yes	—
286	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
287	Q₈×C₂₃	—	2	6	no	—
288	Q₈×C₂₃	—	2	6	no	—
289	Q₈×C₂₃	C₄×D₄	1	4	yes	—
290	D₄×C₂₃	—	2	12	no	—
291	D₄×C₂₃	—	2	12	no	—
292	D₄×C₂₃	—	2	2	no	—
293	D₄×C₂₃	—	2	6	no	—
294	D₄×C₂₃	—	2	6	no	—
295	D₄×C₂₃	—	2	6	no	—
296	D₄×C₂₃	—	4	3	no	—
297	D₄×C₂₃	—	4	3	no	—
298	D₄×C₂₃	—	4	6	no	—
299	D₄×C₂₃	C₄×D₄	1	12	yes	—
300	C₂×C₄×C₂₃	—	2	6	no	—
301	C₂×C₄×C₂₃	—	2	6	no	—
302	C₂×C₄×C₂₃	—	2	6	no	—
303	C₂×C₄×C₂₃	—	2	6	no	—
304	C₂×C₄×C₂₃	—	2	6	no	—
305	C₂×C₄×C₂₃	—	2	6	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	3	no	—
308	C₂×C₄×C₂₃	—	2	3	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	3	no	—
313	C₂×C₄×C₂₃	—	2	3	no	—
314	C₂×C₄×C₂₃	—	4	3	no	—
315	C₂×C₄×C₂₃	—	4	3	no	—
316	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
317	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₂₃	C₂³×C₄	1	3	yes	—
319	C₂×C₄×C₂₃	C₂³×C₄	1	3	yes	—
320	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
321	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
322	C₂×C₄×C₂₃	C₂³×C₄	1	3	yes	—
323	C₂×C₄×C₂₃	C₂³×C₄	1	3	yes	—
324	C₂×C₄×C₂₃	C₂³×C₄	1	3	yes	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	6	yes	—
326	C₂×C₄×C₂₃	C₂×#41	1	6	yes	—
327	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
328	C₈×C₂₃	—	2	1	no	—
329	C₈×C₂₃	—	2	3	no	—
330	C₈×C₂₃	—	2	1	no	—
331	C₈×C₂₃	—	2	3	no	—
332	C₈×C₂₃	—	2	1	no	—
333	C₈×C₂₃	—	2	3	no	—
334	C₈×C₂₃	C₂²×D₄	1	2	yes	—
335	C₈×C₂₃	C₂²×D₄	1	6	yes	—
336	C₂×#568	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂²×#131	C₂×C₂₃	1	1	yes	characteristic, complemented
338	D₄×#41	C₂×C₂₃	1	1	yes	characteristic
339	#2935	C₂×C₂₃	1	3	yes	complemented
340	D₄×M₁₆	C₂×C₂₃	1	3	yes	complemented
341	#2933	C₂×C₂₃	1	3	yes	complemented
342	#2933	C₂×C₂₃	1	3	yes	complemented
343	#2932	C₂×C₂₃	1	3	yes	complemented
344	#2930	C₂×C₂₃	1	3	yes	complemented
345	#2929	C₂×C₂₃	1	3	yes	complemented
346	C₂×#435	C₂×C₂₃	1	3	yes	complemented
347	#2906	C₂×C₂₃	1	1	yes	characteristic, complemented
348	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
349	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2875	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂²×C₂₃	—	2	1	no	—
352	C₂²×C₂₃	—	2	3	no	—
353	C₂²×C₂₃	—	2	3	no	—
354	C₂²×C₂₃	—	2	1	no	—
355	C₂²×C₂₃	—	2	1	no	—
356	C₂²×C₂₃	—	2	3	no	—
357	C₂²×C₂₃	—	2	3	no	—
358	C₂²×C₂₃	—	2	1	no	—
359	C₂²×C₂₃	—	2	3	no	—
360	C₂²×C₂₃	—	2	3	no	—
361	C₂²×C₂₃	—	2	3	no	—
362	C₂²×C₂₃	—	2	3	no	—
363	C₂²×C₂₃	—	2	1	no	—
364	C₂²×C₂₃	—	4	12	no	—
365	C₂²×C₂₃	—	8	6	no	—
366	C₂²×C₂₃	C₂×C₄×D₄	1	6	yes	—
367	C₂²×C₂₃	#568	1	2	yes	complemented
368	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
369	C₄×C₂₃	—	2	1	no	—
370	C₄×C₂₃	—	2	1	no	—
371	C₄×C₂₃	—	2	3	no	—
372	C₄×C₂₃	—	2	3	no	—
373	C₄×C₂₃	—	2	1	no	—
374	C₄×C₂₃	—	2	3	no	—
375	C₄×C₂₃	—	2	1	no	—
376	C₄×C₂₃	—	2	3	no	—
377	C₄×C₂₃	C₂×C₄×D₄	1	6	yes	—
378	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
379	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
380	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
381	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
382	#568	—	2	8	no	—
383	C₂×#131	—	2	8	no	—
384	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
385	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
386	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×#131	C₂²×C₂₃	1	3	yes	complemented
389	C₂×#131	C₂²×C₂₃	1	3	yes	complemented
390	C₂×#131	C₂²×C₂₃	1	3	yes	complemented
391	C₂×#131	C₂²×C₂₃	1	3	yes	complemented
392	C₂²×M₁₆	C₂²×C₂₃	1	3	yes	complemented
393	C₂²×M₁₆	C₂²×C₂₃	1	3	yes	complemented
394	C₂²×M₁₆	C₂²×C₂₃	1	3	yes	complemented
395	C₂³×C₈	C₂²×C₂₃	1	3	yes	complemented
396	#550	C₄×C₂₃	1	1	yes	characteristic
397	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
398	#548	C₄×C₂₃	1	1	yes	characteristic
399	#548	C₄×C₂₃	1	1	yes	characteristic
400	#547	C₄×C₂₃	1	3	yes	—
401	#546	C₄×C₂₃	1	3	yes	—
402	#546	C₄×C₂₃	1	3	yes	—
403	D₄²	C₄×C₂₃	1	3	yes	—
404	#532	C₂²×C₂₃	1	3	yes	—
405	#525	C₂²×C₂₃	1	3	yes	—
406	#525	C₂²×C₂₃	1	3	yes	—
407	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
408	C₂×C₄×D₄	C₂²×C₂₃	1	3	yes	—
409	#436	C₂²×C₂₃	1	6	yes	complemented
410	#436	C₂²×C₂₃	1	6	yes	complemented
411	#435	C₂²×C₂₃	1	1	yes	characteristic
412	#435	C₂²×C₂₃	1	3	yes	—
413	#435	C₂²×C₂₃	1	3	yes	complemented
414	#435	C₂²×C₂₃	1	3	yes	complemented
415	#435	C₂²×C₂₃	1	3	yes	complemented
416	#435	C₂²×C₂₃	1	3	yes	complemented
417	#435	C₂²×C₂₃	1	3	yes	complemented
418	#435	C₂²×C₂₃	1	3	yes	complemented
419	#435	C₂²×C₂₃	1	6	yes	complemented
420	#435	C₂²×C₂₃	1	6	yes	complemented
421	#435	C₂²×C₂₃	1	6	yes	complemented
422	C₈×D₄	C₂²×C₂₃	1	6	yes	complemented
423	C₈×D₄	C₂²×C₂₃	1	6	yes	complemented
424	#424	C₂²×C₂₃	1	3	yes	complemented
425	#424	C₂²×C₂₃	1	3	yes	complemented
426	#423	C₂²×C₂₃	1	3	yes	complemented
427	C₂×C₄⋊C₈	C₂²×C₂₃	1	3	yes	complemented
428	#408	C₂²×C₂₃	1	3	yes	complemented
429	#408	C₂²×C₂₃	1	3	yes	complemented
430	#408	C₂²×C₂₃	1	3	yes	complemented
431	#408	C₂²×C₂₃	1	3	yes	complemented
432	#407	C₂²×C₂₃	1	3	yes	complemented
433	#407	C₂²×C₂₃	1	3	yes	complemented
434	C₂×C₂²⋊C₈	C₂²×C₂₃	1	3	yes	complemented
435	C₂×C₂²⋊C₈	C₂²×C₂₃	1	3	yes	complemented
436	#405	C₂²×C₂₃	1	3	yes	complemented
437	#405	C₂²×C₂₃	1	3	yes	complemented
438	C₄×M₁₆	C₂²×C₂₃	1	3	yes	complemented
439	C₂×#97	C₂²×C₂₃	1	3	yes	complemented
440	C₂×C₂₃	—	2	2	no	—
441	C₂×C₂₃	—	2	6	no	—
442	C₂×C₂₃	—	4	3	no	—
443	C₂×C₂₃	—	4	3	no	—
444	C₂×C₂₃	—	4	1	no	—
445	C₂×C₂₃	C₂²×C₄×D₄	1	1	yes	characteristic
446	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
447	C₂×C₂₃	#3573	1	1	yes	characteristic
448	C₂×#41	—	2	4	no	—
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	—	2	4	no	—
452	C₂×#41	C₂×C₄×C₂₃	1	3	yes	—
453	C₂×#41	C₂×C₄×C₂₃	1	3	yes	—
454	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
455	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
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	C₂×C₄×C₂₃	1	1	yes	characteristic
460	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
461	C₂²×D₄	C₂×C₄×C₂₃	1	3	yes	—
462	C₂²×D₄	C₂×C₄×C₂₃	1	3	yes	—
463	C₂²×D₄	C₂×C₄×C₂₃	1	3	yes	—
464	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
465	C₂³×C₄	C₂³×C₂₃	1	3	yes	—
466	#131	—	2	4	no	—
467	#131	—	2	4	no	—
468	#131	—	2	4	no	—
469	#131	—	2	12	no	—
470	#131	—	2	12	no	—
471	#131	—	2	12	no	—
472	#131	—	2	12	no	—
473	#131	D₄×C₂₃	1	8	yes	complemented
474	C₂×M₁₆	—	2	12	no	—
475	C₂×M₁₆	—	2	12	no	—
476	C₂×M₁₆	—	2	12	no	—
477	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
478	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
479	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
480	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
481	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
482	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
483	C₂×M₁₆	C₂³×C₂₃	1	6	yes	—
484	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
485	C₂×M₁₆	C₂³×C₂₃	1	3	yes	—
486	C₂²×C₈	—	2	12	no	—
487	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
488	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
489	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
490	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
491	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
492	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
493	C₂²×C₈	C₂³×C₂₃	1	6	yes	—
494	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
495	C₂²×C₈	C₂³×C₂₃	1	3	yes	—
496	C₄⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
497	#127	C₂×C₄×C₂₃	1	3	yes	—
498	#124	C₂×C₄×C₂₃	1	3	yes	—
499	#124	C₂×C₄×C₂₃	1	3	yes	—
500	#123	C₂×C₄×C₂₃	1	6	yes	—
501	#123	C₂×C₄×C₂₃	1	6	yes	—
502	C₂²⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
503	C₂²⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
504	C₂²⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
505	C₂²⋊Q₈	C₂×C₄×C₂₃	1	3	yes	—
506	#121	C₂×C₄×C₂₃	1	3	yes	—
507	#121	C₂×C₄×C₂₃	1	3	yes	—
508	#121	C₂×C₄×C₂₃	1	3	yes	—
509	#121	C₂×C₄×C₂₃	1	3	yes	—
510	#121	C₂×C₄×C₂₃	1	6	yes	—
511	#121	C₂×C₄×C₂₃	1	6	yes	—
512	#120	C₂×C₄×C₂₃	1	6	yes	—
513	#120	C₂×C₄×C₂₃	1	6	yes	—
514	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
515	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
516	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
517	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
518	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
519	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
520	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
521	C₄×D₄	C₂×C₄×C₂₃	1	3	yes	—
522	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₄×D₄	C₂³×C₂₃	1	3	yes	—
524	C₄×D₄	C₂³×C₂₃	1	3	yes	—
525	C₄×D₄	C₂³×C₂₃	1	3	yes	—
526	C₄×D₄	C₂³×C₂₃	1	6	yes	—
527	#117	C₂³×C₂₃	1	3	yes	—
528	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	3	yes	—
529	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	3	yes	—
530	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	3	yes	—
531	C₂×C₄²	C₂³×C₂₃	1	3	yes	—
532	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
533	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
534	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
535	C₄⋊C₈	C₂³×C₂₃	1	3	yes	—
536	C₄⋊C₈	C₂³×C₂₃	1	6	yes	—
537	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
539	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
540	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
541	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
542	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
543	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
544	C₂²⋊C₈	C₂³×C₂₃	1	3	yes	—
545	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	—
546	C₂²⋊C₈	C₂³×C₂₃	1	6	yes	—
547	#97	C₂³×C₂₃	1	1	yes	characteristic
548	#97	C₂³×C₂₃	1	3	yes	—
549	#97	C₂³×C₂₃	1	3	yes	—
550	#97	C₂³×C₂₃	1	3	yes	—
551	C₄×C₈	C₂³×C₂₃	1	6	yes	—
552	C₂₃	#60146	1	1	yes	characteristic, direct product factor, Sylow
553	C₂⁴	C₂²×C₄×C₂₃	1	3	yes	—
554	C₂⁴	C₂²×C₄×C₂₃	1	3	yes	—
555	#41	—	2	4	no	—
556	#41	—	2	4	no	—
557	#41	—	2	12	no	—
558	#41	—	2	12	no	—
559	#41	—	2	6	no	—
560	#41	—	2	6	no	—
561	#41	—	2	6	no	—
562	#41	—	2	6	no	—
563	#41	C₂×D₄×C₂₃	1	4	yes	—
564	#41	#41×C₂₃	1	4	yes	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	4	no	—
567	C₂×Q₈	C₂²×C₄×C₂₃	1	3	yes	—
568	C₂×Q₈	C₂²×C₄×C₂₃	1	3	yes	—
569	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
570	C₂×D₄	—	2	12	no	—
571	C₂×D₄	—	2	12	no	—
572	C₂×D₄	—	4	6	no	—
573	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
574	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
575	C₂×D₄	C₂²×C₄×C₂₃	1	6	yes	—
576	C₂×D₄	C₂²×C₄×C₂₃	1	6	yes	—
577	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
578	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
579	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
580	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
581	C₂×D₄	C₂²×C₄×C₂₃	1	6	yes	—
582	C₂×D₄	C₂²×C₄×C₂₃	1	3	yes	—
583	C₂²×C₄	—	2	6	no	—
584	C₂²×C₄	—	2	6	no	—
585	C₂²×C₄	—	2	6	no	—
586	C₂²×C₄	—	2	6	no	—
587	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
588	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
589	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
590	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
591	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
592	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
593	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
594	C₂²×C₄	C₂²×C₄×C₂₃	1	3	yes	—
595	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
598	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₂₃	1	3	yes	—
600	M₁₆	—	2	6	no	—
601	M₁₆	—	2	6	no	—
602	M₁₆	—	2	6	no	—
603	M₁₆	—	2	2	no	—
604	M₁₆	—	2	6	no	—
605	M₁₆	—	2	6	no	—
606	M₁₆	—	2	12	no	—
607	M₁₆	—	2	6	no	—
608	M₁₆	C₂×D₄×C₂₃	1	12	yes	complemented
609	C₂×C₈	—	2	6	no	—
610	C₂×C₈	—	2	6	no	—
611	C₂×C₈	—	2	6	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	2	6	no	—
614	C₂×C₈	—	2	6	no	—
615	C₂×C₈	—	2	6	no	—
616	C₂×C₈	—	2	12	no	—
617	C₂×C₈	C₂×D₄×C₂₃	1	12	yes	complemented
618	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
619	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
621	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
623	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
624	C₂×C₈	C₂⁴×C₂₃	1	3	yes	—
625	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
626	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
627	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
628	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
629	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
630	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
631	C₄⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
632	C₄⋊C₄	C₂²×C₄×C₂₃	1	6	yes	—
633	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
634	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
635	C₂²⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
636	C₂²⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
637	C₂²⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
638	C₂²⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
639	C₂²⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
640	C₂²⋊C₄	C₂²×C₄×C₂₃	1	3	yes	—
641	C₂²⋊C₄	C₂²×C₄×C₂₃	1	6	yes	—
642	C₂²⋊C₄	C₂²×C₄×C₂₃	1	6	yes	—
643	C₂²⋊C₄	C₂²×C₄×C₂₃	1	6	yes	—
644	C₄²	C₂²×C₄×C₂₃	1	3	yes	—
645	C₄²	C₂²×C₄×C₂₃	1	3	yes	—
646	C₄²	C₂⁴×C₂₃	1	3	yes	—
647	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
648	C₂³	—	2	6	no	—
649	C₂³	—	2	6	no	—
650	C₂³	—	2	6	no	—
651	C₂³	—	4	3	no	—
652	C₂³	—	4	3	no	—
653	C₂³	—	4	3	no	—
654	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
655	C₂³	C₂³×C₄×C₂₃	1	3	yes	—
656	C₂³	C₂³×C₄×C₂₃	1	3	yes	—
657	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
658	C₂³	C₂³×C₄×C₂₃	1	3	yes	—
659	Q₈	—	2	6	no	—
660	Q₈	—	2	6	no	—
661	Q₈	C₄×D₄×C₂₃	1	4	yes	—
662	D₄	—	2	2	no	—
663	D₄	—	2	6	no	—
664	D₄	—	2	12	no	—
665	D₄	—	2	12	no	—
666	D₄	—	2	6	no	—
667	D₄	—	2	6	no	—
668	D₄	—	4	3	no	—
669	D₄	—	4	3	no	—
670	D₄	—	4	6	no	—
671	D₄	C₄×D₄×C₂₃	1	12	yes	—
672	C₂×C₄	—	2	6	no	—
673	C₂×C₄	—	2	6	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	3	no	—
676	C₂×C₄	—	2	3	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	3	no	—
681	C₂×C₄	—	2	3	no	—
682	C₂×C₄	—	2	6	no	—
683	C₂×C₄	—	2	6	no	—
684	C₂×C₄	—	2	6	no	—
685	C₂×C₄	—	2	6	no	—
686	C₂×C₄	—	4	3	no	—
687	C₂×C₄	—	4	3	no	—
688	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
689	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
690	C₂×C₄	C₂³×C₄×C₂₃	1	3	yes	—
691	C₂×C₄	C₂³×C₄×C₂₃	1	3	yes	—
692	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
693	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
694	C₂×C₄	C₂³×C₄×C₂₃	1	3	yes	—
695	C₂×C₄	C₂³×C₄×C₂₃	1	3	yes	—
696	C₂×C₄	C₂³×C₄×C₂₃	1	3	yes	—
697	C₂×C₄	C₂²×D₄×C₂₃	1	6	yes	—
698	C₂×C₄	C₂×#41×C₂₃	1	6	yes	—
699	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
700	C₈	—	2	1	no	—
701	C₈	—	2	3	no	—
702	C₈	—	2	1	no	—
703	C₈	—	2	3	no	—
704	C₈	—	2	1	no	—
705	C₈	—	2	3	no	—
706	C₈	C₂²×D₄×C₂₃	1	2	yes	—
707	C₈	C₂²×D₄×C₂₃	1	6	yes	—
708	C₂²	—	2	1	no	—
709	C₂²	—	2	3	no	—
710	C₂²	—	2	3	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	3	no	—
714	C₂²	—	2	3	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	3	no	—
717	C₂²	—	2	3	no	—
718	C₂²	—	2	3	no	—
719	C₂²	—	2	3	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	12	no	—
722	C₂²	—	8	6	no	—
723	C₂²	C₂×C₄×D₄×C₂₃	1	6	yes	—
724	C₂²	C₂₃×#568	1	2	yes	complemented
725	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	2	3	no	—
729	C₄	—	2	3	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	3	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	3	no	—
734	C₄	C₂×C₄×D₄×C₂₃	1	6	yes	—
735	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
736	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
737	C₂	—	2	2	no	—
738	C₂	—	2	6	no	—
739	C₂	—	4	3	no	—
740	C₂	—	4	1	no	—
741	C₂	—	4	3	no	—
742	C₂	C₂²×C₄×D₄×C₂₃	1	1	yes	characteristic
743	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
744	C₂	C₂₃×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	D₄×#41×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#568	C₂	semidirect
2. C₂²×C₂₃×#131	C₂	semidirect
4. C₂₃×#2935	C₂	semidirect
5. D₄×M₁₆×C₂₃	C₂	semidirect
6. C₂₃×#2933	C₂	semidirect
7. C₂₃×#2933	C₂	semidirect
8. C₂₃×#2932	C₂	semidirect
9. C₂₃×#2930	C₂	semidirect
10. C₂₃×#2929	C₂	semidirect
11. C₂×C₂₃×#435	C₂	semidirect
12. C₂₃×#2906	C₂	semidirect
13. C₂₃×#2880	C₂	semidirect
14. C₂₃×#2880	C₂	semidirect
15. C₂₃×#2875	C₂	semidirect
24. C₂×C₂₃×#131	C₂²	semidirect
25. C₂×C₂₃×#131	C₂²	semidirect
26. C₂×C₂₃×#131	C₂²	semidirect
27. C₂×C₂₃×#131	C₂²	semidirect
28. C₂²×M₁₆×C₂₃	C₂²	semidirect
29. C₂²×M₁₆×C₂₃	C₂²	semidirect
30. C₂²×M₁₆×C₂₃	C₂²	semidirect
31. C₂³×C₈×C₂₃	C₂²	semidirect
45. C₂₃×#436	C₂²	semidirect
46. C₂₃×#436	C₂²	semidirect
49. C₂₃×#435	C₂²	semidirect
50. C₂₃×#435	C₂²	semidirect
51. C₂₃×#435	C₂²	semidirect
52. C₂₃×#435	C₂²	semidirect
53. C₂₃×#435	C₂²	semidirect
54. C₂₃×#435	C₂²	semidirect
55. C₂₃×#435	C₂²	semidirect
56. C₂₃×#435	C₂²	semidirect
57. C₂₃×#435	C₂²	semidirect
58. C₈×D₄×C₂₃	C₂²	semidirect
59. C₈×D₄×C₂₃	C₂²	semidirect
60. C₂₃×#424	C₂²	semidirect
61. C₂₃×#424	C₂²	semidirect
62. C₂₃×#423	C₂²	semidirect
63. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
64. C₂₃×#408	C₂²	semidirect
65. C₂₃×#408	C₂²	semidirect
66. C₂₃×#408	C₂²	semidirect
67. C₂₃×#408	C₂²	semidirect
68. C₂₃×#407	C₂²	semidirect
69. C₂₃×#407	C₂²	semidirect
70. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
71. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
72. C₂₃×#405	C₂²	semidirect
73. C₂₃×#405	C₂²	semidirect
74. C₄×M₁₆×C₂₃	C₂²	semidirect
75. C₂×C₂₃×#97	C₂²	semidirect
101. C₂₃×#131	D₄	semidirect
235. M₁₆×C₂₃	C₂×D₄	semidirect
244. C₂×C₈×C₂₃	C₂×D₄	semidirect
275. #60146	C₂₃	direct (N × H)
336. C₂×#568	C₂×C₂₃	semidirect
337. C₂²×#131	C₂×C₂₃	semidirect
339. #2935	C₂×C₂₃	semidirect
340. D₄×M₁₆	C₂×C₂₃	semidirect
341. #2933	C₂×C₂₃	semidirect
342. #2933	C₂×C₂₃	semidirect
343. #2932	C₂×C₂₃	semidirect
344. #2930	C₂×C₂₃	semidirect
345. #2929	C₂×C₂₃	semidirect
346. C₂×#435	C₂×C₂₃	semidirect
347. #2906	C₂×C₂₃	semidirect
348. #2880	C₂×C₂₃	semidirect
349. #2880	C₂×C₂₃	semidirect
350. #2875	C₂×C₂₃	semidirect
367. C₂²×C₂₃	#568	semidirect
388. C₂×#131	C₂²×C₂₃	semidirect
389. C₂×#131	C₂²×C₂₃	semidirect
390. C₂×#131	C₂²×C₂₃	semidirect
391. C₂×#131	C₂²×C₂₃	semidirect
392. C₂²×M₁₆	C₂²×C₂₃	semidirect
393. C₂²×M₁₆	C₂²×C₂₃	semidirect
394. C₂²×M₁₆	C₂²×C₂₃	semidirect
395. C₂³×C₈	C₂²×C₂₃	semidirect
409. #436	C₂²×C₂₃	semidirect
410. #436	C₂²×C₂₃	semidirect
413. #435	C₂²×C₂₃	semidirect
414. #435	C₂²×C₂₃	semidirect
415. #435	C₂²×C₂₃	semidirect
416. #435	C₂²×C₂₃	semidirect
417. #435	C₂²×C₂₃	semidirect
418. #435	C₂²×C₂₃	semidirect
419. #435	C₂²×C₂₃	semidirect
420. #435	C₂²×C₂₃	semidirect
421. #435	C₂²×C₂₃	semidirect
422. C₈×D₄	C₂²×C₂₃	semidirect
423. C₈×D₄	C₂²×C₂₃	semidirect
424. #424	C₂²×C₂₃	semidirect
425. #424	C₂²×C₂₃	semidirect
426. #423	C₂²×C₂₃	semidirect
427. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
428. #408	C₂²×C₂₃	semidirect
429. #408	C₂²×C₂₃	semidirect
430. #408	C₂²×C₂₃	semidirect
431. #408	C₂²×C₂₃	semidirect
432. #407	C₂²×C₂₃	semidirect
433. #407	C₂²×C₂₃	semidirect
434. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
435. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
436. #405	C₂²×C₂₃	semidirect
437. #405	C₂²×C₂₃	semidirect
438. C₄×M₁₆	C₂²×C₂₃	semidirect
439. C₂×#97	C₂²×C₂₃	semidirect
473. #131	D₄×C₂₃	semidirect
552. C₂₃	#60146	direct (N × H)
608. M₁₆	C₂×D₄×C₂₃	semidirect
617. C₂×C₈	C₂×D₄×C₂₃	semidirect
724. C₂²	C₂₃×#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#568	2
C₂²×C₂₃×#131	2
D₄×#41×C₂₃	2
C₂₃×#2935	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2932	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂×C₂₃×#435	2
C₂₃×#2906	2
C₂₃×#2880	2
C₂₃×#2875	2
#60146	23

Subgroups — C23×#60146 #19207772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60146 #19207772