Subgroups — C₂₃×#22849 #19170475

Order 5888.

1144 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2388	C₂	1	1	yes	maximal, characteristic
6	C₂₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#436	—	2	4	no	—
26	C₂₃×#435	—	2	4	no	—
27	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂₃×#408	—	2	4	no	—
31	C₂₃×#408	—	2	4	no	—
32	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#395	C₄	1	1	yes	characteristic
47	C₂₃×#394	C₄	1	1	yes	characteristic
48	C₂₃×#394	C₄	1	1	yes	characteristic
49	C₂₃×#394	C₄	1	1	yes	characteristic
50	C₂₃×#393	C₄	1	1	yes	characteristic
51	C₂₃×#392	C₄	1	1	yes	characteristic
52	C₂₃×#392	C₄	1	1	yes	characteristic
53	C₂₃×#392	C₄	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic
58	C₂₃×#336	C₂²	1	1	yes	characteristic
59	C₂₃×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₃	—	2	2	no	—
64	C₂×#41×C₂₃	—	2	2	no	—
65	C₂×#41×C₂₃	—	2	2	no	—
66	C₂×#41×C₂₃	—	2	2	no	—
67	C₂×#41×C₂₃	—	4	1	no	—
68	C₂×#41×C₂₃	—	4	1	no	—
69	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂×M₁₆×C₂₃	—	2	2	no	—
81	C₂×M₁₆×C₂₃	—	2	2	no	—
82	C₂×M₁₆×C₂₃	—	2	2	no	—
83	C₂×M₁₆×C₂₃	—	2	2	no	—
84	C₂×M₁₆×C₂₃	—	2	2	no	—
85	C₂×M₁₆×C₂₃	—	2	2	no	—
86	C₂×M₁₆×C₂₃	—	4	1	no	—
87	C₂×M₁₆×C₂₃	—	4	1	no	—
88	C₂×M₁₆×C₂₃	—	4	1	no	—
89	C₂²×C₈×C₂₃	—	2	2	no	—
90	C₂²×C₈×C₂₃	—	2	2	no	—
91	C₂²×C₈×C₂₃	—	2	2	no	—
92	C₂²×C₈×C₂₃	—	2	2	no	—
93	C₂²×C₈×C₂₃	—	4	1	no	—
94	C₂²×C₈×C₂₃	—	4	1	no	—
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₂₃	—	2	2	no	—
104	C₄×D₄×C₂₃	—	2	2	no	—
105	C₄×D₄×C₂₃	—	2	2	no	—
106	C₄×D₄×C₂₃	—	2	2	no	—
107	C₄×D₄×C₂₃	—	4	1	no	—
108	C₄×D₄×C₂₃	—	4	1	no	—
109	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
127	C₂₃×C₄⋊C₈	—	2	2	no	—
128	C₂₃×C₄⋊C₈	—	2	2	no	—
129	C₂₃×C₄⋊C₈	—	4	1	no	—
130	C₂₃×C₂²⋊C₈	—	2	2	no	—
131	C₂₃×C₂²⋊C₈	—	2	2	no	—
132	C₂₃×C₂²⋊C₈	—	2	2	no	—
133	C₂₃×C₂²⋊C₈	—	2	2	no	—
134	C₂₃×C₂²⋊C₈	—	2	2	no	—
135	C₂₃×C₂²⋊C₈	—	2	2	no	—
136	C₂₃×C₂²⋊C₈	—	2	2	no	—
137	C₂₃×C₂²⋊C₈	—	2	2	no	—
138	C₂₃×C₂²⋊C₈	—	4	1	no	—
139	C₂₃×C₂²⋊C₈	D₄	1	4	yes	complemented
140	C₂₃×C₂²⋊C₈	D₄	1	4	yes	complemented
141	C₂₃×#97	—	2	2	no	—
142	C₂₃×#97	—	4	1	no	—
143	C₄×C₈×C₂₃	—	2	2	no	—
144	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
145	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
146	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
147	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
148	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
149	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
150	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
152	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
154	#41×C₂₃	—	4	4	no	—
155	#41×C₂₃	—	4	4	no	—
156	#41×C₂₃	—	4	4	no	—
157	#41×C₂₃	—	4	4	no	—
158	C₂×Q₈×C₂₃	—	2	2	no	—
159	C₂×Q₈×C₂₃	—	2	2	no	—
160	C₂×Q₈×C₂₃	—	4	1	no	—
161	C₂×D₄×C₂₃	—	2	2	no	—
162	C₂×D₄×C₂₃	—	2	2	no	—
163	C₂×D₄×C₂₃	—	2	2	no	—
164	C₂×D₄×C₂₃	—	2	2	no	—
165	C₂×D₄×C₂₃	—	2	2	no	—
166	C₂×D₄×C₂₃	—	2	2	no	—
167	C₂×D₄×C₂₃	—	2	2	no	—
168	C₂×D₄×C₂₃	—	2	2	no	—
169	C₂×D₄×C₂₃	—	2	2	no	—
170	C₂×D₄×C₂₃	—	4	1	no	—
171	C₂×D₄×C₂₃	—	4	1	no	—
172	C₂×D₄×C₂₃	—	4	1	no	—
173	C₂×D₄×C₂₃	—	4	1	no	—
174	C₂×D₄×C₂₃	—	4	1	no	—
175	C₂×D₄×C₂₃	—	4	1	no	—
176	C₂×D₄×C₂₃	—	4	1	no	—
177	C₂×D₄×C₂₃	—	4	1	no	—
178	C₂×D₄×C₂₃	—	4	1	no	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	2	1	no	—
188	C₂²×C₄×C₂₃	—	2	1	no	—
189	C₂²×C₄×C₂₃	—	2	1	no	—
190	C₂²×C₄×C₂₃	—	2	1	no	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₂₃	C₂²×C₄	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	#41	1	2	yes	—
212	C₂²×C₄×C₂₃	#41	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
214	M₁₆×C₂₃	—	4	4	no	—
215	M₁₆×C₂₃	—	4	4	no	—
216	M₁₆×C₂₃	—	4	4	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	—	2	1	no	—
231	C₂×C₈×C₂₃	—	2	1	no	—
232	C₂×C₈×C₂₃	—	2	1	no	—
233	C₂×C₈×C₂₃	—	2	1	no	—
234	C₂×C₈×C₂₃	—	2	1	no	—
235	C₂×C₈×C₂₃	—	2	1	no	—
236	C₂×C₈×C₂₃	—	2	1	no	—
237	C₂×C₈×C₂₃	—	4	4	no	—
238	C₂×C₈×C₂₃	—	4	4	no	—
239	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
240	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
241	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
242	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
243	C₄⋊C₄×C₂₃	—	2	2	no	—
244	C₄⋊C₄×C₂₃	—	2	2	no	—
245	C₄⋊C₄×C₂₃	—	4	1	no	—
246	C₂²⋊C₄×C₂₃	—	2	2	no	—
247	C₂²⋊C₄×C₂₃	—	2	2	no	—
248	C₂²⋊C₄×C₂₃	—	2	2	no	—
249	C₂²⋊C₄×C₂₃	—	2	2	no	—
250	C₂²⋊C₄×C₂₃	—	2	2	no	—
251	C₂²⋊C₄×C₂₃	—	2	2	no	—
252	C₂²⋊C₄×C₂₃	—	4	1	no	—
253	C₂²⋊C₄×C₂₃	—	4	1	no	—
254	C₂²⋊C₄×C₂₃	—	4	1	no	—
255	C₂²⋊C₄×C₂₃	—	4	1	no	—
256	C₂²⋊C₄×C₂₃	—	4	1	no	—
257	C₂²⋊C₄×C₂₃	—	4	1	no	—
258	C₄²×C₂₃	—	2	1	no	—
259	C₄²×C₂₃	—	2	1	no	—
260	C₄²×C₂₃	—	2	1	no	—
261	C₄²×C₂₃	—	2	1	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	1	no	—
264	#22849	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂³×C₂₃	—	2	1	no	—
266	C₂³×C₂₃	—	2	1	no	—
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	1	no	—
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	1	no	—
281	C₂³×C₂₃	—	2	1	no	—
282	C₂³×C₂₃	—	2	1	no	—
283	C₂³×C₂₃	—	2	1	no	—
284	C₂³×C₂₃	—	2	1	no	—
285	C₂³×C₂₃	—	2	1	no	—
286	C₂³×C₂₃	—	2	1	no	—
287	C₂³×C₂₃	—	2	1	no	—
288	C₂³×C₂₃	—	2	1	no	—
289	C₂³×C₂₃	—	2	1	no	—
290	C₂³×C₂₃	—	2	1	no	—
291	C₂³×C₂₃	C₄×D₄	1	2	yes	—
292	C₂³×C₂₃	C₄×D₄	1	2	yes	—
293	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
294	Q₈×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	4	no	—
300	D₄×C₂₃	—	4	4	no	—
301	C₂×C₄×C₂₃	—	2	1	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	1	no	—
321	C₂×C₄×C₂₃	—	2	1	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	1	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	1	no	—
344	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
345	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
346	C₂×C₄×C₂₃	#131	1	2	yes	—
347	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
348	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
349	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
350	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
351	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
353	C₈×C₂₃	—	2	2	no	—
354	C₈×C₂₃	—	2	2	no	—
355	C₈×C₂₃	—	2	2	no	—
356	C₈×C₂₃	—	2	2	no	—
357	C₈×C₂₃	—	4	1	no	—
358	C₈×C₂₃	—	4	1	no	—
359	C₈×C₂₃	—	4	1	no	—
360	C₈×C₂₃	—	4	1	no	—
361	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2388	C₂×C₂₃	1	1	yes	characteristic
366	#1955	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1851	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#1753	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#1752	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₂²×C₂₃	—	2	2	no	—
377	C₂²×C₂₃	—	2	2	no	—
378	C₂²×C₂₃	—	2	2	no	—
379	C₂²×C₂₃	—	2	2	no	—
380	C₂²×C₂₃	—	2	2	no	—
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	4	1	no	—
383	C₂²×C₂₃	—	4	1	no	—
384	C₂²×C₂₃	—	4	1	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	4	1	no	—
387	C₂²×C₂₃	—	4	1	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	4	1	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	4	1	no	—
392	C₂²×C₂₃	—	4	1	no	—
393	C₂²×C₂₃	—	4	1	no	—
394	C₂²×C₂₃	—	4	1	no	—
395	C₂²×C₂₃	—	4	1	no	—
396	C₂²×C₂₃	—	4	1	no	—
397	C₂²×C₂₃	—	4	1	no	—
398	C₂²×C₂₃	—	4	1	no	—
399	C₂²×C₂₃	—	4	1	no	—
400	C₂²×C₂₃	—	4	1	no	—
401	C₂²×C₂₃	—	4	1	no	—
402	C₂²×C₂₃	—	4	1	no	—
403	C₂²×C₂₃	—	4	1	no	—
404	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
405	C₂²×C₂₃	C₂×C₄×D₄	1	1	yes	characteristic
406	C₂²×C₂₃	#518	1	1	yes	characteristic
407	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
408	C₂²×C₂₃	#568	1	1	yes	characteristic
409	C₂²×C₂₃	#568	1	1	yes	characteristic
410	C₂²×C₂₃	#568	1	1	yes	characteristic
411	C₄×C₂₃	—	2	2	no	—
412	C₄×C₂₃	—	2	2	no	—
413	C₄×C₂₃	—	2	2	no	—
414	C₄×C₂₃	—	4	1	no	—
415	C₄×C₂₃	—	4	1	no	—
416	C₄×C₂₃	—	4	1	no	—
417	C₄×C₂₃	—	4	1	no	—
418	C₄×C₂₃	—	4	1	no	—
419	C₄×C₂₃	—	4	1	no	—
420	C₄×C₂₃	—	4	1	no	—
421	C₄×C₂₃	D₄²	1	1	yes	characteristic
422	C₄×C₂₃	#546	1	1	yes	characteristic
423	C₄×C₂₃	#546	1	1	yes	characteristic
424	C₄×C₂₃	#551	1	1	yes	characteristic
425	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
426	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
427	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
429	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
434	#436	—	2	4	no	—
435	#435	—	2	4	no	—
436	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	#408	—	2	4	no	—
440	#408	—	2	4	no	—
441	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
455	#395	C₄×C₂₃	1	1	yes	characteristic
456	#394	C₄×C₂₃	1	1	yes	characteristic
457	#394	C₄×C₂₃	1	1	yes	characteristic
458	#394	C₄×C₂₃	1	1	yes	characteristic
459	#393	C₄×C₂₃	1	1	yes	characteristic
460	#392	C₄×C₂₃	1	1	yes	characteristic
461	#392	C₄×C₂₃	1	1	yes	characteristic
462	#392	C₄×C₂₃	1	1	yes	characteristic
463	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
464	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
465	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
466	#336	C₂²×C₂₃	1	1	yes	characteristic
467	#336	C₂²×C₂₃	1	1	yes	characteristic
468	#336	C₂²×C₂₃	1	1	yes	characteristic
469	#336	C₂²×C₂₃	1	1	yes	characteristic
470	#336	C₂²×C₂₃	1	1	yes	characteristic
471	#336	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₂₃	—	4	2	no	—
473	C₂×C₂₃	—	4	2	no	—
474	C₂×C₂₃	—	8	1	no	—
475	C₂×C₂₃	—	8	1	no	—
476	C₂×C₂₃	#2358	1	1	yes	characteristic
477	C₂×C₂₃	#2930	1	1	yes	characteristic
478	C₂×C₂₃	#2932	1	1	yes	characteristic
479	C₂×C₂₃	#2933	1	1	yes	characteristic
480	C₂×C₂₃	#2935	1	1	yes	characteristic
481	C₂×C₂₃	#2978	1	1	yes	characteristic
482	C₂×C₂₃	#2981	1	1	yes	characteristic
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	2	2	no	—
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	4	1	no	—
488	C₂×#41	—	4	1	no	—
489	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
490	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
491	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
492	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
493	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
494	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
495	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
496	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
497	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
498	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂×M₁₆	—	2	2	no	—
501	C₂×M₁₆	—	2	2	no	—
502	C₂×M₁₆	—	2	2	no	—
503	C₂×M₁₆	—	2	2	no	—
504	C₂×M₁₆	—	2	2	no	—
505	C₂×M₁₆	—	2	2	no	—
506	C₂×M₁₆	—	4	1	no	—
507	C₂×M₁₆	—	4	1	no	—
508	C₂×M₁₆	—	4	1	no	—
509	C₂²×C₈	—	2	2	no	—
510	C₂²×C₈	—	2	2	no	—
511	C₂²×C₈	—	2	2	no	—
512	C₂²×C₈	—	2	2	no	—
513	C₂²×C₈	—	4	1	no	—
514	C₂²×C₈	—	4	1	no	—
515	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
520	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
522	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	—	2	2	no	—
527	C₄×D₄	—	4	1	no	—
528	C₄×D₄	—	4	1	no	—
529	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
530	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
531	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
535	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
537	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
538	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
547	C₄⋊C₈	—	2	2	no	—
548	C₄⋊C₈	—	2	2	no	—
549	C₄⋊C₈	—	4	1	no	—
550	C₂²⋊C₈	—	2	2	no	—
551	C₂²⋊C₈	—	2	2	no	—
552	C₂²⋊C₈	—	2	2	no	—
553	C₂²⋊C₈	—	2	2	no	—
554	C₂²⋊C₈	—	2	2	no	—
555	C₂²⋊C₈	—	2	2	no	—
556	C₂²⋊C₈	—	2	2	no	—
557	C₂²⋊C₈	—	2	2	no	—
558	C₂²⋊C₈	—	4	1	no	—
559	C₂²⋊C₈	D₄×C₂₃	1	4	yes	complemented
560	C₂²⋊C₈	D₄×C₂₃	1	4	yes	complemented
561	#97	—	2	2	no	—
562	#97	—	4	1	no	—
563	C₄×C₈	—	2	2	no	—
564	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
565	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
566	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
567	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
568	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
569	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
570	C₂₃	#22849	1	1	yes	characteristic, direct product factor, Sylow
571	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
572	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
573	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
574	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
575	#41	—	4	4	no	—
576	#41	—	4	4	no	—
577	#41	—	4	4	no	—
578	#41	—	4	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	4	1	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	2	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	4	1	no	—
592	C₂×D₄	—	4	1	no	—
593	C₂×D₄	—	4	1	no	—
594	C₂×D₄	—	4	1	no	—
595	C₂×D₄	—	4	1	no	—
596	C₂×D₄	—	4	1	no	—
597	C₂×D₄	—	4	1	no	—
598	C₂×D₄	—	4	1	no	—
599	C₂×D₄	—	4	1	no	—
600	C₂²×C₄	—	2	1	no	—
601	C₂²×C₄	—	2	1	no	—
602	C₂²×C₄	—	2	1	no	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	1	no	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	1	no	—
616	C₂²×C₄	—	2	1	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
624	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
625	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
626	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
627	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
628	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
629	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
630	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
631	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
632	C₂²×C₄	#41×C₂₃	1	2	yes	—
633	C₂²×C₄	#41×C₂₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
635	M₁₆	—	4	4	no	—
636	M₁₆	—	4	4	no	—
637	M₁₆	—	4	4	no	—
638	C₂×C₈	—	2	1	no	—
639	C₂×C₈	—	2	1	no	—
640	C₂×C₈	—	2	1	no	—
641	C₂×C₈	—	2	1	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	—	4	4	no	—
659	C₂×C₈	—	4	4	no	—
660	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
661	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
662	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
663	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
664	C₄⋊C₄	—	2	2	no	—
665	C₄⋊C₄	—	2	2	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₂²⋊C₄	—	2	2	no	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	2	no	—
670	C₂²⋊C₄	—	2	2	no	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	4	1	no	—
674	C₂²⋊C₄	—	4	1	no	—
675	C₂²⋊C₄	—	4	1	no	—
676	C₂²⋊C₄	—	4	1	no	—
677	C₂²⋊C₄	—	4	1	no	—
678	C₂²⋊C₄	—	4	1	no	—
679	C₄²	—	2	1	no	—
680	C₄²	—	2	1	no	—
681	C₄²	—	2	1	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	1	no	—
703	C₂³	—	2	1	no	—
704	C₂³	—	2	1	no	—
705	C₂³	—	2	1	no	—
706	C₂³	—	2	1	no	—
707	C₂³	—	2	1	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	C₄×D₄×C₂₃	1	2	yes	—
712	C₂³	C₄×D₄×C₂₃	1	2	yes	—
713	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
714	Q₈	—	4	4	no	—
715	D₄	—	4	4	no	—
716	D₄	—	4	4	no	—
717	D₄	—	4	4	no	—
718	D₄	—	4	4	no	—
719	D₄	—	4	4	no	—
720	D₄	—	4	4	no	—
721	C₂×C₄	—	2	1	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	1	no	—
737	C₂×C₄	—	2	1	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
765	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
766	C₂×C₄	C₂₃×#131	1	2	yes	—
767	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
769	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
770	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
771	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
773	C₈	—	2	2	no	—
774	C₈	—	2	2	no	—
775	C₈	—	2	2	no	—
776	C₈	—	2	2	no	—
777	C₈	—	4	1	no	—
778	C₈	—	4	1	no	—
779	C₈	—	4	1	no	—
780	C₈	—	4	1	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	2	no	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	2	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	1	no	—
791	C₂²	—	4	1	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	1	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	4	1	no	—
800	C₂²	—	4	1	no	—
801	C₂²	—	4	1	no	—
802	C₂²	—	4	1	no	—
803	C₂²	—	4	1	no	—
804	C₂²	—	4	1	no	—
805	C₂²	—	4	1	no	—
806	C₂²	—	4	1	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
810	C₂²	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
811	C₂²	C₂₃×#518	1	1	yes	characteristic
812	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
813	C₂²	C₂₃×#568	1	1	yes	characteristic
814	C₂²	C₂₃×#568	1	1	yes	characteristic
815	C₂²	C₂₃×#568	1	1	yes	characteristic
816	C₄	—	2	2	no	—
817	C₄	—	2	2	no	—
818	C₄	—	2	2	no	—
819	C₄	—	4	1	no	—
820	C₄	—	4	1	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	D₄²×C₂₃	1	1	yes	characteristic
827	C₄	C₂₃×#546	1	1	yes	characteristic
828	C₄	C₂₃×#546	1	1	yes	characteristic
829	C₄	C₂₃×#551	1	1	yes	characteristic
830	C₂	—	4	2	no	—
831	C₂	—	4	2	no	—
832	C₂	—	8	1	no	—
833	C₂	—	8	1	no	—
834	C₂	C₂₃×#2358	1	1	yes	characteristic
835	C₂	C₂₃×#2930	1	1	yes	characteristic
836	C₂	C₂₃×#2932	1	1	yes	characteristic
837	C₂	C₂₃×#2933	1	1	yes	characteristic
838	C₂	C₂₃×#2935	1	1	yes	characteristic
839	C₂	C₂₃×#2978	1	1	yes	characteristic
840	C₂	C₂₃×#2981	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂₃×#2388	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#436	C₂	semidirect
2. C₂×C₂₃×#435	C₂	semidirect
3. C₂×C₂₃×#408	C₂	semidirect
4. C₂×C₂₃×#408	C₂	semidirect
6. C₂₃×#1955	C₂	semidirect
7. C₂₃×#1924	C₂	semidirect
8. C₂₃×#1923	C₂	semidirect
9. C₂₃×#1870	C₂	semidirect
10. C₂₃×#1870	C₂	semidirect
11. C₂₃×#1869	C₂	semidirect
12. C₂₃×#1851	C₂	semidirect
13. C₂₃×#1850	C₂	semidirect
14. C₂₃×#1753	C₂	semidirect
15. C₂₃×#1752	C₂	semidirect
139. C₂₃×C₂²⋊C₈	D₄	semidirect
140. C₂₃×C₂²⋊C₈	D₄	semidirect
264. #22849	C₂₃	direct (N × H)
361. C₂×#436	C₂×C₂₃	semidirect
362. C₂×#435	C₂×C₂₃	semidirect
363. C₂×#408	C₂×C₂₃	semidirect
364. C₂×#408	C₂×C₂₃	semidirect
366. #1955	C₂×C₂₃	semidirect
367. #1924	C₂×C₂₃	semidirect
368. #1923	C₂×C₂₃	semidirect
369. #1870	C₂×C₂₃	semidirect
370. #1870	C₂×C₂₃	semidirect
371. #1869	C₂×C₂₃	semidirect
372. #1851	C₂×C₂₃	semidirect
373. #1850	C₂×C₂₃	semidirect
374. #1753	C₂×C₂₃	semidirect
375. #1752	C₂×C₂₃	semidirect
559. C₂²⋊C₈	D₄×C₂₃	semidirect
560. C₂²⋊C₈	D₄×C₂₃	semidirect
570. C₂₃	#22849	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×#436	2
C₂×C₂₃×#435	2
C₂×C₂₃×#408	2
C₂₃×#2388	2
C₂₃×#1955	2
C₂₃×#1924	2
C₂₃×#1923	2
C₂₃×#1870	2
C₂₃×#1869	2
C₂₃×#1851	2
C₂₃×#1850	2
C₂₃×#1753	2
C₂₃×#1752	2
#22849	23

Subgroups — C23×#22849 #19170475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22849 #19170475