Subgroups — C₂₃×#22039 #19169665

Order 5888.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 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×#408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2388	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1780	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1753	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	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#436	—	2	4	no	—
24	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂₃×#408	—	2	4	no	—
28	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
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×#97	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#395	C₄	1	1	yes	characteristic
45	C₂₃×#394	C₄	1	1	yes	characteristic
46	C₂₃×#394	C₄	1	1	yes	characteristic
47	C₂₃×#394	C₄	1	1	yes	characteristic
48	C₂₃×#393	C₄	1	1	yes	characteristic
49	C₂₃×#392	C₄	1	1	yes	characteristic
50	C₂₃×#392	C₄	1	1	yes	characteristic
51	C₂₃×#392	C₄	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#336	C₂²	1	1	yes	characteristic
56	C₂₃×#336	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	C₂×#41×C₂₃	—	2	2	no	—
62	C₂×#41×C₂₃	—	2	2	no	—
63	C₂×#41×C₂₃	—	4	1	no	—
64	C₂×#41×C₂₃	—	4	1	no	—
65	C₂×#41×C₂₃	—	4	1	no	—
66	C₂×#41×C₂₃	—	4	1	no	—
67	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×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	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₂₃	—	2	2	no	—
79	C₂×M₁₆×C₂₃	—	4	1	no	—
80	C₂×M₁₆×C₂₃	—	4	1	no	—
81	C₂×M₁₆×C₂₃	—	4	1	no	—
82	C₂×M₁₆×C₂₃	—	4	1	no	—
83	C₂×M₁₆×C₂₃	D₄	1	4	yes	complemented
84	C₂²×C₈×C₂₃	—	2	2	no	—
85	C₂²×C₈×C₂₃	—	4	1	no	—
86	C₂²×C₈×C₂₃	—	4	1	no	—
87	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₂₃	—	2	2	no	—
96	C₄×D₄×C₂₃	—	2	2	no	—
97	C₄×D₄×C₂₃	—	4	1	no	—
98	C₄×D₄×C₂₃	—	4	1	no	—
99	C₄×D₄×C₂₃	—	4	1	no	—
100	C₄×D₄×C₂₃	—	4	1	no	—
101	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₂²⋊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×C₄²×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊C₈	—	2	2	no	—
120	C₂₃×C₄⋊C₈	—	4	1	no	—
121	C₂₃×C₄⋊C₈	—	4	1	no	—
122	C₂₃×C₂²⋊C₈	—	2	2	no	—
123	C₂₃×C₂²⋊C₈	—	2	2	no	—
124	C₂₃×C₂²⋊C₈	—	2	2	no	—
125	C₂₃×C₂²⋊C₈	—	2	2	no	—
126	C₂₃×C₂²⋊C₈	—	2	2	no	—
127	C₂₃×C₂²⋊C₈	—	2	2	no	—
128	C₂₃×C₂²⋊C₈	—	2	2	no	—
129	C₂₃×C₂²⋊C₈	—	4	1	no	—
130	C₂₃×C₂²⋊C₈	—	4	1	no	—
131	C₂₃×C₂²⋊C₈	—	4	1	no	—
132	C₂₃×C₂²⋊C₈	—	4	1	no	—
133	C₂₃×C₂²⋊C₈	—	4	1	no	—
134	C₂₃×C₂²⋊C₈	—	4	1	no	—
135	C₂₃×#97	—	4	1	no	—
136	C₄×C₈×C₂₃	—	2	2	no	—
137	C₄×C₈×C₂₃	—	4	1	no	—
138	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
139	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
140	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
141	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
142	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
143	C₂₃×#95	C₂×C₄	1	1	yes	characteristic
144	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
145	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
146	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
147	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
148	#41×C₂₃	—	4	4	no	—
149	#41×C₂₃	—	4	4	no	—
150	#41×C₂₃	—	4	4	no	—
151	#41×C₂₃	—	4	4	no	—
152	C₂×Q₈×C₂₃	—	2	2	no	—
153	C₂×Q₈×C₂₃	—	4	1	no	—
154	C₂×Q₈×C₂₃	—	4	1	no	—
155	C₂×D₄×C₂₃	—	2	2	no	—
156	C₂×D₄×C₂₃	—	2	2	no	—
157	C₂×D₄×C₂₃	—	2	2	no	—
158	C₂×D₄×C₂₃	—	2	2	no	—
159	C₂×D₄×C₂₃	—	2	2	no	—
160	C₂×D₄×C₂₃	—	2	2	no	—
161	C₂×D₄×C₂₃	—	4	1	no	—
162	C₂×D₄×C₂₃	—	4	1	no	—
163	C₂×D₄×C₂₃	—	4	1	no	—
164	C₂×D₄×C₂₃	—	4	1	no	—
165	C₂×D₄×C₂₃	—	4	1	no	—
166	C₂×D₄×C₂₃	—	4	1	no	—
167	C₂×D₄×C₂₃	—	4	1	no	—
168	C₂×D₄×C₂₃	—	4	1	no	—
169	C₂×D₄×C₂₃	—	4	1	no	—
170	C₂×D₄×C₂₃	—	4	1	no	—
171	C₂×D₄×C₂₃	—	4	1	no	—
172	C₂×D₄×C₂₃	—	4	1	no	—
173	C₂²×C₄×C₂₃	—	2	1	no	—
174	C₂²×C₄×C₂₃	—	2	1	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	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	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₂₃	#41	1	2	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
208	M₁₆×C₂₃	—	4	4	no	—
209	M₁₆×C₂₃	—	4	4	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	2	1	no	—
212	C₂×C₈×C₂₃	—	2	1	no	—
213	C₂×C₈×C₂₃	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	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	—	4	4	no	—
233	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
234	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₄⋊C₄×C₂₃	—	4	1	no	—
237	C₄⋊C₄×C₂₃	—	4	1	no	—
238	C₂²⋊C₄×C₂₃	—	2	2	no	—
239	C₂²⋊C₄×C₂₃	—	2	2	no	—
240	C₂²⋊C₄×C₂₃	—	2	2	no	—
241	C₂²⋊C₄×C₂₃	—	2	2	no	—
242	C₂²⋊C₄×C₂₃	—	2	2	no	—
243	C₂²⋊C₄×C₂₃	—	2	2	no	—
244	C₂²⋊C₄×C₂₃	—	4	1	no	—
245	C₂²⋊C₄×C₂₃	—	4	1	no	—
246	C₂²⋊C₄×C₂₃	—	4	1	no	—
247	C₂²⋊C₄×C₂₃	—	4	1	no	—
248	C₂²⋊C₄×C₂₃	—	4	1	no	—
249	C₂²⋊C₄×C₂₃	—	4	1	no	—
250	C₄²×C₂₃	—	2	1	no	—
251	C₄²×C₂₃	—	2	1	no	—
252	C₄²×C₂₃	—	2	1	no	—
253	C₄²×C₂₃	—	2	1	no	—
254	C₄²×C₂₃	—	2	1	no	—
255	C₄²×C₂₃	—	2	1	no	—
256	#22039	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	1	no	—
259	C₂³×C₂₃	—	2	1	no	—
260	C₂³×C₂₃	—	2	1	no	—
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	1	no	—
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	C₄×D₄	1	2	yes	—
285	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
286	Q₈×C₂₃	—	4	4	no	—
287	D₄×C₂₃	—	4	4	no	—
288	D₄×C₂₃	—	4	4	no	—
289	D₄×C₂₃	—	4	4	no	—
290	D₄×C₂₃	—	4	4	no	—
291	D₄×C₂₃	—	4	4	no	—
292	D₄×C₂₃	—	4	4	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	1	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	1	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	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	1	no	—
308	C₂×C₄×C₂₃	—	2	1	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	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	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	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	—	4	1	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	C₄×D₄	1	2	yes	—
337	C₂×C₄×C₂₃	#131	1	2	yes	—
338	C₂×C₄×C₂₃	#131	1	2	yes	—
339	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
341	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
345	C₈×C₂₃	—	2	2	no	—
346	C₈×C₂₃	—	2	2	no	—
347	C₈×C₂₃	—	4	1	no	—
348	C₈×C₂₃	—	4	1	no	—
349	C₈×C₂₃	—	4	1	no	—
350	C₈×C₂₃	—	4	1	no	—
351	C₈×C₂₃	—	4	1	no	—
352	C₈×C₂₃	—	4	1	no	—
353	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#2388	C₂×C₂₃	1	1	yes	characteristic
356	#1955	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1924	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
362	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
363	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
364	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#1850	C₂×C₂₃	1	1	yes	characteristic, complemented
366	#1780	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#1753	C₂×C₂₃	1	1	yes	characteristic, complemented
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	—	2	2	no	—
370	C₂²×C₂₃	—	2	2	no	—
371	C₂²×C₂₃	—	4	1	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	4	1	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	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	C₂×C₄×D₄	1	1	yes	characteristic
397	C₂²×C₂₃	#518	1	1	yes	characteristic
398	C₂²×C₂₃	#518	1	1	yes	characteristic
399	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
400	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
401	C₂²×C₂₃	#568	1	1	yes	characteristic
402	C₂²×C₂₃	#568	1	1	yes	characteristic
403	C₄×C₂₃	—	2	2	no	—
404	C₄×C₂₃	—	2	2	no	—
405	C₄×C₂₃	—	2	2	no	—
406	C₄×C₂₃	—	4	1	no	—
407	C₄×C₂₃	—	4	1	no	—
408	C₄×C₂₃	—	4	1	no	—
409	C₄×C₂₃	—	4	1	no	—
410	C₄×C₂₃	—	4	1	no	—
411	C₄×C₂₃	—	4	1	no	—
412	C₄×C₂₃	—	4	1	no	—
413	C₄×C₂₃	#534	1	1	yes	characteristic
414	C₄×C₂₃	#535	1	1	yes	characteristic
415	C₄×C₂₃	#538	1	1	yes	characteristic
416	C₄×C₂₃	#538	1	1	yes	characteristic
417	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
418	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
419	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
420	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
424	#436	—	2	4	no	—
425	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
428	#408	—	2	4	no	—
429	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
445	#395	C₄×C₂₃	1	1	yes	characteristic
446	#394	C₄×C₂₃	1	1	yes	characteristic
447	#394	C₄×C₂₃	1	1	yes	characteristic
448	#394	C₄×C₂₃	1	1	yes	characteristic
449	#393	C₄×C₂₃	1	1	yes	characteristic
450	#392	C₄×C₂₃	1	1	yes	characteristic
451	#392	C₄×C₂₃	1	1	yes	characteristic
452	#392	C₄×C₂₃	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
454	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
455	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
456	#336	C₂²×C₂₃	1	1	yes	characteristic
457	#336	C₂²×C₂₃	1	1	yes	characteristic
458	#336	C₂²×C₂₃	1	1	yes	characteristic
459	#336	C₂²×C₂₃	1	1	yes	characteristic
460	#336	C₂²×C₂₃	1	1	yes	characteristic
461	#336	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₂₃	—	4	2	no	—
463	C₂×C₂₃	—	8	1	no	—
464	C₂×C₂₃	—	8	1	no	—
465	C₂×C₂₃	—	8	1	no	—
466	C₂×C₂₃	#2321	1	1	yes	characteristic
467	C₂×C₂₃	#2933	1	1	yes	characteristic
468	C₂×C₂₃	#2935	1	1	yes	characteristic
469	C₂×C₂₃	#2976	1	1	yes	characteristic
470	C₂×C₂₃	#2978	1	1	yes	characteristic
471	C₂×C₂₃	#2979	1	1	yes	characteristic
472	C₂×C₂₃	#2981	1	1	yes	characteristic
473	C₂×#41	—	2	2	no	—
474	C₂×#41	—	2	2	no	—
475	C₂×#41	—	4	1	no	—
476	C₂×#41	—	4	1	no	—
477	C₂×#41	—	4	1	no	—
478	C₂×#41	—	4	1	no	—
479	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
480	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
481	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
482	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
483	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
484	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
485	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂×M₁₆	—	2	2	no	—
491	C₂×M₁₆	—	4	1	no	—
492	C₂×M₁₆	—	4	1	no	—
493	C₂×M₁₆	—	4	1	no	—
494	C₂×M₁₆	—	4	1	no	—
495	C₂×M₁₆	D₄×C₂₃	1	4	yes	complemented
496	C₂²×C₈	—	2	2	no	—
497	C₂²×C₈	—	4	1	no	—
498	C₂²×C₈	—	4	1	no	—
499	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
500	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
507	C₄×D₄	—	2	2	no	—
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	4	1	no	—
510	C₄×D₄	—	4	1	no	—
511	C₄×D₄	—	4	1	no	—
512	C₄×D₄	—	4	1	no	—
513	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
525	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
527	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	C₄⋊C₈	—	2	2	no	—
532	C₄⋊C₈	—	4	1	no	—
533	C₄⋊C₈	—	4	1	no	—
534	C₂²⋊C₈	—	2	2	no	—
535	C₂²⋊C₈	—	2	2	no	—
536	C₂²⋊C₈	—	2	2	no	—
537	C₂²⋊C₈	—	2	2	no	—
538	C₂²⋊C₈	—	2	2	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	4	1	no	—
542	C₂²⋊C₈	—	4	1	no	—
543	C₂²⋊C₈	—	4	1	no	—
544	C₂²⋊C₈	—	4	1	no	—
545	C₂²⋊C₈	—	4	1	no	—
546	C₂²⋊C₈	—	4	1	no	—
547	#97	—	4	1	no	—
548	C₄×C₈	—	2	2	no	—
549	C₄×C₈	—	4	1	no	—
550	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
551	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
552	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
553	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
554	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
555	#95	C₂×C₄×C₂₃	1	1	yes	characteristic
556	C₂₃	#22039	1	1	yes	characteristic, direct product factor, Sylow
557	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
558	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
559	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
560	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
561	#41	—	4	4	no	—
562	#41	—	4	4	no	—
563	#41	—	4	4	no	—
564	#41	—	4	4	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	4	1	no	—
567	C₂×Q₈	—	4	1	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	1	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	—	4	1	no	—
581	C₂×D₄	—	4	1	no	—
582	C₂×D₄	—	4	1	no	—
583	C₂×D₄	—	4	1	no	—
584	C₂×D₄	—	4	1	no	—
585	C₂×D₄	—	4	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	2	1	no	—
596	C₂²×C₄	—	2	1	no	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	1	no	—
599	C₂²×C₄	—	2	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	C₂²×C₄×C₂₃	1	1	yes	characteristic
609	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
610	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
611	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
612	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
613	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
614	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
615	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
616	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
617	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
618	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
619	C₂²×C₄	#41×C₂₃	1	2	yes	—
620	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
621	M₁₆	—	4	4	no	—
622	M₁₆	—	4	4	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	2	1	no	—
629	C₂×C₈	—	2	1	no	—
630	C₂×C₈	—	2	1	no	—
631	C₂×C₈	—	2	1	no	—
632	C₂×C₈	—	2	1	no	—
633	C₂×C₈	—	2	1	no	—
634	C₂×C₈	—	2	1	no	—
635	C₂×C₈	—	2	1	no	—
636	C₂×C₈	—	2	1	no	—
637	C₂×C₈	—	2	1	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	—	4	4	no	—
646	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
647	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
648	C₄⋊C₄	—	2	2	no	—
649	C₄⋊C₄	—	4	1	no	—
650	C₄⋊C₄	—	4	1	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	—	2	2	no	—
656	C₂²⋊C₄	—	2	2	no	—
657	C₂²⋊C₄	—	4	1	no	—
658	C₂²⋊C₄	—	4	1	no	—
659	C₂²⋊C₄	—	4	1	no	—
660	C₂²⋊C₄	—	4	1	no	—
661	C₂²⋊C₄	—	4	1	no	—
662	C₂²⋊C₄	—	4	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	—	2	1	no	—
665	C₄²	—	2	1	no	—
666	C₄²	—	2	1	no	—
667	C₄²	—	2	1	no	—
668	C₄²	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	2	1	no	—
679	C₂³	—	2	1	no	—
680	C₂³	—	2	1	no	—
681	C₂³	—	2	1	no	—
682	C₂³	—	2	1	no	—
683	C₂³	—	2	1	no	—
684	C₂³	—	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	C₄×D₄×C₂₃	1	2	yes	—
697	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
698	Q₈	—	4	4	no	—
699	D₄	—	4	4	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	4	4	no	—
703	D₄	—	4	4	no	—
704	D₄	—	4	4	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	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	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	1	no	—
738	C₂×C₄	—	4	1	no	—
739	C₂×C₄	—	4	1	no	—
740	C₂×C₄	—	4	1	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	C₄×D₄×C₂₃	1	2	yes	—
749	C₂×C₄	C₂₃×#131	1	2	yes	—
750	C₂×C₄	C₂₃×#131	1	2	yes	—
751	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
752	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
753	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
755	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
756	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
757	C₈	—	2	2	no	—
758	C₈	—	2	2	no	—
759	C₈	—	4	1	no	—
760	C₈	—	4	1	no	—
761	C₈	—	4	1	no	—
762	C₈	—	4	1	no	—
763	C₈	—	4	1	no	—
764	C₈	—	4	1	no	—
765	C₂²	—	2	2	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	2	no	—
768	C₂²	—	4	1	no	—
769	C₂²	—	4	1	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	1	no	—
774	C₂²	—	4	1	no	—
775	C₂²	—	4	1	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	4	1	no	—
780	C₂²	—	4	1	no	—
781	C₂²	—	4	1	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	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	C₂×C₄×D₄×C₂₃	1	1	yes	characteristic
794	C₂²	C₂₃×#518	1	1	yes	characteristic
795	C₂²	C₂₃×#518	1	1	yes	characteristic
796	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
797	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
798	C₂²	C₂₃×#568	1	1	yes	characteristic
799	C₂²	C₂₃×#568	1	1	yes	characteristic
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	2	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	4	1	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	1	no	—
808	C₄	—	4	1	no	—
809	C₄	—	4	1	no	—
810	C₄	C₂₃×#534	1	1	yes	characteristic
811	C₄	C₂₃×#535	1	1	yes	characteristic
812	C₄	C₂₃×#538	1	1	yes	characteristic
813	C₄	C₂₃×#538	1	1	yes	characteristic
814	C₂	—	4	2	no	—
815	C₂	—	8	1	no	—
816	C₂	—	8	1	no	—
817	C₂	—	8	1	no	—
818	C₂	C₂₃×#2321	1	1	yes	characteristic
819	C₂	C₂₃×#2933	1	1	yes	characteristic
820	C₂	C₂₃×#2935	1	1	yes	characteristic
821	C₂	C₂₃×#2976	1	1	yes	characteristic
822	C₂	C₂₃×#2978	1	1	yes	characteristic
823	C₂	C₂₃×#2979	1	1	yes	characteristic
824	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×#408	C₂	semidirect
4. C₂₃×#1955	C₂	semidirect
5. C₂₃×#1954	C₂	semidirect
6. C₂₃×#1924	C₂	semidirect
7. C₂₃×#1923	C₂	semidirect
8. C₂₃×#1923	C₂	semidirect
9. C₂₃×#1923	C₂	semidirect
10. C₂₃×#1870	C₂	semidirect
11. C₂₃×#1870	C₂	semidirect
12. C₂₃×#1869	C₂	semidirect
13. C₂₃×#1850	C₂	semidirect
14. C₂₃×#1780	C₂	semidirect
15. C₂₃×#1753	C₂	semidirect
83. C₂×M₁₆×C₂₃	D₄	semidirect
256. #22039	C₂₃	direct (N × H)
353. C₂×#436	C₂×C₂₃	semidirect
354. C₂×#408	C₂×C₂₃	semidirect
356. #1955	C₂×C₂₃	semidirect
357. #1954	C₂×C₂₃	semidirect
358. #1924	C₂×C₂₃	semidirect
359. #1923	C₂×C₂₃	semidirect
360. #1923	C₂×C₂₃	semidirect
361. #1923	C₂×C₂₃	semidirect
362. #1870	C₂×C₂₃	semidirect
363. #1870	C₂×C₂₃	semidirect
364. #1869	C₂×C₂₃	semidirect
365. #1850	C₂×C₂₃	semidirect
366. #1780	C₂×C₂₃	semidirect
367. #1753	C₂×C₂₃	semidirect
495. C₂×M₁₆	D₄×C₂₃	semidirect
556. C₂₃	#22039	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×#408	2
C₂₃×#2388	2
C₂₃×#1955	2
C₂₃×#1954	2
C₂₃×#1924	2
C₂₃×#1923	2
C₂₃×#1870	2
C₂₃×#1869	2
C₂₃×#1850	2
C₂₃×#1780	2
C₂₃×#1753	2
#22039	23

Subgroups — C23×#22039 #19169665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22039 #19169665