Subgroups — C₂₃×#22477 #19170103

Order 5888.

1294 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#551	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2342	C₂	1	2	yes	maximal, complemented
3	C₂₃×#1996	C₂	1	2	yes	maximal, complemented
4	C₂₃×#1899	C₂	1	2	yes	maximal, complemented
5	C₂₃×#1898	C₂	1	2	yes	maximal
6	C₂₃×#1820	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1819	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1799	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂₃×#99	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1740	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#342	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#551	—	2	2	no	—
13	C₂₃×#551	—	2	2	no	—
14	C₂₃×#551	—	2	2	no	—
15	C₂₃×#551	—	2	2	no	—
16	C₂×C₂₃×#126	C₄	1	1	yes	characteristic, complemented
17	C₂×C₂₃×#126	C₄	1	1	yes	characteristic, complemented
18	C₂×C₂₃×#124	C₄	1	1	yes	characteristic, complemented
19	C₂×C₂₃×#123	C₄	1	1	yes	characteristic, complemented
20	C₂×C₂₃×#123	C₄	1	1	yes	characteristic, complemented
21	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic, complemented
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₄	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#117	C₄	1	1	yes	characteristic, complemented
28	C₂×C₂₃×#117	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#99	C₂²	1	2	yes	—
34	C₂×C₂₃×#99	C₂²	1	2	yes	—
35	C₂₃×#388	—	2	2	no	—
36	C₂₃×#388	—	2	2	no	—
37	C₂₃×#385	—	2	2	no	—
38	C₂₃×#381	C₂²	1	2	yes	—
39	C₂₃×#380	C₂²	1	2	yes	—
40	C₂₃×#379	C₂²	1	2	yes	—
41	C₄×C₂²⋊C₄×C₂₃	—	2	2	no	—
42	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
43	C₂₃×#342	C₂²	1	2	yes	—
44	C₂₃×#342	C₂²	1	2	yes	—
45	C₂₃×#342	C₂²	1	2	yes	—
46	C₂₃×#342	C₂²	1	2	yes	—
47	C₂₃×#342	C₂²	1	1	yes	characteristic
48	C₂₃×#342	C₂²	1	1	yes	characteristic
49	C₂₃×#342	C₂²	1	1	yes	characteristic
50	C₂₃×#342	C₂²	1	1	yes	characteristic
51	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₂₃	—	2	2	no	—
57	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
62	C₂₃×#126	—	2	2	no	—
63	C₂₃×#126	—	2	2	no	—
64	C₂₃×#126	—	2	2	no	—
65	C₂₃×#126	—	2	2	no	—
66	C₂₃×#124	—	2	2	no	—
67	C₂₃×#124	—	2	2	no	—
68	C₂₃×#123	—	2	2	no	—
69	C₂₃×#123	—	2	2	no	—
70	C₂₃×#123	—	2	2	no	—
71	C₂₃×#123	—	2	2	no	—
72	C₂₃×#123	—	2	2	no	—
73	C₂₃×#123	—	2	2	no	—
74	C₂₃×C₂²⋊Q₈	—	2	2	no	—
75	C₂₃×C₂²⋊Q₈	—	2	2	no	—
76	C₂₃×C₂²⋊Q₈	—	2	2	no	—
77	C₂₃×C₂²⋊Q₈	—	2	2	no	—
78	C₂₃×#120	—	2	2	no	—
79	C₂₃×#120	—	2	2	no	—
80	C₄×D₄×C₂₃	—	2	2	no	—
81	C₄×D₄×C₂₃	—	2	2	no	—
82	C₄×D₄×C₂₃	—	2	1	no	—
83	C₄×D₄×C₂₃	—	2	1	no	—
84	C₄×D₄×C₂₃	—	2	1	no	—
85	C₄×D₄×C₂₃	—	2	1	no	—
86	C₂₃×#117	—	2	2	no	—
87	C₂₃×#117	—	2	2	no	—
88	C₂₃×#117	—	2	1	no	—
89	C₂₃×#117	—	2	1	no	—
90	C₂₃×#117	—	2	1	no	—
91	C₂₃×#117	—	2	1	no	—
92	C₂₃×#117	—	2	4	no	—
93	C₂₃×#117	—	4	2	no	—
94	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
96	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
97	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
98	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
99	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
100	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
101	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
103	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
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×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, complemented
120	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
121	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
123	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
124	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
125	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
126	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₂₃	—	2	2	no	—
134	C₂×C₄²×C₂₃	—	2	2	no	—
135	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
136	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
137	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic, complemented
138	C₂₃×#99	—	2	4	no	—
139	C₂₃×#99	—	4	2	no	—
140	C₂₃×#95	—	2	2	no	—
141	C₂₃×#95	—	2	2	no	—
142	C₂₃×#95	—	2	2	no	—
143	C₂₃×#95	—	2	2	no	—
144	C₂⁴×C₂₃	—	2	2	no	—
145	C₂⁴×C₂₃	—	2	1	no	—
146	C₂⁴×C₂₃	—	2	1	no	—
147	C₂⁴×C₂₃	—	4	2	no	—
148	C₂⁴×C₂₃	—	8	1	no	—
149	C₂⁴×C₂₃	C₂²×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	C₂×D₄	1	2	yes	—
153	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
154	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
155	C₂×Q₈×C₂₃	—	2	2	no	—
156	C₂×Q₈×C₂₃	—	8	1	no	—
157	C₂×D₄×C₂₃	—	2	1	no	—
158	C₂×D₄×C₂₃	—	2	1	no	—
159	C₂×D₄×C₂₃	—	2	2	no	—
160	C₂×D₄×C₂₃	—	2	2	no	—
161	C₂×D₄×C₂₃	—	2	1	no	—
162	C₂×D₄×C₂₃	—	2	1	no	—
163	C₂×D₄×C₂₃	—	2	2	no	—
164	C₂×D₄×C₂₃	—	4	2	no	—
165	C₂×D₄×C₂₃	—	8	1	no	—
166	C₂²×C₄×C₂₃	—	2	2	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	—	2	1	no	—
169	C₂²×C₄×C₂₃	—	2	1	no	—
170	C₂²×C₄×C₂₃	—	2	1	no	—
171	C₂²×C₄×C₂₃	—	2	2	no	—
172	C₂²×C₄×C₂₃	—	2	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	2	no	—
177	C₂²×C₄×C₂₃	—	2	2	no	—
178	C₂²×C₄×C₂₃	—	2	2	no	—
179	C₂²×C₄×C₂₃	—	4	4	no	—
180	C₂²×C₄×C₂₃	—	4	2	no	—
181	C₂²×C₄×C₂₃	—	4	4	no	—
182	C₂²×C₄×C₂₃	—	8	1	no	—
183	C₂²×C₄×C₂₃	—	8	2	no	—
184	C₂²×C₄×C₂₃	—	8	1	no	—
185	C₂²×C₄×C₂₃	—	8	1	no	—
186	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
199	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₂₃	—	2	2	no	—
202	C₄⋊C₄×C₂₃	—	2	1	no	—
203	C₄⋊C₄×C₂₃	—	2	1	no	—
204	C₄⋊C₄×C₂₃	—	2	2	no	—
205	C₄⋊C₄×C₂₃	—	2	1	no	—
206	C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₄⋊C₄×C₂₃	—	2	2	no	—
208	C₄⋊C₄×C₂₃	—	2	1	no	—
209	C₄⋊C₄×C₂₃	—	2	1	no	—
210	C₄⋊C₄×C₂₃	—	2	2	no	—
211	C₄⋊C₄×C₂₃	—	2	2	no	—
212	C₄⋊C₄×C₂₃	—	4	4	no	—
213	C₄⋊C₄×C₂₃	—	8	2	no	—
214	C₂²⋊C₄×C₂₃	—	2	2	no	—
215	C₂²⋊C₄×C₂₃	—	2	2	no	—
216	C₂²⋊C₄×C₂₃	—	2	1	no	—
217	C₂²⋊C₄×C₂₃	—	2	1	no	—
218	C₂²⋊C₄×C₂₃	—	2	2	no	—
219	C₂²⋊C₄×C₂₃	—	2	2	no	—
220	C₂²⋊C₄×C₂₃	—	2	2	no	—
221	C₂²⋊C₄×C₂₃	—	2	2	no	—
222	C₂²⋊C₄×C₂₃	—	2	2	no	—
223	C₂²⋊C₄×C₂₃	—	2	2	no	—
224	C₂²⋊C₄×C₂₃	—	2	1	no	—
225	C₂²⋊C₄×C₂₃	—	2	1	no	—
226	C₂²⋊C₄×C₂₃	—	2	2	no	—
227	C₂²⋊C₄×C₂₃	—	2	2	no	—
228	C₂²⋊C₄×C₂₃	—	2	2	no	—
229	C₂²⋊C₄×C₂₃	—	2	2	no	—
230	C₂²⋊C₄×C₂₃	—	2	2	no	—
231	C₂²⋊C₄×C₂₃	—	2	2	no	—
232	C₂²⋊C₄×C₂₃	—	2	2	no	—
233	C₂²⋊C₄×C₂₃	—	4	4	no	—
234	C₂²⋊C₄×C₂₃	—	4	4	no	—
235	C₂²⋊C₄×C₂₃	—	8	2	no	—
236	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
237	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
238	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
239	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
240	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
241	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
242	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
243	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
244	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
245	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	2	yes	—
246	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
247	C₄²×C₂₃	—	2	1	no	—
248	C₄²×C₂₃	—	2	1	no	—
249	C₄²×C₂₃	—	2	1	no	—
250	C₄²×C₂₃	—	2	1	no	—
251	C₄²×C₂₃	—	2	1	no	—
252	C₄²×C₂₃	—	2	1	no	—
253	C₄²×C₂₃	—	4	4	no	—
254	C₄²×C₂₃	—	8	2	no	—
255	#22477	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂³×C₂₃	—	2	1	no	—
257	C₂³×C₂₃	—	2	1	no	—
258	C₂³×C₂₃	—	2	2	no	—
259	C₂³×C₂₃	—	2	2	no	—
260	C₂³×C₂₃	—	2	4	no	—
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	1	no	—
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	1	no	—
269	C₂³×C₂₃	—	4	1	no	—
270	C₂³×C₂₃	—	4	2	no	—
271	C₂³×C₂₃	—	4	1	no	—
272	C₂³×C₂₃	—	4	1	no	—
273	C₂³×C₂₃	—	4	2	no	—
274	C₂³×C₂₃	—	4	1	no	—
275	C₂³×C₂₃	—	4	1	no	—
276	C₂³×C₂₃	—	4	2	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	—	4	1	no	—
279	C₂³×C₂₃	—	8	4	no	—
280	C₂³×C₂₃	—	8	2	no	—
281	C₂³×C₂₃	—	8	2	no	—
282	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
283	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂³×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
286	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
287	C₂³×C₂₃	C₂×#41	1	2	yes	—
288	C₂³×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
289	C₂³×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
290	Q₈×C₂₃	—	8	2	no	—
291	D₄×C₂₃	—	4	2	no	—
292	D₄×C₂₃	—	4	2	no	—
293	D₄×C₂₃	—	4	2	no	—
294	D₄×C₂₃	—	4	2	no	—
295	D₄×C₂₃	—	8	2	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	1	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	2	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	4	no	—
314	C₂×C₄×C₂₃	—	4	2	no	—
315	C₂×C₄×C₂₃	—	4	2	no	—
316	C₂×C₄×C₂₃	—	4	1	no	—
317	C₂×C₄×C₂₃	—	4	1	no	—
318	C₂×C₄×C₂₃	—	4	2	no	—
319	C₂×C₄×C₂₃	—	4	2	no	—
320	C₂×C₄×C₂₃	—	4	2	no	—
321	C₂×C₄×C₂₃	—	4	2	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	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	2	no	—
329	C₂×C₄×C₂₃	—	4	2	no	—
330	C₂×C₄×C₂₃	—	4	2	no	—
331	C₂×C₄×C₂₃	—	4	2	no	—
332	C₂×C₄×C₂₃	—	4	2	no	—
333	C₂×C₄×C₂₃	—	4	2	no	—
334	C₂×C₄×C₂₃	—	4	2	no	—
335	C₂×C₄×C₂₃	—	4	2	no	—
336	C₂×C₄×C₂₃	—	4	2	no	—
337	C₂×C₄×C₂₃	—	8	1	no	—
338	C₂×C₄×C₂₃	—	8	1	no	—
339	C₂×C₄×C₂₃	—	8	1	no	—
340	C₂×C₄×C₂₃	—	8	1	no	—
341	C₂×C₄×C₂₃	—	8	8	no	—
342	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
344	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
346	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
347	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂×#551	C₂×C₂₃	1	1	yes	characteristic
349	#2342	C₂×C₂₃	1	2	yes	complemented
350	#1996	C₂×C₂₃	1	2	yes	complemented
351	#1899	C₂×C₂₃	1	2	yes	complemented
352	#1898	C₂×C₂₃	1	2	yes	—
353	#1820	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1819	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1799	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₄×#99	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1740	C₂×C₂₃	1	1	yes	characteristic, complemented
358	C₂×#342	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂²×C₂₃	—	2	1	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	2	1	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	1	no	—
364	C₂²×C₂₃	—	2	1	no	—
365	C₂²×C₂₃	—	2	1	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	2	1	no	—
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	—	2	1	no	—
370	C₂²×C₂₃	—	2	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	4	4	no	—
375	C₂²×C₂₃	—	4	4	no	—
376	C₂²×C₂₃	—	4	2	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	8	2	no	—
382	C₂²×C₂₃	—	8	2	no	—
383	C₂²×C₂₃	—	8	1	no	—
384	C₂²×C₂₃	—	8	1	no	—
385	C₂²×C₂₃	—	8	1	no	—
386	C₂²×C₂₃	—	8	1	no	—
387	C₂²×C₂₃	#410	1	2	yes	—
388	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²×C₂₃	C₄×#41	1	1	yes	characteristic
390	C₂²×C₂₃	#520	1	1	yes	characteristic
391	C₂²×C₂₃	#546	1	2	yes	—
392	C₂²×C₂₃	#547	1	2	yes	—
393	C₄×C₂₃	—	2	1	no	—
394	C₄×C₂₃	—	2	2	no	—
395	C₄×C₂₃	—	2	1	no	—
396	C₄×C₂₃	—	2	1	no	—
397	C₄×C₂₃	—	2	1	no	—
398	C₄×C₂₃	—	2	2	no	—
399	C₄×C₂₃	—	4	4	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	—	4	1	no	—
402	C₄×C₂₃	—	4	1	no	—
403	C₄×C₂₃	—	4	1	no	—
404	C₄×C₂₃	—	4	1	no	—
405	C₄×C₂₃	—	4	1	no	—
406	C₄×C₂₃	—	4	1	no	—
407	C₄×C₂₃	—	8	2	no	—
408	C₄×C₂₃	—	8	2	no	—
409	C₄×C₂₃	—	8	2	no	—
410	#551	—	2	2	no	—
411	#551	—	2	2	no	—
412	#551	—	2	2	no	—
413	#551	—	2	2	no	—
414	C₂×#126	C₄×C₂₃	1	1	yes	characteristic, complemented
415	C₂×#126	C₄×C₂₃	1	1	yes	characteristic, complemented
416	C₂×#124	C₄×C₂₃	1	1	yes	characteristic, complemented
417	C₂×#123	C₄×C₂₃	1	1	yes	characteristic, complemented
418	C₂×#123	C₄×C₂₃	1	1	yes	characteristic, complemented
419	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic, complemented
421	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×C₄×D₄	C₄×C₂₃	1	1	yes	characteristic, complemented
424	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×#117	C₄×C₂₃	1	1	yes	characteristic, complemented
426	C₂×#117	C₂²×C₂₃	1	2	yes	—
427	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
429	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
430	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#99	C₂²×C₂₃	1	2	yes	—
432	C₂×#99	C₂²×C₂₃	1	2	yes	—
433	#388	—	2	2	no	—
434	#388	—	2	2	no	—
435	#385	—	2	2	no	—
436	#381	C₂²×C₂₃	1	2	yes	—
437	#380	C₂²×C₂₃	1	2	yes	—
438	#379	C₂²×C₂₃	1	2	yes	—
439	C₄×C₂²⋊C₄	—	2	2	no	—
440	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
441	#342	C₂²×C₂₃	1	1	yes	characteristic
442	#342	C₂²×C₂₃	1	1	yes	characteristic
443	#342	C₂²×C₂₃	1	1	yes	characteristic
444	#342	C₂²×C₂₃	1	2	yes	—
445	#342	C₂²×C₂₃	1	2	yes	—
446	#342	C₂²×C₂₃	1	2	yes	—
447	#342	C₂²×C₂₃	1	2	yes	—
448	#342	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×C₂₃	—	2	2	no	—
450	C₂×C₂₃	—	2	2	no	—
451	C₂×C₂₃	—	2	2	no	—
452	C₂×C₂₃	—	2	1	no	—
453	C₂×C₂₃	—	2	1	no	—
454	C₂×C₂₃	—	4	1	no	—
455	C₂×C₂₃	—	4	2	no	—
456	C₂×C₂₃	—	8	1	no	—
457	C₂×C₂₃	#2339	1	1	yes	characteristic
458	C₂×C₂₃	C₂×#410	1	1	yes	characteristic
459	C₂×C₂₃	#2883	1	1	yes	characteristic
460	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
461	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
462	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
463	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
465	C₂³×C₄	—	2	2	no	—
466	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
467	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
468	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
469	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
471	#126	—	2	2	no	—
472	#126	—	2	2	no	—
473	#126	—	2	2	no	—
474	#126	—	2	2	no	—
475	#124	—	2	2	no	—
476	#124	—	2	2	no	—
477	#123	—	2	2	no	—
478	#123	—	2	2	no	—
479	#123	—	2	2	no	—
480	#123	—	2	2	no	—
481	#123	—	2	2	no	—
482	#123	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	2	no	—
486	C₂²⋊Q₈	—	2	2	no	—
487	#120	—	2	2	no	—
488	#120	—	2	2	no	—
489	C₄×D₄	—	2	2	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	#117	—	2	2	no	—
496	#117	—	2	2	no	—
497	#117	—	2	1	no	—
498	#117	—	2	1	no	—
499	#117	—	2	1	no	—
500	#117	—	2	1	no	—
501	#117	—	2	4	no	—
502	#117	—	4	2	no	—
503	C₂×C₄⋊C₄	—	2	2	no	—
504	C₂×C₄⋊C₄	—	2	2	no	—
505	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
506	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
507	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
508	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
509	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
510	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
511	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
512	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
513	C₂×C₂²⋊C₄	—	2	2	no	—
514	C₂×C₂²⋊C₄	—	2	2	no	—
515	C₂×C₂²⋊C₄	—	2	4	no	—
516	C₂×C₂²⋊C₄	—	2	2	no	—
517	C₂×C₂²⋊C₄	—	2	2	no	—
518	C₂×C₂²⋊C₄	—	2	2	no	—
519	C₂×C₂²⋊C₄	—	4	2	no	—
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×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
529	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
530	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
531	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
532	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
533	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
534	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
542	C₂×C₄²	—	2	2	no	—
543	C₂×C₄²	—	2	2	no	—
544	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
545	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
546	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic, complemented
547	#99	—	2	4	no	—
548	#99	—	4	2	no	—
549	#95	—	2	2	no	—
550	#95	—	2	2	no	—
551	#95	—	2	2	no	—
552	#95	—	2	2	no	—
553	C₂₃	#22477	1	1	yes	characteristic, direct product factor, Sylow
554	C₂⁴	—	2	2	no	—
555	C₂⁴	—	2	1	no	—
556	C₂⁴	—	2	1	no	—
557	C₂⁴	—	4	2	no	—
558	C₂⁴	—	8	1	no	—
559	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
560	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
561	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
562	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
563	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
564	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	8	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	8	1	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	4	4	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	4	no	—
592	C₂²×C₄	—	8	1	no	—
593	C₂²×C₄	—	8	2	no	—
594	C₂²×C₄	—	8	1	no	—
595	C₂²×C₄	—	8	1	no	—
596	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
604	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
605	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
606	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
608	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
609	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
610	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	4	4	no	—
623	C₄⋊C₄	—	8	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	1	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	2	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	1	no	—
635	C₂²⋊C₄	—	2	1	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	2	no	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	—	4	4	no	—
645	C₂²⋊C₄	—	8	2	no	—
646	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
647	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
648	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
649	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	1	yes	characteristic
650	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
651	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
652	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
653	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
654	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
655	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	2	yes	—
656	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
657	C₄²	—	2	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	2	1	no	—
660	C₄²	—	2	1	no	—
661	C₄²	—	2	1	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	4	4	no	—
664	C₄²	—	8	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	2	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	1	no	—
684	C₂³	—	4	1	no	—
685	C₂³	—	4	2	no	—
686	C₂³	—	4	1	no	—
687	C₂³	—	4	1	no	—
688	C₂³	—	8	4	no	—
689	C₂³	—	8	2	no	—
690	C₂³	—	8	2	no	—
691	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
692	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
693	C₂³	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
694	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
695	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
696	C₂³	C₂×#41×C₂₃	1	2	yes	—
697	C₂³	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂³	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
699	Q₈	—	8	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	4	2	no	—
702	D₄	—	4	2	no	—
703	D₄	—	4	2	no	—
704	D₄	—	8	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	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	1	no	—
714	C₂×C₄	—	2	1	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	4	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	4	1	no	—
737	C₂×C₄	—	4	2	no	—
738	C₂×C₄	—	4	2	no	—
739	C₂×C₄	—	4	2	no	—
740	C₂×C₄	—	4	2	no	—
741	C₂×C₄	—	4	2	no	—
742	C₂×C₄	—	4	2	no	—
743	C₂×C₄	—	4	2	no	—
744	C₂×C₄	—	4	2	no	—
745	C₂×C₄	—	4	2	no	—
746	C₂×C₄	—	8	1	no	—
747	C₂×C₄	—	8	1	no	—
748	C₂×C₄	—	8	1	no	—
749	C₂×C₄	—	8	1	no	—
750	C₂×C₄	—	8	8	no	—
751	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
752	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
753	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
754	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
755	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
756	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
757	C₂²	—	2	1	no	—
758	C₂²	—	2	2	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	1	no	—
766	C₂²	—	2	2	no	—
767	C₂²	—	2	1	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	1	no	—
772	C₂²	—	4	4	no	—
773	C₂²	—	4	4	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	1	no	—
777	C₂²	—	4	1	no	—
778	C₂²	—	4	1	no	—
779	C₂²	—	8	2	no	—
780	C₂²	—	8	2	no	—
781	C₂²	—	8	1	no	—
782	C₂²	—	8	1	no	—
783	C₂²	—	8	1	no	—
784	C₂²	—	8	1	no	—
785	C₂²	C₂₃×#410	1	2	yes	—
786	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
787	C₂²	C₄×#41×C₂₃	1	1	yes	characteristic
788	C₂²	C₂₃×#520	1	1	yes	characteristic
789	C₂²	C₂₃×#546	1	2	yes	—
790	C₂²	C₂₃×#547	1	2	yes	—
791	C₄	—	2	1	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	1	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	2	no	—
797	C₄	—	4	4	no	—
798	C₄	—	4	1	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	1	no	—
802	C₄	—	4	1	no	—
803	C₄	—	4	1	no	—
804	C₄	—	4	1	no	—
805	C₄	—	8	2	no	—
806	C₄	—	8	2	no	—
807	C₄	—	8	2	no	—
808	C₂	—	2	2	no	—
809	C₂	—	2	2	no	—
810	C₂	—	2	2	no	—
811	C₂	—	2	1	no	—
812	C₂	—	2	1	no	—
813	C₂	—	4	1	no	—
814	C₂	—	4	2	no	—
815	C₂	—	8	1	no	—
816	C₂	C₂₃×#2339	1	1	yes	characteristic
817	C₂	C₂×C₂₃×#410	1	1	yes	characteristic
818	C₂	C₂₃×#2883	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂⁴×C₂₃
prime radical	C₂×C₂₃×#120	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂²×C₂²⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2342	C₂	semidirect
3. C₂₃×#1996	C₂	semidirect
4. C₂₃×#1899	C₂	semidirect
6. C₂₃×#1820	C₂	semidirect
7. C₂₃×#1819	C₂	semidirect
8. C₂₃×#1799	C₂	semidirect
9. C₄×C₂₃×#99	C₂	semidirect
10. C₂₃×#1740	C₂	semidirect
11. C₂×C₂₃×#342	C₂	semidirect
16. C₂×C₂₃×#126	C₄	semidirect
17. C₂×C₂₃×#126	C₄	semidirect
18. C₂×C₂₃×#124	C₄	semidirect
19. C₂×C₂₃×#123	C₄	semidirect
20. C₂×C₂₃×#123	C₄	semidirect
22. C₂×C₂₃×C₂²⋊Q₈	C₄	semidirect
25. C₂×C₄×D₄×C₂₃	C₄	semidirect
27. C₂×C₂₃×#117	C₄	semidirect
52. C₂²×Q₈×C₂₃	C₂×C₄	semidirect
59. C₂³×C₄×C₂₃	C₂×C₄	semidirect
96. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
97. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
98. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
99. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
100. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
101. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
102. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
103. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
119. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
120. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
121. C₂×C₂²⋊C₄×C₂₃	C₂×C₄	semidirect
135. C₂×C₄²×C₂₃	C₂×C₄	semidirect
136. C₂×C₄²×C₂₃	C₂×C₄	semidirect
137. C₂×C₄²×C₂₃	C₂×C₄	semidirect
255. #22477	C₂₃	direct (N × H)
349. #2342	C₂×C₂₃	semidirect
350. #1996	C₂×C₂₃	semidirect
351. #1899	C₂×C₂₃	semidirect
353. #1820	C₂×C₂₃	semidirect
354. #1819	C₂×C₂₃	semidirect
355. #1799	C₂×C₂₃	semidirect
356. C₄×#99	C₂×C₂₃	semidirect
357. #1740	C₂×C₂₃	semidirect
358. C₂×#342	C₂×C₂₃	semidirect
414. C₂×#126	C₄×C₂₃	semidirect
415. C₂×#126	C₄×C₂₃	semidirect
416. C₂×#124	C₄×C₂₃	semidirect
417. C₂×#123	C₄×C₂₃	semidirect
418. C₂×#123	C₄×C₂₃	semidirect
420. C₂×C₂²⋊Q₈	C₄×C₂₃	semidirect
423. C₂×C₄×D₄	C₄×C₂₃	semidirect
425. C₂×#117	C₄×C₂₃	semidirect
461. C₂²×Q₈	C₂×C₄×C₂₃	semidirect
468. C₂³×C₄	C₂×C₄×C₂₃	semidirect
505. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
506. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
507. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
508. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
509. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
510. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
511. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
512. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
528. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
529. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
530. C₂×C₂²⋊C₄	C₂×C₄×C₂₃	semidirect
544. C₂×C₄²	C₂×C₄×C₂₃	semidirect
545. C₂×C₄²	C₂×C₄×C₂₃	semidirect
546. C₂×C₄²	C₂×C₄×C₂₃	semidirect
553. C₂₃	#22477	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×#551	2
C₂₃×#2342	2
C₂₃×#1996	2
C₂₃×#1899	2
C₂₃×#1898	2
C₂₃×#1820	2
C₂₃×#1819	2
C₂₃×#1799	2
C₄×C₂₃×#99	2
C₂₃×#1740	2
C₂×C₂₃×#342	2
#22477	23

Subgroups — C23×#22477 #19170103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#22477 #19170103