Subgroups — C₂₃×#25148 #19172774

Order 5888.

1402 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₂₃×#121	—	2	1	no	—
23	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
29	C₂₃×#459	—	2	4	no	—
30	C₂₃×#447	—	2	4	no	—
31	C₂₃×#447	—	2	4	no	—
32	C₄×D₈×C₂₃	—	2	4	no	—
33	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#394	—	2	1	no	—
48	C₂₃×#392	—	2	1	no	—
49	C₂₃×#390	C₂²	1	1	yes	characteristic
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#386	—	2	1	no	—
54	C₂₃×#386	—	2	1	no	—
55	C₂₃×#386	—	2	1	no	—
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₂₃×#379	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#340	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#336	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₂₃	—	2	1	no	—
64	C₂²×D₄×C₂₃	—	2	2	no	—
65	C₂²×D₄×C₂₃	—	2	2	no	—
66	C₂²×D₄×C₂₃	—	2	2	no	—
67	C₂²×D₄×C₂₃	—	2	2	no	—
68	C₂²×D₄×C₂₃	—	2	1	no	—
69	C₂²×D₄×C₂₃	—	2	1	no	—
70	C₂²×D₄×C₂₃	—	2	1	no	—
71	C₂²×D₄×C₂₃	—	2	1	no	—
72	C₂²×D₄×C₂₃	—	2	1	no	—
73	C₂²×D₄×C₂₃	—	4	1	no	—
74	C₂²×D₄×C₂₃	—	4	1	no	—
75	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₂₃	—	2	1	no	—
80	C₂³×C₄×C₂₃	—	2	1	no	—
81	C₂³×C₄×C₂₃	—	2	1	no	—
82	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂×D₈×C₂₃	—	2	2	no	—
84	C₂×D₈×C₂₃	—	2	2	no	—
85	C₂×D₈×C₂₃	—	2	2	no	—
86	C₂×D₈×C₂₃	—	2	2	no	—
87	C₂×D₈×C₂₃	—	2	2	no	—
88	C₂×D₈×C₂₃	—	2	2	no	—
89	C₂×D₈×C₂₃	—	2	2	no	—
90	C₂×D₈×C₂₃	—	2	2	no	—
91	C₂×D₈×C₂₃	—	2	2	no	—
92	C₂×D₈×C₂₃	—	4	1	no	—
93	C₂×D₈×C₂₃	—	4	1	no	—
94	C₂×D₈×C₂₃	D₄	1	4	yes	complemented
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	C₂₃×#127	—	2	2	no	—
100	C₂₃×#127	—	4	1	no	—
101	C₂₃×#121	—	2	2	no	—
102	C₂₃×#121	—	2	2	no	—
103	C₂₃×#121	—	4	1	no	—
104	C₂₃×#121	—	4	1	no	—
105	C₂₃×#121	—	4	4	no	—
106	C₄×D₄×C₂₃	—	2	2	no	—
107	C₄×D₄×C₂₃	—	2	2	no	—
108	C₄×D₄×C₂₃	—	2	2	no	—
109	C₄×D₄×C₂₃	—	4	1	no	—
110	C₄×D₄×C₂₃	—	4	1	no	—
111	C₄×D₄×C₂₃	—	4	1	no	—
112	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
125	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
129	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
130	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
131	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂₃×#107	—	2	2	no	—
135	C₂₃×#107	—	4	1	no	—
136	C₂₃×C₄⋊C₈	—	2	2	no	—
137	C₂₃×#102	—	2	2	no	—
138	C₂₃×#102	—	2	2	no	—
139	C₂₃×#102	—	2	2	no	—
140	C₂₃×#102	—	2	2	no	—
141	C₂₃×#102	—	2	2	no	—
142	C₂₃×#102	—	2	2	no	—
143	C₂₃×#102	—	4	1	no	—
144	C₂₃×#102	D₄	1	4	yes	complemented
145	C₂₃×C₂²⋊C₈	—	2	2	no	—
146	C₂₃×C₂²⋊C₈	—	2	2	no	—
147	C₄×C₈×C₂₃	—	2	2	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	—	2	1	no	—
150	C₂₃×#95	D₄	1	1	yes	characteristic
151	C₂₃×#95	D₄	1	1	yes	characteristic
152	C₂⁴×C₂₃	—	2	1	no	—
153	C₂⁴×C₂₃	—	2	4	no	—
154	C₂⁴×C₂₃	—	2	1	no	—
155	C₂⁴×C₂₃	—	2	1	no	—
156	C₂⁴×C₂₃	—	2	1	no	—
157	C₂⁴×C₂₃	—	4	2	no	—
158	C₂⁴×C₂₃	—	4	2	no	—
159	C₂⁴×C₂₃	—	4	2	no	—
160	C₂⁴×C₂₃	—	4	2	no	—
161	C₂⁴×C₂₃	—	8	1	no	—
162	C₂⁴×C₂₃	—	8	1	no	—
163	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₂₃	—	2	4	no	—
165	C₂×D₄×C₂₃	—	2	1	no	—
166	C₂×D₄×C₂₃	—	2	1	no	—
167	C₂×D₄×C₂₃	—	2	1	no	—
168	C₂×D₄×C₂₃	—	2	1	no	—
169	C₂×D₄×C₂₃	—	2	1	no	—
170	C₂×D₄×C₂₃	—	2	1	no	—
171	C₂×D₄×C₂₃	—	2	1	no	—
172	C₂×D₄×C₂₃	—	2	1	no	—
173	C₂×D₄×C₂₃	—	2	1	no	—
174	C₂×D₄×C₂₃	—	2	1	no	—
175	C₂×D₄×C₂₃	—	2	1	no	—
176	C₂×D₄×C₂₃	—	2	1	no	—
177	C₂×D₄×C₂₃	—	2	1	no	—
178	C₂×D₄×C₂₃	—	2	1	no	—
179	C₂×D₄×C₂₃	—	2	1	no	—
180	C₂×D₄×C₂₃	—	2	1	no	—
181	C₂×D₄×C₂₃	—	2	1	no	—
182	C₂×D₄×C₂₃	—	2	1	no	—
183	C₂×D₄×C₂₃	—	2	1	no	—
184	C₂×D₄×C₂₃	—	4	2	no	—
185	C₂×D₄×C₂₃	—	4	2	no	—
186	C₂×D₄×C₂₃	—	4	2	no	—
187	C₂×D₄×C₂₃	—	4	2	no	—
188	C₂×D₄×C₂₃	—	4	2	no	—
189	C₂×D₄×C₂₃	—	4	2	no	—
190	C₂×D₄×C₂₃	—	4	4	no	—
191	C₂×D₄×C₂₃	—	4	4	no	—
192	C₂×D₄×C₂₃	—	4	4	no	—
193	C₂×D₄×C₂₃	—	4	4	no	—
194	C₂×D₄×C₂₃	—	4	2	no	—
195	C₂×D₄×C₂₃	—	4	2	no	—
196	C₂×D₄×C₂₃	—	4	2	no	—
197	C₂×D₄×C₂₃	—	4	2	no	—
198	C₂×D₄×C₂₃	—	8	1	no	—
199	C₂×D₄×C₂₃	—	8	1	no	—
200	C₂×D₄×C₂₃	—	8	1	no	—
201	C₂×D₄×C₂₃	—	8	1	no	—
202	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
203	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₂₃	#41	1	2	yes	—
206	C₂×D₄×C₂₃	#41	1	2	yes	—
207	C₂²×C₄×C₂₃	—	2	1	no	—
208	C₂²×C₄×C₂₃	—	2	1	no	—
209	C₂²×C₄×C₂₃	—	2	1	no	—
210	C₂²×C₄×C₂₃	—	2	1	no	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	1	no	—
213	C₂²×C₄×C₂₃	—	2	1	no	—
214	C₂²×C₄×C₂₃	—	2	1	no	—
215	C₂²×C₄×C₂₃	—	2	1	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	4	2	no	—
218	C₂²×C₄×C₂₃	—	4	2	no	—
219	C₂²×C₄×C₂₃	—	4	2	no	—
220	C₂²×C₄×C₂₃	—	4	2	no	—
221	C₂²×C₄×C₂₃	—	4	2	no	—
222	C₂²×C₄×C₂₃	—	4	2	no	—
223	C₂²×C₄×C₂₃	—	8	1	no	—
224	C₂²×C₄×C₂₃	—	8	1	no	—
225	C₂²×C₄×C₂₃	—	8	1	no	—
226	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
232	D₈×C₂₃	—	2	8	no	—
233	D₈×C₂₃	—	4	4	no	—
234	D₈×C₂₃	—	4	4	no	—
235	D₈×C₂₃	—	4	4	no	—
236	C₂×C₈×C₂₃	—	2	1	no	—
237	C₂×C₈×C₂₃	—	2	1	no	—
238	C₂×C₈×C₂₃	—	2	1	no	—
239	C₂×C₈×C₂₃	—	2	1	no	—
240	C₂×C₈×C₂₃	—	2	1	no	—
241	C₂×C₈×C₂₃	—	2	1	no	—
242	C₂×C₈×C₂₃	—	2	1	no	—
243	C₂×C₈×C₂₃	—	2	1	no	—
244	C₂×C₈×C₂₃	—	2	1	no	—
245	C₂×C₈×C₂₃	—	2	1	no	—
246	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
247	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	—	2	1	no	—
250	C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₄⋊C₄×C₂₃	—	2	1	no	—
254	C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₄⋊C₄×C₂₃	—	4	2	no	—
256	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₂²⋊C₄×C₂₃	—	4	1	no	—
258	C₂²⋊C₄×C₂₃	—	4	2	no	—
259	C₂²⋊C₄×C₂₃	—	4	2	no	—
260	C₂²⋊C₄×C₂₃	—	4	2	no	—
261	C₂²⋊C₄×C₂₃	—	4	2	no	—
262	C₂²⋊C₄×C₂₃	—	4	2	no	—
263	C₂²⋊C₄×C₂₃	—	4	2	no	—
264	C₂²⋊C₄×C₂₃	—	4	2	no	—
265	C₂²⋊C₄×C₂₃	—	4	2	no	—
266	C₂²⋊C₄×C₂₃	—	4	2	no	—
267	C₂²⋊C₄×C₂₃	—	8	1	no	—
268	C₂²⋊C₄×C₂₃	—	8	1	no	—
269	C₂²⋊C₄×C₂₃	—	8	1	no	—
270	C₂²⋊C₄×C₂₃	D₈	1	4	yes	complemented
271	C₄²×C₂₃	—	2	1	no	—
272	C₄²×C₂₃	—	2	1	no	—
273	C₄²×C₂₃	—	2	1	no	—
274	C₄²×C₂₃	—	2	1	no	—
275	#25148	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	2	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	2	no	—
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	4	8	no	—
288	C₂³×C₂₃	—	4	8	no	—
289	C₂³×C₂₃	—	4	1	no	—
290	C₂³×C₂₃	—	4	1	no	—
291	C₂³×C₂₃	—	4	1	no	—
292	C₂³×C₂₃	—	4	1	no	—
293	C₂³×C₂₃	—	4	1	no	—
294	C₂³×C₂₃	—	4	1	no	—
295	C₂³×C₂₃	—	4	1	no	—
296	C₂³×C₂₃	—	4	1	no	—
297	C₂³×C₂₃	—	4	1	no	—
298	C₂³×C₂₃	—	4	1	no	—
299	C₂³×C₂₃	—	4	1	no	—
300	C₂³×C₂₃	—	4	1	no	—
301	C₂³×C₂₃	—	4	1	no	—
302	C₂³×C₂₃	—	4	1	no	—
303	C₂³×C₂₃	—	4	1	no	—
304	C₂³×C₂₃	—	4	1	no	—
305	C₂³×C₂₃	—	4	1	no	—
306	C₂³×C₂₃	—	4	1	no	—
307	C₂³×C₂₃	—	4	1	no	—
308	C₂³×C₂₃	—	4	1	no	—
309	C₂³×C₂₃	—	4	1	no	—
310	C₂³×C₂₃	—	4	1	no	—
311	C₂³×C₂₃	—	4	1	no	—
312	C₂³×C₂₃	—	8	4	no	—
313	C₂³×C₂₃	—	8	4	no	—
314	C₂³×C₂₃	—	8	4	no	—
315	C₂³×C₂₃	—	8	4	no	—
316	C₂³×C₂₃	—	8	4	no	—
317	C₂³×C₂₃	C₂×D₈	1	2	yes	—
318	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	D₄×C₂₃	—	2	2	no	—
320	D₄×C₂₃	—	2	2	no	—
321	D₄×C₂₃	—	2	2	no	—
322	D₄×C₂₃	—	2	2	no	—
323	D₄×C₂₃	—	2	2	no	—
324	D₄×C₂₃	—	2	2	no	—
325	D₄×C₂₃	—	2	2	no	—
326	D₄×C₂₃	—	4	8	no	—
327	D₄×C₂₃	—	4	1	no	—
328	D₄×C₂₃	—	4	1	no	—
329	D₄×C₂₃	—	4	1	no	—
330	D₄×C₂₃	—	4	1	no	—
331	D₄×C₂₃	—	4	1	no	—
332	D₄×C₂₃	—	4	1	no	—
333	D₄×C₂₃	—	4	1	no	—
334	D₄×C₂₃	—	4	1	no	—
335	D₄×C₂₃	—	8	4	no	—
336	D₄×C₂₃	—	8	4	no	—
337	D₄×C₂₃	—	8	4	no	—
338	D₄×C₂₃	—	8	4	no	—
339	D₄×C₂₃	#121	1	4	yes	complemented
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	1	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	2	1	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	1	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	1	no	—
351	C₂×C₄×C₂₃	—	2	1	no	—
352	C₂×C₄×C₂₃	—	2	1	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	4	1	no	—
355	C₂×C₄×C₂₃	—	4	1	no	—
356	C₂×C₄×C₂₃	—	4	1	no	—
357	C₂×C₄×C₂₃	—	4	1	no	—
358	C₂×C₄×C₂₃	—	4	1	no	—
359	C₂×C₄×C₂₃	—	4	1	no	—
360	C₂×C₄×C₂₃	—	4	1	no	—
361	C₂×C₄×C₂₃	—	4	1	no	—
362	C₂×C₄×C₂₃	—	4	1	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	1	no	—
368	C₂×C₄×C₂₃	—	4	1	no	—
369	C₂×C₄×C₂₃	—	8	4	no	—
370	C₂×C₄×C₂₃	—	8	4	no	—
371	C₂×C₄×C₂₃	—	8	4	no	—
372	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
373	C₂×C₄×C₂₃	C₂×D₈	1	2	yes	—
374	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
380	C₈×C₂₃	—	2	2	no	—
381	C₈×C₂₃	—	2	2	no	—
382	C₈×C₂₃	—	4	1	no	—
383	C₈×C₂₃	—	4	1	no	—
384	C₂×#459	C₂×C₂₃	1	1	yes	characteristic, complemented
385	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
386	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#2428	C₂×C₂₃	1	1	yes	characteristic, complemented
389	D₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#2067	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#2011	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#1970	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#1862	C₂×C₂₃	1	1	yes	characteristic, complemented
399	C₂²×C₂₃	—	2	2	no	—
400	C₂²×C₂₃	—	2	4	no	—
401	C₂²×C₂₃	—	2	2	no	—
402	C₂²×C₂₃	—	2	2	no	—
403	C₂²×C₂₃	—	4	2	no	—
404	C₂²×C₂₃	—	4	1	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	1	no	—
407	C₂²×C₂₃	—	4	1	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	2	no	—
414	C₂²×C₂₃	—	4	2	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	2	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	2	no	—
419	C₂²×C₂₃	—	8	16	no	—
420	C₂²×C₂₃	—	8	1	no	—
421	C₂²×C₂₃	—	8	1	no	—
422	C₂²×C₂₃	—	8	1	no	—
423	C₂²×C₂₃	—	8	1	no	—
424	C₂²×C₂₃	—	8	1	no	—
425	C₂²×C₂₃	—	8	1	no	—
426	C₂²×C₂₃	—	8	1	no	—
427	C₂²×C₂₃	—	8	1	no	—
428	C₂²×C₂₃	—	8	1	no	—
429	C₂²×C₂₃	—	8	1	no	—
430	C₂²×C₂₃	—	8	1	no	—
431	C₂²×C₂₃	—	8	1	no	—
432	C₂²×C₂₃	—	8	1	no	—
433	C₂²×C₂₃	—	8	1	no	—
434	C₂²×C₂₃	—	8	1	no	—
435	C₂²×C₂₃	#525	1	1	yes	characteristic
436	C₂²×C₂₃	D₄²	1	1	yes	characteristic
437	C₂²×C₂₃	D₄²	1	1	yes	characteristic
438	C₂²×C₂₃	C₂²×D₈	1	1	yes	characteristic
439	C₂²×C₂₃	#575	1	1	yes	characteristic
440	C₂²×C₂₃	#576	1	1	yes	characteristic
441	C₂²×C₂₃	#576	1	1	yes	characteristic
442	C₄×C₂₃	—	2	2	no	—
443	C₄×C₂₃	—	2	2	no	—
444	C₄×C₂₃	—	4	1	no	—
445	C₄×C₂₃	—	4	1	no	—
446	C₄×C₂₃	—	4	1	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	—	8	1	no	—
449	C₄×C₂₃	—	8	1	no	—
450	C₄×C₂₃	—	8	1	no	—
451	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
452	C₄×C₂₃	#538	1	1	yes	characteristic
453	C₄×C₂₃	#546	1	1	yes	characteristic
454	C₄×C₂₃	#546	1	1	yes	characteristic
455	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
456	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
457	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
459	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	C₂×#121	—	2	1	no	—
462	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	C₂²×C₂²⋊C₄	—	2	1	no	—
468	#459	—	2	4	no	—
469	#447	—	2	4	no	—
470	#447	—	2	4	no	—
471	C₄×D₈	—	2	4	no	—
472	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
480	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
486	#394	—	2	1	no	—
487	#392	—	2	1	no	—
488	#390	C₂²×C₂₃	1	1	yes	characteristic
489	#390	C₂²×C₂₃	1	1	yes	characteristic
490	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	#386	—	2	1	no	—
493	#386	—	2	1	no	—
494	#386	—	2	1	no	—
495	#380	C₂²×C₂₃	1	1	yes	characteristic
496	#379	—	2	1	no	—
497	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
498	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	#340	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	#336	C₂²×C₂₃	1	1	yes	characteristic, complemented
502	C₂×C₂₃	—	4	2	no	—
503	C₂×C₂₃	—	4	4	no	—
504	C₂×C₂₃	—	8	2	no	—
505	C₂×C₂₃	—	8	2	no	—
506	C₂×C₂₃	—	16	1	no	—
507	C₂×C₂₃	#2424	1	1	yes	characteristic
508	C₂×C₂₃	#3100	1	1	yes	characteristic
509	C₂×C₂₃	#3122	1	1	yes	characteristic
510	C₂×C₂₃	#3268	1	1	yes	characteristic
511	C₂×C₂₃	#3273	1	1	yes	characteristic
512	C₂×C₂₃	D₄×D₈	1	1	yes	characteristic
513	C₂×C₂₃	D₄×D₈	1	1	yes	characteristic
514	C₂⁵	—	2	1	no	—
515	C₂²×D₄	—	2	2	no	—
516	C₂²×D₄	—	2	2	no	—
517	C₂²×D₄	—	2	2	no	—
518	C₂²×D₄	—	2	2	no	—
519	C₂²×D₄	—	2	1	no	—
520	C₂²×D₄	—	2	1	no	—
521	C₂²×D₄	—	2	1	no	—
522	C₂²×D₄	—	2	1	no	—
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	4	1	no	—
525	C₂²×D₄	—	4	1	no	—
526	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
527	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×D₈	—	2	2	no	—
535	C₂×D₈	—	2	2	no	—
536	C₂×D₈	—	2	2	no	—
537	C₂×D₈	—	2	2	no	—
538	C₂×D₈	—	2	2	no	—
539	C₂×D₈	—	2	2	no	—
540	C₂×D₈	—	2	2	no	—
541	C₂×D₈	—	2	2	no	—
542	C₂×D₈	—	2	2	no	—
543	C₂×D₈	—	4	1	no	—
544	C₂×D₈	—	4	1	no	—
545	C₂×D₈	D₄×C₂₃	1	4	yes	complemented
546	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
547	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
550	#127	—	2	2	no	—
551	#127	—	4	1	no	—
552	#121	—	2	2	no	—
553	#121	—	2	2	no	—
554	#121	—	4	1	no	—
555	#121	—	4	1	no	—
556	#121	—	4	4	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	4	1	no	—
561	C₄×D₄	—	4	1	no	—
562	C₄×D₄	—	4	1	no	—
563	C₂×C₄⋊C₄	—	2	1	no	—
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	—	2	1	no	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	1	no	—
571	C₂×C₂²⋊C₄	—	2	1	no	—
572	C₂×C₂²⋊C₄	—	2	1	no	—
573	C₂×C₂²⋊C₄	—	2	1	no	—
574	C₂×C₂²⋊C₄	—	2	1	no	—
575	C₂×C₂²⋊C₄	—	2	1	no	—
576	C₂×C₂²⋊C₄	—	2	1	no	—
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	4	4	no	—
581	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
583	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
584	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
585	#107	—	2	2	no	—
586	#107	—	4	1	no	—
587	C₄⋊C₈	—	2	2	no	—
588	#102	—	2	2	no	—
589	#102	—	2	2	no	—
590	#102	—	2	2	no	—
591	#102	—	2	2	no	—
592	#102	—	2	2	no	—
593	#102	—	2	2	no	—
594	#102	—	4	1	no	—
595	#102	D₄×C₂₃	1	4	yes	complemented
596	C₂²⋊C₈	—	2	2	no	—
597	C₂²⋊C₈	—	2	2	no	—
598	C₄×C₈	—	2	2	no	—
599	#95	—	2	1	no	—
600	#95	—	2	1	no	—
601	#95	D₄×C₂₃	1	1	yes	characteristic
602	#95	D₄×C₂₃	1	1	yes	characteristic
603	C₂₃	#25148	1	1	yes	characteristic, direct product factor, Sylow
604	C₂⁴	—	2	1	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	1	no	—
607	C₂⁴	—	2	1	no	—
608	C₂⁴	—	2	1	no	—
609	C₂⁴	—	4	2	no	—
610	C₂⁴	—	4	2	no	—
611	C₂⁴	—	4	2	no	—
612	C₂⁴	—	4	2	no	—
613	C₂⁴	—	8	1	no	—
614	C₂⁴	—	8	1	no	—
615	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	1	no	—
618	C₂×D₄	—	2	1	no	—
619	C₂×D₄	—	2	1	no	—
620	C₂×D₄	—	2	1	no	—
621	C₂×D₄	—	2	1	no	—
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	1	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	1	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	2	1	no	—
636	C₂×D₄	—	4	2	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	2	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	2	no	—
642	C₂×D₄	—	4	4	no	—
643	C₂×D₄	—	4	4	no	—
644	C₂×D₄	—	4	4	no	—
645	C₂×D₄	—	4	4	no	—
646	C₂×D₄	—	4	2	no	—
647	C₂×D₄	—	4	2	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	8	1	no	—
651	C₂×D₄	—	8	1	no	—
652	C₂×D₄	—	8	1	no	—
653	C₂×D₄	—	8	1	no	—
654	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
655	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
656	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
657	C₂×D₄	#41×C₂₃	1	2	yes	—
658	C₂×D₄	#41×C₂₃	1	2	yes	—
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	8	1	no	—
676	C₂²×C₄	—	8	1	no	—
677	C₂²×C₄	—	8	1	no	—
678	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
684	D₈	—	2	8	no	—
685	D₈	—	4	4	no	—
686	D₈	—	4	4	no	—
687	D₈	—	4	4	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	2	1	no	—
690	C₂×C₈	—	2	1	no	—
691	C₂×C₈	—	2	1	no	—
692	C₂×C₈	—	2	1	no	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	1	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
699	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	1	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
709	C₂²⋊C₄	—	4	1	no	—
710	C₂²⋊C₄	—	4	2	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₂²⋊C₄	—	4	2	no	—
713	C₂²⋊C₄	—	4	2	no	—
714	C₂²⋊C₄	—	4	2	no	—
715	C₂²⋊C₄	—	4	2	no	—
716	C₂²⋊C₄	—	4	2	no	—
717	C₂²⋊C₄	—	4	2	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	8	1	no	—
720	C₂²⋊C₄	—	8	1	no	—
721	C₂²⋊C₄	—	8	1	no	—
722	C₂²⋊C₄	D₈×C₂₃	1	4	yes	complemented
723	C₄²	—	2	1	no	—
724	C₄²	—	2	1	no	—
725	C₄²	—	2	1	no	—
726	C₄²	—	2	1	no	—
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	4	8	no	—
739	C₂³	—	4	8	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	4	1	no	—
742	C₂³	—	4	1	no	—
743	C₂³	—	4	1	no	—
744	C₂³	—	4	1	no	—
745	C₂³	—	4	1	no	—
746	C₂³	—	4	1	no	—
747	C₂³	—	4	1	no	—
748	C₂³	—	4	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	—	4	1	no	—
757	C₂³	—	4	1	no	—
758	C₂³	—	4	1	no	—
759	C₂³	—	4	1	no	—
760	C₂³	—	4	1	no	—
761	C₂³	—	4	1	no	—
762	C₂³	—	4	1	no	—
763	C₂³	—	8	4	no	—
764	C₂³	—	8	4	no	—
765	C₂³	—	8	4	no	—
766	C₂³	—	8	4	no	—
767	C₂³	—	8	4	no	—
768	C₂³	C₂×D₈×C₂₃	1	2	yes	—
769	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	2	2	no	—
773	D₄	—	2	2	no	—
774	D₄	—	2	2	no	—
775	D₄	—	2	2	no	—
776	D₄	—	2	2	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	4	1	no	—
781	D₄	—	4	1	no	—
782	D₄	—	4	1	no	—
783	D₄	—	4	1	no	—
784	D₄	—	4	1	no	—
785	D₄	—	4	1	no	—
786	D₄	—	8	4	no	—
787	D₄	—	8	4	no	—
788	D₄	—	8	4	no	—
789	D₄	—	8	4	no	—
790	D₄	C₂₃×#121	1	4	yes	complemented
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	1	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	8	4	no	—
821	C₂×C₄	—	8	4	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
824	C₂×C₄	C₂×D₈×C₂₃	1	2	yes	—
825	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
828	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
829	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
830	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
831	C₈	—	2	2	no	—
832	C₈	—	2	2	no	—
833	C₈	—	4	1	no	—
834	C₈	—	4	1	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	8	16	no	—
856	C₂²	—	8	1	no	—
857	C₂²	—	8	1	no	—
858	C₂²	—	8	1	no	—
859	C₂²	—	8	1	no	—
860	C₂²	—	8	1	no	—
861	C₂²	—	8	1	no	—
862	C₂²	—	8	1	no	—
863	C₂²	—	8	1	no	—
864	C₂²	—	8	1	no	—
865	C₂²	—	8	1	no	—
866	C₂²	—	8	1	no	—
867	C₂²	—	8	1	no	—
868	C₂²	—	8	1	no	—
869	C₂²	—	8	1	no	—
870	C₂²	—	8	1	no	—
871	C₂²	C₂₃×#525	1	1	yes	characteristic
872	C₂²	D₄²×C₂₃	1	1	yes	characteristic
873	C₂²	D₄²×C₂₃	1	1	yes	characteristic
874	C₂²	C₂²×D₈×C₂₃	1	1	yes	characteristic
875	C₂²	C₂₃×#575	1	1	yes	characteristic
876	C₂²	C₂₃×#576	1	1	yes	characteristic
877	C₂²	C₂₃×#576	1	1	yes	characteristic
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	4	1	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	1	no	—
883	C₄	—	4	2	no	—
884	C₄	—	8	1	no	—
885	C₄	—	8	1	no	—
886	C₄	—	8	1	no	—
887	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
888	C₄	C₂₃×#538	1	1	yes	characteristic
889	C₄	C₂₃×#546	1	1	yes	characteristic
890	C₄	C₂₃×#546	1	1	yes	characteristic
891	C₂	—	4	2	no	—
892	C₂	—	4	4	no	—
893	C₂	—	8	2	no	—
894	C₂	—	8	2	no	—
895	C₂	—	16	1	no	—
896	C₂	C₂₃×#2424	1	1	yes	characteristic
897	C₂	C₂₃×#3100	1	1	yes	characteristic
898	C₂	C₂₃×#3122	1	1	yes	characteristic
899	C₂	C₂₃×#3268	1	1	yes	characteristic
900	C₂	C₂₃×#3273	1	1	yes	characteristic
901	C₂	D₄×D₈×C₂₃	1	1	yes	characteristic
902	C₂	D₄×D₈×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₄×C₂²⋊C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#459	C₂	semidirect
2. C₂×C₂₃×#447	C₂	semidirect
3. C₂×C₂₃×#447	C₂	semidirect
4. C₂×C₄×D₈×C₂₃	C₂	semidirect
5. C₂₃×#2428	C₂	semidirect
6. D₄×C₂²⋊C₄×C₂₃	C₂	semidirect
7. C₂₃×#2067	C₂	semidirect
8. C₂₃×#2033	C₂	semidirect
9. C₂₃×#2033	C₂	semidirect
10. C₂₃×#2011	C₂	semidirect
11. C₂₃×#1970	C₂	semidirect
12. C₂₃×#1923	C₂	semidirect
13. C₂₃×#1879	C₂	semidirect
14. C₂₃×#1879	C₂	semidirect
15. C₂₃×#1862	C₂	semidirect
21. C₂×C₂₃×#127	C₂²	semidirect
27. C₂×C₄×D₄×C₂₃	C₂²	semidirect
33. C₂×C₂₃×#107	C₂²	semidirect
34. C₂×C₂₃×#107	C₂²	semidirect
35. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
40. C₂×C₂₃×#102	C₂²	semidirect
41. C₂×C₂₃×#102	C₂²	semidirect
42. C₂×C₂₃×#102	C₂²	semidirect
43. C₂×C₂₃×#102	C₂²	semidirect
46. C₂×C₄×C₈×C₂₃	C₂²	semidirect
51. C₂₃×#390	C₂²	semidirect
52. C₂₃×#389	C₂²	semidirect
59. C₂₃×#340	C₂²	semidirect
60. C₂₃×#340	C₂²	semidirect
61. C₂₃×#336	C₂²	semidirect
62. C₂₃×#336	C₂²	semidirect
94. C₂×D₈×C₂₃	D₄	semidirect
144. C₂₃×#102	D₄	semidirect
270. C₂²⋊C₄×C₂₃	D₈	semidirect
275. #25148	C₂₃	direct (N × H)
339. D₄×C₂₃	#121	semidirect
384. C₂×#459	C₂×C₂₃	semidirect
385. C₂×#447	C₂×C₂₃	semidirect
386. C₂×#447	C₂×C₂₃	semidirect
387. C₂×C₄×D₈	C₂×C₂₃	semidirect
388. #2428	C₂×C₂₃	semidirect
389. D₄×C₂²⋊C₄	C₂×C₂₃	semidirect
390. #2067	C₂×C₂₃	semidirect
391. #2033	C₂×C₂₃	semidirect
392. #2033	C₂×C₂₃	semidirect
393. #2011	C₂×C₂₃	semidirect
394. #1970	C₂×C₂₃	semidirect
395. #1923	C₂×C₂₃	semidirect
396. #1879	C₂×C₂₃	semidirect
397. #1879	C₂×C₂₃	semidirect
398. #1862	C₂×C₂₃	semidirect
460. C₂×#127	C₂²×C₂₃	semidirect
466. C₂×C₄×D₄	C₂²×C₂₃	semidirect
472. C₂×#107	C₂²×C₂₃	semidirect
473. C₂×#107	C₂²×C₂₃	semidirect
474. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
479. C₂×#102	C₂²×C₂₃	semidirect
480. C₂×#102	C₂²×C₂₃	semidirect
481. C₂×#102	C₂²×C₂₃	semidirect
482. C₂×#102	C₂²×C₂₃	semidirect
485. C₂×C₄×C₈	C₂²×C₂₃	semidirect
490. #390	C₂²×C₂₃	semidirect
491. #389	C₂²×C₂₃	semidirect
498. #340	C₂²×C₂₃	semidirect
499. #340	C₂²×C₂₃	semidirect
500. #336	C₂²×C₂₃	semidirect
501. #336	C₂²×C₂₃	semidirect
545. C₂×D₈	D₄×C₂₃	semidirect
595. #102	D₄×C₂₃	semidirect
603. C₂₃	#25148	direct (N × H)
722. C₂²⋊C₄	D₈×C₂₃	semidirect
790. D₄	C₂₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#459	2
C₂×C₂₃×#447	2
C₂×C₄×D₈×C₂₃	2
C₂₃×#2428	2
D₄×C₂²⋊C₄×C₂₃	2
C₂₃×#2067	2
C₂₃×#2033	2
C₂₃×#2011	2
C₂₃×#1970	2
C₂₃×#1923	2
C₂₃×#1879	2
C₂₃×#1862	2
#25148	23

Subgroups — C23×#25148 #19172774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25148 #19172774