Subgroups — C₂₃×#25140 #19172766

Order 5888.

1140 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3003	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#447	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃×#100	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1907	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
25	C₂₃×#525	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
27	C₂₃×#472	—	2	4	no	—
28	C₂₃×#469	—	2	1	no	—
29	C₂₃×#468	—	2	1	no	—
30	C₂₃×#466	—	2	1	no	—
31	C₂₃×#465	—	2	1	no	—
32	C₂₃×#450	—	2	1	no	—
33	C₂₃×#450	—	2	1	no	—
34	C₂₃×#447	—	2	1	no	—
35	C₂₃×#447	—	2	1	no	—
36	C₂₃×#447	—	2	1	no	—
37	C₂₃×#447	—	2	1	no	—
38	C₂₃×#447	—	2	1	no	—
39	C₂₃×#447	—	2	1	no	—
40	C₂₃×#436	—	2	1	no	—
41	C₂₃×#435	—	2	1	no	—
42	C₂₃×#435	—	2	1	no	—
43	C₈×D₄×C₂₃	—	2	1	no	—
44	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#418	C₂²	1	1	yes	characteristic
49	C₂₃×#418	C₂²	1	1	yes	characteristic
50	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#100	—	2	4	no	—
55	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#407	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
64	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#343	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#343	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#341	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#341	C₂²	1	1	yes	characteristic, complemented
69	C₂⁵×C₂₃	—	2	1	no	—
70	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₂₃	—	2	2	no	—
72	C₂²×D₄×C₂₃	—	2	2	no	—
73	C₂²×D₄×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	—	2	1	no	—
75	C₂²×D₄×C₂₃	—	2	1	no	—
76	C₂²×D₄×C₂₃	—	2	1	no	—
77	C₂²×D₄×C₂₃	—	2	1	no	—
78	C₂²×D₄×C₂₃	—	2	1	no	—
79	C₂²×D₄×C₂₃	—	4	1	no	—
80	C₂²×D₄×C₂₃	—	4	1	no	—
81	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
86	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
87	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
88	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
89	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
90	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
91	C₂×SD₁₆×C₂₃	—	2	1	no	—
92	C₂×SD₁₆×C₂₃	—	2	1	no	—
93	C₂×SD₁₆×C₂₃	—	2	1	no	—
94	C₂×D₈×C₂₃	—	2	2	no	—
95	C₂×D₈×C₂₃	—	2	1	no	—
96	C₂×D₈×C₂₃	—	2	1	no	—
97	C₂×D₈×C₂₃	—	2	1	no	—
98	C₂×D₈×C₂₃	—	2	2	no	—
99	C₂×D₈×C₂₃	—	2	1	no	—
100	C₂×D₈×C₂₃	—	2	1	no	—
101	C₂×D₈×C₂₃	—	2	1	no	—
102	C₂×D₈×C₂₃	—	2	1	no	—
103	C₂×D₈×C₂₃	—	4	1	no	—
104	C₂×D₈×C₂₃	—	4	1	no	—
105	C₂₃×#131	—	2	2	no	—
106	C₂₃×#131	—	4	1	no	—
107	C₂×M₁₆×C₂₃	—	2	1	no	—
108	C₂×M₁₆×C₂₃	—	2	1	no	—
109	C₂×M₁₆×C₂₃	—	2	1	no	—
110	C₂×M₁₆×C₂₃	—	2	2	no	—
111	C₂×M₁₆×C₂₃	—	2	2	no	—
112	C₂×M₁₆×C₂₃	—	4	1	no	—
113	C₂×M₁₆×C₂₃	—	4	1	no	—
114	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
116	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₃	—	2	1	no	—
121	C₂²×C₈×C₂₃	—	2	1	no	—
122	C₂²×C₈×C₂₃	—	2	1	no	—
123	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂₃×#123	—	2	1	no	—
126	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
127	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₂₃×#121	—	2	1	no	—
129	C₂₃×#121	—	2	1	no	—
130	C₂₃×#121	—	2	1	no	—
131	C₂₃×#121	—	2	1	no	—
132	C₂₃×#121	D₄	1	1	yes	characteristic
133	C₂₃×#121	D₄	1	1	yes	characteristic
134	C₂₃×#120	—	2	1	no	—
135	C₄×D₄×C₂₃	—	2	1	no	—
136	C₄×D₄×C₂₃	—	2	1	no	—
137	C₂₃×#117	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
140	C₂₃×#108	—	2	2	no	—
141	C₂₃×#108	—	4	1	no	—
142	C₂₃×#107	—	2	1	no	—
143	C₂₃×#106	—	2	1	no	—
144	C₂₃×C₄⋊C₈	—	2	1	no	—
145	C₂₃×C₄⋊C₈	—	2	1	no	—
146	C₂₃×#103	—	2	1	no	—
147	C₂₃×#102	—	2	1	no	—
148	C₂₃×#102	—	2	1	no	—
149	C₂₃×#102	—	2	1	no	—
150	C₂₃×#102	—	2	1	no	—
151	C₂₃×#102	—	2	1	no	—
152	C₂₃×#102	—	2	1	no	—
153	C₂₃×#102	—	2	1	no	—
154	C₂₃×#102	—	2	1	no	—
155	C₂₃×#102	—	2	1	no	—
156	C₂₃×#102	—	2	1	no	—
157	C₂₃×#102	—	2	1	no	—
158	C₂₃×#100	—	2	2	no	—
159	C₂₃×#100	—	2	2	no	—
160	C₂₃×#100	—	2	2	no	—
161	C₂₃×#100	—	2	2	no	—
162	C₂₃×#100	—	4	1	no	—
163	C₂₃×#100	D₄	1	4	yes	complemented
164	C₂₃×C₂²⋊C₈	—	2	1	no	—
165	C₂₃×C₂²⋊C₈	—	2	1	no	—
166	C₂₃×C₂²⋊C₈	—	2	1	no	—
167	C₂₃×C₂²⋊C₈	—	2	1	no	—
168	C₂₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₂₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₂₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₂₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
172	C₂₃×#97	—	2	1	no	—
173	C₄×C₈×C₂₃	—	2	1	no	—
174	C₂⁴×C₂₃	—	2	4	no	—
175	C₂⁴×C₂₃	—	2	1	no	—
176	C₂⁴×C₂₃	—	2	1	no	—
177	C₂⁴×C₂₃	—	2	1	no	—
178	C₂⁴×C₂₃	—	4	2	no	—
179	C₂⁴×C₂₃	—	4	1	no	—
180	C₂⁴×C₂₃	—	4	1	no	—
181	C₂⁴×C₂₃	—	8	2	no	—
182	C₂⁴×C₂₃	—	8	2	no	—
183	C₂⁴×C₂₃	#41	1	1	yes	characteristic
184	#41×C₂₃	—	2	1	no	—
185	#41×C₂₃	—	2	1	no	—
186	#41×C₂₃	—	2	1	no	—
187	#41×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₂₃	—	2	4	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	2	1	no	—
192	C₂×D₄×C₂₃	—	2	1	no	—
193	C₂×D₄×C₂₃	—	2	1	no	—
194	C₂×D₄×C₂₃	—	2	1	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	1	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	1	no	—
201	C₂×D₄×C₂₃	—	2	1	no	—
202	C₂×D₄×C₂₃	—	2	1	no	—
203	C₂×D₄×C₂₃	—	2	1	no	—
204	C₂×D₄×C₂₃	—	2	1	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	2	1	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	2	1	no	—
209	C₂×D₄×C₂₃	—	4	2	no	—
210	C₂×D₄×C₂₃	—	4	2	no	—
211	C₂×D₄×C₂₃	—	4	2	no	—
212	C₂×D₄×C₂₃	—	4	2	no	—
213	C₂×D₄×C₂₃	—	4	2	no	—
214	C₂×D₄×C₂₃	—	4	2	no	—
215	C₂×D₄×C₂₃	—	4	2	no	—
216	C₂×D₄×C₂₃	—	4	2	no	—
217	C₂×D₄×C₂₃	—	4	2	no	—
218	C₂×D₄×C₂₃	—	4	1	no	—
219	C₂×D₄×C₂₃	—	4	1	no	—
220	C₂×D₄×C₂₃	—	4	1	no	—
221	C₂×D₄×C₂₃	—	4	1	no	—
222	C₂×D₄×C₂₃	—	8	2	no	—
223	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
224	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂×D₄×C₂₃	#41	1	2	yes	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
237	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
238	SD₁₆×C₂₃	—	4	2	no	—
239	SD₁₆×C₂₃	—	4	2	no	—
240	SD₁₆×C₂₃	—	4	2	no	—
241	D₈×C₂₃	—	4	2	no	—
242	D₈×C₂₃	—	4	2	no	—
243	D₈×C₂₃	—	4	2	no	—
244	D₈×C₂₃	—	4	2	no	—
245	D₈×C₂₃	—	4	2	no	—
246	D₈×C₂₃	—	4	2	no	—
247	D₈×C₂₃	—	4	2	no	—
248	M₁₆×C₂₃	—	2	1	no	—
249	M₁₆×C₂₃	—	2	1	no	—
250	M₁₆×C₂₃	—	2	1	no	—
251	M₁₆×C₂₃	—	2	1	no	—
252	M₁₆×C₂₃	—	2	1	no	—
253	M₁₆×C₂₃	—	2	1	no	—
254	M₁₆×C₂₃	—	2	1	no	—
255	M₁₆×C₂₃	—	2	1	no	—
256	M₁₆×C₂₃	—	2	1	no	—
257	M₁₆×C₂₃	—	2	1	no	—
258	M₁₆×C₂₃	—	4	2	no	—
259	M₁₆×C₂₃	—	4	2	no	—
260	M₁₆×C₂₃	—	4	2	no	—
261	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
262	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
263	C₂×C₈×C₂₃	—	2	1	no	—
264	C₂×C₈×C₂₃	—	2	1	no	—
265	C₂×C₈×C₂₃	—	2	1	no	—
266	C₂×C₈×C₂₃	—	2	1	no	—
267	C₂×C₈×C₂₃	—	2	1	no	—
268	C₂×C₈×C₂₃	—	2	1	no	—
269	C₂×C₈×C₂₃	—	2	1	no	—
270	C₂×C₈×C₂₃	—	2	1	no	—
271	C₂×C₈×C₂₃	—	2	1	no	—
272	C₂×C₈×C₂₃	—	2	1	no	—
273	C₂×C₈×C₂₃	—	4	2	no	—
274	C₂×C₈×C₂₃	—	4	2	no	—
275	C₂×C₈×C₂₃	—	4	2	no	—
276	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
279	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
285	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂²⋊C₄×C₂₃	—	2	1	no	—
287	C₂²⋊C₄×C₂₃	—	2	1	no	—
288	C₂²⋊C₄×C₂₃	—	2	1	no	—
289	C₂²⋊C₄×C₂₃	—	2	1	no	—
290	C₂²⋊C₄×C₂₃	—	2	1	no	—
291	C₂²⋊C₄×C₂₃	—	4	1	no	—
292	C₂²⋊C₄×C₂₃	—	4	1	no	—
293	C₄²×C₂₃	—	2	1	no	—
294	#25140	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₂₃	—	2	1	no	—
296	C₂³×C₂₃	—	2	1	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	2	1	no	—
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	4	1	no	—
302	C₂³×C₂₃	—	4	4	no	—
303	C₂³×C₂₃	—	4	4	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	—	8	1	no	—
312	C₂³×C₂₃	—	8	1	no	—
313	C₂³×C₂₃	—	8	1	no	—
314	C₂³×C₂₃	—	8	1	no	—
315	C₂³×C₂₃	—	8	2	no	—
316	C₂³×C₂₃	—	8	2	no	—
317	C₂³×C₂₃	—	8	2	no	—
318	C₂³×C₂₃	—	8	1	no	—
319	C₂³×C₂₃	—	8	1	no	—
320	C₂³×C₂₃	—	8	8	no	—
321	C₂³×C₂₃	—	8	8	no	—
322	C₂³×C₂₃	—	8	2	no	—
323	C₂³×C₂₃	#121	1	1	yes	characteristic
324	C₂³×C₂₃	#121	1	1	yes	characteristic
325	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
326	Q₈×C₂₃	—	2	1	no	—
327	Q₈×C₂₃	—	2	1	no	—
328	D₄×C₂₃	—	2	1	no	—
329	D₄×C₂₃	—	2	2	no	—
330	D₄×C₂₃	—	2	2	no	—
331	D₄×C₂₃	—	2	2	no	—
332	D₄×C₂₃	—	2	1	no	—
333	D₄×C₂₃	—	2	2	no	—
334	D₄×C₂₃	—	4	4	no	—
335	D₄×C₂₃	—	4	4	no	—
336	D₄×C₂₃	—	4	1	no	—
337	D₄×C₂₃	—	4	1	no	—
338	D₄×C₂₃	—	4	2	no	—
339	D₄×C₂₃	—	4	1	no	—
340	D₄×C₂₃	—	4	1	no	—
341	D₄×C₂₃	—	4	1	no	—
342	D₄×C₂₃	—	4	1	no	—
343	D₄×C₂₃	—	4	1	no	—
344	D₄×C₂₃	—	4	1	no	—
345	D₄×C₂₃	—	4	1	no	—
346	D₄×C₂₃	—	4	1	no	—
347	D₄×C₂₃	—	8	1	no	—
348	D₄×C₂₃	—	8	2	no	—
349	D₄×C₂₃	—	8	2	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	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	1	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	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	—	8	1	no	—
367	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
368	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
369	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
373	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
374	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
375	C₈×C₂₃	—	2	1	no	—
376	C₈×C₂₃	—	2	1	no	—
377	C₈×C₂₃	—	2	2	no	—
378	C₈×C₂₃	—	2	2	no	—
379	C₈×C₂₃	—	2	1	no	—
380	C₈×C₂₃	—	2	1	no	—
381	C₈×C₂₃	—	4	1	no	—
382	C₈×C₂₃	—	4	1	no	—
383	C₈×C₂₃	—	4	1	no	—
384	C₈×C₂₃	—	4	1	no	—
385	C₂×#472	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#3055	C₂×C₂₃	1	1	yes	characteristic, complemented
387	#3003	C₂×C₂₃	1	1	yes	characteristic, complemented
388	C₂×#447	C₂×C₂₃	1	1	yes	characteristic, complemented
389	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
390	C₂²×#100	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#2063	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#2051	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#2045	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#2018	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#1978	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#1931	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#1907	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#1900	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#1855	C₂×C₂₃	1	1	yes	characteristic, complemented
400	C₂²×C₂₃	—	2	1	no	—
401	C₂²×C₂₃	—	2	1	no	—
402	C₂²×C₂₃	—	2	1	no	—
403	C₂²×C₂₃	—	2	1	no	—
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	2	1	no	—
406	C₂²×C₂₃	—	2	1	no	—
407	C₂²×C₂₃	—	4	2	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	1	no	—
413	C₂²×C₂₃	—	4	1	no	—
414	C₂²×C₂₃	—	8	2	no	—
415	C₂²×C₂₃	—	8	2	no	—
416	C₂²×C₂₃	—	8	8	no	—
417	C₂²×C₂₃	—	8	2	no	—
418	C₂²×C₂₃	—	8	2	no	—
419	C₂²×C₂₃	—	8	8	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	—	16	1	no	—
428	C₂²×C₂₃	—	16	1	no	—
429	C₂²×C₂₃	#472	1	2	yes	complemented
430	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
431	C₂²×C₂₃	#525	1	1	yes	characteristic
432	C₂²×C₂₃	#538	1	1	yes	characteristic
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	1	no	—
435	C₄×C₂₃	—	4	1	no	—
436	C₄×C₂₃	—	4	1	no	—
437	C₄×C₂₃	—	4	1	no	—
438	C₄×C₂₃	—	8	1	no	—
439	C₄×C₂₃	D₄²	1	1	yes	characteristic
440	C₄×C₂₃	D₄²	1	1	yes	characteristic
441	C₄×C₂₃	#546	1	1	yes	characteristic
442	C₄×C₂₃	#546	1	1	yes	characteristic
443	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
448	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
451	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
452	#525	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
454	#472	—	2	4	no	—
455	#469	—	2	1	no	—
456	#468	—	2	1	no	—
457	#466	—	2	1	no	—
458	#465	—	2	1	no	—
459	#450	—	2	1	no	—
460	#450	—	2	1	no	—
461	#447	—	2	1	no	—
462	#447	—	2	1	no	—
463	#447	—	2	1	no	—
464	#447	—	2	1	no	—
465	#447	—	2	1	no	—
466	#447	—	2	1	no	—
467	#436	—	2	1	no	—
468	#435	—	2	1	no	—
469	#435	—	2	1	no	—
470	C₈×D₄	—	2	1	no	—
471	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
474	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	#418	C₂²×C₂₃	1	1	yes	characteristic
476	#418	C₂²×C₂₃	1	1	yes	characteristic
477	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
479	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
481	C₂×#100	—	2	4	no	—
482	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
483	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
486	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#407	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
491	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
492	#343	C₂²×C₂₃	1	1	yes	characteristic, complemented
493	#343	C₂²×C₂₃	1	1	yes	characteristic, complemented
494	#341	C₂²×C₂₃	1	1	yes	characteristic, complemented
495	#341	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	C₂×C₂₃	—	2	1	no	—
497	C₂×C₂₃	—	2	1	no	—
498	C₂×C₂₃	—	2	2	no	—
499	C₂×C₂₃	—	4	1	no	—
500	C₂×C₂₃	—	8	1	no	—
501	C₂×C₂₃	—	8	2	no	—
502	C₂×C₂₃	—	8	2	no	—
503	C₂×C₂₃	—	16	1	no	—
504	C₂×C₂₃	#2424	1	1	yes	characteristic
505	C₂×C₂₃	C₂×#472	1	1	yes	characteristic
506	C₂×C₂₃	#3068	1	1	yes	characteristic
507	C₂⁵	—	2	1	no	—
508	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	—	2	1	no	—
513	C₂²×D₄	—	2	1	no	—
514	C₂²×D₄	—	2	1	no	—
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	—	2	1	no	—
517	C₂²×D₄	—	4	1	no	—
518	C₂²×D₄	—	4	1	no	—
519	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
523	AGL(1,ℤ/8)	—	2	2	no	—
524	AGL(1,ℤ/8)	—	2	2	no	—
525	AGL(1,ℤ/8)	—	2	2	no	—
526	AGL(1,ℤ/8)	—	4	1	no	—
527	AGL(1,ℤ/8)	—	4	1	no	—
528	AGL(1,ℤ/8)	—	4	1	no	—
529	C₂×SD₁₆	—	2	1	no	—
530	C₂×SD₁₆	—	2	1	no	—
531	C₂×SD₁₆	—	2	1	no	—
532	C₂×D₈	—	2	2	no	—
533	C₂×D₈	—	2	1	no	—
534	C₂×D₈	—	2	1	no	—
535	C₂×D₈	—	2	1	no	—
536	C₂×D₈	—	2	2	no	—
537	C₂×D₈	—	2	1	no	—
538	C₂×D₈	—	2	1	no	—
539	C₂×D₈	—	2	1	no	—
540	C₂×D₈	—	2	1	no	—
541	C₂×D₈	—	4	1	no	—
542	C₂×D₈	—	4	1	no	—
543	#131	—	2	2	no	—
544	#131	—	4	1	no	—
545	C₂×M₁₆	—	2	1	no	—
546	C₂×M₁₆	—	2	1	no	—
547	C₂×M₁₆	—	2	1	no	—
548	C₂×M₁₆	—	2	2	no	—
549	C₂×M₁₆	—	2	2	no	—
550	C₂×M₁₆	—	4	1	no	—
551	C₂×M₁₆	—	4	1	no	—
552	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
553	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
554	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
555	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
556	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
557	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
558	C₂²×C₈	—	2	1	no	—
559	C₂²×C₈	—	2	1	no	—
560	C₂²×C₈	—	2	1	no	—
561	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
562	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
563	#123	—	2	1	no	—
564	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
565	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
566	#121	—	2	1	no	—
567	#121	—	2	1	no	—
568	#121	—	2	1	no	—
569	#121	—	2	1	no	—
570	#121	D₄×C₂₃	1	1	yes	characteristic
571	#121	D₄×C₂₃	1	1	yes	characteristic
572	#120	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	#117	C₂³×C₂₃	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
577	C₂×C₂²⋊C₄	—	2	1	no	—
578	#108	—	2	2	no	—
579	#108	—	4	1	no	—
580	#107	—	2	1	no	—
581	#106	—	2	1	no	—
582	C₄⋊C₈	—	2	1	no	—
583	C₄⋊C₈	—	2	1	no	—
584	#103	—	2	1	no	—
585	#102	—	2	1	no	—
586	#102	—	2	1	no	—
587	#102	—	2	1	no	—
588	#102	—	2	1	no	—
589	#102	—	2	1	no	—
590	#102	—	2	1	no	—
591	#102	—	2	1	no	—
592	#102	—	2	1	no	—
593	#102	—	2	1	no	—
594	#102	—	2	1	no	—
595	#102	—	2	1	no	—
596	#100	—	2	2	no	—
597	#100	—	2	2	no	—
598	#100	—	2	2	no	—
599	#100	—	2	2	no	—
600	#100	—	4	1	no	—
601	#100	D₄×C₂₃	1	4	yes	complemented
602	C₂²⋊C₈	—	2	1	no	—
603	C₂²⋊C₈	—	2	1	no	—
604	C₂²⋊C₈	—	2	1	no	—
605	C₂²⋊C₈	—	2	1	no	—
606	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
607	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
608	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
609	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
610	#97	—	2	1	no	—
611	C₄×C₈	—	2	1	no	—
612	C₂₃	#25140	1	1	yes	characteristic, direct product factor, Sylow
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	2	1	no	—
615	C₂⁴	—	2	1	no	—
616	C₂⁴	—	2	1	no	—
617	C₂⁴	—	4	2	no	—
618	C₂⁴	—	4	1	no	—
619	C₂⁴	—	4	1	no	—
620	C₂⁴	—	8	2	no	—
621	C₂⁴	—	8	2	no	—
622	C₂⁴	#41×C₂₃	1	1	yes	characteristic
623	#41	—	2	1	no	—
624	#41	—	2	1	no	—
625	#41	—	2	1	no	—
626	#41	—	2	1	no	—
627	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
628	C₂×D₄	—	2	4	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	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	2	no	—
651	C₂×D₄	—	4	2	no	—
652	C₂×D₄	—	4	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	1	no	—
658	C₂×D₄	—	4	1	no	—
659	C₂×D₄	—	4	1	no	—
660	C₂×D₄	—	4	1	no	—
661	C₂×D₄	—	8	2	no	—
662	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
663	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₂×D₄	#41×C₂₃	1	2	yes	—
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	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
677	SD₁₆	—	4	2	no	—
678	SD₁₆	—	4	2	no	—
679	SD₁₆	—	4	2	no	—
680	D₈	—	4	2	no	—
681	D₈	—	4	2	no	—
682	D₈	—	4	2	no	—
683	D₈	—	4	2	no	—
684	D₈	—	4	2	no	—
685	D₈	—	4	2	no	—
686	D₈	—	4	2	no	—
687	M₁₆	—	2	1	no	—
688	M₁₆	—	2	1	no	—
689	M₁₆	—	2	1	no	—
690	M₁₆	—	2	1	no	—
691	M₁₆	—	2	1	no	—
692	M₁₆	—	2	1	no	—
693	M₁₆	—	2	1	no	—
694	M₁₆	—	2	1	no	—
695	M₁₆	—	2	1	no	—
696	M₁₆	—	2	1	no	—
697	M₁₆	—	4	2	no	—
698	M₁₆	—	4	2	no	—
699	M₁₆	—	4	2	no	—
700	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
701	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	2	1	no	—
710	C₂×C₈	—	2	1	no	—
711	C₂×C₈	—	2	1	no	—
712	C₂×C₈	—	4	2	no	—
713	C₂×C₈	—	4	2	no	—
714	C₂×C₈	—	4	2	no	—
715	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
716	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
717	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
725	C₂²⋊C₄	—	2	1	no	—
726	C₂²⋊C₄	—	2	1	no	—
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	1	no	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	4	1	no	—
731	C₂²⋊C₄	—	4	1	no	—
732	C₄²	—	2	1	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	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	—	8	1	no	—
750	C₂³	—	8	1	no	—
751	C₂³	—	8	1	no	—
752	C₂³	—	8	1	no	—
753	C₂³	—	8	2	no	—
754	C₂³	—	8	2	no	—
755	C₂³	—	8	2	no	—
756	C₂³	—	8	1	no	—
757	C₂³	—	8	1	no	—
758	C₂³	—	8	8	no	—
759	C₂³	—	8	8	no	—
760	C₂³	—	8	2	no	—
761	C₂³	C₂₃×#121	1	1	yes	characteristic
762	C₂³	C₂₃×#121	1	1	yes	characteristic
763	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
764	Q₈	—	2	1	no	—
765	Q₈	—	2	1	no	—
766	D₄	—	2	1	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	1	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	1	no	—
776	D₄	—	4	1	no	—
777	D₄	—	4	1	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	—	8	1	no	—
786	D₄	—	8	2	no	—
787	D₄	—	8	2	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
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	—	4	1	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	8	1	no	—
805	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
806	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
809	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
810	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
811	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
812	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
813	C₈	—	2	1	no	—
814	C₈	—	2	1	no	—
815	C₈	—	2	2	no	—
816	C₈	—	2	2	no	—
817	C₈	—	2	1	no	—
818	C₈	—	2	1	no	—
819	C₈	—	4	1	no	—
820	C₈	—	4	1	no	—
821	C₈	—	4	1	no	—
822	C₈	—	4	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	1	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	8	2	no	—
838	C₂²	—	8	2	no	—
839	C₂²	—	8	2	no	—
840	C₂²	—	8	2	no	—
841	C₂²	—	8	8	no	—
842	C₂²	—	8	8	no	—
843	C₂²	—	8	1	no	—
844	C₂²	—	8	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	8	1	no	—
847	C₂²	—	8	1	no	—
848	C₂²	—	8	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	16	1	no	—
851	C₂²	—	16	1	no	—
852	C₂²	C₂₃×#472	1	2	yes	complemented
853	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
854	C₂²	C₂₃×#525	1	1	yes	characteristic
855	C₂²	C₂₃×#538	1	1	yes	characteristic
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	8	1	no	—
862	C₄	D₄²×C₂₃	1	1	yes	characteristic
863	C₄	D₄²×C₂₃	1	1	yes	characteristic
864	C₄	C₂₃×#546	1	1	yes	characteristic
865	C₄	C₂₃×#546	1	1	yes	characteristic
866	C₂	—	2	1	no	—
867	C₂	—	2	1	no	—
868	C₂	—	2	2	no	—
869	C₂	—	4	1	no	—
870	C₂	—	8	1	no	—
871	C₂	—	8	2	no	—
872	C₂	—	8	2	no	—
873	C₂	—	16	1	no	—
874	C₂	C₂₃×#2424	1	1	yes	characteristic
875	C₂	C₂×C₂₃×#472	1	1	yes	characteristic
876	C₂	C₂₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#472	C₂	semidirect
2. C₂₃×#3055	C₂	semidirect
3. C₂₃×#3003	C₂	semidirect
4. C₂×C₂₃×#447	C₂	semidirect
5. C₂₃×#2933	C₂	semidirect
6. C₂²×C₂₃×#100	C₂	semidirect
7. C₂₃×#2063	C₂	semidirect
8. C₂₃×#2051	C₂	semidirect
9. C₂₃×#2045	C₂	semidirect
10. C₂₃×#2018	C₂	semidirect
11. C₂₃×#1978	C₂	semidirect
12. C₂₃×#1931	C₂	semidirect
13. C₂₃×#1907	C₂	semidirect
14. C₂₃×#1900	C₂	semidirect
15. C₂₃×#1855	C₂	semidirect
19. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₂₃×#131	C₂²	semidirect
44. C₂×C₂₃×#108	C₂²	semidirect
45. C₂×C₂₃×#108	C₂²	semidirect
46. C₂₃×#428	C₂²	semidirect
47. C₂₃×#424	C₂²	semidirect
50. C₂₃×#418	C₂²	semidirect
51. C₂₃×#417	C₂²	semidirect
59. C₂×C₂₃×#100	C₂²	semidirect
60. C₂×C₂₃×#100	C₂²	semidirect
61. C₂₃×#408	C₂²	semidirect
64. C₂₃×#405	C₂²	semidirect
65. C₂₃×#343	C₂²	semidirect
66. C₂₃×#343	C₂²	semidirect
67. C₂₃×#341	C₂²	semidirect
68. C₂₃×#341	C₂²	semidirect
163. C₂₃×#100	D₄	semidirect
294. #25140	C₂₃	direct (N × H)
385. C₂×#472	C₂×C₂₃	semidirect
386. #3055	C₂×C₂₃	semidirect
387. #3003	C₂×C₂₃	semidirect
388. C₂×#447	C₂×C₂₃	semidirect
389. #2933	C₂×C₂₃	semidirect
390. C₂²×#100	C₂×C₂₃	semidirect
391. #2063	C₂×C₂₃	semidirect
392. #2051	C₂×C₂₃	semidirect
393. #2045	C₂×C₂₃	semidirect
394. #2018	C₂×C₂₃	semidirect
395. #1978	C₂×C₂₃	semidirect
396. #1931	C₂×C₂₃	semidirect
397. #1907	C₂×C₂₃	semidirect
398. #1900	C₂×C₂₃	semidirect
399. #1855	C₂×C₂₃	semidirect
429. C₂²×C₂₃	#472	semidirect
446. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
449. C₂×#131	C₂²×C₂₃	semidirect
471. C₂×#108	C₂²×C₂₃	semidirect
472. C₂×#108	C₂²×C₂₃	semidirect
473. #428	C₂²×C₂₃	semidirect
474. #424	C₂²×C₂₃	semidirect
477. #418	C₂²×C₂₃	semidirect
478. #417	C₂²×C₂₃	semidirect
486. C₂×#100	C₂²×C₂₃	semidirect
487. C₂×#100	C₂²×C₂₃	semidirect
488. #408	C₂²×C₂₃	semidirect
491. #405	C₂²×C₂₃	semidirect
492. #343	C₂²×C₂₃	semidirect
493. #343	C₂²×C₂₃	semidirect
494. #341	C₂²×C₂₃	semidirect
495. #341	C₂²×C₂₃	semidirect
601. #100	D₄×C₂₃	semidirect
612. C₂₃	#25140	direct (N × H)
852. C₂²	C₂₃×#472	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#472	2
C₂₃×#3055	2
C₂₃×#3003	2
C₂×C₂₃×#447	2
C₂₃×#2933	2
C₂²×C₂₃×#100	2
C₂₃×#2063	2
C₂₃×#2051	2
C₂₃×#2045	2
C₂₃×#2018	2
C₂₃×#1978	2
C₂₃×#1931	2
C₂₃×#1907	2
C₂₃×#1900	2
C₂₃×#1855	2
#25140	23

Subgroups — C23×#25140 #19172766

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25140 #19172766