Subgroups — C₂₃×#25146 #19172772

Order 5888.

1012 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#471	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3055	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3004	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂₃×#101	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2052	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2019	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1908	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×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic
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×#471	—	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×#451	—	2	1	no	—
33	C₂₃×#451	—	2	1	no	—
34	C₂₃×#448	—	2	1	no	—
35	C₂₃×#448	—	2	1	no	—
36	C₂₃×#448	—	2	1	no	—
37	C₂₃×#448	—	2	1	no	—
38	C₂₃×#448	—	2	1	no	—
39	C₂₃×#448	—	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
45	C₂×C₂₃×#108	C₂²	1	1	yes	characteristic
46	C₂₃×#428	C₂²	1	1	yes	characteristic
47	C₂₃×#424	C₂²	1	1	yes	characteristic
48	C₂₃×#419	C₂²	1	1	yes	characteristic
49	C₂₃×#419	C₂²	1	1	yes	characteristic
50	C₂₃×#418	C₂²	1	1	yes	characteristic
51	C₂₃×#417	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#101	—	2	4	no	—
55	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#101	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#100	C₂²	1	1	yes	characteristic
61	C₂₃×#408	C₂²	1	1	yes	characteristic
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
65	C₂₃×#343	C₂²	1	1	yes	characteristic
66	C₂₃×#343	C₂²	1	1	yes	characteristic
67	C₂₃×#341	C₂²	1	1	yes	characteristic
68	C₂₃×#341	C₂²	1	1	yes	characteristic
69	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₂₃	—	2	2	no	—
71	C₂²×Q₈×C₂₃	—	2	2	no	—
72	C₂²×Q₈×C₂₃	—	2	1	no	—
73	C₂²×Q₈×C₂₃	—	2	1	no	—
74	C₂²×Q₈×C₂₃	—	2	1	no	—
75	C₂²×Q₈×C₂₃	—	2	1	no	—
76	C₂²×Q₈×C₂₃	—	2	1	no	—
77	C₂²×Q₈×C₂₃	—	4	1	no	—
78	C₂²×Q₈×C₂₃	—	4	1	no	—
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂₃×#137	—	2	2	no	—
86	C₂₃×#137	—	2	2	no	—
87	C₂₃×#137	—	4	1	no	—
88	C₂₃×#137	—	4	1	no	—
89	C₂₃×AGL(1,ℤ/8)	—	2	2	no	—
90	C₂₃×AGL(1,ℤ/8)	—	4	1	no	—
91	C₂×Q₁₆×C₂₃	—	2	1	no	—
92	C₂×Q₁₆×C₂₃	—	2	1	no	—
93	C₂×SD₁₆×C₂₃	—	2	2	no	—
94	C₂×SD₁₆×C₂₃	—	2	1	no	—
95	C₂×SD₁₆×C₂₃	—	2	2	no	—
96	C₂×SD₁₆×C₂₃	—	2	1	no	—
97	C₂×SD₁₆×C₂₃	—	2	1	no	—
98	C₂×SD₁₆×C₂₃	—	2	1	no	—
99	C₂×SD₁₆×C₂₃	—	2	1	no	—
100	C₂×SD₁₆×C₂₃	—	2	1	no	—
101	C₂×SD₁₆×C₂₃	—	2	1	no	—
102	C₂×SD₁₆×C₂₃	—	4	1	no	—
103	C₂×SD₁₆×C₂₃	—	4	1	no	—
104	C₂×D₈×C₂₃	—	2	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×#103	—	2	1	no	—
148	C₂₃×#103	—	2	1	no	—
149	C₂₃×#103	—	2	1	no	—
150	C₂₃×#103	—	2	1	no	—
151	C₂₃×#103	—	2	1	no	—
152	C₂₃×#103	—	2	1	no	—
153	C₂₃×#103	—	2	1	no	—
154	C₂₃×#103	—	2	1	no	—
155	C₂₃×#102	—	2	1	no	—
156	C₂₃×#102	—	2	1	no	—
157	C₂₃×#102	—	2	1	no	—
158	C₂₃×#101	—	2	2	no	—
159	C₂₃×#101	—	2	2	no	—
160	C₂₃×#101	—	2	2	no	—
161	C₂₃×#101	D₄	1	4	yes	complemented
162	C₂₃×#100	—	2	2	no	—
163	C₂₃×#100	—	4	1	no	—
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	1	no	—
175	C₂⁴×C₂₃	#41	1	1	yes	characteristic
176	#41×C₂₃	—	2	1	no	—
177	#41×C₂₃	—	2	1	no	—
178	#41×C₂₃	—	2	1	no	—
179	#41×C₂₃	—	2	1	no	—
180	C₂×Q₈×C₂₃	—	2	4	no	—
181	C₂×Q₈×C₂₃	—	2	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	—	2	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	—	2	1	no	—
187	C₂×Q₈×C₂₃	—	2	1	no	—
188	C₂×Q₈×C₂₃	—	2	1	no	—
189	C₂×Q₈×C₂₃	—	2	1	no	—
190	C₂×Q₈×C₂₃	—	2	1	no	—
191	C₂×Q₈×C₂₃	—	4	2	no	—
192	C₂×Q₈×C₂₃	—	4	2	no	—
193	C₂×Q₈×C₂₃	—	4	2	no	—
194	C₂×Q₈×C₂₃	—	4	2	no	—
195	C₂×Q₈×C₂₃	—	4	2	no	—
196	C₂×Q₈×C₂₃	—	4	2	no	—
197	C₂×Q₈×C₂₃	—	4	2	no	—
198	C₂×Q₈×C₂₃	—	4	2	no	—
199	C₂×Q₈×C₂₃	—	4	2	no	—
200	C₂×Q₈×C₂₃	—	4	1	no	—
201	C₂×Q₈×C₂₃	—	4	1	no	—
202	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
203	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
204	C₂×Q₈×C₂₃	#41	1	2	yes	—
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	—	2	1	no	—
210	C₂×D₄×C₂₃	—	2	1	no	—
211	C₂×D₄×C₂₃	—	2	1	no	—
212	C₂×D₄×C₂₃	—	2	1	no	—
213	C₂×D₄×C₂₃	—	2	1	no	—
214	C₂×D₄×C₂₃	—	4	1	no	—
215	C₂×D₄×C₂₃	—	4	1	no	—
216	C₂×D₄×C₂₃	—	8	2	no	—
217	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	1	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	1	no	—
224	C₂²×C₄×C₂₃	—	2	1	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	4	2	no	—
228	C₂²×C₄×C₂₃	—	4	1	no	—
229	C₂²×C₄×C₂₃	—	4	1	no	—
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₂₃	#41	1	1	yes	characteristic
235	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
236	Q₁₆×C₂₃	—	4	2	no	—
237	Q₁₆×C₂₃	—	4	2	no	—
238	SD₁₆×C₂₃	—	4	2	no	—
239	SD₁₆×C₂₃	—	4	2	no	—
240	SD₁₆×C₂₃	—	4	2	no	—
241	SD₁₆×C₂₃	—	4	2	no	—
242	SD₁₆×C₂₃	—	4	2	no	—
243	SD₁₆×C₂₃	—	4	2	no	—
244	SD₁₆×C₂₃	—	4	2	no	—
245	D₈×C₂₃	—	4	2	no	—
246	M₁₆×C₂₃	—	2	1	no	—
247	M₁₆×C₂₃	—	2	1	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	—	4	2	no	—
257	M₁₆×C₂₃	—	4	2	no	—
258	M₁₆×C₂₃	—	4	2	no	—
259	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
260	M₁₆×C₂₃	C₂×D₄	1	2	yes	—
261	C₂×C₈×C₂₃	—	2	1	no	—
262	C₂×C₈×C₂₃	—	2	1	no	—
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	—	4	2	no	—
272	C₂×C₈×C₂₃	—	4	2	no	—
273	C₂×C₈×C₂₃	—	4	2	no	—
274	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂×C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
283	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₂²⋊C₄×C₂₃	—	2	1	no	—
285	C₂²⋊C₄×C₂₃	—	2	1	no	—
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	—	4	1	no	—
290	C₂²⋊C₄×C₂₃	—	4	1	no	—
291	C₄²×C₂₃	—	2	1	no	—
292	#25146	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂³×C₂₃	—	2	1	no	—
294	C₂³×C₂₃	—	2	1	no	—
295	C₂³×C₂₃	—	2	2	no	—
296	C₂³×C₂₃	—	2	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	—	8	1	no	—
302	C₂³×C₂₃	—	8	1	no	—
303	C₂³×C₂₃	#121	1	1	yes	characteristic
304	C₂³×C₂₃	#121	1	1	yes	characteristic
305	C₂³×C₂₃	C₂×#41	1	1	yes	characteristic
306	Q₈×C₂₃	—	2	1	no	—
307	Q₈×C₂₃	—	2	2	no	—
308	Q₈×C₂₃	—	2	2	no	—
309	Q₈×C₂₃	—	2	2	no	—
310	Q₈×C₂₃	—	2	2	no	—
311	Q₈×C₂₃	—	2	1	no	—
312	Q₈×C₂₃	—	4	4	no	—
313	Q₈×C₂₃	—	4	4	no	—
314	Q₈×C₂₃	—	4	1	no	—
315	Q₈×C₂₃	—	4	1	no	—
316	Q₈×C₂₃	—	4	1	no	—
317	Q₈×C₂₃	—	4	1	no	—
318	D₄×C₂₃	—	2	1	no	—
319	D₄×C₂₃	—	2	1	no	—
320	D₄×C₂₃	—	4	1	no	—
321	D₄×C₂₃	—	4	1	no	—
322	D₄×C₂₃	—	4	2	no	—
323	D₄×C₂₃	—	4	1	no	—
324	D₄×C₂₃	—	4	1	no	—
325	D₄×C₂₃	—	4	1	no	—
326	D₄×C₂₃	—	4	1	no	—
327	D₄×C₂₃	—	8	1	no	—
328	D₄×C₂₃	—	8	2	no	—
329	D₄×C₂₃	—	8	2	no	—
330	C₂×C₄×C₂₃	—	2	1	no	—
331	C₂×C₄×C₂₃	—	2	1	no	—
332	C₂×C₄×C₂₃	—	2	1	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	1	no	—
336	C₂×C₄×C₂₃	—	2	1	no	—
337	C₂×C₄×C₂₃	—	2	1	no	—
338	C₂×C₄×C₂₃	—	2	1	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
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	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	4	4	no	—
346	C₂×C₄×C₂₃	—	4	4	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	4	1	no	—
351	C₂×C₄×C₂₃	—	4	1	no	—
352	C₂×C₄×C₂₃	—	4	1	no	—
353	C₂×C₄×C₂₃	—	4	1	no	—
354	C₂×C₄×C₂₃	—	8	1	no	—
355	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
356	C₂×C₄×C₂₃	#121	1	1	yes	characteristic
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
361	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
363	C₈×C₂₃	—	2	1	no	—
364	C₈×C₂₃	—	2	1	no	—
365	C₈×C₂₃	—	2	2	no	—
366	C₈×C₂₃	—	2	2	no	—
367	C₈×C₂₃	—	2	1	no	—
368	C₈×C₂₃	—	2	1	no	—
369	C₈×C₂₃	—	4	1	no	—
370	C₈×C₂₃	—	4	1	no	—
371	C₈×C₂₃	—	4	1	no	—
372	C₈×C₂₃	—	4	1	no	—
373	C₂×#471	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#3055	C₂×C₂₃	1	1	yes	characteristic
375	#3004	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂²×#101	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#2064	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2052	C₂×C₂₃	1	1	yes	characteristic, complemented
381	#2046	C₂×C₂₃	1	1	yes	characteristic, complemented
382	#2019	C₂×C₂₃	1	1	yes	characteristic, complemented
383	#1977	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#1930	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#1908	C₂×C₂₃	1	1	yes	characteristic, complemented
386	#1900	C₂×C₂₃	1	1	yes	characteristic, complemented
387	#1855	C₂×C₂₃	1	1	yes	characteristic, complemented
388	C₂²×C₂₃	—	2	1	no	—
389	C₂²×C₂₃	—	2	1	no	—
390	C₂²×C₂₃	—	2	1	no	—
391	C₂²×C₂₃	—	2	1	no	—
392	C₂²×C₂₃	—	2	1	no	—
393	C₂²×C₂₃	—	2	1	no	—
394	C₂²×C₂₃	—	2	1	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	4	1	no	—
398	C₂²×C₂₃	—	4	1	no	—
399	C₂²×C₂₃	—	4	1	no	—
400	C₂²×C₂₃	—	8	1	no	—
401	C₂²×C₂₃	—	8	1	no	—
402	C₂²×C₂₃	—	8	1	no	—
403	C₂²×C₂₃	—	16	1	no	—
404	C₂²×C₂₃	—	16	1	no	—
405	C₂²×C₂₃	#471	1	2	yes	complemented
406	C₂²×C₂₃	C₂×#121	1	1	yes	characteristic
407	C₂²×C₂₃	#525	1	1	yes	characteristic
408	C₂²×C₂₃	#538	1	1	yes	characteristic
409	C₄×C₂₃	—	2	1	no	—
410	C₄×C₂₃	—	2	1	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	2	no	—
413	C₄×C₂₃	—	4	1	no	—
414	C₄×C₂₃	—	4	1	no	—
415	C₄×C₂₃	—	4	1	no	—
416	C₄×C₂₃	—	8	1	no	—
417	C₄×C₂₃	D₄²	1	1	yes	characteristic
418	C₄×C₂₃	D₄²	1	1	yes	characteristic
419	C₄×C₂₃	#546	1	1	yes	characteristic
420	C₄×C₂₃	#546	1	1	yes	characteristic
421	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
425	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
426	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
429	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
430	#525	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
432	#471	—	2	4	no	—
433	#469	—	2	1	no	—
434	#468	—	2	1	no	—
435	#466	—	2	1	no	—
436	#465	—	2	1	no	—
437	#451	—	2	1	no	—
438	#451	—	2	1	no	—
439	#448	—	2	1	no	—
440	#448	—	2	1	no	—
441	#448	—	2	1	no	—
442	#448	—	2	1	no	—
443	#448	—	2	1	no	—
444	#448	—	2	1	no	—
445	#436	—	2	1	no	—
446	#435	—	2	1	no	—
447	#435	—	2	1	no	—
448	C₈×D₄	—	2	1	no	—
449	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×#108	C₂²×C₂₃	1	1	yes	characteristic
451	#428	C₂²×C₂₃	1	1	yes	characteristic
452	#424	C₂²×C₂₃	1	1	yes	characteristic
453	#419	C₂²×C₂₃	1	1	yes	characteristic
454	#419	C₂²×C₂₃	1	1	yes	characteristic
455	#418	C₂²×C₂₃	1	1	yes	characteristic
456	#417	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×#101	—	2	4	no	—
460	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×#101	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#100	C₂²×C₂₃	1	1	yes	characteristic
466	#408	C₂²×C₂₃	1	1	yes	characteristic
467	#407	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
469	#405	C₂²×C₂₃	1	1	yes	characteristic
470	#343	C₂²×C₂₃	1	1	yes	characteristic
471	#343	C₂²×C₂₃	1	1	yes	characteristic
472	#341	C₂²×C₂₃	1	1	yes	characteristic
473	#341	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×C₂₃	—	2	1	no	—
475	C₂×C₂₃	—	2	1	no	—
476	C₂×C₂₃	—	2	2	no	—
477	C₂×C₂₃	—	4	1	no	—
478	C₂×C₂₃	—	8	1	no	—
479	C₂×C₂₃	—	16	1	no	—
480	C₂×C₂₃	#2424	1	1	yes	characteristic
481	C₂×C₂₃	C₂×#471	1	1	yes	characteristic
482	C₂×C₂₃	#3069	1	1	yes	characteristic
483	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
484	C₂²×Q₈	—	2	2	no	—
485	C₂²×Q₈	—	2	2	no	—
486	C₂²×Q₈	—	2	1	no	—
487	C₂²×Q₈	—	2	1	no	—
488	C₂²×Q₈	—	2	1	no	—
489	C₂²×Q₈	—	2	1	no	—
490	C₂²×Q₈	—	2	1	no	—
491	C₂²×Q₈	—	4	1	no	—
492	C₂²×Q₈	—	4	1	no	—
493	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
494	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
497	C₂³×C₄	—	2	1	no	—
498	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
499	#137	—	2	2	no	—
500	#137	—	2	2	no	—
501	#137	—	4	1	no	—
502	#137	—	4	1	no	—
503	AGL(1,ℤ/8)	—	2	2	no	—
504	AGL(1,ℤ/8)	—	4	1	no	—
505	C₂×Q₁₆	—	2	1	no	—
506	C₂×Q₁₆	—	2	1	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	—	2	1	no	—
509	C₂×SD₁₆	—	2	2	no	—
510	C₂×SD₁₆	—	2	1	no	—
511	C₂×SD₁₆	—	2	1	no	—
512	C₂×SD₁₆	—	2	1	no	—
513	C₂×SD₁₆	—	2	1	no	—
514	C₂×SD₁₆	—	2	1	no	—
515	C₂×SD₁₆	—	2	1	no	—
516	C₂×SD₁₆	—	4	1	no	—
517	C₂×SD₁₆	—	4	1	no	—
518	C₂×D₈	—	2	1	no	—
519	#131	—	2	2	no	—
520	#131	—	4	1	no	—
521	C₂×M₁₆	—	2	1	no	—
522	C₂×M₁₆	—	2	1	no	—
523	C₂×M₁₆	—	2	1	no	—
524	C₂×M₁₆	—	2	2	no	—
525	C₂×M₁₆	—	2	2	no	—
526	C₂×M₁₆	—	4	1	no	—
527	C₂×M₁₆	—	4	1	no	—
528	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
533	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
534	C₂²×C₈	—	2	1	no	—
535	C₂²×C₈	—	2	1	no	—
536	C₂²×C₈	—	2	1	no	—
537	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
539	#123	—	2	1	no	—
540	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
541	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	D₄×C₂₃	1	1	yes	characteristic
547	#121	D₄×C₂₃	1	1	yes	characteristic
548	#120	—	2	1	no	—
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	—	2	1	no	—
551	#117	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₄	—	2	1	no	—
554	#108	—	2	2	no	—
555	#108	—	4	1	no	—
556	#107	—	2	1	no	—
557	#106	—	2	1	no	—
558	C₄⋊C₈	—	2	1	no	—
559	C₄⋊C₈	—	2	1	no	—
560	#103	—	2	1	no	—
561	#103	—	2	1	no	—
562	#103	—	2	1	no	—
563	#103	—	2	1	no	—
564	#103	—	2	1	no	—
565	#103	—	2	1	no	—
566	#103	—	2	1	no	—
567	#103	—	2	1	no	—
568	#103	—	2	1	no	—
569	#102	—	2	1	no	—
570	#102	—	2	1	no	—
571	#102	—	2	1	no	—
572	#101	—	2	2	no	—
573	#101	—	2	2	no	—
574	#101	—	2	2	no	—
575	#101	D₄×C₂₃	1	4	yes	complemented
576	#100	—	2	2	no	—
577	#100	—	4	1	no	—
578	C₂²⋊C₈	—	2	1	no	—
579	C₂²⋊C₈	—	2	1	no	—
580	C₂²⋊C₈	—	2	1	no	—
581	C₂²⋊C₈	—	2	1	no	—
582	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
583	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
584	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
585	C₂²⋊C₈	D₄×C₂₃	1	1	yes	characteristic
586	#97	—	2	1	no	—
587	C₄×C₈	—	2	1	no	—
588	C₂₃	#25146	1	1	yes	characteristic, direct product factor, Sylow
589	C₂⁴	—	2	1	no	—
590	C₂⁴	#41×C₂₃	1	1	yes	characteristic
591	#41	—	2	1	no	—
592	#41	—	2	1	no	—
593	#41	—	2	1	no	—
594	#41	—	2	1	no	—
595	C₂×Q₈	—	2	4	no	—
596	C₂×Q₈	—	2	1	no	—
597	C₂×Q₈	—	2	1	no	—
598	C₂×Q₈	—	2	1	no	—
599	C₂×Q₈	—	2	1	no	—
600	C₂×Q₈	—	2	1	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	1	no	—
604	C₂×Q₈	—	2	1	no	—
605	C₂×Q₈	—	2	1	no	—
606	C₂×Q₈	—	4	2	no	—
607	C₂×Q₈	—	4	2	no	—
608	C₂×Q₈	—	4	2	no	—
609	C₂×Q₈	—	4	2	no	—
610	C₂×Q₈	—	4	2	no	—
611	C₂×Q₈	—	4	2	no	—
612	C₂×Q₈	—	4	2	no	—
613	C₂×Q₈	—	4	2	no	—
614	C₂×Q₈	—	4	2	no	—
615	C₂×Q₈	—	4	1	no	—
616	C₂×Q₈	—	4	1	no	—
617	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
618	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
619	C₂×Q₈	#41×C₂₃	1	2	yes	—
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	—	4	1	no	—
630	C₂×D₄	—	4	1	no	—
631	C₂×D₄	—	8	2	no	—
632	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	—	2	1	no	—
634	C₂²×C₄	—	2	1	no	—
635	C₂²×C₄	—	2	1	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	4	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	4	2	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	—	4	1	no	—
645	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
646	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
647	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	#41×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
651	Q₁₆	—	4	2	no	—
652	Q₁₆	—	4	2	no	—
653	SD₁₆	—	4	2	no	—
654	SD₁₆	—	4	2	no	—
655	SD₁₆	—	4	2	no	—
656	SD₁₆	—	4	2	no	—
657	SD₁₆	—	4	2	no	—
658	SD₁₆	—	4	2	no	—
659	SD₁₆	—	4	2	no	—
660	D₈	—	4	2	no	—
661	M₁₆	—	2	1	no	—
662	M₁₆	—	2	1	no	—
663	M₁₆	—	2	1	no	—
664	M₁₆	—	2	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	—	2	1	no	—
671	M₁₆	—	4	2	no	—
672	M₁₆	—	4	2	no	—
673	M₁₆	—	4	2	no	—
674	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
675	M₁₆	C₂×D₄×C₂₃	1	2	yes	—
676	C₂×C₈	—	2	1	no	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	4	2	no	—
687	C₂×C₈	—	4	2	no	—
688	C₂×C₈	—	4	2	no	—
689	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂×C₈	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₂²⋊C₄	—	2	1	no	—
700	C₂²⋊C₄	—	2	1	no	—
701	C₂²⋊C₄	—	2	1	no	—
702	C₂²⋊C₄	—	2	1	no	—
703	C₂²⋊C₄	—	2	1	no	—
704	C₂²⋊C₄	—	4	1	no	—
705	C₂²⋊C₄	—	4	1	no	—
706	C₄²	—	2	1	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	1	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	8	1	no	—
716	C₂³	—	8	1	no	—
717	C₂³	C₂₃×#121	1	1	yes	characteristic
718	C₂³	C₂₃×#121	1	1	yes	characteristic
719	C₂³	C₂×#41×C₂₃	1	1	yes	characteristic
720	Q₈	—	2	1	no	—
721	Q₈	—	2	2	no	—
722	Q₈	—	2	2	no	—
723	Q₈	—	2	2	no	—
724	Q₈	—	2	2	no	—
725	Q₈	—	2	1	no	—
726	Q₈	—	4	4	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	1	no	—
729	Q₈	—	4	1	no	—
730	Q₈	—	4	1	no	—
731	Q₈	—	4	1	no	—
732	D₄	—	2	1	no	—
733	D₄	—	2	1	no	—
734	D₄	—	4	2	no	—
735	D₄	—	4	1	no	—
736	D₄	—	4	1	no	—
737	D₄	—	4	1	no	—
738	D₄	—	4	1	no	—
739	D₄	—	4	1	no	—
740	D₄	—	4	1	no	—
741	D₄	—	8	1	no	—
742	D₄	—	8	2	no	—
743	D₄	—	8	2	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	8	1	no	—
769	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
770	C₂×C₄	C₂₃×#121	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
773	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
774	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
775	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
776	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
777	C₈	—	2	1	no	—
778	C₈	—	2	1	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	2	no	—
781	C₈	—	2	1	no	—
782	C₈	—	2	1	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₈	—	4	1	no	—
786	C₈	—	4	1	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	1	no	—
798	C₂²	—	4	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	16	1	no	—
803	C₂²	—	16	1	no	—
804	C₂²	C₂₃×#471	1	2	yes	complemented
805	C₂²	C₂×C₂₃×#121	1	1	yes	characteristic
806	C₂²	C₂₃×#525	1	1	yes	characteristic
807	C₂²	C₂₃×#538	1	1	yes	characteristic
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	1	no	—
813	C₄	—	4	1	no	—
814	C₄	—	4	1	no	—
815	C₄	—	8	1	no	—
816	C₄	D₄²×C₂₃	1	1	yes	characteristic
817	C₄	D₄²×C₂₃	1	1	yes	characteristic
818	C₄	C₂₃×#546	1	1	yes	characteristic
819	C₄	C₂₃×#546	1	1	yes	characteristic
820	C₂	—	2	1	no	—
821	C₂	—	2	1	no	—
822	C₂	—	2	2	no	—
823	C₂	—	4	1	no	—
824	C₂	—	8	1	no	—
825	C₂	—	16	1	no	—
826	C₂	C₂₃×#2424	1	1	yes	characteristic
827	C₂	C₂×C₂₃×#471	1	1	yes	characteristic
828	C₂	C₂₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#3055	C₂
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×#471	C₂	semidirect
3. C₂₃×#3004	C₂	semidirect
4. C₂×C₂₃×#448	C₂	semidirect
5. C₂₃×#2933	C₂	semidirect
6. C₂²×C₂₃×#101	C₂	semidirect
7. C₂₃×#2064	C₂	semidirect
8. C₂₃×#2052	C₂	semidirect
9. C₂₃×#2046	C₂	semidirect
10. C₂₃×#2019	C₂	semidirect
11. C₂₃×#1977	C₂	semidirect
12. C₂₃×#1930	C₂	semidirect
13. C₂₃×#1908	C₂	semidirect
14. C₂₃×#1900	C₂	semidirect
15. C₂₃×#1855	C₂	semidirect
161. C₂₃×#101	D₄	semidirect
292. #25146	C₂₃	direct (N × H)
373. C₂×#471	C₂×C₂₃	semidirect
375. #3004	C₂×C₂₃	semidirect
376. C₂×#448	C₂×C₂₃	semidirect
377. #2933	C₂×C₂₃	semidirect
378. C₂²×#101	C₂×C₂₃	semidirect
379. #2064	C₂×C₂₃	semidirect
380. #2052	C₂×C₂₃	semidirect
381. #2046	C₂×C₂₃	semidirect
382. #2019	C₂×C₂₃	semidirect
383. #1977	C₂×C₂₃	semidirect
384. #1930	C₂×C₂₃	semidirect
385. #1908	C₂×C₂₃	semidirect
386. #1900	C₂×C₂₃	semidirect
387. #1855	C₂×C₂₃	semidirect
405. C₂²×C₂₃	#471	semidirect
575. #101	D₄×C₂₃	semidirect
588. C₂₃	#25146	direct (N × H)
804. C₂²	C₂₃×#471	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#471	2
C₂₃×#3055	2
C₂₃×#3004	2
C₂×C₂₃×#448	2
C₂₃×#2933	2
C₂²×C₂₃×#101	2
C₂₃×#2064	2
C₂₃×#2052	2
C₂₃×#2046	2
C₂₃×#2019	2
C₂₃×#1977	2
C₂₃×#1930	2
C₂₃×#1908	2
C₂₃×#1900	2
C₂₃×#1855	2
#25146	23

Subgroups — C23×#25146 #19172772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25146 #19172772