Subgroups — C₂₃×#23981 #19171607

Order 5888.

1300 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×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2407	C₂	1	1	yes	maximal, characteristic
5	C₂₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1874	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#554	—	2	4	no	—
21	C₂₃×#554	—	2	4	no	—
22	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×#125	—	2	1	no	—
24	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₃	—	2	1	no	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#452	—	2	4	no	—
36	C₂₃×#417	—	2	4	no	—
37	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂₃×#394	—	2	1	no	—
49	C₂₃×#392	—	2	1	no	—
50	C₂₃×#391	C₂²	1	1	yes	characteristic
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#386	—	2	1	no	—
53	C₂₃×#385	—	2	1	no	—
54	C₂₃×#380	C₂²	1	1	yes	characteristic
55	C₂₃×#340	C₂²	1	1	yes	characteristic
56	C₂₃×#340	C₂²	1	1	yes	characteristic
57	C₂₃×#340	C₂²	1	1	yes	characteristic
58	C₂₃×#340	C₂²	1	1	yes	characteristic
59	C₂₃×#340	C₂²	1	1	yes	characteristic
60	C₂₃×#340	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂×#41×C₂₃	—	2	2	no	—
64	C₂×#41×C₂₃	—	2	2	no	—
65	C₂×#41×C₂₃	—	2	2	no	—
66	C₂×#41×C₂₃	—	2	2	no	—
67	C₂×#41×C₂₃	—	4	1	no	—
68	C₂×#41×C₂₃	—	4	1	no	—
69	C₂²×Q₈×C₂₃	—	2	1	no	—
70	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₂₃	—	2	1	no	—
73	C₂²×D₄×C₂₃	—	2	1	no	—
74	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₂₃	—	2	1	no	—
77	C₂³×C₄×C₂₃	—	2	1	no	—
78	C₂³×C₄×C₂₃	—	2	1	no	—
79	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×Q₁₆×C₂₃	—	2	2	no	—
82	C₂×Q₁₆×C₂₃	—	2	2	no	—
83	C₂×Q₁₆×C₂₃	—	4	1	no	—
84	C₂×SD₁₆×C₂₃	—	2	2	no	—
85	C₂×SD₁₆×C₂₃	—	2	2	no	—
86	C₂×SD₁₆×C₂₃	—	4	1	no	—
87	C₂×M₁₆×C₂₃	—	2	2	no	—
88	C₂×M₁₆×C₂₃	—	4	1	no	—
89	C₂×M₁₆×C₂₃	—	4	1	no	—
90	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×C₄⋊Q₈	—	2	2	no	—
95	C₂₃×C₄⋊Q₈	—	2	2	no	—
96	C₂₃×#125	—	2	8	no	—
97	C₂₃×C₂²⋊Q₈	—	2	8	no	—
98	C₂₃×C₂²⋊Q₈	—	2	8	no	—
99	C₂₃×C₂²⋊Q₈	—	2	2	no	—
100	C₂₃×C₂²⋊Q₈	—	2	2	no	—
101	C₂₃×C₂²⋊Q₈	—	2	2	no	—
102	C₂₃×C₂²⋊Q₈	—	2	2	no	—
103	C₂₃×C₂²⋊Q₈	—	4	1	no	—
104	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
105	C₂₃×#121	—	2	2	no	—
106	C₂₃×#121	—	4	1	no	—
107	C₄×Q₈×C₂₃	—	2	2	no	—
108	C₄×Q₈×C₂₃	—	2	2	no	—
109	C₄×D₄×C₂₃	—	2	8	no	—
110	C₄×D₄×C₂₃	—	2	2	no	—
111	C₄×D₄×C₂₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
113	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
115	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
116	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
117	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
118	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
119	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
120	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
121	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
122	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₂₃	D₄	1	4	yes	complemented
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
130	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
132	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
138	C₂×C₄²×C₂₃	—	2	1	no	—
139	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
140	C₂₃×#103	—	2	2	no	—
141	C₂₃×#103	—	2	2	no	—
142	C₂₃×#103	—	2	2	no	—
143	C₂₃×#103	—	4	1	no	—
144	C₂₃×#103	—	4	1	no	—
145	C₂₃×#102	—	2	2	no	—
146	C₂₃×#102	—	2	2	no	—
147	C₂₃×#102	—	2	2	no	—
148	C₂₃×C₂²⋊C₈	—	2	2	no	—
149	C₂₃×C₂²⋊C₈	—	4	1	no	—
150	C₂₃×C₂²⋊C₈	—	4	1	no	—
151	C₂₃×#95	—	2	1	no	—
152	C₂₃×#95	—	2	1	no	—
153	C₂₃×#95	—	2	1	no	—
154	C₂⁴×C₂₃	—	2	1	no	—
155	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
157	#41×C₂₃	—	2	8	no	—
158	#41×C₂₃	—	4	4	no	—
159	#41×C₂₃	—	4	4	no	—
160	#41×C₂₃	—	4	4	no	—
161	C₂×Q₈×C₂₃	—	2	4	no	—
162	C₂×Q₈×C₂₃	—	2	1	no	—
163	C₂×Q₈×C₂₃	—	2	1	no	—
164	C₂×Q₈×C₂₃	—	2	1	no	—
165	C₂×Q₈×C₂₃	—	2	1	no	—
166	C₂×Q₈×C₂₃	—	2	1	no	—
167	C₂×Q₈×C₂₃	—	2	1	no	—
168	C₂×Q₈×C₂₃	—	2	1	no	—
169	C₂×Q₈×C₂₃	—	2	1	no	—
170	C₂×Q₈×C₂₃	—	2	1	no	—
171	C₂×Q₈×C₂₃	—	2	1	no	—
172	C₂×Q₈×C₂₃	—	8	1	no	—
173	C₂×Q₈×C₂₃	—	8	1	no	—
174	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
175	C₂×Q₈×C₂₃	#41	1	2	yes	—
176	C₂×D₄×C₂₃	—	2	2	no	—
177	C₂×D₄×C₂₃	—	2	2	no	—
178	C₂×D₄×C₂₃	—	2	2	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	—	8	1	no	—
190	C₂×D₄×C₂₃	#41	1	2	yes	—
191	C₂²×C₄×C₂₃	—	2	1	no	—
192	C₂²×C₄×C₂₃	—	2	1	no	—
193	C₂²×C₄×C₂₃	—	2	1	no	—
194	C₂²×C₄×C₂₃	—	2	1	no	—
195	C₂²×C₄×C₂₃	—	2	1	no	—
196	C₂²×C₄×C₂₃	—	2	1	no	—
197	C₂²×C₄×C₂₃	—	2	1	no	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	1	no	—
200	C₂²×C₄×C₂₃	—	2	4	no	—
201	C₂²×C₄×C₂₃	—	2	4	no	—
202	C₂²×C₄×C₂₃	—	2	1	no	—
203	C₂²×C₄×C₂₃	—	2	1	no	—
204	C₂²×C₄×C₂₃	—	2	1	no	—
205	C₂²×C₄×C₂₃	—	2	1	no	—
206	C₂²×C₄×C₂₃	—	2	1	no	—
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	—	4	2	no	—
211	C₂²×C₄×C₂₃	—	4	2	no	—
212	C₂²×C₄×C₂₃	—	4	2	no	—
213	C₂²×C₄×C₂₃	—	8	1	no	—
214	C₂²×C₄×C₂₃	—	8	1	no	—
215	C₂²×C₄×C₂₃	—	8	1	no	—
216	C₂²×C₄×C₂₃	—	8	1	no	—
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
224	Q₁₆×C₂₃	—	4	4	no	—
225	SD₁₆×C₂₃	—	4	4	no	—
226	M₁₆×C₂₃	—	4	4	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	2	1	no	—
229	C₂×C₈×C₂₃	—	2	1	no	—
230	C₂×C₈×C₂₃	—	2	1	no	—
231	C₂×C₈×C₂₃	—	2	1	no	—
232	C₂×C₈×C₂₃	—	2	1	no	—
233	C₂×C₈×C₂₃	—	2	1	no	—
234	C₂×C₈×C₂₃	—	2	1	no	—
235	C₂×C₈×C₂₃	—	2	1	no	—
236	C₂×C₈×C₂₃	—	2	1	no	—
237	C₂×C₈×C₂₃	—	2	1	no	—
238	C₂×C₈×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	2	no	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	1	no	—
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	—	4	2	no	—
254	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	2	no	—
260	C₂²⋊C₄×C₂₃	—	2	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	—	8	1	no	—
265	C₂²⋊C₄×C₂₃	—	8	1	no	—
266	C₄²×C₂₃	—	2	4	no	—
267	C₄²×C₂₃	—	2	1	no	—
268	C₄²×C₂₃	—	2	1	no	—
269	#23981	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	—	2	1	no	—
280	C₂³×C₂₃	—	2	1	no	—
281	C₂³×C₂₃	—	2	1	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	4	1	no	—
284	C₂³×C₂₃	—	4	1	no	—
285	C₂³×C₂₃	—	4	1	no	—
286	C₂³×C₂₃	—	4	1	no	—
287	C₂³×C₂₃	—	4	1	no	—
288	C₂³×C₂₃	—	4	1	no	—
289	C₂³×C₂₃	#120	1	2	yes	—
290	C₂³×C₂₃	#137	1	2	yes	—
291	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
292	Q₈×C₂₃	—	2	2	no	—
293	Q₈×C₂₃	—	2	2	no	—
294	Q₈×C₂₃	—	2	2	no	—
295	Q₈×C₂₃	—	2	2	no	—
296	Q₈×C₂₃	—	4	1	no	—
297	Q₈×C₂₃	—	4	1	no	—
298	Q₈×C₂₃	—	4	1	no	—
299	Q₈×C₂₃	—	4	1	no	—
300	Q₈×C₂₃	—	8	4	no	—
301	D₄×C₂₃	—	2	8	no	—
302	D₄×C₂₃	—	2	2	no	—
303	D₄×C₂₃	—	2	2	no	—
304	D₄×C₂₃	—	4	8	no	—
305	D₄×C₂₃	—	4	1	no	—
306	D₄×C₂₃	—	4	1	no	—
307	D₄×C₂₃	—	8	4	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	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	1	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	1	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	1	no	—
325	C₂×C₄×C₂₃	—	2	1	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	4	8	no	—
328	C₂×C₄×C₂₃	—	4	1	no	—
329	C₂×C₄×C₂₃	—	4	1	no	—
330	C₂×C₄×C₂₃	—	4	1	no	—
331	C₂×C₄×C₂₃	—	4	1	no	—
332	C₂×C₄×C₂₃	—	4	1	no	—
333	C₂×C₄×C₂₃	—	4	1	no	—
334	C₂×C₄×C₂₃	—	4	1	no	—
335	C₂×C₄×C₂₃	—	4	1	no	—
336	C₂×C₄×C₂₃	—	4	1	no	—
337	C₂×C₄×C₂₃	—	4	1	no	—
338	C₂×C₄×C₂₃	—	4	1	no	—
339	C₂×C₄×C₂₃	—	4	1	no	—
340	C₂×C₄×C₂₃	—	4	1	no	—
341	C₂×C₄×C₂₃	—	4	1	no	—
342	C₂×C₄×C₂₃	—	4	1	no	—
343	C₂×C₄×C₂₃	—	4	1	no	—
344	C₂×C₄×C₂₃	—	4	1	no	—
345	C₂×C₄×C₂₃	—	4	1	no	—
346	C₂×C₄×C₂₃	—	4	1	no	—
347	C₂×C₄×C₂₃	—	4	1	no	—
348	C₂×C₄×C₂₃	—	8	4	no	—
349	C₂×C₄×C₂₃	—	8	4	no	—
350	C₂×C₄×C₂₃	#120	1	2	yes	—
351	C₂×C₄×C₂₃	#137	1	2	yes	—
352	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
353	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
355	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
358	C₈×C₂₃	—	4	1	no	—
359	C₈×C₂₃	—	4	1	no	—
360	C₈×C₂₃	—	4	1	no	—
361	C₈×C₂₃	—	4	1	no	—
362	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
365	#2407	C₂×C₂₃	1	1	yes	characteristic
366	#2024	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#2023	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#2001	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#2000	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#1894	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#1878	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#1874	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#1872	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#1823	C₂×C₂₃	1	1	yes	characteristic, complemented
377	C₂²×C₂₃	—	2	2	no	—
378	C₂²×C₂₃	—	2	2	no	—
379	C₂²×C₂₃	—	2	2	no	—
380	C₂²×C₂₃	—	2	2	no	—
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	2	2	no	—
383	C₂²×C₂₃	—	4	1	no	—
384	C₂²×C₂₃	—	4	1	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	4	1	no	—
387	C₂²×C₂₃	—	4	1	no	—
388	C₂²×C₂₃	—	4	1	no	—
389	C₂²×C₂₃	—	4	1	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	8	1	no	—
395	C₂²×C₂₃	—	8	1	no	—
396	C₂²×C₂₃	—	8	1	no	—
397	C₂²×C₂₃	—	8	1	no	—
398	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
399	C₂²×C₂₃	#546	1	1	yes	characteristic
400	C₂²×C₂₃	#546	1	1	yes	characteristic
401	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
402	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
403	C₂²×C₂₃	#576	1	1	yes	characteristic
404	C₂²×C₂₃	#577	1	1	yes	characteristic
405	C₄×C₂₃	—	2	2	no	—
406	C₄×C₂₃	—	2	2	no	—
407	C₄×C₂₃	—	4	1	no	—
408	C₄×C₂₃	—	4	2	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	—	4	1	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	2	no	—
413	C₄×C₂₃	—	4	2	no	—
414	C₄×C₂₃	—	8	1	no	—
415	C₄×C₂₃	—	8	1	no	—
416	C₄×C₂₃	#525	1	1	yes	characteristic
417	C₄×C₂₃	#535	1	1	yes	characteristic
418	C₄×C₂₃	#546	1	1	yes	characteristic
419	C₄×C₂₃	#546	1	1	yes	characteristic
420	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
421	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
422	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
423	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
424	#554	—	2	4	no	—
425	#554	—	2	4	no	—
426	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#125	—	2	1	no	—
428	C₂×C₂²⋊Q₈	—	2	1	no	—
429	C₂×C₂²⋊Q₈	—	2	1	no	—
430	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×C₄×D₄	—	2	1	no	—
436	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
438	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
439	#452	—	2	4	no	—
440	#417	—	2	4	no	—
441	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
452	#394	—	2	1	no	—
453	#392	—	2	1	no	—
454	#391	C₂²×C₂₃	1	1	yes	characteristic
455	#390	C₂²×C₂₃	1	1	yes	characteristic
456	#386	—	2	1	no	—
457	#385	—	2	1	no	—
458	#380	C₂²×C₂₃	1	1	yes	characteristic
459	#340	C₂²×C₂₃	1	1	yes	characteristic
460	#340	C₂²×C₂₃	1	1	yes	characteristic
461	#340	C₂²×C₂₃	1	1	yes	characteristic
462	#340	C₂²×C₂₃	1	1	yes	characteristic
463	#340	C₂²×C₂₃	1	1	yes	characteristic
464	#340	C₂²×C₂₃	1	1	yes	characteristic
465	#336	C₂²×C₂₃	1	1	yes	characteristic
466	#336	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×C₂₃	—	4	2	no	—
468	C₂×C₂₃	—	4	2	no	—
469	C₂×C₂₃	—	8	2	no	—
470	C₂×C₂₃	#2404	1	1	yes	characteristic
471	C₂×C₂₃	#3004	1	1	yes	characteristic
472	C₂×C₂₃	#3012	1	1	yes	characteristic
473	C₂×C₂₃	#3314	1	1	yes	characteristic
474	C₂×C₂₃	#3316	1	1	yes	characteristic
475	C₂×C₂₃	#3331	1	1	yes	characteristic
476	C₂×C₂₃	#3333	1	1	yes	characteristic
477	C₂×#41	—	2	2	no	—
478	C₂×#41	—	2	2	no	—
479	C₂×#41	—	2	2	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	—	4	1	no	—
482	C₂×#41	—	4	1	no	—
483	C₂²×Q₈	—	2	1	no	—
484	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
485	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	1	no	—
488	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
489	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	C₂³×C₄	—	2	1	no	—
492	C₂³×C₄	—	2	1	no	—
493	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
494	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
495	C₂×Q₁₆	—	2	2	no	—
496	C₂×Q₁₆	—	2	2	no	—
497	C₂×Q₁₆	—	4	1	no	—
498	C₂×SD₁₆	—	2	2	no	—
499	C₂×SD₁₆	—	2	2	no	—
500	C₂×SD₁₆	—	4	1	no	—
501	C₂×M₁₆	—	2	2	no	—
502	C₂×M₁₆	—	4	1	no	—
503	C₂×M₁₆	—	4	1	no	—
504	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
505	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
506	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
507	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	2	no	—
510	#125	—	2	8	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₂²⋊Q₈	—	2	8	no	—
513	C₂²⋊Q₈	—	2	2	no	—
514	C₂²⋊Q₈	—	2	2	no	—
515	C₂²⋊Q₈	—	2	2	no	—
516	C₂²⋊Q₈	—	2	2	no	—
517	C₂²⋊Q₈	—	4	1	no	—
518	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	complemented
519	#121	—	2	2	no	—
520	#121	—	4	1	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×D₄	—	2	8	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	2	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	2	no	—
534	C₂×C₄⋊C₄	—	2	2	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	D₄×C₂₃	1	4	yes	complemented
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
551	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
552	C₂×C₄²	—	2	1	no	—
553	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
554	#103	—	2	2	no	—
555	#103	—	2	2	no	—
556	#103	—	2	2	no	—
557	#103	—	4	1	no	—
558	#103	—	4	1	no	—
559	#102	—	2	2	no	—
560	#102	—	2	2	no	—
561	#102	—	2	2	no	—
562	C₂²⋊C₈	—	2	2	no	—
563	C₂²⋊C₈	—	4	1	no	—
564	C₂²⋊C₈	—	4	1	no	—
565	#95	—	2	1	no	—
566	#95	—	2	1	no	—
567	#95	—	2	1	no	—
568	C₂₃	#23981	1	1	yes	characteristic, direct product factor, Sylow
569	C₂⁴	—	2	1	no	—
570	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
571	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
572	#41	—	2	8	no	—
573	#41	—	4	4	no	—
574	#41	—	4	4	no	—
575	#41	—	4	4	no	—
576	C₂×Q₈	—	2	4	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	—	2	1	no	—
587	C₂×Q₈	—	8	1	no	—
588	C₂×Q₈	—	8	1	no	—
589	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
590	C₂×Q₈	#41×C₂₃	1	2	yes	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	2	1	no	—
597	C₂×D₄	—	2	1	no	—
598	C₂×D₄	—	2	1	no	—
599	C₂×D₄	—	4	2	no	—
600	C₂×D₄	—	4	2	no	—
601	C₂×D₄	—	4	2	no	—
602	C₂×D₄	—	4	2	no	—
603	C₂×D₄	—	4	2	no	—
604	C₂×D₄	—	8	1	no	—
605	C₂×D₄	#41×C₂₃	1	2	yes	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	1	no	—
614	C₂²×C₄	—	2	1	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	2	1	no	—
618	C₂²×C₄	—	2	1	no	—
619	C₂²×C₄	—	2	1	no	—
620	C₂²×C₄	—	2	1	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	—	8	1	no	—
629	C₂²×C₄	—	8	1	no	—
630	C₂²×C₄	—	8	1	no	—
631	C₂²×C₄	—	8	1	no	—
632	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
633	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
634	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
635	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
636	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
637	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
638	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
639	Q₁₆	—	4	4	no	—
640	SD₁₆	—	4	4	no	—
641	M₁₆	—	4	4	no	—
642	C₂×C₈	—	2	1	no	—
643	C₂×C₈	—	2	1	no	—
644	C₂×C₈	—	2	1	no	—
645	C₂×C₈	—	2	1	no	—
646	C₂×C₈	—	2	1	no	—
647	C₂×C₈	—	2	1	no	—
648	C₂×C₈	—	2	1	no	—
649	C₂×C₈	—	2	1	no	—
650	C₂×C₈	—	2	1	no	—
651	C₂×C₈	—	2	1	no	—
652	C₂×C₈	—	2	1	no	—
653	C₂×C₈	—	2	1	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	2	no	—
661	C₄⋊C₄	—	2	1	no	—
662	C₄⋊C₄	—	2	1	no	—
663	C₄⋊C₄	—	2	1	no	—
664	C₄⋊C₄	—	2	1	no	—
665	C₄⋊C₄	—	2	1	no	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	1	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
670	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
671	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	2	no	—
675	C₂²⋊C₄	—	2	2	no	—
676	C₂²⋊C₄	—	4	2	no	—
677	C₂²⋊C₄	—	4	2	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	8	1	no	—
680	C₂²⋊C₄	—	8	1	no	—
681	C₄²	—	2	4	no	—
682	C₄²	—	2	1	no	—
683	C₄²	—	2	1	no	—
684	C₂³	—	2	1	no	—
685	C₂³	—	2	1	no	—
686	C₂³	—	2	1	no	—
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	2	1	no	—
695	C₂³	—	2	1	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	4	1	no	—
698	C₂³	—	4	1	no	—
699	C₂³	—	4	1	no	—
700	C₂³	—	4	1	no	—
701	C₂³	—	4	1	no	—
702	C₂³	—	4	1	no	—
703	C₂³	C₂₃×#120	1	2	yes	—
704	C₂³	C₂₃×#137	1	2	yes	—
705	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
706	Q₈	—	2	2	no	—
707	Q₈	—	2	2	no	—
708	Q₈	—	2	2	no	—
709	Q₈	—	2	2	no	—
710	Q₈	—	4	1	no	—
711	Q₈	—	4	1	no	—
712	Q₈	—	4	1	no	—
713	Q₈	—	4	1	no	—
714	Q₈	—	8	4	no	—
715	D₄	—	2	8	no	—
716	D₄	—	2	2	no	—
717	D₄	—	2	2	no	—
718	D₄	—	4	8	no	—
719	D₄	—	4	1	no	—
720	D₄	—	4	1	no	—
721	D₄	—	8	4	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	1	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	1	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	4	8	no	—
742	C₂×C₄	—	4	1	no	—
743	C₂×C₄	—	4	1	no	—
744	C₂×C₄	—	4	1	no	—
745	C₂×C₄	—	4	1	no	—
746	C₂×C₄	—	4	1	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	1	no	—
751	C₂×C₄	—	4	1	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	1	no	—
754	C₂×C₄	—	4	1	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	1	no	—
757	C₂×C₄	—	4	1	no	—
758	C₂×C₄	—	4	1	no	—
759	C₂×C₄	—	4	1	no	—
760	C₂×C₄	—	4	1	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	8	4	no	—
763	C₂×C₄	—	8	4	no	—
764	C₂×C₄	C₂₃×#120	1	2	yes	—
765	C₂×C₄	C₂₃×#137	1	2	yes	—
766	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
767	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
768	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
769	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
770	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₈	—	4	1	no	—
773	C₈	—	4	1	no	—
774	C₈	—	4	1	no	—
775	C₈	—	4	1	no	—
776	C₂²	—	2	2	no	—
777	C₂²	—	2	2	no	—
778	C₂²	—	2	2	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	2	no	—
782	C₂²	—	4	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	1	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	8	1	no	—
794	C₂²	—	8	1	no	—
795	C₂²	—	8	1	no	—
796	C₂²	—	8	1	no	—
797	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
798	C₂²	C₂₃×#546	1	1	yes	characteristic
799	C₂²	C₂₃×#546	1	1	yes	characteristic
800	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
801	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
802	C₂²	C₂₃×#576	1	1	yes	characteristic
803	C₂²	C₂₃×#577	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	2	no	—
806	C₄	—	4	1	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	1	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	2	no	—
813	C₄	—	8	1	no	—
814	C₄	—	8	1	no	—
815	C₄	C₂₃×#525	1	1	yes	characteristic
816	C₄	C₂₃×#535	1	1	yes	characteristic
817	C₄	C₂₃×#546	1	1	yes	characteristic
818	C₄	C₂₃×#546	1	1	yes	characteristic
819	C₂	—	4	2	no	—
820	C₂	—	4	2	no	—
821	C₂	—	8	2	no	—
822	C₂	C₂₃×#2404	1	1	yes	characteristic
823	C₂	C₂₃×#3004	1	1	yes	characteristic
824	C₂	C₂₃×#3012	1	1	yes	characteristic
825	C₂	C₂₃×#3314	1	1	yes	characteristic
826	C₂	C₂₃×#3316	1	1	yes	characteristic
827	C₂	C₂₃×#3331	1	1	yes	characteristic
828	C₂	C₂₃×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#2407	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#554	C₂	semidirect
2. C₂×C₂₃×#452	C₂	semidirect
3. C₂×C₂₃×#417	C₂	semidirect
5. C₂₃×#2024	C₂	semidirect
6. C₂₃×#2023	C₂	semidirect
7. C₂₃×#2001	C₂	semidirect
8. C₂₃×#2000	C₂	semidirect
9. C₂₃×#1894	C₂	semidirect
10. C₂₃×#1880	C₂	semidirect
11. C₂₃×#1878	C₂	semidirect
12. C₂₃×#1874	C₂	semidirect
13. C₂₃×#1872	C₂	semidirect
14. C₂₃×#1870	C₂	semidirect
15. C₂₃×#1823	C₂	semidirect
104. C₂₃×C₂²⋊Q₈	D₄	semidirect
123. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
269. #23981	C₂₃	direct (N × H)
362. C₂×#554	C₂×C₂₃	semidirect
363. C₂×#452	C₂×C₂₃	semidirect
364. C₂×#417	C₂×C₂₃	semidirect
366. #2024	C₂×C₂₃	semidirect
367. #2023	C₂×C₂₃	semidirect
368. #2001	C₂×C₂₃	semidirect
369. #2000	C₂×C₂₃	semidirect
370. #1894	C₂×C₂₃	semidirect
371. #1880	C₂×C₂₃	semidirect
372. #1878	C₂×C₂₃	semidirect
373. #1874	C₂×C₂₃	semidirect
374. #1872	C₂×C₂₃	semidirect
375. #1870	C₂×C₂₃	semidirect
376. #1823	C₂×C₂₃	semidirect
518. C₂²⋊Q₈	D₄×C₂₃	semidirect
537. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
568. C₂₃	#23981	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×#554	2
C₂×C₂₃×#452	2
C₂×C₂₃×#417	2
C₂₃×#2407	2
C₂₃×#2024	2
C₂₃×#2023	2
C₂₃×#2001	2
C₂₃×#2000	2
C₂₃×#1894	2
C₂₃×#1880	2
C₂₃×#1878	2
C₂₃×#1874	2
C₂₃×#1872	2
C₂₃×#1870	2
C₂₃×#1823	2
#23981	23

Subgroups — C23×#23981 #19171607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#23981 #19171607