Subgroups — C₂₃×#25159 #19172785

Order 5888.

1212 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#449	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2428	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2065	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2034	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×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×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
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×Q₈×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#460	—	2	4	no	—
29	C₂₃×#449	—	2	4	no	—
30	C₂₃×#449	—	2	4	no	—
31	C₄×SD₁₆×C₂₃	—	2	4	no	—
32	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#103	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
41	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂₃×#394	—	2	1	no	—
47	C₂₃×#392	—	2	1	no	—
48	C₂₃×#390	—	2	1	no	—
49	C₂₃×#390	—	2	1	no	—
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#390	C₂²	1	1	yes	characteristic
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#386	—	2	1	no	—
55	C₂₃×#380	—	2	1	no	—
56	C₂₃×#380	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₂₃	—	2	1	no	—
58	C₄×C₂²⋊C₄×C₂₃	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	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
74	C₂²×D₄×C₂₃	—	2	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	C₂³×C₄×C₂₃	—	2	1	no	—
79	C₂³×C₄×C₂₃	—	2	1	no	—
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂×SD₁₆×C₂₃	—	2	2	no	—
82	C₂×SD₁₆×C₂₃	—	2	2	no	—
83	C₂×SD₁₆×C₂₃	—	2	2	no	—
84	C₂×SD₁₆×C₂₃	—	2	2	no	—
85	C₂×SD₁₆×C₂₃	—	2	2	no	—
86	C₂×SD₁₆×C₂₃	D₄	1	4	yes	complemented
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	—	4	1	no	—
92	C₂×D₈×C₂₃	—	4	1	no	—
93	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
97	C₂₃×#127	—	2	2	no	—
98	C₂₃×#127	—	4	1	no	—
99	C₂₃×#121	—	2	2	no	—
100	C₂₃×#121	—	2	2	no	—
101	C₂₃×#121	—	4	4	no	—
102	C₂₃×#121	—	4	1	no	—
103	C₂₃×#121	—	4	1	no	—
104	C₄×Q₈×C₂₃	—	2	2	no	—
105	C₄×Q₈×C₂₃	—	2	2	no	—
106	C₄×Q₈×C₂₃	—	4	1	no	—
107	C₄×Q₈×C₂₃	—	4	1	no	—
108	C₄×D₄×C₂₃	—	2	2	no	—
109	C₄×D₄×C₂₃	—	4	1	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	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	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₂₃	—	2	1	no	—
130	C₂×C₄²×C₂₃	—	2	1	no	—
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂₃×#107	—	4	1	no	—
134	C₂₃×#106	—	2	2	no	—
135	C₂₃×C₄⋊C₈	—	2	2	no	—
136	C₂₃×#103	—	2	2	no	—
137	C₂₃×#103	D₄	1	4	yes	complemented
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×C₂²⋊C₈	—	2	2	no	—
145	C₂₃×C₂²⋊C₈	—	2	2	no	—
146	C₄×C₈×C₂₃	—	2	2	no	—
147	C₂₃×#95	—	2	1	no	—
148	C₂₃×#95	—	2	1	no	—
149	C₂₃×#95	D₄	1	1	yes	characteristic
150	C₂₃×#95	D₄	1	1	yes	characteristic
151	C₂⁴×C₂₃	—	2	1	no	—
152	C₂⁴×C₂₃	—	2	1	no	—
153	C₂⁴×C₂₃	—	2	1	no	—
154	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
155	#41×C₂₃	—	4	4	no	—
156	#41×C₂₃	—	4	4	no	—
157	#41×C₂₃	—	4	4	no	—
158	#41×C₂₃	—	4	4	no	—
159	C₂×Q₈×C₂₃	—	2	1	no	—
160	C₂×Q₈×C₂₃	—	2	1	no	—
161	C₂×Q₈×C₂₃	—	2	1	no	—
162	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
163	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
164	C₂×Q₈×C₂₃	#41	1	2	yes	—
165	C₂×D₄×C₂₃	—	2	4	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	—	4	2	no	—
183	C₂×D₄×C₂₃	—	4	2	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	2	no	—
191	C₂×D₄×C₂₃	—	4	2	no	—
192	C₂×D₄×C₂₃	—	8	1	no	—
193	C₂×D₄×C₂₃	—	8	1	no	—
194	C₂×D₄×C₂₃	—	8	1	no	—
195	C₂×D₄×C₂₃	—	8	1	no	—
196	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₂₃	#41	1	2	yes	—
198	C₂²×C₄×C₂₃	—	2	1	no	—
199	C₂²×C₄×C₂₃	—	2	4	no	—
200	C₂²×C₄×C₂₃	—	2	1	no	—
201	C₂²×C₄×C₂₃	—	2	1	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	—	4	2	no	—
214	C₂²×C₄×C₂₃	—	8	1	no	—
215	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
221	SD₁₆×C₂₃	—	2	8	no	—
222	SD₁₆×C₂₃	—	4	4	no	—
223	D₈×C₂₃	—	4	4	no	—
224	D₈×C₂₃	—	4	4	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	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	C₂×D₄	1	2	yes	—
236	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₂₃	—	2	1	no	—
238	C₄⋊C₄×C₂₃	—	2	1	no	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	1	no	—
242	C₄⋊C₄×C₂₃	—	2	1	no	—
243	C₄⋊C₄×C₂₃	—	2	1	no	—
244	C₄⋊C₄×C₂₃	—	4	2	no	—
245	C₄⋊C₄×C₂₃	—	4	2	no	—
246	C₄⋊C₄×C₂₃	—	4	2	no	—
247	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₂²⋊C₄×C₂₃	—	2	2	no	—
249	C₂²⋊C₄×C₂₃	—	2	2	no	—
250	C₂²⋊C₄×C₂₃	—	4	2	no	—
251	C₂²⋊C₄×C₂₃	—	4	2	no	—
252	C₂²⋊C₄×C₂₃	—	4	2	no	—
253	C₂²⋊C₄×C₂₃	—	4	2	no	—
254	C₂²⋊C₄×C₂₃	—	4	2	no	—
255	C₂²⋊C₄×C₂₃	—	4	2	no	—
256	C₂²⋊C₄×C₂₃	—	8	1	no	—
257	C₂²⋊C₄×C₂₃	—	8	1	no	—
258	C₂²⋊C₄×C₂₃	—	8	1	no	—
259	C₂²⋊C₄×C₂₃	—	8	1	no	—
260	C₄²×C₂₃	—	2	1	no	—
261	C₄²×C₂₃	—	2	1	no	—
262	C₄²×C₂₃	—	2	1	no	—
263	C₄²×C₂₃	—	2	1	no	—
264	C₄²×C₂₃	—	4	2	no	—
265	C₄²×C₂₃	—	4	2	no	—
266	#25159	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	2	no	—
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	—	4	1	no	—
277	C₂³×C₂₃	—	4	1	no	—
278	C₂³×C₂₃	—	4	1	no	—
279	C₂³×C₂₃	—	4	1	no	—
280	C₂³×C₂₃	—	4	1	no	—
281	C₂³×C₂₃	—	4	1	no	—
282	C₂³×C₂₃	—	4	1	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	—	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	C₂²×D₄	1	1	yes	characteristic
296	Q₈×C₂₃	—	2	2	no	—
297	Q₈×C₂₃	—	2	2	no	—
298	Q₈×C₂₃	—	2	2	no	—
299	Q₈×C₂₃	#121	1	4	yes	complemented
300	D₄×C₂₃	—	2	2	no	—
301	D₄×C₂₃	—	2	2	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	—	4	1	no	—
308	D₄×C₂₃	—	4	1	no	—
309	D₄×C₂₃	—	4	1	no	—
310	D₄×C₂₃	—	4	1	no	—
311	D₄×C₂₃	—	4	1	no	—
312	D₄×C₂₃	—	4	1	no	—
313	D₄×C₂₃	—	8	4	no	—
314	D₄×C₂₃	—	8	4	no	—
315	D₄×C₂₃	—	8	4	no	—
316	D₄×C₂₃	—	8	4	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	1	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	1	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	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	1	no	—
329	C₂×C₄×C₂₃	—	2	1	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	—	4	8	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	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	1	no	—
350	C₂×C₄×C₂₃	—	8	4	no	—
351	C₂×C₄×C₂₃	#135	1	2	yes	—
352	C₂×C₄×C₂₃	AGL(1,ℤ/8)	1	2	yes	—
353	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
354	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
356	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
357	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
359	C₈×C₂₃	—	2	2	no	—
360	C₈×C₂₃	—	2	2	no	—
361	C₈×C₂₃	—	4	1	no	—
362	C₈×C₂₃	—	4	1	no	—
363	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
365	C₂×#449	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
367	#2428	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#2341	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#2065	C₂×C₂₃	1	1	yes	characteristic, complemented
370	#2034	C₂×C₂₃	1	1	yes	characteristic, complemented
371	#2033	C₂×C₂₃	1	1	yes	characteristic, complemented
372	#2011	C₂×C₂₃	1	1	yes	characteristic, complemented
373	#1970	C₂×C₂₃	1	1	yes	characteristic, complemented
374	#1923	C₂×C₂₃	1	1	yes	characteristic, complemented
375	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#1879	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#1863	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	2	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	2	no	—
382	C₂²×C₂₃	—	4	2	no	—
383	C₂²×C₂₃	—	4	1	no	—
384	C₂²×C₂₃	—	4	2	no	—
385	C₂²×C₂₃	—	4	1	no	—
386	C₂²×C₂₃	—	4	1	no	—
387	C₂²×C₂₃	—	4	2	no	—
388	C₂²×C₂₃	—	4	2	no	—
389	C₂²×C₂₃	—	4	1	no	—
390	C₂²×C₂₃	—	4	1	no	—
391	C₂²×C₂₃	—	8	1	no	—
392	C₂²×C₂₃	—	8	1	no	—
393	C₂²×C₂₃	—	8	1	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	—	8	1	no	—
399	C₂²×C₂₃	—	8	1	no	—
400	C₂²×C₂₃	—	8	1	no	—
401	C₂²×C₂₃	—	8	1	no	—
402	C₂²×C₂₃	—	8	1	no	—
403	C₂²×C₂₃	—	8	1	no	—
404	C₂²×C₂₃	—	8	1	no	—
405	C₂²×C₂₃	—	8	1	no	—
406	C₂²×C₂₃	#525	1	1	yes	characteristic
407	C₂²×C₂₃	D₄²	1	1	yes	characteristic
408	C₂²×C₂₃	D₄²	1	1	yes	characteristic
409	C₂²×C₂₃	C₂×#135	1	1	yes	characteristic
410	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂²×C₂₃	#576	1	1	yes	characteristic
412	C₂²×C₂₃	#577	1	1	yes	characteristic
413	C₄×C₂₃	—	2	4	no	—
414	C₄×C₂₃	—	2	2	no	—
415	C₄×C₂₃	—	2	2	no	—
416	C₄×C₂₃	—	4	1	no	—
417	C₄×C₂₃	—	4	2	no	—
418	C₄×C₂₃	—	4	1	no	—
419	C₄×C₂₃	—	4	1	no	—
420	C₄×C₂₃	—	8	1	no	—
421	C₄×C₂₃	—	8	1	no	—
422	C₄×C₂₃	—	8	1	no	—
423	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
424	C₄×C₂₃	#538	1	1	yes	characteristic
425	C₄×C₂₃	#546	1	1	yes	characteristic
426	C₄×C₂₃	#546	1	1	yes	characteristic
427	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
428	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
429	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
430	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
431	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#121	—	2	1	no	—
434	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
439	#460	—	2	4	no	—
440	#449	—	2	4	no	—
441	#449	—	2	4	no	—
442	C₄×SD₁₆	—	2	4	no	—
443	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
457	#394	—	2	1	no	—
458	#392	—	2	1	no	—
459	#390	—	2	1	no	—
460	#390	—	2	1	no	—
461	#390	C₂²×C₂₃	1	1	yes	characteristic
462	#390	C₂²×C₂₃	1	1	yes	characteristic
463	#390	C₂²×C₂₃	1	1	yes	characteristic
464	#389	C₂²×C₂₃	1	1	yes	characteristic
465	#386	—	2	1	no	—
466	#380	—	2	1	no	—
467	#380	C₂²×C₂₃	1	1	yes	characteristic
468	C₄×C₂²⋊C₄	—	2	1	no	—
469	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
470	#340	C₂²×C₂₃	1	1	yes	characteristic
471	#340	C₂²×C₂₃	1	1	yes	characteristic
472	#336	C₂²×C₂₃	1	1	yes	characteristic
473	#336	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×C₂₃	—	8	1	no	—
475	C₂×C₂₃	—	8	2	no	—
476	C₂×C₂₃	—	8	2	no	—
477	C₂×C₂₃	—	16	1	no	—
478	C₂×C₂₃	#2424	1	1	yes	characteristic
479	C₂×C₂₃	#3106	1	1	yes	characteristic
480	C₂×C₂₃	#3119	1	1	yes	characteristic
481	C₂×C₂₃	#3265	1	1	yes	characteristic
482	C₂×C₂₃	#3274	1	1	yes	characteristic
483	C₂×C₂₃	#3282	1	1	yes	characteristic
484	C₂×C₂₃	#3287	1	1	yes	characteristic
485	C₂×#41	—	2	2	no	—
486	C₂×#41	—	2	2	no	—
487	C₂×#41	—	2	2	no	—
488	C₂×#41	—	2	2	no	—
489	C₂×#41	—	4	1	no	—
490	C₂×#41	—	4	1	no	—
491	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
503	C₂×SD₁₆	—	2	2	no	—
504	C₂×SD₁₆	—	2	2	no	—
505	C₂×SD₁₆	—	2	2	no	—
506	C₂×SD₁₆	—	2	2	no	—
507	C₂×SD₁₆	—	2	2	no	—
508	C₂×SD₁₆	D₄×C₂₃	1	4	yes	complemented
509	C₂×D₈	—	2	2	no	—
510	C₂×D₈	—	2	2	no	—
511	C₂×D₈	—	2	2	no	—
512	C₂×D₈	—	2	2	no	—
513	C₂×D₈	—	4	1	no	—
514	C₂×D₈	—	4	1	no	—
515	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
519	#127	—	2	2	no	—
520	#127	—	4	1	no	—
521	#121	—	2	2	no	—
522	#121	—	2	2	no	—
523	#121	—	4	4	no	—
524	#121	—	4	1	no	—
525	#121	—	4	1	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	4	1	no	—
529	C₄×Q₈	—	4	1	no	—
530	C₄×D₄	—	2	2	no	—
531	C₄×D₄	—	4	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₂²⋊C₄	—	2	1	no	—
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	1	no	—
542	C₂×C₂²⋊C₄	—	2	1	no	—
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	D₄×C₂₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
551	C₂×C₄²	—	2	1	no	—
552	C₂×C₄²	—	2	1	no	—
553	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
554	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
555	#107	—	4	1	no	—
556	#106	—	2	2	no	—
557	C₄⋊C₈	—	2	2	no	—
558	#103	—	2	2	no	—
559	#103	D₄×C₂₃	1	4	yes	complemented
560	#102	—	2	2	no	—
561	#102	—	2	2	no	—
562	#102	—	2	2	no	—
563	#102	—	2	2	no	—
564	#102	—	2	2	no	—
565	#102	—	4	1	no	—
566	C₂²⋊C₈	—	2	2	no	—
567	C₂²⋊C₈	—	2	2	no	—
568	C₄×C₈	—	2	2	no	—
569	#95	—	2	1	no	—
570	#95	—	2	1	no	—
571	#95	D₄×C₂₃	1	1	yes	characteristic
572	#95	D₄×C₂₃	1	1	yes	characteristic
573	C₂₃	#25159	1	1	yes	characteristic, direct product factor, Sylow
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	2	1	no	—
577	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
578	#41	—	4	4	no	—
579	#41	—	4	4	no	—
580	#41	—	4	4	no	—
581	#41	—	4	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
586	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
587	C₂×Q₈	#41×C₂₃	1	2	yes	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	1	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	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	—	2	1	no	—
600	C₂×D₄	—	2	1	no	—
601	C₂×D₄	—	2	1	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	1	no	—
604	C₂×D₄	—	2	1	no	—
605	C₂×D₄	—	4	2	no	—
606	C₂×D₄	—	4	2	no	—
607	C₂×D₄	—	4	2	no	—
608	C₂×D₄	—	4	2	no	—
609	C₂×D₄	—	4	2	no	—
610	C₂×D₄	—	4	2	no	—
611	C₂×D₄	—	4	2	no	—
612	C₂×D₄	—	4	2	no	—
613	C₂×D₄	—	4	2	no	—
614	C₂×D₄	—	4	2	no	—
615	C₂×D₄	—	8	1	no	—
616	C₂×D₄	—	8	1	no	—
617	C₂×D₄	—	8	1	no	—
618	C₂×D₄	—	8	1	no	—
619	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
620	C₂×D₄	#41×C₂₃	1	2	yes	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	—	2	1	no	—
625	C₂²×C₄	—	2	1	no	—
626	C₂²×C₄	—	2	1	no	—
627	C₂²×C₄	—	2	1	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	1	no	—
630	C₂²×C₄	—	2	1	no	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	1	no	—
633	C₂²×C₄	—	4	2	no	—
634	C₂²×C₄	—	4	2	no	—
635	C₂²×C₄	—	4	2	no	—
636	C₂²×C₄	—	4	2	no	—
637	C₂²×C₄	—	8	1	no	—
638	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
639	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
640	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
641	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
642	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
644	SD₁₆	—	2	8	no	—
645	SD₁₆	—	4	4	no	—
646	D₈	—	4	4	no	—
647	D₈	—	4	4	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	C₂×C₈	—	2	1	no	—
655	C₂×C₈	—	2	1	no	—
656	C₂×C₈	—	2	1	no	—
657	C₂×C₈	—	2	1	no	—
658	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
659	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
660	C₄⋊C₄	—	2	1	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	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	2	no	—
670	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
671	C₂²⋊C₄	—	2	2	no	—
672	C₂²⋊C₄	—	2	2	no	—
673	C₂²⋊C₄	—	4	2	no	—
674	C₂²⋊C₄	—	4	2	no	—
675	C₂²⋊C₄	—	4	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	C₂²⋊C₄	—	8	1	no	—
682	C₂²⋊C₄	—	8	1	no	—
683	C₄²	—	2	1	no	—
684	C₄²	—	2	1	no	—
685	C₄²	—	2	1	no	—
686	C₄²	—	2	1	no	—
687	C₄²	—	4	2	no	—
688	C₄²	—	4	2	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	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	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	—	4	1	no	—
704	C₂³	—	4	1	no	—
705	C₂³	—	4	1	no	—
706	C₂³	—	4	1	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	1	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	1	no	—
711	C₂³	—	4	1	no	—
712	C₂³	—	4	1	no	—
713	C₂³	—	4	1	no	—
714	C₂³	—	4	1	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	1	no	—
717	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	C₂₃×#121	1	4	yes	complemented
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	4	8	no	—
727	D₄	—	4	1	no	—
728	D₄	—	4	1	no	—
729	D₄	—	4	1	no	—
730	D₄	—	4	1	no	—
731	D₄	—	4	1	no	—
732	D₄	—	4	1	no	—
733	D₄	—	4	1	no	—
734	D₄	—	4	1	no	—
735	D₄	—	8	4	no	—
736	D₄	—	8	4	no	—
737	D₄	—	8	4	no	—
738	D₄	—	8	4	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	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	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	1	no	—
756	C₂×C₄	—	4	8	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	—	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	—	4	1	no	—
769	C₂×C₄	—	4	1	no	—
770	C₂×C₄	—	4	1	no	—
771	C₂×C₄	—	4	1	no	—
772	C₂×C₄	—	8	4	no	—
773	C₂×C₄	C₂₃×#135	1	2	yes	—
774	C₂×C₄	C₂₃×AGL(1,ℤ/8)	1	2	yes	—
775	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
777	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
778	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
779	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
780	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
781	C₈	—	2	2	no	—
782	C₈	—	2	2	no	—
783	C₈	—	4	1	no	—
784	C₈	—	4	1	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	1	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	1	no	—
789	C₂²	—	4	1	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	1	no	—
793	C₂²	—	4	1	no	—
794	C₂²	—	4	1	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	1	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	8	1	no	—
799	C₂²	—	8	1	no	—
800	C₂²	—	8	1	no	—
801	C₂²	—	8	1	no	—
802	C₂²	—	8	1	no	—
803	C₂²	—	8	1	no	—
804	C₂²	—	8	1	no	—
805	C₂²	—	8	1	no	—
806	C₂²	—	8	1	no	—
807	C₂²	—	8	1	no	—
808	C₂²	—	8	1	no	—
809	C₂²	—	8	1	no	—
810	C₂²	—	8	1	no	—
811	C₂²	—	8	1	no	—
812	C₂²	—	8	1	no	—
813	C₂²	C₂₃×#525	1	1	yes	characteristic
814	C₂²	D₄²×C₂₃	1	1	yes	characteristic
815	C₂²	D₄²×C₂₃	1	1	yes	characteristic
816	C₂²	C₂×C₂₃×#135	1	1	yes	characteristic
817	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
818	C₂²	C₂₃×#576	1	1	yes	characteristic
819	C₂²	C₂₃×#577	1	1	yes	characteristic
820	C₄	—	2	4	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	2	no	—
823	C₄	—	4	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	1	no	—
827	C₄	—	8	1	no	—
828	C₄	—	8	1	no	—
829	C₄	—	8	1	no	—
830	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
831	C₄	C₂₃×#538	1	1	yes	characteristic
832	C₄	C₂₃×#546	1	1	yes	characteristic
833	C₄	C₂₃×#546	1	1	yes	characteristic
834	C₂	—	8	1	no	—
835	C₂	—	8	2	no	—
836	C₂	—	8	2	no	—
837	C₂	—	16	1	no	—
838	C₂	C₂₃×#2424	1	1	yes	characteristic
839	C₂	C₂₃×#3106	1	1	yes	characteristic
840	C₂	C₂₃×#3119	1	1	yes	characteristic
841	C₂	C₂₃×#3265	1	1	yes	characteristic
842	C₂	C₂₃×#3274	1	1	yes	characteristic
843	C₂	C₂₃×#3282	1	1	yes	characteristic
844	C₂	C₂₃×#3287	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×#460	C₂	semidirect
2. C₂×C₂₃×#449	C₂	semidirect
3. C₂×C₂₃×#449	C₂	semidirect
4. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
5. C₂₃×#2428	C₂	semidirect
6. C₂₃×#2341	C₂	semidirect
7. C₂₃×#2065	C₂	semidirect
8. C₂₃×#2034	C₂	semidirect
9. C₂₃×#2033	C₂	semidirect
10. C₂₃×#2011	C₂	semidirect
11. C₂₃×#1970	C₂	semidirect
12. C₂₃×#1923	C₂	semidirect
13. C₂₃×#1880	C₂	semidirect
14. C₂₃×#1879	C₂	semidirect
15. C₂₃×#1863	C₂	semidirect
86. C₂×SD₁₆×C₂₃	D₄	semidirect
137. C₂₃×#103	D₄	semidirect
266. #25159	C₂₃	direct (N × H)
299. Q₈×C₂₃	#121	semidirect
363. C₂×#460	C₂×C₂₃	semidirect
364. C₂×#449	C₂×C₂₃	semidirect
365. C₂×#449	C₂×C₂₃	semidirect
366. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
367. #2428	C₂×C₂₃	semidirect
368. #2341	C₂×C₂₃	semidirect
369. #2065	C₂×C₂₃	semidirect
370. #2034	C₂×C₂₃	semidirect
371. #2033	C₂×C₂₃	semidirect
372. #2011	C₂×C₂₃	semidirect
373. #1970	C₂×C₂₃	semidirect
374. #1923	C₂×C₂₃	semidirect
375. #1880	C₂×C₂₃	semidirect
376. #1879	C₂×C₂₃	semidirect
377. #1863	C₂×C₂₃	semidirect
508. C₂×SD₁₆	D₄×C₂₃	semidirect
559. #103	D₄×C₂₃	semidirect
573. C₂₃	#25159	direct (N × H)
721. Q₈	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×#460	2
C₂×C₂₃×#449	2
C₂×C₄×SD₁₆×C₂₃	2
C₂₃×#2428	2
C₂₃×#2341	2
C₂₃×#2065	2
C₂₃×#2034	2
C₂₃×#2033	2
C₂₃×#2011	2
C₂₃×#1970	2
C₂₃×#1923	2
C₂₃×#1880	2
C₂₃×#1879	2
C₂₃×#1863	2
#25159	23

Subgroups — C23×#25159 #19172785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#25159 #19172785