Subgroups — C₂₃×#61679 #19209305

Order 5888.

2224 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3549	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3325	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3319	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3303	C₂	1	2	yes	maximal, complemented
6	D₄×D₈×C₂₃	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3264	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3198	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3008	C₂	1	4	yes	maximal, complemented
15	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂²×D₈×C₂₃	C₂²	1	4	yes	complemented
19	C₂₃×H(3,𝔽₄)	—	2	2	no	—
20	C₂₃×#555	—	2	1	no	—
21	C₂₃×#555	C₂²	1	2	yes	complemented
22	C₂₃×#555	C₂²	1	2	yes	complemented
23	C₂₃×#547	—	2	1	no	—
24	C₂₃×#547	C₂²	1	2	yes	complemented
25	C₂₃×#546	—	2	2	no	—
26	C₂₃×#546	C₂²	1	4	yes	complemented
27	D₄²×C₂₃	—	2	1	no	—
28	D₄²×C₂₃	—	2	1	no	—
29	D₄²×C₂₃	C₂²	1	2	yes	complemented
30	D₄²×C₂₃	C₂²	1	2	yes	complemented
31	D₄²×C₂₃	C₂²	1	2	yes	complemented
32	C₂₃×#537	C₂²	1	2	yes	complemented
33	C₂₃×#535	—	2	2	no	—
34	C₂₃×#535	—	2	2	no	—
35	C₂₃×#535	C₂²	1	4	yes	complemented
36	C₂₃×#534	—	2	2	no	—
37	C₂₃×#532	C₂²	1	1	yes	characteristic
38	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
39	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×#121	—	2	2	no	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
43	C₂₃×#496	C₂²	1	2	yes	complemented
44	C₂₃×#493	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#489	C₂²	1	2	yes	complemented
47	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#485	C₂²	1	4	yes	complemented
50	C₂₃×#482	C₂²	1	4	yes	complemented
51	C₂₃×#481	C₂²	1	2	yes	complemented
52	C₂₃×#480	C₂²	1	2	yes	complemented
53	C₂₃×#476	C₂²	1	2	yes	complemented
54	C₂₃×#474	C₂²	1	2	yes	complemented
55	C₂₃×#469	C₂²	1	4	yes	complemented
56	C₂₃×#468	C₂²	1	4	yes	complemented
57	C₂₃×#466	C₂²	1	4	yes	complemented
58	C₂₃×#465	C₂²	1	4	yes	complemented
59	C₂₃×#463	C₂²	1	4	yes	complemented
60	C₂₃×#461	C₂²	1	2	yes	complemented
61	C₂₃×#459	C₂²	1	2	yes	complemented
62	C₂₃×#459	C₂²	1	2	yes	complemented
63	C₂₃×#459	C₂²	1	2	yes	complemented
64	C₂₃×#450	C₂²	1	4	yes	complemented
65	C₂₃×#449	C₂²	1	4	yes	complemented
66	C₂₃×#449	C₂²	1	4	yes	complemented
67	C₂₃×#449	C₂²	1	4	yes	complemented
68	C₂₃×#449	C₂²	1	4	yes	complemented
69	C₂₃×#447	C₂²	1	4	yes	complemented
70	C₂₃×#447	C₂²	1	2	yes	complemented
71	C₂₃×#447	C₂²	1	2	yes	complemented
72	C₂₃×#447	C₂²	1	4	yes	complemented
73	C₂₃×#447	C₂²	1	4	yes	complemented
74	C₂₃×#442	C₂²	1	4	yes	complemented
75	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
76	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
77	C₂₃×#436	C₂²	1	2	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#418	C₂²	1	4	yes	complemented
83	C₂₃×#416	C₂²	1	4	yes	complemented
84	C₂₃×#408	C₂²	1	4	yes	complemented
85	C₂₃×H(5,𝔽₂)	—	4	8	no	—
86	C₂×#41×C₂₃	—	2	2	no	—
87	C₂×#41×C₂₃	—	2	1	no	—
88	C₂×#41×C₂₃	—	2	1	no	—
89	C₂×#41×C₂₃	C₂³	1	4	yes	—
90	C₂×#41×C₂₃	C₂³	1	2	yes	—
91	C₂×#41×C₂₃	C₂³	1	2	yes	—
92	C₂²×D₄×C₂₃	—	2	4	no	—
93	C₂²×D₄×C₂₃	—	2	2	no	—
94	C₂²×D₄×C₂₃	—	2	2	no	—
95	C₂²×D₄×C₂₃	—	2	2	no	—
96	C₂²×D₄×C₂₃	—	2	2	no	—
97	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
100	C₂³×C₄×C₂₃	—	2	1	no	—
101	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
102	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×D₈×C₂₃	—	4	8	no	—
105	C₂×D₈×C₂₃	C₂³	1	2	yes	—
106	C₂×D₈×C₂₃	C₂³	1	4	yes	—
107	C₂×D₈×C₂₃	C₂³	1	2	yes	—
108	C₂×D₈×C₂₃	C₂³	1	4	yes	—
109	C₂×D₈×C₂₃	C₂³	1	4	yes	—
110	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
112	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×#127	—	2	4	no	—
117	C₂₃×#127	D₄	1	1	yes	characteristic
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#127	C₂³	1	1	yes	characteristic
120	C₂₃×#127	C₂³	1	1	yes	characteristic
121	C₂₃×#124	—	2	4	no	—
122	C₂₃×#124	—	2	4	no	—
123	C₂₃×#124	—	2	4	no	—
124	C₂₃×#124	—	2	1	no	—
125	C₂₃×#124	—	2	1	no	—
126	C₂₃×#124	D₄	1	2	yes	—
127	C₂₃×#124	C₂³	1	2	yes	—
128	C₂₃×#123	—	2	4	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₂₃×#121	—	2	2	no	—
133	C₂₃×#121	—	2	2	no	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	4	no	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	—	2	1	no	—
139	C₂₃×#121	—	2	1	no	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	2	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	2	no	—
144	C₂₃×#121	—	2	4	no	—
145	C₂₃×#121	D₄	1	2	yes	—
146	C₂₃×#121	D₄	1	2	yes	—
147	C₂₃×#121	C₂³	1	4	yes	—
148	C₂₃×#121	C₂³	1	4	yes	—
149	C₂₃×#121	C₂³	1	2	yes	—
150	C₂₃×#121	C₂³	1	2	yes	—
151	C₂₃×#121	C₂³	1	4	yes	—
152	C₂₃×#120	—	2	4	no	—
153	C₂₃×#120	—	2	4	no	—
154	C₂₃×#120	—	2	4	no	—
155	C₂₃×#120	—	2	4	no	—
156	C₂₃×#120	—	2	4	no	—
157	C₂₃×#120	—	2	4	no	—
158	C₄×D₄×C₂₃	—	2	1	no	—
159	C₄×D₄×C₂₃	—	2	1	no	—
160	C₄×D₄×C₂₃	—	2	1	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	C₂³	1	2	yes	—
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₄×D₄×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	C₂³	1	2	yes	—
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₂₃×#117	—	2	2	no	—
171	C₂₃×#117	—	2	2	no	—
172	C₂₃×#117	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂₃×#107	C₂³	1	2	yes	—
179	C₂₃×#107	C₂³	1	2	yes	—
180	C₂₃×#106	C₂³	1	4	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#102	C₂³	1	2	yes	—
186	C₂₃×#102	C₂³	1	4	yes	—
187	C₂₃×#102	C₂³	1	2	yes	—
188	C₂₃×#102	C₂³	1	4	yes	—
189	C₂₃×#102	C₂³	1	4	yes	—
190	C₂₃×#102	C₂³	1	2	yes	—
191	C₂₃×#102	C₂³	1	2	yes	—
192	C₂₃×#102	C₂³	1	4	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₂⁴×C₂₃	—	2	1	no	—
201	C₂⁴×C₂₃	—	2	4	no	—
202	C₂⁴×C₂₃	—	2	4	no	—
203	#41×C₂₃	—	2	8	no	—
204	#41×C₂₃	—	4	4	no	—
205	#41×C₂₃	—	4	4	no	—
206	#41×C₂₃	—	4	4	no	—
207	#41×C₂₃	—	4	8	no	—
208	#41×C₂₃	—	8	2	no	—
209	#41×C₂₃	—	8	2	no	—
210	C₂×Q₈×C₂₃	—	2	1	no	—
211	C₂×Q₈×C₂₃	—	2	1	no	—
212	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
213	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
214	C₂×D₄×C₂₃	—	2	4	no	—
215	C₂×D₄×C₂₃	—	2	8	no	—
216	C₂×D₄×C₂₃	—	2	4	no	—
217	C₂×D₄×C₂₃	—	2	2	no	—
218	C₂×D₄×C₂₃	—	2	4	no	—
219	C₂×D₄×C₂₃	—	2	4	no	—
220	C₂×D₄×C₂₃	—	2	4	no	—
221	C₂×D₄×C₂₃	—	2	2	no	—
222	C₂×D₄×C₂₃	—	2	2	no	—
223	C₂×D₄×C₂₃	—	2	1	no	—
224	C₂×D₄×C₂₃	—	2	1	no	—
225	C₂×D₄×C₂₃	—	2	1	no	—
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	2	1	no	—
231	C₂×D₄×C₂₃	—	2	4	no	—
232	C₂×D₄×C₂₃	—	4	4	no	—
233	C₂×D₄×C₂₃	—	4	4	no	—
234	C₂×D₄×C₂₃	—	4	4	no	—
235	C₂×D₄×C₂₃	—	4	8	no	—
236	C₂×D₄×C₂₃	—	4	16	no	—
237	C₂×D₄×C₂₃	—	8	4	no	—
238	C₂×D₄×C₂₃	—	8	4	no	—
239	C₂×D₄×C₂₃	—	8	4	no	—
240	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
241	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
242	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
244	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
247	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₂₃	—	2	1	no	—
249	C₂²×C₄×C₂₃	—	2	4	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	2	2	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	8	2	no	—
256	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
260	SD₁₆×C₂₃	—	4	4	no	—
261	SD₁₆×C₂₃	—	4	4	no	—
262	D₈×C₂₃	—	2	4	no	—
263	D₈×C₂₃	—	2	8	no	—
264	D₈×C₂₃	—	2	4	no	—
265	D₈×C₂₃	—	4	4	no	—
266	D₈×C₂₃	—	4	4	no	—
267	M₁₆×C₂₃	—	4	4	no	—
268	C₂×C₈×C₂₃	—	4	4	no	—
269	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
271	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	4	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	—	2	2	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	4	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	2	2	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	2	no	—
296	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
297	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
298	C₄²×C₂₃	—	2	4	no	—
299	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
303	#61679	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₂₃	—	2	4	no	—
305	C₂³×C₂₃	—	2	2	no	—
306	C₂³×C₂₃	—	2	2	no	—
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	2	2	no	—
309	C₂³×C₂₃	—	4	8	no	—
310	C₂³×C₂₃	—	8	1	no	—
311	C₂³×C₂₃	—	8	1	no	—
312	C₂³×C₂₃	—	8	4	no	—
313	C₂³×C₂₃	—	8	4	no	—
314	C₂³×C₂₃	—	8	4	no	—
315	C₂³×C₂₃	—	8	4	no	—
316	C₂³×C₂₃	—	8	4	no	—
317	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
318	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₂₃	—	2	4	no	—
320	Q₈×C₂₃	—	4	2	no	—
321	Q₈×C₂₃	—	8	1	no	—
322	Q₈×C₂₃	—	8	1	no	—
323	D₄×C₂₃	—	2	4	no	—
324	D₄×C₂₃	—	2	4	no	—
325	D₄×C₂₃	—	2	2	no	—
326	D₄×C₂₃	—	2	2	no	—
327	D₄×C₂₃	—	2	4	no	—
328	D₄×C₂₃	—	2	2	no	—
329	D₄×C₂₃	—	2	4	no	—
330	D₄×C₂₃	—	4	2	no	—
331	D₄×C₂₃	—	4	4	no	—
332	D₄×C₂₃	—	4	2	no	—
333	D₄×C₂₃	—	4	8	no	—
334	D₄×C₂₃	—	4	2	no	—
335	D₄×C₂₃	—	4	8	no	—
336	D₄×C₂₃	—	4	4	no	—
337	D₄×C₂₃	—	4	2	no	—
338	D₄×C₂₃	—	4	2	no	—
339	D₄×C₂₃	—	8	1	no	—
340	D₄×C₂₃	—	8	4	no	—
341	D₄×C₂₃	—	8	1	no	—
342	D₄×C₂₃	—	8	1	no	—
343	D₄×C₂₃	—	8	4	no	—
344	D₄×C₂₃	—	8	4	no	—
345	D₄×C₂₃	—	8	4	no	—
346	D₄×C₂₃	—	8	2	no	—
347	D₄×C₂₃	—	8	2	no	—
348	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	4	no	—
351	C₂×C₄×C₂₃	—	2	4	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	4	1	no	—
358	C₂×C₄×C₂₃	—	4	8	no	—
359	C₂×C₄×C₂₃	—	4	4	no	—
360	C₂×C₄×C₂₃	—	4	4	no	—
361	C₂×C₄×C₂₃	—	4	4	no	—
362	C₂×C₄×C₂₃	—	4	4	no	—
363	C₂×C₄×C₂₃	—	8	2	no	—
364	C₂×C₄×C₂₃	—	8	1	no	—
365	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
366	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₂₃	C₂²×D₄	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	C₂⁵	1	1	yes	characteristic
372	C₈×C₂₃	—	2	2	no	—
373	C₈×C₂₃	—	2	4	no	—
374	C₈×C₂₃	—	2	2	no	—
375	#3549	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#3325	C₂×C₂₃	1	2	yes	complemented
378	#3319	C₂×C₂₃	1	4	yes	complemented
379	#3303	C₂×C₂₃	1	2	yes	complemented
380	D₄×D₈	C₂×C₂₃	1	2	yes	complemented
381	#3272	C₂×C₂₃	1	2	yes	complemented
382	#3264	C₂×C₂₃	1	4	yes	complemented
383	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
384	#3207	C₂×C₂₃	1	1	yes	characteristic, complemented
385	#3198	C₂×C₂₃	1	4	yes	complemented
386	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
387	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#3008	C₂×C₂₃	1	4	yes	complemented
389	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
390	C₂²×C₂₃	—	2	1	no	—
391	C₂²×C₂₃	—	2	4	no	—
392	C₂²×C₂₃	—	2	1	no	—
393	C₂²×C₂₃	—	2	4	no	—
394	C₂²×C₂₃	—	2	4	no	—
395	C₂²×C₂₃	—	2	1	no	—
396	C₂²×C₂₃	—	2	4	no	—
397	C₂²×C₂₃	—	4	2	no	—
398	C₂²×C₂₃	—	4	2	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	4	2	no	—
401	C₂²×C₂₃	—	4	2	no	—
402	C₂²×C₂₃	—	4	2	no	—
403	C₂²×C₂₃	—	4	2	no	—
404	C₂²×C₂₃	—	4	2	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	2	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	8	4	no	—
409	C₂²×C₂₃	—	16	8	no	—
410	C₂²×C₂₃	—	16	8	no	—
411	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
412	C₄×C₂₃	—	2	1	no	—
413	C₄×C₂₃	—	2	1	no	—
414	C₄×C₂₃	—	2	1	no	—
415	C₄×C₂₃	—	2	4	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	4	2	no	—
418	C₄×C₂₃	—	4	2	no	—
419	C₄×C₂₃	—	4	2	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	#576	1	2	yes	—
422	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
423	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	complemented
424	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
425	C₂²×D₈	C₂²×C₂₃	1	4	yes	complemented
426	H(3,𝔽₄)	—	2	2	no	—
427	#555	—	2	1	no	—
428	#555	C₂²×C₂₃	1	2	yes	complemented
429	#555	C₂²×C₂₃	1	2	yes	complemented
430	#547	—	2	1	no	—
431	#547	C₂²×C₂₃	1	2	yes	complemented
432	#546	—	2	2	no	—
433	#546	C₂²×C₂₃	1	4	yes	complemented
434	D₄²	—	2	1	no	—
435	D₄²	—	2	1	no	—
436	D₄²	C₂²×C₂₃	1	2	yes	complemented
437	D₄²	C₂²×C₂₃	1	2	yes	complemented
438	D₄²	C₂²×C₂₃	1	2	yes	complemented
439	#537	C₂²×C₂₃	1	2	yes	complemented
440	#535	—	2	2	no	—
441	#535	—	2	2	no	—
442	#535	C₂²×C₂₃	1	4	yes	complemented
443	#534	—	2	2	no	—
444	#532	C₂²×C₂₃	1	1	yes	characteristic
445	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
447	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
448	C₂×#121	—	2	2	no	—
449	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#496	C₂²×C₂₃	1	2	yes	complemented
451	#493	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	#489	C₂²×C₂₃	1	2	yes	complemented
454	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#485	C₂²×C₂₃	1	4	yes	complemented
457	#482	C₂²×C₂₃	1	4	yes	complemented
458	#481	C₂²×C₂₃	1	2	yes	complemented
459	#480	C₂²×C₂₃	1	2	yes	complemented
460	#476	C₂²×C₂₃	1	2	yes	complemented
461	#474	C₂²×C₂₃	1	2	yes	complemented
462	#469	C₂²×C₂₃	1	4	yes	complemented
463	#468	C₂²×C₂₃	1	4	yes	complemented
464	#466	C₂²×C₂₃	1	4	yes	complemented
465	#465	C₂²×C₂₃	1	4	yes	complemented
466	#463	C₂²×C₂₃	1	4	yes	complemented
467	#461	C₂²×C₂₃	1	2	yes	complemented
468	#459	C₂²×C₂₃	1	2	yes	complemented
469	#459	C₂²×C₂₃	1	2	yes	complemented
470	#459	C₂²×C₂₃	1	2	yes	complemented
471	#450	C₂²×C₂₃	1	4	yes	complemented
472	#449	C₂²×C₂₃	1	4	yes	complemented
473	#449	C₂²×C₂₃	1	4	yes	complemented
474	#449	C₂²×C₂₃	1	4	yes	complemented
475	#449	C₂²×C₂₃	1	4	yes	complemented
476	#447	C₂²×C₂₃	1	2	yes	complemented
477	#447	C₂²×C₂₃	1	2	yes	complemented
478	#447	C₂²×C₂₃	1	4	yes	complemented
479	#447	C₂²×C₂₃	1	4	yes	complemented
480	#447	C₂²×C₂₃	1	4	yes	complemented
481	#442	C₂²×C₂₃	1	4	yes	complemented
482	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
483	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
484	#436	C₂²×C₂₃	1	2	yes	complemented
485	#435	C₂²×C₂₃	1	4	yes	complemented
486	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
487	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
488	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#418	C₂²×C₂₃	1	4	yes	complemented
490	#416	C₂²×C₂₃	1	4	yes	complemented
491	#408	C₂²×C₂₃	1	4	yes	complemented
492	C₂×C₂₃	—	4	1	no	—
493	C₂×C₂₃	—	4	4	no	—
494	C₂×C₂₃	—	4	4	no	—
495	C₂×C₂₃	—	8	2	no	—
496	C₂×C₂₃	—	8	2	no	—
497	C₂×C₂₃	—	8	2	no	—
498	C₂×C₂₃	#3484	1	1	yes	characteristic
499	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
500	C₂×C₂₃	#3585	1	1	yes	characteristic
501	H(5,𝔽₂)	—	4	8	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	—	2	1	no	—
504	C₂×#41	—	2	1	no	—
505	C₂×#41	C₂³×C₂₃	1	4	yes	—
506	C₂×#41	C₂³×C₂₃	1	2	yes	—
507	C₂×#41	C₂³×C₂₃	1	2	yes	—
508	C₂²×D₄	—	2	4	no	—
509	C₂²×D₄	—	2	2	no	—
510	C₂²×D₄	—	2	2	no	—
511	C₂²×D₄	—	2	2	no	—
512	C₂²×D₄	—	2	2	no	—
513	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
514	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
515	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
516	C₂³×C₄	—	2	1	no	—
517	AGL(1,ℤ/8)	—	4	8	no	—
518	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
519	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
520	C₂×D₈	—	4	8	no	—
521	C₂×D₈	C₂³×C₂₃	1	2	yes	—
522	C₂×D₈	C₂³×C₂₃	1	4	yes	—
523	C₂×D₈	C₂³×C₂₃	1	2	yes	—
524	C₂×D₈	C₂³×C₂₃	1	4	yes	—
525	C₂×D₈	C₂³×C₂₃	1	4	yes	—
526	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
527	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
528	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
529	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
530	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
531	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
532	#127	—	2	4	no	—
533	#127	D₄×C₂₃	1	1	yes	characteristic
534	#127	C₂³×C₂₃	1	1	yes	characteristic
535	#127	C₂³×C₂₃	1	1	yes	characteristic
536	#127	C₂³×C₂₃	1	1	yes	characteristic
537	#124	—	2	4	no	—
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	2	1	no	—
541	#124	—	2	1	no	—
542	#124	D₄×C₂₃	1	2	yes	—
543	#124	C₂³×C₂₃	1	2	yes	—
544	#123	—	2	4	no	—
545	#123	—	2	4	no	—
546	C₂²⋊Q₈	—	2	2	no	—
547	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
548	#121	—	2	4	no	—
549	#121	—	2	2	no	—
550	#121	—	2	2	no	—
551	#121	—	2	2	no	—
552	#121	—	2	2	no	—
553	#121	—	2	1	no	—
554	#121	—	2	1	no	—
555	#121	—	2	1	no	—
556	#121	—	2	1	no	—
557	#121	—	2	2	no	—
558	#121	—	2	2	no	—
559	#121	—	2	2	no	—
560	#121	—	2	4	no	—
561	#121	D₄×C₂₃	1	2	yes	—
562	#121	D₄×C₂₃	1	2	yes	—
563	#121	C₂³×C₂₃	1	2	yes	—
564	#121	C₂³×C₂₃	1	2	yes	—
565	#121	C₂³×C₂₃	1	4	yes	—
566	#121	C₂³×C₂₃	1	4	yes	—
567	#121	C₂³×C₂₃	1	4	yes	—
568	#120	—	2	4	no	—
569	#120	—	2	4	no	—
570	#120	—	2	4	no	—
571	#120	—	2	4	no	—
572	#120	—	2	4	no	—
573	#120	—	2	4	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	1	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	1	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	C₂³×C₂₃	1	2	yes	—
581	C₄×D₄	C₂³×C₂₃	1	2	yes	—
582	C₄×D₄	C₂³×C₂₃	1	2	yes	—
583	C₄×D₄	C₂³×C₂₃	1	2	yes	—
584	C₄×D₄	C₂³×C₂₃	1	2	yes	—
585	C₄×D₄	C₂³×C₂₃	1	2	yes	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	C₂³×C₂₃	1	4	yes	—
589	C₂×C₄⋊C₄	—	2	2	no	—
590	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
591	C₂×C₂²⋊C₄	—	2	1	no	—
592	C₂×C₂²⋊C₄	—	2	4	no	—
593	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
594	#107	C₂³×C₂₃	1	2	yes	—
595	#107	C₂³×C₂₃	1	2	yes	—
596	#106	C₂³×C₂₃	1	4	yes	—
597	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
598	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
599	#103	C₂³×C₂₃	1	4	yes	—
600	#103	C₂³×C₂₃	1	4	yes	—
601	#102	C₂³×C₂₃	1	2	yes	—
602	#102	C₂³×C₂₃	1	4	yes	—
603	#102	C₂³×C₂₃	1	2	yes	—
604	#102	C₂³×C₂₃	1	4	yes	—
605	#102	C₂³×C₂₃	1	4	yes	—
606	#102	C₂³×C₂₃	1	2	yes	—
607	#102	C₂³×C₂₃	1	2	yes	—
608	#102	C₂³×C₂₃	1	4	yes	—
609	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
610	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
611	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
612	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
613	#97	C₂³×C₂₃	1	2	yes	—
614	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
615	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
616	C₂₃	#61679	1	1	yes	characteristic, direct product factor, Sylow
617	C₂⁴	—	2	1	no	—
618	C₂⁴	—	2	4	no	—
619	C₂⁴	—	2	4	no	—
620	#41	—	2	8	no	—
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	#41	—	4	8	no	—
625	#41	—	8	2	no	—
626	#41	—	8	2	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
630	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
631	C₂×D₄	—	2	4	no	—
632	C₂×D₄	—	2	8	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	4	no	—
636	C₂×D₄	—	2	4	no	—
637	C₂×D₄	—	2	4	no	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	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	4	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	4	4	no	—
650	C₂×D₄	—	4	4	no	—
651	C₂×D₄	—	4	4	no	—
652	C₂×D₄	—	4	8	no	—
653	C₂×D₄	—	4	16	no	—
654	C₂×D₄	—	8	4	no	—
655	C₂×D₄	—	8	4	no	—
656	C₂×D₄	—	8	4	no	—
657	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
658	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
659	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
660	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
661	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
662	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
663	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
664	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	8	2	no	—
673	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
677	SD₁₆	—	4	4	no	—
678	SD₁₆	—	4	4	no	—
679	D₈	—	2	4	no	—
680	D₈	—	2	8	no	—
681	D₈	—	2	4	no	—
682	D₈	—	4	4	no	—
683	D₈	—	4	4	no	—
684	M₁₆	—	4	4	no	—
685	C₂×C₈	—	4	4	no	—
686	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
687	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
688	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	1	no	—
692	C₄⋊C₄	—	2	1	no	—
693	C₄⋊C₄	—	2	1	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
696	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
697	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
698	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
699	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	—	2	4	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	2	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	2	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	2	no	—
713	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
714	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
715	C₄²	—	2	4	no	—
716	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
719	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
720	C₂³	—	2	4	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	4	8	no	—
726	C₂³	—	8	1	no	—
727	C₂³	—	8	1	no	—
728	C₂³	—	8	4	no	—
729	C₂³	—	8	4	no	—
730	C₂³	—	8	4	no	—
731	C₂³	—	8	4	no	—
732	C₂³	—	8	4	no	—
733	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
734	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
735	Q₈	—	2	4	no	—
736	Q₈	—	4	2	no	—
737	Q₈	—	8	1	no	—
738	Q₈	—	8	1	no	—
739	D₄	—	2	4	no	—
740	D₄	—	2	4	no	—
741	D₄	—	2	2	no	—
742	D₄	—	2	2	no	—
743	D₄	—	2	4	no	—
744	D₄	—	2	2	no	—
745	D₄	—	2	4	no	—
746	D₄	—	4	2	no	—
747	D₄	—	4	4	no	—
748	D₄	—	4	2	no	—
749	D₄	—	4	8	no	—
750	D₄	—	4	2	no	—
751	D₄	—	4	8	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	2	no	—
754	D₄	—	4	2	no	—
755	D₄	—	8	4	no	—
756	D₄	—	8	1	no	—
757	D₄	—	8	1	no	—
758	D₄	—	8	1	no	—
759	D₄	—	8	4	no	—
760	D₄	—	8	4	no	—
761	D₄	—	8	4	no	—
762	D₄	—	8	2	no	—
763	D₄	—	8	2	no	—
764	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	4	no	—
767	C₂×C₄	—	2	4	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	1	no	—
774	C₂×C₄	—	4	8	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	—	8	1	no	—
781	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
782	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
785	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
786	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
787	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
788	C₈	—	2	2	no	—
789	C₈	—	2	4	no	—
790	C₈	—	2	2	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	4	no	—
793	C₂²	—	2	4	no	—
794	C₂²	—	2	1	no	—
795	C₂²	—	2	4	no	—
796	C₂²	—	2	1	no	—
797	C₂²	—	2	4	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	8	4	no	—
810	C₂²	—	16	8	no	—
811	C₂²	—	16	8	no	—
812	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	4	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	4	2	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	C₂₃×#576	1	2	yes	—
823	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
824	C₂	—	4	1	no	—
825	C₂	—	4	4	no	—
826	C₂	—	4	4	no	—
827	C₂	—	8	2	no	—
828	C₂	—	8	2	no	—
829	C₂	—	8	2	no	—
830	C₂	C₂₃×#3484	1	1	yes	characteristic
831	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
832	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3549	C₂	semidirect
2. C₂₃×#3496	C₂	semidirect
3. C₂₃×#3325	C₂	semidirect
4. C₂₃×#3319	C₂	semidirect
5. C₂₃×#3303	C₂	semidirect
6. D₄×D₈×C₂₃	C₂	semidirect
7. C₂₃×#3272	C₂	semidirect
8. C₂₃×#3264	C₂	semidirect
9. C₂₃×#3214	C₂	semidirect
10. C₂₃×#3207	C₂	semidirect
11. C₂₃×#3198	C₂	semidirect
12. C₂₃×#3109	C₂	semidirect
13. C₂₃×#3100	C₂	semidirect
14. C₂₃×#3008	C₂	semidirect
15. C₂₃×#2981	C₂	semidirect
16. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂²×D₈×C₂₃	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#555	C₂²	semidirect
24. C₂₃×#547	C₂²	semidirect
26. C₂₃×#546	C₂²	semidirect
29. D₄²×C₂₃	C₂²	semidirect
30. D₄²×C₂₃	C₂²	semidirect
31. D₄²×C₂₃	C₂²	semidirect
32. C₂₃×#537	C₂²	semidirect
35. C₂₃×#535	C₂²	semidirect
38. C₂₃×#532	C₂²	semidirect
39. C₂₃×#532	C₂²	semidirect
40. C₂₃×#532	C₂²	semidirect
42. C₂×C₄×D₄×C₂₃	C₂²	semidirect
43. C₂₃×#496	C₂²	semidirect
44. C₂₃×#493	C₂²	semidirect
45. C₂₃×#492	C₂²	semidirect
46. C₂₃×#489	C₂²	semidirect
47. C₂₃×#487	C₂²	semidirect
48. C₂₃×#486	C₂²	semidirect
49. C₂₃×#485	C₂²	semidirect
50. C₂₃×#482	C₂²	semidirect
51. C₂₃×#481	C₂²	semidirect
52. C₂₃×#480	C₂²	semidirect
53. C₂₃×#476	C₂²	semidirect
54. C₂₃×#474	C₂²	semidirect
55. C₂₃×#469	C₂²	semidirect
56. C₂₃×#468	C₂²	semidirect
57. C₂₃×#466	C₂²	semidirect
58. C₂₃×#465	C₂²	semidirect
59. C₂₃×#463	C₂²	semidirect
60. C₂₃×#461	C₂²	semidirect
61. C₂₃×#459	C₂²	semidirect
62. C₂₃×#459	C₂²	semidirect
63. C₂₃×#459	C₂²	semidirect
64. C₂₃×#450	C₂²	semidirect
65. C₂₃×#449	C₂²	semidirect
66. C₂₃×#449	C₂²	semidirect
67. C₂₃×#449	C₂²	semidirect
68. C₂₃×#449	C₂²	semidirect
69. C₂₃×#447	C₂²	semidirect
70. C₂₃×#447	C₂²	semidirect
71. C₂₃×#447	C₂²	semidirect
72. C₂₃×#447	C₂²	semidirect
73. C₂₃×#447	C₂²	semidirect
74. C₂₃×#442	C₂²	semidirect
75. C₄×D₈×C₂₃	C₂²	semidirect
76. C₄×D₈×C₂₃	C₂²	semidirect
77. C₂₃×#436	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₂₃×#432	C₂²	semidirect
81. C₂₃×#431	C₂²	semidirect
82. C₂₃×#418	C₂²	semidirect
83. C₂₃×#416	C₂²	semidirect
84. C₂₃×#408	C₂²	semidirect
303. #61679	C₂₃	direct (N × H)
375. #3549	C₂×C₂₃	semidirect
376. #3496	C₂×C₂₃	semidirect
377. #3325	C₂×C₂₃	semidirect
378. #3319	C₂×C₂₃	semidirect
379. #3303	C₂×C₂₃	semidirect
380. D₄×D₈	C₂×C₂₃	semidirect
381. #3272	C₂×C₂₃	semidirect
382. #3264	C₂×C₂₃	semidirect
383. #3214	C₂×C₂₃	semidirect
384. #3207	C₂×C₂₃	semidirect
385. #3198	C₂×C₂₃	semidirect
386. #3109	C₂×C₂₃	semidirect
387. #3100	C₂×C₂₃	semidirect
388. #3008	C₂×C₂₃	semidirect
389. #2981	C₂×C₂₃	semidirect
423. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
424. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
425. C₂²×D₈	C₂²×C₂₃	semidirect
428. #555	C₂²×C₂₃	semidirect
429. #555	C₂²×C₂₃	semidirect
431. #547	C₂²×C₂₃	semidirect
433. #546	C₂²×C₂₃	semidirect
436. D₄²	C₂²×C₂₃	semidirect
437. D₄²	C₂²×C₂₃	semidirect
438. D₄²	C₂²×C₂₃	semidirect
439. #537	C₂²×C₂₃	semidirect
442. #535	C₂²×C₂₃	semidirect
445. #532	C₂²×C₂₃	semidirect
446. #532	C₂²×C₂₃	semidirect
447. #532	C₂²×C₂₃	semidirect
449. C₂×C₄×D₄	C₂²×C₂₃	semidirect
450. #496	C₂²×C₂₃	semidirect
451. #493	C₂²×C₂₃	semidirect
452. #492	C₂²×C₂₃	semidirect
453. #489	C₂²×C₂₃	semidirect
454. #487	C₂²×C₂₃	semidirect
455. #486	C₂²×C₂₃	semidirect
456. #485	C₂²×C₂₃	semidirect
457. #482	C₂²×C₂₃	semidirect
458. #481	C₂²×C₂₃	semidirect
459. #480	C₂²×C₂₃	semidirect
460. #476	C₂²×C₂₃	semidirect
461. #474	C₂²×C₂₃	semidirect
462. #469	C₂²×C₂₃	semidirect
463. #468	C₂²×C₂₃	semidirect
464. #466	C₂²×C₂₃	semidirect
465. #465	C₂²×C₂₃	semidirect
466. #463	C₂²×C₂₃	semidirect
467. #461	C₂²×C₂₃	semidirect
468. #459	C₂²×C₂₃	semidirect
469. #459	C₂²×C₂₃	semidirect
470. #459	C₂²×C₂₃	semidirect
471. #450	C₂²×C₂₃	semidirect
472. #449	C₂²×C₂₃	semidirect
473. #449	C₂²×C₂₃	semidirect
474. #449	C₂²×C₂₃	semidirect
475. #449	C₂²×C₂₃	semidirect
476. #447	C₂²×C₂₃	semidirect
477. #447	C₂²×C₂₃	semidirect
478. #447	C₂²×C₂₃	semidirect
479. #447	C₂²×C₂₃	semidirect
480. #447	C₂²×C₂₃	semidirect
481. #442	C₂²×C₂₃	semidirect
482. C₄×D₈	C₂²×C₂₃	semidirect
483. C₄×D₈	C₂²×C₂₃	semidirect
484. #436	C₂²×C₂₃	semidirect
485. #435	C₂²×C₂₃	semidirect
486. C₈×D₄	C₂²×C₂₃	semidirect
487. #432	C₂²×C₂₃	semidirect
488. #431	C₂²×C₂₃	semidirect
489. #418	C₂²×C₂₃	semidirect
490. #416	C₂²×C₂₃	semidirect
491. #408	C₂²×C₂₃	semidirect
616. C₂₃	#61679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3549	2
C₂₃×#3496	2
C₂₃×#3325	2
C₂₃×#3319	2
C₂₃×#3303	2
D₄×D₈×C₂₃	2
C₂₃×#3272	2
C₂₃×#3264	2
C₂₃×#3214	2
C₂₃×#3207	2
C₂₃×#3198	2
C₂₃×#3109	2
C₂₃×#3100	2
C₂₃×#3008	2
C₂₃×#2981	2
#61679	23

Subgroups — C23×#61679 #19209305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61679 #19209305