Subgroups — C₂₃×#62556 #19210182

Order 5888.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3558	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3365	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3316	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3310	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3300	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3296	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3244	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3234	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3222	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3178	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#3136	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#564	—	2	1	no	—
21	C₂₃×#563	—	2	1	no	—
22	C₂₃×#562	—	2	1	no	—
23	C₂₃×H(3,𝔽₄)	—	2	1	no	—
24	C₂₃×#559	C₂²	1	2	yes	—
25	C₂₃×#557	C₂²	1	2	yes	complemented
26	C₂₃×#554	C₂²	1	2	yes	complemented
27	C₂₃×#552	—	2	2	no	—
28	C₂₃×#552	C₂²	1	2	yes	complemented
29	C₂₃×#552	C₂²	1	2	yes	complemented
30	C₂₃×#548	C₂²	1	2	yes	—
31	C₂₃×#546	—	2	2	no	—
32	C₂₃×#546	C₂²	1	2	yes	—
33	D₄²×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#544	—	2	1	no	—
35	C₂₃×#544	C₂²	1	2	yes	complemented
36	C₂₃×#542	C₂²	1	2	yes	—
37	C₂₃×#541	—	2	2	no	—
38	C₂₃×#541	C₂²	1	2	yes	complemented
39	C₂₃×#539	—	2	1	no	—
40	C₂₃×#538	—	2	2	no	—
41	C₂₃×#538	—	2	1	no	—
42	C₂₃×#535	C₂²	1	2	yes	—
43	C₂₃×#534	—	2	1	no	—
44	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#532	C₂²	1	1	yes	characteristic
46	C₂₃×#529	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
49	C₂₃×#501	C₂²	1	2	yes	complemented
50	C₂₃×#498	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#497	C₂²	1	2	yes	complemented
52	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#490	C₂²	1	2	yes	—
54	C₂₃×#490	C₂²	1	2	yes	complemented
55	C₂₃×#489	C₂²	1	2	yes	complemented
56	C₂₃×#489	C₂²	1	2	yes	complemented
57	C₂₃×#488	C₂²	1	2	yes	complemented
58	C₂₃×#488	C₂²	1	2	yes	complemented
59	C₂₃×#488	C₂²	1	2	yes	complemented
60	C₂₃×#488	C₂²	1	2	yes	complemented
61	C₂₃×#488	C₂²	1	2	yes	complemented
62	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#486	C₂²	1	2	yes	—
64	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#485	C₂²	1	2	yes	complemented
66	C₂₃×#483	C₂²	1	2	yes	complemented
67	C₂₃×#482	C₂²	1	2	yes	—
68	C₂₃×#481	C₂²	1	2	yes	—
69	C₂₃×#481	C₂²	1	2	yes	complemented
70	C₂₃×#480	C₂²	1	2	yes	complemented
71	C₂₃×#479	C₂²	1	2	yes	complemented
72	C₂₃×#478	C₂²	1	2	yes	complemented
73	C₂₃×#478	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#476	C₂²	1	2	yes	complemented
76	C₂₃×#475	C₂²	1	2	yes	complemented
77	C₂₃×#470	C₂²	1	2	yes	complemented
78	C₂₃×#468	C₂²	1	2	yes	—
79	C₂₃×#467	C₂²	1	2	yes	complemented
80	C₂₃×#465	C₂²	1	2	yes	—
81	C₂₃×#465	C₂²	1	2	yes	complemented
82	C₂₃×#465	C₂²	1	2	yes	complemented
83	C₂₃×#464	C₂²	1	2	yes	complemented
84	C₂₃×#464	C₂²	1	2	yes	complemented
85	C₂₃×#464	C₂²	1	2	yes	complemented
86	C₂₃×#464	C₂²	1	2	yes	complemented
87	C₂₃×#460	C₂²	1	2	yes	—
88	C₂₃×#460	C₂²	1	2	yes	—
89	C₂₃×#452	C₂²	1	2	yes	complemented
90	C₂₃×#452	C₂²	1	2	yes	complemented
91	C₂₃×#451	C₂²	1	2	yes	complemented
92	C₂₃×#450	C₂²	1	2	yes	—
93	C₂₃×#450	C₂²	1	2	yes	complemented
94	C₂₃×#450	C₂²	1	2	yes	complemented
95	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
96	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
97	C₂₃×#441	C₂²	1	2	yes	complemented
98	C₂₃×#440	C₂²	1	2	yes	complemented
99	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
100	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
101	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
103	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
104	C₂₃×#435	C₂²	1	2	yes	complemented
105	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
106	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#433	C₂²	1	2	yes	complemented
108	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#418	C₂²	1	2	yes	complemented
110	C₂₃×#417	C₂²	1	2	yes	complemented
111	C₂₃×#416	C₂²	1	2	yes	complemented
112	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
115	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
116	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
117	C₂₃×#405	C₂²	1	2	yes	complemented
118	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₂₃	—	2	1	no	—
120	C₂×#41×C₂₃	C₂³	1	2	yes	—
121	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₂₃	—	2	2	no	—
123	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
135	C₂₃×C₄⋊Q₈	—	2	2	no	—
136	C₂₃×C₄⋊Q₈	—	2	2	no	—
137	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
141	C₂₃×#127	C₂³	1	2	yes	—
142	C₂₃×#127	C₂³	1	1	yes	characteristic
143	C₂₃×#126	—	2	2	no	—
144	C₂₃×#126	—	2	2	no	—
145	C₂₃×#126	—	2	2	no	—
146	C₂₃×#126	—	2	2	no	—
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	D₄	1	2	yes	—
149	C₂₃×#125	—	2	2	no	—
150	C₂₃×#125	—	2	2	no	—
151	C₂₃×#125	—	2	2	no	—
152	C₂₃×#125	—	2	2	no	—
153	C₂₃×#125	—	2	2	no	—
154	C₂₃×#125	—	2	2	no	—
155	C₂₃×#125	—	2	2	no	—
156	C₂₃×#125	—	2	2	no	—
157	C₂₃×#125	—	2	1	no	—
158	C₂₃×#125	—	2	1	no	—
159	C₂₃×#125	—	2	1	no	—
160	C₂₃×#125	D₄	1	1	yes	characteristic
161	C₂₃×#125	C₂³	1	2	yes	—
162	C₂₃×#125	C₂³	1	2	yes	—
163	C₂₃×#125	C₂³	1	2	yes	—
164	C₂₃×#124	—	2	2	no	—
165	C₂₃×#124	—	2	2	no	—
166	C₂₃×#124	—	2	2	no	—
167	C₂₃×#124	—	2	1	no	—
168	C₂₃×#124	—	2	1	no	—
169	C₂₃×#124	—	2	1	no	—
170	C₂₃×#124	D₄	1	1	yes	characteristic
171	C₂₃×#124	C₂³	1	2	yes	—
172	C₂₃×#124	C₂³	1	2	yes	—
173	C₂₃×#124	C₂³	1	2	yes	—
174	C₂₃×#123	—	2	2	no	—
175	C₂₃×#123	—	2	2	no	—
176	C₂₃×#123	—	2	2	no	—
177	C₂₃×#123	—	2	2	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	D₄	1	2	yes	—
181	C₂₃×C₂²⋊Q₈	—	2	1	no	—
182	C₂₃×C₂²⋊Q₈	—	2	2	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	—	2	2	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	2	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
189	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
193	C₂₃×#121	—	2	2	no	—
194	C₂₃×#121	—	2	1	no	—
195	C₂₃×#121	—	2	2	no	—
196	C₂₃×#121	—	2	2	no	—
197	C₂₃×#121	—	2	2	no	—
198	C₂₃×#121	—	2	2	no	—
199	C₂₃×#121	D₄	1	1	yes	characteristic
200	C₂₃×#121	C₂³	1	2	yes	—
201	C₂₃×#121	C₂³	1	2	yes	—
202	C₂₃×#120	—	2	2	no	—
203	C₂₃×#120	—	2	2	no	—
204	C₂₃×#120	—	2	2	no	—
205	C₂₃×#120	—	2	2	no	—
206	C₂₃×#120	—	2	2	no	—
207	C₄×Q₈×C₂₃	—	2	2	no	—
208	C₄×Q₈×C₂₃	—	2	1	no	—
209	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
210	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
211	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
212	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
213	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₂₃	—	2	2	no	—
215	C₄×D₄×C₂₃	—	2	2	no	—
216	C₄×D₄×C₂₃	—	2	2	no	—
217	C₄×D₄×C₂₃	—	2	1	no	—
218	C₄×D₄×C₂₃	C₂³	1	2	yes	—
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	C₂³	1	2	yes	—
221	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₂₃×#117	—	2	1	no	—
223	C₂₃×#117	—	2	2	no	—
224	C₂₃×#117	—	2	2	no	—
225	C₂₃×#117	C₂³	1	2	yes	—
226	C₂₃×#117	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
228	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
233	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
234	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
235	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
236	C₂₃×#107	C₂³	1	2	yes	—
237	C₂₃×#107	C₂³	1	2	yes	—
238	C₂₃×#106	C₂³	1	2	yes	—
239	C₂₃×#106	C₂³	1	2	yes	—
240	C₂₃×#106	C₂³	1	2	yes	—
241	C₂₃×#106	C₂³	1	2	yes	—
242	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
243	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
244	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
246	C₂₃×#103	C₂³	1	2	yes	—
247	C₂₃×#103	C₂³	1	2	yes	—
248	C₂₃×#103	C₂³	1	2	yes	—
249	C₂₃×#103	C₂³	1	2	yes	—
250	C₂₃×#103	C₂³	1	2	yes	—
251	C₂₃×#103	C₂³	1	2	yes	—
252	C₂₃×#103	C₂³	1	2	yes	—
253	C₂₃×#103	C₂³	1	2	yes	—
254	C₂₃×#102	C₂³	1	2	yes	—
255	C₂₃×#102	C₂³	1	2	yes	—
256	C₂₃×#102	C₂³	1	2	yes	—
257	C₂₃×#102	C₂³	1	2	yes	—
258	C₂₃×#102	C₂³	1	2	yes	—
259	C₂₃×#102	C₂³	1	2	yes	—
260	C₂₃×#102	C₂³	1	2	yes	—
261	C₂₃×#102	C₂³	1	2	yes	—
262	C₂₃×#102	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
267	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
268	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
269	C₂₃×#97	C₂³	1	2	yes	—
270	C₂₃×#97	C₂³	1	2	yes	—
271	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
272	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
273	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
274	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
275	C₄×C₈×C₂₃	C₂³	1	2	yes	—
276	C₂⁴×C₂₃	—	2	1	no	—
277	C₂⁴×C₂₃	—	2	2	no	—
278	#41×C₂₃	—	4	2	no	—
279	#41×C₂₃	—	4	2	no	—
280	#41×C₂₃	—	8	2	no	—
281	C₂×Q₈×C₂₃	—	2	1	no	—
282	C₂×Q₈×C₂₃	—	2	2	no	—
283	C₂×Q₈×C₂₃	—	2	1	no	—
284	C₂×Q₈×C₂₃	—	2	1	no	—
285	C₂×Q₈×C₂₃	—	4	1	no	—
286	C₂×Q₈×C₂₃	—	4	1	no	—
287	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
289	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
290	C₂×D₄×C₂₃	—	2	2	no	—
291	C₂×D₄×C₂₃	—	2	2	no	—
292	C₂×D₄×C₂₃	—	2	2	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	1	no	—
295	C₂×D₄×C₂₃	—	2	1	no	—
296	C₂×D₄×C₂₃	—	2	1	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	2	no	—
299	C₂×D₄×C₂₃	—	4	1	no	—
300	C₂×D₄×C₂₃	—	4	1	no	—
301	C₂×D₄×C₂₃	—	4	2	no	—
302	C₂×D₄×C₂₃	—	4	2	no	—
303	C₂×D₄×C₂₃	—	8	4	no	—
304	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	—	2	1	no	—
309	C₂²×C₄×C₂₃	—	2	1	no	—
310	C₂²×C₄×C₂₃	—	2	1	no	—
311	C₂²×C₄×C₂₃	—	2	2	no	—
312	C₂²×C₄×C₂₃	—	2	2	no	—
313	C₂²×C₄×C₂₃	—	2	2	no	—
314	C₂²×C₄×C₂₃	—	2	2	no	—
315	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	Q₁₆×C₂₃	—	4	2	no	—
320	Q₁₆×C₂₃	—	4	2	no	—
321	SD₁₆×C₂₃	—	4	2	no	—
322	SD₁₆×C₂₃	—	4	2	no	—
323	SD₁₆×C₂₃	—	4	2	no	—
324	SD₁₆×C₂₃	—	4	2	no	—
325	M₁₆×C₂₃	—	4	2	no	—
326	C₂×C₈×C₂₃	—	4	1	no	—
327	C₂×C₈×C₂₃	—	4	2	no	—
328	C₂×C₈×C₂₃	—	4	1	no	—
329	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
332	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
333	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	1	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	1	no	—
342	C₄⋊C₄×C₂₃	—	2	1	no	—
343	C₄⋊C₄×C₂₃	—	2	2	no	—
344	C₄⋊C₄×C₂₃	—	2	2	no	—
345	C₄⋊C₄×C₂₃	—	2	2	no	—
346	C₄⋊C₄×C₂₃	—	2	1	no	—
347	C₄⋊C₄×C₂₃	—	2	2	no	—
348	C₄⋊C₄×C₂₃	—	2	1	no	—
349	C₄⋊C₄×C₂₃	—	2	2	no	—
350	C₄⋊C₄×C₂₃	—	2	2	no	—
351	C₄⋊C₄×C₂₃	—	2	2	no	—
352	C₄⋊C₄×C₂₃	—	2	1	no	—
353	C₄⋊C₄×C₂₃	—	2	2	no	—
354	C₄⋊C₄×C₂₃	—	2	2	no	—
355	C₄⋊C₄×C₂₃	—	2	2	no	—
356	C₄⋊C₄×C₂₃	—	2	2	no	—
357	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
367	C₂²⋊C₄×C₂₃	—	2	2	no	—
368	C₂²⋊C₄×C₂₃	—	2	2	no	—
369	C₂²⋊C₄×C₂₃	—	2	2	no	—
370	C₂²⋊C₄×C₂₃	—	2	2	no	—
371	C₂²⋊C₄×C₂₃	—	2	2	no	—
372	C₂²⋊C₄×C₂₃	—	2	2	no	—
373	C₂²⋊C₄×C₂₃	—	2	2	no	—
374	C₂²⋊C₄×C₂₃	—	2	2	no	—
375	C₂²⋊C₄×C₂₃	—	2	2	no	—
376	C₂²⋊C₄×C₂₃	—	2	2	no	—
377	C₂²⋊C₄×C₂₃	—	2	2	no	—
378	C₂²⋊C₄×C₂₃	—	2	2	no	—
379	C₂²⋊C₄×C₂₃	—	2	2	no	—
380	C₂²⋊C₄×C₂₃	—	2	2	no	—
381	C₂²⋊C₄×C₂₃	—	2	2	no	—
382	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
383	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
387	C₄²×C₂₃	—	2	2	no	—
388	C₄²×C₂₃	—	2	2	no	—
389	C₄²×C₂₃	—	2	2	no	—
390	C₄²×C₂₃	—	2	2	no	—
391	C₄²×C₂₃	—	2	2	no	—
392	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₄²×C₂₃	C₂⁴	1	2	yes	—
396	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
397	#62556	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂³×C₂₃	—	2	2	no	—
399	C₂³×C₂₃	—	2	2	no	—
400	C₂³×C₂₃	—	4	2	no	—
401	C₂³×C₂₃	—	8	1	no	—
402	C₂³×C₂₃	—	8	2	no	—
403	C₂³×C₂₃	—	8	2	no	—
404	C₂³×C₂₃	—	8	1	no	—
405	C₂³×C₂₃	—	8	2	no	—
406	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
407	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
408	Q₈×C₂₃	—	2	2	no	—
409	Q₈×C₂₃	—	2	2	no	—
410	Q₈×C₂₃	—	2	2	no	—
411	Q₈×C₂₃	—	2	2	no	—
412	Q₈×C₂₃	—	4	1	no	—
413	Q₈×C₂₃	—	8	1	no	—
414	Q₈×C₂₃	—	8	2	no	—
415	Q₈×C₂₃	—	8	1	no	—
416	Q₈×C₂₃	—	8	1	no	—
417	D₄×C₂₃	—	2	4	no	—
418	D₄×C₂₃	—	2	2	no	—
419	D₄×C₂₃	—	2	2	no	—
420	D₄×C₂₃	—	2	2	no	—
421	D₄×C₂₃	—	2	2	no	—
422	D₄×C₂₃	—	4	1	no	—
423	D₄×C₂₃	—	4	4	no	—
424	D₄×C₂₃	—	8	1	no	—
425	D₄×C₂₃	—	8	2	no	—
426	D₄×C₂₃	—	8	2	no	—
427	D₄×C₂₃	—	8	1	no	—
428	D₄×C₂₃	—	8	2	no	—
429	D₄×C₂₃	—	8	1	no	—
430	D₄×C₂₃	—	8	2	no	—
431	D₄×C₂₃	—	8	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	1	no	—
434	C₂×C₄×C₂₃	—	2	1	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	2	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	2	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	4	1	no	—
444	C₂×C₄×C₂₃	—	4	2	no	—
445	C₂×C₄×C₂₃	—	8	2	no	—
446	C₂×C₄×C₂₃	—	8	2	no	—
447	C₂×C₄×C₂₃	—	8	2	no	—
448	C₂×C₄×C₂₃	—	8	1	no	—
449	C₂×C₄×C₂₃	—	8	2	no	—
450	C₂×C₄×C₂₃	—	8	1	no	—
451	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
455	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
460	C₈×C₂₃	—	2	1	no	—
461	C₈×C₂₃	—	2	1	no	—
462	C₈×C₂₃	—	2	1	no	—
463	C₈×C₂₃	—	2	1	no	—
464	C₈×C₂₃	—	2	2	no	—
465	C₈×C₂₃	—	2	2	no	—
466	#3563	C₂×C₂₃	1	1	yes	characteristic, complemented
467	#3558	C₂×C₂₃	1	1	yes	characteristic
468	#3371	C₂×C₂₃	1	2	yes	complemented
469	#3365	C₂×C₂₃	1	2	yes	complemented
470	#3323	C₂×C₂₃	1	2	yes	complemented
471	#3316	C₂×C₂₃	1	2	yes	complemented
472	#3310	C₂×C₂₃	1	2	yes	complemented
473	#3300	C₂×C₂₃	1	2	yes	complemented
474	#3296	C₂×C₂₃	1	2	yes	complemented
475	#3295	C₂×C₂₃	1	2	yes	complemented
476	#3244	C₂×C₂₃	1	2	yes	complemented
477	#3234	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#3222	C₂×C₂₃	1	2	yes	complemented
479	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#3178	C₂×C₂₃	1	2	yes	complemented
481	#3167	C₂×C₂₃	1	1	yes	characteristic, complemented
482	#3136	C₂×C₂₃	1	2	yes	complemented
483	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
484	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
485	C₂²×C₂₃	—	2	1	no	—
486	C₂²×C₂₃	—	2	1	no	—
487	C₂²×C₂₃	—	2	2	no	—
488	C₂²×C₂₃	—	2	2	no	—
489	C₂²×C₂₃	—	2	2	no	—
490	C₂²×C₂₃	—	4	2	no	—
491	C₂²×C₂₃	—	4	2	no	—
492	C₂²×C₂₃	—	4	2	no	—
493	C₂²×C₂₃	—	4	2	no	—
494	C₂²×C₂₃	—	4	2	no	—
495	C₂²×C₂₃	—	4	2	no	—
496	C₂²×C₂₃	—	16	2	no	—
497	C₂²×C₂₃	—	16	4	no	—
498	C₂²×C₂₃	#577	1	2	yes	—
499	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₂₃	—	2	1	no	—
501	C₄×C₂₃	—	2	1	no	—
502	C₄×C₂₃	—	2	2	no	—
503	C₄×C₂₃	—	2	2	no	—
504	C₄×C₂₃	—	2	1	no	—
505	C₄×C₂₃	—	2	1	no	—
506	C₄×C₂₃	—	2	1	no	—
507	C₄×C₂₃	—	2	2	no	—
508	C₄×C₂₃	—	4	2	no	—
509	C₄×C₂₃	—	4	2	no	—
510	C₄×C₂₃	—	4	2	no	—
511	C₄×C₂₃	—	4	2	no	—
512	C₄×C₂₃	—	4	2	no	—
513	C₄×C₂₃	—	4	2	no	—
514	C₄×C₂₃	#585	1	1	yes	characteristic
515	C₄×C₂₃	#585	1	1	yes	characteristic
516	#564	—	2	1	no	—
517	#563	—	2	1	no	—
518	#562	—	2	1	no	—
519	H(3,𝔽₄)	—	2	1	no	—
520	#559	C₂²×C₂₃	1	2	yes	—
521	#557	C₂²×C₂₃	1	2	yes	complemented
522	#554	C₂²×C₂₃	1	2	yes	complemented
523	#552	—	2	2	no	—
524	#552	C₂²×C₂₃	1	2	yes	complemented
525	#552	C₂²×C₂₃	1	2	yes	complemented
526	#548	C₂²×C₂₃	1	2	yes	—
527	#546	—	2	2	no	—
528	#546	C₂²×C₂₃	1	2	yes	—
529	D₄²	C₂²×C₂₃	1	2	yes	—
530	#544	—	2	1	no	—
531	#544	C₂²×C₂₃	1	2	yes	complemented
532	#542	C₂²×C₂₃	1	2	yes	—
533	#541	—	2	2	no	—
534	#541	C₂²×C₂₃	1	2	yes	complemented
535	#539	—	2	1	no	—
536	#538	—	2	2	no	—
537	#538	—	2	1	no	—
538	#535	C₂²×C₂₃	1	2	yes	—
539	#534	—	2	1	no	—
540	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
541	#532	C₂²×C₂₃	1	1	yes	characteristic
542	#529	C₂²×C₂₃	1	1	yes	characteristic
543	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
544	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
545	#501	C₂²×C₂₃	1	2	yes	complemented
546	#498	C₂²×C₂₃	1	1	yes	characteristic, complemented
547	#497	C₂²×C₂₃	1	2	yes	complemented
548	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
549	#490	C₂²×C₂₃	1	2	yes	—
550	#490	C₂²×C₂₃	1	2	yes	complemented
551	#489	C₂²×C₂₃	1	2	yes	complemented
552	#489	C₂²×C₂₃	1	2	yes	complemented
553	#488	C₂²×C₂₃	1	2	yes	complemented
554	#488	C₂²×C₂₃	1	2	yes	complemented
555	#488	C₂²×C₂₃	1	2	yes	complemented
556	#488	C₂²×C₂₃	1	2	yes	complemented
557	#488	C₂²×C₂₃	1	2	yes	complemented
558	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
559	#486	C₂²×C₂₃	1	2	yes	—
560	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
561	#485	C₂²×C₂₃	1	2	yes	complemented
562	#483	C₂²×C₂₃	1	2	yes	complemented
563	#482	C₂²×C₂₃	1	2	yes	—
564	#481	C₂²×C₂₃	1	2	yes	—
565	#481	C₂²×C₂₃	1	2	yes	complemented
566	#480	C₂²×C₂₃	1	2	yes	complemented
567	#479	C₂²×C₂₃	1	2	yes	complemented
568	#478	C₂²×C₂₃	1	2	yes	complemented
569	#478	C₂²×C₂₃	1	2	yes	complemented
570	#478	C₂²×C₂₃	1	2	yes	complemented
571	#476	C₂²×C₂₃	1	2	yes	complemented
572	#475	C₂²×C₂₃	1	2	yes	complemented
573	#470	C₂²×C₂₃	1	2	yes	complemented
574	#468	C₂²×C₂₃	1	2	yes	—
575	#467	C₂²×C₂₃	1	2	yes	complemented
576	#465	C₂²×C₂₃	1	2	yes	—
577	#465	C₂²×C₂₃	1	2	yes	complemented
578	#465	C₂²×C₂₃	1	2	yes	complemented
579	#464	C₂²×C₂₃	1	2	yes	complemented
580	#464	C₂²×C₂₃	1	2	yes	complemented
581	#464	C₂²×C₂₃	1	2	yes	complemented
582	#464	C₂²×C₂₃	1	2	yes	complemented
583	#460	C₂²×C₂₃	1	2	yes	—
584	#460	C₂²×C₂₃	1	2	yes	—
585	#452	C₂²×C₂₃	1	2	yes	complemented
586	#452	C₂²×C₂₃	1	2	yes	complemented
587	#451	C₂²×C₂₃	1	2	yes	complemented
588	#450	C₂²×C₂₃	1	2	yes	—
589	#450	C₂²×C₂₃	1	2	yes	complemented
590	#450	C₂²×C₂₃	1	2	yes	complemented
591	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
592	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
593	#441	C₂²×C₂₃	1	2	yes	complemented
594	#440	C₂²×C₂₃	1	2	yes	complemented
595	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
596	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
597	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
598	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
599	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
600	#435	C₂²×C₂₃	1	2	yes	complemented
601	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
602	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
603	#433	C₂²×C₂₃	1	2	yes	complemented
604	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	#418	C₂²×C₂₃	1	2	yes	complemented
606	#417	C₂²×C₂₃	1	2	yes	complemented
607	#416	C₂²×C₂₃	1	2	yes	complemented
608	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
609	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic, complemented
610	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
611	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
612	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
613	#405	C₂²×C₂₃	1	2	yes	complemented
614	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
615	C₂×C₂₃	—	2	2	no	—
616	C₂×C₂₃	—	4	2	no	—
617	C₂×C₂₃	—	8	2	no	—
618	C₂×C₂₃	—	8	2	no	—
619	C₂×C₂₃	#3500	1	1	yes	characteristic
620	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
621	C₂×C₂₃	#3584	1	1	yes	characteristic
622	C₂×#41	—	2	1	no	—
623	C₂×#41	C₂³×C₂₃	1	2	yes	—
624	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
625	C₂²×D₄	—	2	2	no	—
626	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
627	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
628	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
629	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
634	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
635	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
636	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
638	C₄⋊Q₈	—	2	2	no	—
639	C₄⋊Q₈	—	2	2	no	—
640	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
641	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
642	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
644	#127	C₂³×C₂₃	1	1	yes	characteristic
645	#127	C₂³×C₂₃	1	2	yes	—
646	#126	—	2	2	no	—
647	#126	—	2	2	no	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	D₄×C₂₃	1	2	yes	—
652	#125	—	2	2	no	—
653	#125	—	2	2	no	—
654	#125	—	2	2	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	1	no	—
661	#125	—	2	1	no	—
662	#125	—	2	1	no	—
663	#125	D₄×C₂₃	1	1	yes	characteristic
664	#125	C₂³×C₂₃	1	2	yes	—
665	#125	C₂³×C₂₃	1	2	yes	—
666	#125	C₂³×C₂₃	1	2	yes	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	1	no	—
671	#124	—	2	1	no	—
672	#124	—	2	1	no	—
673	#124	D₄×C₂₃	1	1	yes	characteristic
674	#124	C₂³×C₂₃	1	2	yes	—
675	#124	C₂³×C₂₃	1	2	yes	—
676	#124	C₂³×C₂₃	1	2	yes	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	D₄×C₂₃	1	2	yes	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	2	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
692	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
693	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
694	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
695	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
696	#121	—	2	2	no	—
697	#121	—	2	1	no	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	2	no	—
701	#121	—	2	2	no	—
702	#121	D₄×C₂₃	1	1	yes	characteristic
703	#121	C₂³×C₂₃	1	2	yes	—
704	#121	C₂³×C₂₃	1	2	yes	—
705	#120	—	2	2	no	—
706	#120	—	2	2	no	—
707	#120	—	2	2	no	—
708	#120	—	2	2	no	—
709	#120	—	2	2	no	—
710	C₄×Q₈	—	2	2	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
713	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
714	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
715	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
716	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
717	C₄×D₄	—	2	2	no	—
718	C₄×D₄	—	2	2	no	—
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	1	no	—
721	C₄×D₄	C₂³×C₂₃	1	2	yes	—
722	C₄×D₄	C₂³×C₂₃	1	2	yes	—
723	C₄×D₄	C₂³×C₂₃	1	2	yes	—
724	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
725	#117	—	2	1	no	—
726	#117	—	2	2	no	—
727	#117	—	2	2	no	—
728	#117	C₂³×C₂₃	1	2	yes	—
729	#117	C₂³×C₂₃	1	2	yes	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	1	no	—
732	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
735	C₂×C₂²⋊C₄	—	2	1	no	—
736	C₂×C₂²⋊C₄	—	2	1	no	—
737	C₂×C₂²⋊C₄	—	2	2	no	—
738	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
739	#107	C₂³×C₂₃	1	2	yes	—
740	#107	C₂³×C₂₃	1	2	yes	—
741	#106	C₂³×C₂₃	1	2	yes	—
742	#106	C₂³×C₂₃	1	2	yes	—
743	#106	C₂³×C₂₃	1	2	yes	—
744	#106	C₂³×C₂₃	1	2	yes	—
745	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
746	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
747	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
749	#103	C₂³×C₂₃	1	2	yes	—
750	#103	C₂³×C₂₃	1	2	yes	—
751	#103	C₂³×C₂₃	1	2	yes	—
752	#103	C₂³×C₂₃	1	2	yes	—
753	#103	C₂³×C₂₃	1	2	yes	—
754	#103	C₂³×C₂₃	1	2	yes	—
755	#103	C₂³×C₂₃	1	2	yes	—
756	#103	C₂³×C₂₃	1	2	yes	—
757	#102	C₂³×C₂₃	1	2	yes	—
758	#102	C₂³×C₂₃	1	2	yes	—
759	#102	C₂³×C₂₃	1	2	yes	—
760	#102	C₂³×C₂₃	1	2	yes	—
761	#102	C₂³×C₂₃	1	2	yes	—
762	#102	C₂³×C₂₃	1	2	yes	—
763	#102	C₂³×C₂₃	1	2	yes	—
764	#102	C₂³×C₂₃	1	2	yes	—
765	#102	C₂³×C₂₃	1	2	yes	—
766	#102	C₂³×C₂₃	1	2	yes	—
767	#102	C₂³×C₂₃	1	2	yes	—
768	#102	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
772	#97	C₂³×C₂₃	1	2	yes	—
773	#97	C₂³×C₂₃	1	2	yes	—
774	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
775	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
776	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
777	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
778	C₄×C₈	C₂³×C₂₃	1	2	yes	—
779	C₂₃	#62556	1	1	yes	characteristic, direct product factor, Sylow
780	C₂⁴	—	2	1	no	—
781	C₂⁴	—	2	2	no	—
782	#41	—	4	2	no	—
783	#41	—	4	2	no	—
784	#41	—	8	2	no	—
785	C₂×Q₈	—	2	1	no	—
786	C₂×Q₈	—	2	2	no	—
787	C₂×Q₈	—	2	1	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	4	1	no	—
790	C₂×Q₈	—	4	1	no	—
791	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	1	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	4	1	no	—
804	C₂×D₄	—	4	1	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	4	2	no	—
807	C₂×D₄	—	8	4	no	—
808	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
809	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
810	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
811	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	1	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
821	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
822	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
823	Q₁₆	—	4	2	no	—
824	Q₁₆	—	4	2	no	—
825	SD₁₆	—	4	2	no	—
826	SD₁₆	—	4	2	no	—
827	SD₁₆	—	4	2	no	—
828	SD₁₆	—	4	2	no	—
829	M₁₆	—	4	2	no	—
830	C₂×C₈	—	4	1	no	—
831	C₂×C₈	—	4	2	no	—
832	C₂×C₈	—	4	1	no	—
833	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
834	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
835	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
836	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
837	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
838	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	1	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	1	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	2	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
862	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
863	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
865	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
866	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
867	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	—	2	2	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
890	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
897	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
898	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
899	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
900	C₄²	C₂⁴×C₂₃	1	2	yes	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	4	2	no	—
904	C₂³	—	8	1	no	—
905	C₂³	—	8	2	no	—
906	C₂³	—	8	2	no	—
907	C₂³	—	8	1	no	—
908	C₂³	—	8	2	no	—
909	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
910	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
911	Q₈	—	2	2	no	—
912	Q₈	—	2	2	no	—
913	Q₈	—	2	2	no	—
914	Q₈	—	2	2	no	—
915	Q₈	—	4	1	no	—
916	Q₈	—	8	1	no	—
917	Q₈	—	8	1	no	—
918	Q₈	—	8	1	no	—
919	Q₈	—	8	2	no	—
920	D₄	—	2	4	no	—
921	D₄	—	2	2	no	—
922	D₄	—	2	2	no	—
923	D₄	—	2	2	no	—
924	D₄	—	2	2	no	—
925	D₄	—	4	1	no	—
926	D₄	—	4	4	no	—
927	D₄	—	8	2	no	—
928	D₄	—	8	1	no	—
929	D₄	—	8	2	no	—
930	D₄	—	8	1	no	—
931	D₄	—	8	1	no	—
932	D₄	—	8	2	no	—
933	D₄	—	8	2	no	—
934	D₄	—	8	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	1	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	—	8	2	no	—
951	C₂×C₄	—	8	1	no	—
952	C₂×C₄	—	8	1	no	—
953	C₂×C₄	—	8	2	no	—
954	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
956	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
962	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
963	C₈	—	2	1	no	—
964	C₈	—	2	1	no	—
965	C₈	—	2	1	no	—
966	C₈	—	2	1	no	—
967	C₈	—	2	2	no	—
968	C₈	—	2	2	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	—	4	2	no	—
978	C₂²	—	4	2	no	—
979	C₂²	—	4	2	no	—
980	C₂²	—	16	2	no	—
981	C₂²	—	16	4	no	—
982	C₂²	C₂₃×#577	1	2	yes	—
983	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
984	C₄	—	2	2	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	2	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	2	no	—
992	C₄	—	4	2	no	—
993	C₄	—	4	2	no	—
994	C₄	—	4	2	no	—
995	C₄	—	4	2	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	2	no	—
998	C₄	C₂₃×#585	1	1	yes	characteristic
999	C₄	C₂₃×#585	1	1	yes	characteristic
1000	C₂	—	2	2	no	—
1001	C₂	—	4	2	no	—
1002	C₂	—	8	2	no	—
1003	C₂	—	8	2	no	—
1004	C₂	C₂₃×#3500	1	1	yes	characteristic
1005	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
1006	C₂	C₂₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3558	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3563	C₂	semidirect
3. C₂₃×#3371	C₂	semidirect
4. C₂₃×#3365	C₂	semidirect
5. C₂₃×#3323	C₂	semidirect
6. C₂₃×#3316	C₂	semidirect
7. C₂₃×#3310	C₂	semidirect
8. C₂₃×#3300	C₂	semidirect
9. C₂₃×#3296	C₂	semidirect
10. C₂₃×#3295	C₂	semidirect
11. C₂₃×#3244	C₂	semidirect
12. C₂₃×#3234	C₂	semidirect
13. C₂₃×#3222	C₂	semidirect
14. C₂₃×#3215	C₂	semidirect
15. C₂₃×#3178	C₂	semidirect
16. C₂₃×#3167	C₂	semidirect
17. C₂₃×#3136	C₂	semidirect
18. C₂×C₂₃×#488	C₂	semidirect
19. C₂₃×#2966	C₂	semidirect
25. C₂₃×#557	C₂²	semidirect
26. C₂₃×#554	C₂²	semidirect
28. C₂₃×#552	C₂²	semidirect
29. C₂₃×#552	C₂²	semidirect
35. C₂₃×#544	C₂²	semidirect
38. C₂₃×#541	C₂²	semidirect
44. C₂₃×#533	C₂²	semidirect
47. C₂×C₂₃×#125	C₂²	semidirect
49. C₂₃×#501	C₂²	semidirect
50. C₂₃×#498	C₂²	semidirect
51. C₂₃×#497	C₂²	semidirect
52. C₂₃×#492	C₂²	semidirect
54. C₂₃×#490	C₂²	semidirect
55. C₂₃×#489	C₂²	semidirect
56. C₂₃×#489	C₂²	semidirect
57. C₂₃×#488	C₂²	semidirect
58. C₂₃×#488	C₂²	semidirect
59. C₂₃×#488	C₂²	semidirect
60. C₂₃×#488	C₂²	semidirect
61. C₂₃×#488	C₂²	semidirect
62. C₂₃×#487	C₂²	semidirect
64. C₂₃×#486	C₂²	semidirect
65. C₂₃×#485	C₂²	semidirect
66. C₂₃×#483	C₂²	semidirect
69. C₂₃×#481	C₂²	semidirect
70. C₂₃×#480	C₂²	semidirect
71. C₂₃×#479	C₂²	semidirect
72. C₂₃×#478	C₂²	semidirect
73. C₂₃×#478	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#476	C₂²	semidirect
76. C₂₃×#475	C₂²	semidirect
77. C₂₃×#470	C₂²	semidirect
79. C₂₃×#467	C₂²	semidirect
81. C₂₃×#465	C₂²	semidirect
82. C₂₃×#465	C₂²	semidirect
83. C₂₃×#464	C₂²	semidirect
84. C₂₃×#464	C₂²	semidirect
85. C₂₃×#464	C₂²	semidirect
86. C₂₃×#464	C₂²	semidirect
89. C₂₃×#452	C₂²	semidirect
90. C₂₃×#452	C₂²	semidirect
91. C₂₃×#451	C₂²	semidirect
93. C₂₃×#450	C₂²	semidirect
94. C₂₃×#450	C₂²	semidirect
95. C₂₃×#446	C₂²	semidirect
96. C₈×Q₈×C₂₃	C₂²	semidirect
97. C₂₃×#441	C₂²	semidirect
98. C₂₃×#440	C₂²	semidirect
99. C₄×Q₁₆×C₂₃	C₂²	semidirect
100. C₄×SD₁₆×C₂₃	C₂²	semidirect
101. C₄×SD₁₆×C₂₃	C₂²	semidirect
102. C₄×SD₁₆×C₂₃	C₂²	semidirect
103. C₂₃×#436	C₂²	semidirect
104. C₂₃×#435	C₂²	semidirect
105. C₈×D₄×C₂₃	C₂²	semidirect
106. C₈×D₄×C₂₃	C₂²	semidirect
107. C₂₃×#433	C₂²	semidirect
108. C₂₃×#432	C₂²	semidirect
109. C₂₃×#418	C₂²	semidirect
110. C₂₃×#417	C₂²	semidirect
111. C₂₃×#416	C₂²	semidirect
112. C₂×C₂₃×#103	C₂²	semidirect
113. C₂×C₂₃×#103	C₂²	semidirect
116. C₂×C₂₃×#102	C₂²	semidirect
117. C₂₃×#405	C₂²	semidirect
118. C₂×C₄×C₈×C₂₃	C₂²	semidirect
397. #62556	C₂₃	direct (N × H)
466. #3563	C₂×C₂₃	semidirect
468. #3371	C₂×C₂₃	semidirect
469. #3365	C₂×C₂₃	semidirect
470. #3323	C₂×C₂₃	semidirect
471. #3316	C₂×C₂₃	semidirect
472. #3310	C₂×C₂₃	semidirect
473. #3300	C₂×C₂₃	semidirect
474. #3296	C₂×C₂₃	semidirect
475. #3295	C₂×C₂₃	semidirect
476. #3244	C₂×C₂₃	semidirect
477. #3234	C₂×C₂₃	semidirect
478. #3222	C₂×C₂₃	semidirect
479. #3215	C₂×C₂₃	semidirect
480. #3178	C₂×C₂₃	semidirect
481. #3167	C₂×C₂₃	semidirect
482. #3136	C₂×C₂₃	semidirect
483. C₂×#488	C₂×C₂₃	semidirect
484. #2966	C₂×C₂₃	semidirect
521. #557	C₂²×C₂₃	semidirect
522. #554	C₂²×C₂₃	semidirect
524. #552	C₂²×C₂₃	semidirect
525. #552	C₂²×C₂₃	semidirect
531. #544	C₂²×C₂₃	semidirect
534. #541	C₂²×C₂₃	semidirect
540. #533	C₂²×C₂₃	semidirect
543. C₂×#125	C₂²×C₂₃	semidirect
545. #501	C₂²×C₂₃	semidirect
546. #498	C₂²×C₂₃	semidirect
547. #497	C₂²×C₂₃	semidirect
548. #492	C₂²×C₂₃	semidirect
550. #490	C₂²×C₂₃	semidirect
551. #489	C₂²×C₂₃	semidirect
552. #489	C₂²×C₂₃	semidirect
553. #488	C₂²×C₂₃	semidirect
554. #488	C₂²×C₂₃	semidirect
555. #488	C₂²×C₂₃	semidirect
556. #488	C₂²×C₂₃	semidirect
557. #488	C₂²×C₂₃	semidirect
558. #487	C₂²×C₂₃	semidirect
560. #486	C₂²×C₂₃	semidirect
561. #485	C₂²×C₂₃	semidirect
562. #483	C₂²×C₂₃	semidirect
565. #481	C₂²×C₂₃	semidirect
566. #480	C₂²×C₂₃	semidirect
567. #479	C₂²×C₂₃	semidirect
568. #478	C₂²×C₂₃	semidirect
569. #478	C₂²×C₂₃	semidirect
570. #478	C₂²×C₂₃	semidirect
571. #476	C₂²×C₂₃	semidirect
572. #475	C₂²×C₂₃	semidirect
573. #470	C₂²×C₂₃	semidirect
575. #467	C₂²×C₂₃	semidirect
577. #465	C₂²×C₂₃	semidirect
578. #465	C₂²×C₂₃	semidirect
579. #464	C₂²×C₂₃	semidirect
580. #464	C₂²×C₂₃	semidirect
581. #464	C₂²×C₂₃	semidirect
582. #464	C₂²×C₂₃	semidirect
585. #452	C₂²×C₂₃	semidirect
586. #452	C₂²×C₂₃	semidirect
587. #451	C₂²×C₂₃	semidirect
589. #450	C₂²×C₂₃	semidirect
590. #450	C₂²×C₂₃	semidirect
591. #446	C₂²×C₂₃	semidirect
592. C₈×Q₈	C₂²×C₂₃	semidirect
593. #441	C₂²×C₂₃	semidirect
594. #440	C₂²×C₂₃	semidirect
595. C₄×Q₁₆	C₂²×C₂₃	semidirect
596. C₄×SD₁₆	C₂²×C₂₃	semidirect
597. C₄×SD₁₆	C₂²×C₂₃	semidirect
598. C₄×SD₁₆	C₂²×C₂₃	semidirect
599. #436	C₂²×C₂₃	semidirect
600. #435	C₂²×C₂₃	semidirect
601. C₈×D₄	C₂²×C₂₃	semidirect
602. C₈×D₄	C₂²×C₂₃	semidirect
603. #433	C₂²×C₂₃	semidirect
604. #432	C₂²×C₂₃	semidirect
605. #418	C₂²×C₂₃	semidirect
606. #417	C₂²×C₂₃	semidirect
607. #416	C₂²×C₂₃	semidirect
608. C₂×#103	C₂²×C₂₃	semidirect
609. C₂×#103	C₂²×C₂₃	semidirect
612. C₂×#102	C₂²×C₂₃	semidirect
613. #405	C₂²×C₂₃	semidirect
614. C₂×C₄×C₈	C₂²×C₂₃	semidirect
779. C₂₃	#62556	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×#3563	2
C₂₃×#3558	2
C₂₃×#3371	2
C₂₃×#3365	2
C₂₃×#3323	2
C₂₃×#3316	2
C₂₃×#3310	2
C₂₃×#3300	2
C₂₃×#3296	2
C₂₃×#3295	2
C₂₃×#3244	2
C₂₃×#3234	2
C₂₃×#3222	2
C₂₃×#3215	2
C₂₃×#3178	2
C₂₃×#3167	2
C₂₃×#3136	2
C₂×C₂₃×#488	2
C₂₃×#2966	2
#62556	23

Subgroups — C23×#62556 #19210182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62556 #19210182