Subgroups — C₂₃×#61833 #19209459

Order 5888.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3388	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3371	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3370	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3240	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3235	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3115	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3111	C₂	1	2	yes	maximal, complemented
21	C₂₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#559	C₂²	1	2	yes	—
25	C₂₃×#559	C₂²	1	1	yes	characteristic
26	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
27	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
28	C₂₃×#557	C₂²	1	1	yes	characteristic
29	C₂₃×#557	C₂²	1	2	yes	—
30	C₂₃×#554	—	2	1	no	—
31	C₂₃×#554	—	2	2	no	—
32	C₂₃×#554	C₂²	1	1	yes	characteristic
33	C₂₃×#554	C₂²	1	2	yes	—
34	C₂₃×#554	C₂²	1	1	yes	characteristic
35	C₂₃×#554	C₂²	1	2	yes	—
36	C₂₃×#550	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₂₃	—	2	1	no	—
38	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
39	C₂₃×#548	—	2	1	no	—
40	C₂₃×#547	—	2	2	no	—
41	C₂₃×#547	—	2	1	no	—
42	C₂₃×#542	—	2	1	no	—
43	C₂₃×#542	—	2	2	no	—
44	C₂₃×#533	—	2	1	no	—
45	C₂₃×#533	—	2	2	no	—
46	C₂₃×#533	C₂²	1	1	yes	characteristic
47	C₂₃×#533	C₂²	1	2	yes	—
48	C₂₃×#532	C₂²	1	1	yes	characteristic
49	C₂₃×#532	C₂²	1	2	yes	—
50	C₂₃×#529	C₂²	1	1	yes	characteristic
51	C₂₃×#529	C₂²	1	2	yes	—
52	C₂₃×#520	—	2	1	no	—
53	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
54	C₄×#41×C₂₃	C₂²	1	2	yes	—
55	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
56	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#501	C₂²	1	2	yes	—
58	C₂₃×#501	C₂²	1	2	yes	—
59	C₂₃×#501	C₂²	1	2	yes	—
60	C₂₃×#501	C₂²	1	2	yes	—
61	C₂₃×#500	C₂²	1	1	yes	characteristic
62	C₂₃×#499	C₂²	1	2	yes	—
63	C₂₃×#498	C₂²	1	1	yes	characteristic
64	C₂₃×#490	C₂²	1	2	yes	—
65	C₂₃×#490	C₂²	1	2	yes	—
66	C₂₃×#489	C₂²	1	2	yes	—
67	C₂₃×#489	C₂²	1	2	yes	—
68	C₂₃×#488	C₂²	1	2	yes	—
69	C₂₃×#486	C₂²	1	1	yes	characteristic
70	C₂₃×#486	C₂²	1	1	yes	characteristic
71	C₂₃×#485	C₂²	1	2	yes	—
72	C₂₃×#485	C₂²	1	1	yes	characteristic
73	C₂₃×#482	C₂²	1	2	yes	—
74	C₂₃×#482	C₂²	1	2	yes	—
75	C₂₃×#482	C₂²	1	2	yes	—
76	C₂₃×#482	C₂²	1	1	yes	characteristic
77	C₂₃×#482	C₂²	1	2	yes	—
78	C₂₃×#479	C₂²	1	2	yes	—
79	C₂₃×#479	C₂²	1	2	yes	—
80	C₂₃×#479	C₂²	1	1	yes	characteristic
81	C₂₃×#479	C₂²	1	2	yes	—
82	C₂₃×#478	C₂²	1	2	yes	—
83	C₂₃×#478	C₂²	1	2	yes	—
84	C₂₃×#478	C₂²	1	2	yes	—
85	C₂₃×#478	C₂²	1	2	yes	—
86	C₂₃×#478	C₂²	1	1	yes	characteristic
87	C₂₃×#478	C₂²	1	2	yes	—
88	C₂₃×#477	C₂²	1	1	yes	characteristic
89	C₂₃×#477	C₂²	1	1	yes	characteristic
90	C₂₃×#476	C₂²	1	1	yes	characteristic
91	C₂₃×#476	C₂²	1	2	yes	—
92	C₂₃×#476	C₂²	1	2	yes	—
93	C₂₃×#476	C₂²	1	1	yes	characteristic
94	C₂₃×#475	C₂²	1	1	yes	characteristic
95	C₂₃×#475	C₂²	1	2	yes	—
96	C₂₃×#474	C₂²	1	1	yes	characteristic
97	C₂₃×#474	C₂²	1	2	yes	—
98	C₂₃×#474	C₂²	1	2	yes	—
99	C₂₃×#474	C₂²	1	2	yes	—
100	C₂₃×#464	C₂²	1	1	yes	characteristic
101	C₂₃×#464	C₂²	1	2	yes	—
102	C₂₃×#463	C₂²	1	1	yes	characteristic
103	C₂₃×#463	C₂²	1	2	yes	—
104	C₂₃×#460	C₂²	1	1	yes	characteristic
105	C₂₃×#460	C₂²	1	2	yes	—
106	C₂₃×#459	C₂²	1	1	yes	characteristic
107	C₂₃×#459	C₂²	1	2	yes	—
108	C₂₃×#452	C₂²	1	1	yes	characteristic
109	C₂₃×#449	C₂²	1	1	yes	characteristic
110	C₂₃×#449	C₂²	1	2	yes	—
111	C₂₃×#446	C₂²	1	1	yes	characteristic
112	C₂₃×#446	C₂²	1	1	yes	characteristic
113	C₂₃×#446	C₂²	1	2	yes	—
114	C₂₃×#446	C₂²	1	2	yes	—
115	C₂₃×#446	C₂²	1	1	yes	characteristic
116	C₂₃×#446	C₂²	1	1	yes	characteristic
117	C₂₃×#442	C₂²	1	2	yes	—
118	C₂₃×#442	C₂²	1	2	yes	—
119	C₂₃×#442	C₂²	1	2	yes	—
120	C₂₃×#441	C₂²	1	2	yes	—
121	C₂₃×#440	C₂²	1	2	yes	—
122	C₂₃×#440	C₂²	1	2	yes	—
123	C₂₃×#440	C₂²	1	2	yes	—
124	C₂₃×#440	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
129	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₂₃	C₂²	1	2	yes	—
131	C₂₃×#432	C₂²	1	2	yes	—
132	C₂₃×#432	C₂²	1	2	yes	—
133	C₂₃×#431	C₂²	1	1	yes	characteristic
134	C₂₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	—	2	1	no	—
136	C₂×#41×C₂₃	—	2	1	no	—
137	C₂×#41×C₂₃	—	2	2	no	—
138	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₂₃	—	2	1	no	—
140	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
141	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×D₈×C₂₃	C₂³	1	2	yes	—
147	C₂₃×C₄⋊Q₈	—	2	1	no	—
148	C₂₃×C₄⋊Q₈	—	2	2	no	—
149	C₂₃×C₄⋊Q₈	—	2	1	no	—
150	C₂₃×C₄⋊Q₈	—	2	2	no	—
151	C₂₃×C₄⋊Q₈	—	2	1	no	—
152	C₂₃×C₄⋊Q₈	—	2	2	no	—
153	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
156	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×#127	C₂³	1	1	yes	characteristic
160	C₂₃×#127	C₂³	1	2	yes	—
161	C₂₃×#126	—	2	2	no	—
162	C₂₃×#126	—	2	1	no	—
163	C₂₃×#125	—	2	2	no	—
164	C₂₃×#125	—	2	2	no	—
165	C₂₃×#125	—	2	2	no	—
166	C₂₃×#125	C₂³	1	1	yes	characteristic
167	C₂₃×#125	C₂³	1	2	yes	—
168	C₂₃×#125	C₂³	1	2	yes	—
169	C₂₃×#125	C₂³	1	2	yes	—
170	C₂₃×#125	C₂³	1	2	yes	—
171	C₂₃×#124	—	2	1	no	—
172	C₂₃×#124	—	2	2	no	—
173	C₂₃×#124	—	2	2	no	—
174	C₂₃×#124	—	2	1	no	—
175	C₂₃×#124	C₂³	1	1	yes	characteristic
176	C₂₃×#124	C₂³	1	2	yes	—
177	C₂₃×#123	—	2	1	no	—
178	C₂₃×#123	—	2	2	no	—
179	C₂₃×#123	—	2	2	no	—
180	C₂₃×#123	—	2	2	no	—
181	C₂₃×#123	—	2	2	no	—
182	C₂₃×C₂²⋊Q₈	—	2	1	no	—
183	C₂₃×C₂²⋊Q₈	—	2	2	no	—
184	C₂₃×C₂²⋊Q₈	—	2	1	no	—
185	C₂₃×C₂²⋊Q₈	—	2	2	no	—
186	C₂₃×C₂²⋊Q₈	—	2	1	no	—
187	C₂₃×C₂²⋊Q₈	—	2	2	no	—
188	C₂₃×C₂²⋊Q₈	—	2	1	no	—
189	C₂₃×C₂²⋊Q₈	—	2	2	no	—
190	C₂₃×C₂²⋊Q₈	—	2	2	no	—
191	C₂₃×C₂²⋊Q₈	—	2	2	no	—
192	C₂₃×C₂²⋊Q₈	—	2	2	no	—
193	C₂₃×C₂²⋊Q₈	—	2	1	no	—
194	C₂₃×C₂²⋊Q₈	—	2	2	no	—
195	C₂₃×C₂²⋊Q₈	—	2	2	no	—
196	C₂₃×C₂²⋊Q₈	—	2	2	no	—
197	C₂₃×C₂²⋊Q₈	—	2	2	no	—
198	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
199	C₂₃×#121	—	2	1	no	—
200	C₂₃×#121	—	2	2	no	—
201	C₂₃×#121	—	2	1	no	—
202	C₂₃×#121	—	2	2	no	—
203	C₂₃×#121	C₂³	1	1	yes	characteristic
204	C₂₃×#121	C₂³	1	2	yes	—
205	C₄×Q₈×C₂₃	—	2	1	no	—
206	C₄×Q₈×C₂₃	—	2	1	no	—
207	C₄×Q₈×C₂₃	—	2	1	no	—
208	C₄×Q₈×C₂₃	—	2	2	no	—
209	C₄×Q₈×C₂₃	—	2	1	no	—
210	C₄×Q₈×C₂₃	—	2	2	no	—
211	C₄×Q₈×C₂₃	—	2	2	no	—
212	C₄×Q₈×C₂₃	—	2	1	no	—
213	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
214	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₂₃	D₄	1	2	yes	—
216	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
218	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
220	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
223	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
224	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	—	2	1	no	—
226	C₄×D₄×C₂₃	—	2	2	no	—
227	C₄×D₄×C₂₃	—	2	1	no	—
228	C₄×D₄×C₂₃	—	2	2	no	—
229	C₄×D₄×C₂₃	—	2	1	no	—
230	C₄×D₄×C₂₃	—	2	2	no	—
231	C₄×D₄×C₂₃	—	2	2	no	—
232	C₄×D₄×C₂₃	—	2	1	no	—
233	C₄×D₄×C₂₃	—	2	1	no	—
234	C₄×D₄×C₂₃	—	2	2	no	—
235	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₂₃	C₂³	1	2	yes	—
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₂₃	C₂³	1	2	yes	—
241	C₄×D₄×C₂₃	C₂³	1	2	yes	—
242	C₄×D₄×C₂₃	C₂³	1	2	yes	—
243	C₄×D₄×C₂₃	C₂³	1	2	yes	—
244	C₂₃×#117	—	2	2	no	—
245	C₂₃×#117	—	2	1	no	—
246	C₂₃×#117	—	2	1	no	—
247	C₂₃×#117	—	2	2	no	—
248	C₂₃×#117	C₂³	1	2	yes	—
249	C₂₃×#117	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
251	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
254	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
255	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
256	C₂×C₄²×C₂₃	—	2	1	no	—
257	C₂×C₄²×C₂₃	—	2	2	no	—
258	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
259	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
260	C₂₃×#107	C₂³	1	2	yes	—
261	C₂₃×#107	C₂³	1	1	yes	characteristic
262	C₂₃×#107	C₂³	1	1	yes	characteristic
263	C₂₃×#107	C₂³	1	2	yes	—
264	C₂₃×#107	C₂³	1	2	yes	—
265	C₂₃×#107	C₂³	1	2	yes	—
266	C₂₃×#107	C₂³	1	2	yes	—
267	C₂₃×#106	C₂³	1	1	yes	characteristic
268	C₂₃×#106	C₂³	1	2	yes	—
269	C₂₃×#106	C₂³	1	1	yes	characteristic
270	C₂₃×#106	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	2	yes	—
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	2	yes	—
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×#103	C₂³	1	1	yes	characteristic
283	C₂₃×#103	C₂³	1	2	yes	—
284	C₂₃×#103	C₂³	1	1	yes	characteristic
285	C₂₃×#103	C₂³	1	1	yes	characteristic
286	C₂₃×#103	C₂³	1	1	yes	characteristic
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#102	C₂³	1	2	yes	—
290	C₂₃×#102	C₂³	1	1	yes	characteristic
291	C₂₃×#102	C₂³	1	2	yes	—
292	C₂₃×#102	C₂³	1	1	yes	characteristic
293	C₂₃×#102	C₂³	1	1	yes	characteristic
294	C₂₃×#102	C₂³	1	2	yes	—
295	C₂₃×#102	C₂³	1	1	yes	characteristic
296	C₂₃×#102	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	2	yes	—
298	C₂₃×#102	C₂³	1	2	yes	—
299	C₂₃×#102	C₂³	1	2	yes	—
300	C₂₃×#102	C₂³	1	2	yes	—
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂₃×#97	C₂³	1	2	yes	—
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₂₃×#97	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	2	yes	—
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
312	#41×C₂₃	—	2	2	no	—
313	#41×C₂₃	—	2	2	no	—
314	#41×C₂₃	—	4	4	no	—
315	#41×C₂₃	—	8	2	no	—
316	#41×C₂₃	—	8	4	no	—
317	C₂×Q₈×C₂₃	—	2	2	no	—
318	C₂×Q₈×C₂₃	—	2	1	no	—
319	C₂×Q₈×C₂₃	—	2	2	no	—
320	C₂×Q₈×C₂₃	—	2	1	no	—
321	C₂×Q₈×C₂₃	—	2	2	no	—
322	C₂×Q₈×C₂₃	—	2	1	no	—
323	C₂×Q₈×C₂₃	—	4	2	no	—
324	C₂×Q₈×C₂₃	—	4	4	no	—
325	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
327	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
328	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₂₃	—	2	1	no	—
331	C₂×D₄×C₂₃	—	2	1	no	—
332	C₂×D₄×C₂₃	—	2	2	no	—
333	C₂×D₄×C₂₃	—	2	2	no	—
334	C₂×D₄×C₂₃	—	2	1	no	—
335	C₂×D₄×C₂₃	—	2	2	no	—
336	C₂×D₄×C₂₃	—	2	1	no	—
337	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
338	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	C₂²×C₄×C₂₃	—	2	1	no	—
341	C₂²×C₄×C₂₃	—	2	2	no	—
342	C₂²×C₄×C₂₃	—	2	1	no	—
343	C₂²×C₄×C₂₃	—	2	2	no	—
344	C₂²×C₄×C₂₃	—	2	1	no	—
345	C₂²×C₄×C₂₃	—	2	1	no	—
346	C₂²×C₄×C₂₃	—	2	2	no	—
347	C₂²×C₄×C₂₃	—	2	2	no	—
348	C₂²×C₄×C₂₃	—	2	2	no	—
349	C₂²×C₄×C₂₃	—	2	2	no	—
350	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	Q₁₆×C₂₃	—	2	2	no	—
356	SD₁₆×C₂₃	—	2	2	no	—
357	SD₁₆×C₂₃	—	2	4	no	—
358	SD₁₆×C₂₃	—	2	2	no	—
359	D₈×C₂₃	—	2	2	no	—
360	D₈×C₂₃	—	2	4	no	—
361	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
363	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₂₃	—	2	1	no	—
368	C₄⋊C₄×C₂₃	—	2	2	no	—
369	C₄⋊C₄×C₂₃	—	2	2	no	—
370	C₄⋊C₄×C₂₃	—	2	1	no	—
371	C₄⋊C₄×C₂₃	—	2	2	no	—
372	C₄⋊C₄×C₂₃	—	2	2	no	—
373	C₄⋊C₄×C₂₃	—	2	2	no	—
374	C₄⋊C₄×C₂₃	—	2	2	no	—
375	C₄⋊C₄×C₂₃	—	2	1	no	—
376	C₄⋊C₄×C₂₃	—	2	1	no	—
377	C₄⋊C₄×C₂₃	—	2	2	no	—
378	C₄⋊C₄×C₂₃	—	2	1	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	1	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	1	no	—
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	1	no	—
385	C₄⋊C₄×C₂₃	—	2	2	no	—
386	C₄⋊C₄×C₂₃	—	2	2	no	—
387	C₄⋊C₄×C₂₃	—	2	2	no	—
388	C₄⋊C₄×C₂₃	—	2	2	no	—
389	C₄⋊C₄×C₂₃	—	2	1	no	—
390	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
392	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₂₃	—	2	2	no	—
405	C₂²⋊C₄×C₂₃	—	2	1	no	—
406	C₂²⋊C₄×C₂₃	—	2	1	no	—
407	C₂²⋊C₄×C₂₃	—	2	1	no	—
408	C₂²⋊C₄×C₂₃	—	2	2	no	—
409	C₂²⋊C₄×C₂₃	—	2	1	no	—
410	C₂²⋊C₄×C₂₃	—	2	2	no	—
411	C₂²⋊C₄×C₂₃	—	2	2	no	—
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	2	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	1	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	1	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	2	no	—
422	C₄²×C₂₃	—	2	1	no	—
423	C₄²×C₂₃	—	2	2	no	—
424	C₄²×C₂₃	—	2	1	no	—
425	C₄²×C₂₃	—	2	2	no	—
426	C₄²×C₂₃	—	2	2	no	—
427	C₄²×C₂₃	—	2	1	no	—
428	C₄²×C₂₃	—	2	2	no	—
429	C₄²×C₂₃	—	2	1	no	—
430	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₂₃	C₂×D₄	1	2	yes	—
432	C₄²×C₂₃	C₂×D₄	1	2	yes	—
433	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₂₃	C₂⁴	1	2	yes	—
436	C₄²×C₂₃	C₂⁴	1	2	yes	—
437	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
438	#61833	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
439	C₂³×C₂₃	—	2	1	no	—
440	C₂³×C₂₃	—	2	2	no	—
441	C₂³×C₂₃	—	2	1	no	—
442	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₂₃	—	2	2	no	—
444	Q₈×C₂₃	—	2	2	no	—
445	Q₈×C₂₃	—	2	1	no	—
446	Q₈×C₂₃	—	2	1	no	—
447	Q₈×C₂₃	—	2	1	no	—
448	Q₈×C₂₃	—	4	2	no	—
449	Q₈×C₂₃	—	4	4	no	—
450	Q₈×C₂₃	—	4	2	no	—
451	Q₈×C₂₃	—	8	2	no	—
452	Q₈×C₂₃	—	8	1	no	—
453	Q₈×C₂₃	—	8	2	no	—
454	Q₈×C₂₃	—	8	1	no	—
455	Q₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
456	D₄×C₂₃	—	2	4	no	—
457	D₄×C₂₃	—	2	1	no	—
458	D₄×C₂₃	—	2	2	no	—
459	D₄×C₂₃	—	2	1	no	—
460	D₄×C₂₃	—	2	2	no	—
461	D₄×C₂₃	—	2	1	no	—
462	D₄×C₂₃	—	4	4	no	—
463	D₄×C₂₃	—	4	4	no	—
464	D₄×C₂₃	—	4	2	no	—
465	D₄×C₂₃	—	4	2	no	—
466	D₄×C₂₃	—	8	2	no	—
467	D₄×C₂₃	—	8	1	no	—
468	D₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
469	C₂×C₄×C₂₃	—	2	4	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	2	no	—
472	C₂×C₄×C₂₃	—	2	1	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	1	no	—
475	C₂×C₄×C₂₃	—	2	2	no	—
476	C₂×C₄×C₂₃	—	2	1	no	—
477	C₂×C₄×C₂₃	—	2	2	no	—
478	C₂×C₄×C₂₃	—	2	1	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	1	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	4	2	no	—
483	C₂×C₄×C₂₃	—	4	1	no	—
484	C₂×C₄×C₂₃	—	4	2	no	—
485	C₂×C₄×C₂₃	—	4	4	no	—
486	C₂×C₄×C₂₃	—	4	4	no	—
487	C₂×C₄×C₂₃	—	4	2	no	—
488	C₂×C₄×C₂₃	—	4	2	no	—
489	C₂×C₄×C₂₃	—	8	1	no	—
490	C₂×C₄×C₂₃	—	8	2	no	—
491	C₂×C₄×C₂₃	—	8	2	no	—
492	C₂×C₄×C₂₃	—	8	2	no	—
493	C₂×C₄×C₂₃	—	8	2	no	—
494	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
501	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
504	C₈×C₂₃	—	2	2	no	—
505	C₈×C₂₃	—	2	1	no	—
506	C₈×C₂₃	—	2	2	no	—
507	C₈×C₂₃	—	2	1	no	—
508	C₈×C₂₃	—	2	1	no	—
509	C₈×C₂₃	—	2	1	no	—
510	#3522	C₂×C₂₃	1	1	yes	characteristic, complemented
511	Q₈×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
512	#3389	C₂×C₂₃	1	2	yes	complemented
513	#3388	C₂×C₂₃	1	2	yes	complemented
514	#3387	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#3385	C₂×C₂₃	1	1	yes	characteristic, complemented
516	#3385	C₂×C₂₃	1	1	yes	characteristic, complemented
517	#3384	C₂×C₂₃	1	1	yes	characteristic, complemented
518	#3375	C₂×C₂₃	1	1	yes	characteristic, complemented
519	#3373	C₂×C₂₃	1	1	yes	characteristic, complemented
520	#3371	C₂×C₂₃	1	2	yes	complemented
521	#3370	C₂×C₂₃	1	2	yes	complemented
522	#3368	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3366	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#3240	C₂×C₂₃	1	2	yes	complemented
525	#3235	C₂×C₂₃	1	2	yes	complemented
526	#3233	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#3228	C₂×C₂₃	1	1	yes	characteristic, complemented
528	#3115	C₂×C₂₃	1	2	yes	complemented
529	#3111	C₂×C₂₃	1	2	yes	complemented
530	#3106	C₂×C₂₃	1	1	yes	characteristic, complemented
531	#3102	C₂×C₂₃	1	1	yes	characteristic, complemented
532	#2983	C₂×C₂₃	1	1	yes	characteristic, complemented
533	C₂²×C₂₃	—	2	1	no	—
534	C₂²×C₂₃	—	2	1	no	—
535	C₂²×C₂₃	—	2	2	no	—
536	C₂²×C₂₃	—	2	1	no	—
537	C₂²×C₂₃	—	4	1	no	—
538	C₂²×C₂₃	—	4	1	no	—
539	C₂²×C₂₃	—	4	2	no	—
540	C₂²×C₂₃	—	4	1	no	—
541	C₂²×C₂₃	—	4	2	no	—
542	C₂²×C₂₃	—	4	1	no	—
543	C₂²×C₂₃	—	4	2	no	—
544	C₂²×C₂₃	—	4	1	no	—
545	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
546	C₄×C₂₃	—	2	1	no	—
547	C₄×C₂₃	—	2	2	no	—
548	C₄×C₂₃	—	2	2	no	—
549	C₄×C₂₃	—	2	1	no	—
550	C₄×C₂₃	—	2	1	no	—
551	C₄×C₂₃	—	2	2	no	—
552	C₄×C₂₃	—	2	1	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	2	2	no	—
555	C₄×C₂₃	—	4	2	no	—
556	C₄×C₂₃	—	4	1	no	—
557	C₄×C₂₃	—	4	1	no	—
558	C₄×C₂₃	—	4	2	no	—
559	C₄×C₂₃	—	4	1	no	—
560	C₄×C₂₃	—	4	1	no	—
561	C₄×C₂₃	—	4	2	no	—
562	C₄×C₂₃	—	4	1	no	—
563	C₄×C₂₃	#575	1	2	yes	—
564	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
565	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
566	#559	C₂²×C₂₃	1	2	yes	—
567	#559	C₂²×C₂₃	1	1	yes	characteristic
568	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
569	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
570	#557	C₂²×C₂₃	1	1	yes	characteristic
571	#557	C₂²×C₂₃	1	2	yes	—
572	#554	—	2	1	no	—
573	#554	—	2	2	no	—
574	#554	C₂²×C₂₃	1	1	yes	characteristic
575	#554	C₂²×C₂₃	1	2	yes	—
576	#554	C₂²×C₂₃	1	1	yes	characteristic
577	#554	C₂²×C₂₃	1	2	yes	—
578	#550	C₂²×C₂₃	1	1	yes	characteristic
579	D₄×Q₈	—	2	1	no	—
580	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
581	#548	—	2	1	no	—
582	#547	—	2	2	no	—
583	#547	—	2	1	no	—
584	#542	—	2	1	no	—
585	#542	—	2	2	no	—
586	#533	—	2	1	no	—
587	#533	—	2	2	no	—
588	#533	C₂²×C₂₃	1	1	yes	characteristic
589	#533	C₂²×C₂₃	1	2	yes	—
590	#532	C₂²×C₂₃	1	1	yes	characteristic
591	#532	C₂²×C₂₃	1	2	yes	—
592	#529	C₂²×C₂₃	1	1	yes	characteristic
593	#529	C₂²×C₂₃	1	2	yes	—
594	#520	—	2	1	no	—
595	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
596	C₄×#41	C₂²×C₂₃	1	2	yes	—
597	C₂×C₄×Q₈	—	2	1	no	—
598	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
599	#501	C₂²×C₂₃	1	2	yes	—
600	#501	C₂²×C₂₃	1	2	yes	—
601	#501	C₂²×C₂₃	1	2	yes	—
602	#501	C₂²×C₂₃	1	2	yes	—
603	#500	C₂²×C₂₃	1	1	yes	characteristic
604	#499	C₂²×C₂₃	1	2	yes	—
605	#498	C₂²×C₂₃	1	1	yes	characteristic
606	#490	C₂²×C₂₃	1	2	yes	—
607	#490	C₂²×C₂₃	1	2	yes	—
608	#489	C₂²×C₂₃	1	2	yes	—
609	#489	C₂²×C₂₃	1	2	yes	—
610	#488	C₂²×C₂₃	1	2	yes	—
611	#486	C₂²×C₂₃	1	1	yes	characteristic
612	#486	C₂²×C₂₃	1	1	yes	characteristic
613	#485	C₂²×C₂₃	1	1	yes	characteristic
614	#485	C₂²×C₂₃	1	2	yes	—
615	#482	C₂²×C₂₃	1	1	yes	characteristic
616	#482	C₂²×C₂₃	1	2	yes	—
617	#482	C₂²×C₂₃	1	2	yes	—
618	#482	C₂²×C₂₃	1	2	yes	—
619	#482	C₂²×C₂₃	1	2	yes	—
620	#479	C₂²×C₂₃	1	1	yes	characteristic
621	#479	C₂²×C₂₃	1	2	yes	—
622	#479	C₂²×C₂₃	1	2	yes	—
623	#479	C₂²×C₂₃	1	2	yes	—
624	#478	C₂²×C₂₃	1	1	yes	characteristic
625	#478	C₂²×C₂₃	1	2	yes	—
626	#478	C₂²×C₂₃	1	2	yes	—
627	#478	C₂²×C₂₃	1	2	yes	—
628	#478	C₂²×C₂₃	1	2	yes	—
629	#478	C₂²×C₂₃	1	2	yes	—
630	#477	C₂²×C₂₃	1	1	yes	characteristic
631	#477	C₂²×C₂₃	1	1	yes	characteristic
632	#476	C₂²×C₂₃	1	1	yes	characteristic
633	#476	C₂²×C₂₃	1	1	yes	characteristic
634	#476	C₂²×C₂₃	1	2	yes	—
635	#476	C₂²×C₂₃	1	2	yes	—
636	#475	C₂²×C₂₃	1	2	yes	—
637	#475	C₂²×C₂₃	1	1	yes	characteristic
638	#474	C₂²×C₂₃	1	1	yes	characteristic
639	#474	C₂²×C₂₃	1	2	yes	—
640	#474	C₂²×C₂₃	1	2	yes	—
641	#474	C₂²×C₂₃	1	2	yes	—
642	#464	C₂²×C₂₃	1	1	yes	characteristic
643	#464	C₂²×C₂₃	1	2	yes	—
644	#463	C₂²×C₂₃	1	1	yes	characteristic
645	#463	C₂²×C₂₃	1	2	yes	—
646	#460	C₂²×C₂₃	1	1	yes	characteristic
647	#460	C₂²×C₂₃	1	2	yes	—
648	#459	C₂²×C₂₃	1	1	yes	characteristic
649	#459	C₂²×C₂₃	1	2	yes	—
650	#452	C₂²×C₂₃	1	1	yes	characteristic
651	#449	C₂²×C₂₃	1	1	yes	characteristic
652	#449	C₂²×C₂₃	1	2	yes	—
653	#446	C₂²×C₂₃	1	1	yes	characteristic
654	#446	C₂²×C₂₃	1	1	yes	characteristic
655	#446	C₂²×C₂₃	1	2	yes	—
656	#446	C₂²×C₂₃	1	2	yes	—
657	#446	C₂²×C₂₃	1	1	yes	characteristic
658	#446	C₂²×C₂₃	1	1	yes	characteristic
659	#442	C₂²×C₂₃	1	2	yes	—
660	#442	C₂²×C₂₃	1	2	yes	—
661	#442	C₂²×C₂₃	1	2	yes	—
662	#441	C₂²×C₂₃	1	2	yes	—
663	#440	C₂²×C₂₃	1	2	yes	—
664	#440	C₂²×C₂₃	1	2	yes	—
665	#440	C₂²×C₂₃	1	2	yes	—
666	#440	C₂²×C₂₃	1	2	yes	—
667	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
669	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
671	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
672	C₄×D₈	C₂²×C₂₃	1	2	yes	—
673	#432	C₂²×C₂₃	1	2	yes	—
674	#432	C₂²×C₂₃	1	2	yes	—
675	#431	C₂²×C₂₃	1	1	yes	characteristic
676	#431	C₂²×C₂₃	1	1	yes	characteristic
677	C₂×C₂₃	—	4	1	no	—
678	C₂×C₂₃	—	4	2	no	—
679	C₂×C₂₃	—	8	2	no	—
680	C₂×C₂₃	—	8	1	no	—
681	C₂×C₂₃	#3486	1	1	yes	characteristic
682	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
683	C₂×C₂₃	#3585	1	1	yes	characteristic
684	C₂×#41	—	2	1	no	—
685	C₂×#41	—	2	1	no	—
686	C₂×#41	—	2	2	no	—
687	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
688	C₂²×Q₈	—	2	1	no	—
689	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
690	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
691	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
692	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
694	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
695	C₂×D₈	C₂³×C₂₃	1	2	yes	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	—	2	2	no	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	—	2	2	no	—
700	C₄⋊Q₈	—	2	1	no	—
701	C₄⋊Q₈	—	2	2	no	—
702	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
707	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
708	#127	C₂³×C₂₃	1	1	yes	characteristic
709	#127	C₂³×C₂₃	1	2	yes	—
710	#126	—	2	2	no	—
711	#126	—	2	1	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	C₂³×C₂₃	1	1	yes	characteristic
716	#125	C₂³×C₂₃	1	2	yes	—
717	#125	C₂³×C₂₃	1	2	yes	—
718	#125	C₂³×C₂₃	1	2	yes	—
719	#125	C₂³×C₂₃	1	2	yes	—
720	#124	—	2	1	no	—
721	#124	—	2	2	no	—
722	#124	—	2	2	no	—
723	#124	—	2	1	no	—
724	#124	C₂³×C₂₃	1	1	yes	characteristic
725	#124	C₂³×C₂₃	1	2	yes	—
726	#123	—	2	1	no	—
727	#123	—	2	2	no	—
728	#123	—	2	2	no	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	2	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	1	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	2	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
748	#121	—	2	1	no	—
749	#121	—	2	2	no	—
750	#121	—	2	1	no	—
751	#121	—	2	2	no	—
752	#121	C₂³×C₂₃	1	1	yes	characteristic
753	#121	C₂³×C₂₃	1	2	yes	—
754	C₄×Q₈	—	2	1	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	2	1	no	—
757	C₄×Q₈	—	2	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	2	no	—
760	C₄×Q₈	—	2	2	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
763	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
764	C₄×Q₈	D₄×C₂₃	1	2	yes	—
765	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
766	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
767	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
769	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
771	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	2	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
785	C₄×D₄	C₂³×C₂₃	1	2	yes	—
786	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
787	C₄×D₄	C₂³×C₂₃	1	2	yes	—
788	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₂₃	1	2	yes	—
790	C₄×D₄	C₂³×C₂₃	1	2	yes	—
791	C₄×D₄	C₂³×C₂₃	1	2	yes	—
792	C₄×D₄	C₂³×C₂₃	1	2	yes	—
793	#117	—	2	2	no	—
794	#117	—	2	1	no	—
795	#117	—	2	1	no	—
796	#117	—	2	2	no	—
797	#117	C₂³×C₂₃	1	1	yes	characteristic
798	#117	C₂³×C₂₃	1	2	yes	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	2	2	no	—
801	C₂×C₄⋊C₄	—	2	2	no	—
802	C₂×C₄⋊C₄	—	2	1	no	—
803	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
804	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄²	—	2	1	no	—
806	C₂×C₄²	—	2	2	no	—
807	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
808	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
809	#107	C₂³×C₂₃	1	2	yes	—
810	#107	C₂³×C₂₃	1	1	yes	characteristic
811	#107	C₂³×C₂₃	1	1	yes	characteristic
812	#107	C₂³×C₂₃	1	2	yes	—
813	#107	C₂³×C₂₃	1	2	yes	—
814	#107	C₂³×C₂₃	1	2	yes	—
815	#107	C₂³×C₂₃	1	2	yes	—
816	#106	C₂³×C₂₃	1	1	yes	characteristic
817	#106	C₂³×C₂₃	1	2	yes	—
818	#106	C₂³×C₂₃	1	1	yes	characteristic
819	#106	C₂³×C₂₃	1	2	yes	—
820	#106	C₂³×C₂₃	1	2	yes	—
821	#106	C₂³×C₂₃	1	2	yes	—
822	#106	C₂³×C₂₃	1	2	yes	—
823	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
825	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
826	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
828	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
829	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
831	#103	C₂³×C₂₃	1	1	yes	characteristic
832	#103	C₂³×C₂₃	1	2	yes	—
833	#103	C₂³×C₂₃	1	1	yes	characteristic
834	#103	C₂³×C₂₃	1	1	yes	characteristic
835	#103	C₂³×C₂₃	1	1	yes	characteristic
836	#103	C₂³×C₂₃	1	2	yes	—
837	#103	C₂³×C₂₃	1	2	yes	—
838	#102	C₂³×C₂₃	1	2	yes	—
839	#102	C₂³×C₂₃	1	1	yes	characteristic
840	#102	C₂³×C₂₃	1	2	yes	—
841	#102	C₂³×C₂₃	1	1	yes	characteristic
842	#102	C₂³×C₂₃	1	1	yes	characteristic
843	#102	C₂³×C₂₃	1	2	yes	—
844	#102	C₂³×C₂₃	1	1	yes	characteristic
845	#102	C₂³×C₂₃	1	2	yes	—
846	#102	C₂³×C₂₃	1	2	yes	—
847	#102	C₂³×C₂₃	1	2	yes	—
848	#102	C₂³×C₂₃	1	2	yes	—
849	#102	C₂³×C₂₃	1	2	yes	—
850	#102	C₂³×C₂₃	1	2	yes	—
851	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
852	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
853	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
854	#97	C₂³×C₂₃	1	2	yes	—
855	#97	C₂³×C₂₃	1	2	yes	—
856	#97	C₂³×C₂₃	1	2	yes	—
857	#97	C₂³×C₂₃	1	2	yes	—
858	C₄×C₈	C₂³×C₂₃	1	2	yes	—
859	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₂₃	#61833	1	1	yes	characteristic, direct product factor, Sylow
862	#41	—	2	2	no	—
863	#41	—	2	2	no	—
864	#41	—	4	4	no	—
865	#41	—	8	2	no	—
866	#41	—	8	4	no	—
867	C₂×Q₈	—	2	2	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	2	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	4	2	no	—
874	C₂×Q₈	—	4	4	no	—
875	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
876	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
877	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
878	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
879	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
880	C₂×D₄	—	2	1	no	—
881	C₂×D₄	—	2	1	no	—
882	C₂×D₄	—	2	2	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	2	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
888	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
889	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	2	2	no	—
900	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
901	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
902	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
903	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
905	Q₁₆	—	2	2	no	—
906	SD₁₆	—	2	2	no	—
907	SD₁₆	—	2	4	no	—
908	SD₁₆	—	2	2	no	—
909	D₈	—	2	2	no	—
910	D₈	—	2	4	no	—
911	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
912	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
913	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
916	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
951	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	1	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	2	no	—
979	C₄²	—	2	1	no	—
980	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
981	C₄²	C₂×D₄×C₂₃	1	2	yes	—
982	C₄²	C₂×D₄×C₂₃	1	2	yes	—
983	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
984	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
986	C₄²	C₂⁴×C₂₃	1	2	yes	—
987	C₄²	C₂⁴×C₂₃	1	2	yes	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	—	2	1	no	—
991	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	4	2	no	—
998	Q₈	—	4	4	no	—
999	Q₈	—	4	2	no	—
1000	Q₈	—	8	2	no	—
1001	Q₈	—	8	1	no	—
1002	Q₈	—	8	2	no	—
1003	Q₈	—	8	1	no	—
1004	Q₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
1005	D₄	—	2	4	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	2	no	—
1008	D₄	—	2	1	no	—
1009	D₄	—	2	2	no	—
1010	D₄	—	2	1	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	4	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	1	no	—
1017	D₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1018	C₂×C₄	—	2	4	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	1	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	2	no	—
1043	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1045	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1046	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1053	C₈	—	2	2	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	1	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	1	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	2	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	2	no	—
1089	C₄	C₂₃×#575	1	2	yes	—
1090	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1091	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1092	C₂	—	4	1	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	2	no	—
1095	C₂	—	8	1	no	—
1096	C₂	C₂₃×#3486	1	1	yes	characteristic
1097	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
1098	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 ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3522	C₂	semidirect
2. Q₈×#41×C₂₃	C₂	semidirect
3. C₂₃×#3389	C₂	semidirect
4. C₂₃×#3388	C₂	semidirect
5. C₂₃×#3387	C₂	semidirect
6. C₂₃×#3385	C₂	semidirect
7. C₂₃×#3385	C₂	semidirect
8. C₂₃×#3384	C₂	semidirect
9. C₂₃×#3375	C₂	semidirect
10. C₂₃×#3373	C₂	semidirect
11. C₂₃×#3371	C₂	semidirect
12. C₂₃×#3370	C₂	semidirect
13. C₂₃×#3368	C₂	semidirect
14. C₂₃×#3366	C₂	semidirect
15. C₂₃×#3240	C₂	semidirect
16. C₂₃×#3235	C₂	semidirect
17. C₂₃×#3233	C₂	semidirect
18. C₂₃×#3228	C₂	semidirect
19. C₂₃×#3115	C₂	semidirect
20. C₂₃×#3111	C₂	semidirect
21. C₂₃×#3106	C₂	semidirect
22. C₂₃×#3102	C₂	semidirect
23. C₂₃×#2983	C₂	semidirect
438. #61833	C₂₃	direct (N × H)
510. #3522	C₂×C₂₃	semidirect
511. Q₈×#41	C₂×C₂₃	semidirect
512. #3389	C₂×C₂₃	semidirect
513. #3388	C₂×C₂₃	semidirect
514. #3387	C₂×C₂₃	semidirect
515. #3385	C₂×C₂₃	semidirect
516. #3385	C₂×C₂₃	semidirect
517. #3384	C₂×C₂₃	semidirect
518. #3375	C₂×C₂₃	semidirect
519. #3373	C₂×C₂₃	semidirect
520. #3371	C₂×C₂₃	semidirect
521. #3370	C₂×C₂₃	semidirect
522. #3368	C₂×C₂₃	semidirect
523. #3366	C₂×C₂₃	semidirect
524. #3240	C₂×C₂₃	semidirect
525. #3235	C₂×C₂₃	semidirect
526. #3233	C₂×C₂₃	semidirect
527. #3228	C₂×C₂₃	semidirect
528. #3115	C₂×C₂₃	semidirect
529. #3111	C₂×C₂₃	semidirect
530. #3106	C₂×C₂₃	semidirect
531. #3102	C₂×C₂₃	semidirect
532. #2983	C₂×C₂₃	semidirect
861. C₂₃	#61833	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×#3522	2
Q₈×#41×C₂₃	2
C₂₃×#3389	2
C₂₃×#3388	2
C₂₃×#3387	2
C₂₃×#3385	2
C₂₃×#3384	2
C₂₃×#3375	2
C₂₃×#3373	2
C₂₃×#3371	2
C₂₃×#3370	2
C₂₃×#3368	2
C₂₃×#3366	2
C₂₃×#3240	2
C₂₃×#3235	2
C₂₃×#3233	2
C₂₃×#3228	2
C₂₃×#3115	2
C₂₃×#3111	2
C₂₃×#3106	2
C₂₃×#3102	2
C₂₃×#2983	2
#61833	23

Subgroups — C23×#61833 #19209459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61833 #19209459