Subgroups — C₂₃×#61922 #19209548

Order 5888.

1640 conjugacy classes of subgroups.

The subgroup lattice has 1084 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3402	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3398	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3374	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3225	C₂	1	2	yes	maximal
16	C₂₃×#3223	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#3127	C₂	1	2	yes	maximal, complemented
20	C₂₃×#3121	C₂	1	2	yes	maximal, complemented
21	C₂₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#3102	C₂	1	1	yes	maximal, characteristic
23	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#563	—	2	2	no	—
25	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
26	C₂₃×#557	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	1	yes	characteristic
28	C₂₃×#557	C₂²	1	2	yes	—
29	C₂₃×#557	C₂²	1	1	yes	characteristic
30	C₂₃×#557	C₂²	1	2	yes	—
31	C₂₃×#556	—	2	1	no	—
32	C₂₃×#556	C₂²	1	1	yes	characteristic
33	C₂₃×#556	C₂²	1	1	yes	characteristic
34	C₂₃×#556	C₂²	1	2	yes	—
35	C₂₃×#556	C₂²	1	1	yes	characteristic
36	C₂₃×#556	C₂²	1	2	yes	—
37	C₂₃×#554	C₂²	1	1	yes	characteristic
38	C₂₃×#552	—	2	1	no	—
39	C₂₃×#552	—	2	1	no	—
40	C₂₃×#552	—	2	2	no	—
41	C₂₃×#552	—	2	1	no	—
42	C₂₃×#544	—	2	1	no	—
43	C₂₃×#542	C₂²	1	2	yes	—
44	C₂₃×#541	—	2	1	no	—
45	C₂₃×#541	—	2	2	no	—
46	C₂₃×#541	—	2	2	no	—
47	C₂₃×#541	C₂²	1	2	yes	—
48	C₂₃×#536	C₂²	1	2	yes	—
49	C₂₃×#533	—	2	1	no	—
50	C₂₃×#533	—	2	1	no	—
51	C₂₃×#533	C₂²	1	1	yes	characteristic
52	C₂₃×#533	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
54	C₂₃×#529	C₂²	1	1	yes	characteristic
55	C₂₃×#519	C₂²	1	2	yes	—
56	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
57	C₂₃×#497	C₂²	1	2	yes	—
58	C₂₃×#497	C₂²	1	2	yes	—
59	C₂₃×#497	C₂²	1	2	yes	—
60	C₂₃×#495	C₂²	1	2	yes	—
61	C₂₃×#494	C₂²	1	1	yes	characteristic
62	C₂₃×#494	C₂²	1	1	yes	characteristic
63	C₂₃×#494	C₂²	1	2	yes	—
64	C₂₃×#491	C₂²	1	2	yes	—
65	C₂₃×#491	C₂²	1	2	yes	—
66	C₂₃×#489	C₂²	1	2	yes	—
67	C₂₃×#488	C₂²	1	2	yes	—
68	C₂₃×#487	C₂²	1	1	yes	characteristic
69	C₂₃×#487	C₂²	1	1	yes	characteristic
70	C₂₃×#487	C₂²	1	2	yes	—
71	C₂₃×#485	C₂²	1	1	yes	characteristic
72	C₂₃×#485	C₂²	1	2	yes	—
73	C₂₃×#482	C₂²	1	1	yes	characteristic
74	C₂₃×#479	C₂²	1	1	yes	characteristic
75	C₂₃×#479	C₂²	1	2	yes	—
76	C₂₃×#479	C₂²	1	2	yes	—
77	C₂₃×#478	C₂²	1	1	yes	characteristic
78	C₂₃×#477	C₂²	1	1	yes	characteristic
79	C₂₃×#477	C₂²	1	2	yes	—
80	C₂₃×#476	C₂²	1	1	yes	characteristic
81	C₂₃×#475	C₂²	1	2	yes	—
82	C₂₃×#464	C₂²	1	2	yes	—
83	C₂₃×#464	C₂²	1	2	yes	—
84	C₂₃×#464	C₂²	1	2	yes	—
85	C₂₃×#464	C₂²	1	1	yes	characteristic
86	C₂₃×#464	C₂²	1	2	yes	—
87	C₂₃×#464	C₂²	1	2	yes	—
88	C₂₃×#463	C₂²	1	2	yes	—
89	C₂₃×#463	C₂²	1	1	yes	characteristic
90	C₂₃×#462	C₂²	1	2	yes	—
91	C₂₃×#462	C₂²	1	2	yes	—
92	C₂₃×#462	C₂²	1	1	yes	characteristic
93	C₂₃×#462	C₂²	1	1	yes	characteristic
94	C₂₃×#462	C₂²	1	2	yes	—
95	C₂₃×#462	C₂²	1	2	yes	—
96	C₂₃×#462	C₂²	1	2	yes	—
97	C₂₃×#462	C₂²	1	1	yes	characteristic
98	C₂₃×#462	C₂²	1	2	yes	—
99	C₂₃×#462	C₂²	1	2	yes	—
100	C₂₃×#461	C₂²	1	1	yes	characteristic
101	C₂₃×#461	C₂²	1	1	yes	characteristic
102	C₂₃×#461	C₂²	1	2	yes	—
103	C₂₃×#461	C₂²	1	1	yes	characteristic
104	C₂₃×#452	C₂²	1	1	yes	characteristic
105	C₂₃×#452	C₂²	1	2	yes	—
106	C₂₃×#451	C₂²	1	2	yes	—
107	C₂₃×#451	C₂²	1	2	yes	—
108	C₂₃×#451	C₂²	1	2	yes	—
109	C₂₃×#449	C₂²	1	1	yes	characteristic
110	C₂₃×#448	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	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
117	C₂₃×#441	C₂²	1	2	yes	—
118	C₂₃×#441	C₂²	1	2	yes	—
119	C₂₃×#441	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	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
126	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
130	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
131	C₂₃×#433	C₂²	1	2	yes	—
132	C₂₃×#433	C₂²	1	2	yes	—
133	C₂₃×#432	C₂²	1	1	yes	characteristic
134	C₂₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
136	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
137	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
138	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
144	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
151	C₂₃×C₄⋊Q₈	—	2	2	no	—
152	C₂₃×C₄⋊Q₈	—	2	1	no	—
153	C₂₃×C₄⋊Q₈	—	2	2	no	—
154	C₂₃×C₄⋊Q₈	—	2	1	no	—
155	C₂₃×C₄⋊Q₈	—	2	1	no	—
156	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
157	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
158	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
159	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₂₃×#126	—	2	2	no	—
168	C₂₃×#126	—	2	2	no	—
169	C₂₃×#126	—	2	2	no	—
170	C₂₃×#126	—	2	2	no	—
171	C₂₃×#126	—	2	2	no	—
172	C₂₃×#126	—	2	2	no	—
173	C₂₃×#126	—	2	2	no	—
174	C₂₃×#126	—	2	2	no	—
175	C₂₃×#126	—	2	2	no	—
176	C₂₃×#126	—	2	2	no	—
177	C₂₃×#126	—	2	1	no	—
178	C₂₃×#125	—	2	1	no	—
179	C₂₃×#125	—	2	1	no	—
180	C₂₃×#125	—	2	2	no	—
181	C₂₃×#125	—	2	2	no	—
182	C₂₃×#125	—	2	2	no	—
183	C₂₃×#125	—	2	2	no	—
184	C₂₃×#125	—	2	2	no	—
185	C₂₃×#125	—	2	2	no	—
186	C₂₃×#125	—	2	1	no	—
187	C₂₃×#125	—	2	2	no	—
188	C₂₃×#125	—	2	2	no	—
189	C₂₃×#125	—	2	2	no	—
190	C₂₃×#125	—	2	2	no	—
191	C₂₃×#125	—	2	1	no	—
192	C₂₃×#125	D₄	1	2	yes	—
193	C₂₃×#125	C₂³	1	2	yes	—
194	C₂₃×#125	C₂³	1	1	yes	characteristic
195	C₂₃×#124	—	2	2	no	—
196	C₂₃×#124	C₂³	1	2	yes	—
197	C₂₃×#124	C₂³	1	1	yes	characteristic
198	C₂₃×#124	C₂³	1	2	yes	—
199	C₂₃×#124	C₂³	1	2	yes	—
200	C₂₃×#123	—	2	1	no	—
201	C₂₃×#123	—	2	2	no	—
202	C₂₃×#123	—	2	2	no	—
203	C₂₃×#123	—	2	2	no	—
204	C₂₃×C₂²⋊Q₈	—	2	1	no	—
205	C₂₃×C₂²⋊Q₈	—	2	1	no	—
206	C₂₃×C₂²⋊Q₈	—	2	2	no	—
207	C₂₃×C₂²⋊Q₈	—	2	1	no	—
208	C₂₃×C₂²⋊Q₈	—	2	1	no	—
209	C₂₃×C₂²⋊Q₈	—	2	2	no	—
210	C₂₃×C₂²⋊Q₈	—	2	1	no	—
211	C₂₃×C₂²⋊Q₈	—	2	2	no	—
212	C₂₃×C₂²⋊Q₈	—	2	2	no	—
213	C₂₃×C₂²⋊Q₈	—	2	2	no	—
214	C₂₃×C₂²⋊Q₈	—	2	2	no	—
215	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
216	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
217	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
218	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
219	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
220	C₂₃×#121	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₂₃	—	2	1	no	—
222	C₄×Q₈×C₂₃	—	2	1	no	—
223	C₄×Q₈×C₂₃	—	2	2	no	—
224	C₄×Q₈×C₂₃	—	2	1	no	—
225	C₄×Q₈×C₂₃	—	2	1	no	—
226	C₄×Q₈×C₂₃	—	2	2	no	—
227	C₄×Q₈×C₂₃	—	2	2	no	—
228	C₄×Q₈×C₂₃	—	2	2	no	—
229	C₄×Q₈×C₂₃	—	2	1	no	—
230	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
231	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
232	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
233	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
234	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
235	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
236	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
237	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₂₃	—	2	1	no	—
245	C₄×D₄×C₂₃	—	2	1	no	—
246	C₄×D₄×C₂₃	—	2	1	no	—
247	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
248	C₄×D₄×C₂₃	C₂³	1	2	yes	—
249	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
251	C₂₃×#117	—	2	1	no	—
252	C₂₃×#117	—	2	1	no	—
253	C₂₃×#117	—	2	1	no	—
254	C₂₃×#117	—	2	2	no	—
255	C₂₃×#117	—	2	2	no	—
256	C₂₃×#117	—	2	1	no	—
257	C₂₃×#117	—	2	2	no	—
258	C₂₃×#117	—	2	2	no	—
259	C₂₃×#117	—	2	1	no	—
260	C₂₃×#117	—	2	1	no	—
261	C₂₃×#117	C₂³	1	1	yes	characteristic
262	C₂₃×#117	C₂³	1	2	yes	—
263	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
266	C₂×C₄²×C₂₃	—	2	1	no	—
267	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
268	C₂₃×#107	C₂³	1	1	yes	characteristic
269	C₂₃×#107	C₂³	1	1	yes	characteristic
270	C₂₃×#107	C₂³	1	2	yes	—
271	C₂₃×#106	C₂³	1	1	yes	characteristic
272	C₂₃×#106	C₂³	1	2	yes	—
273	C₂₃×#106	C₂³	1	1	yes	characteristic
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	2	yes	—
287	C₂₃×#103	C₂³	1	2	yes	—
288	C₂₃×#103	C₂³	1	2	yes	—
289	C₂₃×#103	C₂³	1	1	yes	characteristic
290	C₂₃×#103	C₂³	1	2	yes	—
291	C₂₃×#103	C₂³	1	2	yes	—
292	C₂₃×#103	C₂³	1	2	yes	—
293	C₂₃×#103	C₂³	1	2	yes	—
294	C₂₃×#103	C₂³	1	2	yes	—
295	C₂₃×#103	C₂³	1	2	yes	—
296	C₂₃×#103	C₂³	1	2	yes	—
297	C₂₃×#102	C₂³	1	1	yes	characteristic
298	C₂₃×#102	C₂³	1	1	yes	characteristic
299	C₂₃×#102	C₂³	1	1	yes	characteristic
300	C₂₃×#102	C₂³	1	1	yes	characteristic
301	C₂₃×#102	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₂₃×#97	C₂³	1	2	yes	—
306	C₂₃×#97	C₂³	1	2	yes	—
307	C₂₃×#97	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	2	yes	—
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	#41×C₂₃	—	4	1	no	—
313	#41×C₂₃	—	4	1	no	—
314	C₂×Q₈×C₂₃	—	2	2	no	—
315	C₂×Q₈×C₂₃	—	2	1	no	—
316	C₂×Q₈×C₂₃	—	2	2	no	—
317	C₂×Q₈×C₂₃	—	4	2	no	—
318	C₂×Q₈×C₂₃	—	4	2	no	—
319	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
323	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
327	C₂×D₄×C₂₃	—	2	1	no	—
328	C₂×D₄×C₂₃	—	2	1	no	—
329	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₂₃	—	2	2	no	—
332	C₂²×C₄×C₂₃	—	2	1	no	—
333	C₂²×C₄×C₂₃	—	2	1	no	—
334	C₂²×C₄×C₂₃	—	2	1	no	—
335	C₂²×C₄×C₂₃	—	2	1	no	—
336	C₂²×C₄×C₂₃	—	2	2	no	—
337	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
340	Q₁₆×C₂₃	—	4	2	no	—
341	Q₁₆×C₂₃	—	4	2	no	—
342	Q₁₆×C₂₃	—	4	2	no	—
343	Q₁₆×C₂₃	—	4	2	no	—
344	Q₁₆×C₂₃	—	4	2	no	—
345	Q₁₆×C₂₃	—	4	2	no	—
346	Q₁₆×C₂₃	—	4	2	no	—
347	Q₁₆×C₂₃	—	4	1	no	—
348	SD₁₆×C₂₃	—	4	2	no	—
349	SD₁₆×C₂₃	—	4	2	no	—
350	SD₁₆×C₂₃	—	4	2	no	—
351	SD₁₆×C₂₃	—	4	1	no	—
352	SD₁₆×C₂₃	—	4	1	no	—
353	D₈×C₂₃	—	4	1	no	—
354	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
358	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₂₃	—	2	2	no	—
361	C₄⋊C₄×C₂₃	—	2	1	no	—
362	C₄⋊C₄×C₂₃	—	2	1	no	—
363	C₄⋊C₄×C₂₃	—	2	1	no	—
364	C₄⋊C₄×C₂₃	—	2	2	no	—
365	C₄⋊C₄×C₂₃	—	2	2	no	—
366	C₄⋊C₄×C₂₃	—	2	1	no	—
367	C₄⋊C₄×C₂₃	—	2	1	no	—
368	C₄⋊C₄×C₂₃	—	2	1	no	—
369	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
376	C₄⋊C₄×C₂₃	—	2	1	no	—
377	C₄⋊C₄×C₂₃	—	2	1	no	—
378	C₄⋊C₄×C₂₃	—	2	1	no	—
379	C₄⋊C₄×C₂₃	—	2	2	no	—
380	C₄⋊C₄×C₂₃	—	2	2	no	—
381	C₄⋊C₄×C₂₃	—	2	2	no	—
382	C₄⋊C₄×C₂₃	—	2	2	no	—
383	C₄⋊C₄×C₂₃	—	2	2	no	—
384	C₄⋊C₄×C₂₃	—	2	2	no	—
385	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
390	C₄⋊C₄×C₂₃	—	2	2	no	—
391	C₄⋊C₄×C₂₃	—	2	2	no	—
392	C₄⋊C₄×C₂₃	—	2	1	no	—
393	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
394	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
401	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
411	C₂²⋊C₄×C₂₃	—	2	1	no	—
412	C₂²⋊C₄×C₂₃	—	2	1	no	—
413	C₂²⋊C₄×C₂₃	—	2	1	no	—
414	C₂²⋊C₄×C₂₃	—	2	1	no	—
415	C₂²⋊C₄×C₂₃	—	2	2	no	—
416	C₂²⋊C₄×C₂₃	—	2	2	no	—
417	C₂²⋊C₄×C₂₃	—	2	2	no	—
418	C₂²⋊C₄×C₂₃	—	2	2	no	—
419	C₂²⋊C₄×C₂₃	—	2	2	no	—
420	C₂²⋊C₄×C₂₃	—	2	2	no	—
421	C₂²⋊C₄×C₂₃	—	2	1	no	—
422	C₂²⋊C₄×C₂₃	—	2	2	no	—
423	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
425	C₄²×C₂₃	—	2	1	no	—
426	C₄²×C₂₃	—	2	1	no	—
427	C₄²×C₂₃	—	2	1	no	—
428	C₄²×C₂₃	—	2	2	no	—
429	C₄²×C₂₃	—	2	2	no	—
430	C₄²×C₂₃	—	2	2	no	—
431	C₄²×C₂₃	—	2	2	no	—
432	C₄²×C₂₃	—	2	2	no	—
433	C₄²×C₂₃	—	2	1	no	—
434	C₄²×C₂₃	—	2	2	no	—
435	C₄²×C₂₃	—	2	2	no	—
436	C₄²×C₂₃	—	2	2	no	—
437	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₄²×C₂₃	C₂⁴	1	2	yes	—
442	C₄²×C₂₃	C₂⁴	1	2	yes	—
443	#61922	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₂₃	—	2	1	no	—
445	C₂³×C₂₃	—	2	1	no	—
446	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₂₃	—	2	2	no	—
448	Q₈×C₂₃	—	2	2	no	—
449	Q₈×C₂₃	—	2	1	no	—
450	Q₈×C₂₃	—	2	2	no	—
451	Q₈×C₂₃	—	2	2	no	—
452	Q₈×C₂₃	—	2	2	no	—
453	Q₈×C₂₃	—	2	1	no	—
454	Q₈×C₂₃	—	2	2	no	—
455	Q₈×C₂₃	—	2	1	no	—
456	Q₈×C₂₃	—	2	2	no	—
457	Q₈×C₂₃	—	2	2	no	—
458	Q₈×C₂₃	—	2	1	no	—
459	Q₈×C₂₃	—	4	2	no	—
460	Q₈×C₂₃	—	4	4	no	—
461	Q₈×C₂₃	—	8	1	no	—
462	Q₈×C₂₃	—	8	2	no	—
463	D₄×C₂₃	—	2	1	no	—
464	D₄×C₂₃	—	2	1	no	—
465	D₄×C₂₃	—	2	1	no	—
466	D₄×C₂₃	—	2	1	no	—
467	D₄×C₂₃	—	4	2	no	—
468	D₄×C₂₃	—	8	1	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	1	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	2	no	—
475	C₂×C₄×C₂₃	—	2	1	no	—
476	C₂×C₄×C₂₃	—	2	1	no	—
477	C₂×C₄×C₂₃	—	2	1	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	2	2	no	—
480	C₂×C₄×C₂₃	—	2	2	no	—
481	C₂×C₄×C₂₃	—	2	1	no	—
482	C₂×C₄×C₂₃	—	4	1	no	—
483	C₂×C₄×C₂₃	—	4	2	no	—
484	C₂×C₄×C₂₃	—	4	2	no	—
485	C₂×C₄×C₂₃	—	4	4	no	—
486	C₂×C₄×C₂₃	—	4	2	no	—
487	C₂×C₄×C₂₃	—	4	2	no	—
488	C₂×C₄×C₂₃	—	8	2	no	—
489	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
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	1	yes	characteristic
497	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
499	C₈×C₂₃	—	2	1	no	—
500	C₈×C₂₃	—	2	2	no	—
501	C₈×C₂₃	—	2	1	no	—
502	C₈×C₂₃	—	2	2	no	—
503	C₈×C₂₃	—	2	1	no	—
504	C₈×C₂₃	—	2	1	no	—
505	#3555	C₂×C₂₃	1	1	yes	characteristic, complemented
506	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
507	#3402	C₂×C₂₃	1	2	yes	complemented
508	#3398	C₂×C₂₃	1	1	yes	characteristic, complemented
509	#3398	C₂×C₂₃	1	1	yes	characteristic, complemented
510	#3398	C₂×C₂₃	1	2	yes	complemented
511	#3395	C₂×C₂₃	1	1	yes	characteristic, complemented
512	#3393	C₂×C₂₃	1	1	yes	characteristic, complemented
513	#3377	C₂×C₂₃	1	2	yes	complemented
514	#3374	C₂×C₂₃	1	2	yes	complemented
515	#3372	C₂×C₂₃	1	1	yes	characteristic, complemented
516	#3369	C₂×C₂₃	1	1	yes	characteristic, complemented
517	#3363	C₂×C₂₃	1	1	yes	characteristic, complemented
518	#3360	C₂×C₂₃	1	1	yes	characteristic, complemented
519	#3225	C₂×C₂₃	1	2	yes	—
520	#3223	C₂×C₂₃	1	2	yes	complemented
521	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
522	#3209	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#3127	C₂×C₂₃	1	2	yes	complemented
524	#3121	C₂×C₂₃	1	2	yes	complemented
525	#3116	C₂×C₂₃	1	1	yes	characteristic, complemented
526	#3102	C₂×C₂₃	1	1	yes	characteristic
527	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
528	C₂²×C₂₃	—	2	1	no	—
529	C₂²×C₂₃	—	2	1	no	—
530	C₂²×C₂₃	—	2	1	no	—
531	C₂²×C₂₃	—	4	1	no	—
532	C₂²×C₂₃	—	4	1	no	—
533	C₂²×C₂₃	—	4	1	no	—
534	C₂²×C₂₃	—	4	1	no	—
535	C₂²×C₂₃	—	4	1	no	—
536	C₂²×C₂₃	—	4	1	no	—
537	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
538	C₄×C₂₃	—	2	1	no	—
539	C₄×C₂₃	—	2	1	no	—
540	C₄×C₂₃	—	2	2	no	—
541	C₄×C₂₃	—	2	2	no	—
542	C₄×C₂₃	—	2	1	no	—
543	C₄×C₂₃	—	2	1	no	—
544	C₄×C₂₃	—	2	2	no	—
545	C₄×C₂₃	—	2	2	no	—
546	C₄×C₂₃	—	4	1	no	—
547	C₄×C₂₃	—	4	2	no	—
548	C₄×C₂₃	—	4	1	no	—
549	C₄×C₂₃	—	4	1	no	—
550	C₄×C₂₃	—	4	2	no	—
551	C₄×C₂₃	—	4	2	no	—
552	C₄×C₂₃	—	4	2	no	—
553	C₄×C₂₃	—	4	1	no	—
554	C₄×C₂₃	—	4	1	no	—
555	C₄×C₂₃	—	4	1	no	—
556	C₄×C₂₃	#578	1	2	yes	—
557	C₄×C₂₃	#585	1	1	yes	characteristic
558	C₄×C₂₃	#585	1	1	yes	characteristic
559	#563	—	2	2	no	—
560	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
561	#557	C₂²×C₂₃	1	1	yes	characteristic
562	#557	C₂²×C₂₃	1	1	yes	characteristic
563	#557	C₂²×C₂₃	1	2	yes	—
564	#557	C₂²×C₂₃	1	1	yes	characteristic
565	#557	C₂²×C₂₃	1	2	yes	—
566	#556	—	2	1	no	—
567	#556	C₂²×C₂₃	1	1	yes	characteristic
568	#556	C₂²×C₂₃	1	1	yes	characteristic
569	#556	C₂²×C₂₃	1	2	yes	—
570	#556	C₂²×C₂₃	1	1	yes	characteristic
571	#556	C₂²×C₂₃	1	2	yes	—
572	#554	C₂²×C₂₃	1	1	yes	characteristic
573	#552	—	2	1	no	—
574	#552	—	2	1	no	—
575	#552	—	2	2	no	—
576	#552	—	2	1	no	—
577	#544	—	2	1	no	—
578	#542	C₂²×C₂₃	1	2	yes	—
579	#541	—	2	1	no	—
580	#541	—	2	2	no	—
581	#541	—	2	2	no	—
582	#541	C₂²×C₂₃	1	2	yes	—
583	#536	C₂²×C₂₃	1	2	yes	—
584	#533	—	2	1	no	—
585	#533	—	2	1	no	—
586	#533	C₂²×C₂₃	1	1	yes	characteristic
587	#533	C₂²×C₂₃	1	1	yes	characteristic
588	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
589	#529	C₂²×C₂₃	1	1	yes	characteristic
590	#519	C₂²×C₂₃	1	2	yes	—
591	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
592	#497	C₂²×C₂₃	1	2	yes	—
593	#497	C₂²×C₂₃	1	2	yes	—
594	#497	C₂²×C₂₃	1	2	yes	—
595	#495	C₂²×C₂₃	1	2	yes	—
596	#494	C₂²×C₂₃	1	1	yes	characteristic
597	#494	C₂²×C₂₃	1	2	yes	—
598	#494	C₂²×C₂₃	1	1	yes	characteristic
599	#491	C₂²×C₂₃	1	2	yes	—
600	#491	C₂²×C₂₃	1	2	yes	—
601	#489	C₂²×C₂₃	1	2	yes	—
602	#488	C₂²×C₂₃	1	2	yes	—
603	#487	C₂²×C₂₃	1	1	yes	characteristic
604	#487	C₂²×C₂₃	1	2	yes	—
605	#487	C₂²×C₂₃	1	1	yes	characteristic
606	#485	C₂²×C₂₃	1	1	yes	characteristic
607	#485	C₂²×C₂₃	1	2	yes	—
608	#482	C₂²×C₂₃	1	1	yes	characteristic
609	#479	C₂²×C₂₃	1	1	yes	characteristic
610	#479	C₂²×C₂₃	1	2	yes	—
611	#479	C₂²×C₂₃	1	2	yes	—
612	#478	C₂²×C₂₃	1	1	yes	characteristic
613	#477	C₂²×C₂₃	1	1	yes	characteristic
614	#477	C₂²×C₂₃	1	2	yes	—
615	#476	C₂²×C₂₃	1	1	yes	characteristic
616	#475	C₂²×C₂₃	1	2	yes	—
617	#464	C₂²×C₂₃	1	1	yes	characteristic
618	#464	C₂²×C₂₃	1	2	yes	—
619	#464	C₂²×C₂₃	1	2	yes	—
620	#464	C₂²×C₂₃	1	2	yes	—
621	#464	C₂²×C₂₃	1	2	yes	—
622	#464	C₂²×C₂₃	1	2	yes	—
623	#463	C₂²×C₂₃	1	1	yes	characteristic
624	#463	C₂²×C₂₃	1	2	yes	—
625	#462	C₂²×C₂₃	1	1	yes	characteristic
626	#462	C₂²×C₂₃	1	2	yes	—
627	#462	C₂²×C₂₃	1	1	yes	characteristic
628	#462	C₂²×C₂₃	1	1	yes	characteristic
629	#462	C₂²×C₂₃	1	2	yes	—
630	#462	C₂²×C₂₃	1	2	yes	—
631	#462	C₂²×C₂₃	1	2	yes	—
632	#462	C₂²×C₂₃	1	2	yes	—
633	#462	C₂²×C₂₃	1	2	yes	—
634	#462	C₂²×C₂₃	1	2	yes	—
635	#461	C₂²×C₂₃	1	1	yes	characteristic
636	#461	C₂²×C₂₃	1	1	yes	characteristic
637	#461	C₂²×C₂₃	1	1	yes	characteristic
638	#461	C₂²×C₂₃	1	2	yes	—
639	#452	C₂²×C₂₃	1	1	yes	characteristic
640	#452	C₂²×C₂₃	1	2	yes	—
641	#451	C₂²×C₂₃	1	2	yes	—
642	#451	C₂²×C₂₃	1	2	yes	—
643	#451	C₂²×C₂₃	1	2	yes	—
644	#449	C₂²×C₂₃	1	1	yes	characteristic
645	#448	C₂²×C₂₃	1	2	yes	—
646	#446	C₂²×C₂₃	1	1	yes	characteristic
647	#446	C₂²×C₂₃	1	1	yes	characteristic
648	#446	C₂²×C₂₃	1	2	yes	—
649	#446	C₂²×C₂₃	1	2	yes	—
650	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
651	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
652	#441	C₂²×C₂₃	1	2	yes	—
653	#441	C₂²×C₂₃	1	2	yes	—
654	#441	C₂²×C₂₃	1	2	yes	—
655	#441	C₂²×C₂₃	1	2	yes	—
656	#440	C₂²×C₂₃	1	2	yes	—
657	#440	C₂²×C₂₃	1	2	yes	—
658	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
659	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
660	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
662	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
663	C₄×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
664	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
665	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
666	#433	C₂²×C₂₃	1	2	yes	—
667	#433	C₂²×C₂₃	1	2	yes	—
668	#432	C₂²×C₂₃	1	1	yes	characteristic
669	#431	C₂²×C₂₃	1	1	yes	characteristic
670	C₂×C₂₃	—	4	1	no	—
671	C₂×C₂₃	—	8	1	no	—
672	C₂×C₂₃	—	8	1	no	—
673	C₂×C₂₃	#3487	1	1	yes	characteristic
674	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
675	C₂×C₂₃	#3586	1	1	yes	characteristic
676	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
677	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
679	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
680	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
682	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
684	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
685	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
689	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
690	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
691	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	—	2	1	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	1	no	—
697	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
698	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
706	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
707	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	1	no	—
719	#125	—	2	1	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	2	no	—
729	#125	—	2	2	no	—
730	#125	—	2	2	no	—
731	#125	—	2	1	no	—
732	#125	—	2	1	no	—
733	#125	D₄×C₂₃	1	2	yes	—
734	#125	C₂³×C₂₃	1	1	yes	characteristic
735	#125	C₂³×C₂₃	1	2	yes	—
736	#124	—	2	2	no	—
737	#124	C₂³×C₂₃	1	1	yes	characteristic
738	#124	C₂³×C₂₃	1	2	yes	—
739	#124	C₂³×C₂₃	1	2	yes	—
740	#124	C₂³×C₂₃	1	2	yes	—
741	#123	—	2	1	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	1	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	1	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	1	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
757	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
758	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
759	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
760	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
761	#121	C₂³×C₂₃	1	1	yes	characteristic
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	2	no	—
768	C₄×Q₈	—	2	2	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
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×Q₈	C₂³×C₂₃	1	2	yes	—
775	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
776	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
777	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
778	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
779	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
780	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
781	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
782	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
783	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
784	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
789	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
791	C₄×D₄	C₂³×C₂₃	1	2	yes	—
792	#117	—	2	1	no	—
793	#117	—	2	1	no	—
794	#117	—	2	1	no	—
795	#117	—	2	2	no	—
796	#117	—	2	2	no	—
797	#117	—	2	1	no	—
798	#117	—	2	2	no	—
799	#117	—	2	2	no	—
800	#117	—	2	1	no	—
801	#117	—	2	1	no	—
802	#117	C₂³×C₂₃	1	1	yes	characteristic
803	#117	C₂³×C₂₃	1	2	yes	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	1	no	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄²	—	2	1	no	—
808	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
809	#107	C₂³×C₂₃	1	1	yes	characteristic
810	#107	C₂³×C₂₃	1	1	yes	characteristic
811	#107	C₂³×C₂₃	1	2	yes	—
812	#106	C₂³×C₂₃	1	1	yes	characteristic
813	#106	C₂³×C₂₃	1	2	yes	—
814	#106	C₂³×C₂₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
820	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
821	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
822	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
823	#103	C₂³×C₂₃	1	1	yes	characteristic
824	#103	C₂³×C₂₃	1	2	yes	—
825	#103	C₂³×C₂₃	1	1	yes	characteristic
826	#103	C₂³×C₂₃	1	1	yes	characteristic
827	#103	C₂³×C₂₃	1	2	yes	—
828	#103	C₂³×C₂₃	1	2	yes	—
829	#103	C₂³×C₂₃	1	2	yes	—
830	#103	C₂³×C₂₃	1	1	yes	characteristic
831	#103	C₂³×C₂₃	1	2	yes	—
832	#103	C₂³×C₂₃	1	2	yes	—
833	#103	C₂³×C₂₃	1	2	yes	—
834	#103	C₂³×C₂₃	1	2	yes	—
835	#103	C₂³×C₂₃	1	2	yes	—
836	#103	C₂³×C₂₃	1	2	yes	—
837	#103	C₂³×C₂₃	1	2	yes	—
838	#102	C₂³×C₂₃	1	1	yes	characteristic
839	#102	C₂³×C₂₃	1	1	yes	characteristic
840	#102	C₂³×C₂₃	1	1	yes	characteristic
841	#102	C₂³×C₂₃	1	1	yes	characteristic
842	#102	C₂³×C₂₃	1	2	yes	—
843	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
844	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
846	#97	C₂³×C₂₃	1	2	yes	—
847	#97	C₂³×C₂₃	1	2	yes	—
848	#97	C₂³×C₂₃	1	2	yes	—
849	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₂₃	1	2	yes	—
852	C₄×C₈	C₂³×C₂₃	1	2	yes	—
853	C₂₃	#61922	1	1	yes	characteristic, direct product factor, Sylow
854	#41	—	4	1	no	—
855	#41	—	4	1	no	—
856	C₂×Q₈	—	2	2	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	4	2	no	—
860	C₂×Q₈	—	4	2	no	—
861	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
862	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
863	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
864	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
865	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
866	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
867	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	2	1	no	—
871	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
872	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	1	no	—
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	2	no	—
879	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
880	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
882	Q₁₆	—	4	2	no	—
883	Q₁₆	—	4	2	no	—
884	Q₁₆	—	4	2	no	—
885	Q₁₆	—	4	2	no	—
886	Q₁₆	—	4	2	no	—
887	Q₁₆	—	4	2	no	—
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	1	no	—
890	SD₁₆	—	4	2	no	—
891	SD₁₆	—	4	2	no	—
892	SD₁₆	—	4	2	no	—
893	SD₁₆	—	4	1	no	—
894	SD₁₆	—	4	1	no	—
895	D₈	—	4	1	no	—
896	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
898	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
899	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
900	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
901	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	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	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	1	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
943	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
946	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
966	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	2	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	2	no	—
979	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
980	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
981	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₄²	C₂⁴×C₂₃	1	2	yes	—
983	C₄²	C₂⁴×C₂₃	1	2	yes	—
984	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₂³	—	2	1	no	—
986	C₂³	—	2	1	no	—
987	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
988	Q₈	—	2	2	no	—
989	Q₈	—	2	2	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	4	2	no	—
1001	Q₈	—	4	4	no	—
1002	Q₈	—	8	1	no	—
1003	Q₈	—	8	2	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	4	2	no	—
1009	D₄	—	8	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	4	4	no	—
1027	C₂×C₄	—	4	2	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1031	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1032	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1033	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1034	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1038	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1039	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1040	C₈	—	2	1	no	—
1041	C₈	—	2	2	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	2	no	—
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₂²	—	2	1	no	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	4	1	no	—
1050	C₂²	—	4	1	no	—
1051	C₂²	—	4	1	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	2	no	—
1066	C₄	—	4	2	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	C₂₃×#578	1	2	yes	—
1075	C₄	C₂₃×#585	1	1	yes	characteristic
1076	C₄	C₂₃×#585	1	1	yes	characteristic
1077	C₂	—	4	1	no	—
1078	C₂	—	8	1	no	—
1079	C₂	—	8	1	no	—
1080	C₂	C₂₃×#3487	1	1	yes	characteristic
1081	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
1082	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#449	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3555	C₂	semidirect
2. C₂₃×#3509	C₂	semidirect
3. C₂₃×#3402	C₂	semidirect
4. C₂₃×#3398	C₂	semidirect
5. C₂₃×#3398	C₂	semidirect
6. C₂₃×#3398	C₂	semidirect
7. C₂₃×#3395	C₂	semidirect
8. C₂₃×#3393	C₂	semidirect
9. C₂₃×#3377	C₂	semidirect
10. C₂₃×#3374	C₂	semidirect
11. C₂₃×#3372	C₂	semidirect
12. C₂₃×#3369	C₂	semidirect
13. C₂₃×#3363	C₂	semidirect
14. C₂₃×#3360	C₂	semidirect
16. C₂₃×#3223	C₂	semidirect
17. C₂₃×#3218	C₂	semidirect
18. C₂₃×#3209	C₂	semidirect
19. C₂₃×#3127	C₂	semidirect
20. C₂₃×#3121	C₂	semidirect
21. C₂₃×#3116	C₂	semidirect
23. C₂₃×#2985	C₂	semidirect
443. #61922	C₂₃	direct (N × H)
505. #3555	C₂×C₂₃	semidirect
506. #3509	C₂×C₂₃	semidirect
507. #3402	C₂×C₂₃	semidirect
508. #3398	C₂×C₂₃	semidirect
509. #3398	C₂×C₂₃	semidirect
510. #3398	C₂×C₂₃	semidirect
511. #3395	C₂×C₂₃	semidirect
512. #3393	C₂×C₂₃	semidirect
513. #3377	C₂×C₂₃	semidirect
514. #3374	C₂×C₂₃	semidirect
515. #3372	C₂×C₂₃	semidirect
516. #3369	C₂×C₂₃	semidirect
517. #3363	C₂×C₂₃	semidirect
518. #3360	C₂×C₂₃	semidirect
520. #3223	C₂×C₂₃	semidirect
521. #3218	C₂×C₂₃	semidirect
522. #3209	C₂×C₂₃	semidirect
523. #3127	C₂×C₂₃	semidirect
524. #3121	C₂×C₂₃	semidirect
525. #3116	C₂×C₂₃	semidirect
527. #2985	C₂×C₂₃	semidirect
853. C₂₃	#61922	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×#3555	2
C₂₃×#3509	2
C₂₃×#3402	2
C₂₃×#3398	2
C₂₃×#3395	2
C₂₃×#3393	2
C₂₃×#3377	2
C₂₃×#3374	2
C₂₃×#3372	2
C₂₃×#3369	2
C₂₃×#3363	2
C₂₃×#3360	2
C₂₃×#3225	2
C₂₃×#3223	2
C₂₃×#3218	2
C₂₃×#3209	2
C₂₃×#3127	2
C₂₃×#3121	2
C₂₃×#3116	2
C₂₃×#3102	2
C₂₃×#2985	2
#61922	23

Subgroups — C23×#61922 #19209548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61922 #19209548