Subgroups — C₂₃×#61905 #19209531

Order 5888.

1724 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3398	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3393	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3377	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3367	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3215	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3211	C₂	1	2	yes	maximal
12	C₂₃×#3209	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic
16	C₂₃×#3104	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#557	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#557	C₂²	1	2	yes	complemented
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#556	—	2	1	no	—
23	C₂₃×#556	—	2	2	no	—
24	C₂₃×#556	C₂²	1	2	yes	—
25	C₂₃×#556	C₂²	1	2	yes	—
26	C₂₃×#556	C₂²	1	4	yes	—
27	C₂₃×#556	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#556	C₂²	1	2	yes	complemented
29	C₂₃×#552	—	2	1	no	—
30	C₂₃×#552	—	2	2	no	—
31	D₄×Q₈×C₂₃	—	2	1	no	—
32	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#541	—	2	1	no	—
34	C₂₃×#541	—	2	2	no	—
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂₃×#533	C₂²	1	2	yes	—
37	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂₃×#529	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#126	—	2	2	no	—
41	C₂×C₂₃×#124	C₂²	1	2	yes	—
42	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
43	C₂₃×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#117	—	2	1	no	—
48	C₂₃×#497	C₂²	1	4	yes	—
49	C₂₃×#497	C₂²	1	2	yes	complemented
50	C₂₃×#495	C₂²	1	4	yes	—
51	C₂₃×#494	C₂²	1	2	yes	complemented
52	C₂₃×#491	C₂²	1	2	yes	complemented
53	C₂₃×#489	C₂²	1	4	yes	—
54	C₂₃×#488	C₂²	1	4	yes	—
55	C₂₃×#487	C₂²	1	2	yes	complemented
56	C₂₃×#484	C₂²	1	1	yes	characteristic
57	C₂₃×#484	C₂²	1	2	yes	—
58	C₂₃×#481	C₂²	1	1	yes	characteristic
59	C₂₃×#479	C₂²	1	4	yes	complemented
60	C₂₃×#478	C₂²	1	2	yes	—
61	C₂₃×#477	C₂²	1	4	yes	complemented
62	C₂₃×#474	C₂²	1	2	yes	—
63	C₂₃×#464	C₂²	1	4	yes	—
64	C₂₃×#464	C₂²	1	4	yes	—
65	C₂₃×#464	C₂²	1	4	yes	—
66	C₂₃×#464	C₂²	1	4	yes	complemented
67	C₂₃×#463	C₂²	1	4	yes	—
68	C₂₃×#463	C₂²	1	2	yes	—
69	C₂₃×#462	C₂²	1	4	yes	complemented
70	C₂₃×#462	C₂²	1	2	yes	complemented
71	C₂₃×#462	C₂²	1	4	yes	complemented
72	C₂₃×#461	C₂²	1	2	yes	—
73	C₂₃×#461	C₂²	1	2	yes	complemented
74	C₂₃×#451	C₂²	1	2	yes	—
75	C₂₃×#451	C₂²	1	2	yes	—
76	C₂₃×#451	C₂²	1	2	yes	—
77	C₂₃×#450	C₂²	1	2	yes	—
78	C₂₃×#450	C₂²	1	1	yes	characteristic
79	C₂₃×#448	C₂²	1	2	yes	—
80	C₂₃×#447	C₂²	1	1	yes	characteristic
81	C₂₃×#446	C₂²	1	2	yes	complemented
82	C₂₃×#446	C₂²	1	4	yes	complemented
83	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#441	C₂²	1	4	yes	complemented
85	C₂₃×#440	C₂²	1	4	yes	—
86	C₂₃×#440	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
88	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
90	C₄×D₈×C₂₃	C₂²	1	2	yes	—
91	C₂₃×#432	C₂²	1	2	yes	—
92	C₂₃×#432	C₂²	1	1	yes	characteristic
93	C₂₃×#431	C₂²	1	1	yes	characteristic
94	C₂₃×#431	C₂²	1	2	yes	—
95	C₂²×Q₈×C₂₃	—	2	1	no	—
96	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
97	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
98	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₂₃	—	2	1	no	—
100	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×D₈×C₂₃	C₂³	1	2	yes	—
107	C₂₃×C₄⋊Q₈	—	2	1	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×#126	—	2	2	no	—
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	2	no	—
120	C₂₃×#126	—	2	4	no	—
121	C₂₃×#126	—	2	4	no	—
122	C₂₃×#126	—	2	4	no	—
123	C₂₃×#126	—	2	4	no	—
124	C₂₃×#126	—	2	1	no	—
125	C₂₃×#126	—	2	2	no	—
126	C₂₃×#125	—	2	2	no	—
127	C₂₃×#125	—	2	2	no	—
128	C₂₃×#125	—	2	2	no	—
129	C₂₃×#125	—	2	1	no	—
130	C₂₃×#125	—	2	2	no	—
131	C₂₃×#125	—	2	1	no	—
132	C₂₃×#125	—	2	2	no	—
133	C₂₃×#125	C₂³	1	1	yes	characteristic
134	C₂₃×#125	C₂³	1	2	yes	—
135	C₂₃×#124	—	2	2	no	—
136	C₂₃×#124	—	2	2	no	—
137	C₂₃×#124	C₂³	1	4	yes	—
138	C₂₃×#124	C₂³	1	4	yes	—
139	C₂₃×#124	C₂³	1	1	yes	characteristic
140	C₂₃×#124	C₂³	1	2	yes	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	1	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	4	no	—
148	C₂₃×C₂²⋊Q₈	—	2	1	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	1	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
154	C₂₃×#121	C₂³	1	1	yes	characteristic
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	—	2	2	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	—	2	2	no	—
160	C₄×Q₈×C₂₃	—	2	1	no	—
161	C₄×Q₈×C₂₃	—	2	2	no	—
162	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
164	C₄×Q₈×C₂₃	D₄	1	2	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
170	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
172	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	1	no	—
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₄×D₄×C₂₃	C₂³	1	2	yes	—
182	C₄×D₄×C₂₃	C₂³	1	2	yes	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	1	no	—
185	C₂₃×#117	—	2	1	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	2	no	—
188	C₂₃×#117	—	2	2	no	—
189	C₂₃×#117	—	2	4	no	—
190	C₂₃×#117	—	2	1	no	—
191	C₂₃×#117	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
194	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
197	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₄²×C₂₃	—	2	2	no	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
204	C₂₃×#107	C₂³	1	2	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#106	C₂³	1	2	yes	—
207	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
208	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
211	C₂₃×#103	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	2	yes	—
218	C₂₃×#102	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
224	C₂₃×#97	C₂³	1	2	yes	—
225	C₂₃×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₂₃	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	4	yes	—
228	C₂⁴×C₂₃	—	2	1	no	—
229	C₂×Q₈×C₂₃	—	2	2	no	—
230	C₂×Q₈×C₂₃	—	2	1	no	—
231	C₂×Q₈×C₂₃	—	2	2	no	—
232	C₂×Q₈×C₂₃	—	4	2	no	—
233	C₂×Q₈×C₂₃	—	4	4	no	—
234	C₂×Q₈×C₂₃	—	4	4	no	—
235	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
236	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
237	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
238	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
239	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×D₄×C₂₃	—	2	1	no	—
242	C₂×D₄×C₂₃	—	2	1	no	—
243	C₂×D₄×C₂₃	—	4	2	no	—
244	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
245	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	—	2	1	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	4	4	no	—
253	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
257	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	Q₁₆×C₂₃	—	4	4	no	—
259	Q₁₆×C₂₃	—	4	4	no	—
260	Q₁₆×C₂₃	—	4	4	no	—
261	SD₁₆×C₂₃	—	4	4	no	—
262	SD₁₆×C₂₃	—	4	4	no	—
263	SD₁₆×C₂₃	—	4	2	no	—
264	D₈×C₂₃	—	4	2	no	—
265	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
266	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
267	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	1	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
294	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
295	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
297	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₂²⋊C₄×C₂₃	—	2	1	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	—	2	4	no	—
319	C₄²×C₂₃	—	2	4	no	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	—	2	2	no	—
322	C₄²×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	—	2	1	no	—
325	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₂₃	C₂×D₄	1	2	yes	—
327	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
330	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
331	C₄²×C₂₃	C₂⁴	1	2	yes	—
332	C₄²×C₂₃	C₂⁴	1	2	yes	—
333	#61905	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂³×C₂₃	—	2	1	no	—
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	4	2	no	—
337	C₂³×C₂₃	—	4	2	no	—
338	C₂³×C₂₃	—	4	2	no	—
339	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₂₃	—	2	2	no	—
341	Q₈×C₂₃	—	2	2	no	—
342	Q₈×C₂₃	—	2	4	no	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	4	no	—
345	Q₈×C₂₃	—	2	4	no	—
346	Q₈×C₂₃	—	4	2	no	—
347	Q₈×C₂₃	—	4	4	no	—
348	Q₈×C₂₃	—	4	4	no	—
349	Q₈×C₂₃	—	4	2	no	—
350	D₄×C₂₃	—	2	2	no	—
351	D₄×C₂₃	—	2	2	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	4	2	no	—
354	D₄×C₂₃	—	4	2	no	—
355	C₂×C₄×C₂₃	—	2	4	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	4	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	4	2	no	—
367	C₂×C₄×C₂₃	—	4	4	no	—
368	C₂×C₄×C₂₃	—	4	4	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	4	no	—
371	C₂×C₄×C₂₃	—	4	4	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
374	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
379	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
383	C₈×C₂₃	—	2	2	no	—
384	C₈×C₂₃	—	2	4	no	—
385	C₈×C₂₃	—	2	2	no	—
386	#3523	C₂×C₂₃	1	1	yes	characteristic, complemented
387	C₂×#556	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#3402	C₂×C₂₃	1	4	yes	complemented
389	#3398	C₂×C₂₃	1	2	yes	complemented
390	#3393	C₂×C₂₃	1	2	yes	complemented
391	#3377	C₂×C₂₃	1	4	yes	complemented
392	#3367	C₂×C₂₃	1	2	yes	complemented
393	#3364	C₂×C₂₃	1	2	yes	complemented
394	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
395	#3215	C₂×C₂₃	1	2	yes	complemented
396	#3211	C₂×C₂₃	1	2	yes	—
397	#3209	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#3117	C₂×C₂₃	1	2	yes	complemented
399	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3105	C₂×C₂₃	1	1	yes	characteristic
401	#3104	C₂×C₂₃	1	2	yes	complemented
402	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂²×C₂₃	—	2	1	no	—
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	4	2	no	—
406	C₂²×C₂₃	—	4	1	no	—
407	C₂²×C₂₃	—	4	1	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	8	4	no	—
412	C₂²×C₂₃	#578	1	2	yes	—
413	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
414	C₄×C₂₃	—	2	1	no	—
415	C₄×C₂₃	—	2	1	no	—
416	C₄×C₂₃	—	2	2	no	—
417	C₄×C₂₃	—	2	2	no	—
418	C₄×C₂₃	—	2	2	no	—
419	C₄×C₂₃	—	2	2	no	—
420	C₄×C₂₃	—	2	1	no	—
421	C₄×C₂₃	—	2	1	no	—
422	C₄×C₂₃	—	4	4	no	—
423	C₄×C₂₃	—	4	1	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	1	no	—
428	C₄×C₂₃	—	4	1	no	—
429	C₄×C₂₃	#575	1	2	yes	—
430	C₄×C₂₃	#585	1	2	yes	—
431	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
432	#557	C₂²×C₂₃	1	1	yes	characteristic, complemented
433	#557	C₂²×C₂₃	1	2	yes	complemented
434	#556	—	2	1	no	—
435	#556	—	2	1	no	—
436	#556	—	2	2	no	—
437	#556	C₂²×C₂₃	1	2	yes	—
438	#556	C₂²×C₂₃	1	2	yes	—
439	#556	C₂²×C₂₃	1	4	yes	—
440	#556	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	#556	C₂²×C₂₃	1	2	yes	complemented
442	#552	—	2	1	no	—
443	#552	—	2	2	no	—
444	D₄×Q₈	—	2	1	no	—
445	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	#541	—	2	1	no	—
447	#541	—	2	2	no	—
448	#533	C₂²×C₂₃	1	2	yes	—
449	#533	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
451	#529	C₂²×C₂₃	1	1	yes	characteristic
452	#529	C₂²×C₂₃	1	2	yes	—
453	C₂×#126	—	2	2	no	—
454	C₂×#124	C₂²×C₂₃	1	2	yes	—
455	C₂×C₂²⋊Q₈	—	2	1	no	—
456	#519	—	2	1	no	—
457	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
458	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×#117	—	2	1	no	—
461	#497	C₂²×C₂₃	1	4	yes	—
462	#497	C₂²×C₂₃	1	2	yes	complemented
463	#495	C₂²×C₂₃	1	4	yes	—
464	#494	C₂²×C₂₃	1	2	yes	complemented
465	#491	C₂²×C₂₃	1	2	yes	complemented
466	#489	C₂²×C₂₃	1	4	yes	—
467	#488	C₂²×C₂₃	1	4	yes	—
468	#487	C₂²×C₂₃	1	2	yes	complemented
469	#484	C₂²×C₂₃	1	1	yes	characteristic
470	#484	C₂²×C₂₃	1	2	yes	—
471	#481	C₂²×C₂₃	1	1	yes	characteristic
472	#479	C₂²×C₂₃	1	4	yes	complemented
473	#478	C₂²×C₂₃	1	2	yes	—
474	#477	C₂²×C₂₃	1	4	yes	complemented
475	#474	C₂²×C₂₃	1	2	yes	—
476	#464	C₂²×C₂₃	1	4	yes	—
477	#464	C₂²×C₂₃	1	4	yes	—
478	#464	C₂²×C₂₃	1	4	yes	—
479	#464	C₂²×C₂₃	1	4	yes	complemented
480	#463	C₂²×C₂₃	1	2	yes	—
481	#463	C₂²×C₂₃	1	4	yes	—
482	#462	C₂²×C₂₃	1	4	yes	complemented
483	#462	C₂²×C₂₃	1	2	yes	complemented
484	#462	C₂²×C₂₃	1	4	yes	complemented
485	#461	C₂²×C₂₃	1	2	yes	—
486	#461	C₂²×C₂₃	1	2	yes	complemented
487	#451	C₂²×C₂₃	1	2	yes	—
488	#451	C₂²×C₂₃	1	2	yes	—
489	#451	C₂²×C₂₃	1	2	yes	—
490	#450	C₂²×C₂₃	1	1	yes	characteristic
491	#450	C₂²×C₂₃	1	2	yes	—
492	#448	C₂²×C₂₃	1	2	yes	—
493	#447	C₂²×C₂₃	1	1	yes	characteristic
494	#446	C₂²×C₂₃	1	2	yes	complemented
495	#446	C₂²×C₂₃	1	4	yes	complemented
496	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
497	#441	C₂²×C₂₃	1	4	yes	complemented
498	#440	C₂²×C₂₃	1	4	yes	—
499	#440	C₂²×C₂₃	1	4	yes	complemented
500	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
501	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
502	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
503	C₄×D₈	C₂²×C₂₃	1	2	yes	—
504	#432	C₂²×C₂₃	1	1	yes	characteristic
505	#432	C₂²×C₂₃	1	2	yes	—
506	#431	C₂²×C₂₃	1	2	yes	—
507	#431	C₂²×C₂₃	1	1	yes	characteristic
508	C₂×C₂₃	—	2	2	no	—
509	C₂×C₂₃	—	8	1	no	—
510	C₂×C₂₃	—	8	2	no	—
511	C₂×C₂₃	#3487	1	1	yes	characteristic
512	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
513	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
514	C₂²×Q₈	—	2	1	no	—
515	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
516	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
517	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂³×C₄	—	2	1	no	—
519	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
520	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
521	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
522	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
523	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
524	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
525	C₂×D₈	C₂³×C₂₃	1	2	yes	—
526	C₄⋊Q₈	—	2	1	no	—
527	C₄⋊Q₈	—	2	2	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	1	no	—
530	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
531	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
532	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
533	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
534	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
535	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#126	—	2	4	no	—
539	#126	—	2	4	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#126	—	2	2	no	—
543	#126	—	2	1	no	—
544	#126	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	1	no	—
549	#125	—	2	2	no	—
550	#125	—	2	1	no	—
551	#125	—	2	2	no	—
552	#125	C₂³×C₂₃	1	1	yes	characteristic
553	#125	C₂³×C₂₃	1	2	yes	—
554	#124	—	2	2	no	—
555	#124	—	2	2	no	—
556	#124	C₂³×C₂₃	1	4	yes	—
557	#124	C₂³×C₂₃	1	4	yes	—
558	#124	C₂³×C₂₃	1	1	yes	characteristic
559	#124	C₂³×C₂₃	1	2	yes	—
560	#123	—	2	2	no	—
561	#123	—	2	1	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	4	no	—
565	C₂²⋊Q₈	—	2	1	no	—
566	C₂²⋊Q₈	—	2	2	no	—
567	C₂²⋊Q₈	—	2	1	no	—
568	C₂²⋊Q₈	—	2	2	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	2	no	—
571	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
572	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
573	#121	C₂³×C₂₃	1	1	yes	characteristic
574	C₄×Q₈	—	2	1	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	2	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
582	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
583	C₄×Q₈	D₄×C₂₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
585	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
586	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
587	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
588	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	C₂³×C₂₃	1	2	yes	—
599	C₄×D₄	C₂³×C₂₃	1	2	yes	—
600	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
601	C₄×D₄	C₂³×C₂₃	1	2	yes	—
602	#117	—	2	2	no	—
603	#117	—	2	1	no	—
604	#117	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	—	2	4	no	—
607	#117	—	2	1	no	—
608	#117	—	2	2	no	—
609	#117	—	2	1	no	—
610	#117	—	2	2	no	—
611	C₂×C₄⋊C₄	—	2	1	no	—
612	C₂×C₄⋊C₄	—	2	2	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	—	2	2	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	2	no	—
620	C₂×C₄²	—	2	2	no	—
621	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
623	#107	C₂³×C₂₃	1	2	yes	—
624	#107	C₂³×C₂₃	1	4	yes	—
625	#106	C₂³×C₂₃	1	2	yes	—
626	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
628	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
629	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
630	#103	C₂³×C₂₃	1	2	yes	—
631	#103	C₂³×C₂₃	1	4	yes	—
632	#103	C₂³×C₂₃	1	4	yes	—
633	#103	C₂³×C₂₃	1	4	yes	—
634	#103	C₂³×C₂₃	1	4	yes	—
635	#103	C₂³×C₂₃	1	4	yes	—
636	#102	C₂³×C₂₃	1	2	yes	—
637	#102	C₂³×C₂₃	1	2	yes	—
638	#102	C₂³×C₂₃	1	2	yes	—
639	#102	C₂³×C₂₃	1	4	yes	—
640	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
641	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
642	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
643	#97	C₂³×C₂₃	1	2	yes	—
644	#97	C₂³×C₂₃	1	4	yes	—
645	C₄×C₈	C₂³×C₂₃	1	2	yes	—
646	C₄×C₈	C₂³×C₂₃	1	4	yes	—
647	C₂₃	#61905	1	1	yes	characteristic, direct product factor, Sylow
648	C₂⁴	—	2	1	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	1	no	—
651	C₂×Q₈	—	2	2	no	—
652	C₂×Q₈	—	4	2	no	—
653	C₂×Q₈	—	4	4	no	—
654	C₂×Q₈	—	4	4	no	—
655	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
659	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
660	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	1	no	—
663	C₂×D₄	—	4	2	no	—
664	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
665	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	4	4	no	—
673	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
674	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
676	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
678	Q₁₆	—	4	4	no	—
679	Q₁₆	—	4	4	no	—
680	Q₁₆	—	4	4	no	—
681	SD₁₆	—	4	4	no	—
682	SD₁₆	—	4	4	no	—
683	SD₁₆	—	4	2	no	—
684	D₈	—	4	2	no	—
685	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
686	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
687	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	1	no	—
697	C₄⋊C₄	—	2	1	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
713	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
715	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
716	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
717	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
718	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
720	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
722	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	2	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	1	no	—
738	C₄²	—	2	4	no	—
739	C₄²	—	2	4	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	1	no	—
745	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₂₃	1	2	yes	—
747	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₂₃	1	2	yes	—
749	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₂₃	1	2	yes	—
751	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₄²	C₂⁴×C₂₃	1	2	yes	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	—	4	2	no	—
758	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	4	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	2	4	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	4	no	—
767	Q₈	—	4	4	no	—
768	Q₈	—	4	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	2	no	—
772	D₄	—	4	2	no	—
773	D₄	—	4	2	no	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	1	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	2	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
793	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
795	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
796	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
798	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
802	C₈	—	2	2	no	—
803	C₈	—	2	4	no	—
804	C₈	—	2	2	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	2	1	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	4	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	2	no	—
813	C₂²	—	8	4	no	—
814	C₂²	C₂₃×#578	1	2	yes	—
815	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	2	no	—
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	4	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	1	no	—
831	C₄	C₂₃×#575	1	2	yes	—
832	C₄	C₂₃×#585	1	2	yes	—
833	C₂	—	2	2	no	—
834	C₂	—	8	2	no	—
835	C₂	—	8	1	no	—
836	C₂	C₂₃×#3487	1	1	yes	characteristic
837	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
838	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#447	C₂²
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×#3523	C₂	semidirect
2. C₂×C₂₃×#556	C₂	semidirect
3. C₂₃×#3402	C₂	semidirect
4. C₂₃×#3398	C₂	semidirect
5. C₂₃×#3393	C₂	semidirect
6. C₂₃×#3377	C₂	semidirect
7. C₂₃×#3367	C₂	semidirect
8. C₂₃×#3364	C₂	semidirect
9. C₂₃×#3218	C₂	semidirect
10. C₂₃×#3215	C₂	semidirect
12. C₂₃×#3209	C₂	semidirect
13. C₂₃×#3117	C₂	semidirect
14. C₂₃×#3110	C₂	semidirect
16. C₂₃×#3104	C₂	semidirect
17. C₂₃×#2984	C₂	semidirect
18. C₂₃×#557	C₂²	semidirect
19. C₂₃×#557	C₂²	semidirect
20. C₂₃×#557	C₂²	semidirect
27. C₂₃×#556	C₂²	semidirect
28. C₂₃×#556	C₂²	semidirect
32. D₄×Q₈×C₂₃	C₂²	semidirect
49. C₂₃×#497	C₂²	semidirect
51. C₂₃×#494	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
55. C₂₃×#487	C₂²	semidirect
59. C₂₃×#479	C₂²	semidirect
61. C₂₃×#477	C₂²	semidirect
66. C₂₃×#464	C₂²	semidirect
69. C₂₃×#462	C₂²	semidirect
70. C₂₃×#462	C₂²	semidirect
71. C₂₃×#462	C₂²	semidirect
73. C₂₃×#461	C₂²	semidirect
81. C₂₃×#446	C₂²	semidirect
82. C₂₃×#446	C₂²	semidirect
83. C₈×Q₈×C₂₃	C₂²	semidirect
84. C₂₃×#441	C₂²	semidirect
86. C₂₃×#440	C₂²	semidirect
87. C₄×Q₁₆×C₂₃	C₂²	semidirect
88. C₄×Q₁₆×C₂₃	C₂²	semidirect
333. #61905	C₂₃	direct (N × H)
386. #3523	C₂×C₂₃	semidirect
387. C₂×#556	C₂×C₂₃	semidirect
388. #3402	C₂×C₂₃	semidirect
389. #3398	C₂×C₂₃	semidirect
390. #3393	C₂×C₂₃	semidirect
391. #3377	C₂×C₂₃	semidirect
392. #3367	C₂×C₂₃	semidirect
393. #3364	C₂×C₂₃	semidirect
394. #3218	C₂×C₂₃	semidirect
395. #3215	C₂×C₂₃	semidirect
397. #3209	C₂×C₂₃	semidirect
398. #3117	C₂×C₂₃	semidirect
399. #3110	C₂×C₂₃	semidirect
401. #3104	C₂×C₂₃	semidirect
402. #2984	C₂×C₂₃	semidirect
431. #557	C₂²×C₂₃	semidirect
432. #557	C₂²×C₂₃	semidirect
433. #557	C₂²×C₂₃	semidirect
440. #556	C₂²×C₂₃	semidirect
441. #556	C₂²×C₂₃	semidirect
445. D₄×Q₈	C₂²×C₂₃	semidirect
462. #497	C₂²×C₂₃	semidirect
464. #494	C₂²×C₂₃	semidirect
465. #491	C₂²×C₂₃	semidirect
468. #487	C₂²×C₂₃	semidirect
472. #479	C₂²×C₂₃	semidirect
474. #477	C₂²×C₂₃	semidirect
479. #464	C₂²×C₂₃	semidirect
482. #462	C₂²×C₂₃	semidirect
483. #462	C₂²×C₂₃	semidirect
484. #462	C₂²×C₂₃	semidirect
486. #461	C₂²×C₂₃	semidirect
494. #446	C₂²×C₂₃	semidirect
495. #446	C₂²×C₂₃	semidirect
496. C₈×Q₈	C₂²×C₂₃	semidirect
497. #441	C₂²×C₂₃	semidirect
499. #440	C₂²×C₂₃	semidirect
500. C₄×Q₁₆	C₂²×C₂₃	semidirect
501. C₄×Q₁₆	C₂²×C₂₃	semidirect
647. C₂₃	#61905	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×#3523	2
C₂×C₂₃×#556	2
C₂₃×#3402	2
C₂₃×#3398	2
C₂₃×#3393	2
C₂₃×#3377	2
C₂₃×#3367	2
C₂₃×#3364	2
C₂₃×#3218	2
C₂₃×#3215	2
C₂₃×#3211	2
C₂₃×#3209	2
C₂₃×#3117	2
C₂₃×#3110	2
C₂₃×#3105	2
C₂₃×#3104	2
C₂₃×#2984	2
#61905	23

Subgroups — C23×#61905 #19209531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61905 #19209531