Subgroups — C₂₃×#61842 #19209468

Order 5888.

1668 conjugacy classes of subgroups.

The subgroup lattice has 812 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
2	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3390	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3386	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3383	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3377	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3374	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3364	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#3236	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3232	C₂	1	2	yes	maximal
12	C₂₃×#3230	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3117	C₂	1	2	yes	maximal
14	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3108	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	—	2	1	no	—
19	C₂₃×#557	—	2	1	no	—
20	C₂₃×#557	—	2	2	no	—
21	C₂₃×#557	C₂²	1	1	yes	characteristic
22	C₂₃×#557	C₂²	1	2	yes	—
23	C₂₃×#557	C₂²	1	2	yes	—
24	C₂₃×#557	C₂²	1	4	yes	—
25	C₂₃×#557	C₂²	1	1	yes	characteristic
26	C₂₃×#557	C₂²	1	2	yes	—
27	C₂₃×#556	C₂²	1	1	yes	characteristic
28	C₂₃×#556	C₂²	1	2	yes	—
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
33	C₂₃×#541	—	2	2	no	—
34	C₂₃×#541	—	2	1	no	—
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂₃×#533	C₂²	1	2	yes	—
37	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
38	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₂₃×#529	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#125	—	2	2	no	—
42	C₂×C₂₃×#125	C₂²	1	2	yes	—
43	C₂₃×#519	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂₃×#501	C₂²	1	4	yes	—
49	C₂₃×#501	C₂²	1	2	yes	—
50	C₂₃×#500	C₂²	1	2	yes	—
51	C₂₃×#499	C₂²	1	4	yes	—
52	C₂₃×#491	C₂²	1	4	yes	—
53	C₂₃×#489	C₂²	1	2	yes	—
54	C₂₃×#488	C₂²	1	4	yes	—
55	C₂₃×#487	C₂²	1	2	yes	—
56	C₂₃×#484	C₂²	1	2	yes	—
57	C₂₃×#484	C₂²	1	2	yes	—
58	C₂₃×#484	C₂²	1	2	yes	—
59	C₂₃×#483	C₂²	1	2	yes	—
60	C₂₃×#483	C₂²	1	1	yes	characteristic
61	C₂₃×#481	C₂²	1	2	yes	—
62	C₂₃×#480	C₂²	1	1	yes	characteristic
63	C₂₃×#479	C₂²	1	4	yes	—
64	C₂₃×#479	C₂²	1	4	yes	—
65	C₂₃×#479	C₂²	1	4	yes	—
66	C₂₃×#479	C₂²	1	2	yes	—
67	C₂₃×#479	C₂²	1	4	yes	—
68	C₂₃×#478	C₂²	1	4	yes	—
69	C₂₃×#477	C₂²	1	4	yes	—
70	C₂₃×#477	C₂²	1	4	yes	—
71	C₂₃×#475	C₂²	1	2	yes	—
72	C₂₃×#475	C₂²	1	2	yes	—
73	C₂₃×#474	C₂²	1	2	yes	—
74	C₂₃×#464	C₂²	1	2	yes	—
75	C₂₃×#464	C₂²	1	4	yes	—
76	C₂₃×#462	C₂²	1	4	yes	—
77	C₂₃×#462	C₂²	1	2	yes	—
78	C₂₃×#451	C₂²	1	1	yes	characteristic
79	C₂₃×#451	C₂²	1	2	yes	—
80	C₂₃×#448	C₂²	1	1	yes	characteristic
81	C₂₃×#446	C₂²	1	2	yes	—
82	C₂₃×#446	C₂²	1	4	yes	—
83	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
84	C₂₃×#441	C₂²	1	4	yes	—
85	C₂₃×#441	C₂²	1	4	yes	—
86	C₂₃×#440	C₂²	1	4	yes	—
87	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
88	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
89	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
90	C₄×SD₁₆×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	—	2	1	no	—
97	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
98	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
100	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂₃×C₄⋊Q₈	—	2	1	no	—
103	C₂₃×C₄⋊Q₈	—	2	2	no	—
104	C₂₃×C₄⋊Q₈	—	2	2	no	—
105	C₂₃×C₄⋊Q₈	—	2	2	no	—
106	C₂₃×C₄⋊Q₈	—	2	4	no	—
107	C₂₃×C₄⋊Q₈	—	2	1	no	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×#126	—	2	2	no	—
116	C₂₃×#126	—	2	2	no	—
117	C₂₃×#126	—	2	2	no	—
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	1	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	2	no	—
123	C₂₃×#125	—	2	1	no	—
124	C₂₃×#125	—	2	2	no	—
125	C₂₃×#125	—	2	4	no	—
126	C₂₃×#125	—	2	4	no	—
127	C₂₃×#125	—	2	4	no	—
128	C₂₃×#125	—	2	4	no	—
129	C₂₃×#125	—	2	2	no	—
130	C₂₃×#125	—	2	2	no	—
131	C₂₃×#125	—	2	2	no	—
132	C₂₃×#125	—	2	1	no	—
133	C₂₃×#125	C₂³	1	4	yes	—
134	C₂₃×#125	C₂³	1	4	yes	—
135	C₂₃×#125	C₂³	1	2	yes	—
136	C₂₃×#125	C₂³	1	1	yes	characteristic
137	C₂₃×#124	C₂³	1	2	yes	—
138	C₂₃×#124	C₂³	1	1	yes	characteristic
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	1	no	—
141	C₂₃×C₂²⋊Q₈	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	—	2	2	no	—
143	C₂₃×C₂²⋊Q₈	—	2	1	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	1	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
148	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
149	C₂₃×#121	C₂³	1	1	yes	characteristic
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	2	no	—
154	C₄×Q₈×C₂₃	—	2	2	no	—
155	C₄×Q₈×C₂₃	—	2	4	no	—
156	C₄×Q₈×C₂₃	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	2	no	—
158	C₄×Q₈×C₂₃	—	2	1	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	—	2	2	no	—
161	C₄×Q₈×C₂₃	—	2	1	no	—
162	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₂₃	D₄	1	2	yes	—
164	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
165	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
170	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
172	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	—	2	1	no	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	1	no	—
183	C₂₃×#117	—	2	1	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
193	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	—	2	2	no	—
197	C₂×C₄²×C₂₃	—	2	1	no	—
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂₃×#107	C₂³	1	4	yes	—
201	C₂₃×#107	C₂³	1	4	yes	—
202	C₂₃×#107	C₂³	1	2	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#106	C₂³	1	2	yes	—
205	C₂₃×#106	C₂³	1	4	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₂₃×C₄⋊C₈	C₂³	1	2	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	2	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	4	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	1	yes	characteristic
223	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₂₃×#97	C₂³	1	4	yes	—
225	C₂₃×#97	C₂³	1	2	yes	—
226	C₄×C₈×C₂₃	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	4	yes	—
228	C₂×Q₈×C₂₃	—	2	4	no	—
229	C₂×Q₈×C₂₃	—	2	1	no	—
230	C₂×Q₈×C₂₃	—	2	2	no	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	2	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	4	2	no	—
235	C₂×Q₈×C₂₃	—	4	4	no	—
236	C₂×Q₈×C₂₃	—	4	4	no	—
237	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
238	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
239	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
240	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	—	2	1	no	—
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	1	no	—
250	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	Q₁₆×C₂₃	—	2	4	no	—
256	Q₁₆×C₂₃	—	2	8	no	—
257	SD₁₆×C₂₃	—	2	4	no	—
258	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
259	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	—	2	4	no	—
262	C₄⋊C₄×C₂₃	—	2	4	no	—
263	C₄⋊C₄×C₂₃	—	2	2	no	—
264	C₄⋊C₄×C₂₃	—	2	2	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	2	no	—
268	C₄⋊C₄×C₂₃	—	2	2	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
278	C₄⋊C₄×C₂₃	—	2	1	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	1	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂⁴	1	4	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	C₂²⋊C₄×C₂₃	—	2	1	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	1	no	—
305	C₂²⋊C₄×C₂₃	—	2	2	no	—
306	C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	1	no	—
311	C₄²×C₂₃	—	2	4	no	—
312	C₄²×C₂₃	—	2	4	no	—
313	C₄²×C₂₃	—	2	2	no	—
314	C₄²×C₂₃	—	2	2	no	—
315	C₄²×C₂₃	—	2	2	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	—	2	2	no	—
318	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	2	1	no	—
320	C₄²×C₂₃	C₂×D₄	1	2	yes	—
321	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₂₃	C₂×D₄	1	2	yes	—
323	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₂₃	C₂⁴	1	2	yes	—
325	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
326	C₄²×C₂₃	C₂⁴	1	2	yes	—
327	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
328	#61842	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	1	no	—
330	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
331	Q₈×C₂₃	—	2	4	no	—
332	Q₈×C₂₃	—	2	2	no	—
333	Q₈×C₂₃	—	2	2	no	—
334	Q₈×C₂₃	—	2	2	no	—
335	Q₈×C₂₃	—	2	2	no	—
336	Q₈×C₂₃	—	2	4	no	—
337	Q₈×C₂₃	—	4	2	no	—
338	Q₈×C₂₃	—	4	4	no	—
339	Q₈×C₂₃	—	4	4	no	—
340	Q₈×C₂₃	—	4	2	no	—
341	Q₈×C₂₃	—	4	4	no	—
342	Q₈×C₂₃	2₋¹⁺⁴	1	4	yes	—
343	D₄×C₂₃	—	2	2	no	—
344	D₄×C₂₃	—	4	2	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	2	4	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	1	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	4	no	—
358	C₂×C₄×C₂₃	—	4	2	no	—
359	C₂×C₄×C₂₃	—	4	4	no	—
360	C₂×C₄×C₂₃	—	4	4	no	—
361	C₂×C₄×C₂₃	—	4	2	no	—
362	C₂×C₄×C₂₃	—	4	2	no	—
363	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
364	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
365	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
368	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
371	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
373	C₈×C₂₃	—	2	2	no	—
374	C₈×C₂₃	—	2	4	no	—
375	C₈×C₂₃	—	2	2	no	—
376	#3523	C₂×C₂₃	1	1	yes	characteristic
377	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
378	#3390	C₂×C₂₃	1	4	yes	complemented
379	#3386	C₂×C₂₃	1	2	yes	complemented
380	#3383	C₂×C₂₃	1	2	yes	complemented
381	#3377	C₂×C₂₃	1	4	yes	complemented
382	#3374	C₂×C₂₃	1	2	yes	complemented
383	#3364	C₂×C₂₃	1	2	yes	complemented
384	#3239	C₂×C₂₃	1	1	yes	characteristic
385	#3236	C₂×C₂₃	1	2	yes	complemented
386	#3232	C₂×C₂₃	1	2	yes	—
387	#3230	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#3117	C₂×C₂₃	1	2	yes	—
389	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#3108	C₂×C₂₃	1	1	yes	characteristic
391	#3104	C₂×C₂₃	1	2	yes	complemented
392	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂²×C₂₃	—	2	1	no	—
394	C₂²×C₂₃	—	2	1	no	—
395	C₂²×C₂₃	—	4	1	no	—
396	C₂²×C₂₃	—	4	1	no	—
397	C₂²×C₂₃	—	4	1	no	—
398	C₂²×C₂₃	#578	1	2	yes	—
399	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₂₃	—	2	4	no	—
401	C₄×C₂₃	—	2	1	no	—
402	C₄×C₂₃	—	2	1	no	—
403	C₄×C₂₃	—	2	2	no	—
404	C₄×C₂₃	—	2	2	no	—
405	C₄×C₂₃	—	2	2	no	—
406	C₄×C₂₃	—	2	2	no	—
407	C₄×C₂₃	—	2	1	no	—
408	C₄×C₂₃	—	2	1	no	—
409	C₄×C₂₃	—	4	1	no	—
410	C₄×C₂₃	—	4	2	no	—
411	C₄×C₂₃	—	4	2	no	—
412	C₄×C₂₃	—	4	1	no	—
413	C₄×C₂₃	—	4	4	no	—
414	C₄×C₂₃	—	4	2	no	—
415	C₄×C₂₃	—	4	1	no	—
416	C₄×C₂₃	#575	1	2	yes	—
417	C₄×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
418	#557	—	2	1	no	—
419	#557	—	2	1	no	—
420	#557	—	2	2	no	—
421	#557	C₂²×C₂₃	1	1	yes	characteristic
422	#557	C₂²×C₂₃	1	2	yes	—
423	#557	C₂²×C₂₃	1	2	yes	—
424	#557	C₂²×C₂₃	1	4	yes	—
425	#557	C₂²×C₂₃	1	1	yes	characteristic
426	#557	C₂²×C₂₃	1	2	yes	—
427	#556	C₂²×C₂₃	1	1	yes	characteristic
428	#556	C₂²×C₂₃	1	2	yes	—
429	#552	—	2	1	no	—
430	#552	—	2	2	no	—
431	D₄×Q₈	—	2	1	no	—
432	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
433	#541	—	2	2	no	—
434	#541	—	2	1	no	—
435	#533	C₂²×C₂₃	1	2	yes	—
436	#533	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₄⋊Q₈	—	2	1	no	—
438	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
439	#529	C₂²×C₂₃	1	1	yes	characteristic
440	#529	C₂²×C₂₃	1	2	yes	—
441	C₂×#125	—	2	2	no	—
442	C₂×#125	C₂²×C₂₃	1	2	yes	—
443	#519	—	2	1	no	—
444	C₂×C₄×Q₈	—	2	1	no	—
445	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
446	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
448	#501	C₂²×C₂₃	1	4	yes	—
449	#501	C₂²×C₂₃	1	2	yes	—
450	#500	C₂²×C₂₃	1	2	yes	—
451	#499	C₂²×C₂₃	1	4	yes	—
452	#491	C₂²×C₂₃	1	4	yes	—
453	#489	C₂²×C₂₃	1	2	yes	—
454	#488	C₂²×C₂₃	1	4	yes	—
455	#487	C₂²×C₂₃	1	2	yes	—
456	#484	C₂²×C₂₃	1	2	yes	—
457	#484	C₂²×C₂₃	1	2	yes	—
458	#484	C₂²×C₂₃	1	2	yes	—
459	#483	C₂²×C₂₃	1	1	yes	characteristic
460	#483	C₂²×C₂₃	1	2	yes	—
461	#481	C₂²×C₂₃	1	2	yes	—
462	#480	C₂²×C₂₃	1	1	yes	characteristic
463	#479	C₂²×C₂₃	1	2	yes	—
464	#479	C₂²×C₂₃	1	4	yes	—
465	#479	C₂²×C₂₃	1	4	yes	—
466	#479	C₂²×C₂₃	1	4	yes	—
467	#479	C₂²×C₂₃	1	4	yes	—
468	#478	C₂²×C₂₃	1	4	yes	—
469	#477	C₂²×C₂₃	1	4	yes	—
470	#477	C₂²×C₂₃	1	4	yes	—
471	#475	C₂²×C₂₃	1	2	yes	—
472	#475	C₂²×C₂₃	1	2	yes	—
473	#474	C₂²×C₂₃	1	2	yes	—
474	#464	C₂²×C₂₃	1	2	yes	—
475	#464	C₂²×C₂₃	1	4	yes	—
476	#462	C₂²×C₂₃	1	4	yes	—
477	#462	C₂²×C₂₃	1	2	yes	—
478	#451	C₂²×C₂₃	1	1	yes	characteristic
479	#451	C₂²×C₂₃	1	2	yes	—
480	#448	C₂²×C₂₃	1	1	yes	characteristic
481	#446	C₂²×C₂₃	1	2	yes	—
482	#446	C₂²×C₂₃	1	4	yes	—
483	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
484	#441	C₂²×C₂₃	1	4	yes	—
485	#441	C₂²×C₂₃	1	4	yes	—
486	#440	C₂²×C₂₃	1	4	yes	—
487	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
488	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
489	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
490	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
491	#432	C₂²×C₂₃	1	1	yes	characteristic
492	#432	C₂²×C₂₃	1	2	yes	—
493	#431	C₂²×C₂₃	1	2	yes	—
494	#431	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₂₃	—	2	2	no	—
496	C₂×C₂₃	—	8	1	no	—
497	C₂×C₂₃	#3486	1	1	yes	characteristic
498	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
499	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
500	C₂²×Q₈	—	2	1	no	—
501	C₂²×Q₈	—	2	1	no	—
502	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
503	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
504	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
505	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
506	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	—	2	2	no	—
509	C₄⋊Q₈	—	2	4	no	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	2	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	—	2	1	no	—
514	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
517	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
518	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
519	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
520	#126	—	2	2	no	—
521	#126	—	2	2	no	—
522	#126	—	2	2	no	—
523	#126	—	2	2	no	—
524	#126	—	2	1	no	—
525	#125	—	2	4	no	—
526	#125	—	2	4	no	—
527	#125	—	2	4	no	—
528	#125	—	2	4	no	—
529	#125	—	2	2	no	—
530	#125	—	2	2	no	—
531	#125	—	2	2	no	—
532	#125	—	2	1	no	—
533	#125	—	2	2	no	—
534	#125	—	2	2	no	—
535	#125	—	2	2	no	—
536	#125	—	2	2	no	—
537	#125	—	2	1	no	—
538	#125	C₂³×C₂₃	1	4	yes	—
539	#125	C₂³×C₂₃	1	4	yes	—
540	#125	C₂³×C₂₃	1	2	yes	—
541	#125	C₂³×C₂₃	1	1	yes	characteristic
542	#124	C₂³×C₂₃	1	2	yes	—
543	#124	C₂³×C₂₃	1	1	yes	characteristic
544	#123	—	2	2	no	—
545	#123	—	2	1	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	2	no	—
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
553	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
554	#121	C₂³×C₂₃	1	1	yes	characteristic
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	4	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	2	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
568	C₄×Q₈	D₄×C₂₃	1	2	yes	—
569	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
570	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
571	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
572	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
573	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
574	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
576	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
577	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
578	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
579	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
581	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
582	C₄×D₄	—	2	1	no	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
585	C₄×D₄	C₂³×C₂₃	1	2	yes	—
586	#117	—	2	2	no	—
587	#117	—	2	1	no	—
588	#117	—	2	1	no	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	1	no	—
592	C₂×C₄⋊C₄	—	2	2	no	—
593	C₂×C₄⋊C₄	—	2	1	no	—
594	C₂×C₄⋊C₄	—	2	2	no	—
595	C₂×C₄⋊C₄	—	2	1	no	—
596	C₂×C₄⋊C₄	—	2	2	no	—
597	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
601	C₂×C₄²	—	2	2	no	—
602	C₂×C₄²	—	2	1	no	—
603	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
604	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
605	#107	C₂³×C₂₃	1	4	yes	—
606	#107	C₂³×C₂₃	1	4	yes	—
607	#107	C₂³×C₂₃	1	2	yes	—
608	#107	C₂³×C₂₃	1	4	yes	—
609	#106	C₂³×C₂₃	1	2	yes	—
610	#106	C₂³×C₂₃	1	4	yes	—
611	#106	C₂³×C₂₃	1	4	yes	—
612	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
613	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
614	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
615	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
616	#103	C₂³×C₂₃	1	2	yes	—
617	#103	C₂³×C₂₃	1	4	yes	—
618	#103	C₂³×C₂₃	1	2	yes	—
619	#103	C₂³×C₂₃	1	4	yes	—
620	#103	C₂³×C₂₃	1	4	yes	—
621	#103	C₂³×C₂₃	1	2	yes	—
622	#103	C₂³×C₂₃	1	4	yes	—
623	#103	C₂³×C₂₃	1	4	yes	—
624	#102	C₂³×C₂₃	1	2	yes	—
625	#102	C₂³×C₂₃	1	4	yes	—
626	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
627	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
628	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
629	#97	C₂³×C₂₃	1	4	yes	—
630	#97	C₂³×C₂₃	1	2	yes	—
631	C₄×C₈	C₂³×C₂₃	1	2	yes	—
632	C₄×C₈	C₂³×C₂₃	1	4	yes	—
633	C₂₃	#61842	1	1	yes	characteristic, direct product factor, Sylow
634	C₂×Q₈	—	2	4	no	—
635	C₂×Q₈	—	2	1	no	—
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	2	1	no	—
638	C₂×Q₈	—	2	2	no	—
639	C₂×Q₈	—	2	2	no	—
640	C₂×Q₈	—	4	2	no	—
641	C₂×Q₈	—	4	4	no	—
642	C₂×Q₈	—	4	4	no	—
643	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
644	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
645	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
647	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
648	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	—	2	1	no	—
652	C₂²×C₄	—	2	1	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	1	no	—
656	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
657	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
661	Q₁₆	—	2	4	no	—
662	Q₁₆	—	2	8	no	—
663	SD₁₆	—	2	4	no	—
664	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
665	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
666	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	2	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	1	no	—
689	C₄⋊C₄	—	2	1	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
697	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
698	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
700	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
701	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
702	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
703	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
704	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
705	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
706	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
707	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	2	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	2	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	—	2	1	no	—
714	C₂²⋊C₄	—	2	2	no	—
715	C₂²⋊C₄	—	2	2	no	—
716	C₂²⋊C₄	—	2	1	no	—
717	C₄²	—	2	4	no	—
718	C₄²	—	2	4	no	—
719	C₄²	—	2	2	no	—
720	C₄²	—	2	2	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	2	no	—
724	C₄²	—	2	2	no	—
725	C₄²	—	2	1	no	—
726	C₄²	C₂×D₄×C₂₃	1	2	yes	—
727	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
728	C₄²	C₂×D₄×C₂₃	1	2	yes	—
729	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
730	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
731	C₄²	C₂⁴×C₂₃	1	2	yes	—
732	C₄²	C₂⁴×C₂₃	1	2	yes	—
733	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
734	C₂³	—	2	1	no	—
735	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
736	Q₈	—	2	4	no	—
737	Q₈	—	2	2	no	—
738	Q₈	—	2	2	no	—
739	Q₈	—	2	2	no	—
740	Q₈	—	2	2	no	—
741	Q₈	—	2	4	no	—
742	Q₈	—	4	2	no	—
743	Q₈	—	4	4	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	4	2	no	—
746	Q₈	—	4	4	no	—
747	Q₈	C₂₃×2₋¹⁺⁴	1	4	yes	—
748	D₄	—	2	2	no	—
749	D₄	—	4	2	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	4	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	4	no	—
763	C₂×C₄	—	4	2	no	—
764	C₂×C₄	—	4	4	no	—
765	C₂×C₄	—	4	4	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	4	2	no	—
768	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
769	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
770	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
771	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
772	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
773	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
774	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
776	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
777	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
778	C₈	—	2	2	no	—
779	C₈	—	2	2	no	—
780	C₈	—	2	4	no	—
781	C₂²	—	2	1	no	—
782	C₂²	—	2	1	no	—
783	C₂²	—	4	1	no	—
784	C₂²	—	4	1	no	—
785	C₂²	—	4	1	no	—
786	C₂²	C₂₃×#578	1	2	yes	—
787	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
788	C₄	—	2	4	no	—
789	C₄	—	2	1	no	—
790	C₄	—	2	1	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	2	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	1	no	—
797	C₄	—	4	1	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	—	4	1	no	—
801	C₄	—	4	4	no	—
802	C₄	—	4	2	no	—
803	C₄	—	4	1	no	—
804	C₄	C₂₃×#575	1	2	yes	—
805	C₄	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
806	C₂	—	2	2	no	—
807	C₂	—	8	1	no	—
808	C₂	C₂₃×#3486	1	1	yes	characteristic
809	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
810	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×#121	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
2. C₂×C₂₃×#557	C₂	semidirect
3. C₂₃×#3390	C₂	semidirect
4. C₂₃×#3386	C₂	semidirect
5. C₂₃×#3383	C₂	semidirect
6. C₂₃×#3377	C₂	semidirect
7. C₂₃×#3374	C₂	semidirect
8. C₂₃×#3364	C₂	semidirect
10. C₂₃×#3236	C₂	semidirect
12. C₂₃×#3230	C₂	semidirect
14. C₂₃×#3113	C₂	semidirect
16. C₂₃×#3104	C₂	semidirect
17. C₂₃×#2984	C₂	semidirect
328. #61842	C₂₃	direct (N × H)
377. C₂×#557	C₂×C₂₃	semidirect
378. #3390	C₂×C₂₃	semidirect
379. #3386	C₂×C₂₃	semidirect
380. #3383	C₂×C₂₃	semidirect
381. #3377	C₂×C₂₃	semidirect
382. #3374	C₂×C₂₃	semidirect
383. #3364	C₂×C₂₃	semidirect
385. #3236	C₂×C₂₃	semidirect
387. #3230	C₂×C₂₃	semidirect
389. #3113	C₂×C₂₃	semidirect
391. #3104	C₂×C₂₃	semidirect
392. #2984	C₂×C₂₃	semidirect
633. C₂₃	#61842	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×#557	2
C₂₃×#3390	2
C₂₃×#3386	2
C₂₃×#3383	2
C₂₃×#3377	2
C₂₃×#3374	2
C₂₃×#3364	2
C₂₃×#3239	2
C₂₃×#3236	2
C₂₃×#3232	2
C₂₃×#3230	2
C₂₃×#3117	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3104	2
C₂₃×#2984	2
#61842	23

Subgroups — C23×#61842 #19209468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61842 #19209468