Subgroups — C₂₃×#61899 #19209525

Order 5888.

1780 conjugacy classes of subgroups.

The subgroup lattice has 866 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	C₂×C₂₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3397	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3394	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3376	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3369	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3360	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3213	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3211	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3117	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3103	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
19	C₂₃×#559	C₂²	1	2	yes	complemented
20	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, 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×#554	C₂²	1	1	yes	characteristic, complemented
28	C₂₃×#554	C₂²	1	2	yes	complemented
29	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
30	C₂₃×#548	—	2	1	no	—
31	C₂₃×#547	—	2	1	no	—
32	C₂₃×#547	—	2	2	no	—
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#542	—	2	2	no	—
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂₃×#532	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×#520	—	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	2	yes	complemented
49	C₂₃×#496	C₂²	1	4	yes	—
50	C₂₃×#495	C₂²	1	4	yes	—
51	C₂₃×#492	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×#481	C₂²	1	1	yes	characteristic
58	C₂₃×#481	C₂²	1	2	yes	—
59	C₂₃×#479	C₂²	1	4	yes	complemented
60	C₂₃×#478	C₂²	1	2	yes	—
61	C₂₃×#476	C₂²	1	2	yes	—
62	C₂₃×#475	C₂²	1	4	yes	complemented
63	C₂₃×#464	C₂²	1	4	yes	—
64	C₂₃×#464	C₂²	1	4	yes	complemented
65	C₂₃×#463	C₂²	1	4	yes	—
66	C₂₃×#463	C₂²	1	4	yes	—
67	C₂₃×#463	C₂²	1	4	yes	—
68	C₂₃×#463	C₂²	1	2	yes	—
69	C₂₃×#462	C₂²	1	2	yes	complemented
70	C₂₃×#461	C₂²	1	4	yes	complemented
71	C₂₃×#461	C₂²	1	2	yes	complemented
72	C₂₃×#460	C₂²	1	4	yes	complemented
73	C₂₃×#459	C₂²	1	2	yes	—
74	C₂₃×#451	C₂²	1	2	yes	—
75	C₂₃×#450	C₂²	1	1	yes	characteristic
76	C₂₃×#448	C₂²	1	2	yes	—
77	C₂₃×#448	C₂²	1	2	yes	—
78	C₂₃×#448	C₂²	1	2	yes	—
79	C₂₃×#447	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×#442	C₂²	1	4	yes	—
85	C₂₃×#441	C₂²	1	4	yes	complemented
86	C₂₃×#440	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
88	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
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	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
100	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	—	2	1	no	—
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×SD₁₆×C₂₃	C₂³	1	4	yes	—
107	C₂×D₈×C₂₃	C₂³	1	2	yes	—
108	C₂×D₈×C₂₃	C₂³	1	4	yes	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	—	2	2	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#127	C₂³	1	2	yes	—
119	C₂₃×#126	—	2	4	no	—
120	C₂₃×#126	—	2	4	no	—
121	C₂₃×#126	—	2	4	no	—
122	C₂₃×#126	—	2	4	no	—
123	C₂₃×#126	—	2	1	no	—
124	C₂₃×#126	—	2	2	no	—
125	C₂₃×#125	C₂³	1	1	yes	characteristic
126	C₂₃×#125	C₂³	1	2	yes	—
127	C₂₃×#124	—	2	1	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	2	no	—
130	C₂₃×#124	—	2	2	no	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	C₂³	1	4	yes	—
134	C₂₃×#124	C₂³	1	4	yes	—
135	C₂₃×#124	C₂³	1	1	yes	characteristic
136	C₂₃×#124	C₂³	1	2	yes	—
137	C₂₃×#123	—	2	2	no	—
138	C₂₃×#123	—	2	1	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	2	no	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	—	2	1	no	—
143	C₂₃×C₂²⋊Q₈	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	4	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
151	C₂₃×#121	—	2	1	no	—
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	—	2	1	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	C₂³	1	2	yes	—
156	C₂₃×#121	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	—	2	2	no	—
160	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
162	C₄×Q₈×C₂₃	D₄	1	2	yes	—
163	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
167	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	1	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
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	C₄×D₄×C₂₃	C₂³	1	2	yes	—
184	C₄×D₄×C₂₃	C₂³	1	2	yes	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	4	no	—
188	C₂₃×#117	—	2	1	no	—
189	C₂₃×#117	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₂₃	—	2	2	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×#106	C₂³	1	2	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	4	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#102	C₂³	1	2	yes	—
217	C₂₃×#102	C₂³	1	2	yes	—
218	C₂₃×#102	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	4	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	C₂⁴×C₂₃	—	2	1	no	—
229	#41×C₂₃	—	4	4	no	—
230	#41×C₂₃	—	8	4	no	—
231	#41×C₂₃	—	8	2	no	—
232	C₂×Q₈×C₂₃	—	2	2	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	1	no	—
235	C₂×Q₈×C₂₃	—	4	2	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	4	yes	—
241	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₂₃	—	2	1	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	1	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	4	2	no	—
250	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₂₃	—	2	1	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	1	no	—
257	C₂²×C₄×C₂₃	—	2	2	no	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	4	4	no	—
263	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	Q₁₆×C₂₃	—	4	4	no	—
269	SD₁₆×C₂₃	—	4	4	no	—
270	SD₁₆×C₂₃	—	4	4	no	—
271	SD₁₆×C₂₃	—	4	4	no	—
272	SD₁₆×C₂₃	—	4	2	no	—
273	D₈×C₂₃	—	4	2	no	—
274	D₈×C₂₃	—	4	4	no	—
275	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
277	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	1	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	—	2	4	no	—
285	C₄⋊C₄×C₂₃	—	2	4	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	1	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
295	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
296	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
297	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	2	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	no	—
312	C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	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	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	1	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	4	no	—
324	C₄²×C₂₃	—	2	4	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	1	no	—
327	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂×D₄	1	2	yes	—
331	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	2	yes	—
334	C₄²×C₂₃	C₂⁴	1	2	yes	—
335	#61899	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	1	no	—
339	C₂³×C₂₃	—	4	2	no	—
340	C₂³×C₂₃	—	4	2	no	—
341	C₂³×C₂₃	—	4	2	no	—
342	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	4	no	—
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	2	4	no	—
348	Q₈×C₂₃	—	4	2	no	—
349	Q₈×C₂₃	—	4	4	no	—
350	Q₈×C₂₃	—	8	2	no	—
351	Q₈×C₂₃	—	8	1	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	4	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	4	2	no	—
357	D₄×C₂₃	—	4	4	no	—
358	D₄×C₂₃	—	4	2	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	8	2	no	—
362	D₄×C₂₃	—	8	1	no	—
363	C₂×C₄×C₂₃	—	2	4	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	4	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	4	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	4	4	no	—
378	C₂×C₄×C₂₃	—	4	4	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	8	2	no	—
381	C₂×C₄×C₂₃	—	8	2	no	—
382	C₂×C₄×C₂₃	—	8	2	no	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
385	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
393	C₈×C₂₃	—	2	2	no	—
394	C₈×C₂₃	—	2	4	no	—
395	C₈×C₂₃	—	2	2	no	—
396	#3522	C₂×C₂₃	1	1	yes	characteristic, complemented
397	C₂×#556	C₂×C₂₃	1	1	yes	characteristic, complemented
398	#3401	C₂×C₂₃	1	4	yes	complemented
399	#3397	C₂×C₂₃	1	2	yes	complemented
400	#3394	C₂×C₂₃	1	2	yes	complemented
401	#3376	C₂×C₂₃	1	4	yes	complemented
402	#3369	C₂×C₂₃	1	2	yes	complemented
403	#3360	C₂×C₂₃	1	2	yes	complemented
404	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#3213	C₂×C₂₃	1	2	yes	complemented
406	#3211	C₂×C₂₃	1	2	yes	complemented
407	#3206	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3117	C₂×C₂₃	1	2	yes	complemented
409	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3103	C₂×C₂₃	1	2	yes	complemented
412	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	1	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	2	no	—
417	C₂²×C₂₃	—	4	1	no	—
418	C₂²×C₂₃	—	4	2	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	—	4	2	no	—
422	C₂²×C₂₃	—	4	1	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	8	4	no	—
425	C₂²×C₂₃	#577	1	2	yes	—
426	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
427	C₄×C₂₃	—	2	1	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	2	no	—
430	C₄×C₂₃	—	2	2	no	—
431	C₄×C₂₃	—	2	2	no	—
432	C₄×C₂₃	—	2	1	no	—
433	C₄×C₂₃	—	2	2	no	—
434	C₄×C₂₃	—	2	1	no	—
435	C₄×C₂₃	—	4	4	no	—
436	C₄×C₂₃	—	4	1	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	2	no	—
440	C₄×C₂₃	—	4	1	no	—
441	C₄×C₂₃	#575	1	2	yes	—
442	C₄×C₂₃	#585	1	2	yes	—
443	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#559	C₂²×C₂₃	1	2	yes	complemented
445	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
446	#556	—	2	1	no	—
447	#556	—	2	1	no	—
448	#556	—	2	2	no	—
449	#556	C₂²×C₂₃	1	2	yes	—
450	#556	C₂²×C₂₃	1	2	yes	—
451	#556	C₂²×C₂₃	1	4	yes	—
452	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
453	#554	C₂²×C₂₃	1	2	yes	complemented
454	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	#548	—	2	1	no	—
456	#547	—	2	1	no	—
457	#547	—	2	2	no	—
458	#542	—	2	1	no	—
459	#542	—	2	2	no	—
460	#532	C₂²×C₂₃	1	2	yes	—
461	#532	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
463	#529	C₂²×C₂₃	1	1	yes	characteristic
464	#529	C₂²×C₂₃	1	2	yes	—
465	C₂×#126	—	2	2	no	—
466	C₂×#124	C₂²×C₂₃	1	2	yes	—
467	C₂×C₂²⋊Q₈	—	2	1	no	—
468	#520	—	2	1	no	—
469	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
470	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×#117	—	2	1	no	—
473	#497	C₂²×C₂₃	1	2	yes	complemented
474	#496	C₂²×C₂₃	1	4	yes	—
475	#495	C₂²×C₂₃	1	4	yes	—
476	#492	C₂²×C₂₃	1	2	yes	complemented
477	#491	C₂²×C₂₃	1	2	yes	complemented
478	#489	C₂²×C₂₃	1	4	yes	—
479	#488	C₂²×C₂₃	1	4	yes	—
480	#487	C₂²×C₂₃	1	2	yes	complemented
481	#484	C₂²×C₂₃	1	1	yes	characteristic
482	#481	C₂²×C₂₃	1	1	yes	characteristic
483	#481	C₂²×C₂₃	1	2	yes	—
484	#479	C₂²×C₂₃	1	4	yes	complemented
485	#478	C₂²×C₂₃	1	2	yes	—
486	#476	C₂²×C₂₃	1	2	yes	—
487	#475	C₂²×C₂₃	1	4	yes	complemented
488	#464	C₂²×C₂₃	1	4	yes	—
489	#464	C₂²×C₂₃	1	4	yes	complemented
490	#463	C₂²×C₂₃	1	4	yes	—
491	#463	C₂²×C₂₃	1	2	yes	—
492	#463	C₂²×C₂₃	1	4	yes	—
493	#463	C₂²×C₂₃	1	4	yes	—
494	#462	C₂²×C₂₃	1	2	yes	complemented
495	#461	C₂²×C₂₃	1	2	yes	complemented
496	#461	C₂²×C₂₃	1	4	yes	complemented
497	#460	C₂²×C₂₃	1	4	yes	complemented
498	#459	C₂²×C₂₃	1	2	yes	—
499	#451	C₂²×C₂₃	1	2	yes	—
500	#450	C₂²×C₂₃	1	1	yes	characteristic
501	#448	C₂²×C₂₃	1	2	yes	—
502	#448	C₂²×C₂₃	1	2	yes	—
503	#448	C₂²×C₂₃	1	2	yes	—
504	#447	C₂²×C₂₃	1	1	yes	characteristic
505	#447	C₂²×C₂₃	1	2	yes	—
506	#446	C₂²×C₂₃	1	2	yes	complemented
507	#446	C₂²×C₂₃	1	4	yes	complemented
508	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
509	#442	C₂²×C₂₃	1	4	yes	—
510	#441	C₂²×C₂₃	1	4	yes	complemented
511	#440	C₂²×C₂₃	1	4	yes	complemented
512	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
513	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
514	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
515	C₄×D₈	C₂²×C₂₃	1	2	yes	—
516	#432	C₂²×C₂₃	1	1	yes	characteristic
517	#432	C₂²×C₂₃	1	2	yes	—
518	#431	C₂²×C₂₃	1	2	yes	—
519	#431	C₂²×C₂₃	1	1	yes	characteristic
520	C₂×C₂₃	—	2	2	no	—
521	C₂×C₂₃	—	8	2	no	—
522	C₂×C₂₃	—	8	1	no	—
523	C₂×C₂₃	—	8	2	no	—
524	C₂×C₂₃	#3487	1	1	yes	characteristic
525	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
526	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
527	C₂×#41	—	2	1	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	—	2	1	no	—
530	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
531	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
532	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
533	C₂³×C₄	—	2	1	no	—
534	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
535	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
537	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
538	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
539	C₂×D₈	C₂³×C₂₃	1	2	yes	—
540	C₂×D₈	C₂³×C₂₃	1	4	yes	—
541	C₄⋊Q₈	—	2	1	no	—
542	C₄⋊Q₈	—	2	2	no	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	—	2	1	no	—
545	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
547	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
548	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
549	#127	C₂³×C₂₃	1	1	yes	characteristic
550	#127	C₂³×C₂₃	1	2	yes	—
551	#126	—	2	4	no	—
552	#126	—	2	4	no	—
553	#126	—	2	4	no	—
554	#126	—	2	4	no	—
555	#126	—	2	1	no	—
556	#126	—	2	2	no	—
557	#125	C₂³×C₂₃	1	1	yes	characteristic
558	#125	C₂³×C₂₃	1	2	yes	—
559	#124	—	2	1	no	—
560	#124	—	2	2	no	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	1	no	—
564	#124	—	2	2	no	—
565	#124	C₂³×C₂₃	1	4	yes	—
566	#124	C₂³×C₂₃	1	4	yes	—
567	#124	C₂³×C₂₃	1	1	yes	characteristic
568	#124	C₂³×C₂₃	1	2	yes	—
569	#123	—	2	2	no	—
570	#123	—	2	1	no	—
571	#123	—	2	2	no	—
572	#123	—	2	2	no	—
573	#123	—	2	2	no	—
574	C₂²⋊Q₈	—	2	2	no	—
575	C₂²⋊Q₈	—	2	2	no	—
576	C₂²⋊Q₈	—	2	4	no	—
577	C₂²⋊Q₈	—	2	1	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	2	no	—
581	C₂²⋊Q₈	—	2	2	no	—
582	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
583	#121	—	2	1	no	—
584	#121	—	2	2	no	—
585	#121	—	2	1	no	—
586	#121	—	2	2	no	—
587	#121	C₂³×C₂₃	1	1	yes	characteristic
588	#121	C₂³×C₂₃	1	2	yes	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	—	2	2	no	—
591	C₄×Q₈	—	2	2	no	—
592	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
593	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
594	C₄×Q₈	D₄×C₂₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
596	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
597	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
598	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
599	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
600	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
601	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	C₂³×C₂₃	1	2	yes	—
611	C₄×D₄	C₂³×C₂₃	1	2	yes	—
612	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₄×D₄	C₂³×C₂₃	1	2	yes	—
614	C₄×D₄	C₂³×C₂₃	1	2	yes	—
615	C₄×D₄	C₂³×C₂₃	1	2	yes	—
616	C₄×D₄	C₂³×C₂₃	1	2	yes	—
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	—	2	4	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	—	2	1	no	—
625	C₂×C₄⋊C₄	—	2	1	no	—
626	C₂×C₄⋊C₄	—	2	2	no	—
627	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₂²⋊C₄	—	2	1	no	—
632	C₂×C₂²⋊C₄	—	2	2	no	—
633	C₂×C₄²	—	2	2	no	—
634	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
636	#107	C₂³×C₂₃	1	2	yes	—
637	#106	C₂³×C₂₃	1	2	yes	—
638	#106	C₂³×C₂₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
640	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
641	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
642	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
643	#103	C₂³×C₂₃	1	2	yes	—
644	#103	C₂³×C₂₃	1	4	yes	—
645	#103	C₂³×C₂₃	1	4	yes	—
646	#103	C₂³×C₂₃	1	4	yes	—
647	#103	C₂³×C₂₃	1	4	yes	—
648	#102	C₂³×C₂₃	1	2	yes	—
649	#102	C₂³×C₂₃	1	2	yes	—
650	#102	C₂³×C₂₃	1	2	yes	—
651	#102	C₂³×C₂₃	1	4	yes	—
652	#102	C₂³×C₂₃	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
654	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
655	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
656	#97	C₂³×C₂₃	1	4	yes	—
657	#97	C₂³×C₂₃	1	2	yes	—
658	C₄×C₈	C₂³×C₂₃	1	2	yes	—
659	C₄×C₈	C₂³×C₂₃	1	4	yes	—
660	C₂₃	#61899	1	1	yes	characteristic, direct product factor, Sylow
661	C₂⁴	—	2	1	no	—
662	#41	—	4	4	no	—
663	#41	—	8	4	no	—
664	#41	—	8	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂×Q₈	—	4	4	no	—
670	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
671	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
672	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
674	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	4	2	no	—
683	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
684	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
685	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	2	2	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
697	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
699	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
700	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
701	Q₁₆	—	4	4	no	—
702	SD₁₆	—	4	4	no	—
703	SD₁₆	—	4	4	no	—
704	SD₁₆	—	4	4	no	—
705	SD₁₆	—	4	2	no	—
706	D₈	—	4	2	no	—
707	D₈	—	4	4	no	—
708	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
710	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
729	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
731	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
732	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₂²⋊C₄	—	2	1	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	1	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	1	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
761	C₄²	C₂×D₄×C₂₃	1	2	yes	—
762	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₄²	C₂×D₄×C₂₃	1	2	yes	—
764	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₂₃	1	2	yes	—
766	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
767	C₄²	C₂⁴×C₂₃	1	2	yes	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	1	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
775	Q₈	—	2	2	no	—
776	Q₈	—	2	2	no	—
777	Q₈	—	2	4	no	—
778	Q₈	—	2	2	no	—
779	Q₈	—	2	4	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	4	no	—
782	Q₈	—	8	2	no	—
783	Q₈	—	8	1	no	—
784	D₄	—	2	2	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	2	no	—
788	D₄	—	4	2	no	—
789	D₄	—	4	4	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	1	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	4	2	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	4	4	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	—	8	2	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
818	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
819	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
820	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
821	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
822	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
823	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
824	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
825	C₈	—	2	2	no	—
826	C₈	—	2	4	no	—
827	C₈	—	2	2	no	—
828	C₂²	—	2	1	no	—
829	C₂²	—	2	1	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	1	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	8	4	no	—
840	C₂²	C₂₃×#577	1	2	yes	—
841	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	2	no	—
846	C₄	—	2	2	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	1	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	1	no	—
856	C₄	C₂₃×#575	1	2	yes	—
857	C₄	C₂₃×#585	1	2	yes	—
858	C₂	—	2	2	no	—
859	C₂	—	8	2	no	—
860	C₂	—	8	2	no	—
861	C₂	—	8	1	no	—
862	C₂	C₂₃×#3487	1	1	yes	characteristic
863	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
864	C₂	C₂×C₂₃×#577	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. C₂×C₂₃×#556	C₂	semidirect
3. C₂₃×#3401	C₂	semidirect
4. C₂₃×#3397	C₂	semidirect
5. C₂₃×#3394	C₂	semidirect
6. C₂₃×#3376	C₂	semidirect
7. C₂₃×#3369	C₂	semidirect
8. C₂₃×#3360	C₂	semidirect
9. C₂₃×#3218	C₂	semidirect
10. C₂₃×#3213	C₂	semidirect
11. C₂₃×#3211	C₂	semidirect
12. C₂₃×#3206	C₂	semidirect
13. C₂₃×#3117	C₂	semidirect
14. C₂₃×#3109	C₂	semidirect
15. C₂₃×#3105	C₂	semidirect
16. C₂₃×#3103	C₂	semidirect
17. C₂₃×#2984	C₂	semidirect
18. C₂₃×#559	C₂²	semidirect
19. C₂₃×#559	C₂²	semidirect
20. Q₈²×C₂₃	C₂²	semidirect
27. C₂₃×#554	C₂²	semidirect
28. C₂₃×#554	C₂²	semidirect
29. C₂₃×#550	C₂²	semidirect
48. C₂₃×#497	C₂²	semidirect
51. C₂₃×#492	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
55. C₂₃×#487	C₂²	semidirect
59. C₂₃×#479	C₂²	semidirect
62. C₂₃×#475	C₂²	semidirect
64. C₂₃×#464	C₂²	semidirect
69. C₂₃×#462	C₂²	semidirect
70. C₂₃×#461	C₂²	semidirect
71. C₂₃×#461	C₂²	semidirect
72. C₂₃×#460	C₂²	semidirect
81. C₂₃×#446	C₂²	semidirect
82. C₂₃×#446	C₂²	semidirect
83. C₈×Q₈×C₂₃	C₂²	semidirect
85. C₂₃×#441	C₂²	semidirect
86. C₂₃×#440	C₂²	semidirect
88. C₄×SD₁₆×C₂₃	C₂²	semidirect
89. C₄×SD₁₆×C₂₃	C₂²	semidirect
335. #61899	C₂₃	direct (N × H)
396. #3522	C₂×C₂₃	semidirect
397. C₂×#556	C₂×C₂₃	semidirect
398. #3401	C₂×C₂₃	semidirect
399. #3397	C₂×C₂₃	semidirect
400. #3394	C₂×C₂₃	semidirect
401. #3376	C₂×C₂₃	semidirect
402. #3369	C₂×C₂₃	semidirect
403. #3360	C₂×C₂₃	semidirect
404. #3218	C₂×C₂₃	semidirect
405. #3213	C₂×C₂₃	semidirect
406. #3211	C₂×C₂₃	semidirect
407. #3206	C₂×C₂₃	semidirect
408. #3117	C₂×C₂₃	semidirect
409. #3109	C₂×C₂₃	semidirect
410. #3105	C₂×C₂₃	semidirect
411. #3103	C₂×C₂₃	semidirect
412. #2984	C₂×C₂₃	semidirect
443. #559	C₂²×C₂₃	semidirect
444. #559	C₂²×C₂₃	semidirect
445. Q₈²	C₂²×C₂₃	semidirect
452. #554	C₂²×C₂₃	semidirect
453. #554	C₂²×C₂₃	semidirect
454. #550	C₂²×C₂₃	semidirect
473. #497	C₂²×C₂₃	semidirect
476. #492	C₂²×C₂₃	semidirect
477. #491	C₂²×C₂₃	semidirect
480. #487	C₂²×C₂₃	semidirect
484. #479	C₂²×C₂₃	semidirect
487. #475	C₂²×C₂₃	semidirect
489. #464	C₂²×C₂₃	semidirect
494. #462	C₂²×C₂₃	semidirect
495. #461	C₂²×C₂₃	semidirect
496. #461	C₂²×C₂₃	semidirect
497. #460	C₂²×C₂₃	semidirect
506. #446	C₂²×C₂₃	semidirect
507. #446	C₂²×C₂₃	semidirect
508. C₈×Q₈	C₂²×C₂₃	semidirect
510. #441	C₂²×C₂₃	semidirect
511. #440	C₂²×C₂₃	semidirect
513. C₄×SD₁₆	C₂²×C₂₃	semidirect
514. C₄×SD₁₆	C₂²×C₂₃	semidirect
660. C₂₃	#61899	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
C₂×C₂₃×#556	2
C₂₃×#3401	2
C₂₃×#3397	2
C₂₃×#3394	2
C₂₃×#3376	2
C₂₃×#3369	2
C₂₃×#3360	2
C₂₃×#3218	2
C₂₃×#3213	2
C₂₃×#3211	2
C₂₃×#3206	2
C₂₃×#3117	2
C₂₃×#3109	2
C₂₃×#3105	2
C₂₃×#3103	2
C₂₃×#2984	2
#61899	23

Subgroups — C23×#61899 #19209525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61899 #19209525