Subgroups — C₂₃×#61898 #19209524

Order 5888.

1844 conjugacy classes of subgroups.

The subgroup lattice has 878 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×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3403	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3399	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3396	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3375	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3370	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3361	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3217	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×#3205	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3114	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3112	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3100	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#559	—	2	1	no	—
19	C₂₃×#559	—	2	1	no	—
20	C₂₃×#559	—	2	2	no	—
21	C₂₃×#559	C₂²	1	2	yes	—
22	C₂₃×#559	C₂²	1	4	yes	—
23	C₂₃×#559	C₂²	1	2	yes	—
24	C₂₃×#559	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#559	C₂²	1	2	yes	complemented
26	Q₈²×C₂₃	C₂²	1	1	yes	characteristic, complemented
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	2	no	—
34	C₂₃×#542	—	2	1	no	—
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂₃×#532	C₂²	1	2	yes	—
37	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂₃×#529	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#124	—	2	1	no	—
41	C₂×C₂₃×#124	C₂²	1	2	yes	—
42	C₂×C₂₃×#123	—	2	2	no	—
43	C₂₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	—	2	1	no	—
47	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
48	C₂₃×#496	C₂²	1	2	yes	—
49	C₂₃×#496	C₂²	1	4	yes	complemented
50	C₂₃×#495	C₂²	1	4	yes	complemented
51	C₂₃×#493	C₂²	1	2	yes	—
52	C₂₃×#490	C₂²	1	2	yes	—
53	C₂₃×#489	C₂²	1	4	yes	complemented
54	C₂₃×#488	C₂²	1	4	yes	complemented
55	C₂₃×#486	C₂²	1	2	yes	—
56	C₂₃×#483	C₂²	1	1	yes	characteristic
57	C₂₃×#480	C₂²	1	1	yes	characteristic
58	C₂₃×#480	C₂²	1	2	yes	—
59	C₂₃×#479	C₂²	1	2	yes	complemented
60	C₂₃×#478	C₂²	1	4	yes	complemented
61	C₂₃×#477	C₂²	1	2	yes	complemented
62	C₂₃×#474	C₂²	1	4	yes	complemented
63	C₂₃×#464	C₂²	1	4	yes	complemented
64	C₂₃×#464	C₂²	1	2	yes	complemented
65	C₂₃×#463	C₂²	1	4	yes	complemented
66	C₂₃×#463	C₂²	1	4	yes	complemented
67	C₂₃×#463	C₂²	1	4	yes	complemented
68	C₂₃×#463	C₂²	1	4	yes	complemented
69	C₂₃×#460	C₂²	1	2	yes	—
70	C₂₃×#460	C₂²	1	2	yes	complemented
71	C₂₃×#459	C₂²	1	4	yes	—
72	C₂₃×#459	C₂²	1	2	yes	—
73	C₂₃×#459	C₂²	1	4	yes	complemented
74	C₂₃×#451	C₂²	1	1	yes	characteristic
75	C₂₃×#450	C₂²	1	2	yes	—
76	C₂₃×#448	C₂²	1	2	yes	—
77	C₂₃×#448	C₂²	1	1	yes	characteristic
78	C₂₃×#447	C₂²	1	2	yes	—
79	C₂₃×#447	C₂²	1	2	yes	—
80	C₂₃×#447	C₂²	1	2	yes	—
81	C₂₃×#446	C₂²	1	4	yes	complemented
82	C₂₃×#446	C₂²	1	2	yes	complemented
83	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#442	C₂²	1	4	yes	complemented
85	C₂₃×#440	C₂²	1	4	yes	complemented
86	C₂₃×#440	C₂²	1	4	yes	complemented
87	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
88	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
89	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
90	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
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	1	yes	characteristic
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	—	2	1	no	—
102	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₂₃	—	2	2	no	—
104	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
107	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
108	C₂×D₈×C₂₃	C₂³	1	4	yes	—
109	C₂×D₈×C₂₃	C₂³	1	4	yes	—
110	C₂×D₈×C₂₃	C₂³	1	4	yes	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	—	2	2	no	—
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×#127	—	2	1	no	—
116	C₂₃×#127	—	2	1	no	—
117	C₂₃×#127	C₂³	1	2	yes	—
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#127	C₂³	1	2	yes	—
120	C₂₃×#127	C₂³	1	2	yes	—
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	1	no	—
123	C₂₃×#125	C₂³	1	2	yes	—
124	C₂₃×#125	C₂³	1	1	yes	characteristic
125	C₂₃×#124	—	2	1	no	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	4	no	—
130	C₂₃×#124	—	2	2	no	—
131	C₂₃×#124	—	2	2	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	—	2	1	no	—
134	C₂₃×#124	C₂³	1	4	yes	—
135	C₂₃×#124	C₂³	1	4	yes	—
136	C₂₃×#124	C₂³	1	2	yes	—
137	C₂₃×#124	C₂³	1	1	yes	characteristic
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×#123	—	2	1	no	—
140	C₂₃×#123	—	2	2	no	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	4	no	—
144	C₂₃×#123	—	2	4	no	—
145	C₂₃×#123	—	2	4	no	—
146	C₂₃×#123	—	2	4	no	—
147	C₂₃×C₂²⋊Q₈	—	2	1	no	—
148	C₂₃×C₂²⋊Q₈	—	2	2	no	—
149	C₂₃×C₂²⋊Q₈	—	2	2	no	—
150	C₂₃×C₂²⋊Q₈	—	2	2	no	—
151	C₂₃×C₂²⋊Q₈	—	2	2	no	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
153	C₂₃×#121	—	2	1	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	1	no	—
156	C₂₃×#121	—	2	2	no	—
157	C₂₃×#121	C₂³	1	2	yes	—
158	C₂₃×#121	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	—	2	1	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	1	yes	characteristic
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	1	yes	characteristic
170	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
171	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
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	2	no	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	4	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	2	no	—
181	C₄×D₄×C₂₃	—	2	2	no	—
182	C₄×D₄×C₂₃	—	2	1	no	—
183	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₄×D₄×C₂₃	C₂³	1	2	yes	—
185	C₄×D₄×C₂₃	C₂³	1	2	yes	—
186	C₄×D₄×C₂₃	C₂³	1	2	yes	—
187	C₄×D₄×C₂₃	C₂³	1	2	yes	—
188	C₄×D₄×C₂₃	C₂³	1	4	yes	—
189	C₄×D₄×C₂₃	C₂³	1	4	yes	—
190	C₂₃×#117	—	2	2	no	—
191	C₂₃×#117	—	2	1	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	2	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₄²×C₂₃	—	2	1	no	—
202	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
213	C₂₃×#103	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#102	C₂³	1	2	yes	—
216	C₂₃×#102	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	4	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	2	yes	—
225	C₂₃×#97	C₂³	1	4	yes	—
226	C₄×C₈×C₂₃	C₂³	1	4	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	2	no	—
229	#41×C₂₃	—	4	4	no	—
230	#41×C₂₃	—	8	4	no	—
231	#41×C₂₃	—	8	2	no	—
232	C₂×Q₈×C₂₃	—	2	1	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	2	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	2	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	2	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	1	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂×D₄×C₂₃	—	2	2	no	—
253	C₂×D₄×C₂₃	—	4	4	no	—
254	C₂×D₄×C₂₃	—	4	4	no	—
255	C₂×D₄×C₂₃	—	8	2	no	—
256	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	1	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	4	no	—
267	C₂²×C₄×C₂₃	—	2	4	no	—
268	C₂²×C₄×C₂₃	—	8	4	no	—
269	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₂₃	—	4	2	no	—
275	SD₁₆×C₂₃	—	4	2	no	—
276	SD₁₆×C₂₃	—	4	4	no	—
277	SD₁₆×C₂₃	—	4	4	no	—
278	D₈×C₂₃	—	4	4	no	—
279	D₈×C₂₃	—	4	4	no	—
280	D₈×C₂₃	—	4	4	no	—
281	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
283	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
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	1	yes	characteristic
299	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	no	—
312	C₂²⋊C₄×C₂₃	—	2	4	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	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	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	—	2	2	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	1	no	—
329	C₄²×C₂₃	C₂×D₄	1	2	yes	—
330	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₂₃	C₂×D₄	1	2	yes	—
332	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	2	yes	—
334	C₄²×C₂₃	C₂⁴	1	2	yes	—
335	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
337	#61898	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	1	no	—
340	C₂³×C₂₃	—	2	4	no	—
341	C₂³×C₂₃	—	4	4	no	—
342	C₂³×C₂₃	—	4	4	no	—
343	C₂³×C₂₃	—	4	4	no	—
344	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
345	Q₈×C₂₃	—	2	2	no	—
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	4	2	no	—
351	Q₈×C₂₃	—	4	2	no	—
352	Q₈×C₂₃	—	8	2	no	—
353	Q₈×C₂₃	—	8	1	no	—
354	D₄×C₂₃	—	2	4	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	2	4	no	—
357	D₄×C₂₃	—	2	4	no	—
358	D₄×C₂₃	—	4	4	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	4	4	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	4	4	no	—
363	D₄×C₂₃	—	4	4	no	—
364	D₄×C₂₃	—	4	2	no	—
365	D₄×C₂₃	—	8	2	no	—
366	D₄×C₂₃	—	8	2	no	—
367	D₄×C₂₃	—	8	2	no	—
368	D₄×C₂₃	—	8	1	no	—
369	C₂×C₄×C₂₃	—	2	4	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	1	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	4	no	—
381	C₂×C₄×C₂₃	—	4	2	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	4	2	no	—
384	C₂×C₄×C₂₃	—	8	4	no	—
385	C₂×C₄×C₂₃	—	8	4	no	—
386	C₂×C₄×C₂₃	—	8	2	no	—
387	C₂×C₄×C₂₃	—	8	2	no	—
388	C₂×C₄×C₂₃	—	8	2	no	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
399	C₈×C₂₃	—	2	2	no	—
400	C₈×C₂₃	—	2	2	no	—
401	C₈×C₂₃	—	2	4	no	—
402	#3522	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂×#559	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3403	C₂×C₂₃	1	4	yes	complemented
405	#3399	C₂×C₂₃	1	2	yes	complemented
406	#3396	C₂×C₂₃	1	2	yes	complemented
407	#3375	C₂×C₂₃	1	2	yes	complemented
408	#3370	C₂×C₂₃	1	4	yes	complemented
409	#3361	C₂×C₂₃	1	2	yes	complemented
410	#3217	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3213	C₂×C₂₃	1	2	yes	complemented
412	#3211	C₂×C₂₃	1	2	yes	complemented
413	#3205	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#3114	C₂×C₂₃	1	2	yes	complemented
415	#3112	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#3100	C₂×C₂₃	1	2	yes	complemented
418	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
419	C₂²×C₂₃	—	2	1	no	—
420	C₂²×C₂₃	—	2	1	no	—
421	C₂²×C₂₃	—	4	4	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	1	no	—
424	C₂²×C₂₃	—	4	2	no	—
425	C₂²×C₂₃	—	4	1	no	—
426	C₂²×C₂₃	—	4	4	no	—
427	C₂²×C₂₃	—	4	1	no	—
428	C₂²×C₂₃	—	4	2	no	—
429	C₂²×C₂₃	—	4	4	no	—
430	C₂²×C₂₃	—	8	8	no	—
431	C₂²×C₂₃	#576	1	2	yes	—
432	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	1	no	—
435	C₄×C₂₃	—	2	2	no	—
436	C₄×C₂₃	—	2	2	no	—
437	C₄×C₂₃	—	2	2	no	—
438	C₄×C₂₃	—	2	1	no	—
439	C₄×C₂₃	—	2	2	no	—
440	C₄×C₂₃	—	2	1	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	1	no	—
443	C₄×C₂₃	—	4	1	no	—
444	C₄×C₂₃	—	4	2	no	—
445	C₄×C₂₃	—	4	1	no	—
446	C₄×C₂₃	—	4	2	no	—
447	C₄×C₂₃	#575	1	2	yes	—
448	C₄×C₂₃	#585	1	2	yes	—
449	#559	—	2	1	no	—
450	#559	—	2	1	no	—
451	#559	—	2	2	no	—
452	#559	C₂²×C₂₃	1	2	yes	—
453	#559	C₂²×C₂₃	1	4	yes	—
454	#559	C₂²×C₂₃	1	2	yes	—
455	#559	C₂²×C₂₃	1	1	yes	characteristic, complemented
456	#559	C₂²×C₂₃	1	2	yes	complemented
457	Q₈²	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	#554	C₂²×C₂₃	1	2	yes	complemented
460	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#548	—	2	1	no	—
462	#547	—	2	1	no	—
463	#547	—	2	2	no	—
464	#542	—	2	2	no	—
465	#542	—	2	1	no	—
466	#532	C₂²×C₂₃	1	2	yes	—
467	#532	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
469	#529	C₂²×C₂₃	1	1	yes	characteristic
470	#529	C₂²×C₂₃	1	2	yes	—
471	C₂×#124	—	2	1	no	—
472	C₂×#124	C₂²×C₂₃	1	2	yes	—
473	C₂×#123	—	2	2	no	—
474	#520	—	2	1	no	—
475	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×C₄×D₄	—	2	1	no	—
478	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
479	#496	C₂²×C₂₃	1	2	yes	—
480	#496	C₂²×C₂₃	1	4	yes	complemented
481	#495	C₂²×C₂₃	1	4	yes	complemented
482	#493	C₂²×C₂₃	1	2	yes	—
483	#490	C₂²×C₂₃	1	2	yes	—
484	#489	C₂²×C₂₃	1	4	yes	complemented
485	#488	C₂²×C₂₃	1	4	yes	complemented
486	#486	C₂²×C₂₃	1	2	yes	—
487	#483	C₂²×C₂₃	1	1	yes	characteristic
488	#480	C₂²×C₂₃	1	1	yes	characteristic
489	#480	C₂²×C₂₃	1	2	yes	—
490	#479	C₂²×C₂₃	1	2	yes	complemented
491	#478	C₂²×C₂₃	1	4	yes	complemented
492	#477	C₂²×C₂₃	1	2	yes	complemented
493	#474	C₂²×C₂₃	1	4	yes	complemented
494	#464	C₂²×C₂₃	1	2	yes	complemented
495	#464	C₂²×C₂₃	1	4	yes	complemented
496	#463	C₂²×C₂₃	1	4	yes	complemented
497	#463	C₂²×C₂₃	1	4	yes	complemented
498	#463	C₂²×C₂₃	1	4	yes	complemented
499	#463	C₂²×C₂₃	1	4	yes	complemented
500	#460	C₂²×C₂₃	1	2	yes	—
501	#460	C₂²×C₂₃	1	2	yes	complemented
502	#459	C₂²×C₂₃	1	2	yes	—
503	#459	C₂²×C₂₃	1	4	yes	—
504	#459	C₂²×C₂₃	1	4	yes	complemented
505	#451	C₂²×C₂₃	1	1	yes	characteristic
506	#450	C₂²×C₂₃	1	2	yes	—
507	#448	C₂²×C₂₃	1	1	yes	characteristic
508	#448	C₂²×C₂₃	1	2	yes	—
509	#447	C₂²×C₂₃	1	2	yes	—
510	#447	C₂²×C₂₃	1	2	yes	—
511	#447	C₂²×C₂₃	1	2	yes	—
512	#446	C₂²×C₂₃	1	4	yes	complemented
513	#446	C₂²×C₂₃	1	2	yes	complemented
514	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
515	#442	C₂²×C₂₃	1	4	yes	complemented
516	#440	C₂²×C₂₃	1	4	yes	complemented
517	#440	C₂²×C₂₃	1	4	yes	complemented
518	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
519	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
520	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
521	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
522	#432	C₂²×C₂₃	1	1	yes	characteristic
523	#432	C₂²×C₂₃	1	2	yes	—
524	#431	C₂²×C₂₃	1	2	yes	—
525	#431	C₂²×C₂₃	1	1	yes	characteristic
526	C₂×C₂₃	—	2	2	no	—
527	C₂×C₂₃	—	8	2	no	—
528	C₂×C₂₃	—	8	1	no	—
529	C₂×C₂₃	—	8	4	no	—
530	C₂×C₂₃	#3487	1	1	yes	characteristic
531	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
532	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
533	C₂×#41	—	2	1	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	—	2	1	no	—
536	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
538	C₂²×D₄	—	2	1	no	—
539	C₂²×D₄	—	2	1	no	—
540	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
541	C₂³×C₄	—	2	2	no	—
542	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
543	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
544	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
546	C₂×D₈	C₂³×C₂₃	1	4	yes	—
547	C₂×D₈	C₂³×C₂₃	1	4	yes	—
548	C₂×D₈	C₂³×C₂₃	1	4	yes	—
549	C₄⋊Q₈	—	2	1	no	—
550	C₄⋊Q₈	—	2	2	no	—
551	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
552	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
553	#127	—	2	1	no	—
554	#127	—	2	1	no	—
555	#127	C₂³×C₂₃	1	2	yes	—
556	#127	C₂³×C₂₃	1	2	yes	—
557	#127	C₂³×C₂₃	1	2	yes	—
558	#127	C₂³×C₂₃	1	1	yes	characteristic
559	#126	—	2	2	no	—
560	#126	—	2	1	no	—
561	#125	C₂³×C₂₃	1	2	yes	—
562	#125	C₂³×C₂₃	1	1	yes	characteristic
563	#124	—	2	2	no	—
564	#124	—	2	2	no	—
565	#124	—	2	4	no	—
566	#124	—	2	1	no	—
567	#124	—	2	2	no	—
568	#124	—	2	2	no	—
569	#124	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	—	2	1	no	—
572	#124	C₂³×C₂₃	1	4	yes	—
573	#124	C₂³×C₂₃	1	4	yes	—
574	#124	C₂³×C₂₃	1	2	yes	—
575	#124	C₂³×C₂₃	1	1	yes	characteristic
576	#123	—	2	2	no	—
577	#123	—	2	1	no	—
578	#123	—	2	4	no	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	4	no	—
582	#123	—	2	2	no	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	C₂²⋊Q₈	—	2	1	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	—	2	2	no	—
590	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
591	#121	—	2	1	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	C₂³×C₂₃	1	1	yes	characteristic
596	#121	C₂³×C₂₃	1	2	yes	—
597	C₄×Q₈	—	2	1	no	—
598	C₄×Q₈	—	2	1	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
601	C₄×Q₈	D₄×C₂₃	1	2	yes	—
602	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
603	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
604	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
605	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
606	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
607	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
608	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
609	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	2	no	—
612	C₄×D₄	—	2	2	no	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	4	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	C₂³×C₂₃	1	4	yes	—
622	C₄×D₄	C₂³×C₂₃	1	4	yes	—
623	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₄×D₄	C₂³×C₂₃	1	2	yes	—
625	C₄×D₄	C₂³×C₂₃	1	2	yes	—
626	C₄×D₄	C₂³×C₂₃	1	2	yes	—
627	C₄×D₄	C₂³×C₂₃	1	2	yes	—
628	#117	—	2	2	no	—
629	#117	—	2	1	no	—
630	C₂×C₄⋊C₄	—	2	1	no	—
631	C₂×C₄⋊C₄	—	2	1	no	—
632	C₂×C₄⋊C₄	—	2	2	no	—
633	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	—	2	2	no	—
637	C₂×C₂²⋊C₄	—	2	2	no	—
638	C₂×C₂²⋊C₄	—	2	2	no	—
639	C₂×C₄²	—	2	1	no	—
640	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
641	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
642	#107	C₂³×C₂₃	1	2	yes	—
643	#107	C₂³×C₂₃	1	4	yes	—
644	#106	C₂³×C₂₃	1	2	yes	—
645	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
646	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
647	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
648	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
649	#103	C₂³×C₂₃	1	2	yes	—
650	#103	C₂³×C₂₃	1	2	yes	—
651	#103	C₂³×C₂₃	1	2	yes	—
652	#103	C₂³×C₂₃	1	4	yes	—
653	#102	C₂³×C₂₃	1	2	yes	—
654	#102	C₂³×C₂₃	1	4	yes	—
655	#102	C₂³×C₂₃	1	4	yes	—
656	#102	C₂³×C₂₃	1	4	yes	—
657	#102	C₂³×C₂₃	1	4	yes	—
658	#102	C₂³×C₂₃	1	4	yes	—
659	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
660	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
661	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
662	#97	C₂³×C₂₃	1	2	yes	—
663	#97	C₂³×C₂₃	1	4	yes	—
664	C₄×C₈	C₂³×C₂₃	1	4	yes	—
665	C₄×C₈	C₂³×C₂₃	1	2	yes	—
666	C₂₃	#61898	1	1	yes	characteristic, direct product factor, Sylow
667	C₂⁴	—	2	2	no	—
668	#41	—	4	4	no	—
669	#41	—	8	4	no	—
670	#41	—	8	2	no	—
671	C₂×Q₈	—	2	1	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	—	4	2	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
677	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
679	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
680	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	2	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	4	4	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	8	2	no	—
695	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
696	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
697	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	8	4	no	—
708	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
709	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
710	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
711	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
713	Q₁₆	—	4	2	no	—
714	SD₁₆	—	4	2	no	—
715	SD₁₆	—	4	4	no	—
716	SD₁₆	—	4	4	no	—
717	D₈	—	4	4	no	—
718	D₈	—	4	4	no	—
719	D₈	—	4	4	no	—
720	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
721	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
722	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
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	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	—	2	2	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
739	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
741	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
742	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	1	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	—	2	2	no	—
767	C₄²	—	2	1	no	—
768	C₄²	C₂×D₄×C₂₃	1	2	yes	—
769	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
770	C₄²	C₂×D₄×C₂₃	1	2	yes	—
771	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
772	C₄²	C₂⁴×C₂₃	1	2	yes	—
773	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
774	C₄²	C₂⁴×C₂₃	1	2	yes	—
775	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	4	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	4	no	—
781	C₂³	—	4	4	no	—
782	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
783	Q₈	—	2	2	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	2	2	no	—
786	Q₈	—	2	2	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	4	2	no	—
790	Q₈	—	8	2	no	—
791	Q₈	—	8	1	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	4	no	—
802	D₄	—	4	2	no	—
803	D₄	—	8	2	no	—
804	D₄	—	8	2	no	—
805	D₄	—	8	2	no	—
806	D₄	—	8	1	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	4	2	no	—
821	C₂×C₄	—	4	2	no	—
822	C₂×C₄	—	8	4	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	—	8	2	no	—
825	C₂×C₄	—	8	2	no	—
826	C₂×C₄	—	8	2	no	—
827	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
829	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
830	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
831	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
835	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
836	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
837	C₈	—	2	2	no	—
838	C₈	—	2	2	no	—
839	C₈	—	2	4	no	—
840	C₂²	—	2	1	no	—
841	C₂²	—	2	1	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	4	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	4	no	—
851	C₂²	—	8	8	no	—
852	C₂²	C₂₃×#576	1	2	yes	—
853	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	1	no	—
867	C₄	—	4	2	no	—
868	C₄	C₂₃×#575	1	2	yes	—
869	C₄	C₂₃×#585	1	2	yes	—
870	C₂	—	2	2	no	—
871	C₂	—	8	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂₃×#3487	1	1	yes	characteristic
875	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
876	C₂	C₂×C₂₃×#576	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×#559	C₂	semidirect
3. C₂₃×#3403	C₂	semidirect
4. C₂₃×#3399	C₂	semidirect
5. C₂₃×#3396	C₂	semidirect
6. C₂₃×#3375	C₂	semidirect
7. C₂₃×#3370	C₂	semidirect
8. C₂₃×#3361	C₂	semidirect
9. C₂₃×#3217	C₂	semidirect
10. C₂₃×#3213	C₂	semidirect
11. C₂₃×#3211	C₂	semidirect
12. C₂₃×#3205	C₂	semidirect
13. C₂₃×#3114	C₂	semidirect
14. C₂₃×#3112	C₂	semidirect
15. C₂₃×#3108	C₂	semidirect
16. C₂₃×#3100	C₂	semidirect
17. C₂₃×#2984	C₂	semidirect
24. C₂₃×#559	C₂²	semidirect
25. C₂₃×#559	C₂²	semidirect
26. Q₈²×C₂₃	C₂²	semidirect
27. C₂₃×#554	C₂²	semidirect
28. C₂₃×#554	C₂²	semidirect
29. C₂₃×#550	C₂²	semidirect
49. C₂₃×#496	C₂²	semidirect
50. C₂₃×#495	C₂²	semidirect
53. C₂₃×#489	C₂²	semidirect
54. C₂₃×#488	C₂²	semidirect
59. C₂₃×#479	C₂²	semidirect
60. C₂₃×#478	C₂²	semidirect
61. C₂₃×#477	C₂²	semidirect
62. C₂₃×#474	C₂²	semidirect
63. C₂₃×#464	C₂²	semidirect
64. C₂₃×#464	C₂²	semidirect
65. C₂₃×#463	C₂²	semidirect
66. C₂₃×#463	C₂²	semidirect
67. C₂₃×#463	C₂²	semidirect
68. C₂₃×#463	C₂²	semidirect
70. C₂₃×#460	C₂²	semidirect
73. C₂₃×#459	C₂²	semidirect
81. C₂₃×#446	C₂²	semidirect
82. C₂₃×#446	C₂²	semidirect
83. C₈×Q₈×C₂₃	C₂²	semidirect
84. C₂₃×#442	C₂²	semidirect
85. C₂₃×#440	C₂²	semidirect
86. C₂₃×#440	C₂²	semidirect
87. C₄×Q₁₆×C₂₃	C₂²	semidirect
88. C₄×SD₁₆×C₂₃	C₂²	semidirect
89. C₄×D₈×C₂₃	C₂²	semidirect
90. C₄×D₈×C₂₃	C₂²	semidirect
337. #61898	C₂₃	direct (N × H)
402. #3522	C₂×C₂₃	semidirect
403. C₂×#559	C₂×C₂₃	semidirect
404. #3403	C₂×C₂₃	semidirect
405. #3399	C₂×C₂₃	semidirect
406. #3396	C₂×C₂₃	semidirect
407. #3375	C₂×C₂₃	semidirect
408. #3370	C₂×C₂₃	semidirect
409. #3361	C₂×C₂₃	semidirect
410. #3217	C₂×C₂₃	semidirect
411. #3213	C₂×C₂₃	semidirect
412. #3211	C₂×C₂₃	semidirect
413. #3205	C₂×C₂₃	semidirect
414. #3114	C₂×C₂₃	semidirect
415. #3112	C₂×C₂₃	semidirect
416. #3108	C₂×C₂₃	semidirect
417. #3100	C₂×C₂₃	semidirect
418. #2984	C₂×C₂₃	semidirect
455. #559	C₂²×C₂₃	semidirect
456. #559	C₂²×C₂₃	semidirect
457. Q₈²	C₂²×C₂₃	semidirect
458. #554	C₂²×C₂₃	semidirect
459. #554	C₂²×C₂₃	semidirect
460. #550	C₂²×C₂₃	semidirect
480. #496	C₂²×C₂₃	semidirect
481. #495	C₂²×C₂₃	semidirect
484. #489	C₂²×C₂₃	semidirect
485. #488	C₂²×C₂₃	semidirect
490. #479	C₂²×C₂₃	semidirect
491. #478	C₂²×C₂₃	semidirect
492. #477	C₂²×C₂₃	semidirect
493. #474	C₂²×C₂₃	semidirect
494. #464	C₂²×C₂₃	semidirect
495. #464	C₂²×C₂₃	semidirect
496. #463	C₂²×C₂₃	semidirect
497. #463	C₂²×C₂₃	semidirect
498. #463	C₂²×C₂₃	semidirect
499. #463	C₂²×C₂₃	semidirect
501. #460	C₂²×C₂₃	semidirect
504. #459	C₂²×C₂₃	semidirect
512. #446	C₂²×C₂₃	semidirect
513. #446	C₂²×C₂₃	semidirect
514. C₈×Q₈	C₂²×C₂₃	semidirect
515. #442	C₂²×C₂₃	semidirect
516. #440	C₂²×C₂₃	semidirect
517. #440	C₂²×C₂₃	semidirect
518. C₄×Q₁₆	C₂²×C₂₃	semidirect
519. C₄×SD₁₆	C₂²×C₂₃	semidirect
520. C₄×D₈	C₂²×C₂₃	semidirect
521. C₄×D₈	C₂²×C₂₃	semidirect
666. C₂₃	#61898	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×#559	2
C₂₃×#3403	2
C₂₃×#3399	2
C₂₃×#3396	2
C₂₃×#3375	2
C₂₃×#3370	2
C₂₃×#3361	2
C₂₃×#3217	2
C₂₃×#3213	2
C₂₃×#3211	2
C₂₃×#3205	2
C₂₃×#3114	2
C₂₃×#3112	2
C₂₃×#3108	2
C₂₃×#3100	2
C₂₃×#2984	2
#61898	23

Subgroups — C23×#61898 #19209524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61898 #19209524