Subgroups — C₂₃×#61421 #19209047

Order 5888.

1964 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3401	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3400	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3399	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3397	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3396	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3392	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3154	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3045	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3042	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2946	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₂₃×#135	C₂²	1	2	yes	—
22	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
23	C₂₃×#559	C₂²	1	2	yes	—
24	C₂₃×#559	C₂²	1	2	yes	—
25	C₂₃×#559	C₂²	1	2	yes	complemented
26	C₂₃×#557	C₂²	1	2	yes	complemented
27	C₂₃×#556	—	2	1	no	—
28	C₂₃×#556	C₂²	1	4	yes	complemented
29	C₂₃×#554	—	2	1	no	—
30	C₂₃×#552	—	2	2	no	—
31	C₂₃×#550	C₂²	1	2	yes	—
32	C₂₃×#550	C₂²	1	2	yes	—
33	C₂₃×#546	—	2	2	no	—
34	C₂₃×#546	—	2	2	no	—
35	C₂₃×#540	—	2	2	no	—
36	C₂₃×#539	—	2	2	no	—
37	C₂₃×#536	C₂²	1	2	yes	—
38	C₂₃×#535	C₂²	1	2	yes	—
39	C₂₃×#533	C₂²	1	1	yes	characteristic
40	C₂₃×#532	—	2	1	no	—
41	C₂₃×#532	—	2	1	no	—
42	C₂₃×#532	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
44	C₂₃×#529	—	2	2	no	—
45	C₂₃×#520	C₂²	1	2	yes	—
46	C₂₃×#518	C₂²	1	2	yes	—
47	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
49	C₂₃×#497	C₂²	1	4	yes	complemented
50	C₂₃×#496	C₂²	1	4	yes	—
51	C₂₃×#496	C₂²	1	4	yes	complemented
52	C₂₃×#495	C₂²	1	4	yes	complemented
53	C₂₃×#493	C₂²	1	2	yes	—
54	C₂₃×#492	C₂²	1	2	yes	—
55	C₂₃×#492	C₂²	1	4	yes	complemented
56	C₂₃×#464	C₂²	1	2	yes	complemented
57	C₂₃×#464	C₂²	1	4	yes	complemented
58	C₂₃×#463	C₂²	1	2	yes	complemented
59	C₂₃×#463	C₂²	1	4	yes	complemented
60	C₂₃×#463	C₂²	1	4	yes	complemented
61	C₂₃×#463	C₂²	1	4	yes	complemented
62	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#461	C₂²	1	4	yes	complemented
65	C₂₃×#461	C₂²	1	4	yes	complemented
66	C₂₃×#460	C₂²	1	2	yes	—
67	C₂₃×#460	C₂²	1	4	yes	—
68	C₂₃×#460	C₂²	1	2	yes	—
69	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#460	C₂²	1	4	yes	complemented
71	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#459	C₂²	1	4	yes	complemented
73	C₂₃×#446	C₂²	1	4	yes	complemented
74	C₂₃×#446	C₂²	1	2	yes	complemented
75	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
76	C₂₃×#442	C₂²	1	4	yes	complemented
77	C₂₃×#441	C₂²	1	2	yes	complemented
78	C₂₃×#440	C₂²	1	2	yes	complemented
79	C₂₃×#440	C₂²	1	4	yes	complemented
80	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
81	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
83	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
84	C₂₃×#428	C₂²	1	1	yes	characteristic
85	C₂₃×#424	C₂²	1	2	yes	—
86	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
87	C₂₃×#419	C₂²	1	1	yes	characteristic
88	C₂₃×#417	C₂²	1	1	yes	characteristic
89	C₂₃×#416	C₂²	1	2	yes	—
90	C₂×C₂₃×#102	C₂²	1	2	yes	—
91	C₂₃×#405	C₂²	1	2	yes	—
92	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
93	C₂×#41×C₂₃	—	2	2	no	—
94	C₂×#41×C₂₃	—	2	2	no	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×D₄×C₂₃	—	2	1	no	—
99	C₂²×D₄×C₂₃	—	2	1	no	—
100	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
101	C₂₃×#137	—	2	4	no	—
102	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
103	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
104	C₂₃×#135	—	4	4	no	—
105	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×SD₁₆×C₂₃	—	4	4	no	—
108	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
110	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×D₈×C₂₃	C₂³	1	4	yes	—
116	C₂×D₈×C₂₃	C₂³	1	2	yes	—
117	C₂×D₈×C₂₃	C₂³	1	4	yes	—
118	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
121	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
122	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
123	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
124	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₂₃×#127	—	2	1	no	—
126	C₂₃×#127	—	2	1	no	—
127	C₂₃×#127	C₂³	1	4	yes	—
128	C₂₃×#127	C₂³	1	2	yes	—
129	C₂₃×#127	C₂³	1	2	yes	—
130	C₂₃×#127	C₂³	1	1	yes	characteristic
131	C₂₃×#126	—	2	4	no	—
132	C₂₃×#126	—	2	4	no	—
133	C₂₃×#125	—	2	4	no	—
134	C₂₃×#125	—	2	2	no	—
135	C₂₃×#125	D₄	1	2	yes	—
136	C₂₃×#124	—	2	2	no	—
137	C₂₃×#124	—	2	2	no	—
138	C₂₃×#124	—	2	2	no	—
139	C₂₃×#124	C₂³	1	2	yes	—
140	C₂₃×#124	C₂³	1	4	yes	—
141	C₂₃×#124	C₂³	1	4	yes	—
142	C₂₃×#123	—	2	4	no	—
143	C₂₃×#123	—	2	4	no	—
144	C₂₃×#123	—	2	4	no	—
145	C₂₃×#123	—	2	4	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	D₄	1	2	yes	—
150	C₂₃×C₂²⋊Q₈	D₄	1	2	yes	—
151	C₂₃×#121	—	2	1	no	—
152	C₂₃×#121	—	2	1	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	2	no	—
155	C₂₃×#121	—	2	4	no	—
156	C₂₃×#121	—	2	4	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	2	no	—
159	C₂₃×#120	—	2	4	no	—
160	C₄×Q₈×C₂₃	—	2	2	no	—
161	C₄×Q₈×C₂₃	—	2	1	no	—
162	C₄×Q₈×C₂₃	—	2	1	no	—
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
167	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
168	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
169	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	2	no	—
175	C₄×D₄×C₂₃	—	2	2	no	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	4	no	—
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	—	2	1	no	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₂₃	C₂³	1	4	yes	—
183	C₄×D₄×C₂₃	C₂³	1	4	yes	—
184	C₄×D₄×C₂₃	C₂³	1	4	yes	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	4	no	—
187	C₂₃×#117	—	2	1	no	—
188	C₂₃×#117	C₂³	1	1	yes	characteristic
189	C₂₃×#117	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
194	C₂×C₄²×C₂₃	—	2	1	no	—
195	C₂×C₄²×C₂₃	—	2	1	no	—
196	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
197	C₂₃×#107	C₂³	1	2	yes	—
198	C₂₃×#106	C₂³	1	2	yes	—
199	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
201	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
203	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
204	C₂₃×#103	C₂³	1	2	yes	—
205	C₂₃×#103	C₂³	1	2	yes	—
206	C₂₃×#103	C₂³	1	2	yes	—
207	C₂₃×#103	C₂³	1	2	yes	—
208	C₂₃×#103	C₂³	1	2	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×#102	C₂³	1	4	yes	—
211	C₂₃×#102	C₂³	1	2	yes	—
212	C₂₃×#102	C₂³	1	2	yes	—
213	C₂₃×#102	C₂³	1	2	yes	—
214	C₂₃×#97	C₂³	1	2	yes	—
215	C₂₃×#97	C₂³	1	4	yes	—
216	C₄×C₈×C₂₃	C₂³	1	2	yes	—
217	C₄×C₈×C₂₃	C₂³	1	4	yes	—
218	C₂⁴×C₂₃	—	2	2	no	—
219	#41×C₂₃	—	2	4	no	—
220	#41×C₂₃	—	2	2	no	—
221	#41×C₂₃	—	2	2	no	—
222	#41×C₂₃	—	2	4	no	—
223	#41×C₂₃	—	8	4	no	—
224	#41×C₂₃	—	8	4	no	—
225	C₂×Q₈×C₂₃	—	2	1	no	—
226	C₂×Q₈×C₂₃	—	2	2	no	—
227	C₂×Q₈×C₂₃	—	2	2	no	—
228	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
229	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
230	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
231	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
232	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	2	no	—
235	C₂×D₄×C₂₃	—	2	1	no	—
236	C₂×D₄×C₂₃	—	2	2	no	—
237	C₂×D₄×C₂₃	—	2	2	no	—
238	C₂×D₄×C₂₃	—	2	2	no	—
239	C₂×D₄×C₂₃	—	2	1	no	—
240	C₂×D₄×C₂₃	—	2	4	no	—
241	C₂×D₄×C₂₃	—	2	4	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	4	no	—
246	C₂×D₄×C₂₃	—	8	2	no	—
247	C₂×D₄×C₂₃	—	8	2	no	—
248	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
250	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	1	no	—
253	C₂²×C₄×C₂₃	—	2	1	no	—
254	C₂²×C₄×C₂₃	—	2	1	no	—
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	4	no	—
258	C₂²×C₄×C₂₃	—	2	4	no	—
259	C₂²×C₄×C₂₃	—	2	4	no	—
260	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
263	Q₁₆×C₂₃	—	2	4	no	—
264	Q₁₆×C₂₃	—	4	2	no	—
265	SD₁₆×C₂₃	—	2	8	no	—
266	SD₁₆×C₂₃	—	2	4	no	—
267	SD₁₆×C₂₃	—	4	4	no	—
268	SD₁₆×C₂₃	—	4	4	no	—
269	SD₁₆×C₂₃	—	4	2	no	—
270	SD₁₆×C₂₃	—	4	2	no	—
271	SD₁₆×C₂₃	—	4	4	no	—
272	D₈×C₂₃	—	2	8	no	—
273	D₈×C₂₃	—	4	2	no	—
274	D₈×C₂₃	—	4	4	no	—
275	M₁₆×C₂₃	—	2	2	no	—
276	M₁₆×C₂₃	#41	1	4	yes	complemented
277	C₂×C₈×C₂₃	—	2	4	no	—
278	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
279	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
280	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
281	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₂₃	—	2	1	no	—
283	C₄⋊C₄×C₂₃	—	2	4	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	2	no	—
286	C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₄⋊C₄×C₂₃	—	2	1	no	—
288	C₄⋊C₄×C₂₃	—	2	4	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	4	no	—
292	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
294	C₄⋊C₄×C₂₃	C₂×D₄	1	4	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	4	yes	—
298	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₂²⋊C₄×C₂₃	—	2	1	no	—
302	C₂²⋊C₄×C₂₃	—	2	4	no	—
303	C₂²⋊C₄×C₂₃	—	2	4	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	1	no	—
306	C₂²⋊C₄×C₂₃	—	2	1	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	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	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	4	no	—
313	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
314	C₄²×C₂₃	—	2	2	no	—
315	C₄²×C₂₃	—	2	1	no	—
316	C₄²×C₂₃	—	2	1	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	2	4	no	—
320	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₄²×C₂₃	C₂⁴	1	4	yes	—
325	#61421	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂³×C₂₃	—	2	2	no	—
327	C₂³×C₂₃	—	2	4	no	—
328	C₂³×C₂₃	—	2	1	no	—
329	C₂³×C₂₃	—	4	4	no	—
330	C₂³×C₂₃	—	8	2	no	—
331	C₂³×C₂₃	—	8	2	no	—
332	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
333	Q₈×C₂₃	—	2	4	no	—
334	Q₈×C₂₃	—	2	2	no	—
335	Q₈×C₂₃	—	2	2	no	—
336	Q₈×C₂₃	—	2	1	no	—
337	Q₈×C₂₃	—	2	2	no	—
338	Q₈×C₂₃	—	2	2	no	—
339	Q₈×C₂₃	—	2	1	no	—
340	Q₈×C₂₃	—	4	2	no	—
341	Q₈×C₂₃	—	4	2	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	2	4	no	—
344	D₄×C₂₃	—	2	1	no	—
345	D₄×C₂₃	—	2	2	no	—
346	D₄×C₂₃	—	2	1	no	—
347	D₄×C₂₃	—	2	4	no	—
348	D₄×C₂₃	—	4	4	no	—
349	D₄×C₂₃	—	4	2	no	—
350	D₄×C₂₃	—	4	4	no	—
351	D₄×C₂₃	—	4	4	no	—
352	D₄×C₂₃	—	4	2	no	—
353	D₄×C₂₃	—	4	4	no	—
354	D₄×C₂₃	—	8	1	no	—
355	D₄×C₂₃	—	8	2	no	—
356	D₄×C₂₃	—	8	2	no	—
357	D₄×C₂₃	—	8	4	no	—
358	D₄×C₂₃	—	8	4	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	1	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	2	no	—
368	C₂×C₄×C₂₃	—	4	2	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	4	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	8	4	no	—
373	C₂×C₄×C₂₃	—	8	4	no	—
374	C₂×C₄×C₂₃	—	8	4	no	—
375	C₂×C₄×C₂₃	—	8	1	no	—
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
379	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
384	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
385	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₂₃	—	2	2	no	—
387	C₈×C₂₃	—	2	2	no	—
388	C₈×C₂₃	—	2	2	no	—
389	C₈×C₂₃	C₂×#41	1	4	yes	—
390	#3508	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3507	C₂×C₂₃	1	1	yes	characteristic, complemented
392	#3401	C₂×C₂₃	1	4	yes	complemented
393	#3400	C₂×C₂₃	1	2	yes	complemented
394	#3399	C₂×C₂₃	1	2	yes	complemented
395	#3397	C₂×C₂₃	1	4	yes	complemented
396	#3396	C₂×C₂₃	1	2	yes	complemented
397	#3392	C₂×C₂₃	1	2	yes	complemented
398	#3154	C₂×C₂₃	1	2	yes	complemented
399	#3151	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3045	C₂×C₂₃	1	2	yes	complemented
401	#3042	C₂×C₂₃	1	2	yes	complemented
402	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#2946	C₂×C₂₃	1	2	yes	complemented
406	C₄×#137	C₂×C₂₃	1	1	yes	characteristic, complemented
407	C₂²×C₂₃	—	2	1	no	—
408	C₂²×C₂₃	—	2	1	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	4	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	1	no	—
414	C₂²×C₂₃	—	4	4	no	—
415	C₂²×C₂₃	—	4	1	no	—
416	C₂²×C₂₃	—	4	4	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	16	4	no	—
419	C₂²×C₂₃	#550	1	2	yes	—
420	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₂₃	—	2	1	no	—
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	4	no	—
424	C₄×C₂₃	—	2	1	no	—
425	C₄×C₂₃	—	2	4	no	—
426	C₄×C₂₃	—	4	1	no	—
427	C₄×C₂₃	—	4	2	no	—
428	C₄×C₂₃	—	4	1	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	2	no	—
431	C₄×C₂₃	—	4	1	no	—
432	C₄×C₂₃	#550	1	2	yes	—
433	C₄×C₂₃	#577	1	2	yes	—
434	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
435	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
438	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
439	C₂×#135	C₂²×C₂₃	1	2	yes	—
440	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
441	#559	C₂²×C₂₃	1	2	yes	—
442	#559	C₂²×C₂₃	1	2	yes	—
443	#559	C₂²×C₂₃	1	2	yes	complemented
444	#557	C₂²×C₂₃	1	2	yes	complemented
445	#556	—	2	1	no	—
446	#556	C₂²×C₂₃	1	4	yes	complemented
447	#554	—	2	1	no	—
448	#552	—	2	2	no	—
449	#550	C₂²×C₂₃	1	2	yes	—
450	#550	C₂²×C₂₃	1	2	yes	—
451	#546	—	2	2	no	—
452	#546	—	2	2	no	—
453	#540	—	2	2	no	—
454	#539	—	2	2	no	—
455	#536	C₂²×C₂₃	1	2	yes	—
456	#535	C₂²×C₂₃	1	2	yes	—
457	#533	C₂²×C₂₃	1	1	yes	characteristic
458	#532	—	2	1	no	—
459	#532	—	2	1	no	—
460	#532	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
462	#529	—	2	2	no	—
463	#520	C₂²×C₂₃	1	2	yes	—
464	#518	C₂²×C₂₃	1	2	yes	—
465	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
467	#497	C₂²×C₂₃	1	4	yes	complemented
468	#496	C₂²×C₂₃	1	4	yes	—
469	#496	C₂²×C₂₃	1	4	yes	complemented
470	#495	C₂²×C₂₃	1	4	yes	complemented
471	#493	C₂²×C₂₃	1	2	yes	—
472	#492	C₂²×C₂₃	1	2	yes	—
473	#492	C₂²×C₂₃	1	4	yes	complemented
474	#464	C₂²×C₂₃	1	4	yes	complemented
475	#464	C₂²×C₂₃	1	2	yes	complemented
476	#463	C₂²×C₂₃	1	4	yes	complemented
477	#463	C₂²×C₂₃	1	4	yes	complemented
478	#463	C₂²×C₂₃	1	2	yes	complemented
479	#463	C₂²×C₂₃	1	4	yes	complemented
480	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	#461	C₂²×C₂₃	1	4	yes	complemented
483	#461	C₂²×C₂₃	1	4	yes	complemented
484	#460	C₂²×C₂₃	1	2	yes	—
485	#460	C₂²×C₂₃	1	4	yes	—
486	#460	C₂²×C₂₃	1	2	yes	—
487	#460	C₂²×C₂₃	1	4	yes	complemented
488	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#459	C₂²×C₂₃	1	4	yes	complemented
490	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
491	#446	C₂²×C₂₃	1	4	yes	complemented
492	#446	C₂²×C₂₃	1	2	yes	complemented
493	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
494	#442	C₂²×C₂₃	1	4	yes	complemented
495	#441	C₂²×C₂₃	1	2	yes	complemented
496	#440	C₂²×C₂₃	1	2	yes	complemented
497	#440	C₂²×C₂₃	1	4	yes	complemented
498	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
499	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
500	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
501	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
502	#428	C₂²×C₂₃	1	1	yes	characteristic
503	#424	C₂²×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
505	#419	C₂²×C₂₃	1	1	yes	characteristic
506	#417	C₂²×C₂₃	1	1	yes	characteristic
507	#416	C₂²×C₂₃	1	2	yes	—
508	C₂×#102	C₂²×C₂₃	1	2	yes	—
509	#405	C₂²×C₂₃	1	2	yes	—
510	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
511	C₂×C₂₃	—	2	2	no	—
512	C₂×C₂₃	—	8	1	no	—
513	C₂×C₂₃	—	8	2	no	—
514	C₂×C₂₃	—	8	4	no	—
515	C₂×C₂₃	C₂×#550	1	1	yes	characteristic
516	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
517	C₂×C₂₃	#3585	1	1	yes	characteristic
518	C₂×#41	—	2	2	no	—
519	C₂×#41	—	2	2	no	—
520	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
521	C₂×#41	C₂³×C₂₃	1	2	yes	—
522	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
523	C₂²×D₄	—	2	1	no	—
524	C₂²×D₄	—	2	1	no	—
525	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
526	#137	—	2	4	no	—
527	AGL(1,ℤ/8)	—	2	8	no	—
528	AGL(1,ℤ/8)	—	4	4	no	—
529	#135	—	4	4	no	—
530	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
531	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
532	C₂×SD₁₆	—	4	4	no	—
533	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
534	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
535	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
536	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
537	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
539	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
540	C₂×D₈	C₂³×C₂₃	1	4	yes	—
541	C₂×D₈	C₂³×C₂₃	1	2	yes	—
542	C₂×D₈	C₂³×C₂₃	1	4	yes	—
543	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
545	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
546	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
547	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
548	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
550	#127	—	2	1	no	—
551	#127	—	2	1	no	—
552	#127	C₂³×C₂₃	1	2	yes	—
553	#127	C₂³×C₂₃	1	2	yes	—
554	#127	C₂³×C₂₃	1	1	yes	characteristic
555	#127	C₂³×C₂₃	1	4	yes	—
556	#126	—	2	4	no	—
557	#126	—	2	4	no	—
558	#125	—	2	2	no	—
559	#125	—	2	4	no	—
560	#125	D₄×C₂₃	1	2	yes	—
561	#124	—	2	2	no	—
562	#124	—	2	2	no	—
563	#124	—	2	2	no	—
564	#124	C₂³×C₂₃	1	2	yes	—
565	#124	C₂³×C₂₃	1	4	yes	—
566	#124	C₂³×C₂₃	1	4	yes	—
567	#123	—	2	4	no	—
568	#123	—	2	4	no	—
569	#123	—	2	4	no	—
570	#123	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
575	C₂²⋊Q₈	D₄×C₂₃	1	2	yes	—
576	#121	—	2	1	no	—
577	#121	—	2	1	no	—
578	#121	—	2	2	no	—
579	#121	—	2	2	no	—
580	#121	—	2	2	no	—
581	#121	—	2	2	no	—
582	#121	—	2	4	no	—
583	#121	—	2	4	no	—
584	#120	—	2	4	no	—
585	C₄×Q₈	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
589	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
593	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
594	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
595	C₄×D₄	—	2	1	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	2	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	4	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	1	no	—
605	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₂₃	1	4	yes	—
608	C₄×D₄	C₂³×C₂₃	1	4	yes	—
609	C₄×D₄	C₂³×C₂₃	1	4	yes	—
610	#117	—	2	2	no	—
611	#117	—	2	4	no	—
612	#117	—	2	1	no	—
613	#117	C₂³×C₂₃	1	1	yes	characteristic
614	#117	C₂³×C₂₃	1	2	yes	—
615	C₂×C₄⋊C₄	—	2	1	no	—
616	C₂×C₄⋊C₄	—	2	2	no	—
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	—	2	4	no	—
619	C₂×C₄²	—	2	1	no	—
620	C₂×C₄²	—	2	1	no	—
621	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
622	#107	C₂³×C₂₃	1	2	yes	—
623	#106	C₂³×C₂₃	1	2	yes	—
624	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
625	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
626	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
628	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
629	#103	C₂³×C₂₃	1	2	yes	—
630	#103	C₂³×C₂₃	1	2	yes	—
631	#103	C₂³×C₂₃	1	2	yes	—
632	#103	C₂³×C₂₃	1	2	yes	—
633	#103	C₂³×C₂₃	1	2	yes	—
634	#102	C₂³×C₂₃	1	4	yes	—
635	#102	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	#97	C₂³×C₂₃	1	2	yes	—
640	#97	C₂³×C₂₃	1	4	yes	—
641	C₄×C₈	C₂³×C₂₃	1	2	yes	—
642	C₄×C₈	C₂³×C₂₃	1	4	yes	—
643	C₂₃	#61421	1	1	yes	characteristic, direct product factor, Sylow
644	C₂⁴	—	2	2	no	—
645	#41	—	2	4	no	—
646	#41	—	2	2	no	—
647	#41	—	2	2	no	—
648	#41	—	2	4	no	—
649	#41	—	8	4	no	—
650	#41	—	8	4	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	2	no	—
654	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
655	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
656	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
657	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
658	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	2	no	—
661	C₂×D₄	—	2	1	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	4	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	4	no	—
672	C₂×D₄	—	8	2	no	—
673	C₂×D₄	—	8	2	no	—
674	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
675	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
676	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	4	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	4	no	—
686	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
687	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
688	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
689	Q₁₆	—	2	4	no	—
690	Q₁₆	—	4	2	no	—
691	SD₁₆	—	2	8	no	—
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	4	4	no	—
694	SD₁₆	—	4	4	no	—
695	SD₁₆	—	4	2	no	—
696	SD₁₆	—	4	2	no	—
697	SD₁₆	—	4	4	no	—
698	D₈	—	2	8	no	—
699	D₈	—	4	2	no	—
700	D₈	—	4	4	no	—
701	M₁₆	—	2	2	no	—
702	M₁₆	#41×C₂₃	1	4	yes	complemented
703	C₂×C₈	—	2	4	no	—
704	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
705	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
706	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
721	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
723	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
724	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₂²⋊C₄	—	2	1	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	1	no	—
732	C₂²⋊C₄	—	2	1	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	1	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	4	no	—
746	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
747	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
748	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
749	C₄²	C₂⁴×C₂₃	1	4	yes	—
750	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	8	2	no	—
756	C₂³	—	8	2	no	—
757	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
758	Q₈	—	2	4	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	1	no	—
765	Q₈	—	4	2	no	—
766	Q₈	—	4	2	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	4	no	—
769	D₄	—	2	1	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	4	no	—
773	D₄	—	4	4	no	—
774	D₄	—	4	2	no	—
775	D₄	—	4	4	no	—
776	D₄	—	4	4	no	—
777	D₄	—	4	4	no	—
778	D₄	—	4	2	no	—
779	D₄	—	8	2	no	—
780	D₄	—	8	2	no	—
781	D₄	—	8	4	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	8	4	no	—
798	C₂×C₄	—	8	4	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	—	8	1	no	—
801	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
804	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
806	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
807	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
809	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
810	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
811	C₈	—	2	2	no	—
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	C₂×#41×C₂₃	1	4	yes	—
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	1	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	4	1	no	—
821	C₂²	—	4	4	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	4	no	—
826	C₂²	—	16	4	no	—
827	C₂²	C₂₃×#550	1	2	yes	—
828	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
829	C₄	—	2	1	no	—
830	C₄	—	2	4	no	—
831	C₄	—	2	1	no	—
832	C₄	—	2	1	no	—
833	C₄	—	2	4	no	—
834	C₄	—	4	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	1	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	2	no	—
840	C₄	C₂₃×#550	1	2	yes	—
841	C₄	C₂₃×#577	1	2	yes	—
842	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
843	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	8	4	no	—
846	C₂	—	8	1	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₂₃×#550	1	1	yes	characteristic
849	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
850	C₂	C₂₃×#3585	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 ◁ C₂₃×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3508	C₂	semidirect
2. C₂₃×#3507	C₂	semidirect
3. C₂₃×#3401	C₂	semidirect
4. C₂₃×#3400	C₂	semidirect
5. C₂₃×#3399	C₂	semidirect
6. C₂₃×#3397	C₂	semidirect
7. C₂₃×#3396	C₂	semidirect
8. C₂₃×#3392	C₂	semidirect
9. C₂₃×#3154	C₂	semidirect
10. C₂₃×#3151	C₂	semidirect
11. C₂₃×#3045	C₂	semidirect
12. C₂₃×#3042	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂×C₂₃×#460	C₂	semidirect
15. C₂₃×#2962	C₂	semidirect
16. C₂₃×#2946	C₂	semidirect
17. C₄×C₂₃×#137	C₂	semidirect
25. C₂₃×#559	C₂²	semidirect
26. C₂₃×#557	C₂²	semidirect
28. C₂₃×#556	C₂²	semidirect
49. C₂₃×#497	C₂²	semidirect
51. C₂₃×#496	C₂²	semidirect
52. C₂₃×#495	C₂²	semidirect
55. C₂₃×#492	C₂²	semidirect
56. C₂₃×#464	C₂²	semidirect
57. C₂₃×#464	C₂²	semidirect
58. C₂₃×#463	C₂²	semidirect
59. C₂₃×#463	C₂²	semidirect
60. C₂₃×#463	C₂²	semidirect
61. C₂₃×#463	C₂²	semidirect
62. C₂₃×#462	C₂²	semidirect
63. C₂₃×#461	C₂²	semidirect
64. C₂₃×#461	C₂²	semidirect
65. C₂₃×#461	C₂²	semidirect
69. C₂₃×#460	C₂²	semidirect
70. C₂₃×#460	C₂²	semidirect
71. C₂₃×#459	C₂²	semidirect
72. C₂₃×#459	C₂²	semidirect
73. C₂₃×#446	C₂²	semidirect
74. C₂₃×#446	C₂²	semidirect
75. C₈×Q₈×C₂₃	C₂²	semidirect
76. C₂₃×#442	C₂²	semidirect
77. C₂₃×#441	C₂²	semidirect
78. C₂₃×#440	C₂²	semidirect
79. C₂₃×#440	C₂²	semidirect
80. C₄×Q₁₆×C₂₃	C₂²	semidirect
81. C₄×SD₁₆×C₂₃	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×D₈×C₂₃	C₂²	semidirect
276. M₁₆×C₂₃	#41	semidirect
325. #61421	C₂₃	direct (N × H)
390. #3508	C₂×C₂₃	semidirect
391. #3507	C₂×C₂₃	semidirect
392. #3401	C₂×C₂₃	semidirect
393. #3400	C₂×C₂₃	semidirect
394. #3399	C₂×C₂₃	semidirect
395. #3397	C₂×C₂₃	semidirect
396. #3396	C₂×C₂₃	semidirect
397. #3392	C₂×C₂₃	semidirect
398. #3154	C₂×C₂₃	semidirect
399. #3151	C₂×C₂₃	semidirect
400. #3045	C₂×C₂₃	semidirect
401. #3042	C₂×C₂₃	semidirect
402. #3035	C₂×C₂₃	semidirect
403. C₂×#460	C₂×C₂₃	semidirect
404. #2962	C₂×C₂₃	semidirect
405. #2946	C₂×C₂₃	semidirect
406. C₄×#137	C₂×C₂₃	semidirect
443. #559	C₂²×C₂₃	semidirect
444. #557	C₂²×C₂₃	semidirect
446. #556	C₂²×C₂₃	semidirect
467. #497	C₂²×C₂₃	semidirect
469. #496	C₂²×C₂₃	semidirect
470. #495	C₂²×C₂₃	semidirect
473. #492	C₂²×C₂₃	semidirect
474. #464	C₂²×C₂₃	semidirect
475. #464	C₂²×C₂₃	semidirect
476. #463	C₂²×C₂₃	semidirect
477. #463	C₂²×C₂₃	semidirect
478. #463	C₂²×C₂₃	semidirect
479. #463	C₂²×C₂₃	semidirect
480. #462	C₂²×C₂₃	semidirect
481. #461	C₂²×C₂₃	semidirect
482. #461	C₂²×C₂₃	semidirect
483. #461	C₂²×C₂₃	semidirect
487. #460	C₂²×C₂₃	semidirect
488. #460	C₂²×C₂₃	semidirect
489. #459	C₂²×C₂₃	semidirect
490. #459	C₂²×C₂₃	semidirect
491. #446	C₂²×C₂₃	semidirect
492. #446	C₂²×C₂₃	semidirect
493. C₈×Q₈	C₂²×C₂₃	semidirect
494. #442	C₂²×C₂₃	semidirect
495. #441	C₂²×C₂₃	semidirect
496. #440	C₂²×C₂₃	semidirect
497. #440	C₂²×C₂₃	semidirect
498. C₄×Q₁₆	C₂²×C₂₃	semidirect
499. C₄×SD₁₆	C₂²×C₂₃	semidirect
500. C₄×SD₁₆	C₂²×C₂₃	semidirect
501. C₄×D₈	C₂²×C₂₃	semidirect
643. C₂₃	#61421	direct (N × H)
702. M₁₆	#41×C₂₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3508	2
C₂₃×#3507	2
C₂₃×#3401	2
C₂₃×#3400	2
C₂₃×#3399	2
C₂₃×#3397	2
C₂₃×#3396	2
C₂₃×#3392	2
C₂₃×#3154	2
C₂₃×#3151	2
C₂₃×#3045	2
C₂₃×#3042	2
C₂₃×#3035	2
C₂×C₂₃×#460	2
C₂₃×#2962	2
C₂₃×#2946	2
C₄×C₂₃×#137	2
#61421	23

Subgroups — C23×#61421 #19209047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61421 #19209047