Subgroups — C₂₃×#61418 #19209044

Order 5888.

1854 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3401	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3400	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3398	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3154	C₂	1	1	yes	maximal, characteristic
9	C₂×C₂₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2961	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2950	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
25	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#559	C₂²	1	4	yes	—
30	C₂₃×#557	C₂²	1	4	yes	complemented
31	C₂₃×#556	C₂²	1	4	yes	—
32	C₂₃×#556	C₂²	1	4	yes	complemented
33	C₂₃×#552	—	2	4	no	—
34	C₂₃×#551	—	2	4	no	—
35	C₂₃×#542	—	2	2	no	—
36	C₂₃×#541	—	2	2	no	—
37	C₂₃×#536	C₂²	1	1	yes	characteristic
38	C₂₃×#536	C₂²	1	1	yes	characteristic
39	C₂₃×#536	C₂²	1	1	yes	characteristic
40	C₂₃×#535	C₂²	1	1	yes	characteristic
41	C₂₃×#533	—	2	2	no	—
42	C₂₃×#533	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₂₃×#529	—	2	2	no	—
45	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
46	C₂₃×#519	C₂²	1	1	yes	characteristic
47	C₂₃×#519	C₂²	1	1	yes	characteristic
48	C₂₃×#519	C₂²	1	1	yes	characteristic
49	C₂₃×#518	C₂²	1	1	yes	characteristic
50	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
51	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
52	C₂₃×#497	C₂²	1	2	yes	—
53	C₂₃×#497	C₂²	1	4	yes	—
54	C₂₃×#497	C₂²	1	4	yes	—
55	C₂₃×#497	C₂²	1	2	yes	complemented
56	C₂₃×#497	C₂²	1	2	yes	complemented
57	C₂₃×#496	C₂²	1	2	yes	—
58	C₂₃×#495	C₂²	1	2	yes	—
59	C₂₃×#495	C₂²	1	2	yes	complemented
60	C₂₃×#494	C₂²	1	2	yes	complemented
61	C₂₃×#492	C₂²	1	2	yes	—
62	C₂₃×#464	C₂²	1	4	yes	—
63	C₂₃×#464	C₂²	1	4	yes	—
64	C₂₃×#464	C₂²	1	4	yes	complemented
65	C₂₃×#464	C₂²	1	4	yes	complemented
66	C₂₃×#463	C₂²	1	4	yes	—
67	C₂₃×#463	C₂²	1	4	yes	—
68	C₂₃×#462	C₂²	1	4	yes	complemented
69	C₂₃×#462	C₂²	1	4	yes	complemented
70	C₂₃×#462	C₂²	1	4	yes	complemented
71	C₂₃×#461	C₂²	1	4	yes	—
72	C₂₃×#461	C₂²	1	4	yes	complemented
73	C₂₃×#460	C₂²	1	4	yes	—
74	C₂₃×#446	C₂²	1	4	yes	complemented
75	C₂₃×#446	C₂²	1	4	yes	complemented
76	C₂₃×#442	C₂²	1	2	yes	complemented
77	C₂₃×#441	C₂²	1	2	yes	complemented
78	C₂₃×#441	C₂²	1	4	yes	complemented
79	C₂₃×#440	C₂²	1	4	yes	—
80	C₂₃×#440	C₂²	1	2	yes	complemented
81	C₂₃×#440	C₂²	1	2	yes	complemented
82	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
84	C₂₃×#427	C₂²	1	1	yes	characteristic
85	C₂₃×#424	C₂²	1	1	yes	characteristic
86	C₂₃×#424	C₂²	1	1	yes	characteristic
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂₃×#419	C₂²	1	1	yes	characteristic
89	C₂₃×#419	C₂²	1	1	yes	characteristic
90	C₂₃×#419	C₂²	1	1	yes	characteristic
91	C₂₃×#418	C₂²	1	1	yes	characteristic
92	C₂₃×#416	C₂²	1	1	yes	characteristic
93	C₂₃×#416	C₂²	1	1	yes	characteristic
94	C₂₃×#405	C₂²	1	1	yes	characteristic
95	C₂₃×#405	C₂²	1	1	yes	characteristic
96	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
101	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
103	C₂₃×#137	—	4	2	no	—
104	C₂₃×#137	—	4	2	no	—
105	C₂₃×#137	—	4	2	no	—
106	C₂₃×AGL(1,ℤ/8)	—	4	2	no	—
107	C₂₃×#135	—	2	4	no	—
108	C₂×Q₁₆×C₂₃	—	2	4	no	—
109	C₂×Q₁₆×C₂₃	—	4	2	no	—
110	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
111	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
113	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
114	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
115	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂×SD₁₆×C₂₃	—	2	4	no	—
118	C₂×SD₁₆×C₂₃	—	4	2	no	—
119	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
120	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
121	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₂₃	C₂³	1	1	yes	characteristic
123	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂₃×C₄⋊Q₈	—	2	1	no	—
135	C₂₃×C₄⋊Q₈	—	2	1	no	—
136	C₂₃×C₄⋊Q₈	D₄	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
139	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₂₃×#127	C₂³	1	2	yes	—
142	C₂₃×#126	—	2	4	no	—
143	C₂₃×#126	—	2	4	no	—
144	C₂₃×#126	—	2	4	no	—
145	C₂₃×#126	—	2	4	no	—
146	C₂₃×#125	—	2	4	no	—
147	C₂₃×#125	—	2	4	no	—
148	C₂₃×#125	—	2	4	no	—
149	C₂₃×#125	D₄	1	2	yes	—
150	C₂₃×#124	—	2	4	no	—
151	C₂₃×#124	—	2	1	no	—
152	C₂₃×#124	—	2	1	no	—
153	C₂₃×#124	C₂³	1	2	yes	—
154	C₂₃×#124	C₂³	1	4	yes	—
155	C₂₃×#124	C₂³	1	2	yes	—
156	C₂₃×#124	C₂³	1	2	yes	—
157	C₂₃×#124	C₂³	1	2	yes	—
158	C₂₃×#123	—	2	4	no	—
159	C₂₃×#123	—	2	4	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×#123	—	2	2	no	—
162	C₂₃×#123	—	2	2	no	—
163	C₂₃×C₂²⋊Q₈	—	2	4	no	—
164	C₂₃×C₂²⋊Q₈	—	2	4	no	—
165	C₂₃×C₂²⋊Q₈	—	2	2	no	—
166	C₂₃×C₂²⋊Q₈	—	2	2	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	—
169	C₂₃×#121	—	2	2	no	—
170	C₂₃×#120	—	2	2	no	—
171	C₄×Q₈×C₂₃	—	2	4	no	—
172	C₄×Q₈×C₂₃	—	2	2	no	—
173	C₄×Q₈×C₂₃	—	2	2	no	—
174	C₄×Q₈×C₂₃	—	2	2	no	—
175	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
176	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
177	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
178	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
179	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
180	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
181	C₄×D₄×C₂₃	—	2	2	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	4	no	—
184	C₄×D₄×C₂₃	—	2	2	no	—
185	C₄×D₄×C₂₃	C₂³	1	4	yes	—
186	C₄×D₄×C₂₃	C₂³	1	2	yes	—
187	C₄×D₄×C₂₃	C₂³	1	2	yes	—
188	C₂₃×#117	—	2	4	no	—
189	C₂₃×#117	—	2	4	no	—
190	C₂₃×#117	—	2	2	no	—
191	C₂₃×#117	—	2	2	no	—
192	C₂₃×#117	—	2	2	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	C₂³	1	1	yes	characteristic
196	C₂₃×#117	C₂³	1	1	yes	characteristic
197	C₂₃×#117	C₂³	1	1	yes	characteristic
198	C₂₃×#117	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
202	C₂×C₄²×C₂₃	—	2	1	no	—
203	C₂×C₄²×C₂₃	—	2	1	no	—
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂₃×#107	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	2	yes	—
207	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
208	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
210	C₂₃×#103	C₂³	1	2	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×#102	C₂³	1	2	yes	—
216	C₂₃×#102	C₂³	1	2	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#97	C₂³	1	2	yes	—
219	C₂₃×#97	C₂³	1	2	yes	—
220	C₂₃×#97	C₂³	1	2	yes	—
221	C₂₃×#97	C₂³	1	2	yes	—
222	C₄×C₈×C₂₃	C₂³	1	2	yes	—
223	C₄×C₈×C₂₃	C₂³	1	2	yes	—
224	C₂⁴×C₂₃	—	2	1	no	—
225	#41×C₂₃	—	2	2	no	—
226	#41×C₂₃	—	2	2	no	—
227	#41×C₂₃	—	2	2	no	—
228	#41×C₂₃	—	2	2	no	—
229	C₂×Q₈×C₂₃	—	2	1	no	—
230	C₂×Q₈×C₂₃	—	2	1	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	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
239	C₂×Q₈×C₂₃	C₂⁴	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×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂×D₄×C₂₃	—	2	1	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	1	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
258	C₂²×C₄×C₂₃	—	2	1	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	4	no	—
261	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
263	Q₁₆×C₂₃	—	2	4	no	—
264	Q₁₆×C₂₃	—	2	4	no	—
265	Q₁₆×C₂₃	—	2	2	no	—
266	Q₁₆×C₂₃	—	4	4	no	—
267	Q₁₆×C₂₃	—	4	2	no	—
268	Q₁₆×C₂₃	—	4	2	no	—
269	Q₁₆×C₂₃	—	4	2	no	—
270	SD₁₆×C₂₃	—	2	4	no	—
271	SD₁₆×C₂₃	—	2	4	no	—
272	SD₁₆×C₂₃	—	2	2	no	—
273	SD₁₆×C₂₃	—	2	2	no	—
274	SD₁₆×C₂₃	—	4	4	no	—
275	SD₁₆×C₂₃	—	4	2	no	—
276	SD₁₆×C₂₃	—	4	2	no	—
277	SD₁₆×C₂₃	—	4	2	no	—
278	SD₁₆×C₂₃	—	4	2	no	—
279	D₈×C₂₃	—	2	2	no	—
280	D₈×C₂₃	—	4	2	no	—
281	M₁₆×C₂₃	—	2	2	no	—
282	M₁₆×C₂₃	—	2	2	no	—
283	C₂×C₈×C₂₃	—	2	2	no	—
284	C₂×C₈×C₂₃	#41	1	4	yes	—
285	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₄⋊C₄×C₂₃	—	2	4	no	—
291	C₄⋊C₄×C₂₃	—	2	4	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	4	no	—
295	C₄⋊C₄×C₂₃	—	2	4	no	—
296	C₄⋊C₄×C₂₃	—	2	4	no	—
297	C₄⋊C₄×C₂₃	—	2	4	no	—
298	C₄⋊C₄×C₂₃	—	2	4	no	—
299	C₄⋊C₄×C₂₃	—	2	4	no	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	1	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	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	4	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	4	no	—
318	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
319	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	—	2	1	no	—
322	C₄²×C₂₃	—	2	1	no	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	—	2	4	no	—
325	C₄²×C₂₃	—	2	4	no	—
326	C₄²×C₂₃	—	2	4	no	—
327	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₂₃	C₂⁴	1	2	yes	—
330	C₄²×C₂₃	C₂⁴	1	2	yes	—
331	C₄²×C₂₃	C₂⁴	1	2	yes	—
332	#61418	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂³×C₂₃	—	2	1	no	—
334	C₂³×C₂₃	—	2	2	no	—
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	—	4	2	no	—
337	C₂³×C₂₃	—	8	2	no	—
338	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
339	Q₈×C₂₃	—	2	2	no	—
340	Q₈×C₂₃	—	2	1	no	—
341	Q₈×C₂₃	—	2	1	no	—
342	Q₈×C₂₃	—	2	2	no	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	1	no	—
346	Q₈×C₂₃	—	2	2	no	—
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	1	no	—
349	Q₈×C₂₃	—	4	4	no	—
350	Q₈×C₂₃	—	4	2	no	—
351	Q₈×C₂₃	—	4	2	no	—
352	Q₈×C₂₃	—	4	2	no	—
353	D₄×C₂₃	—	2	1	no	—
354	D₄×C₂₃	—	2	1	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	2	1	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	1	no	—
359	D₄×C₂₃	—	4	2	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	8	4	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	4	2	no	—
371	C₂×C₄×C₂₃	—	4	4	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	2	no	—
375	C₂×C₄×C₂₃	—	4	2	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	8	2	no	—
378	C₂×C₄×C₂₃	—	8	4	no	—
379	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
380	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
381	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
385	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
386	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
387	C₈×C₂₃	—	2	2	no	—
388	C₈×C₂₃	—	2	2	no	—
389	C₈×C₂₃	—	2	2	no	—
390	C₈×C₂₃	C₂×#41	1	2	yes	—
391	C₈×C₂₃	C₂×#41	1	2	yes	—
392	#3510	C₂×C₂₃	1	1	yes	characteristic, complemented
393	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
394	#3402	C₂×C₂₃	1	4	yes	complemented
395	#3401	C₂×C₂₃	1	4	yes	complemented
396	#3400	C₂×C₂₃	1	4	yes	complemented
397	#3398	C₂×C₂₃	1	4	yes	complemented
398	#3156	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#3154	C₂×C₂₃	1	1	yes	characteristic
400	C₂×#497	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3044	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#3044	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#3043	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3042	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#3040	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#3039	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#2961	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#2950	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#2949	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#2943	C₂×C₂₃	1	1	yes	characteristic, complemented
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	2	no	—
414	C₂²×C₂₃	—	4	4	no	—
415	C₂²×C₂₃	—	4	1	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	16	2	no	—
419	C₂²×C₂₃	#550	1	2	yes	—
420	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₂₃	—	2	2	no	—
422	C₄×C₂₃	—	2	2	no	—
423	C₄×C₂₃	—	2	4	no	—
424	C₄×C₂₃	—	2	4	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	1	no	—
428	C₄×C₂₃	—	4	1	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	2	no	—
431	C₄×C₂₃	—	4	2	no	—
432	C₄×C₂₃	#550	1	2	yes	—
433	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
434	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
440	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
441	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
442	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
443	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
444	#559	C₂²×C₂₃	1	4	yes	—
445	#557	C₂²×C₂₃	1	4	yes	complemented
446	#556	C₂²×C₂₃	1	4	yes	—
447	#556	C₂²×C₂₃	1	4	yes	complemented
448	#552	—	2	4	no	—
449	#551	—	2	4	no	—
450	#542	—	2	2	no	—
451	#541	—	2	2	no	—
452	#536	C₂²×C₂₃	1	1	yes	characteristic
453	#536	C₂²×C₂₃	1	1	yes	characteristic
454	#536	C₂²×C₂₃	1	1	yes	characteristic
455	#535	C₂²×C₂₃	1	1	yes	characteristic
456	#533	—	2	2	no	—
457	#533	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
459	#529	—	2	2	no	—
460	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
461	#519	C₂²×C₂₃	1	1	yes	characteristic
462	#519	C₂²×C₂₃	1	1	yes	characteristic
463	#519	C₂²×C₂₃	1	1	yes	characteristic
464	#518	C₂²×C₂₃	1	1	yes	characteristic
465	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
466	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
467	#497	C₂²×C₂₃	1	2	yes	—
468	#497	C₂²×C₂₃	1	4	yes	—
469	#497	C₂²×C₂₃	1	4	yes	—
470	#497	C₂²×C₂₃	1	2	yes	complemented
471	#497	C₂²×C₂₃	1	2	yes	complemented
472	#496	C₂²×C₂₃	1	2	yes	—
473	#495	C₂²×C₂₃	1	2	yes	—
474	#495	C₂²×C₂₃	1	2	yes	complemented
475	#494	C₂²×C₂₃	1	2	yes	complemented
476	#492	C₂²×C₂₃	1	2	yes	—
477	#464	C₂²×C₂₃	1	4	yes	—
478	#464	C₂²×C₂₃	1	4	yes	—
479	#464	C₂²×C₂₃	1	4	yes	complemented
480	#464	C₂²×C₂₃	1	4	yes	complemented
481	#463	C₂²×C₂₃	1	4	yes	—
482	#463	C₂²×C₂₃	1	4	yes	—
483	#462	C₂²×C₂₃	1	4	yes	complemented
484	#462	C₂²×C₂₃	1	4	yes	complemented
485	#462	C₂²×C₂₃	1	4	yes	complemented
486	#461	C₂²×C₂₃	1	4	yes	—
487	#461	C₂²×C₂₃	1	4	yes	complemented
488	#460	C₂²×C₂₃	1	4	yes	—
489	#446	C₂²×C₂₃	1	4	yes	complemented
490	#446	C₂²×C₂₃	1	4	yes	complemented
491	#442	C₂²×C₂₃	1	2	yes	complemented
492	#441	C₂²×C₂₃	1	2	yes	complemented
493	#441	C₂²×C₂₃	1	4	yes	complemented
494	#440	C₂²×C₂₃	1	4	yes	—
495	#440	C₂²×C₂₃	1	2	yes	complemented
496	#440	C₂²×C₂₃	1	2	yes	complemented
497	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
498	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
499	#427	C₂²×C₂₃	1	1	yes	characteristic
500	#424	C₂²×C₂₃	1	1	yes	characteristic
501	#424	C₂²×C₂₃	1	1	yes	characteristic
502	#423	C₂²×C₂₃	1	1	yes	characteristic
503	#419	C₂²×C₂₃	1	1	yes	characteristic
504	#419	C₂²×C₂₃	1	1	yes	characteristic
505	#419	C₂²×C₂₃	1	1	yes	characteristic
506	#418	C₂²×C₂₃	1	1	yes	characteristic
507	#416	C₂²×C₂₃	1	1	yes	characteristic
508	#416	C₂²×C₂₃	1	1	yes	characteristic
509	#405	C₂²×C₂₃	1	1	yes	characteristic
510	#405	C₂²×C₂₃	1	1	yes	characteristic
511	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
512	C₂×C₂₃	—	2	2	no	—
513	C₂×C₂₃	—	8	1	no	—
514	C₂×C₂₃	—	8	1	no	—
515	C₂×C₂₃	—	8	2	no	—
516	C₂×C₂₃	C₂×#550	1	1	yes	characteristic
517	C₂×C₂₃	#3586	1	2	yes	—
518	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
520	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
521	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
522	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
523	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
524	#137	—	4	2	no	—
525	#137	—	4	2	no	—
526	#137	—	4	2	no	—
527	AGL(1,ℤ/8)	—	4	2	no	—
528	#135	—	2	4	no	—
529	C₂×Q₁₆	—	2	4	no	—
530	C₂×Q₁₆	—	4	2	no	—
531	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
532	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
533	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
534	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
535	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
536	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
537	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
538	C₂×SD₁₆	—	2	4	no	—
539	C₂×SD₁₆	—	4	2	no	—
540	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
541	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
542	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
543	C₂×SD₁₆	C₂³×C₂₃	1	1	yes	characteristic
544	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
545	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
546	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
547	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
548	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
549	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
550	C₂×D₈	C₂³×C₂₃	1	2	yes	—
551	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
553	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
554	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	—	2	1	no	—
557	C₄⋊Q₈	D₄×C₂₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
559	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
562	#127	C₂³×C₂₃	1	2	yes	—
563	#126	—	2	4	no	—
564	#126	—	2	4	no	—
565	#126	—	2	4	no	—
566	#126	—	2	4	no	—
567	#125	—	2	4	no	—
568	#125	—	2	4	no	—
569	#125	—	2	4	no	—
570	#125	D₄×C₂₃	1	2	yes	—
571	#124	—	2	4	no	—
572	#124	—	2	1	no	—
573	#124	—	2	1	no	—
574	#124	C₂³×C₂₃	1	4	yes	—
575	#124	C₂³×C₂₃	1	2	yes	—
576	#124	C₂³×C₂₃	1	2	yes	—
577	#124	C₂³×C₂₃	1	2	yes	—
578	#124	C₂³×C₂₃	1	2	yes	—
579	#123	—	2	4	no	—
580	#123	—	2	4	no	—
581	#123	—	2	2	no	—
582	#123	—	2	2	no	—
583	#123	—	2	2	no	—
584	C₂²⋊Q₈	—	2	4	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	—	2	2	no	—
588	C₂²⋊Q₈	—	2	2	no	—
589	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	—
590	#121	—	2	2	no	—
591	#120	—	2	2	no	—
592	C₄×Q₈	—	2	4	no	—
593	C₄×Q₈	—	2	2	no	—
594	C₄×Q₈	—	2	2	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
599	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
600	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
601	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	4	no	—
606	C₄×D₄	C₂³×C₂₃	1	2	yes	—
607	C₄×D₄	C₂³×C₂₃	1	2	yes	—
608	C₄×D₄	C₂³×C₂₃	1	4	yes	—
609	#117	—	2	4	no	—
610	#117	—	2	4	no	—
611	#117	—	2	2	no	—
612	#117	—	2	2	no	—
613	#117	—	2	2	no	—
614	#117	—	2	1	no	—
615	#117	—	2	1	no	—
616	#117	C₂³×C₂₃	1	1	yes	characteristic
617	#117	C₂³×C₂₃	1	1	yes	characteristic
618	#117	C₂³×C₂₃	1	1	yes	characteristic
619	#117	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	—	2	2	no	—
621	C₂×C₂²⋊C₄	—	2	2	no	—
622	C₂×C₂²⋊C₄	—	2	2	no	—
623	C₂×C₄²	—	2	1	no	—
624	C₂×C₄²	—	2	1	no	—
625	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
626	#107	C₂³×C₂₃	1	2	yes	—
627	#106	C₂³×C₂₃	1	2	yes	—
628	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
629	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
630	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
631	#103	C₂³×C₂₃	1	2	yes	—
632	#103	C₂³×C₂₃	1	2	yes	—
633	#103	C₂³×C₂₃	1	4	yes	—
634	#103	C₂³×C₂₃	1	4	yes	—
635	#103	C₂³×C₂₃	1	4	yes	—
636	#102	C₂³×C₂₃	1	2	yes	—
637	#102	C₂³×C₂₃	1	2	yes	—
638	#102	C₂³×C₂₃	1	4	yes	—
639	#97	C₂³×C₂₃	1	2	yes	—
640	#97	C₂³×C₂₃	1	2	yes	—
641	#97	C₂³×C₂₃	1	2	yes	—
642	#97	C₂³×C₂₃	1	2	yes	—
643	C₄×C₈	C₂³×C₂₃	1	2	yes	—
644	C₄×C₈	C₂³×C₂₃	1	2	yes	—
645	C₂₃	#61418	1	1	yes	characteristic, direct product factor, Sylow
646	C₂⁴	—	2	1	no	—
647	#41	—	2	2	no	—
648	#41	—	2	2	no	—
649	#41	—	2	2	no	—
650	#41	—	2	2	no	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	1	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
661	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
662	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
663	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
664	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
665	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	4	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
673	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
674	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	4	no	—
683	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
685	Q₁₆	—	2	4	no	—
686	Q₁₆	—	2	4	no	—
687	Q₁₆	—	2	2	no	—
688	Q₁₆	—	4	4	no	—
689	Q₁₆	—	4	2	no	—
690	Q₁₆	—	4	2	no	—
691	Q₁₆	—	4	2	no	—
692	SD₁₆	—	2	4	no	—
693	SD₁₆	—	2	4	no	—
694	SD₁₆	—	2	2	no	—
695	SD₁₆	—	2	2	no	—
696	SD₁₆	—	4	4	no	—
697	SD₁₆	—	4	2	no	—
698	SD₁₆	—	4	2	no	—
699	SD₁₆	—	4	2	no	—
700	SD₁₆	—	4	2	no	—
701	D₈	—	2	2	no	—
702	D₈	—	4	2	no	—
703	M₁₆	—	2	2	no	—
704	M₁₆	—	2	2	no	—
705	C₂×C₈	—	2	2	no	—
706	C₂×C₈	#41×C₂₃	1	4	yes	—
707	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
708	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
709	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
710	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
711	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	4	no	—
717	C₄⋊C₄	—	2	4	no	—
718	C₄⋊C₄	—	2	4	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
723	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
724	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
726	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
727	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
729	C₂²⋊C₄	—	2	1	no	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	4	no	—
739	C₂²⋊C₄	—	2	4	no	—
740	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
741	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	1	no	—
744	C₄²	—	2	1	no	—
745	C₄²	—	2	2	no	—
746	C₄²	—	2	4	no	—
747	C₄²	—	2	4	no	—
748	C₄²	—	2	4	no	—
749	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
751	C₄²	C₂⁴×C₂₃	1	2	yes	—
752	C₄²	C₂⁴×C₂₃	1	2	yes	—
753	C₄²	C₂⁴×C₂₃	1	2	yes	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	1	no	—
757	C₂³	—	4	2	no	—
758	C₂³	—	8	2	no	—
759	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
760	Q₈	—	2	2	no	—
761	Q₈	—	2	1	no	—
762	Q₈	—	2	1	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	1	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	2	2	no	—
769	Q₈	—	2	1	no	—
770	Q₈	—	4	4	no	—
771	Q₈	—	4	2	no	—
772	Q₈	—	4	2	no	—
773	Q₈	—	4	2	no	—
774	D₄	—	2	1	no	—
775	D₄	—	2	1	no	—
776	D₄	—	2	2	no	—
777	D₄	—	2	1	no	—
778	D₄	—	2	2	no	—
779	D₄	—	2	1	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	2	no	—
782	D₄	—	4	2	no	—
783	D₄	—	8	4	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	4	2	no	—
792	C₂×C₄	—	4	4	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	2	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	4	no	—
800	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
801	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
802	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
804	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
806	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
807	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
808	C₈	—	2	2	no	—
809	C₈	—	2	2	no	—
810	C₈	—	2	2	no	—
811	C₈	C₂×#41×C₂₃	1	2	yes	—
812	C₈	C₂×#41×C₂₃	1	2	yes	—
813	C₂²	—	2	2	no	—
814	C₂²	—	4	1	no	—
815	C₂²	—	4	1	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	4	no	—
820	C₂²	—	16	2	no	—
821	C₂²	C₂₃×#550	1	2	yes	—
822	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	4	no	—
826	C₄	—	2	4	no	—
827	C₄	—	4	1	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	C₂₃×#550	1	2	yes	—
835	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
836	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
837	C₂	—	2	2	no	—
838	C₂	—	8	2	no	—
839	C₂	—	8	1	no	—
840	C₂	—	8	1	no	—
841	C₂	C₂×C₂₃×#550	1	1	yes	characteristic
842	C₂	C₂₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3154	C₂
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×#3510	C₂	semidirect
2. C₂₃×#3509	C₂	semidirect
3. C₂₃×#3402	C₂	semidirect
4. C₂₃×#3401	C₂	semidirect
5. C₂₃×#3400	C₂	semidirect
6. C₂₃×#3398	C₂	semidirect
7. C₂₃×#3156	C₂	semidirect
9. C₂×C₂₃×#497	C₂	semidirect
10. C₂₃×#3044	C₂	semidirect
11. C₂₃×#3044	C₂	semidirect
12. C₂₃×#3043	C₂	semidirect
13. C₂₃×#3042	C₂	semidirect
14. C₂₃×#3040	C₂	semidirect
15. C₂₃×#3039	C₂	semidirect
16. C₂₃×#2961	C₂	semidirect
17. C₂₃×#2950	C₂	semidirect
18. C₂₃×#2949	C₂	semidirect
19. C₂₃×#2943	C₂	semidirect
30. C₂₃×#557	C₂²	semidirect
32. C₂₃×#556	C₂²	semidirect
55. C₂₃×#497	C₂²	semidirect
56. C₂₃×#497	C₂²	semidirect
59. C₂₃×#495	C₂²	semidirect
60. C₂₃×#494	C₂²	semidirect
64. C₂₃×#464	C₂²	semidirect
65. C₂₃×#464	C₂²	semidirect
68. C₂₃×#462	C₂²	semidirect
69. C₂₃×#462	C₂²	semidirect
70. C₂₃×#462	C₂²	semidirect
72. C₂₃×#461	C₂²	semidirect
74. C₂₃×#446	C₂²	semidirect
75. C₂₃×#446	C₂²	semidirect
76. C₂₃×#442	C₂²	semidirect
77. C₂₃×#441	C₂²	semidirect
78. C₂₃×#441	C₂²	semidirect
80. C₂₃×#440	C₂²	semidirect
81. C₂₃×#440	C₂²	semidirect
82. C₄×Q₁₆×C₂₃	C₂²	semidirect
332. #61418	C₂₃	direct (N × H)
392. #3510	C₂×C₂₃	semidirect
393. #3509	C₂×C₂₃	semidirect
394. #3402	C₂×C₂₃	semidirect
395. #3401	C₂×C₂₃	semidirect
396. #3400	C₂×C₂₃	semidirect
397. #3398	C₂×C₂₃	semidirect
398. #3156	C₂×C₂₃	semidirect
400. C₂×#497	C₂×C₂₃	semidirect
401. #3044	C₂×C₂₃	semidirect
402. #3044	C₂×C₂₃	semidirect
403. #3043	C₂×C₂₃	semidirect
404. #3042	C₂×C₂₃	semidirect
405. #3040	C₂×C₂₃	semidirect
406. #3039	C₂×C₂₃	semidirect
407. #2961	C₂×C₂₃	semidirect
408. #2950	C₂×C₂₃	semidirect
409. #2949	C₂×C₂₃	semidirect
410. #2943	C₂×C₂₃	semidirect
445. #557	C₂²×C₂₃	semidirect
447. #556	C₂²×C₂₃	semidirect
470. #497	C₂²×C₂₃	semidirect
471. #497	C₂²×C₂₃	semidirect
474. #495	C₂²×C₂₃	semidirect
475. #494	C₂²×C₂₃	semidirect
479. #464	C₂²×C₂₃	semidirect
480. #464	C₂²×C₂₃	semidirect
483. #462	C₂²×C₂₃	semidirect
484. #462	C₂²×C₂₃	semidirect
485. #462	C₂²×C₂₃	semidirect
487. #461	C₂²×C₂₃	semidirect
489. #446	C₂²×C₂₃	semidirect
490. #446	C₂²×C₂₃	semidirect
491. #442	C₂²×C₂₃	semidirect
492. #441	C₂²×C₂₃	semidirect
493. #441	C₂²×C₂₃	semidirect
495. #440	C₂²×C₂₃	semidirect
496. #440	C₂²×C₂₃	semidirect
497. C₄×Q₁₆	C₂²×C₂₃	semidirect
645. C₂₃	#61418	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×#3510	2
C₂₃×#3509	2
C₂₃×#3402	2
C₂₃×#3401	2
C₂₃×#3400	2
C₂₃×#3398	2
C₂₃×#3156	2
C₂₃×#3154	2
C₂×C₂₃×#497	2
C₂₃×#3044	2
C₂₃×#3043	2
C₂₃×#3042	2
C₂₃×#3040	2
C₂₃×#3039	2
C₂₃×#2961	2
C₂₃×#2950	2
C₂₃×#2949	2
C₂₃×#2943	2
#61418	23

Subgroups — C23×#61418 #19209044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61418 #19209044