Subgroups — C₂₃×#60313 #19207939

Order 5888.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3459	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2974	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
14	D₄×M₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
22	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
24	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#543	C₄	1	1	yes	characteristic
26	C₂₃×#539	C₄	1	1	yes	characteristic
27	C₂₃×#539	C₄	1	1	yes	characteristic
28	C₂₃×#539	C₄	1	2	yes	—
29	C₂₃×#539	C₄	1	2	yes	—
30	C₂₃×#538	C₄	1	2	yes	—
31	C₂₃×#538	C₄	1	2	yes	—
32	C₂₃×#538	C₄	1	2	yes	—
33	C₂₃×#534	C₄	1	1	yes	characteristic
34	C₂₃×#534	C₄	1	2	yes	—
35	C₂₃×#529	C₂²	1	2	yes	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#525	C₂²	1	1	yes	characteristic
39	C₂₃×#525	C₂²	1	1	yes	characteristic
40	C₂₃×#525	C₂²	1	2	yes	—
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
44	C₂₃×#446	C₂²	1	2	yes	complemented
45	C₂₃×#446	C₂²	1	2	yes	complemented
46	C₂₃×#446	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₂₃	C₂²	1	2	yes	complemented
48	C₂₃×#436	C₂²	1	2	yes	complemented
49	C₂₃×#436	C₂²	1	2	yes	complemented
50	C₂₃×#436	C₂²	1	2	yes	complemented
51	C₂₃×#436	C₂²	1	2	yes	complemented
52	C₂₃×#436	C₂²	1	2	yes	complemented
53	C₂₃×#436	C₂²	1	2	yes	complemented
54	C₂₃×#436	C₂²	1	2	yes	complemented
55	C₂₃×#436	C₂²	1	2	yes	complemented
56	C₂₃×#436	C₂²	1	2	yes	complemented
57	C₂₃×#436	C₂²	1	2	yes	complemented
58	C₂₃×#436	C₂²	1	2	yes	complemented
59	C₂₃×#435	C₂²	1	2	yes	complemented
60	C₂₃×#435	C₂²	1	2	yes	complemented
61	C₂₃×#435	C₂²	1	2	yes	complemented
62	C₂₃×#435	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	complemented
64	C₂₃×#435	C₂²	1	2	yes	complemented
65	C₂₃×#435	C₂²	1	2	yes	complemented
66	C₂₃×#435	C₂²	1	2	yes	complemented
67	C₂₃×#435	C₂²	1	2	yes	complemented
68	C₂₃×#435	C₂²	1	2	yes	complemented
69	C₂₃×#435	C₂²	1	2	yes	complemented
70	C₂₃×#435	C₂²	1	2	yes	complemented
71	C₂₃×#435	C₂²	1	2	yes	complemented
72	C₂₃×#435	C₂²	1	2	yes	complemented
73	C₂₃×#435	C₂²	1	2	yes	complemented
74	C₂₃×#435	C₂²	1	2	yes	complemented
75	C₂₃×#435	C₂²	1	2	yes	complemented
76	C₂₃×#435	C₂²	1	2	yes	complemented
77	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
78	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
81	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
82	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
83	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#433	C₂²	1	2	yes	complemented
85	C₂₃×#433	C₂²	1	2	yes	complemented
86	C₂₃×#433	C₂²	1	2	yes	complemented
87	C₂₃×#433	C₂²	1	2	yes	complemented
88	C₂₃×#433	C₂²	1	2	yes	complemented
89	C₂₃×#433	C₂²	1	2	yes	complemented
90	C₂₃×#432	C₂²	1	2	yes	complemented
91	C₂₃×#431	C₂²	1	2	yes	complemented
92	C₂₃×#431	C₂²	1	2	yes	complemented
93	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#424	C₂²	1	2	yes	complemented
96	C₂₃×#424	C₂²	1	2	yes	complemented
97	C₂₃×#423	C₂²	1	2	yes	complemented
98	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#408	C₂²	1	2	yes	complemented
102	C₂₃×#408	C₂²	1	2	yes	complemented
103	C₂₃×#407	C₂²	1	2	yes	—
104	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
105	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#407	C₂²	1	2	yes	complemented
107	C₂₃×#407	C₂²	1	2	yes	complemented
108	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
109	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#405	C₂²	1	2	yes	complemented
114	C₂₃×#405	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
120	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
123	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
124	C₂₃×#131	—	4	2	no	—
125	C₂₃×#131	—	4	2	no	—
126	C₂×M₁₆×C₂₃	—	4	2	no	—
127	C₂×M₁₆×C₂₃	—	4	4	no	—
128	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
137	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
138	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₂₃	—	4	2	no	—
141	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
144	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
145	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
146	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
147	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
149	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂₃×#126	C₂×C₄	1	2	yes	—
154	C₂₃×#126	C₂×C₄	1	2	yes	—
155	C₂₃×#126	C₂×C₄	1	2	yes	—
156	C₂₃×#126	C₂×C₄	1	2	yes	—
157	C₂₃×#126	C₂×C₄	1	2	yes	—
158	C₂₃×#126	C₂×C₄	1	2	yes	—
159	C₂₃×#125	C₂×C₄	1	2	yes	—
160	C₂₃×#125	C₂×C₄	1	2	yes	—
161	C₂₃×#125	C₂×C₄	1	2	yes	—
162	C₂₃×#124	C₂×C₄	1	2	yes	—
163	C₂₃×#124	C₂×C₄	1	2	yes	—
164	C₂₃×#124	C₂×C₄	1	2	yes	—
165	C₂₃×#123	C₂×C₄	1	2	yes	—
166	C₂₃×#123	C₂×C₄	1	2	yes	—
167	C₂₃×#123	C₂×C₄	1	2	yes	—
168	C₂₃×#123	C₂×C₄	1	2	yes	—
169	C₂₃×#123	C₂×C₄	1	2	yes	—
170	C₂₃×#123	C₂×C₄	1	2	yes	—
171	C₂₃×#123	C₂×C₄	1	2	yes	—
172	C₂₃×#123	C₂×C₄	1	2	yes	—
173	C₂₃×#123	C₂×C₄	1	2	yes	—
174	C₂₃×#123	C₂×C₄	1	2	yes	—
175	C₂₃×#123	C₂×C₄	1	2	yes	—
176	C₂₃×#123	C₂×C₄	1	2	yes	—
177	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
178	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
179	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
180	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
182	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
183	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
184	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
185	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
188	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
189	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
190	C₂₃×#121	C₂×C₄	1	2	yes	—
191	C₂₃×#121	C₂×C₄	1	2	yes	—
192	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
193	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
194	C₂₃×#121	C₂×C₄	1	2	yes	—
195	C₂₃×#121	C₂×C₄	1	2	yes	—
196	C₂₃×#121	C₂×C₄	1	2	yes	—
197	C₂₃×#121	C₂×C₄	1	2	yes	—
198	C₂₃×#121	C₂×C₄	1	2	yes	—
199	C₂₃×#120	C₂×C₄	1	2	yes	—
200	C₂₃×#120	C₂×C₄	1	2	yes	—
201	C₂₃×#120	C₂×C₄	1	2	yes	—
202	C₂₃×#120	C₂×C₄	1	2	yes	—
203	C₂₃×#120	C₂×C₄	1	2	yes	—
204	C₂₃×#120	C₂×C₄	1	2	yes	—
205	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
206	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
207	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
208	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
209	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
210	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
211	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
212	C₄×D₄×C₂₃	C₂³	1	2	yes	—
213	C₄×D₄×C₂₃	C₂³	1	2	yes	—
214	C₄×D₄×C₂₃	C₂³	1	2	yes	—
215	C₄×D₄×C₂₃	C₂³	1	2	yes	—
216	C₄×D₄×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	C₂³	1	2	yes	—
218	C₄×D₄×C₂₃	C₂³	1	2	yes	—
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	C₂³	1	2	yes	—
221	C₂₃×#117	C₂³	1	1	yes	characteristic
222	C₂₃×#117	C₂³	1	1	yes	characteristic
223	C₂₃×#117	C₂³	1	2	yes	—
224	C₂₃×#117	C₂³	1	2	yes	—
225	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
227	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
228	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
229	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
230	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
231	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
233	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
240	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
241	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
242	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
243	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₂₃×#97	C₂³	1	2	yes	—
264	C₂₃×#97	C₂³	1	2	yes	—
265	C₂₃×#97	C₂³	1	2	yes	—
266	C₂₃×#97	C₂³	1	2	yes	—
267	C₂₃×#97	C₂³	1	2	yes	—
268	C₂₃×#97	C₂³	1	2	yes	—
269	C₄×C₈×C₂₃	C₂³	1	2	yes	—
270	C₄×C₈×C₂₃	C₂³	1	2	yes	—
271	C₄×C₈×C₂₃	C₂³	1	2	yes	—
272	C₄×C₈×C₂₃	C₂³	1	2	yes	—
273	C₄×C₈×C₂₃	C₂³	1	2	yes	—
274	C₄×C₈×C₂₃	C₂³	1	2	yes	—
275	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
277	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
278	#41×C₂₃	—	4	1	no	—
279	#41×C₂₃	—	4	1	no	—
280	#41×C₂₃	—	4	1	no	—
281	#41×C₂₃	—	4	1	no	—
282	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
283	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
284	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
285	C₂×D₄×C₂₃	—	4	2	no	—
286	C₂×D₄×C₂₃	—	4	4	no	—
287	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
289	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
291	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
292	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
297	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
298	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
299	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
300	C₂²×C₄×C₂₃	—	4	1	no	—
301	C₂²×C₄×C₂₃	—	4	1	no	—
302	C₂²×C₄×C₂₃	—	4	2	no	—
303	C₂²×C₄×C₂₃	—	4	1	no	—
304	C₂²×C₄×C₂₃	—	4	1	no	—
305	C₂²×C₄×C₂₃	—	4	2	no	—
306	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
311	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
317	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
320	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
324	M₁₆×C₂₃	—	2	4	no	—
325	M₁₆×C₂₃	—	2	4	no	—
326	M₁₆×C₂₃	—	4	2	no	—
327	M₁₆×C₂₃	—	4	2	no	—
328	M₁₆×C₂₃	—	4	2	no	—
329	M₁₆×C₂₃	—	4	2	no	—
330	M₁₆×C₂₃	—	4	1	no	—
331	M₁₆×C₂₃	—	4	2	no	—
332	M₁₆×C₂₃	—	4	1	no	—
333	M₁₆×C₂₃	—	4	2	no	—
334	M₁₆×C₂₃	—	4	1	no	—
335	M₁₆×C₂₃	—	4	1	no	—
336	C₂×C₈×C₂₃	—	2	2	no	—
337	C₂×C₈×C₂₃	—	2	2	no	—
338	C₂×C₈×C₂₃	—	2	2	no	—
339	C₂×C₈×C₂₃	—	2	4	no	—
340	C₂×C₈×C₂₃	—	4	1	no	—
341	C₂×C₈×C₂₃	—	4	1	no	—
342	C₂×C₈×C₂₃	—	4	1	no	—
343	C₂×C₈×C₂₃	—	4	1	no	—
344	C₂×C₈×C₂₃	—	4	2	no	—
345	C₂×C₈×C₂₃	—	4	1	no	—
346	C₂×C₈×C₂₃	—	4	2	no	—
347	C₂×C₈×C₂₃	—	4	2	no	—
348	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
352	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
353	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
354	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
357	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
362	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
364	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
365	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
366	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
368	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
369	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
371	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
372	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
375	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
376	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
377	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
393	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
394	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
395	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
396	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
397	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
398	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
399	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
400	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
401	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
402	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
403	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
404	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
405	C₄²×C₂₃	C₂⁴	1	2	yes	—
406	C₄²×C₂₃	C₂⁴	1	2	yes	—
407	C₄²×C₂₃	C₂⁴	1	2	yes	—
408	#60313	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
409	C₂³×C₂₃	—	2	2	no	—
410	C₂³×C₂₃	—	2	2	no	—
411	C₂³×C₂₃	—	4	1	no	—
412	C₂³×C₂₃	—	4	1	no	—
413	C₂³×C₂₃	—	4	1	no	—
414	C₂³×C₂₃	—	4	2	no	—
415	C₂³×C₂₃	—	4	2	no	—
416	C₂³×C₂₃	—	4	1	no	—
417	C₂³×C₂₃	—	4	2	no	—
418	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
419	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
420	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
421	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
422	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
423	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
424	Q₈×C₂₃	—	4	2	no	—
425	Q₈×C₂₃	—	4	1	no	—
426	Q₈×C₂₃	—	4	1	no	—
427	D₄×C₂₃	—	2	4	no	—
428	D₄×C₂₃	—	2	4	no	—
429	D₄×C₂₃	—	4	2	no	—
430	D₄×C₂₃	—	4	2	no	—
431	D₄×C₂₃	—	4	2	no	—
432	D₄×C₂₃	—	4	2	no	—
433	D₄×C₂₃	—	4	2	no	—
434	D₄×C₂₃	—	4	2	no	—
435	D₄×C₂₃	—	4	2	no	—
436	D₄×C₂₃	—	4	2	no	—
437	D₄×C₂₃	—	4	1	no	—
438	D₄×C₂₃	—	4	1	no	—
439	D₄×C₂₃	—	4	2	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	1	no	—
442	C₂×C₄×C₂₃	—	2	1	no	—
443	C₂×C₄×C₂₃	—	2	1	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	2	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	2	no	—
450	C₂×C₄×C₂₃	—	2	1	no	—
451	C₂×C₄×C₂₃	—	2	1	no	—
452	C₂×C₄×C₂₃	—	2	2	no	—
453	C₂×C₄×C₂₃	—	4	1	no	—
454	C₂×C₄×C₂₃	—	4	2	no	—
455	C₂×C₄×C₂₃	—	4	1	no	—
456	C₂×C₄×C₂₃	—	4	1	no	—
457	C₂×C₄×C₂₃	—	4	2	no	—
458	C₂×C₄×C₂₃	—	4	2	no	—
459	C₂×C₄×C₂₃	—	4	1	no	—
460	C₂×C₄×C₂₃	—	4	2	no	—
461	C₂×C₄×C₂₃	—	4	1	no	—
462	C₂×C₄×C₂₃	—	4	2	no	—
463	C₂×C₄×C₂₃	—	4	2	no	—
464	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
465	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
468	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
469	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
471	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
472	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
473	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
474	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
475	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
476	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
477	C₈×C₂₃	—	2	1	no	—
478	C₈×C₂₃	—	2	1	no	—
479	C₈×C₂₃	—	2	1	no	—
480	C₈×C₂₃	—	2	2	no	—
481	C₈×C₂₃	—	2	2	no	—
482	C₈×C₂₃	—	2	2	no	—
483	C₈×C₂₃	—	2	2	no	—
484	C₈×C₂₃	—	2	2	no	—
485	C₈×C₂₃	—	2	2	no	—
486	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
487	#3459	C₂×C₂₃	1	1	yes	characteristic
488	#2995	C₂×C₂₃	1	2	yes	complemented
489	#2994	C₂×C₂₃	1	2	yes	complemented
490	#2993	C₂×C₂₃	1	2	yes	complemented
491	#2978	C₂×C₂₃	1	2	yes	complemented
492	#2976	C₂×C₂₃	1	1	yes	characteristic, complemented
493	#2976	C₂×C₂₃	1	1	yes	characteristic, complemented
494	#2976	C₂×C₂₃	1	2	yes	complemented
495	#2975	C₂×C₂₃	1	1	yes	characteristic, complemented
496	#2974	C₂×C₂₃	1	2	yes	complemented
497	#2969	C₂×C₂₃	1	2	yes	complemented
498	#2968	C₂×C₂₃	1	2	yes	complemented
499	#2967	C₂×C₂₃	1	2	yes	complemented
500	D₄×M₁₆	C₂×C₂₃	1	2	yes	complemented
501	#2933	C₂×C₂₃	1	2	yes	complemented
502	#2930	C₂×C₂₃	1	2	yes	complemented
503	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
504	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
505	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
506	C₂²×C₂₃	—	2	1	no	—
507	C₂²×C₂₃	—	2	1	no	—
508	C₂²×C₂₃	—	2	2	no	—
509	C₂²×C₂₃	—	2	1	no	—
510	C₂²×C₂₃	—	2	1	no	—
511	C₂²×C₂₃	—	2	2	no	—
512	C₂²×C₂₃	—	2	2	no	—
513	C₂²×C₂₃	—	2	2	no	—
514	C₂²×C₂₃	—	2	2	no	—
515	C₂²×C₂₃	—	2	2	no	—
516	C₂²×C₂₃	—	2	1	no	—
517	C₂²×C₂₃	—	2	1	no	—
518	C₂²×C₂₃	—	2	2	no	—
519	C₂²×C₂₃	—	2	1	no	—
520	C₂²×C₂₃	—	2	1	no	—
521	C₂²×C₂₃	—	2	2	no	—
522	C₂²×C₂₃	—	2	2	no	—
523	C₂²×C₂₃	—	4	4	no	—
524	C₂²×C₂₃	—	8	2	no	—
525	C₂²×C₂₃	—	8	4	no	—
526	C₂²×C₂₃	#568	1	2	yes	—
527	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
528	C₄×C₂₃	—	2	1	no	—
529	C₄×C₂₃	—	2	2	no	—
530	C₄×C₂₃	—	2	1	no	—
531	C₄×C₂₃	—	2	1	no	—
532	C₄×C₂₃	—	2	2	no	—
533	C₄×C₂₃	—	2	2	no	—
534	C₄×C₂₃	—	2	2	no	—
535	C₄×C₂₃	—	2	2	no	—
536	C₄×C₂₃	—	2	2	no	—
537	C₄×C₂₃	—	2	2	no	—
538	C₄×C₂₃	—	2	2	no	—
539	C₄×C₂₃	—	2	2	no	—
540	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₄×C₂₃	#585	1	1	yes	characteristic
542	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
543	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
544	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
545	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
546	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
547	#543	C₄×C₂₃	1	1	yes	characteristic
548	#539	C₄×C₂₃	1	1	yes	characteristic
549	#539	C₄×C₂₃	1	1	yes	characteristic
550	#539	C₄×C₂₃	1	2	yes	—
551	#539	C₄×C₂₃	1	2	yes	—
552	#538	C₄×C₂₃	1	2	yes	—
553	#538	C₄×C₂₃	1	2	yes	—
554	#538	C₄×C₂₃	1	2	yes	—
555	#534	C₄×C₂₃	1	1	yes	characteristic
556	#534	C₄×C₂₃	1	2	yes	—
557	#529	C₂²×C₂₃	1	2	yes	—
558	#529	C₂²×C₂₃	1	2	yes	—
559	#529	C₂²×C₂₃	1	2	yes	—
560	#525	C₂²×C₂₃	1	1	yes	characteristic
561	#525	C₂²×C₂₃	1	1	yes	characteristic
562	#525	C₂²×C₂₃	1	2	yes	—
563	#525	C₂²×C₂₃	1	2	yes	—
564	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
566	#446	C₂²×C₂₃	1	2	yes	complemented
567	#446	C₂²×C₂₃	1	2	yes	complemented
568	#446	C₂²×C₂₃	1	2	yes	complemented
569	C₈×Q₈	C₂²×C₂₃	1	2	yes	complemented
570	#436	C₂²×C₂₃	1	2	yes	complemented
571	#436	C₂²×C₂₃	1	2	yes	complemented
572	#436	C₂²×C₂₃	1	2	yes	complemented
573	#436	C₂²×C₂₃	1	2	yes	complemented
574	#436	C₂²×C₂₃	1	2	yes	complemented
575	#436	C₂²×C₂₃	1	2	yes	complemented
576	#436	C₂²×C₂₃	1	2	yes	complemented
577	#436	C₂²×C₂₃	1	2	yes	complemented
578	#436	C₂²×C₂₃	1	2	yes	complemented
579	#436	C₂²×C₂₃	1	2	yes	complemented
580	#436	C₂²×C₂₃	1	2	yes	complemented
581	#435	C₂²×C₂₃	1	2	yes	complemented
582	#435	C₂²×C₂₃	1	2	yes	complemented
583	#435	C₂²×C₂₃	1	2	yes	complemented
584	#435	C₂²×C₂₃	1	2	yes	complemented
585	#435	C₂²×C₂₃	1	2	yes	complemented
586	#435	C₂²×C₂₃	1	2	yes	complemented
587	#435	C₂²×C₂₃	1	2	yes	complemented
588	#435	C₂²×C₂₃	1	2	yes	complemented
589	#435	C₂²×C₂₃	1	2	yes	complemented
590	#435	C₂²×C₂₃	1	2	yes	complemented
591	#435	C₂²×C₂₃	1	2	yes	complemented
592	#435	C₂²×C₂₃	1	2	yes	complemented
593	#435	C₂²×C₂₃	1	2	yes	complemented
594	#435	C₂²×C₂₃	1	2	yes	complemented
595	#435	C₂²×C₂₃	1	2	yes	complemented
596	#435	C₂²×C₂₃	1	2	yes	complemented
597	#435	C₂²×C₂₃	1	2	yes	complemented
598	#435	C₂²×C₂₃	1	2	yes	complemented
599	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
600	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
601	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
602	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
603	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
604	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
605	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
606	#433	C₂²×C₂₃	1	2	yes	complemented
607	#433	C₂²×C₂₃	1	2	yes	complemented
608	#433	C₂²×C₂₃	1	2	yes	complemented
609	#433	C₂²×C₂₃	1	2	yes	complemented
610	#433	C₂²×C₂₃	1	2	yes	complemented
611	#433	C₂²×C₂₃	1	2	yes	complemented
612	#432	C₂²×C₂₃	1	2	yes	complemented
613	#431	C₂²×C₂₃	1	2	yes	complemented
614	#431	C₂²×C₂₃	1	2	yes	complemented
615	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
616	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
617	#424	C₂²×C₂₃	1	2	yes	complemented
618	#424	C₂²×C₂₃	1	2	yes	complemented
619	#423	C₂²×C₂₃	1	2	yes	complemented
620	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
623	#408	C₂²×C₂₃	1	2	yes	complemented
624	#408	C₂²×C₂₃	1	2	yes	complemented
625	#407	C₂²×C₂₃	1	2	yes	—
626	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
628	#407	C₂²×C₂₃	1	2	yes	complemented
629	#407	C₂²×C₂₃	1	2	yes	complemented
630	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
631	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
633	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
634	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	#405	C₂²×C₂₃	1	2	yes	complemented
636	#405	C₂²×C₂₃	1	2	yes	complemented
637	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
638	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
639	C₂×C₂₃	—	2	2	no	—
640	C₂×C₂₃	—	4	1	no	—
641	C₂×C₂₃	—	4	1	no	—
642	C₂×C₂₃	—	4	2	no	—
643	C₂×C₂₃	—	4	2	no	—
644	C₂×C₂₃	—	4	2	no	—
645	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
646	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
647	C₂×C₂₃	#3573	1	1	yes	characteristic
648	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
650	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
651	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
652	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
655	#131	—	4	2	no	—
656	#131	—	4	2	no	—
657	C₂×M₁₆	—	4	2	no	—
658	C₂×M₁₆	—	4	4	no	—
659	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
660	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
661	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
662	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
663	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
664	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
665	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
666	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
667	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
668	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
669	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
670	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
671	C₂²×C₈	—	4	2	no	—
672	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
673	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
674	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
676	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
678	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
679	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
680	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
681	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
682	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
683	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
684	#126	C₂×C₄×C₂₃	1	2	yes	—
685	#126	C₂×C₄×C₂₃	1	2	yes	—
686	#126	C₂×C₄×C₂₃	1	2	yes	—
687	#126	C₂×C₄×C₂₃	1	2	yes	—
688	#126	C₂×C₄×C₂₃	1	2	yes	—
689	#126	C₂×C₄×C₂₃	1	2	yes	—
690	#125	C₂×C₄×C₂₃	1	2	yes	—
691	#125	C₂×C₄×C₂₃	1	2	yes	—
692	#125	C₂×C₄×C₂₃	1	2	yes	—
693	#124	C₂×C₄×C₂₃	1	2	yes	—
694	#124	C₂×C₄×C₂₃	1	2	yes	—
695	#124	C₂×C₄×C₂₃	1	2	yes	—
696	#123	C₂×C₄×C₂₃	1	2	yes	—
697	#123	C₂×C₄×C₂₃	1	2	yes	—
698	#123	C₂×C₄×C₂₃	1	2	yes	—
699	#123	C₂×C₄×C₂₃	1	2	yes	—
700	#123	C₂×C₄×C₂₃	1	2	yes	—
701	#123	C₂×C₄×C₂₃	1	2	yes	—
702	#123	C₂×C₄×C₂₃	1	2	yes	—
703	#123	C₂×C₄×C₂₃	1	2	yes	—
704	#123	C₂×C₄×C₂₃	1	2	yes	—
705	#123	C₂×C₄×C₂₃	1	2	yes	—
706	#123	C₂×C₄×C₂₃	1	2	yes	—
707	#123	C₂×C₄×C₂₃	1	2	yes	—
708	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
709	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
710	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
711	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
712	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
713	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
714	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
715	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
716	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
717	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
718	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
719	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
720	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
721	#121	C₂×C₄×C₂₃	1	2	yes	—
722	#121	C₂×C₄×C₂₃	1	2	yes	—
723	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
724	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
725	#121	C₂×C₄×C₂₃	1	2	yes	—
726	#121	C₂×C₄×C₂₃	1	2	yes	—
727	#121	C₂×C₄×C₂₃	1	2	yes	—
728	#121	C₂×C₄×C₂₃	1	2	yes	—
729	#121	C₂×C₄×C₂₃	1	2	yes	—
730	#120	C₂×C₄×C₂₃	1	2	yes	—
731	#120	C₂×C₄×C₂₃	1	2	yes	—
732	#120	C₂×C₄×C₂₃	1	2	yes	—
733	#120	C₂×C₄×C₂₃	1	2	yes	—
734	#120	C₂×C₄×C₂₃	1	2	yes	—
735	#120	C₂×C₄×C₂₃	1	2	yes	—
736	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
737	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
738	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
739	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
740	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
741	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
742	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
743	C₄×D₄	C₂³×C₂₃	1	2	yes	—
744	C₄×D₄	C₂³×C₂₃	1	2	yes	—
745	C₄×D₄	C₂³×C₂₃	1	2	yes	—
746	C₄×D₄	C₂³×C₂₃	1	2	yes	—
747	C₄×D₄	C₂³×C₂₃	1	2	yes	—
748	C₄×D₄	C₂³×C₂₃	1	2	yes	—
749	C₄×D₄	C₂³×C₂₃	1	2	yes	—
750	C₄×D₄	C₂³×C₂₃	1	2	yes	—
751	C₄×D₄	C₂³×C₂₃	1	2	yes	—
752	#117	C₂³×C₂₃	1	1	yes	characteristic
753	#117	C₂³×C₂₃	1	1	yes	characteristic
754	#117	C₂³×C₂₃	1	2	yes	—
755	#117	C₂³×C₂₃	1	2	yes	—
756	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
757	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
759	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
761	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
762	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
763	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
764	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
765	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
766	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
767	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
768	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
769	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
770	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
771	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
772	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
773	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
774	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
775	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
779	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
783	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
784	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
785	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
786	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
787	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
788	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
789	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
793	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
794	#97	C₂³×C₂₃	1	2	yes	—
795	#97	C₂³×C₂₃	1	2	yes	—
796	#97	C₂³×C₂₃	1	2	yes	—
797	#97	C₂³×C₂₃	1	2	yes	—
798	#97	C₂³×C₂₃	1	2	yes	—
799	#97	C₂³×C₂₃	1	2	yes	—
800	C₄×C₈	C₂³×C₂₃	1	2	yes	—
801	C₄×C₈	C₂³×C₂₃	1	2	yes	—
802	C₄×C₈	C₂³×C₂₃	1	2	yes	—
803	C₄×C₈	C₂³×C₂₃	1	2	yes	—
804	C₄×C₈	C₂³×C₂₃	1	2	yes	—
805	C₄×C₈	C₂³×C₂₃	1	2	yes	—
806	C₂₃	#60313	1	1	yes	characteristic, direct product factor, Sylow
807	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
808	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
809	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
810	#41	—	4	1	no	—
811	#41	—	4	1	no	—
812	#41	—	4	1	no	—
813	#41	—	4	1	no	—
814	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
815	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
816	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
817	C₂×D₄	—	4	2	no	—
818	C₂×D₄	—	4	4	no	—
819	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
820	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
821	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
822	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
823	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
824	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
825	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
826	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
827	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
828	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
829	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
830	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
831	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
832	C₂²×C₄	—	4	1	no	—
833	C₂²×C₄	—	4	1	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	—	4	1	no	—
836	C₂²×C₄	—	4	1	no	—
837	C₂²×C₄	—	4	2	no	—
838	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
839	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
840	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
841	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
842	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
843	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
844	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
845	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
846	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
847	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
848	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
849	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
852	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
854	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
856	M₁₆	—	2	4	no	—
857	M₁₆	—	2	4	no	—
858	M₁₆	—	4	2	no	—
859	M₁₆	—	4	2	no	—
860	M₁₆	—	4	2	no	—
861	M₁₆	—	4	2	no	—
862	M₁₆	—	4	1	no	—
863	M₁₆	—	4	1	no	—
864	M₁₆	—	4	2	no	—
865	M₁₆	—	4	1	no	—
866	M₁₆	—	4	2	no	—
867	M₁₆	—	4	1	no	—
868	C₂×C₈	—	2	2	no	—
869	C₂×C₈	—	2	2	no	—
870	C₂×C₈	—	2	2	no	—
871	C₂×C₈	—	2	4	no	—
872	C₂×C₈	—	4	1	no	—
873	C₂×C₈	—	4	1	no	—
874	C₂×C₈	—	4	1	no	—
875	C₂×C₈	—	4	1	no	—
876	C₂×C₈	—	4	2	no	—
877	C₂×C₈	—	4	2	no	—
878	C₂×C₈	—	4	1	no	—
879	C₂×C₈	—	4	2	no	—
880	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
881	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
882	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
883	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
884	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
885	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
886	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
887	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
888	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
889	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
890	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
891	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
892	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
893	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
894	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
895	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
896	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
897	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
898	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
899	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
900	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
901	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
902	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
903	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
904	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
905	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
906	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
907	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
908	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
909	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
912	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
913	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
914	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
915	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
916	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
917	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
918	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
919	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
920	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
921	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
922	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
923	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
924	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
925	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
926	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
927	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
928	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
929	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
930	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
931	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
932	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
933	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
934	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
935	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
936	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
937	C₄²	C₂⁴×C₂₃	1	2	yes	—
938	C₄²	C₂⁴×C₂₃	1	2	yes	—
939	C₄²	C₂⁴×C₂₃	1	2	yes	—
940	C₂³	—	2	2	no	—
941	C₂³	—	2	2	no	—
942	C₂³	—	4	1	no	—
943	C₂³	—	4	1	no	—
944	C₂³	—	4	1	no	—
945	C₂³	—	4	2	no	—
946	C₂³	—	4	2	no	—
947	C₂³	—	4	1	no	—
948	C₂³	—	4	2	no	—
949	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
950	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
951	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
952	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
953	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
954	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
955	Q₈	—	4	1	no	—
956	Q₈	—	4	1	no	—
957	Q₈	—	4	2	no	—
958	D₄	—	2	4	no	—
959	D₄	—	2	4	no	—
960	D₄	—	4	2	no	—
961	D₄	—	4	2	no	—
962	D₄	—	4	2	no	—
963	D₄	—	4	2	no	—
964	D₄	—	4	2	no	—
965	D₄	—	4	1	no	—
966	D₄	—	4	1	no	—
967	D₄	—	4	2	no	—
968	D₄	—	4	2	no	—
969	D₄	—	4	2	no	—
970	D₄	—	4	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	4	1	no	—
985	C₂×C₄	—	4	2	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	2	no	—
989	C₂×C₄	—	4	2	no	—
990	C₂×C₄	—	4	1	no	—
991	C₂×C₄	—	4	2	no	—
992	C₂×C₄	—	4	2	no	—
993	C₂×C₄	—	4	1	no	—
994	C₂×C₄	—	4	2	no	—
995	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
996	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1001	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1002	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1003	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1004	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1005	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1006	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1007	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1008	C₈	—	2	1	no	—
1009	C₈	—	2	1	no	—
1010	C₈	—	2	1	no	—
1011	C₈	—	2	2	no	—
1012	C₈	—	2	2	no	—
1013	C₈	—	2	2	no	—
1014	C₈	—	2	2	no	—
1015	C₈	—	2	2	no	—
1016	C₈	—	2	2	no	—
1017	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1018	C₂²	—	2	1	no	—
1019	C₂²	—	2	1	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	1	no	—
1022	C₂²	—	2	1	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	2	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	2	no	—
1034	C₂²	—	2	2	no	—
1035	C₂²	—	4	4	no	—
1036	C₂²	—	8	2	no	—
1037	C₂²	—	8	4	no	—
1038	C₂²	C₂₃×#568	1	2	yes	—
1039	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1040	C₄	—	2	1	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	2	2	no	—
1052	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1053	C₄	C₂₃×#585	1	1	yes	characteristic
1054	C₂	—	2	2	no	—
1055	C₂	—	4	1	no	—
1056	C₂	—	4	1	no	—
1057	C₂	—	4	2	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1061	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1062	C₂	C₂₃×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3459	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2978	C₂	semidirect
6. C₂₃×#2976	C₂	semidirect
7. C₂₃×#2976	C₂	semidirect
8. C₂₃×#2976	C₂	semidirect
9. C₂₃×#2975	C₂	semidirect
10. C₂₃×#2974	C₂	semidirect
11. C₂₃×#2969	C₂	semidirect
12. C₂₃×#2968	C₂	semidirect
13. C₂₃×#2967	C₂	semidirect
14. D₄×M₁₆×C₂₃	C₂	semidirect
15. C₂₃×#2933	C₂	semidirect
16. C₂₃×#2930	C₂	semidirect
17. C₂₃×#2929	C₂	semidirect
18. C₂₃×#2929	C₂	semidirect
19. C₂×C₂₃×#435	C₂	semidirect
20. C₂×C₂₃×#131	C₂²	semidirect
21. C₂×C₂₃×#131	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
24. C₂³×C₈×C₂₃	C₂²	semidirect
44. C₂₃×#446	C₂²	semidirect
45. C₂₃×#446	C₂²	semidirect
46. C₂₃×#446	C₂²	semidirect
47. C₈×Q₈×C₂₃	C₂²	semidirect
48. C₂₃×#436	C₂²	semidirect
49. C₂₃×#436	C₂²	semidirect
50. C₂₃×#436	C₂²	semidirect
51. C₂₃×#436	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
53. C₂₃×#436	C₂²	semidirect
54. C₂₃×#436	C₂²	semidirect
55. C₂₃×#436	C₂²	semidirect
56. C₂₃×#436	C₂²	semidirect
57. C₂₃×#436	C₂²	semidirect
58. C₂₃×#436	C₂²	semidirect
59. C₂₃×#435	C₂²	semidirect
60. C₂₃×#435	C₂²	semidirect
61. C₂₃×#435	C₂²	semidirect
62. C₂₃×#435	C₂²	semidirect
63. C₂₃×#435	C₂²	semidirect
64. C₂₃×#435	C₂²	semidirect
65. C₂₃×#435	C₂²	semidirect
66. C₂₃×#435	C₂²	semidirect
67. C₂₃×#435	C₂²	semidirect
68. C₂₃×#435	C₂²	semidirect
69. C₂₃×#435	C₂²	semidirect
70. C₂₃×#435	C₂²	semidirect
71. C₂₃×#435	C₂²	semidirect
72. C₂₃×#435	C₂²	semidirect
73. C₂₃×#435	C₂²	semidirect
74. C₂₃×#435	C₂²	semidirect
75. C₂₃×#435	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₈×D₄×C₂₃	C₂²	semidirect
78. C₈×D₄×C₂₃	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₈×D₄×C₂₃	C₂²	semidirect
81. C₈×D₄×C₂₃	C₂²	semidirect
82. C₈×D₄×C₂₃	C₂²	semidirect
83. C₈×D₄×C₂₃	C₂²	semidirect
84. C₂₃×#433	C₂²	semidirect
85. C₂₃×#433	C₂²	semidirect
86. C₂₃×#433	C₂²	semidirect
87. C₂₃×#433	C₂²	semidirect
88. C₂₃×#433	C₂²	semidirect
89. C₂₃×#433	C₂²	semidirect
90. C₂₃×#432	C₂²	semidirect
91. C₂₃×#431	C₂²	semidirect
92. C₂₃×#431	C₂²	semidirect
93. C₂₃×#424	C₂²	semidirect
94. C₂₃×#424	C₂²	semidirect
95. C₂₃×#424	C₂²	semidirect
96. C₂₃×#424	C₂²	semidirect
97. C₂₃×#423	C₂²	semidirect
98. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
99. C₂₃×#408	C₂²	semidirect
100. C₂₃×#408	C₂²	semidirect
101. C₂₃×#408	C₂²	semidirect
102. C₂₃×#408	C₂²	semidirect
104. C₂₃×#407	C₂²	semidirect
105. C₂₃×#407	C₂²	semidirect
106. C₂₃×#407	C₂²	semidirect
107. C₂₃×#407	C₂²	semidirect
109. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
110. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
111. C₂₃×#405	C₂²	semidirect
112. C₂₃×#405	C₂²	semidirect
113. C₂₃×#405	C₂²	semidirect
114. C₂₃×#405	C₂²	semidirect
115. C₄×M₁₆×C₂₃	C₂²	semidirect
116. C₂×C₂₃×#97	C₂²	semidirect
408. #60313	C₂₃	direct (N × H)
488. #2995	C₂×C₂₃	semidirect
489. #2994	C₂×C₂₃	semidirect
490. #2993	C₂×C₂₃	semidirect
491. #2978	C₂×C₂₃	semidirect
492. #2976	C₂×C₂₃	semidirect
493. #2976	C₂×C₂₃	semidirect
494. #2976	C₂×C₂₃	semidirect
495. #2975	C₂×C₂₃	semidirect
496. #2974	C₂×C₂₃	semidirect
497. #2969	C₂×C₂₃	semidirect
498. #2968	C₂×C₂₃	semidirect
499. #2967	C₂×C₂₃	semidirect
500. D₄×M₁₆	C₂×C₂₃	semidirect
501. #2933	C₂×C₂₃	semidirect
502. #2930	C₂×C₂₃	semidirect
503. #2929	C₂×C₂₃	semidirect
504. #2929	C₂×C₂₃	semidirect
505. C₂×#435	C₂×C₂₃	semidirect
542. C₂×#131	C₂²×C₂₃	semidirect
543. C₂×#131	C₂²×C₂₃	semidirect
545. C₂²×M₁₆	C₂²×C₂₃	semidirect
546. C₂³×C₈	C₂²×C₂₃	semidirect
566. #446	C₂²×C₂₃	semidirect
567. #446	C₂²×C₂₃	semidirect
568. #446	C₂²×C₂₃	semidirect
569. C₈×Q₈	C₂²×C₂₃	semidirect
570. #436	C₂²×C₂₃	semidirect
571. #436	C₂²×C₂₃	semidirect
572. #436	C₂²×C₂₃	semidirect
573. #436	C₂²×C₂₃	semidirect
574. #436	C₂²×C₂₃	semidirect
575. #436	C₂²×C₂₃	semidirect
576. #436	C₂²×C₂₃	semidirect
577. #436	C₂²×C₂₃	semidirect
578. #436	C₂²×C₂₃	semidirect
579. #436	C₂²×C₂₃	semidirect
580. #436	C₂²×C₂₃	semidirect
581. #435	C₂²×C₂₃	semidirect
582. #435	C₂²×C₂₃	semidirect
583. #435	C₂²×C₂₃	semidirect
584. #435	C₂²×C₂₃	semidirect
585. #435	C₂²×C₂₃	semidirect
586. #435	C₂²×C₂₃	semidirect
587. #435	C₂²×C₂₃	semidirect
588. #435	C₂²×C₂₃	semidirect
589. #435	C₂²×C₂₃	semidirect
590. #435	C₂²×C₂₃	semidirect
591. #435	C₂²×C₂₃	semidirect
592. #435	C₂²×C₂₃	semidirect
593. #435	C₂²×C₂₃	semidirect
594. #435	C₂²×C₂₃	semidirect
595. #435	C₂²×C₂₃	semidirect
596. #435	C₂²×C₂₃	semidirect
597. #435	C₂²×C₂₃	semidirect
598. #435	C₂²×C₂₃	semidirect
599. C₈×D₄	C₂²×C₂₃	semidirect
600. C₈×D₄	C₂²×C₂₃	semidirect
601. C₈×D₄	C₂²×C₂₃	semidirect
602. C₈×D₄	C₂²×C₂₃	semidirect
603. C₈×D₄	C₂²×C₂₃	semidirect
604. C₈×D₄	C₂²×C₂₃	semidirect
605. C₈×D₄	C₂²×C₂₃	semidirect
606. #433	C₂²×C₂₃	semidirect
607. #433	C₂²×C₂₃	semidirect
608. #433	C₂²×C₂₃	semidirect
609. #433	C₂²×C₂₃	semidirect
610. #433	C₂²×C₂₃	semidirect
611. #433	C₂²×C₂₃	semidirect
612. #432	C₂²×C₂₃	semidirect
613. #431	C₂²×C₂₃	semidirect
614. #431	C₂²×C₂₃	semidirect
615. #424	C₂²×C₂₃	semidirect
616. #424	C₂²×C₂₃	semidirect
617. #424	C₂²×C₂₃	semidirect
618. #424	C₂²×C₂₃	semidirect
619. #423	C₂²×C₂₃	semidirect
620. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
621. #408	C₂²×C₂₃	semidirect
622. #408	C₂²×C₂₃	semidirect
623. #408	C₂²×C₂₃	semidirect
624. #408	C₂²×C₂₃	semidirect
626. #407	C₂²×C₂₃	semidirect
627. #407	C₂²×C₂₃	semidirect
628. #407	C₂²×C₂₃	semidirect
629. #407	C₂²×C₂₃	semidirect
631. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
632. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
633. #405	C₂²×C₂₃	semidirect
634. #405	C₂²×C₂₃	semidirect
635. #405	C₂²×C₂₃	semidirect
636. #405	C₂²×C₂₃	semidirect
637. C₄×M₁₆	C₂²×C₂₃	semidirect
638. C₂×#97	C₂²×C₂₃	semidirect
806. C₂₃	#60313	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×#3459	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2978	2
C₂₃×#2976	2
C₂₃×#2975	2
C₂₃×#2974	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2967	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂×C₂₃×#435	2
#60313	23

Subgroups — C23×#60313 #19207939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60313 #19207939