Subgroups — C₂₃×#36571 #19184197

Order 5888.

1776 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2851	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#2851	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#2588	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2585	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2583	C₂	1	2	yes	maximal
7	C₂₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2550	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2520	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2505	C₂	1	2	yes	maximal
13	C₂₃×#2473	C₂	1	2	yes	maximal
14	C₂₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2451	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2370	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2368	C₂	1	2	yes	maximal
19	C₂₃×#2351	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
21	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
22	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#125	C₂²	1	2	yes	—
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#400	C₂²	1	2	yes	—
39	C₂₃×#400	C₂²	1	2	yes	—
40	C₂₃×#400	C₂²	1	2	yes	—
41	C₂₃×#400	C₂²	1	2	yes	—
42	C₂₃×#398	C₂²	1	2	yes	—
43	C₂₃×#398	C₂²	1	2	yes	—
44	C₂₃×#398	C₂²	1	2	yes	—
45	C₂₃×#398	C₂²	1	2	yes	—
46	C₂₃×#398	C₂²	1	2	yes	—
47	C₂₃×#398	C₂²	1	2	yes	—
48	C₂₃×#395	C₂²	1	2	yes	—
49	C₂₃×#395	C₂²	1	2	yes	—
50	C₂₃×#391	C₂²	1	1	yes	characteristic
51	C₂₃×#391	C₂²	1	1	yes	characteristic
52	C₂₃×#391	C₂²	1	2	yes	—
53	C₂₃×#391	C₂²	1	1	yes	characteristic
54	C₂₃×#391	C₂²	1	2	yes	—
55	C₂₃×#391	C₂²	1	2	yes	—
56	C₂₃×#389	C₂²	1	1	yes	characteristic
57	C₂₃×#389	C₂²	1	1	yes	characteristic
58	C₂₃×#389	C₂²	1	1	yes	characteristic
59	C₂₃×#389	C₂²	1	2	yes	—
60	C₂₃×#389	C₂²	1	1	yes	characteristic
61	C₂₃×#389	C₂²	1	2	yes	—
62	C₂₃×#389	C₂²	1	2	yes	—
63	C₂₃×#389	C₂²	1	1	yes	characteristic
64	C₂₃×#389	C₂²	1	1	yes	characteristic
65	C₂₃×#389	C₂²	1	1	yes	characteristic
66	C₂₃×#389	C₂²	1	1	yes	characteristic
67	C₂₃×#389	C₂²	1	2	yes	—
68	C₂₃×#389	C₂²	1	1	yes	characteristic
69	C₂₃×#389	C₂²	1	2	yes	—
70	C₂₃×#389	C₂²	1	2	yes	—
71	C₂₃×#389	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#387	C₂²	1	2	yes	—
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	—
88	C₂₃×#385	C₂²	1	2	yes	—
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	—
91	C₂₃×#385	C₂²	1	2	yes	—
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#384	C₂²	1	1	yes	characteristic
95	C₂₃×#382	C₂²	1	2	yes	—
96	C₂₃×#382	C₂²	1	1	yes	characteristic
97	C₂₃×#382	C₂²	1	1	yes	characteristic
98	C₂₃×#380	C₂²	1	2	yes	—
99	C₂₃×#380	C₂²	1	1	yes	characteristic
100	C₂₃×#380	C₂²	1	1	yes	characteristic
101	C₂₃×#380	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
122	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂₃×C₄⋊Q₈	—	4	2	no	—
133	C₂₃×#125	—	2	8	no	—
134	C₂₃×#125	—	2	4	no	—
135	C₂₃×#125	—	4	2	no	—
136	C₂₃×C₂²⋊Q₈	—	2	8	no	—
137	C₂₃×C₂²⋊Q₈	Q₈	1	8	yes	complemented
138	C₄×Q₈×C₂₃	—	2	4	no	—
139	C₄×Q₈×C₂₃	—	4	2	no	—
140	C₄×Q₈×C₂₃	—	4	2	no	—
141	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
142	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₂₃	—	2	4	no	—
183	C₂×C₄²×C₂₃	—	4	2	no	—
184	C₂×C₄²×C₂₃	—	4	2	no	—
185	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#95	C₂³	1	1	yes	characteristic
204	C₂₃×#95	C₂³	1	1	yes	characteristic
205	C₂₃×#95	C₂³	1	1	yes	characteristic
206	C₂₃×#95	C₂³	1	1	yes	characteristic
207	C₂₃×#95	C₂³	1	1	yes	characteristic
208	C₂₃×#95	C₂³	1	1	yes	characteristic
209	C₂₃×#95	C₂³	1	1	yes	characteristic
210	C₂₃×#95	C₂³	1	1	yes	characteristic
211	C₂₃×#95	C₂³	1	2	yes	—
212	C₂₃×#95	C₂³	1	2	yes	—
213	C₂₃×#95	C₂³	1	2	yes	—
214	C₂₃×#95	C₂³	1	2	yes	—
215	C₂₃×#95	C₂³	1	2	yes	—
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂₃×#95	C₂³	1	2	yes	—
218	C₂₃×#95	C₂³	1	2	yes	—
219	C₂₃×#95	C₂³	1	2	yes	—
220	C₂₃×#95	C₂³	1	2	yes	—
221	C₂₃×#95	C₂³	1	2	yes	—
222	C₂₃×#95	C₂³	1	2	yes	—
223	C₂₃×#95	C₂³	1	2	yes	—
224	C₂₃×#95	C₂³	1	2	yes	—
225	C₂₃×#95	C₂³	1	2	yes	—
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	2	yes	—
233	C₂₃×#95	C₂³	1	2	yes	—
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	2	yes	—
236	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	2	4	no	—
239	C₂×Q₈×C₂₃	—	2	2	no	—
240	C₂×Q₈×C₂₃	—	4	2	no	—
241	C₂×Q₈×C₂₃	—	4	2	no	—
242	C₂×Q₈×C₂₃	C₂×Q₈	1	4	yes	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	2	2	no	—
251	C₂²×C₄×C₂₃	—	2	2	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	4	1	no	—
256	C₂²×C₄×C₂₃	—	4	1	no	—
257	C₂²×C₄×C₂₃	—	4	1	no	—
258	C₂²×C₄×C₂₃	—	4	1	no	—
259	C₂²×C₄×C₂₃	—	4	1	no	—
260	C₂²×C₄×C₂₃	—	4	1	no	—
261	C₂²×C₄×C₂₃	—	4	1	no	—
262	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
263	C₂²×C₄×C₂₃	#41	1	4	yes	—
264	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	4	no	—
294	C₄⋊C₄×C₂₃	—	2	2	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	—	2	4	no	—
301	C₄⋊C₄×C₂₃	—	2	4	no	—
302	C₄⋊C₄×C₂₃	—	2	4	no	—
303	C₄⋊C₄×C₂₃	—	2	4	no	—
304	C₄⋊C₄×C₂₃	—	2	4	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	2	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	2	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	4	2	no	—
311	C₄⋊C₄×C₂₃	—	4	2	no	—
312	C₄⋊C₄×C₂₃	—	4	2	no	—
313	C₄⋊C₄×C₂₃	—	4	2	no	—
314	C₄⋊C₄×C₂₃	—	4	2	no	—
315	C₄⋊C₄×C₂₃	—	4	2	no	—
316	C₄⋊C₄×C₂₃	—	4	2	no	—
317	C₄⋊C₄×C₂₃	—	4	2	no	—
318	C₄⋊C₄×C₂₃	C₂×Q₈	1	4	yes	—
319	C₄⋊C₄×C₂₃	C₂×Q₈	1	8	yes	—
320	C₄⋊C₄×C₂₃	#41	1	4	yes	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	C₂×Q₈	1	8	yes	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	4	no	—
329	C₄²×C₂₃	—	2	4	no	—
330	C₄²×C₂₃	—	2	2	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	—	2	2	no	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	4	1	no	—
335	C₄²×C₂₃	—	4	1	no	—
336	C₄²×C₂₃	—	4	1	no	—
337	C₄²×C₂₃	—	4	1	no	—
338	C₄²×C₂₃	—	4	2	no	—
339	C₄²×C₂₃	—	4	2	no	—
340	C₄²×C₂₃	—	4	2	no	—
341	C₄²×C₂₃	—	4	2	no	—
342	C₄²×C₂₃	#41	1	4	yes	—
343	#36571	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
344	C₂³×C₂₃	—	2	1	no	—
345	C₂³×C₂₃	—	2	1	no	—
346	C₂³×C₂₃	—	2	1	no	—
347	C₂³×C₂₃	—	2	1	no	—
348	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
349	C₂³×C₂₃	C₂×#41	1	2	yes	—
350	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
351	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
352	Q₈×C₂₃	—	2	8	no	—
353	Q₈×C₂₃	—	8	4	no	—
354	C₂×C₄×C₂₃	—	2	8	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	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	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	8	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	1	no	—
392	C₂×C₄×C₂₃	—	2	1	no	—
393	C₂×C₄×C₂₃	—	2	1	no	—
394	C₂×C₄×C₂₃	—	2	1	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	1	no	—
402	C₂×C₄×C₂₃	—	2	1	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	1	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	4	4	no	—
410	C₂×C₄×C₂₃	—	4	4	no	—
411	C₂×C₄×C₂₃	—	4	4	no	—
412	C₂×C₄×C₂₃	—	4	4	no	—
413	C₂×C₄×C₂₃	—	4	4	no	—
414	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
415	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
416	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
417	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
418	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
419	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
420	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
421	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
422	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
423	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
424	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
425	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
426	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
427	#2857	C₂×C₂₃	1	1	yes	characteristic
428	#2851	C₂×C₂₃	1	1	yes	characteristic
429	#2851	C₂×C₂₃	1	1	yes	characteristic
430	#2588	C₂×C₂₃	1	2	yes	complemented
431	#2585	C₂×C₂₃	1	2	yes	complemented
432	#2583	C₂×C₂₃	1	2	yes	—
433	#2565	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#2550	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#2520	C₂×C₂₃	1	2	yes	complemented
436	#2509	C₂×C₂₃	1	1	yes	characteristic, complemented
437	#2506	C₂×C₂₃	1	1	yes	characteristic, complemented
438	#2505	C₂×C₂₃	1	2	yes	—
439	#2473	C₂×C₂₃	1	2	yes	—
440	#2453	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#2451	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
443	#2370	C₂×C₂₃	1	2	yes	complemented
444	#2368	C₂×C₂₃	1	2	yes	—
445	#2351	C₂×C₂₃	1	1	yes	characteristic, complemented
446	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
447	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
448	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
449	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
450	C₂²×C₂₃	—	2	2	no	—
451	C₂²×C₂₃	—	2	2	no	—
452	C₂²×C₂₃	—	2	2	no	—
453	C₂²×C₂₃	—	2	2	no	—
454	C₂²×C₂₃	—	2	2	no	—
455	C₂²×C₂₃	—	2	2	no	—
456	C₂²×C₂₃	#557	1	4	yes	—
457	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
458	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
462	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂²×C₂₃	#585	1	1	yes	characteristic
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	2	no	—
467	C₄×C₂₃	—	2	4	no	—
468	C₄×C₂₃	—	2	4	no	—
469	C₄×C₂₃	—	2	2	no	—
470	C₄×C₂₃	—	2	2	no	—
471	C₄×C₂₃	—	2	2	no	—
472	C₄×C₂₃	—	2	2	no	—
473	C₄×C₂₃	—	2	2	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	2	no	—
476	C₄×C₂₃	—	4	2	no	—
477	C₄×C₂₃	—	4	1	no	—
478	C₄×C₂₃	—	4	1	no	—
479	C₄×C₂₃	—	4	1	no	—
480	C₄×C₂₃	—	4	2	no	—
481	C₄×C₂₃	—	4	2	no	—
482	C₄×C₂₃	—	4	2	no	—
483	C₄×C₂₃	—	4	1	no	—
484	C₄×C₂₃	—	4	1	no	—
485	C₄×C₂₃	#554	1	4	yes	—
486	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×#125	C₂²×C₂₃	1	2	yes	—
489	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
491	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
495	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
496	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
497	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
498	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
499	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
500	#400	C₂²×C₂₃	1	2	yes	—
501	#400	C₂²×C₂₃	1	2	yes	—
502	#400	C₂²×C₂₃	1	2	yes	—
503	#400	C₂²×C₂₃	1	2	yes	—
504	#398	C₂²×C₂₃	1	2	yes	—
505	#398	C₂²×C₂₃	1	2	yes	—
506	#398	C₂²×C₂₃	1	2	yes	—
507	#398	C₂²×C₂₃	1	2	yes	—
508	#398	C₂²×C₂₃	1	2	yes	—
509	#398	C₂²×C₂₃	1	2	yes	—
510	#395	C₂²×C₂₃	1	2	yes	—
511	#395	C₂²×C₂₃	1	2	yes	—
512	#391	C₂²×C₂₃	1	1	yes	characteristic
513	#391	C₂²×C₂₃	1	1	yes	characteristic
514	#391	C₂²×C₂₃	1	2	yes	—
515	#391	C₂²×C₂₃	1	2	yes	—
516	#391	C₂²×C₂₃	1	2	yes	—
517	#391	C₂²×C₂₃	1	1	yes	characteristic
518	#389	C₂²×C₂₃	1	2	yes	—
519	#389	C₂²×C₂₃	1	2	yes	—
520	#389	C₂²×C₂₃	1	2	yes	—
521	#389	C₂²×C₂₃	1	2	yes	—
522	#389	C₂²×C₂₃	1	2	yes	—
523	#389	C₂²×C₂₃	1	2	yes	—
524	#389	C₂²×C₂₃	1	1	yes	characteristic
525	#389	C₂²×C₂₃	1	1	yes	characteristic
526	#389	C₂²×C₂₃	1	1	yes	characteristic
527	#389	C₂²×C₂₃	1	1	yes	characteristic
528	#389	C₂²×C₂₃	1	1	yes	characteristic
529	#389	C₂²×C₂₃	1	1	yes	characteristic
530	#389	C₂²×C₂₃	1	2	yes	—
531	#389	C₂²×C₂₃	1	1	yes	characteristic
532	#389	C₂²×C₂₃	1	1	yes	characteristic
533	#389	C₂²×C₂₃	1	1	yes	characteristic
534	#387	C₂²×C₂₃	1	2	yes	—
535	#387	C₂²×C₂₃	1	2	yes	—
536	#387	C₂²×C₂₃	1	2	yes	—
537	#387	C₂²×C₂₃	1	2	yes	—
538	#387	C₂²×C₂₃	1	2	yes	—
539	#387	C₂²×C₂₃	1	2	yes	—
540	#387	C₂²×C₂₃	1	2	yes	—
541	#387	C₂²×C₂₃	1	2	yes	—
542	#387	C₂²×C₂₃	1	2	yes	—
543	#387	C₂²×C₂₃	1	2	yes	—
544	#387	C₂²×C₂₃	1	2	yes	—
545	#387	C₂²×C₂₃	1	2	yes	—
546	#387	C₂²×C₂₃	1	2	yes	—
547	#387	C₂²×C₂₃	1	2	yes	—
548	#387	C₂²×C₂₃	1	2	yes	—
549	#385	C₂²×C₂₃	1	2	yes	—
550	#385	C₂²×C₂₃	1	2	yes	—
551	#385	C₂²×C₂₃	1	2	yes	—
552	#385	C₂²×C₂₃	1	2	yes	—
553	#385	C₂²×C₂₃	1	2	yes	—
554	#385	C₂²×C₂₃	1	2	yes	—
555	#385	C₂²×C₂₃	1	2	yes	—
556	#384	C₂²×C₂₃	1	1	yes	characteristic
557	#382	C₂²×C₂₃	1	1	yes	characteristic
558	#382	C₂²×C₂₃	1	1	yes	characteristic
559	#382	C₂²×C₂₃	1	2	yes	—
560	#380	C₂²×C₂₃	1	1	yes	characteristic
561	#380	C₂²×C₂₃	1	1	yes	characteristic
562	#380	C₂²×C₂₃	1	1	yes	characteristic
563	#380	C₂²×C₂₃	1	2	yes	—
564	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
568	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
569	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
570	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
572	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
576	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
577	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
578	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
579	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
583	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
584	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
585	C₂×C₂₃	—	2	4	no	—
586	C₂×C₂₃	#3444	1	1	yes	characteristic
587	C₂×C₂₃	C₂×#554	1	1	yes	characteristic
588	C₂×C₂₃	C₂×#557	1	1	yes	characteristic
589	C₂×C₂₃	Q₈×#41	1	1	yes	characteristic
590	C₂×C₂₃	#3495	1	1	yes	characteristic
591	C₂×C₂₃	#3505	1	1	yes	characteristic
592	C₂×C₂₃	#3520	1	1	yes	characteristic
593	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
594	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
595	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
600	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
602	C₄⋊Q₈	—	4	2	no	—
603	#125	—	2	8	no	—
604	#125	—	2	4	no	—
605	#125	—	4	2	no	—
606	C₂²⋊Q₈	—	2	8	no	—
607	C₂²⋊Q₈	Q₈×C₂₃	1	8	yes	complemented
608	C₄×Q₈	—	2	4	no	—
609	C₄×Q₈	—	4	2	no	—
610	C₄×Q₈	—	4	2	no	—
611	C₂×C₄⋊C₄	—	2	4	no	—
612	C₂×C₄⋊C₄	—	2	4	no	—
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
628	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
652	C₂×C₄²	—	2	4	no	—
653	C₂×C₄²	—	4	2	no	—
654	C₂×C₄²	—	4	2	no	—
655	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
659	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
666	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
667	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
668	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
670	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
673	#95	C₂³×C₂₃	1	1	yes	characteristic
674	#95	C₂³×C₂₃	1	1	yes	characteristic
675	#95	C₂³×C₂₃	1	1	yes	characteristic
676	#95	C₂³×C₂₃	1	1	yes	characteristic
677	#95	C₂³×C₂₃	1	1	yes	characteristic
678	#95	C₂³×C₂₃	1	1	yes	characteristic
679	#95	C₂³×C₂₃	1	1	yes	characteristic
680	#95	C₂³×C₂₃	1	1	yes	characteristic
681	#95	C₂³×C₂₃	1	2	yes	—
682	#95	C₂³×C₂₃	1	2	yes	—
683	#95	C₂³×C₂₃	1	2	yes	—
684	#95	C₂³×C₂₃	1	2	yes	—
685	#95	C₂³×C₂₃	1	2	yes	—
686	#95	C₂³×C₂₃	1	2	yes	—
687	#95	C₂³×C₂₃	1	2	yes	—
688	#95	C₂³×C₂₃	1	2	yes	—
689	#95	C₂³×C₂₃	1	2	yes	—
690	#95	C₂³×C₂₃	1	2	yes	—
691	#95	C₂³×C₂₃	1	2	yes	—
692	#95	C₂³×C₂₃	1	2	yes	—
693	#95	C₂³×C₂₃	1	2	yes	—
694	#95	C₂³×C₂₃	1	2	yes	—
695	#95	C₂³×C₂₃	1	2	yes	—
696	#95	C₂³×C₂₃	1	2	yes	—
697	#95	C₂³×C₂₃	1	2	yes	—
698	#95	C₂³×C₂₃	1	2	yes	—
699	#95	C₂³×C₂₃	1	2	yes	—
700	#95	C₂³×C₂₃	1	2	yes	—
701	#95	C₂³×C₂₃	1	2	yes	—
702	#95	C₂³×C₂₃	1	2	yes	—
703	#95	C₂³×C₂₃	1	2	yes	—
704	#95	C₂³×C₂₃	1	2	yes	—
705	#95	C₂³×C₂₃	1	2	yes	—
706	C₂₃	#36571	1	1	yes	characteristic, direct product factor, Sylow
707	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
708	C₂×Q₈	—	2	2	no	—
709	C₂×Q₈	—	2	4	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	4	2	no	—
712	C₂×Q₈	—	4	2	no	—
713	C₂×Q₈	C₂×Q₈×C₂₃	1	4	yes	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	2	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	—	4	1	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
734	C₂²×C₄	#41×C₂₃	1	4	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
736	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
737	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	2	no	—
785	C₄⋊C₄	—	4	2	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	C₂×Q₈×C₂₃	1	4	yes	—
790	C₄⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
791	C₄⋊C₄	#41×C₂₃	1	4	yes	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
796	C₄²	—	2	2	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	2	no	—
799	C₄²	—	2	4	no	—
800	C₄²	—	2	4	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	2	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	4	1	no	—
806	C₄²	—	4	1	no	—
807	C₄²	—	4	1	no	—
808	C₄²	—	4	1	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	2	no	—
812	C₄²	—	4	2	no	—
813	C₄²	#41×C₂₃	1	4	yes	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
819	C₂³	C₂×#41×C₂₃	1	2	yes	—
820	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
821	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
822	Q₈	—	2	8	no	—
823	Q₈	—	8	4	no	—
824	C₂×C₄	—	2	8	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	8	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	4	no	—
882	C₂×C₄	—	4	4	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
885	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
886	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
887	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
888	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
889	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
890	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
891	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
892	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
893	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
894	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
895	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
896	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	C₂₃×#557	1	4	yes	—
904	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
905	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
906	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
907	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
908	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
909	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
910	C₂²	C₂₃×#585	1	1	yes	characteristic
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	2	no	—
914	C₄	—	2	4	no	—
915	C₄	—	2	4	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	2	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	1	no	—
931	C₄	—	4	2	no	—
932	C₄	C₂₃×#554	1	4	yes	—
933	C₂	—	2	4	no	—
934	C₂	C₂₃×#3444	1	1	yes	characteristic
935	C₂	C₂×C₂₃×#554	1	1	yes	characteristic
936	C₂	C₂×C₂₃×#557	1	1	yes	characteristic
937	C₂	Q₈×#41×C₂₃	1	1	yes	characteristic
938	C₂	C₂₃×#3495	1	1	yes	characteristic
939	C₂	C₂₃×#3505	1	1	yes	characteristic
940	C₂	C₂₃×#3520	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₂₃×#2588	C₂	semidirect
5. C₂₃×#2585	C₂	semidirect
7. C₂₃×#2565	C₂	semidirect
8. C₂₃×#2550	C₂	semidirect
9. C₂₃×#2520	C₂	semidirect
10. C₂₃×#2509	C₂	semidirect
11. C₂₃×#2506	C₂	semidirect
14. C₂₃×#2453	C₂	semidirect
15. C₂₃×#2451	C₂	semidirect
16. C₂₃×#2370	C₂	semidirect
17. C₂₃×#2370	C₂	semidirect
19. C₂₃×#2351	C₂	semidirect
137. C₂₃×C₂²⋊Q₈	Q₈	semidirect
343. #36571	C₂₃	direct (N × H)
430. #2588	C₂×C₂₃	semidirect
431. #2585	C₂×C₂₃	semidirect
433. #2565	C₂×C₂₃	semidirect
434. #2550	C₂×C₂₃	semidirect
435. #2520	C₂×C₂₃	semidirect
436. #2509	C₂×C₂₃	semidirect
437. #2506	C₂×C₂₃	semidirect
440. #2453	C₂×C₂₃	semidirect
441. #2451	C₂×C₂₃	semidirect
442. #2370	C₂×C₂₃	semidirect
443. #2370	C₂×C₂₃	semidirect
445. #2351	C₂×C₂₃	semidirect
607. C₂²⋊Q₈	Q₈×C₂₃	semidirect
706. C₂₃	#36571	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×#2857	2
C₂₃×#2851	2
C₂₃×#2588	2
C₂₃×#2585	2
C₂₃×#2583	2
C₂₃×#2565	2
C₂₃×#2550	2
C₂₃×#2520	2
C₂₃×#2509	2
C₂₃×#2506	2
C₂₃×#2505	2
C₂₃×#2473	2
C₂₃×#2453	2
C₂₃×#2451	2
C₂₃×#2370	2
C₂₃×#2368	2
C₂₃×#2351	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂×C₄×C₄⋊C₄×C₂₃	2
#36571	23

Subgroups — C23×#36571 #19184197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36571 #19184197