Subgroups — C₂₃×#36588 #19184214

Order 5888.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2854	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2595	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2594	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2593	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2573	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2510	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2444	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2416	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2361	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2352	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#123	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#123	C₂²	1	2	yes	—
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
33	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
38	C₂₃×#401	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×#397	C₂²	1	2	yes	—
44	C₂₃×#397	C₂²	1	2	yes	—
45	C₂₃×#397	C₂²	1	2	yes	—
46	C₂₃×#397	C₂²	1	2	yes	—
47	C₂₃×#396	C₂²	1	2	yes	—
48	C₂₃×#394	C₂²	1	2	yes	—
49	C₂₃×#394	C₂²	1	2	yes	—
50	C₂₃×#390	C₂²	1	1	yes	characteristic
51	C₂₃×#390	C₂²	1	1	yes	characteristic
52	C₂₃×#390	C₂²	1	2	yes	—
53	C₂₃×#390	C₂²	1	1	yes	characteristic
54	C₂₃×#390	C₂²	1	1	yes	characteristic
55	C₂₃×#390	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	1	yes	characteristic
60	C₂₃×#389	C₂²	1	1	yes	characteristic
61	C₂₃×#389	C₂²	1	2	yes	—
62	C₂₃×#389	C₂²	1	1	yes	characteristic
63	C₂₃×#389	C₂²	1	2	yes	—
64	C₂₃×#388	C₂²	1	2	yes	—
65	C₂₃×#388	C₂²	1	2	yes	—
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	1	yes	characteristic
72	C₂₃×#388	C₂²	1	1	yes	characteristic
73	C₂₃×#388	C₂²	1	2	yes	—
74	C₂₃×#388	C₂²	1	2	yes	—
75	C₂₃×#388	C₂²	1	2	yes	—
76	C₂₃×#388	C₂²	1	2	yes	—
77	C₂₃×#388	C₂²	1	2	yes	—
78	C₂₃×#388	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	1	yes	characteristic
84	C₂₃×#387	C₂²	1	1	yes	characteristic
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#386	C₂²	1	2	yes	—
87	C₂₃×#386	C₂²	1	1	yes	characteristic
88	C₂₃×#386	C₂²	1	2	yes	—
89	C₂₃×#386	C₂²	1	2	yes	—
90	C₂₃×#386	C₂²	1	2	yes	—
91	C₂₃×#386	C₂²	1	2	yes	—
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	1	yes	characteristic
94	C₂₃×#385	C₂²	1	2	yes	—
95	C₂₃×#383	C₂²	1	2	yes	—
96	C₂₃×#382	C₂²	1	1	yes	characteristic
97	C₂₃×#382	C₂²	1	1	yes	characteristic
98	C₂₃×#381	C₂²	1	2	yes	—
99	C₂₃×#381	C₂²	1	1	yes	characteristic
100	C₂₃×#380	C₂²	1	1	yes	characteristic
101	C₂₃×#380	C₂²	1	2	yes	—
102	C₂₃×#380	C₂²	1	1	yes	characteristic
103	C₂₃×#380	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	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
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	2	yes	—
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
122	C₂×C₂₃×#95	C₂²	1	2	yes	—
123	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂₃×#125	—	2	4	no	—
135	C₂₃×#123	—	2	4	no	—
136	C₂₃×#123	—	2	8	no	—
137	C₂₃×#121	—	2	4	no	—
138	C₂₃×#121	—	2	4	no	—
139	C₂₃×#121	—	4	4	no	—
140	C₄×D₄×C₂₃	—	2	4	no	—
141	C₄×D₄×C₂₃	—	2	4	no	—
142	C₄×D₄×C₂₃	—	4	4	no	—
143	C₂₃×#117	—	2	4	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
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	2	yes	—
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₂₃	—	2	4	no	—
192	C₂×C₄²×C₂₃	—	4	4	no	—
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
205	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
207	C₂₃×#95	C₂³	1	2	yes	—
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂₃×#95	C₂³	1	2	yes	—
211	C₂₃×#95	C₂³	1	1	yes	characteristic
212	C₂₃×#95	C₂³	1	1	yes	characteristic
213	C₂₃×#95	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
218	C₂₃×#95	C₂³	1	1	yes	characteristic
219	C₂₃×#95	C₂³	1	2	yes	—
220	C₂₃×#95	C₂³	1	1	yes	characteristic
221	C₂₃×#95	C₂³	1	1	yes	characteristic
222	C₂₃×#95	C₂³	1	1	yes	characteristic
223	C₂₃×#95	C₂³	1	2	yes	—
224	C₂₃×#95	C₂³	1	1	yes	characteristic
225	C₂₃×#95	C₂³	1	2	yes	—
226	C₂₃×#95	C₂³	1	2	yes	—
227	C₂₃×#95	C₂³	1	1	yes	characteristic
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	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
238	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	4	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	4	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	2	4	no	—
249	C₂×D₄×C₂₃	—	4	2	no	—
250	C₂×D₄×C₂₃	—	4	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	—	2	2	no	—
256	C₂²×C₄×C₂₃	—	2	4	no	—
257	C₂²×C₄×C₂₃	—	2	4	no	—
258	C₂²×C₄×C₂₃	—	2	4	no	—
259	C₂²×C₄×C₂₃	—	2	4	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	—	4	2	no	—
265	C₂²×C₄×C₂₃	—	4	2	no	—
266	C₂²×C₄×C₂₃	—	4	1	no	—
267	C₂²×C₄×C₂₃	—	4	1	no	—
268	C₂²×C₄×C₂₃	—	4	2	no	—
269	C₂²×C₄×C₂₃	—	4	2	no	—
270	C₂²×C₄×C₂₃	#41	1	4	yes	—
271	C₂²×C₄×C₂₃	#41	1	4	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₄⋊C₄×C₂₃	—	2	4	no	—
293	C₄⋊C₄×C₂₃	—	2	4	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	2	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	—	4	2	no	—
307	C₄⋊C₄×C₂₃	—	4	1	no	—
308	C₄⋊C₄×C₂₃	—	4	1	no	—
309	C₄⋊C₄×C₂₃	—	4	2	no	—
310	C₄⋊C₄×C₂₃	—	4	2	no	—
311	C₄⋊C₄×C₂₃	—	4	2	no	—
312	C₄⋊C₄×C₂₃	#41	1	4	yes	—
313	C₄⋊C₄×C₂₃	#41	1	4	yes	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	4	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	4	no	—
321	C₂²⋊C₄×C₂₃	—	2	4	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	—	2	2	no	—
325	C₂²⋊C₄×C₂₃	—	2	4	no	—
326	C₂²⋊C₄×C₂₃	—	2	4	no	—
327	C₂²⋊C₄×C₂₃	—	4	2	no	—
328	C₂²⋊C₄×C₂₃	—	4	2	no	—
329	C₂²⋊C₄×C₂₃	—	4	2	no	—
330	C₂²⋊C₄×C₂₃	—	4	2	no	—
331	C₂²⋊C₄×C₂₃	—	4	2	no	—
332	C₂²⋊C₄×C₂₃	—	4	1	no	—
333	C₂²⋊C₄×C₂₃	—	4	1	no	—
334	C₂²⋊C₄×C₂₃	—	4	2	no	—
335	C₂²⋊C₄×C₂₃	—	4	2	no	—
336	C₂²⋊C₄×C₂₃	—	4	2	no	—
337	C₄²×C₂₃	—	2	2	no	—
338	C₄²×C₂₃	—	2	2	no	—
339	C₄²×C₂₃	—	2	2	no	—
340	C₄²×C₂₃	—	2	2	no	—
341	C₄²×C₂₃	—	2	4	no	—
342	C₄²×C₂₃	—	2	2	no	—
343	C₄²×C₂₃	—	2	2	no	—
344	C₄²×C₂₃	—	2	2	no	—
345	C₄²×C₂₃	—	4	2	no	—
346	C₄²×C₂₃	—	4	2	no	—
347	C₄²×C₂₃	—	4	2	no	—
348	C₄²×C₂₃	—	4	2	no	—
349	C₄²×C₂₃	—	4	2	no	—
350	C₄²×C₂₃	—	4	2	no	—
351	#36588	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂³×C₂₃	—	2	1	no	—
353	C₂³×C₂₃	—	2	1	no	—
354	C₂³×C₂₃	—	2	1	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	2	1	no	—
357	C₂³×C₂₃	—	2	1	no	—
358	C₂³×C₂₃	—	2	2	no	—
359	C₂³×C₂₃	—	2	1	no	—
360	C₂³×C₂₃	—	2	2	no	—
361	C₂³×C₂₃	—	2	2	no	—
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	1	no	—
364	C₂³×C₂₃	—	2	2	no	—
365	C₂³×C₂₃	—	2	1	no	—
366	C₂³×C₂₃	—	2	1	no	—
367	C₂³×C₂₃	—	2	2	no	—
368	C₂³×C₂₃	—	2	2	no	—
369	C₂³×C₂₃	—	2	1	no	—
370	C₂³×C₂₃	C₂×#41	1	2	yes	—
371	C₂³×C₂₃	C₂×#41	1	2	yes	—
372	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
373	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
374	D₄×C₂₃	—	4	4	no	—
375	D₄×C₂₃	—	4	8	no	—
376	D₄×C₂₃	—	4	4	no	—
377	D₄×C₂₃	—	8	4	no	—
378	C₂×C₄×C₂₃	—	2	8	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	2	1	no	—
381	C₂×C₄×C₂₃	—	2	1	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	1	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	8	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	1	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	1	no	—
399	C₂×C₄×C₂₃	—	2	1	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	1	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	1	no	—
405	C₂×C₄×C₂₃	—	2	1	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	2	no	—
412	C₂×C₄×C₂₃	—	2	1	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	1	no	—
417	C₂×C₄×C₂₃	—	2	1	no	—
418	C₂×C₄×C₂₃	—	2	1	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	1	no	—
421	C₂×C₄×C₂₃	—	2	1	no	—
422	C₂×C₄×C₂₃	—	2	1	no	—
423	C₂×C₄×C₂₃	—	2	1	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	1	no	—
427	C₂×C₄×C₂₃	—	2	1	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	1	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	4	8	no	—
433	C₂×C₄×C₂₃	—	4	8	no	—
434	C₂×C₄×C₂₃	—	4	4	no	—
435	C₂×C₄×C₂₃	—	4	4	no	—
436	C₂×C₄×C₂₃	—	8	4	no	—
437	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
438	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
439	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
440	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
441	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
442	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
443	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
444	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
445	#2854	C₂×C₂₃	1	1	yes	characteristic, complemented
446	#2854	C₂×C₂₃	1	2	yes	complemented
447	#2595	C₂×C₂₃	1	2	yes	complemented
448	#2594	C₂×C₂₃	1	2	yes	complemented
449	#2593	C₂×C₂₃	1	2	yes	complemented
450	#2573	C₂×C₂₃	1	2	yes	complemented
451	#2513	C₂×C₂₃	1	1	yes	characteristic, complemented
452	#2510	C₂×C₂₃	1	2	yes	complemented
453	#2509	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#2494	C₂×C₂₃	1	1	yes	characteristic, complemented
455	#2490	C₂×C₂₃	1	1	yes	characteristic, complemented
456	#2444	C₂×C₂₃	1	2	yes	complemented
457	#2442	C₂×C₂₃	1	1	yes	characteristic, complemented
458	#2416	C₂×C₂₃	1	1	yes	characteristic
459	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
460	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
461	#2361	C₂×C₂₃	1	1	yes	characteristic, complemented
462	#2357	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#2352	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#2347	C₂×C₂₃	1	1	yes	characteristic, complemented
465	C₄×#123	C₂×C₂₃	1	1	yes	characteristic, complemented
466	C₄×#123	C₂×C₂₃	1	2	yes	complemented
467	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
468	C₂²×C₂₃	—	2	2	no	—
469	C₂²×C₂₃	—	2	2	no	—
470	C₂²×C₂₃	—	2	2	no	—
471	C₂²×C₂₃	—	2	2	no	—
472	C₂²×C₂₃	—	2	2	no	—
473	C₂²×C₂₃	—	2	2	no	—
474	C₂²×C₂₃	—	4	1	no	—
475	C₂²×C₂₃	—	4	2	no	—
476	C₂²×C₂₃	—	4	1	no	—
477	C₂²×C₂₃	—	4	2	no	—
478	C₂²×C₂₃	—	4	1	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	1	no	—
482	C₂²×C₂₃	—	4	1	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	4	2	no	—
485	C₂²×C₂₃	—	4	1	no	—
486	C₂²×C₂₃	—	4	2	no	—
487	C₂²×C₂₃	—	4	1	no	—
488	C₂²×C₂₃	#553	1	4	yes	—
489	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
490	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
491	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
492	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
493	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂²×C₂₃	#585	1	1	yes	characteristic
495	C₂²×C₂₃	#585	1	1	yes	characteristic
496	C₄×C₂₃	—	2	2	no	—
497	C₄×C₂₃	—	2	2	no	—
498	C₄×C₂₃	—	2	2	no	—
499	C₄×C₂₃	—	2	4	no	—
500	C₄×C₂₃	—	2	4	no	—
501	C₄×C₂₃	—	4	1	no	—
502	C₄×C₂₃	—	4	1	no	—
503	C₄×C₂₃	—	4	2	no	—
504	C₄×C₂₃	—	4	1	no	—
505	C₄×C₂₃	—	4	2	no	—
506	C₄×C₂₃	—	4	1	no	—
507	C₄×C₂₃	—	4	2	no	—
508	C₄×C₂₃	—	4	1	no	—
509	C₄×C₂₃	—	4	1	no	—
510	C₄×C₂₃	—	4	1	no	—
511	C₄×C₂₃	—	4	1	no	—
512	C₄×C₂₃	—	4	2	no	—
513	C₄×C₂₃	—	4	2	no	—
514	C₄×C₂₃	—	4	1	no	—
515	C₄×C₂₃	#529	1	4	yes	—
516	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
517	C₂×#123	C₂²×C₂₃	1	2	yes	—
518	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
519	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
520	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
521	C₂×#121	C₂²×C₂₃	1	2	yes	—
522	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
524	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
525	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
526	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
527	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
528	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
529	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
530	#401	C₂²×C₂₃	1	2	yes	—
531	#400	C₂²×C₂₃	1	2	yes	—
532	#400	C₂²×C₂₃	1	2	yes	—
533	#400	C₂²×C₂₃	1	2	yes	—
534	#398	C₂²×C₂₃	1	2	yes	—
535	#397	C₂²×C₂₃	1	2	yes	—
536	#397	C₂²×C₂₃	1	2	yes	—
537	#397	C₂²×C₂₃	1	2	yes	—
538	#397	C₂²×C₂₃	1	2	yes	—
539	#396	C₂²×C₂₃	1	2	yes	—
540	#394	C₂²×C₂₃	1	2	yes	—
541	#394	C₂²×C₂₃	1	2	yes	—
542	#390	C₂²×C₂₃	1	2	yes	—
543	#390	C₂²×C₂₃	1	2	yes	—
544	#390	C₂²×C₂₃	1	1	yes	characteristic
545	#390	C₂²×C₂₃	1	1	yes	characteristic
546	#390	C₂²×C₂₃	1	1	yes	characteristic
547	#390	C₂²×C₂₃	1	1	yes	characteristic
548	#389	C₂²×C₂₃	1	2	yes	—
549	#389	C₂²×C₂₃	1	2	yes	—
550	#389	C₂²×C₂₃	1	1	yes	characteristic
551	#389	C₂²×C₂₃	1	1	yes	characteristic
552	#389	C₂²×C₂₃	1	1	yes	characteristic
553	#389	C₂²×C₂₃	1	1	yes	characteristic
554	#389	C₂²×C₂₃	1	1	yes	characteristic
555	#389	C₂²×C₂₃	1	1	yes	characteristic
556	#388	C₂²×C₂₃	1	2	yes	—
557	#388	C₂²×C₂₃	1	2	yes	—
558	#388	C₂²×C₂₃	1	1	yes	characteristic
559	#388	C₂²×C₂₃	1	2	yes	—
560	#388	C₂²×C₂₃	1	2	yes	—
561	#388	C₂²×C₂₃	1	2	yes	—
562	#388	C₂²×C₂₃	1	2	yes	—
563	#388	C₂²×C₂₃	1	2	yes	—
564	#388	C₂²×C₂₃	1	2	yes	—
565	#388	C₂²×C₂₃	1	2	yes	—
566	#388	C₂²×C₂₃	1	2	yes	—
567	#388	C₂²×C₂₃	1	2	yes	—
568	#388	C₂²×C₂₃	1	2	yes	—
569	#388	C₂²×C₂₃	1	1	yes	characteristic
570	#388	C₂²×C₂₃	1	2	yes	—
571	#387	C₂²×C₂₃	1	1	yes	characteristic
572	#387	C₂²×C₂₃	1	2	yes	—
573	#387	C₂²×C₂₃	1	2	yes	—
574	#387	C₂²×C₂₃	1	1	yes	characteristic
575	#387	C₂²×C₂₃	1	2	yes	—
576	#387	C₂²×C₂₃	1	2	yes	—
577	#387	C₂²×C₂₃	1	2	yes	—
578	#386	C₂²×C₂₃	1	2	yes	—
579	#386	C₂²×C₂₃	1	2	yes	—
580	#386	C₂²×C₂₃	1	2	yes	—
581	#386	C₂²×C₂₃	1	2	yes	—
582	#386	C₂²×C₂₃	1	2	yes	—
583	#386	C₂²×C₂₃	1	1	yes	characteristic
584	#385	C₂²×C₂₃	1	2	yes	—
585	#385	C₂²×C₂₃	1	2	yes	—
586	#385	C₂²×C₂₃	1	1	yes	characteristic
587	#383	C₂²×C₂₃	1	2	yes	—
588	#382	C₂²×C₂₃	1	1	yes	characteristic
589	#382	C₂²×C₂₃	1	1	yes	characteristic
590	#381	C₂²×C₂₃	1	2	yes	—
591	#381	C₂²×C₂₃	1	1	yes	characteristic
592	#380	C₂²×C₂₃	1	1	yes	characteristic
593	#380	C₂²×C₂₃	1	2	yes	—
594	#380	C₂²×C₂₃	1	1	yes	characteristic
595	#380	C₂²×C₂₃	1	1	yes	characteristic
596	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
597	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
598	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
599	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
600	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
601	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
602	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
603	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
604	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
605	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
606	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
607	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
608	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
609	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
610	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
611	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
612	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
613	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
614	C₂×#95	C₂²×C₂₃	1	2	yes	—
615	C₂×C₂₃	—	2	4	no	—
616	C₂×C₂₃	—	8	1	no	—
617	C₂×C₂₃	—	8	2	no	—
618	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
619	C₂×C₂₃	C₂×#553	1	1	yes	characteristic
620	C₂×C₂₃	#3480	1	1	yes	characteristic
621	C₂×C₂₃	#3480	1	1	yes	characteristic
622	C₂×C₂₃	#3493	1	1	yes	characteristic
623	C₂×C₂₃	#3513	1	1	yes	characteristic
624	C₂×C₂₃	#3513	1	1	yes	characteristic
625	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
626	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
627	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
628	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
629	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
631	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
632	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
634	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
635	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
636	#125	—	2	4	no	—
637	#123	—	2	8	no	—
638	#123	—	2	4	no	—
639	#121	—	2	4	no	—
640	#121	—	2	4	no	—
641	#121	—	4	4	no	—
642	C₄×D₄	—	2	4	no	—
643	C₄×D₄	—	2	4	no	—
644	C₄×D₄	—	4	4	no	—
645	#117	—	2	4	no	—
646	C₂×C₄⋊C₄	—	2	4	no	—
647	C₂×C₄⋊C₄	—	2	4	no	—
648	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
658	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
659	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
660	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
663	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
664	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
667	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
670	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
675	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
676	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
679	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
681	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
682	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
683	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
684	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
685	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
687	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
688	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
690	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
691	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
692	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
693	C₂×C₄²	—	2	4	no	—
694	C₂×C₄²	—	4	4	no	—
695	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
697	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
699	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
700	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
701	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
703	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
704	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
706	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
707	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
708	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
709	#95	C₂³×C₂₃	1	2	yes	—
710	#95	C₂³×C₂₃	1	2	yes	—
711	#95	C₂³×C₂₃	1	2	yes	—
712	#95	C₂³×C₂₃	1	2	yes	—
713	#95	C₂³×C₂₃	1	1	yes	characteristic
714	#95	C₂³×C₂₃	1	1	yes	characteristic
715	#95	C₂³×C₂₃	1	1	yes	characteristic
716	#95	C₂³×C₂₃	1	2	yes	—
717	#95	C₂³×C₂₃	1	2	yes	—
718	#95	C₂³×C₂₃	1	2	yes	—
719	#95	C₂³×C₂₃	1	1	yes	characteristic
720	#95	C₂³×C₂₃	1	1	yes	characteristic
721	#95	C₂³×C₂₃	1	2	yes	—
722	#95	C₂³×C₂₃	1	1	yes	characteristic
723	#95	C₂³×C₂₃	1	1	yes	characteristic
724	#95	C₂³×C₂₃	1	1	yes	characteristic
725	#95	C₂³×C₂₃	1	2	yes	—
726	#95	C₂³×C₂₃	1	1	yes	characteristic
727	#95	C₂³×C₂₃	1	2	yes	—
728	#95	C₂³×C₂₃	1	2	yes	—
729	#95	C₂³×C₂₃	1	1	yes	characteristic
730	#95	C₂³×C₂₃	1	2	yes	—
731	#95	C₂³×C₂₃	1	2	yes	—
732	#95	C₂³×C₂₃	1	2	yes	—
733	#95	C₂³×C₂₃	1	2	yes	—
734	#95	C₂³×C₂₃	1	2	yes	—
735	#95	C₂³×C₂₃	1	2	yes	—
736	#95	C₂³×C₂₃	1	2	yes	—
737	#95	C₂³×C₂₃	1	2	yes	—
738	C₂₃	#36588	1	1	yes	characteristic, direct product factor, Sylow
739	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
741	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₂×D₄	—	2	2	no	—
743	C₂×D₄	—	2	4	no	—
744	C₂×D₄	—	2	2	no	—
745	C₂×D₄	—	2	4	no	—
746	C₂×D₄	—	2	4	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	2	2	no	—
749	C₂×D₄	—	2	2	no	—
750	C₂×D₄	—	2	2	no	—
751	C₂×D₄	—	2	4	no	—
752	C₂×D₄	—	4	2	no	—
753	C₂×D₄	—	4	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	2	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	4	2	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	1	no	—
770	C₂²×C₄	—	4	1	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	#41×C₂₃	1	4	yes	—
774	C₂²×C₄	#41×C₂₃	1	4	yes	—
775	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
781	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
782	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
784	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
786	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
788	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
789	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
790	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
791	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₄⋊C₄	—	2	4	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	4	no	—
807	C₄⋊C₄	—	2	4	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	4	2	no	—
810	C₄⋊C₄	—	4	2	no	—
811	C₄⋊C₄	—	4	2	no	—
812	C₄⋊C₄	—	4	1	no	—
813	C₄⋊C₄	—	4	1	no	—
814	C₄⋊C₄	—	4	2	no	—
815	C₄⋊C₄	#41×C₂₃	1	4	yes	—
816	C₄⋊C₄	#41×C₂₃	1	4	yes	—
817	C₂²⋊C₄	—	2	2	no	—
818	C₂²⋊C₄	—	2	4	no	—
819	C₂²⋊C₄	—	2	2	no	—
820	C₂²⋊C₄	—	2	2	no	—
821	C₂²⋊C₄	—	2	4	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	4	no	—
824	C₂²⋊C₄	—	2	4	no	—
825	C₂²⋊C₄	—	2	4	no	—
826	C₂²⋊C₄	—	2	4	no	—
827	C₂²⋊C₄	—	2	4	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	4	2	no	—
831	C₂²⋊C₄	—	4	2	no	—
832	C₂²⋊C₄	—	4	2	no	—
833	C₂²⋊C₄	—	4	2	no	—
834	C₂²⋊C₄	—	4	2	no	—
835	C₂²⋊C₄	—	4	2	no	—
836	C₂²⋊C₄	—	4	2	no	—
837	C₂²⋊C₄	—	4	2	no	—
838	C₂²⋊C₄	—	4	1	no	—
839	C₂²⋊C₄	—	4	1	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	4	no	—
845	C₄²	—	2	2	no	—
846	C₄²	—	2	2	no	—
847	C₄²	—	2	2	no	—
848	C₄²	—	4	2	no	—
849	C₄²	—	4	2	no	—
850	C₄²	—	4	2	no	—
851	C₄²	—	4	2	no	—
852	C₄²	—	4	2	no	—
853	C₄²	—	4	2	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	2	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	1	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	1	no	—
868	C₂³	—	2	1	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	1	no	—
872	C₂³	C₂×#41×C₂₃	1	2	yes	—
873	C₂³	C₂×#41×C₂₃	1	2	yes	—
874	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
875	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
876	D₄	—	4	4	no	—
877	D₄	—	4	8	no	—
878	D₄	—	4	4	no	—
879	D₄	—	8	4	no	—
880	C₂×C₄	—	2	8	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	8	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	1	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	1	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	1	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	1	no	—
924	C₂×C₄	—	2	1	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	1	no	—
934	C₂×C₄	—	4	8	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	4	no	—
938	C₂×C₄	—	8	4	no	—
939	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
940	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
941	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
942	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
943	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
944	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
945	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
946	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	1	no	—
961	C₂²	—	4	1	no	—
962	C₂²	—	4	2	no	—
963	C₂²	—	4	2	no	—
964	C₂²	—	4	1	no	—
965	C₂²	—	4	2	no	—
966	C₂²	—	4	1	no	—
967	C₂²	C₂₃×#553	1	4	yes	—
968	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
969	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
970	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
971	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
972	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
973	C₂²	C₂₃×#585	1	1	yes	characteristic
974	C₂²	C₂₃×#585	1	1	yes	characteristic
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	4	no	—
979	C₄	—	2	4	no	—
980	C₄	—	4	1	no	—
981	C₄	—	4	1	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	1	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	1	no	—
988	C₄	—	4	1	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	1	no	—
994	C₄	C₂₃×#529	1	4	yes	—
995	C₂	—	2	4	no	—
996	C₂	—	8	1	no	—
997	C₂	—	8	2	no	—
998	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
999	C₂	C₂×C₂₃×#553	1	1	yes	characteristic
1000	C₂	C₂₃×#3480	1	1	yes	characteristic
1001	C₂	C₂₃×#3480	1	1	yes	characteristic
1002	C₂	C₂₃×#3493	1	1	yes	characteristic
1003	C₂	C₂₃×#3513	1	1	yes	characteristic
1004	C₂	C₂₃×#3513	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2416	C₂
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
1. C₂₃×#2854	C₂	semidirect
2. C₂₃×#2854	C₂	semidirect
3. C₂₃×#2595	C₂	semidirect
4. C₂₃×#2594	C₂	semidirect
5. C₂₃×#2593	C₂	semidirect
6. C₂₃×#2573	C₂	semidirect
7. C₂₃×#2513	C₂	semidirect
8. C₂₃×#2510	C₂	semidirect
9. C₂₃×#2509	C₂	semidirect
10. C₂₃×#2494	C₂	semidirect
11. C₂₃×#2490	C₂	semidirect
12. C₂₃×#2444	C₂	semidirect
13. C₂₃×#2442	C₂	semidirect
15. C₂₃×#2370	C₂	semidirect
16. C₂₃×#2363	C₂	semidirect
17. C₂₃×#2361	C₂	semidirect
18. C₂₃×#2357	C₂	semidirect
19. C₂₃×#2352	C₂	semidirect
20. C₂₃×#2347	C₂	semidirect
21. C₄×C₂₃×#123	C₂	semidirect
22. C₄×C₂₃×#123	C₂	semidirect
23. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
351. #36588	C₂₃	direct (N × H)
445. #2854	C₂×C₂₃	semidirect
446. #2854	C₂×C₂₃	semidirect
447. #2595	C₂×C₂₃	semidirect
448. #2594	C₂×C₂₃	semidirect
449. #2593	C₂×C₂₃	semidirect
450. #2573	C₂×C₂₃	semidirect
451. #2513	C₂×C₂₃	semidirect
452. #2510	C₂×C₂₃	semidirect
453. #2509	C₂×C₂₃	semidirect
454. #2494	C₂×C₂₃	semidirect
455. #2490	C₂×C₂₃	semidirect
456. #2444	C₂×C₂₃	semidirect
457. #2442	C₂×C₂₃	semidirect
459. #2370	C₂×C₂₃	semidirect
460. #2363	C₂×C₂₃	semidirect
461. #2361	C₂×C₂₃	semidirect
462. #2357	C₂×C₂₃	semidirect
463. #2352	C₂×C₂₃	semidirect
464. #2347	C₂×C₂₃	semidirect
465. C₄×#123	C₂×C₂₃	semidirect
466. C₄×#123	C₂×C₂₃	semidirect
467. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
738. C₂₃	#36588	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×#2854	2
C₂₃×#2595	2
C₂₃×#2594	2
C₂₃×#2593	2
C₂₃×#2573	2
C₂₃×#2513	2
C₂₃×#2510	2
C₂₃×#2509	2
C₂₃×#2494	2
C₂₃×#2490	2
C₂₃×#2444	2
C₂₃×#2442	2
C₂₃×#2416	2
C₂₃×#2370	2
C₂₃×#2363	2
C₂₃×#2361	2
C₂₃×#2357	2
C₂₃×#2352	2
C₂₃×#2347	2
C₄×C₂₃×#123	2
C₂×C₄×C₄⋊C₄×C₂₃	2
#36588	23

Subgroups — C23×#36588 #19184214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36588 #19184214