Subgroups — C₂₃×#35025 #19182651

Order 5888.

2176 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2861	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2651	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2648	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2593	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2554	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2513	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2480	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2426	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2418	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2408	C₂	1	1	yes	maximal, characteristic
19	C₂₃×#2321	C₂	1	2	yes	maximal, complemented
20	C₂₃×#2312	C₂	1	2	yes	maximal, complemented
21	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
30	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#120	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
43	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#400	C₂²	1	2	yes	complemented
45	C₂₃×#399	C₂²	1	2	yes	complemented
46	C₂₃×#398	C₂²	1	2	yes	complemented
47	C₂₃×#398	C₂²	1	2	yes	complemented
48	C₂₃×#397	C₂²	1	2	yes	complemented
49	C₂₃×#397	C₂²	1	2	yes	complemented
50	C₂₃×#397	C₂²	1	2	yes	complemented
51	C₂₃×#397	C₂²	1	2	yes	complemented
52	C₂₃×#396	C₂²	1	2	yes	complemented
53	C₂₃×#396	C₂²	1	2	yes	complemented
54	C₂₃×#394	C₂²	1	2	yes	—
55	C₂₃×#394	C₂²	1	2	yes	—
56	C₂₃×#394	C₂²	1	2	yes	—
57	C₂₃×#394	C₂²	1	2	yes	complemented
58	C₂₃×#394	C₂²	1	2	yes	complemented
59	C₂₃×#392	C₂²	1	2	yes	—
60	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
61	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#390	C₂²	1	1	yes	characteristic
63	C₂₃×#390	C₂²	1	1	yes	characteristic
64	C₂₃×#390	C₂²	1	1	yes	characteristic
65	C₂₃×#390	C₂²	1	1	yes	characteristic
66	C₂₃×#390	C₂²	1	1	yes	characteristic
67	C₂₃×#390	C₂²	1	1	yes	characteristic
68	C₂₃×#390	C₂²	1	2	yes	—
69	C₂₃×#390	C₂²	1	1	yes	characteristic
70	C₂₃×#390	C₂²	1	1	yes	characteristic
71	C₂₃×#390	C₂²	1	2	yes	—
72	C₂₃×#390	C₂²	1	2	yes	complemented
73	C₂₃×#390	C₂²	1	2	yes	complemented
74	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
76	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#388	C₂²	1	2	yes	complemented
79	C₂₃×#388	C₂²	1	2	yes	complemented
80	C₂₃×#388	C₂²	1	2	yes	complemented
81	C₂₃×#388	C₂²	1	2	yes	complemented
82	C₂₃×#388	C₂²	1	2	yes	complemented
83	C₂₃×#388	C₂²	1	2	yes	complemented
84	C₂₃×#388	C₂²	1	2	yes	complemented
85	C₂₃×#388	C₂²	1	2	yes	complemented
86	C₂₃×#388	C₂²	1	2	yes	complemented
87	C₂₃×#388	C₂²	1	2	yes	complemented
88	C₂₃×#388	C₂²	1	2	yes	complemented
89	C₂₃×#388	C₂²	1	2	yes	complemented
90	C₂₃×#388	C₂²	1	2	yes	complemented
91	C₂₃×#388	C₂²	1	2	yes	complemented
92	C₂₃×#388	C₂²	1	2	yes	complemented
93	C₂₃×#388	C₂²	1	2	yes	complemented
94	C₂₃×#388	C₂²	1	2	yes	complemented
95	C₂₃×#387	C₂²	1	2	yes	complemented
96	C₂₃×#386	C₂²	1	2	yes	—
97	C₂₃×#386	C₂²	1	2	yes	complemented
98	C₂₃×#386	C₂²	1	2	yes	complemented
99	C₂₃×#386	C₂²	1	2	yes	complemented
100	C₂₃×#385	C₂²	1	2	yes	—
101	C₂₃×#385	C₂²	1	2	yes	—
102	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#380	C₂²	1	1	yes	characteristic
104	C₂₃×#380	C₂²	1	2	yes	—
105	C₂₃×#380	C₂²	1	2	yes	—
106	C₂₃×#380	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#379	C₂²	1	2	yes	—
108	C₂₃×#379	C₂²	1	2	yes	—
109	C₂₃×#379	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊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	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
122	C₄³×C₂₃	C₂²	1	1	yes	characteristic, complemented
123	C₂⁵×C₂₃	C₂³	1	2	yes	—
124	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	—	2	4	no	—
126	C₂²×D₄×C₂₃	—	4	2	no	—
127	C₂²×D₄×C₂₃	—	4	2	no	—
128	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
132	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
133	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂₃×#126	—	4	4	no	—
142	C₂₃×#125	—	4	2	no	—
143	C₂₃×#124	—	4	2	no	—
144	C₂₃×#124	—	4	2	no	—
145	C₂₃×#123	—	4	4	no	—
146	C₂₃×C₂²⋊Q₈	—	2	4	no	—
147	C₂₃×C₂²⋊Q₈	—	4	2	no	—
148	C₂₃×#121	—	4	2	no	—
149	C₂₃×#121	—	4	2	no	—
150	C₂₃×#120	—	2	8	no	—
151	C₄×Q₈×C₂₃	—	4	2	no	—
152	C₄×D₄×C₂₃	—	2	4	no	—
153	C₄×D₄×C₂₃	—	2	4	no	—
154	C₄×D₄×C₂₃	—	2	4	no	—
155	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	—	2	8	no	—
175	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₂₃	—	4	2	no	—
209	C₂×C₄²×C₂₃	—	4	2	no	—
210	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
220	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
223	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
225	C₂₃×#95	C₂³	1	1	yes	characteristic
226	C₂₃×#95	C₂³	1	1	yes	characteristic
227	C₂₃×#95	C₂³	1	1	yes	characteristic
228	C₂₃×#95	C₂³	1	1	yes	characteristic
229	C₂₃×#95	C₂³	1	1	yes	characteristic
230	C₂₃×#95	C₂³	1	1	yes	characteristic
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	C₂₃×#95	C₂³	1	2	yes	—
237	C₂₃×#95	C₂³	1	2	yes	—
238	C₂₃×#95	C₂³	1	2	yes	—
239	C₂₃×#95	C₂³	1	2	yes	—
240	C₂₃×#95	C₂³	1	2	yes	—
241	C₂₃×#95	C₂³	1	2	yes	—
242	C₂₃×#95	C₂³	1	2	yes	—
243	C₂₃×#95	C₂³	1	2	yes	—
244	C₂⁴×C₂₃	—	2	4	no	—
245	C₂⁴×C₂₃	—	2	4	no	—
246	C₂⁴×C₂₃	—	2	4	no	—
247	C₂⁴×C₂₃	—	4	2	no	—
248	C₂⁴×C₂₃	—	4	2	no	—
249	C₂⁴×C₂₃	—	4	2	no	—
250	C₂⁴×C₂₃	—	4	2	no	—
251	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
252	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
253	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₂₃	—	2	2	no	—
256	C₂×Q₈×C₂₃	—	2	2	no	—
257	C₂×Q₈×C₂₃	—	2	2	no	—
258	C₂×D₄×C₂₃	—	2	2	no	—
259	C₂×D₄×C₂₃	—	2	2	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	4	no	—
262	C₂×D₄×C₂₃	—	2	4	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	2	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	2	no	—
269	C₂×D₄×C₂₃	—	4	2	no	—
270	C₂×D₄×C₂₃	—	4	2	no	—
271	C₂×D₄×C₂₃	—	4	16	no	—
272	C₂×D₄×C₂₃	—	4	2	no	—
273	C₂×D₄×C₂₃	—	4	2	no	—
274	C₂×D₄×C₂₃	—	4	2	no	—
275	C₂×D₄×C₂₃	—	4	2	no	—
276	C₂×D₄×C₂₃	#41	1	4	yes	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	2	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	4	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	2	2	no	—
284	C₂²×C₄×C₂₃	—	2	2	no	—
285	C₂²×C₄×C₂₃	—	2	2	no	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	4	1	no	—
289	C₂²×C₄×C₂₃	—	4	1	no	—
290	C₂²×C₄×C₂₃	—	4	1	no	—
291	C₂²×C₄×C₂₃	—	4	1	no	—
292	C₂²×C₄×C₂₃	—	4	1	no	—
293	C₂²×C₄×C₂₃	—	4	1	no	—
294	C₂²×C₄×C₂₃	—	4	2	no	—
295	C₂²×C₄×C₂₃	—	4	2	no	—
296	C₂²×C₄×C₂₃	#41	1	4	yes	—
297	C₂²×C₄×C₂₃	#41	1	4	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	2	no	—
320	C₄⋊C₄×C₂₃	—	2	2	no	—
321	C₄⋊C₄×C₂₃	—	2	4	no	—
322	C₄⋊C₄×C₂₃	—	2	2	no	—
323	C₄⋊C₄×C₂₃	—	2	2	no	—
324	C₄⋊C₄×C₂₃	—	2	2	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
326	C₄⋊C₄×C₂₃	—	2	4	no	—
327	C₄⋊C₄×C₂₃	—	4	2	no	—
328	C₄⋊C₄×C₂₃	—	4	2	no	—
329	C₄⋊C₄×C₂₃	—	4	2	no	—
330	C₄⋊C₄×C₂₃	—	4	2	no	—
331	C₄⋊C₄×C₂₃	—	4	2	no	—
332	C₄⋊C₄×C₂₃	—	4	2	no	—
333	C₄⋊C₄×C₂₃	—	4	2	no	—
334	C₄⋊C₄×C₂₃	—	4	2	no	—
335	C₂²⋊C₄×C₂₃	—	2	2	no	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	2	no	—
338	C₂²⋊C₄×C₂₃	—	2	2	no	—
339	C₂²⋊C₄×C₂₃	—	2	4	no	—
340	C₂²⋊C₄×C₂₃	—	2	4	no	—
341	C₂²⋊C₄×C₂₃	—	2	4	no	—
342	C₂²⋊C₄×C₂₃	—	2	4	no	—
343	C₂²⋊C₄×C₂₃	—	2	4	no	—
344	C₂²⋊C₄×C₂₃	—	2	4	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	2	no	—
347	C₂²⋊C₄×C₂₃	—	2	4	no	—
348	C₂²⋊C₄×C₂₃	—	2	4	no	—
349	C₂²⋊C₄×C₂₃	—	2	4	no	—
350	C₂²⋊C₄×C₂₃	—	2	4	no	—
351	C₂²⋊C₄×C₂₃	—	4	2	no	—
352	C₂²⋊C₄×C₂₃	—	4	2	no	—
353	C₂²⋊C₄×C₂₃	—	4	2	no	—
354	C₂²⋊C₄×C₂₃	—	4	2	no	—
355	C₂²⋊C₄×C₂₃	—	4	2	no	—
356	C₂²⋊C₄×C₂₃	—	4	2	no	—
357	C₂²⋊C₄×C₂₃	—	4	2	no	—
358	C₂²⋊C₄×C₂₃	—	4	2	no	—
359	C₂²⋊C₄×C₂₃	—	4	2	no	—
360	C₂²⋊C₄×C₂₃	—	4	2	no	—
361	C₂²⋊C₄×C₂₃	—	4	2	no	—
362	C₂²⋊C₄×C₂₃	—	4	2	no	—
363	C₂²⋊C₄×C₂₃	—	4	2	no	—
364	C₂²⋊C₄×C₂₃	—	4	2	no	—
365	C₂²⋊C₄×C₂₃	—	4	2	no	—
366	C₂²⋊C₄×C₂₃	—	4	2	no	—
367	C₄²×C₂₃	—	2	2	no	—
368	C₄²×C₂₃	—	2	2	no	—
369	C₄²×C₂₃	—	2	2	no	—
370	C₄²×C₂₃	—	2	2	no	—
371	C₄²×C₂₃	—	2	2	no	—
372	C₄²×C₂₃	—	2	2	no	—
373	C₄²×C₂₃	—	2	2	no	—
374	C₄²×C₂₃	—	2	2	no	—
375	C₄²×C₂₃	—	4	1	no	—
376	C₄²×C₂₃	—	4	1	no	—
377	C₄²×C₂₃	—	4	1	no	—
378	C₄²×C₂₃	—	4	1	no	—
379	C₄²×C₂₃	—	4	2	no	—
380	C₄²×C₂₃	—	4	1	no	—
381	C₄²×C₂₃	—	4	2	no	—
382	#35025	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂³×C₂₃	—	2	1	no	—
384	C₂³×C₂₃	—	2	1	no	—
385	C₂³×C₂₃	—	2	1	no	—
386	C₂³×C₂₃	—	2	1	no	—
387	C₂³×C₂₃	—	2	1	no	—
388	C₂³×C₂₃	—	2	1	no	—
389	C₂³×C₂₃	—	2	1	no	—
390	C₂³×C₂₃	—	2	1	no	—
391	C₂³×C₂₃	—	2	1	no	—
392	C₂³×C₂₃	—	2	1	no	—
393	C₂³×C₂₃	—	2	2	no	—
394	C₂³×C₂₃	—	2	2	no	—
395	C₂³×C₂₃	—	2	2	no	—
396	C₂³×C₂₃	—	2	2	no	—
397	C₂³×C₂₃	—	2	2	no	—
398	C₂³×C₂₃	—	2	2	no	—
399	C₂³×C₂₃	—	2	2	no	—
400	C₂³×C₂₃	—	2	2	no	—
401	C₂³×C₂₃	—	2	2	no	—
402	C₂³×C₂₃	—	2	2	no	—
403	C₂³×C₂₃	—	2	2	no	—
404	C₂³×C₂₃	—	2	2	no	—
405	C₂³×C₂₃	—	2	2	no	—
406	C₂³×C₂₃	—	2	2	no	—
407	C₂³×C₂₃	—	4	8	no	—
408	C₂³×C₂₃	—	4	8	no	—
409	C₂³×C₂₃	—	4	8	no	—
410	C₂³×C₂₃	—	8	4	no	—
411	C₂³×C₂₃	—	8	4	no	—
412	C₂³×C₂₃	—	8	4	no	—
413	C₂³×C₂₃	—	8	4	no	—
414	C₂³×C₂₃	C₂×#41	1	2	yes	—
415	C₂³×C₂₃	C₂×#41	1	2	yes	—
416	C₂³×C₂₃	C₂×#41	1	2	yes	—
417	C₂³×C₂₃	C₂×#41	1	2	yes	—
418	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
419	Q₈×C₂₃	—	4	4	no	—
420	D₄×C₂₃	—	2	8	no	—
421	D₄×C₂₃	—	4	8	no	—
422	D₄×C₂₃	—	4	4	no	—
423	D₄×C₂₃	—	4	4	no	—
424	D₄×C₂₃	—	8	4	no	—
425	D₄×C₂₃	—	8	4	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	1	no	—
430	C₂×C₄×C₂₃	—	2	1	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	2	1	no	—
433	C₂×C₄×C₂₃	—	2	1	no	—
434	C₂×C₄×C₂₃	—	2	1	no	—
435	C₂×C₄×C₂₃	—	2	1	no	—
436	C₂×C₄×C₂₃	—	2	8	no	—
437	C₂×C₄×C₂₃	—	2	1	no	—
438	C₂×C₄×C₂₃	—	2	1	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	1	no	—
446	C₂×C₄×C₂₃	—	2	1	no	—
447	C₂×C₄×C₂₃	—	2	1	no	—
448	C₂×C₄×C₂₃	—	2	1	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	1	no	—
453	C₂×C₄×C₂₃	—	2	1	no	—
454	C₂×C₄×C₂₃	—	2	1	no	—
455	C₂×C₄×C₂₃	—	2	1	no	—
456	C₂×C₄×C₂₃	—	2	1	no	—
457	C₂×C₄×C₂₃	—	2	1	no	—
458	C₂×C₄×C₂₃	—	2	2	no	—
459	C₂×C₄×C₂₃	—	2	2	no	—
460	C₂×C₄×C₂₃	—	2	2	no	—
461	C₂×C₄×C₂₃	—	2	2	no	—
462	C₂×C₄×C₂₃	—	2	1	no	—
463	C₂×C₄×C₂₃	—	2	2	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	2	1	no	—
466	C₂×C₄×C₂₃	—	2	1	no	—
467	C₂×C₄×C₂₃	—	2	2	no	—
468	C₂×C₄×C₂₃	—	2	2	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	2	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	2	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	2	no	—
475	C₂×C₄×C₂₃	—	2	1	no	—
476	C₂×C₄×C₂₃	—	4	4	no	—
477	C₂×C₄×C₂₃	—	4	4	no	—
478	C₂×C₄×C₂₃	—	4	4	no	—
479	C₂×C₄×C₂₃	—	4	4	no	—
480	C₂×C₄×C₂₃	—	4	4	no	—
481	C₂×C₄×C₂₃	—	8	4	no	—
482	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
483	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
484	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
485	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
486	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
487	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
488	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
489	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
490	#2861	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#2860	C₂×C₂₃	1	1	yes	characteristic, complemented
492	#2854	C₂×C₂₃	1	1	yes	characteristic, complemented
493	#2850	C₂×C₂₃	1	1	yes	characteristic, complemented
494	#2651	C₂×C₂₃	1	2	yes	complemented
495	#2648	C₂×C₂₃	1	2	yes	complemented
496	#2593	C₂×C₂₃	1	2	yes	complemented
497	#2554	C₂×C₂₃	1	2	yes	complemented
498	#2513	C₂×C₂₃	1	1	yes	characteristic, complemented
499	#2490	C₂×C₂₃	1	1	yes	characteristic, complemented
500	#2480	C₂×C₂₃	1	2	yes	complemented
501	#2448	C₂×C₂₃	1	1	yes	characteristic, complemented
502	#2442	C₂×C₂₃	1	1	yes	characteristic, complemented
503	#2435	C₂×C₂₃	1	1	yes	characteristic, complemented
504	#2426	C₂×C₂₃	1	1	yes	characteristic, complemented
505	#2418	C₂×C₂₃	1	2	yes	complemented
506	#2417	C₂×C₂₃	1	1	yes	characteristic, complemented
507	#2408	C₂×C₂₃	1	1	yes	characteristic
508	#2321	C₂×C₂₃	1	2	yes	complemented
509	#2312	C₂×C₂₃	1	2	yes	complemented
510	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
511	C₂×#390	C₂×C₂₃	1	1	yes	characteristic, complemented
512	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
513	C₂²×C₂₃	—	2	2	no	—
514	C₂²×C₂₃	—	2	2	no	—
515	C₂²×C₂₃	—	2	2	no	—
516	C₂²×C₂₃	—	2	2	no	—
517	C₂²×C₂₃	—	2	2	no	—
518	C₂²×C₂₃	—	2	2	no	—
519	C₂²×C₂₃	—	2	2	no	—
520	C₂²×C₂₃	—	2	2	no	—
521	C₂²×C₂₃	—	2	2	no	—
522	C₂²×C₂₃	—	4	1	no	—
523	C₂²×C₂₃	—	4	1	no	—
524	C₂²×C₂₃	—	4	1	no	—
525	C₂²×C₂₃	—	4	1	no	—
526	C₂²×C₂₃	—	4	2	no	—
527	C₂²×C₂₃	—	4	2	no	—
528	C₂²×C₂₃	—	4	2	no	—
529	C₂²×C₂₃	—	4	2	no	—
530	C₂²×C₂₃	—	4	2	no	—
531	C₂²×C₂₃	—	4	2	no	—
532	C₂²×C₂₃	—	4	2	no	—
533	C₂²×C₂₃	—	4	2	no	—
534	C₂²×C₂₃	—	4	2	no	—
535	C₂²×C₂₃	—	4	2	no	—
536	C₂²×C₂₃	—	4	2	no	—
537	C₂²×C₂₃	—	4	2	no	—
538	C₂²×C₂₃	—	4	2	no	—
539	C₂²×C₂₃	—	4	2	no	—
540	C₂²×C₂₃	—	8	16	no	—
541	C₂²×C₂₃	#529	1	4	yes	—
542	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
543	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
545	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₂₃	#585	1	1	yes	characteristic
549	C₄×C₂₃	—	2	2	no	—
550	C₄×C₂₃	—	2	2	no	—
551	C₄×C₂₃	—	2	2	no	—
552	C₄×C₂₃	—	2	2	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	4	1	no	—
555	C₄×C₂₃	—	4	2	no	—
556	C₄×C₂₃	—	4	1	no	—
557	C₄×C₂₃	—	4	2	no	—
558	C₄×C₂₃	—	4	1	no	—
559	C₄×C₂₃	—	4	1	no	—
560	C₄×C₂₃	—	4	2	no	—
561	C₄×C₂₃	—	4	2	no	—
562	C₄×C₂₃	—	4	1	no	—
563	C₄×C₂₃	—	4	2	no	—
564	C₄×C₂₃	—	4	1	no	—
565	C₄×C₂₃	—	4	1	no	—
566	C₄×C₂₃	—	4	2	no	—
567	C₄×C₂₃	#538	1	4	yes	—
568	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
569	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
570	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
571	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
572	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
573	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
574	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
575	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
576	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
577	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
578	C₂×#120	C₂²×C₂₃	1	2	yes	—
579	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
580	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
581	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
582	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
583	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
584	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
585	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
586	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
587	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
588	#400	C₂²×C₂₃	1	2	yes	complemented
589	#399	C₂²×C₂₃	1	2	yes	complemented
590	#398	C₂²×C₂₃	1	2	yes	complemented
591	#398	C₂²×C₂₃	1	2	yes	complemented
592	#397	C₂²×C₂₃	1	2	yes	complemented
593	#397	C₂²×C₂₃	1	2	yes	complemented
594	#397	C₂²×C₂₃	1	2	yes	complemented
595	#397	C₂²×C₂₃	1	2	yes	complemented
596	#396	C₂²×C₂₃	1	2	yes	complemented
597	#396	C₂²×C₂₃	1	2	yes	complemented
598	#394	C₂²×C₂₃	1	2	yes	—
599	#394	C₂²×C₂₃	1	2	yes	—
600	#394	C₂²×C₂₃	1	2	yes	—
601	#394	C₂²×C₂₃	1	2	yes	complemented
602	#394	C₂²×C₂₃	1	2	yes	complemented
603	#392	C₂²×C₂₃	1	2	yes	—
604	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
606	#390	C₂²×C₂₃	1	2	yes	—
607	#390	C₂²×C₂₃	1	1	yes	characteristic
608	#390	C₂²×C₂₃	1	1	yes	characteristic
609	#390	C₂²×C₂₃	1	1	yes	characteristic
610	#390	C₂²×C₂₃	1	1	yes	characteristic
611	#390	C₂²×C₂₃	1	1	yes	characteristic
612	#390	C₂²×C₂₃	1	1	yes	characteristic
613	#390	C₂²×C₂₃	1	2	yes	—
614	#390	C₂²×C₂₃	1	1	yes	characteristic
615	#390	C₂²×C₂₃	1	1	yes	characteristic
616	#390	C₂²×C₂₃	1	2	yes	complemented
617	#390	C₂²×C₂₃	1	2	yes	complemented
618	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
619	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
621	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
622	#388	C₂²×C₂₃	1	2	yes	complemented
623	#388	C₂²×C₂₃	1	2	yes	complemented
624	#388	C₂²×C₂₃	1	2	yes	complemented
625	#388	C₂²×C₂₃	1	2	yes	complemented
626	#388	C₂²×C₂₃	1	2	yes	complemented
627	#388	C₂²×C₂₃	1	2	yes	complemented
628	#388	C₂²×C₂₃	1	2	yes	complemented
629	#388	C₂²×C₂₃	1	2	yes	complemented
630	#388	C₂²×C₂₃	1	2	yes	complemented
631	#388	C₂²×C₂₃	1	2	yes	complemented
632	#388	C₂²×C₂₃	1	2	yes	complemented
633	#388	C₂²×C₂₃	1	2	yes	complemented
634	#388	C₂²×C₂₃	1	2	yes	complemented
635	#388	C₂²×C₂₃	1	2	yes	complemented
636	#388	C₂²×C₂₃	1	2	yes	complemented
637	#388	C₂²×C₂₃	1	2	yes	complemented
638	#388	C₂²×C₂₃	1	2	yes	complemented
639	#387	C₂²×C₂₃	1	2	yes	complemented
640	#386	C₂²×C₂₃	1	2	yes	—
641	#386	C₂²×C₂₃	1	2	yes	complemented
642	#386	C₂²×C₂₃	1	2	yes	complemented
643	#386	C₂²×C₂₃	1	2	yes	complemented
644	#385	C₂²×C₂₃	1	2	yes	—
645	#385	C₂²×C₂₃	1	2	yes	—
646	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
647	#380	C₂²×C₂₃	1	2	yes	—
648	#380	C₂²×C₂₃	1	2	yes	—
649	#380	C₂²×C₂₃	1	1	yes	characteristic
650	#380	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#379	C₂²×C₂₃	1	2	yes	—
652	#379	C₂²×C₂₃	1	2	yes	—
653	#379	C₂²×C₂₃	1	2	yes	—
654	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
656	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
657	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
660	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
661	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
662	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
663	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
664	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
665	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
666	C₄³	C₂²×C₂₃	1	1	yes	characteristic, complemented
667	C₂×C₂₃	—	2	4	no	—
668	C₂×C₂₃	—	4	2	no	—
669	C₂×C₂₃	—	8	2	no	—
670	C₂×C₂₃	—	8	2	no	—
671	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
672	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
673	C₂×C₂₃	#3460	1	1	yes	characteristic
674	C₂×C₂₃	#3505	1	1	yes	characteristic
675	C₂×C₂₃	#3508	1	1	yes	characteristic
676	C₂×C₂₃	#3514	1	1	yes	characteristic
677	C₂×C₂₃	#3519	1	1	yes	characteristic
678	C₂⁵	C₂³×C₂₃	1	2	yes	—
679	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
680	C₂²×D₄	—	2	4	no	—
681	C₂²×D₄	—	4	2	no	—
682	C₂²×D₄	—	4	2	no	—
683	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
684	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
685	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
686	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
687	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
688	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
689	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
690	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
691	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
692	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
693	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
694	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
696	#126	—	4	4	no	—
697	#125	—	4	2	no	—
698	#124	—	4	2	no	—
699	#124	—	4	2	no	—
700	#123	—	4	4	no	—
701	C₂²⋊Q₈	—	2	4	no	—
702	C₂²⋊Q₈	—	4	2	no	—
703	#121	—	4	2	no	—
704	#121	—	4	2	no	—
705	#120	—	2	8	no	—
706	C₄×Q₈	—	4	2	no	—
707	C₄×D₄	—	2	4	no	—
708	C₄×D₄	—	2	4	no	—
709	C₄×D₄	—	2	4	no	—
710	C₂×C₄⋊C₄	—	4	2	no	—
711	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
713	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
714	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
715	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
716	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
718	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
723	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
724	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
725	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
726	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
728	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
729	C₂×C₂²⋊C₄	—	2	8	no	—
730	C₂×C₂²⋊C₄	—	4	4	no	—
731	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
744	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
745	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
763	C₂×C₄²	—	4	2	no	—
764	C₂×C₄²	—	4	2	no	—
765	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
766	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
767	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
768	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
769	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
770	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
771	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
772	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
773	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
774	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
775	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
776	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
777	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
780	#95	C₂³×C₂₃	1	1	yes	characteristic
781	#95	C₂³×C₂₃	1	1	yes	characteristic
782	#95	C₂³×C₂₃	1	1	yes	characteristic
783	#95	C₂³×C₂₃	1	1	yes	characteristic
784	#95	C₂³×C₂₃	1	1	yes	characteristic
785	#95	C₂³×C₂₃	1	1	yes	characteristic
786	#95	C₂³×C₂₃	1	2	yes	—
787	#95	C₂³×C₂₃	1	2	yes	—
788	#95	C₂³×C₂₃	1	2	yes	—
789	#95	C₂³×C₂₃	1	2	yes	—
790	#95	C₂³×C₂₃	1	2	yes	—
791	#95	C₂³×C₂₃	1	2	yes	—
792	#95	C₂³×C₂₃	1	2	yes	—
793	#95	C₂³×C₂₃	1	2	yes	—
794	#95	C₂³×C₂₃	1	2	yes	—
795	#95	C₂³×C₂₃	1	2	yes	—
796	#95	C₂³×C₂₃	1	2	yes	—
797	#95	C₂³×C₂₃	1	2	yes	—
798	#95	C₂³×C₂₃	1	2	yes	—
799	C₂₃	#35025	1	1	yes	characteristic, direct product factor, Sylow
800	C₂⁴	—	2	4	no	—
801	C₂⁴	—	2	4	no	—
802	C₂⁴	—	2	4	no	—
803	C₂⁴	—	4	2	no	—
804	C₂⁴	—	4	2	no	—
805	C₂⁴	—	4	2	no	—
806	C₂⁴	—	4	2	no	—
807	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
808	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
809	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
810	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
811	C₂×Q₈	—	2	2	no	—
812	C₂×Q₈	—	2	2	no	—
813	C₂×Q₈	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	2	no	—
816	C₂×D₄	—	2	4	no	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	4	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	2	no	—
821	C₂×D₄	—	2	2	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	2	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	4	2	no	—
826	C₂×D₄	—	4	2	no	—
827	C₂×D₄	—	4	16	no	—
828	C₂×D₄	—	4	2	no	—
829	C₂×D₄	—	4	2	no	—
830	C₂×D₄	—	4	2	no	—
831	C₂×D₄	—	4	2	no	—
832	C₂×D₄	#41×C₂₃	1	4	yes	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	2	2	no	—
839	C₂²×C₄	—	2	2	no	—
840	C₂²×C₄	—	2	2	no	—
841	C₂²×C₄	—	2	2	no	—
842	C₂²×C₄	—	2	2	no	—
843	C₂²×C₄	—	2	2	no	—
844	C₂²×C₄	—	4	1	no	—
845	C₂²×C₄	—	4	1	no	—
846	C₂²×C₄	—	4	1	no	—
847	C₂²×C₄	—	4	1	no	—
848	C₂²×C₄	—	4	1	no	—
849	C₂²×C₄	—	4	1	no	—
850	C₂²×C₄	—	4	2	no	—
851	C₂²×C₄	—	4	2	no	—
852	C₂²×C₄	#41×C₂₃	1	4	yes	—
853	C₂²×C₄	#41×C₂₃	1	4	yes	—
854	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
855	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
860	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
861	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
863	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
864	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
865	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
866	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
867	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
868	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
869	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
871	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
872	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	—	2	2	no	—
877	C₄⋊C₄	—	2	4	no	—
878	C₄⋊C₄	—	2	2	no	—
879	C₄⋊C₄	—	2	2	no	—
880	C₄⋊C₄	—	2	2	no	—
881	C₄⋊C₄	—	2	2	no	—
882	C₄⋊C₄	—	2	4	no	—
883	C₄⋊C₄	—	4	2	no	—
884	C₄⋊C₄	—	4	2	no	—
885	C₄⋊C₄	—	4	2	no	—
886	C₄⋊C₄	—	4	2	no	—
887	C₄⋊C₄	—	4	2	no	—
888	C₄⋊C₄	—	4	2	no	—
889	C₄⋊C₄	—	4	2	no	—
890	C₄⋊C₄	—	4	2	no	—
891	C₂²⋊C₄	—	2	2	no	—
892	C₂²⋊C₄	—	2	2	no	—
893	C₂²⋊C₄	—	2	2	no	—
894	C₂²⋊C₄	—	2	2	no	—
895	C₂²⋊C₄	—	2	4	no	—
896	C₂²⋊C₄	—	2	4	no	—
897	C₂²⋊C₄	—	2	4	no	—
898	C₂²⋊C₄	—	2	4	no	—
899	C₂²⋊C₄	—	2	4	no	—
900	C₂²⋊C₄	—	2	4	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	4	no	—
904	C₂²⋊C₄	—	2	4	no	—
905	C₂²⋊C₄	—	2	4	no	—
906	C₂²⋊C₄	—	2	4	no	—
907	C₂²⋊C₄	—	4	2	no	—
908	C₂²⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	4	2	no	—
910	C₂²⋊C₄	—	4	2	no	—
911	C₂²⋊C₄	—	4	2	no	—
912	C₂²⋊C₄	—	4	2	no	—
913	C₂²⋊C₄	—	4	2	no	—
914	C₂²⋊C₄	—	4	2	no	—
915	C₂²⋊C₄	—	4	2	no	—
916	C₂²⋊C₄	—	4	2	no	—
917	C₂²⋊C₄	—	4	2	no	—
918	C₂²⋊C₄	—	4	2	no	—
919	C₂²⋊C₄	—	4	2	no	—
920	C₂²⋊C₄	—	4	2	no	—
921	C₂²⋊C₄	—	4	2	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₄²	—	2	2	no	—
924	C₄²	—	2	2	no	—
925	C₄²	—	2	2	no	—
926	C₄²	—	2	2	no	—
927	C₄²	—	2	2	no	—
928	C₄²	—	2	2	no	—
929	C₄²	—	2	2	no	—
930	C₄²	—	2	2	no	—
931	C₄²	—	4	1	no	—
932	C₄²	—	4	1	no	—
933	C₄²	—	4	1	no	—
934	C₄²	—	4	1	no	—
935	C₄²	—	4	2	no	—
936	C₄²	—	4	2	no	—
937	C₄²	—	4	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	2	no	—
949	C₂³	—	2	2	no	—
950	C₂³	—	2	2	no	—
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	2	2	no	—
954	C₂³	—	2	2	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	4	8	no	—
963	C₂³	—	4	8	no	—
964	C₂³	—	4	8	no	—
965	C₂³	—	8	4	no	—
966	C₂³	—	8	4	no	—
967	C₂³	—	8	4	no	—
968	C₂³	—	8	4	no	—
969	C₂³	C₂×#41×C₂₃	1	2	yes	—
970	C₂³	C₂×#41×C₂₃	1	2	yes	—
971	C₂³	C₂×#41×C₂₃	1	2	yes	—
972	C₂³	C₂×#41×C₂₃	1	2	yes	—
973	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
974	Q₈	—	4	4	no	—
975	D₄	—	2	8	no	—
976	D₄	—	4	8	no	—
977	D₄	—	4	4	no	—
978	D₄	—	4	4	no	—
979	D₄	—	8	4	no	—
980	D₄	—	8	4	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	8	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	4	4	no	—
1032	C₂×C₄	—	4	4	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	4	4	no	—
1035	C₂×C₄	—	4	4	no	—
1036	C₂×C₄	—	8	4	no	—
1037	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1038	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1039	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1040	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1041	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1042	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1043	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1044	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	2	2	no	—
1047	C₂²	—	2	2	no	—
1048	C₂²	—	2	2	no	—
1049	C₂²	—	2	2	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	4	2	no	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	8	16	no	—
1073	C₂²	C₂₃×#529	1	4	yes	—
1074	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1075	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1076	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1077	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1078	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1079	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1080	C₂²	C₂₃×#585	1	1	yes	characteristic
1081	C₄	—	2	2	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	2	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	C₂₃×#538	1	4	yes	—
1100	C₂	—	2	4	no	—
1101	C₂	—	4	2	no	—
1102	C₂	—	8	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
1105	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
1106	C₂	C₂₃×#3460	1	1	yes	characteristic
1107	C₂	C₂₃×#3505	1	1	yes	characteristic
1108	C₂	C₂₃×#3508	1	1	yes	characteristic
1109	C₂	C₂₃×#3514	1	1	yes	characteristic
1110	C₂	C₂₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2408	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×#2861	C₂	semidirect
2. C₂₃×#2860	C₂	semidirect
3. C₂₃×#2854	C₂	semidirect
4. C₂₃×#2850	C₂	semidirect
5. C₂₃×#2651	C₂	semidirect
6. C₂₃×#2648	C₂	semidirect
7. C₂₃×#2593	C₂	semidirect
8. C₂₃×#2554	C₂	semidirect
9. C₂₃×#2513	C₂	semidirect
10. C₂₃×#2490	C₂	semidirect
11. C₂₃×#2480	C₂	semidirect
12. C₂₃×#2448	C₂	semidirect
13. C₂₃×#2442	C₂	semidirect
14. C₂₃×#2435	C₂	semidirect
15. C₂₃×#2426	C₂	semidirect
16. C₂₃×#2418	C₂	semidirect
17. C₂₃×#2417	C₂	semidirect
19. C₂₃×#2321	C₂	semidirect
20. C₂₃×#2312	C₂	semidirect
21. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
22. C₂×C₂₃×#390	C₂	semidirect
23. C₄²×D₄×C₂₃	C₂	semidirect
25. C₂×C₂₃×#126	C₂²	semidirect
26. C₂×C₂₃×#125	C₂²	semidirect
29. C₂×C₂₃×#123	C₂²	semidirect
31. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
35. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
43. C₂²×C₄²×C₂₃	C₂²	semidirect
44. C₂₃×#400	C₂²	semidirect
45. C₂₃×#399	C₂²	semidirect
46. C₂₃×#398	C₂²	semidirect
47. C₂₃×#398	C₂²	semidirect
48. C₂₃×#397	C₂²	semidirect
49. C₂₃×#397	C₂²	semidirect
50. C₂₃×#397	C₂²	semidirect
51. C₂₃×#397	C₂²	semidirect
52. C₂₃×#396	C₂²	semidirect
53. C₂₃×#396	C₂²	semidirect
57. C₂₃×#394	C₂²	semidirect
58. C₂₃×#394	C₂²	semidirect
60. C₂₃×#391	C₂²	semidirect
61. C₂₃×#391	C₂²	semidirect
72. C₂₃×#390	C₂²	semidirect
73. C₂₃×#390	C₂²	semidirect
74. C₂₃×#389	C₂²	semidirect
75. C₂₃×#389	C₂²	semidirect
76. C₂₃×#389	C₂²	semidirect
77. C₂₃×#389	C₂²	semidirect
78. C₂₃×#388	C₂²	semidirect
79. C₂₃×#388	C₂²	semidirect
80. C₂₃×#388	C₂²	semidirect
81. C₂₃×#388	C₂²	semidirect
82. C₂₃×#388	C₂²	semidirect
83. C₂₃×#388	C₂²	semidirect
84. C₂₃×#388	C₂²	semidirect
85. C₂₃×#388	C₂²	semidirect
86. C₂₃×#388	C₂²	semidirect
87. C₂₃×#388	C₂²	semidirect
88. C₂₃×#388	C₂²	semidirect
89. C₂₃×#388	C₂²	semidirect
90. C₂₃×#388	C₂²	semidirect
91. C₂₃×#388	C₂²	semidirect
92. C₂₃×#388	C₂²	semidirect
93. C₂₃×#388	C₂²	semidirect
94. C₂₃×#388	C₂²	semidirect
95. C₂₃×#387	C₂²	semidirect
97. C₂₃×#386	C₂²	semidirect
98. C₂₃×#386	C₂²	semidirect
99. C₂₃×#386	C₂²	semidirect
102. C₂₃×#382	C₂²	semidirect
106. C₂₃×#380	C₂²	semidirect
110. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
111. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
112. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
113. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
114. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
119. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
120. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
122. C₄³×C₂₃	C₂²	semidirect
382. #35025	C₂₃	direct (N × H)
490. #2861	C₂×C₂₃	semidirect
491. #2860	C₂×C₂₃	semidirect
492. #2854	C₂×C₂₃	semidirect
493. #2850	C₂×C₂₃	semidirect
494. #2651	C₂×C₂₃	semidirect
495. #2648	C₂×C₂₃	semidirect
496. #2593	C₂×C₂₃	semidirect
497. #2554	C₂×C₂₃	semidirect
498. #2513	C₂×C₂₃	semidirect
499. #2490	C₂×C₂₃	semidirect
500. #2480	C₂×C₂₃	semidirect
501. #2448	C₂×C₂₃	semidirect
502. #2442	C₂×C₂₃	semidirect
503. #2435	C₂×C₂₃	semidirect
504. #2426	C₂×C₂₃	semidirect
505. #2418	C₂×C₂₃	semidirect
506. #2417	C₂×C₂₃	semidirect
508. #2321	C₂×C₂₃	semidirect
509. #2312	C₂×C₂₃	semidirect
510. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
511. C₂×#390	C₂×C₂₃	semidirect
512. C₄²×D₄	C₂×C₂₃	semidirect
569. C₂×#126	C₂²×C₂₃	semidirect
570. C₂×#125	C₂²×C₂₃	semidirect
573. C₂×#123	C₂²×C₂₃	semidirect
575. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
579. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
587. C₂²×C₄²	C₂²×C₂₃	semidirect
588. #400	C₂²×C₂₃	semidirect
589. #399	C₂²×C₂₃	semidirect
590. #398	C₂²×C₂₃	semidirect
591. #398	C₂²×C₂₃	semidirect
592. #397	C₂²×C₂₃	semidirect
593. #397	C₂²×C₂₃	semidirect
594. #397	C₂²×C₂₃	semidirect
595. #397	C₂²×C₂₃	semidirect
596. #396	C₂²×C₂₃	semidirect
597. #396	C₂²×C₂₃	semidirect
601. #394	C₂²×C₂₃	semidirect
602. #394	C₂²×C₂₃	semidirect
604. #391	C₂²×C₂₃	semidirect
605. #391	C₂²×C₂₃	semidirect
616. #390	C₂²×C₂₃	semidirect
617. #390	C₂²×C₂₃	semidirect
618. #389	C₂²×C₂₃	semidirect
619. #389	C₂²×C₂₃	semidirect
620. #389	C₂²×C₂₃	semidirect
621. #389	C₂²×C₂₃	semidirect
622. #388	C₂²×C₂₃	semidirect
623. #388	C₂²×C₂₃	semidirect
624. #388	C₂²×C₂₃	semidirect
625. #388	C₂²×C₂₃	semidirect
626. #388	C₂²×C₂₃	semidirect
627. #388	C₂²×C₂₃	semidirect
628. #388	C₂²×C₂₃	semidirect
629. #388	C₂²×C₂₃	semidirect
630. #388	C₂²×C₂₃	semidirect
631. #388	C₂²×C₂₃	semidirect
632. #388	C₂²×C₂₃	semidirect
633. #388	C₂²×C₂₃	semidirect
634. #388	C₂²×C₂₃	semidirect
635. #388	C₂²×C₂₃	semidirect
636. #388	C₂²×C₂₃	semidirect
637. #388	C₂²×C₂₃	semidirect
638. #388	C₂²×C₂₃	semidirect
639. #387	C₂²×C₂₃	semidirect
641. #386	C₂²×C₂₃	semidirect
642. #386	C₂²×C₂₃	semidirect
643. #386	C₂²×C₂₃	semidirect
646. #382	C₂²×C₂₃	semidirect
650. #380	C₂²×C₂₃	semidirect
654. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
655. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
656. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
657. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
658. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
663. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
664. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
665. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
666. C₄³	C₂²×C₂₃	semidirect
799. C₂₃	#35025	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×#2861	2
C₂₃×#2860	2
C₂₃×#2854	2
C₂₃×#2850	2
C₂₃×#2651	2
C₂₃×#2648	2
C₂₃×#2593	2
C₂₃×#2554	2
C₂₃×#2513	2
C₂₃×#2490	2
C₂₃×#2480	2
C₂₃×#2448	2
C₂₃×#2442	2
C₂₃×#2435	2
C₂₃×#2426	2
C₂₃×#2418	2
C₂₃×#2417	2
C₂₃×#2408	2
C₂₃×#2321	2
C₂₃×#2312	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂×C₂₃×#390	2
C₄²×D₄×C₂₃	2
#35025	23

Subgroups — C23×#35025 #19182651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#35025 #19182651