Subgroups — C₂₃×#34520 #19182146

Order 5888.

2456 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#560	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2383	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2364	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2363	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2361	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2359	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2358	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2358	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2335	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2325	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2324	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×C₂₃×#126	C₂	1	2	yes	maximal, complemented
20	C₂₃×#560	C₄	1	16	yes	complemented
21	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
22	C₂×C₂₃×#126	C₂²	1	2	yes	—
23	C₂×C₂₃×#123	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#123	C₂²	1	2	yes	—
25	C₂×C₂₃×#121	C₂²	1	2	yes	—
26	C₂×C₂₃×#121	C₂²	1	2	yes	—
27	C₂×C₂₃×#121	C₂²	1	2	yes	—
28	C₂×C₂₃×#120	C₂²	1	2	yes	—
29	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
37	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
38	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
41	C₂₃×#390	C₂²	1	2	yes	—
42	C₂₃×#390	C₂²	1	1	yes	characteristic
43	C₂₃×#390	C₂²	1	2	yes	—
44	C₂₃×#390	C₂²	1	2	yes	—
45	C₂₃×#390	C₂²	1	2	yes	—
46	C₂₃×#390	C₂²	1	2	yes	complemented
47	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#389	C₂²	1	2	yes	complemented
49	C₂₃×#389	C₂²	1	2	yes	complemented
50	C₂₃×#389	C₂²	1	2	yes	complemented
51	C₂₃×#388	C₂²	1	2	yes	—
52	C₂₃×#388	C₂²	1	2	yes	—
53	C₂₃×#388	C₂²	1	2	yes	—
54	C₂₃×#388	C₂²	1	2	yes	—
55	C₂₃×#388	C₂²	1	2	yes	—
56	C₂₃×#388	C₂²	1	2	yes	—
57	C₂₃×#388	C₂²	1	2	yes	—
58	C₂₃×#388	C₂²	1	2	yes	—
59	C₂₃×#388	C₂²	1	2	yes	—
60	C₂₃×#388	C₂²	1	2	yes	complemented
61	C₂₃×#388	C₂²	1	2	yes	complemented
62	C₂₃×#388	C₂²	1	2	yes	complemented
63	C₂₃×#387	C₂²	1	2	yes	complemented
64	C₂₃×#387	C₂²	1	2	yes	complemented
65	C₂₃×#387	C₂²	1	2	yes	complemented
66	C₂₃×#387	C₂²	1	2	yes	complemented
67	C₂₃×#387	C₂²	1	2	yes	complemented
68	C₂₃×#387	C₂²	1	2	yes	complemented
69	C₂₃×#386	C₂²	1	2	yes	—
70	C₂₃×#386	C₂²	1	2	yes	—
71	C₂₃×#386	C₂²	1	2	yes	—
72	C₂₃×#386	C₂²	1	2	yes	—
73	C₂₃×#386	C₂²	1	1	yes	characteristic
74	C₂₃×#386	C₂²	1	1	yes	characteristic
75	C₂₃×#386	C₂²	1	2	yes	—
76	C₂₃×#386	C₂²	1	2	yes	—
77	C₂₃×#386	C₂²	1	2	yes	—
78	C₂₃×#386	C₂²	1	2	yes	—
79	C₂₃×#386	C₂²	1	2	yes	complemented
80	C₂₃×#386	C₂²	1	2	yes	complemented
81	C₂₃×#386	C₂²	1	2	yes	complemented
82	C₂₃×#385	C₂²	1	1	yes	characteristic
83	C₂₃×#385	C₂²	1	2	yes	—
84	C₂₃×#385	C₂²	1	2	yes	—
85	C₂₃×#385	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#385	C₂²	1	2	yes	complemented
89	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#383	C₂²	1	2	yes	complemented
91	C₂₃×#381	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#380	C₂²	1	2	yes	complemented
93	C₂₃×#379	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
98	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
106	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
107	C₄³×C₂₃	C₂²	1	1	yes	characteristic, complemented
108	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
125	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂₃×#127	C₂×C₄	1	8	yes	complemented
127	C₂₃×#126	C₂×C₄	1	16	yes	complemented
128	C₂₃×#123	C₂×C₄	1	8	yes	complemented
129	C₂₃×#123	C₂×C₄	1	16	yes	complemented
130	C₂₃×#121	C₂×C₄	1	16	yes	complemented
131	C₂₃×#121	C₂×C₄	1	16	yes	complemented
132	C₂₃×#121	C₂×C₄	1	16	yes	complemented
133	C₂₃×#120	C₂×C₄	1	16	yes	complemented
134	C₂₃×#120	C₂×C₄	1	8	yes	complemented
135	C₄×D₄×C₂₃	—	4	4	no	—
136	C₄×D₄×C₂₃	—	4	4	no	—
137	C₄×D₄×C₂₃	—	4	4	no	—
138	C₄×D₄×C₂₃	—	4	2	no	—
139	C₄×D₄×C₂₃	—	4	2	no	—
140	C₄×D₄×C₂₃	—	4	4	no	—
141	C₄×D₄×C₂₃	—	4	4	no	—
142	C₂₃×#117	—	4	4	no	—
143	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	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×C₂²⋊C₄×C₂₃	—	4	2	no	—
158	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
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	2	yes	—
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
185	C₂×C₂²⋊C₄×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	2	yes	—
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
191	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	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	2	yes	—
212	C₂₃×#95	C₂³	1	2	yes	—
213	C₂₃×#95	C₂³	1	2	yes	—
214	C₂₃×#95	C₂³	1	2	yes	—
215	C₂⁴×C₂₃	—	4	1	no	—
216	C₂⁴×C₂₃	—	4	2	no	—
217	C₂⁴×C₂₃	—	4	2	no	—
218	C₂⁴×C₂₃	—	4	1	no	—
219	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
220	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
221	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
223	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
224	C₂×D₄×C₂₃	—	4	2	no	—
225	C₂×D₄×C₂₃	—	4	2	no	—
226	C₂×D₄×C₂₃	—	4	2	no	—
227	C₂×D₄×C₂₃	—	4	1	no	—
228	C₂×D₄×C₂₃	—	4	1	no	—
229	C₂×D₄×C₂₃	—	4	2	no	—
230	C₂×D₄×C₂₃	—	4	2	no	—
231	C₂×D₄×C₂₃	—	4	2	no	—
232	C₂×D₄×C₂₃	—	4	2	no	—
233	C₂×D₄×C₂₃	—	4	1	no	—
234	C₂×D₄×C₂₃	—	4	2	no	—
235	C₂×D₄×C₂₃	—	4	2	no	—
236	C₂×D₄×C₂₃	—	4	1	no	—
237	C₂×D₄×C₂₃	—	4	2	no	—
238	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
239	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
240	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
241	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
242	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
243	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
244	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
245	C₂²×C₄×C₂₃	—	2	4	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	4	no	—
249	C₂²×C₄×C₂₃	—	4	1	no	—
250	C₂²×C₄×C₂₃	—	4	2	no	—
251	C₂²×C₄×C₂₃	—	4	1	no	—
252	C₂²×C₄×C₂₃	—	4	2	no	—
253	C₂²×C₄×C₂₃	—	4	1	no	—
254	C₂²×C₄×C₂₃	—	4	2	no	—
255	C₂²×C₄×C₂₃	—	4	1	no	—
256	C₂²×C₄×C₂₃	—	4	2	no	—
257	C₂²×C₄×C₂₃	—	4	2	no	—
258	C₂²×C₄×C₂₃	—	4	2	no	—
259	C₂²×C₄×C₂₃	—	4	2	no	—
260	C₂²×C₄×C₂₃	—	4	2	no	—
261	C₂²×C₄×C₂₃	—	4	2	no	—
262	C₂²×C₄×C₂₃	—	4	2	no	—
263	C₂²×C₄×C₂₃	—	4	2	no	—
264	C₂²×C₄×C₂₃	—	4	2	no	—
265	C₂²×C₄×C₂₃	—	4	2	no	—
266	C₂²×C₄×C₂₃	—	4	2	no	—
267	C₂²×C₄×C₂₃	—	4	2	no	—
268	C₂²×C₄×C₂₃	—	4	2	no	—
269	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
270	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	2	4	no	—
288	C₄⋊C₄×C₂₃	—	4	2	no	—
289	C₄⋊C₄×C₂₃	—	4	2	no	—
290	C₄⋊C₄×C₂₃	—	4	2	no	—
291	C₄⋊C₄×C₂₃	—	4	2	no	—
292	C₄⋊C₄×C₂₃	—	4	2	no	—
293	C₄⋊C₄×C₂₃	—	4	2	no	—
294	C₄⋊C₄×C₂₃	—	4	1	no	—
295	C₄⋊C₄×C₂₃	—	4	1	no	—
296	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
297	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
298	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	—	2	4	no	—
301	C₂²⋊C₄×C₂₃	—	2	4	no	—
302	C₂²⋊C₄×C₂₃	—	2	4	no	—
303	C₂²⋊C₄×C₂₃	—	2	4	no	—
304	C₂²⋊C₄×C₂₃	—	2	4	no	—
305	C₂²⋊C₄×C₂₃	—	4	2	no	—
306	C₂²⋊C₄×C₂₃	—	4	2	no	—
307	C₂²⋊C₄×C₂₃	—	4	2	no	—
308	C₂²⋊C₄×C₂₃	—	4	2	no	—
309	C₂²⋊C₄×C₂₃	—	4	1	no	—
310	C₂²⋊C₄×C₂₃	—	4	2	no	—
311	C₂²⋊C₄×C₂₃	—	4	2	no	—
312	C₂²⋊C₄×C₂₃	—	4	1	no	—
313	C₂²⋊C₄×C₂₃	—	4	2	no	—
314	C₂²⋊C₄×C₂₃	—	4	2	no	—
315	C₂²⋊C₄×C₂₃	—	4	1	no	—
316	C₂²⋊C₄×C₂₃	—	4	1	no	—
317	C₂²⋊C₄×C₂₃	—	4	2	no	—
318	C₂²⋊C₄×C₂₃	—	4	2	no	—
319	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
320	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
322	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
323	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
324	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
325	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
326	C₄²×C₂₃	—	2	4	no	—
327	C₄²×C₂₃	—	2	4	no	—
328	C₄²×C₂₃	—	2	2	no	—
329	C₄²×C₂₃	—	4	1	no	—
330	C₄²×C₂₃	—	4	2	no	—
331	C₄²×C₂₃	—	4	2	no	—
332	C₄²×C₂₃	—	4	2	no	—
333	C₄²×C₂₃	—	4	2	no	—
334	C₄²×C₂₃	—	4	2	no	—
335	C₄²×C₂₃	—	4	2	no	—
336	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
337	#34520	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	2	2	no	—
343	C₂³×C₂₃	—	2	2	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	2	1	no	—
346	C₂³×C₂₃	—	2	1	no	—
347	C₂³×C₂₃	—	2	2	no	—
348	C₂³×C₂₃	—	2	1	no	—
349	C₂³×C₂₃	—	2	2	no	—
350	C₂³×C₂₃	—	2	2	no	—
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	—	2	1	no	—
353	C₂³×C₂₃	—	2	2	no	—
354	C₂³×C₂₃	—	2	2	no	—
355	C₂³×C₂₃	—	2	2	no	—
356	C₂³×C₂₃	—	2	2	no	—
357	C₂³×C₂₃	—	2	2	no	—
358	C₂³×C₂₃	—	4	8	no	—
359	C₂³×C₂₃	—	4	4	no	—
360	C₂³×C₂₃	—	8	2	no	—
361	C₂³×C₂₃	—	8	2	no	—
362	C₂³×C₂₃	—	8	4	no	—
363	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
364	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
365	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
366	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
367	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
368	D₄×C₂₃	—	4	8	no	—
369	D₄×C₂₃	—	4	8	no	—
370	D₄×C₂₃	—	4	8	no	—
371	D₄×C₂₃	—	4	8	no	—
372	D₄×C₂₃	—	4	4	no	—
373	D₄×C₂₃	—	4	8	no	—
374	D₄×C₂₃	—	4	4	no	—
375	C₂×C₄×C₂₃	—	2	2	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	1	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	2	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	1	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	1	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	2	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	—	4	4	no	—
410	C₂×C₄×C₂₃	—	4	8	no	—
411	C₂×C₄×C₂₃	—	8	2	no	—
412	C₂×C₄×C₂₃	—	8	2	no	—
413	C₂×C₄×C₂₃	—	8	4	no	—
414	C₂×C₄×C₂₃	—	8	4	no	—
415	C₂×C₄×C₂₃	—	8	2	no	—
416	C₂×C₄×C₂₃	—	8	4	no	—
417	C₂×C₄×C₂₃	—	8	2	no	—
418	C₂×C₄×C₂₃	—	8	4	no	—
419	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
420	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
422	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
423	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
424	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
425	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
426	C₂×#560	C₂×C₂₃	1	1	yes	characteristic
427	#2383	C₂×C₂₃	1	2	yes	complemented
428	#2380	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#2374	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#2364	C₂×C₂₃	1	2	yes	complemented
431	#2363	C₂×C₂₃	1	2	yes	complemented
432	#2361	C₂×C₂₃	1	2	yes	complemented
433	#2359	C₂×C₂₃	1	2	yes	complemented
434	#2358	C₂×C₂₃	1	2	yes	complemented
435	#2358	C₂×C₂₃	1	1	yes	characteristic, complemented
436	#2335	C₂×C₂₃	1	2	yes	complemented
437	#2333	C₂×C₂₃	1	2	yes	complemented
438	#2325	C₂×C₂₃	1	2	yes	complemented
439	#2324	C₂×C₂₃	1	2	yes	complemented
440	#2322	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#2321	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#2321	C₂×C₂₃	1	2	yes	complemented
443	C₄×#127	C₂×C₂₃	1	1	yes	characteristic, complemented
444	C₄×#126	C₂×C₂₃	1	2	yes	complemented
445	C₂²×C₂₃	—	2	4	no	—
446	C₂²×C₂₃	—	2	2	no	—
447	C₂²×C₂₃	—	2	4	no	—
448	C₂²×C₂₃	—	2	4	no	—
449	C₂²×C₂₃	—	2	4	no	—
450	C₂²×C₂₃	—	2	4	no	—
451	C₂²×C₂₃	—	2	4	no	—
452	C₂²×C₂₃	—	2	4	no	—
453	C₂²×C₂₃	—	2	2	no	—
454	C₂²×C₂₃	—	2	4	no	—
455	C₂²×C₂₃	—	4	1	no	—
456	C₂²×C₂₃	—	4	2	no	—
457	C₂²×C₂₃	—	4	1	no	—
458	C₂²×C₂₃	—	4	2	no	—
459	C₂²×C₂₃	—	4	1	no	—
460	C₂²×C₂₃	—	4	2	no	—
461	C₂²×C₂₃	—	4	1	no	—
462	C₂²×C₂₃	—	4	2	no	—
463	C₂²×C₂₃	—	4	2	no	—
464	C₂²×C₂₃	—	4	2	no	—
465	C₂²×C₂₃	—	4	2	no	—
466	C₂²×C₂₃	—	4	2	no	—
467	C₂²×C₂₃	—	4	2	no	—
468	C₂²×C₂₃	—	4	2	no	—
469	C₂²×C₂₃	—	8	8	no	—
470	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
471	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
473	C₂²×C₂₃	#585	1	2	yes	—
474	C₂²×C₂₃	#585	1	1	yes	characteristic
475	C₄×C₂₃	—	2	4	no	—
476	C₄×C₂₃	—	2	4	no	—
477	C₄×C₂₃	—	2	4	no	—
478	C₄×C₂₃	—	2	2	no	—
479	C₄×C₂₃	—	2	4	no	—
480	C₄×C₂₃	—	2	2	no	—
481	C₄×C₂₃	—	2	4	no	—
482	C₄×C₂₃	—	4	1	no	—
483	C₄×C₂₃	—	4	1	no	—
484	C₄×C₂₃	—	4	2	no	—
485	C₄×C₂₃	—	4	2	no	—
486	C₄×C₂₃	—	4	1	no	—
487	C₄×C₂₃	—	4	2	no	—
488	C₄×C₂₃	—	4	2	no	—
489	C₄×C₂₃	—	4	2	no	—
490	#560	C₄×C₂₃	1	16	yes	complemented
491	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
492	C₂×#126	C₂²×C₂₃	1	2	yes	—
493	C₂×#123	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×#123	C₂²×C₂₃	1	2	yes	—
495	C₂×#121	C₂²×C₂₃	1	2	yes	—
496	C₂×#121	C₂²×C₂₃	1	2	yes	—
497	C₂×#121	C₂²×C₂₃	1	2	yes	—
498	C₂×#120	C₂²×C₂₃	1	2	yes	—
499	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
500	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
501	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
502	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
503	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
504	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
505	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
506	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
507	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
508	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
509	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
510	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
511	#390	C₂²×C₂₃	1	2	yes	—
512	#390	C₂²×C₂₃	1	1	yes	characteristic
513	#390	C₂²×C₂₃	1	2	yes	—
514	#390	C₂²×C₂₃	1	2	yes	—
515	#390	C₂²×C₂₃	1	2	yes	—
516	#390	C₂²×C₂₃	1	2	yes	complemented
517	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	#389	C₂²×C₂₃	1	2	yes	complemented
519	#389	C₂²×C₂₃	1	2	yes	complemented
520	#389	C₂²×C₂₃	1	2	yes	complemented
521	#388	C₂²×C₂₃	1	2	yes	—
522	#388	C₂²×C₂₃	1	2	yes	—
523	#388	C₂²×C₂₃	1	2	yes	—
524	#388	C₂²×C₂₃	1	2	yes	—
525	#388	C₂²×C₂₃	1	2	yes	—
526	#388	C₂²×C₂₃	1	2	yes	—
527	#388	C₂²×C₂₃	1	2	yes	—
528	#388	C₂²×C₂₃	1	2	yes	—
529	#388	C₂²×C₂₃	1	2	yes	—
530	#388	C₂²×C₂₃	1	2	yes	complemented
531	#388	C₂²×C₂₃	1	2	yes	complemented
532	#388	C₂²×C₂₃	1	2	yes	complemented
533	#387	C₂²×C₂₃	1	2	yes	complemented
534	#387	C₂²×C₂₃	1	2	yes	complemented
535	#387	C₂²×C₂₃	1	2	yes	complemented
536	#387	C₂²×C₂₃	1	2	yes	complemented
537	#387	C₂²×C₂₃	1	2	yes	complemented
538	#387	C₂²×C₂₃	1	2	yes	complemented
539	#386	C₂²×C₂₃	1	2	yes	—
540	#386	C₂²×C₂₃	1	2	yes	—
541	#386	C₂²×C₂₃	1	2	yes	—
542	#386	C₂²×C₂₃	1	2	yes	—
543	#386	C₂²×C₂₃	1	1	yes	characteristic
544	#386	C₂²×C₂₃	1	1	yes	characteristic
545	#386	C₂²×C₂₃	1	2	yes	—
546	#386	C₂²×C₂₃	1	2	yes	—
547	#386	C₂²×C₂₃	1	2	yes	—
548	#386	C₂²×C₂₃	1	2	yes	—
549	#386	C₂²×C₂₃	1	2	yes	complemented
550	#386	C₂²×C₂₃	1	2	yes	complemented
551	#386	C₂²×C₂₃	1	2	yes	complemented
552	#385	C₂²×C₂₃	1	1	yes	characteristic
553	#385	C₂²×C₂₃	1	2	yes	—
554	#385	C₂²×C₂₃	1	2	yes	—
555	#385	C₂²×C₂₃	1	2	yes	—
556	#385	C₂²×C₂₃	1	2	yes	—
557	#385	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	#385	C₂²×C₂₃	1	2	yes	complemented
559	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
560	#383	C₂²×C₂₃	1	2	yes	complemented
561	#381	C₂²×C₂₃	1	1	yes	characteristic, complemented
562	#380	C₂²×C₂₃	1	2	yes	complemented
563	#379	C₂²×C₂₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
565	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
566	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
567	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
568	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
569	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
570	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
571	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
572	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
573	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
574	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
575	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
576	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
577	C₄³	C₂²×C₂₃	1	1	yes	characteristic, complemented
578	C₂×C₂₃	—	4	2	no	—
579	C₂×C₂₃	—	4	4	no	—
580	C₂×C₂₃	—	4	2	no	—
581	C₂×C₂₃	—	4	4	no	—
582	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂×C₂₃	C₄×H(5,𝔽₂)	1	2	yes	—
584	C₂×C₂₃	#3543	1	1	yes	characteristic
585	C₂×C₂₃	#3551	1	1	yes	characteristic
586	C₂×C₂₃	#3560	1	2	yes	—
587	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
589	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
590	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
591	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
593	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
595	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
597	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
598	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
599	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
600	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
601	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
603	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
605	#127	C₂×C₄×C₂₃	1	8	yes	complemented
606	#126	C₂×C₄×C₂₃	1	16	yes	complemented
607	#123	C₂×C₄×C₂₃	1	8	yes	complemented
608	#123	C₂×C₄×C₂₃	1	16	yes	complemented
609	#121	C₂×C₄×C₂₃	1	16	yes	complemented
610	#121	C₂×C₄×C₂₃	1	16	yes	complemented
611	#121	C₂×C₄×C₂₃	1	16	yes	complemented
612	#120	C₂×C₄×C₂₃	1	16	yes	complemented
613	#120	C₂×C₄×C₂₃	1	8	yes	complemented
614	C₄×D₄	—	4	4	no	—
615	C₄×D₄	—	4	4	no	—
616	C₄×D₄	—	4	4	no	—
617	C₄×D₄	—	4	2	no	—
618	C₄×D₄	—	4	2	no	—
619	C₄×D₄	—	4	4	no	—
620	C₄×D₄	—	4	4	no	—
621	#117	—	4	4	no	—
622	C₂×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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×C₂²⋊C₄	—	4	2	no	—
637	C₂×C₂²⋊C₄	—	4	4	no	—
638	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
656	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	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	1	yes	characteristic
668	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
669	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
671	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
672	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
675	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
676	#95	C₂³×C₂₃	1	2	yes	—
677	#95	C₂³×C₂₃	1	2	yes	—
678	#95	C₂³×C₂₃	1	2	yes	—
679	#95	C₂³×C₂₃	1	2	yes	—
680	#95	C₂³×C₂₃	1	2	yes	—
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	C₂₃	#34520	1	1	yes	characteristic, direct product factor, Sylow
695	C₂⁴	—	4	1	no	—
696	C₂⁴	—	4	2	no	—
697	C₂⁴	—	4	2	no	—
698	C₂⁴	—	4	1	no	—
699	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
700	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
701	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
702	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
703	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	1	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	—	4	2	no	—
716	C₂×D₄	—	4	1	no	—
717	C₂×D₄	—	4	2	no	—
718	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
719	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
720	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
721	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
722	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
723	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
724	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	4	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	—	4	2	no	—
743	C₂²×C₄	—	4	2	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	—	4	2	no	—
748	C₂²×C₄	—	4	2	no	—
749	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
750	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
751	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
761	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₄⋊C₄	—	4	2	no	—
770	C₄⋊C₄	—	4	2	no	—
771	C₄⋊C₄	—	4	2	no	—
772	C₄⋊C₄	—	4	2	no	—
773	C₄⋊C₄	—	4	1	no	—
774	C₄⋊C₄	—	4	1	no	—
775	C₄⋊C₄	—	4	2	no	—
776	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
777	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
778	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	4	no	—
783	C₂²⋊C₄	—	2	4	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	4	2	no	—
786	C₂²⋊C₄	—	4	2	no	—
787	C₂²⋊C₄	—	4	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	1	no	—
791	C₂²⋊C₄	—	4	1	no	—
792	C₂²⋊C₄	—	4	2	no	—
793	C₂²⋊C₄	—	4	2	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₂²⋊C₄	—	4	1	no	—
796	C₂²⋊C₄	—	4	2	no	—
797	C₂²⋊C₄	—	4	2	no	—
798	C₂²⋊C₄	—	4	1	no	—
799	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
800	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
801	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
802	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
803	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
804	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
805	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
806	C₄²	—	2	4	no	—
807	C₄²	—	2	4	no	—
808	C₄²	—	2	2	no	—
809	C₄²	—	4	2	no	—
810	C₄²	—	4	2	no	—
811	C₄²	—	4	2	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	2	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	4	8	no	—
838	C₂³	—	4	4	no	—
839	C₂³	—	8	2	no	—
840	C₂³	—	8	2	no	—
841	C₂³	—	8	4	no	—
842	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
843	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
844	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
845	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
846	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
847	D₄	—	4	8	no	—
848	D₄	—	4	8	no	—
849	D₄	—	4	8	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	8	no	—
853	D₄	—	4	4	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	8	no	—
890	C₂×C₄	—	8	4	no	—
891	C₂×C₄	—	8	2	no	—
892	C₂×C₄	—	8	2	no	—
893	C₂×C₄	—	8	4	no	—
894	C₂×C₄	—	8	2	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	—	8	2	no	—
897	C₂×C₄	—	8	4	no	—
898	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
899	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
900	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
901	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
902	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
903	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
904	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	2	4	no	—
909	C₂²	—	2	4	no	—
910	C₂²	—	2	4	no	—
911	C₂²	—	2	4	no	—
912	C₂²	—	2	4	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	4	1	no	—
916	C₂²	—	4	1	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	—	4	1	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	2	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	8	8	no	—
930	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
931	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
932	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
933	C₂²	C₂₃×#585	1	2	yes	—
934	C₂²	C₂₃×#585	1	1	yes	characteristic
935	C₄	—	2	4	no	—
936	C₄	—	2	4	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	4	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	4	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	1	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₂	—	4	2	no	—
951	C₂	—	4	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	4	4	no	—
954	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
955	C₂	C₄×C₂₃×H(5,𝔽₂)	1	2	yes	—
956	C₂	C₂₃×#3543	1	1	yes	characteristic
957	C₂	C₂₃×#3551	1	1	yes	characteristic
958	C₂	C₂₃×#3560	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#560	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2383	C₂	semidirect
3. C₂₃×#2380	C₂	semidirect
4. C₂₃×#2374	C₂	semidirect
5. C₂₃×#2364	C₂	semidirect
6. C₂₃×#2363	C₂	semidirect
7. C₂₃×#2361	C₂	semidirect
8. C₂₃×#2359	C₂	semidirect
9. C₂₃×#2358	C₂	semidirect
10. C₂₃×#2358	C₂	semidirect
11. C₂₃×#2335	C₂	semidirect
12. C₂₃×#2333	C₂	semidirect
13. C₂₃×#2325	C₂	semidirect
14. C₂₃×#2324	C₂	semidirect
15. C₂₃×#2322	C₂	semidirect
16. C₂₃×#2321	C₂	semidirect
17. C₂₃×#2321	C₂	semidirect
18. C₄×C₂₃×#127	C₂	semidirect
19. C₄×C₂₃×#126	C₂	semidirect
20. C₂₃×#560	C₄	semidirect
35. C₂×C₄×D₄×C₂₃	C₂²	semidirect
36. C₂×C₄×D₄×C₂₃	C₂²	semidirect
37. C₂×C₂₃×#117	C₂²	semidirect
38. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
46. C₂₃×#390	C₂²	semidirect
47. C₂₃×#390	C₂²	semidirect
48. C₂₃×#389	C₂²	semidirect
49. C₂₃×#389	C₂²	semidirect
50. C₂₃×#389	C₂²	semidirect
60. C₂₃×#388	C₂²	semidirect
61. C₂₃×#388	C₂²	semidirect
62. C₂₃×#388	C₂²	semidirect
63. C₂₃×#387	C₂²	semidirect
64. C₂₃×#387	C₂²	semidirect
65. C₂₃×#387	C₂²	semidirect
66. C₂₃×#387	C₂²	semidirect
67. C₂₃×#387	C₂²	semidirect
68. C₂₃×#387	C₂²	semidirect
79. C₂₃×#386	C₂²	semidirect
80. C₂₃×#386	C₂²	semidirect
81. C₂₃×#386	C₂²	semidirect
87. C₂₃×#385	C₂²	semidirect
88. C₂₃×#385	C₂²	semidirect
89. C₂₃×#384	C₂²	semidirect
90. C₂₃×#383	C₂²	semidirect
91. C₂₃×#381	C₂²	semidirect
92. C₂₃×#380	C₂²	semidirect
94. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
95. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
96. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
106. C₂×C₂₃×#95	C₂²	semidirect
107. C₄³×C₂₃	C₂²	semidirect
126. C₂₃×#127	C₂×C₄	semidirect
127. C₂₃×#126	C₂×C₄	semidirect
128. C₂₃×#123	C₂×C₄	semidirect
129. C₂₃×#123	C₂×C₄	semidirect
130. C₂₃×#121	C₂×C₄	semidirect
131. C₂₃×#121	C₂×C₄	semidirect
132. C₂₃×#121	C₂×C₄	semidirect
133. C₂₃×#120	C₂×C₄	semidirect
134. C₂₃×#120	C₂×C₄	semidirect
337. #34520	C₂₃	direct (N × H)
427. #2383	C₂×C₂₃	semidirect
428. #2380	C₂×C₂₃	semidirect
429. #2374	C₂×C₂₃	semidirect
430. #2364	C₂×C₂₃	semidirect
431. #2363	C₂×C₂₃	semidirect
432. #2361	C₂×C₂₃	semidirect
433. #2359	C₂×C₂₃	semidirect
434. #2358	C₂×C₂₃	semidirect
435. #2358	C₂×C₂₃	semidirect
436. #2335	C₂×C₂₃	semidirect
437. #2333	C₂×C₂₃	semidirect
438. #2325	C₂×C₂₃	semidirect
439. #2324	C₂×C₂₃	semidirect
440. #2322	C₂×C₂₃	semidirect
441. #2321	C₂×C₂₃	semidirect
442. #2321	C₂×C₂₃	semidirect
443. C₄×#127	C₂×C₂₃	semidirect
444. C₄×#126	C₂×C₂₃	semidirect
490. #560	C₄×C₂₃	semidirect
505. C₂×C₄×D₄	C₂²×C₂₃	semidirect
506. C₂×C₄×D₄	C₂²×C₂₃	semidirect
507. C₂×#117	C₂²×C₂₃	semidirect
508. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
516. #390	C₂²×C₂₃	semidirect
517. #390	C₂²×C₂₃	semidirect
518. #389	C₂²×C₂₃	semidirect
519. #389	C₂²×C₂₃	semidirect
520. #389	C₂²×C₂₃	semidirect
530. #388	C₂²×C₂₃	semidirect
531. #388	C₂²×C₂₃	semidirect
532. #388	C₂²×C₂₃	semidirect
533. #387	C₂²×C₂₃	semidirect
534. #387	C₂²×C₂₃	semidirect
535. #387	C₂²×C₂₃	semidirect
536. #387	C₂²×C₂₃	semidirect
537. #387	C₂²×C₂₃	semidirect
538. #387	C₂²×C₂₃	semidirect
549. #386	C₂²×C₂₃	semidirect
550. #386	C₂²×C₂₃	semidirect
551. #386	C₂²×C₂₃	semidirect
557. #385	C₂²×C₂₃	semidirect
558. #385	C₂²×C₂₃	semidirect
559. #384	C₂²×C₂₃	semidirect
560. #383	C₂²×C₂₃	semidirect
561. #381	C₂²×C₂₃	semidirect
562. #380	C₂²×C₂₃	semidirect
564. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
565. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
566. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
572. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
573. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
574. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
575. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
576. C₂×#95	C₂²×C₂₃	semidirect
577. C₄³	C₂²×C₂₃	semidirect
605. #127	C₂×C₄×C₂₃	semidirect
606. #126	C₂×C₄×C₂₃	semidirect
607. #123	C₂×C₄×C₂₃	semidirect
608. #123	C₂×C₄×C₂₃	semidirect
609. #121	C₂×C₄×C₂₃	semidirect
610. #121	C₂×C₄×C₂₃	semidirect
611. #121	C₂×C₄×C₂₃	semidirect
612. #120	C₂×C₄×C₂₃	semidirect
613. #120	C₂×C₄×C₂₃	semidirect
694. C₂₃	#34520	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₂₃×#560	2
C₂₃×#2383	2
C₂₃×#2380	2
C₂₃×#2374	2
C₂₃×#2364	2
C₂₃×#2363	2
C₂₃×#2361	2
C₂₃×#2359	2
C₂₃×#2358	2
C₂₃×#2335	2
C₂₃×#2333	2
C₂₃×#2325	2
C₂₃×#2324	2
C₂₃×#2322	2
C₂₃×#2321	2
C₄×C₂₃×#127	2
C₄×C₂₃×#126	2
#34520	23

Subgroups — C23×#34520 #19182146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34520 #19182146