Subgroups — C₂₃×#36589 #19184215

Order 5888.

1694 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2860	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2597	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2596	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×#2525	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2516	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2509	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2490	C₂	1	1	yes	maximal, characteristic
11	C₂₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2426	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2421	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic
18	C₂₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×C₂₃×#126	C₂	1	2	yes	maximal, complemented
23	C₄²×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#126	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	C₂²	1	2	yes	—
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
35	C₂₃×#400	C₂²	1	2	yes	—
36	C₂₃×#400	C₂²	1	2	yes	—
37	C₂₃×#400	C₂²	1	2	yes	—
38	C₂₃×#400	C₂²	1	2	yes	—
39	C₂₃×#399	C₂²	1	2	yes	—
40	C₂₃×#398	C₂²	1	2	yes	—
41	C₂₃×#397	C₂²	1	2	yes	—
42	C₂₃×#397	C₂²	1	2	yes	—
43	C₂₃×#397	C₂²	1	2	yes	—
44	C₂₃×#396	C₂²	1	2	yes	—
45	C₂₃×#394	C₂²	1	2	yes	—
46	C₂₃×#394	C₂²	1	2	yes	—
47	C₂₃×#391	C₂²	1	1	yes	characteristic
48	C₂₃×#391	C₂²	1	1	yes	characteristic
49	C₂₃×#390	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	1	yes	characteristic
53	C₂₃×#390	C₂²	1	2	yes	—
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	2	yes	—
61	C₂₃×#389	C₂²	1	1	yes	characteristic
62	C₂₃×#389	C₂²	1	2	yes	—
63	C₂₃×#389	C₂²	1	1	yes	characteristic
64	C₂₃×#389	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	1	yes	characteristic
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
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	1	yes	characteristic
78	C₂₃×#388	C₂²	1	1	yes	characteristic
79	C₂₃×#388	C₂²	1	2	yes	—
80	C₂₃×#388	C₂²	1	2	yes	—
81	C₂₃×#388	C₂²	1	2	yes	—
82	C₂₃×#388	C₂²	1	2	yes	—
83	C₂₃×#388	C₂²	1	2	yes	—
84	C₂₃×#388	C₂²	1	2	yes	—
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#387	C₂²	1	2	yes	—
88	C₂₃×#387	C₂²	1	2	yes	—
89	C₂₃×#387	C₂²	1	1	yes	characteristic
90	C₂₃×#387	C₂²	1	2	yes	—
91	C₂₃×#387	C₂²	1	1	yes	characteristic
92	C₂₃×#387	C₂²	1	1	yes	characteristic
93	C₂₃×#387	C₂²	1	2	yes	—
94	C₂₃×#386	C₂²	1	2	yes	—
95	C₂₃×#385	C₂²	1	2	yes	—
96	C₂₃×#383	C₂²	1	2	yes	—
97	C₂₃×#383	C₂²	1	1	yes	characteristic
98	C₂₃×#382	C₂²	1	1	yes	characteristic
99	C₂₃×#381	C₂²	1	2	yes	—
100	C₂₃×#380	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
106	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
107	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
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	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₄³×C₂₃	C₂²	1	2	yes	—
122	C₄³×C₂₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
124	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
128	C₂₃×#126	—	2	4	no	—
129	C₂₃×#126	—	2	8	no	—
130	C₂₃×#125	—	2	4	no	—
131	C₂₃×#124	—	2	4	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×#121	—	2	4	no	—
134	C₄×Q₈×C₂₃	—	2	4	no	—
135	C₄×Q₈×C₂₃	—	2	4	no	—
136	C₄×Q₈×C₂₃	—	2	4	no	—
137	C₄×D₄×C₂₃	—	2	4	no	—
138	C₂₃×#117	—	2	4	no	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	2	yes	—
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	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	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	2	yes	—
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	C₂³	1	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	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#95	C₂³	1	1	yes	characteristic
204	C₂₃×#95	C₂³	1	1	yes	characteristic
205	C₂₃×#95	C₂³	1	1	yes	characteristic
206	C₂₃×#95	C₂³	1	1	yes	characteristic
207	C₂₃×#95	C₂³	1	1	yes	characteristic
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	1	yes	characteristic
210	C₂₃×#95	C₂³	1	2	yes	—
211	C₂₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂₃×#95	C₂³	1	2	yes	—
218	C₂₃×#95	C₂³	1	2	yes	—
219	C₂₃×#95	C₂³	1	1	yes	characteristic
220	C₂₃×#95	C₂³	1	2	yes	—
221	C₂₃×#95	C₂³	1	2	yes	—
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	2	yes	—
228	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	2	yes	—
233	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	#41	1	4	yes	—
238	C₂×D₄×C₂₃	—	2	2	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	—	2	4	no	—
242	C₂×D₄×C₂₃	—	4	2	no	—
243	C₂×D₄×C₂₃	—	4	2	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	4	no	—
248	C₂²×C₄×C₂₃	—	4	2	no	—
249	C₂²×C₄×C₂₃	—	4	2	no	—
250	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	4	no	—
274	C₄⋊C₄×C₂₃	—	2	4	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	4	no	—
285	C₄⋊C₄×C₂₃	—	2	4	no	—
286	C₄⋊C₄×C₂₃	—	2	4	no	—
287	C₄⋊C₄×C₂₃	—	4	2	no	—
288	C₄⋊C₄×C₂₃	—	4	2	no	—
289	C₄⋊C₄×C₂₃	—	4	1	no	—
290	C₄⋊C₄×C₂₃	—	4	1	no	—
291	C₄⋊C₄×C₂₃	—	4	2	no	—
292	C₄⋊C₄×C₂₃	—	4	1	no	—
293	C₄⋊C₄×C₂₃	#41	1	4	yes	—
294	C₄⋊C₄×C₂₃	#41	1	4	yes	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	—	2	4	no	—
297	C₂²⋊C₄×C₂₃	—	2	4	no	—
298	C₂²⋊C₄×C₂₃	—	2	4	no	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	—	2	4	no	—
301	C₂²⋊C₄×C₂₃	—	2	2	no	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	4	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	4	1	no	—
308	C₂²⋊C₄×C₂₃	—	4	2	no	—
309	C₂²⋊C₄×C₂₃	—	4	2	no	—
310	C₂²⋊C₄×C₂₃	—	4	2	no	—
311	C₂²⋊C₄×C₂₃	—	4	2	no	—
312	C₂²⋊C₄×C₂₃	—	4	2	no	—
313	C₂²⋊C₄×C₂₃	—	4	2	no	—
314	C₂²⋊C₄×C₂₃	—	4	1	no	—
315	C₂²⋊C₄×C₂₃	—	4	1	no	—
316	C₄²×C₂₃	—	2	4	no	—
317	C₄²×C₂₃	—	2	2	no	—
318	C₄²×C₂₃	—	2	4	no	—
319	C₄²×C₂₃	—	2	4	no	—
320	C₄²×C₂₃	—	2	4	no	—
321	C₄²×C₂₃	—	2	2	no	—
322	C₄²×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	—	2	2	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	4	2	no	—
327	C₄²×C₂₃	—	4	2	no	—
328	C₄²×C₂₃	—	4	2	no	—
329	C₄²×C₂₃	—	4	1	no	—
330	C₄²×C₂₃	—	4	1	no	—
331	C₄²×C₂₃	—	4	1	no	—
332	C₄²×C₂₃	—	4	2	no	—
333	C₄²×C₂₃	—	4	2	no	—
334	C₄²×C₂₃	#41	1	4	yes	—
335	#36589	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
336	C₂³×C₂₃	—	2	1	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	1	no	—
339	C₂³×C₂₃	—	2	1	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	2	2	no	—
343	C₂³×C₂₃	—	2	1	no	—
344	C₂³×C₂₃	—	2	1	no	—
345	C₂³×C₂₃	—	2	2	no	—
346	C₂³×C₂₃	—	2	2	no	—
347	C₂³×C₂₃	—	2	2	no	—
348	C₂³×C₂₃	—	2	1	no	—
349	C₂³×C₂₃	—	2	1	no	—
350	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
351	Q₈×C₂₃	—	2	8	no	—
352	D₄×C₂₃	—	4	4	no	—
353	D₄×C₂₃	—	8	4	no	—
354	C₂×C₄×C₂₃	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	1	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	1	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	1	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	1	no	—
381	C₂×C₄×C₂₃	—	2	1	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	1	no	—
392	C₂×C₄×C₂₃	—	2	1	no	—
393	C₂×C₄×C₂₃	—	2	2	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	2	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	1	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	1	no	—
404	C₂×C₄×C₂₃	—	2	1	no	—
405	C₂×C₄×C₂₃	—	2	1	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	4	4	no	—
409	C₂×C₄×C₂₃	—	8	4	no	—
410	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
411	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
412	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
413	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
415	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
416	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
418	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
419	#2860	C₂×C₂₃	1	1	yes	characteristic, complemented
420	#2860	C₂×C₂₃	1	2	yes	complemented
421	#2597	C₂×C₂₃	1	2	yes	complemented
422	#2596	C₂×C₂₃	1	2	yes	complemented
423	#2593	C₂×C₂₃	1	2	yes	complemented
424	#2573	C₂×C₂₃	1	2	yes	complemented
425	#2525	C₂×C₂₃	1	2	yes	complemented
426	#2516	C₂×C₂₃	1	2	yes	complemented
427	#2509	C₂×C₂₃	1	1	yes	characteristic, complemented
428	#2490	C₂×C₂₃	1	1	yes	characteristic
429	#2453	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#2448	C₂×C₂₃	1	1	yes	characteristic, complemented
431	#2426	C₂×C₂₃	1	1	yes	characteristic
432	#2421	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#2367	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#2363	C₂×C₂₃	1	1	yes	characteristic
436	#2362	C₂×C₂₃	1	1	yes	characteristic, complemented
437	#2357	C₂×C₂₃	1	1	yes	characteristic, complemented
438	#2347	C₂×C₂₃	1	1	yes	characteristic, complemented
439	C₄×#126	C₂×C₂₃	1	2	yes	complemented
440	C₄×#126	C₂×C₂₃	1	1	yes	characteristic, complemented
441	C₄²×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
442	C₂²×C₂₃	—	4	1	no	—
443	C₂²×C₂₃	—	4	2	no	—
444	C₂²×C₂₃	—	4	1	no	—
445	C₂²×C₂₃	—	4	1	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	4	2	no	—
449	C₂²×C₂₃	—	4	1	no	—
450	C₂²×C₂₃	—	4	2	no	—
451	C₂²×C₂₃	—	4	1	no	—
452	C₂²×C₂₃	—	4	2	no	—
453	C₂²×C₂₃	—	4	1	no	—
454	C₂²×C₂₃	—	4	1	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
457	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
459	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
460	C₂²×C₂₃	#585	1	1	yes	characteristic
461	C₂²×C₂₃	#585	1	1	yes	characteristic
462	C₂²×C₂₃	#585	1	1	yes	characteristic
463	C₄×C₂₃	—	2	4	no	—
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	2	no	—
467	C₄×C₂₃	—	2	4	no	—
468	C₄×C₂₃	—	2	4	no	—
469	C₄×C₂₃	—	4	1	no	—
470	C₄×C₂₃	—	4	1	no	—
471	C₄×C₂₃	—	4	1	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	—	4	1	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	2	no	—
476	C₄×C₂₃	—	4	1	no	—
477	C₄×C₂₃	—	4	1	no	—
478	C₄×C₂₃	—	4	1	no	—
479	C₄×C₂₃	—	4	1	no	—
480	C₄×C₂₃	—	4	1	no	—
481	C₄×C₂₃	—	4	2	no	—
482	C₄×C₂₃	—	4	1	no	—
483	C₄×C₂₃	#529	1	4	yes	—
484	C₂×#126	C₂²×C₂₃	1	2	yes	—
485	C₂×#126	C₂²×C₂₃	1	1	yes	characteristic
486	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
489	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
491	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
492	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
494	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
495	#400	C₂²×C₂₃	1	2	yes	—
496	#400	C₂²×C₂₃	1	2	yes	—
497	#400	C₂²×C₂₃	1	2	yes	—
498	#400	C₂²×C₂₃	1	2	yes	—
499	#399	C₂²×C₂₃	1	2	yes	—
500	#398	C₂²×C₂₃	1	2	yes	—
501	#397	C₂²×C₂₃	1	2	yes	—
502	#397	C₂²×C₂₃	1	2	yes	—
503	#397	C₂²×C₂₃	1	2	yes	—
504	#396	C₂²×C₂₃	1	2	yes	—
505	#394	C₂²×C₂₃	1	2	yes	—
506	#394	C₂²×C₂₃	1	2	yes	—
507	#391	C₂²×C₂₃	1	1	yes	characteristic
508	#391	C₂²×C₂₃	1	1	yes	characteristic
509	#390	C₂²×C₂₃	1	2	yes	—
510	#390	C₂²×C₂₃	1	2	yes	—
511	#390	C₂²×C₂₃	1	1	yes	characteristic
512	#390	C₂²×C₂₃	1	1	yes	characteristic
513	#390	C₂²×C₂₃	1	1	yes	characteristic
514	#390	C₂²×C₂₃	1	2	yes	—
515	#390	C₂²×C₂₃	1	1	yes	characteristic
516	#389	C₂²×C₂₃	1	2	yes	—
517	#389	C₂²×C₂₃	1	2	yes	—
518	#389	C₂²×C₂₃	1	1	yes	characteristic
519	#389	C₂²×C₂₃	1	1	yes	characteristic
520	#389	C₂²×C₂₃	1	1	yes	characteristic
521	#389	C₂²×C₂₃	1	1	yes	characteristic
522	#389	C₂²×C₂₃	1	2	yes	—
523	#389	C₂²×C₂₃	1	1	yes	characteristic
524	#389	C₂²×C₂₃	1	1	yes	characteristic
525	#388	C₂²×C₂₃	1	1	yes	characteristic
526	#388	C₂²×C₂₃	1	2	yes	—
527	#388	C₂²×C₂₃	1	2	yes	—
528	#388	C₂²×C₂₃	1	1	yes	characteristic
529	#388	C₂²×C₂₃	1	2	yes	—
530	#388	C₂²×C₂₃	1	1	yes	characteristic
531	#388	C₂²×C₂₃	1	2	yes	—
532	#388	C₂²×C₂₃	1	2	yes	—
533	#388	C₂²×C₂₃	1	2	yes	—
534	#388	C₂²×C₂₃	1	2	yes	—
535	#388	C₂²×C₂₃	1	2	yes	—
536	#388	C₂²×C₂₃	1	2	yes	—
537	#388	C₂²×C₂₃	1	2	yes	—
538	#388	C₂²×C₂₃	1	2	yes	—
539	#388	C₂²×C₂₃	1	2	yes	—
540	#388	C₂²×C₂₃	1	2	yes	—
541	#388	C₂²×C₂₃	1	2	yes	—
542	#388	C₂²×C₂₃	1	2	yes	—
543	#388	C₂²×C₂₃	1	2	yes	—
544	#388	C₂²×C₂₃	1	2	yes	—
545	#387	C₂²×C₂₃	1	1	yes	characteristic
546	#387	C₂²×C₂₃	1	2	yes	—
547	#387	C₂²×C₂₃	1	1	yes	characteristic
548	#387	C₂²×C₂₃	1	2	yes	—
549	#387	C₂²×C₂₃	1	2	yes	—
550	#387	C₂²×C₂₃	1	1	yes	characteristic
551	#387	C₂²×C₂₃	1	2	yes	—
552	#387	C₂²×C₂₃	1	2	yes	—
553	#387	C₂²×C₂₃	1	2	yes	—
554	#386	C₂²×C₂₃	1	2	yes	—
555	#385	C₂²×C₂₃	1	2	yes	—
556	#383	C₂²×C₂₃	1	1	yes	characteristic
557	#383	C₂²×C₂₃	1	2	yes	—
558	#382	C₂²×C₂₃	1	1	yes	characteristic
559	#381	C₂²×C₂₃	1	2	yes	—
560	#380	C₂²×C₂₃	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
562	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
563	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
565	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
566	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
567	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
569	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
570	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
571	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
572	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
573	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
574	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
575	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
576	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
577	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
579	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
580	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
581	C₄³	C₂²×C₂₃	1	2	yes	—
582	C₄³	C₂²×C₂₃	1	1	yes	characteristic
583	C₂×C₂₃	—	8	1	no	—
584	C₂×C₂₃	—	8	2	no	—
585	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
586	C₂×C₂₃	#3480	1	1	yes	characteristic
587	C₂×C₂₃	#3480	1	1	yes	characteristic
588	C₂×C₂₃	#3480	1	1	yes	characteristic
589	C₂×C₂₃	#3521	1	1	yes	characteristic
590	C₂×C₂₃	#3521	1	1	yes	characteristic
591	C₂×C₂₃	#3524	1	1	yes	characteristic
592	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
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	#126	—	2	8	no	—
598	#126	—	2	4	no	—
599	#125	—	2	4	no	—
600	#124	—	2	4	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	#121	—	2	4	no	—
603	C₄×Q₈	—	2	4	no	—
604	C₄×Q₈	—	2	4	no	—
605	C₄×Q₈	—	2	4	no	—
606	C₄×D₄	—	2	4	no	—
607	#117	—	2	4	no	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
632	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
641	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
642	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
643	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
660	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
661	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
663	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
664	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
665	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
666	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
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	#95	C₂³×C₂₃	1	1	yes	characteristic
673	#95	C₂³×C₂₃	1	1	yes	characteristic
674	#95	C₂³×C₂₃	1	1	yes	characteristic
675	#95	C₂³×C₂₃	1	1	yes	characteristic
676	#95	C₂³×C₂₃	1	1	yes	characteristic
677	#95	C₂³×C₂₃	1	2	yes	—
678	#95	C₂³×C₂₃	1	1	yes	characteristic
679	#95	C₂³×C₂₃	1	2	yes	—
680	#95	C₂³×C₂₃	1	2	yes	—
681	#95	C₂³×C₂₃	1	1	yes	characteristic
682	#95	C₂³×C₂₃	1	1	yes	characteristic
683	#95	C₂³×C₂₃	1	2	yes	—
684	#95	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
689	#95	C₂³×C₂₃	1	2	yes	—
690	#95	C₂³×C₂₃	1	2	yes	—
691	#95	C₂³×C₂₃	1	1	yes	characteristic
692	#95	C₂³×C₂₃	1	2	yes	—
693	#95	C₂³×C₂₃	1	1	yes	characteristic
694	#95	C₂³×C₂₃	1	2	yes	—
695	#95	C₂³×C₂₃	1	2	yes	—
696	#95	C₂³×C₂₃	1	2	yes	—
697	#95	C₂³×C₂₃	1	2	yes	—
698	#95	C₂³×C₂₃	1	2	yes	—
699	#95	C₂³×C₂₃	1	2	yes	—
700	#95	C₂³×C₂₃	1	2	yes	—
701	#95	C₂³×C₂₃	1	2	yes	—
702	C₂₃	#36589	1	1	yes	characteristic, direct product factor, Sylow
703	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
704	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
705	C₂×Q₈	—	2	2	no	—
706	C₂×Q₈	—	2	2	no	—
707	C₂×Q₈	#41×C₂₃	1	4	yes	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	4	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	4	2	no	—
719	C₂²×C₄	—	4	2	no	—
720	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
724	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	4	no	—
744	C₄⋊C₄	—	2	4	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	4	no	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	4	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	2	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	1	no	—
763	C₄⋊C₄	#41×C₂₃	1	4	yes	—
764	C₄⋊C₄	#41×C₂₃	1	4	yes	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	4	1	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	no	—
782	C₂²⋊C₄	—	4	2	no	—
783	C₂²⋊C₄	—	4	2	no	—
784	C₂²⋊C₄	—	4	1	no	—
785	C₂²⋊C₄	—	4	1	no	—
786	C₄²	—	2	4	no	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	4	no	—
789	C₄²	—	2	4	no	—
790	C₄²	—	2	4	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	4	2	no	—
797	C₄²	—	4	2	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	1	no	—
800	C₄²	—	4	1	no	—
801	C₄²	—	4	1	no	—
802	C₄²	—	4	2	no	—
803	C₄²	—	4	2	no	—
804	C₄²	#41×C₂₃	1	4	yes	—
805	C₂³	—	2	1	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	1	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
820	Q₈	—	2	8	no	—
821	D₄	—	4	4	no	—
822	D₄	—	8	4	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	1	no	—
876	C₂×C₄	—	2	1	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	8	4	no	—
879	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
880	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
881	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
882	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
883	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
884	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
885	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
886	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
887	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	1	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	1	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	2	no	—
902	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
903	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
904	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
905	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
906	C₂²	C₂₃×#585	1	1	yes	characteristic
907	C₂²	C₂₃×#585	1	1	yes	characteristic
908	C₂²	C₂₃×#585	1	1	yes	characteristic
909	C₄	—	2	4	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	2	4	no	—
914	C₄	—	2	4	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	—	4	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	1	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	1	no	—
929	C₄	C₂₃×#529	1	4	yes	—
930	C₂	—	8	1	no	—
931	C₂	—	8	2	no	—
932	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
933	C₂	C₂₃×#3480	1	1	yes	characteristic
934	C₂	C₂₃×#3480	1	1	yes	characteristic
935	C₂	C₂₃×#3480	1	1	yes	characteristic
936	C₂	C₂₃×#3521	1	1	yes	characteristic
937	C₂	C₂₃×#3521	1	1	yes	characteristic
938	C₂	C₂₃×#3524	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
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×#2860	C₂	semidirect
2. C₂₃×#2860	C₂	semidirect
3. C₂₃×#2597	C₂	semidirect
4. C₂₃×#2596	C₂	semidirect
5. C₂₃×#2593	C₂	semidirect
6. C₂₃×#2573	C₂	semidirect
7. C₂₃×#2525	C₂	semidirect
8. C₂₃×#2516	C₂	semidirect
9. C₂₃×#2509	C₂	semidirect
11. C₂₃×#2453	C₂	semidirect
12. C₂₃×#2448	C₂	semidirect
14. C₂₃×#2421	C₂	semidirect
15. C₂₃×#2370	C₂	semidirect
16. C₂₃×#2367	C₂	semidirect
18. C₂₃×#2362	C₂	semidirect
19. C₂₃×#2357	C₂	semidirect
20. C₂₃×#2347	C₂	semidirect
21. C₄×C₂₃×#126	C₂	semidirect
22. C₄×C₂₃×#126	C₂	semidirect
23. C₄²×Q₈×C₂₃	C₂	semidirect
335. #36589	C₂₃	direct (N × H)
419. #2860	C₂×C₂₃	semidirect
420. #2860	C₂×C₂₃	semidirect
421. #2597	C₂×C₂₃	semidirect
422. #2596	C₂×C₂₃	semidirect
423. #2593	C₂×C₂₃	semidirect
424. #2573	C₂×C₂₃	semidirect
425. #2525	C₂×C₂₃	semidirect
426. #2516	C₂×C₂₃	semidirect
427. #2509	C₂×C₂₃	semidirect
429. #2453	C₂×C₂₃	semidirect
430. #2448	C₂×C₂₃	semidirect
432. #2421	C₂×C₂₃	semidirect
433. #2370	C₂×C₂₃	semidirect
434. #2367	C₂×C₂₃	semidirect
436. #2362	C₂×C₂₃	semidirect
437. #2357	C₂×C₂₃	semidirect
438. #2347	C₂×C₂₃	semidirect
439. C₄×#126	C₂×C₂₃	semidirect
440. C₄×#126	C₂×C₂₃	semidirect
441. C₄²×Q₈	C₂×C₂₃	semidirect
702. C₂₃	#36589	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×#2860	2
C₂₃×#2597	2
C₂₃×#2596	2
C₂₃×#2593	2
C₂₃×#2573	2
C₂₃×#2525	2
C₂₃×#2516	2
C₂₃×#2509	2
C₂₃×#2490	2
C₂₃×#2453	2
C₂₃×#2448	2
C₂₃×#2426	2
C₂₃×#2421	2
C₂₃×#2370	2
C₂₃×#2367	2
C₂₃×#2363	2
C₂₃×#2362	2
C₂₃×#2357	2
C₂₃×#2347	2
C₄×C₂₃×#126	2
C₄²×Q₈×C₂₃	2
#36589	23

Subgroups — C23×#36589 #19184215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36589 #19184215