Subgroups — C₂₃×#34489 #19182115

Order 5888.

2032 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2378	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2378	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2362	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2357	C₂	1	1	yes	maximal, characteristic
9	C₂₃×#2357	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2354	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2344	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2332	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2332	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2323	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2319	C₂	1	1	yes	maximal, characteristic
19	C₂₃×#2319	C₂	1	1	yes	maximal, characteristic
20	C₂₃×#2313	C₂	1	2	yes	maximal, complemented
21	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2293	C₂	1	1	yes	maximal, characteristic
24	C₂₃×#554	C₄	1	16	yes	complemented
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#117	C₂²	1	2	yes	—
37	C₂×C₂₃×#117	C₂²	1	2	yes	—
38	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
39	C₂₃×#391	C₂²	1	1	yes	characteristic
40	C₂₃×#391	C₂²	1	1	yes	characteristic
41	C₂₃×#391	C₂²	1	2	yes	—
42	C₂₃×#391	C₂²	1	2	yes	—
43	C₂₃×#391	C₂²	1	2	yes	—
44	C₂₃×#391	C₂²	1	2	yes	—
45	C₂₃×#390	C₂²	1	1	yes	characteristic
46	C₂₃×#390	C₂²	1	1	yes	characteristic
47	C₂₃×#390	C₂²	1	1	yes	characteristic
48	C₂₃×#390	C₂²	1	1	yes	characteristic
49	C₂₃×#389	C₂²	1	1	yes	characteristic
50	C₂₃×#389	C₂²	1	1	yes	characteristic
51	C₂₃×#389	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#389	C₂²	1	1	yes	characteristic
55	C₂₃×#389	C₂²	1	1	yes	characteristic
56	C₂₃×#389	C₂²	1	1	yes	characteristic
57	C₂₃×#389	C₂²	1	2	yes	—
58	C₂₃×#389	C₂²	1	2	yes	—
59	C₂₃×#389	C₂²	1	2	yes	—
60	C₂₃×#389	C₂²	1	2	yes	—
61	C₂₃×#388	C₂²	1	2	yes	—
62	C₂₃×#388	C₂²	1	2	yes	—
63	C₂₃×#388	C₂²	1	2	yes	—
64	C₂₃×#388	C₂²	1	2	yes	—
65	C₂₃×#388	C₂²	1	2	yes	—
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	1	yes	characteristic
74	C₂₃×#387	C₂²	1	1	yes	characteristic
75	C₂₃×#387	C₂²	1	1	yes	characteristic
76	C₂₃×#387	C₂²	1	1	yes	characteristic
77	C₂₃×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#387	C₂²	1	2	yes	—
85	C₂₃×#387	C₂²	1	2	yes	—
86	C₂₃×#387	C₂²	1	2	yes	—
87	C₂₃×#387	C₂²	1	2	yes	—
88	C₂₃×#387	C₂²	1	2	yes	—
89	C₂₃×#387	C₂²	1	2	yes	—
90	C₂₃×#387	C₂²	1	2	yes	—
91	C₂₃×#384	C₂²	1	1	yes	characteristic
92	C₂₃×#382	C₂²	1	1	yes	characteristic
93	C₂₃×#382	C₂²	1	1	yes	characteristic
94	C₂₃×#381	C₂²	1	2	yes	—
95	C₂₃×#381	C₂²	1	2	yes	—
96	C₂₃×#381	C₂²	1	2	yes	—
97	C₂₃×#381	C₂²	1	2	yes	—
98	C₂₃×#380	C₂²	1	2	yes	—
99	C₂₃×#380	C₂²	1	2	yes	—
100	C₂₃×#380	C₂²	1	2	yes	—
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	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
110	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
116	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₂₃×#376	C₂²	1	1	yes	characteristic
122	C₂₃×#376	C₂²	1	1	yes	characteristic
123	C₄³×C₂₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
130	C₂₃×C₄⋊Q₈	C₂×C₄	1	8	yes	—
131	C₂₃×#125	C₂×C₄	1	8	yes	—
132	C₂₃×#125	C₂×C₄	1	8	yes	—
133	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
134	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
135	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
136	C₄×Q₈×C₂₃	—	4	4	no	—
137	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	—
138	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
139	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
140	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
141	C₂₃×#117	—	4	4	no	—
142	C₂₃×#117	—	4	4	no	—
143	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	16	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	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	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	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	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	2	yes	—
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
197	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
204	C₂₃×#95	C₂³	1	1	yes	characteristic
205	C₂₃×#95	C₂³	1	1	yes	characteristic
206	C₂₃×#95	C₂³	1	1	yes	characteristic
207	C₂₃×#95	C₂³	1	1	yes	characteristic
208	C₂₃×#95	C₂³	1	1	yes	characteristic
209	C₂₃×#95	C₂³	1	1	yes	characteristic
210	C₂₃×#95	C₂³	1	1	yes	characteristic
211	C₂₃×#95	C₂³	1	1	yes	characteristic
212	C₂₃×#95	C₂³	1	1	yes	characteristic
213	C₂₃×#95	C₂³	1	1	yes	characteristic
214	C₂₃×#95	C₂³	1	2	yes	—
215	C₂₃×#95	C₂³	1	2	yes	—
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂₃×#95	C₂³	1	2	yes	—
218	C₂₃×#95	C₂³	1	1	yes	characteristic
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	2	yes	—
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	C₂₃×#95	C₂³	1	2	yes	—
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	1	yes	characteristic
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
238	C₂×Q₈×C₂₃	—	4	2	no	—
239	C₂×Q₈×C₂₃	—	4	1	no	—
240	C₂×Q₈×C₂₃	—	4	1	no	—
241	C₂×Q₈×C₂₃	—	4	2	no	—
242	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
243	C₂×Q₈×C₂₃	C₂²×C₄	1	8	yes	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
247	C₂²×C₄×C₂₃	—	4	2	no	—
248	C₂²×C₄×C₂₃	—	4	2	no	—
249	C₂²×C₄×C₂₃	—	4	2	no	—
250	C₂²×C₄×C₂₃	—	4	2	no	—
251	C₂²×C₄×C₂₃	—	4	2	no	—
252	C₂²×C₄×C₂₃	—	4	2	no	—
253	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
254	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
255	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
256	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₄⋊C₄×C₂₃	—	2	2	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	2	no	—
285	C₄⋊C₄×C₂₃	—	4	2	no	—
286	C₄⋊C₄×C₂₃	—	4	2	no	—
287	C₄⋊C₄×C₂₃	—	4	1	no	—
288	C₄⋊C₄×C₂₃	—	4	1	no	—
289	C₄⋊C₄×C₂₃	—	4	2	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	—	4	2	no	—
294	C₄⋊C₄×C₂₃	—	4	2	no	—
295	C₄⋊C₄×C₂₃	—	4	2	no	—
296	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
297	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
298	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
299	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
300	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
301	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
302	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
303	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
304	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
305	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
306	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
307	C₂²⋊C₄×C₂₃	—	2	4	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	2	no	—
315	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
316	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
317	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
318	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	2	4	no	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	—	2	2	no	—
322	C₄²×C₂₃	—	2	2	no	—
323	C₄²×C₂₃	—	2	2	no	—
324	C₄²×C₂₃	—	4	2	no	—
325	C₄²×C₂₃	—	4	1	no	—
326	C₄²×C₂₃	—	4	2	no	—
327	C₄²×C₂₃	—	4	2	no	—
328	C₄²×C₂₃	—	4	1	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	C₂²×C₄	1	4	yes	—
336	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
337	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
338	#34489	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	C₂³×C₄	1	4	yes	—
346	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
347	Q₈×C₂₃	—	4	4	no	—
348	Q₈×C₂₃	—	4	8	no	—
349	D₄×C₂₃	—	2	8	no	—
350	C₂×C₄×C₂₃	—	2	1	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	1	no	—
353	C₂×C₄×C₂₃	—	2	2	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	1	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	2	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	2	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	1	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	1	no	—
380	C₂×C₄×C₂₃	—	2	1	no	—
381	C₂×C₄×C₂₃	—	2	1	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	1	no	—
391	C₂×C₄×C₂₃	—	2	1	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	1	no	—
396	C₂×C₄×C₂₃	—	2	1	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	1	no	—
399	C₂×C₄×C₂₃	—	2	1	no	—
400	C₂×C₄×C₂₃	—	2	1	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	1	no	—
403	C₂×C₄×C₂₃	—	4	8	no	—
404	C₂×C₄×C₂₃	—	4	8	no	—
405	C₂×C₄×C₂₃	—	4	8	no	—
406	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
407	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
408	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
409	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
410	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
411	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
412	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
413	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
414	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
415	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
416	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
417	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
418	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
419	C₂×#554	C₂×C₂₃	1	1	yes	characteristic
420	#2378	C₂×C₂₃	1	2	yes	complemented
421	#2378	C₂×C₂₃	1	2	yes	complemented
422	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
424	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#2362	C₂×C₂₃	1	2	yes	complemented
426	#2357	C₂×C₂₃	1	1	yes	characteristic
427	#2357	C₂×C₂₃	1	1	yes	characteristic
428	#2355	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#2354	C₂×C₂₃	1	1	yes	characteristic
430	#2344	C₂×C₂₃	1	2	yes	complemented
431	#2332	C₂×C₂₃	1	2	yes	complemented
432	#2332	C₂×C₂₃	1	2	yes	complemented
433	#2331	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#2330	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#2323	C₂×C₂₃	1	2	yes	complemented
436	#2319	C₂×C₂₃	1	1	yes	characteristic
437	#2319	C₂×C₂₃	1	1	yes	characteristic
438	#2313	C₂×C₂₃	1	2	yes	complemented
439	C₄×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
440	#2295	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#2293	C₂×C₂₃	1	1	yes	characteristic
442	C₂²×C₂₃	—	2	4	no	—
443	C₂²×C₂₃	—	2	4	no	—
444	C₂²×C₂₃	—	2	4	no	—
445	C₂²×C₂₃	—	4	2	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	4	2	no	—
449	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
450	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
452	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂²×C₂₃	#585	1	1	yes	characteristic
454	C₂²×C₂₃	#585	1	1	yes	characteristic
455	C₂²×C₂₃	#585	1	1	yes	characteristic
456	C₄×C₂₃	—	2	2	no	—
457	C₄×C₂₃	—	2	4	no	—
458	C₄×C₂₃	—	2	2	no	—
459	C₄×C₂₃	—	2	2	no	—
460	C₄×C₂₃	—	2	2	no	—
461	C₄×C₂₃	—	2	2	no	—
462	C₄×C₂₃	—	2	4	no	—
463	C₄×C₂₃	—	2	4	no	—
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	4	2	no	—
467	C₄×C₂₃	—	4	1	no	—
468	C₄×C₂₃	—	4	2	no	—
469	C₄×C₂₃	—	4	1	no	—
470	C₄×C₂₃	—	4	2	no	—
471	C₄×C₂₃	—	4	1	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	—	4	1	no	—
474	C₄×C₂₃	—	4	1	no	—
475	C₄×C₂₃	—	4	1	no	—
476	C₄×C₂₃	—	4	1	no	—
477	C₄×C₂₃	#519	1	4	yes	—
478	#554	C₄×C₂₃	1	16	yes	complemented
479	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
481	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
482	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
483	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
484	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
485	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
486	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×#117	C₂²×C₂₃	1	2	yes	—
491	C₂×#117	C₂²×C₂₃	1	2	yes	—
492	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
493	#391	C₂²×C₂₃	1	2	yes	—
494	#391	C₂²×C₂₃	1	2	yes	—
495	#391	C₂²×C₂₃	1	1	yes	characteristic
496	#391	C₂²×C₂₃	1	2	yes	—
497	#391	C₂²×C₂₃	1	2	yes	—
498	#391	C₂²×C₂₃	1	1	yes	characteristic
499	#390	C₂²×C₂₃	1	1	yes	characteristic
500	#390	C₂²×C₂₃	1	1	yes	characteristic
501	#390	C₂²×C₂₃	1	1	yes	characteristic
502	#390	C₂²×C₂₃	1	1	yes	characteristic
503	#389	C₂²×C₂₃	1	1	yes	characteristic
504	#389	C₂²×C₂₃	1	1	yes	characteristic
505	#389	C₂²×C₂₃	1	1	yes	characteristic
506	#389	C₂²×C₂₃	1	1	yes	characteristic
507	#389	C₂²×C₂₃	1	1	yes	characteristic
508	#389	C₂²×C₂₃	1	2	yes	—
509	#389	C₂²×C₂₃	1	2	yes	—
510	#389	C₂²×C₂₃	1	1	yes	characteristic
511	#389	C₂²×C₂₃	1	2	yes	—
512	#389	C₂²×C₂₃	1	2	yes	—
513	#389	C₂²×C₂₃	1	1	yes	characteristic
514	#389	C₂²×C₂₃	1	1	yes	characteristic
515	#388	C₂²×C₂₃	1	2	yes	—
516	#388	C₂²×C₂₃	1	2	yes	—
517	#388	C₂²×C₂₃	1	2	yes	—
518	#388	C₂²×C₂₃	1	2	yes	—
519	#388	C₂²×C₂₃	1	2	yes	—
520	#388	C₂²×C₂₃	1	2	yes	—
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	#387	C₂²×C₂₃	1	2	yes	—
528	#387	C₂²×C₂₃	1	2	yes	—
529	#387	C₂²×C₂₃	1	1	yes	characteristic
530	#387	C₂²×C₂₃	1	2	yes	—
531	#387	C₂²×C₂₃	1	2	yes	—
532	#387	C₂²×C₂₃	1	2	yes	—
533	#387	C₂²×C₂₃	1	2	yes	—
534	#387	C₂²×C₂₃	1	2	yes	—
535	#387	C₂²×C₂₃	1	2	yes	—
536	#387	C₂²×C₂₃	1	2	yes	—
537	#387	C₂²×C₂₃	1	2	yes	—
538	#387	C₂²×C₂₃	1	2	yes	—
539	#387	C₂²×C₂₃	1	1	yes	characteristic
540	#387	C₂²×C₂₃	1	2	yes	—
541	#387	C₂²×C₂₃	1	2	yes	—
542	#387	C₂²×C₂₃	1	2	yes	—
543	#387	C₂²×C₂₃	1	1	yes	characteristic
544	#387	C₂²×C₂₃	1	1	yes	characteristic
545	#384	C₂²×C₂₃	1	1	yes	characteristic
546	#382	C₂²×C₂₃	1	1	yes	characteristic
547	#382	C₂²×C₂₃	1	1	yes	characteristic
548	#381	C₂²×C₂₃	1	2	yes	—
549	#381	C₂²×C₂₃	1	2	yes	—
550	#381	C₂²×C₂₃	1	2	yes	—
551	#381	C₂²×C₂₃	1	2	yes	—
552	#380	C₂²×C₂₃	1	2	yes	—
553	#380	C₂²×C₂₃	1	2	yes	—
554	#380	C₂²×C₂₃	1	2	yes	—
555	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
556	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
558	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
559	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
560	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
561	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
562	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
563	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
564	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
566	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
568	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
573	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
574	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
575	#376	C₂²×C₂₃	1	1	yes	characteristic
576	#376	C₂²×C₂₃	1	1	yes	characteristic
577	C₄³	C₂²×C₂₃	1	1	yes	characteristic
578	C₂×C₂₃	—	4	4	no	—
579	C₂×C₂₃	C₂×#519	1	1	yes	characteristic
580	C₂×C₂₃	#3428	1	1	yes	characteristic
581	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
582	C₂×C₂₃	#3554	1	1	yes	characteristic
583	C₂×C₂₃	#3557	1	1	yes	characteristic
584	C₂×C₂₃	#3559	1	1	yes	characteristic
585	C₂×C₂₃	#3565	1	1	yes	characteristic
586	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
587	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
588	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
590	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
591	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
592	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
593	#125	C₂×C₄×C₂₃	1	8	yes	—
594	#125	C₂×C₄×C₂₃	1	8	yes	—
595	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
596	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
597	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
598	C₄×Q₈	—	4	4	no	—
599	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	—
600	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
601	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
602	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
603	#117	—	4	4	no	—
604	#117	—	4	4	no	—
605	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	16	yes	—
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
632	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₄⋊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	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×C₄²	C₂³×C₂₃	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
648	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
662	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
663	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
664	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
665	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
666	#95	C₂³×C₂₃	1	1	yes	characteristic
667	#95	C₂³×C₂₃	1	1	yes	characteristic
668	#95	C₂³×C₂₃	1	1	yes	characteristic
669	#95	C₂³×C₂₃	1	1	yes	characteristic
670	#95	C₂³×C₂₃	1	1	yes	characteristic
671	#95	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	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	1	yes	characteristic
681	#95	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
687	#95	C₂³×C₂₃	1	2	yes	—
688	#95	C₂³×C₂₃	1	2	yes	—
689	#95	C₂³×C₂₃	1	2	yes	—
690	#95	C₂³×C₂₃	1	2	yes	—
691	#95	C₂³×C₂₃	1	2	yes	—
692	#95	C₂³×C₂₃	1	2	yes	—
693	#95	C₂³×C₂₃	1	2	yes	—
694	#95	C₂³×C₂₃	1	2	yes	—
695	#95	C₂³×C₂₃	1	2	yes	—
696	#95	C₂³×C₂₃	1	2	yes	—
697	#95	C₂³×C₂₃	1	1	yes	characteristic
698	#95	C₂³×C₂₃	1	2	yes	—
699	C₂₃	#34489	1	1	yes	characteristic, direct product factor, Sylow
700	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	—	4	1	no	—
703	C₂×Q₈	—	4	1	no	—
704	C₂×Q₈	—	4	2	no	—
705	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
706	C₂×Q₈	C₂²×C₄×C₂₃	1	8	yes	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	2	no	—
709	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	2	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
717	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
718	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
719	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
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	2	yes	—
724	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
731	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
733	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
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	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	4	2	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	1	no	—
754	C₄⋊C₄	—	4	1	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	1	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
760	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
761	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
762	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
763	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
764	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
765	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
766	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
767	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
768	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
769	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
779	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
780	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
781	C₄²	—	2	2	no	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	2	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	4	2	no	—
788	C₄²	—	4	2	no	—
789	C₄²	—	4	2	no	—
790	C₄²	—	4	2	no	—
791	C₄²	—	4	2	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	1	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	2	no	—
798	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
799	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
800	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
808	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
809	Q₈	—	4	4	no	—
810	Q₈	—	4	8	no	—
811	D₄	—	2	8	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	1	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	1	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	1	no	—
830	C₂×C₄	—	2	1	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	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	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	4	8	no	—
866	C₂×C₄	—	4	8	no	—
867	C₂×C₄	—	4	8	no	—
868	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
869	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
870	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
871	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
872	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
873	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
874	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
875	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
876	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
877	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
878	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
879	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
880	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
881	C₂²	—	2	4	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
889	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
891	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
892	C₂²	C₂₃×#585	1	1	yes	characteristic
893	C₂²	C₂₃×#585	1	1	yes	characteristic
894	C₂²	C₂₃×#585	1	1	yes	characteristic
895	C₄	—	2	2	no	—
896	C₄	—	2	4	no	—
897	C₄	—	2	2	no	—
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	4	no	—
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	1	no	—
911	C₄	—	4	2	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	1	no	—
915	C₄	—	4	1	no	—
916	C₄	C₂₃×#519	1	4	yes	—
917	C₂	—	4	4	no	—
918	C₂	C₂×C₂₃×#519	1	1	yes	characteristic
919	C₂	C₂₃×#3428	1	1	yes	characteristic
920	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
921	C₂	C₂₃×#3554	1	1	yes	characteristic
922	C₂	C₂₃×#3557	1	1	yes	characteristic
923	C₂	C₂₃×#3559	1	1	yes	characteristic
924	C₂	C₂₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂³
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×#2378	C₂	semidirect
3. C₂₃×#2378	C₂	semidirect
4. C₂₃×#2370	C₂	semidirect
5. C₂₃×#2370	C₂	semidirect
6. C₂₃×#2365	C₂	semidirect
7. C₂₃×#2362	C₂	semidirect
10. C₂₃×#2355	C₂	semidirect
12. C₂₃×#2344	C₂	semidirect
13. C₂₃×#2332	C₂	semidirect
14. C₂₃×#2332	C₂	semidirect
15. C₂₃×#2331	C₂	semidirect
16. C₂₃×#2330	C₂	semidirect
17. C₂₃×#2323	C₂	semidirect
20. C₂₃×#2313	C₂	semidirect
21. C₄×C₂₃×#125	C₂	semidirect
22. C₂₃×#2295	C₂	semidirect
24. C₂₃×#554	C₄	semidirect
338. #34489	C₂₃	direct (N × H)
420. #2378	C₂×C₂₃	semidirect
421. #2378	C₂×C₂₃	semidirect
422. #2370	C₂×C₂₃	semidirect
423. #2370	C₂×C₂₃	semidirect
424. #2365	C₂×C₂₃	semidirect
425. #2362	C₂×C₂₃	semidirect
428. #2355	C₂×C₂₃	semidirect
430. #2344	C₂×C₂₃	semidirect
431. #2332	C₂×C₂₃	semidirect
432. #2332	C₂×C₂₃	semidirect
433. #2331	C₂×C₂₃	semidirect
434. #2330	C₂×C₂₃	semidirect
435. #2323	C₂×C₂₃	semidirect
438. #2313	C₂×C₂₃	semidirect
439. C₄×#125	C₂×C₂₃	semidirect
440. #2295	C₂×C₂₃	semidirect
478. #554	C₄×C₂₃	semidirect
699. C₂₃	#34489	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×#554	2
C₂₃×#2378	2
C₂₃×#2370	2
C₂₃×#2365	2
C₂₃×#2362	2
C₂₃×#2357	2
C₂₃×#2355	2
C₂₃×#2354	2
C₂₃×#2344	2
C₂₃×#2332	2
C₂₃×#2331	2
C₂₃×#2330	2
C₂₃×#2323	2
C₂₃×#2319	2
C₂₃×#2313	2
C₄×C₂₃×#125	2
C₂₃×#2295	2
C₂₃×#2293	2
#34489	23

Subgroups — C23×#34489 #19182115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34489 #19182115