Subgroups — C₂₃×#34432 #19182058

Order 5888.

2010 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#544	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2382	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2381	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2371	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2368	C₂	1	2	yes	maximal
6	C₂₃×#2365	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2360	C₂	1	2	yes	maximal
8	C₂₃×#2343	C₂	1	2	yes	maximal
9	C₂₃×#2343	C₂	1	2	yes	maximal
10	C₂₃×#2336	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2336	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2331	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic
14	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic
15	C₂₃×#2327	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2313	C₂	1	1	yes	maximal, characteristic
17	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
18	C₄×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
19	C₂×C₂₃×#387	C₂	1	1	yes	maximal, characteristic
20	C₂₃×#544	C₄	1	16	yes	complemented
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₃×#125	C₂²	1	2	yes	—
24	C₂×C₂₃×#125	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
31	C₂×C₂₃×#117	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#391	C₂²	1	1	yes	characteristic
36	C₂₃×#391	C₂²	1	1	yes	characteristic
37	C₂₃×#391	C₂²	1	2	yes	—
38	C₂₃×#391	C₂²	1	2	yes	—
39	C₂₃×#391	C₂²	1	2	yes	—
40	C₂₃×#391	C₂²	1	2	yes	—
41	C₂₃×#391	C₂²	1	2	yes	—
42	C₂₃×#389	C₂²	1	1	yes	characteristic
43	C₂₃×#389	C₂²	1	1	yes	characteristic
44	C₂₃×#389	C₂²	1	2	yes	—
45	C₂₃×#389	C₂²	1	2	yes	—
46	C₂₃×#389	C₂²	1	2	yes	—
47	C₂₃×#389	C₂²	1	2	yes	—
48	C₂₃×#389	C₂²	1	2	yes	—
49	C₂₃×#387	C₂²	1	2	yes	—
50	C₂₃×#387	C₂²	1	2	yes	—
51	C₂₃×#387	C₂²	1	2	yes	—
52	C₂₃×#387	C₂²	1	2	yes	—
53	C₂₃×#387	C₂²	1	2	yes	—
54	C₂₃×#387	C₂²	1	2	yes	—
55	C₂₃×#387	C₂²	1	2	yes	—
56	C₂₃×#387	C₂²	1	2	yes	—
57	C₂₃×#387	C₂²	1	2	yes	—
58	C₂₃×#387	C₂²	1	2	yes	—
59	C₂₃×#387	C₂²	1	2	yes	—
60	C₂₃×#387	C₂²	1	2	yes	—
61	C₂₃×#387	C₂²	1	2	yes	—
62	C₂₃×#387	C₂²	1	2	yes	—
63	C₂₃×#387	C₂²	1	2	yes	—
64	C₂₃×#387	C₂²	1	2	yes	—
65	C₂₃×#387	C₂²	1	2	yes	—
66	C₂₃×#387	C₂²	1	2	yes	—
67	C₂₃×#387	C₂²	1	2	yes	—
68	C₂₃×#387	C₂²	1	2	yes	—
69	C₂₃×#387	C₂²	1	2	yes	—
70	C₂₃×#387	C₂²	1	2	yes	—
71	C₂₃×#387	C₂²	1	2	yes	—
72	C₂₃×#387	C₂²	1	2	yes	—
73	C₂₃×#387	C₂²	1	2	yes	—
74	C₂₃×#387	C₂²	1	2	yes	—
75	C₂₃×#387	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	2	yes	—
77	C₂₃×#385	C₂²	1	2	yes	—
78	C₂₃×#385	C₂²	1	2	yes	—
79	C₂₃×#385	C₂²	1	2	yes	—
80	C₂₃×#385	C₂²	1	2	yes	—
81	C₂₃×#383	C₂²	1	2	yes	—
82	C₂₃×#383	C₂²	1	2	yes	—
83	C₂₃×#382	C₂²	1	2	yes	—
84	C₂₃×#382	C₂²	1	2	yes	—
85	C₂₃×#381	C₂²	1	2	yes	—
86	C₂₃×#380	C₂²	1	1	yes	characteristic
87	C₂₃×#380	C₂²	1	1	yes	characteristic
88	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
89	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
90	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
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	2	yes	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₂₃×#376	C₂²	1	2	yes	—
103	C₂₃×#376	C₂²	1	2	yes	—
104	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
105	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
107	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
119	C₂₃×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
120	C₂₃×#125	C₂×C₄	1	16	yes	complemented
121	C₂₃×#125	C₂×C₄	1	16	yes	complemented
122	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
123	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
124	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
125	C₄×Q₈×C₂₃	—	4	2	no	—
126	C₄×Q₈×C₂₃	—	4	2	no	—
127	C₄×Q₈×C₂₃	—	4	4	no	—
128	C₂₃×#117	C₂×C₄	1	16	yes	—
129	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
130	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	—
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	2	yes	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	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	2	yes	—
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄²×C₂₃	—	4	2	no	—
161	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
177	C₂₃×#95	C₂³	1	2	yes	—
178	C₂₃×#95	C₂³	1	2	yes	—
179	C₂₃×#95	C₂³	1	2	yes	—
180	C₂₃×#95	C₂³	1	2	yes	—
181	C₂₃×#95	C₂³	1	2	yes	—
182	C₂₃×#95	C₂³	1	2	yes	—
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	2	yes	—
185	C₂₃×#95	C₂³	1	2	yes	—
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	2	yes	—
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
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	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
210	C₂×Q₈×C₂₃	—	4	1	no	—
211	C₂×Q₈×C₂₃	—	4	1	no	—
212	C₂×Q₈×C₂₃	—	4	2	no	—
213	C₂×Q₈×C₂₃	—	4	2	no	—
214	C₂×Q₈×C₂₃	—	4	1	no	—
215	C₂×Q₈×C₂₃	—	4	1	no	—
216	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
217	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
218	C₂×Q₈×C₂₃	C₂²×C₄	1	8	yes	—
219	C₂²×C₄×C₂₃	—	2	2	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	2	no	—
222	C₂²×C₄×C₂₃	—	2	2	no	—
223	C₂²×C₄×C₂₃	—	2	2	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	2	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	4	1	no	—
228	C₂²×C₄×C₂₃	—	4	1	no	—
229	C₂²×C₄×C₂₃	—	4	1	no	—
230	C₂²×C₄×C₂₃	—	4	1	no	—
231	C₂²×C₄×C₂₃	—	4	1	no	—
232	C₂²×C₄×C₂₃	—	4	1	no	—
233	C₂²×C₄×C₂₃	—	4	1	no	—
234	C₂²×C₄×C₂₃	—	4	1	no	—
235	C₂²×C₄×C₂₃	—	4	1	no	—
236	C₂²×C₄×C₂₃	—	4	1	no	—
237	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
238	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
239	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
240	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
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	C₄⋊C₄×C₂₃	—	2	4	no	—
259	C₄⋊C₄×C₂₃	—	2	4	no	—
260	C₄⋊C₄×C₂₃	—	2	4	no	—
261	C₄⋊C₄×C₂₃	—	4	2	no	—
262	C₄⋊C₄×C₂₃	—	4	2	no	—
263	C₄⋊C₄×C₂₃	—	4	2	no	—
264	C₄⋊C₄×C₂₃	—	4	2	no	—
265	C₄⋊C₄×C₂₃	—	4	1	no	—
266	C₄⋊C₄×C₂₃	—	4	1	no	—
267	C₄⋊C₄×C₂₃	—	4	2	no	—
268	C₄⋊C₄×C₂₃	—	4	1	no	—
269	C₄⋊C₄×C₂₃	—	4	1	no	—
270	C₄⋊C₄×C₂₃	—	4	2	no	—
271	C₄⋊C₄×C₂₃	—	4	2	no	—
272	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
273	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
274	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
275	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
276	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
277	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
278	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
279	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
280	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
281	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
282	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
286	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
287	C₄²×C₂₃	—	2	2	no	—
288	C₄²×C₂₃	—	2	2	no	—
289	C₄²×C₂₃	—	2	4	no	—
290	C₄²×C₂₃	—	2	4	no	—
291	C₄²×C₂₃	—	4	1	no	—
292	C₄²×C₂₃	—	4	1	no	—
293	C₄²×C₂₃	—	4	2	no	—
294	C₄²×C₂₃	—	4	2	no	—
295	C₄²×C₂₃	—	4	2	no	—
296	C₄²×C₂₃	—	4	2	no	—
297	C₄²×C₂₃	—	4	2	no	—
298	C₄²×C₂₃	—	4	2	no	—
299	C₄²×C₂₃	—	4	2	no	—
300	C₄²×C₂₃	—	4	2	no	—
301	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
302	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
303	#34432	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂³×C₂₃	—	2	1	no	—
305	C₂³×C₂₃	—	2	1	no	—
306	C₂³×C₂₃	—	2	1	no	—
307	C₂³×C₂₃	—	2	1	no	—
308	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
309	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
310	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
311	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
312	Q₈×C₂₃	—	4	4	no	—
313	Q₈×C₂₃	—	4	4	no	—
314	Q₈×C₂₃	—	4	8	no	—
315	C₂×C₄×C₂₃	—	2	8	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	2	1	no	—
318	C₂×C₄×C₂₃	—	2	1	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	1	no	—
327	C₂×C₄×C₂₃	—	2	1	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	1	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	1	no	—
334	C₂×C₄×C₂₃	—	2	1	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	1	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	1	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	1	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	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	—	4	4	no	—
361	C₂×C₄×C₂₃	—	4	4	no	—
362	C₂×C₄×C₂₃	—	4	4	no	—
363	C₂×C₄×C₂₃	—	4	4	no	—
364	C₂×C₄×C₂₃	—	8	2	no	—
365	C₂×C₄×C₂₃	—	8	2	no	—
366	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
367	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
368	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
369	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
370	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
371	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
372	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
373	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
374	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
376	C₂×#544	C₂×C₂₃	1	1	yes	characteristic
377	#2382	C₂×C₂₃	1	2	yes	complemented
378	#2381	C₂×C₂₃	1	2	yes	complemented
379	#2371	C₂×C₂₃	1	2	yes	complemented
380	#2368	C₂×C₂₃	1	2	yes	—
381	#2365	C₂×C₂₃	1	2	yes	complemented
382	#2360	C₂×C₂₃	1	2	yes	—
383	#2343	C₂×C₂₃	1	2	yes	—
384	#2343	C₂×C₂₃	1	2	yes	—
385	#2336	C₂×C₂₃	1	2	yes	complemented
386	#2336	C₂×C₂₃	1	2	yes	complemented
387	#2331	C₂×C₂₃	1	2	yes	complemented
388	#2329	C₂×C₂₃	1	1	yes	characteristic
389	#2329	C₂×C₂₃	1	1	yes	characteristic
390	#2327	C₂×C₂₃	1	2	yes	complemented
391	#2313	C₂×C₂₃	1	1	yes	characteristic
392	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
393	C₄×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic
394	C₂×#387	C₂×C₂₃	1	1	yes	characteristic
395	C₂²×C₂₃	—	2	2	no	—
396	C₂²×C₂₃	—	2	2	no	—
397	C₂²×C₂₃	—	2	2	no	—
398	C₂²×C₂₃	—	2	2	no	—
399	C₂²×C₂₃	—	2	2	no	—
400	C₂²×C₂₃	—	2	2	no	—
401	C₂²×C₂₃	#519	1	4	yes	—
402	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
403	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
404	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
405	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
406	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
407	C₂²×C₂₃	#585	1	1	yes	characteristic
408	C₂²×C₂₃	#585	1	1	yes	characteristic
409	C₄×C₂₃	—	2	4	no	—
410	C₄×C₂₃	—	2	2	no	—
411	C₄×C₂₃	—	2	2	no	—
412	C₄×C₂₃	—	2	4	no	—
413	C₄×C₂₃	—	2	4	no	—
414	C₄×C₂₃	—	2	4	no	—
415	C₄×C₂₃	—	2	4	no	—
416	C₄×C₂₃	—	2	4	no	—
417	C₄×C₂₃	—	2	2	no	—
418	C₄×C₂₃	—	2	2	no	—
419	C₄×C₂₃	—	4	2	no	—
420	C₄×C₂₃	—	4	1	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	1	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	#544	C₄×C₂₃	1	16	yes	complemented
428	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
429	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
430	C₂×#125	C₂²×C₂₃	1	2	yes	—
431	C₂×#125	C₂²×C₂₃	1	2	yes	—
432	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
435	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
437	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#117	C₂²×C₂₃	1	2	yes	—
439	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
440	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
441	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
442	#391	C₂²×C₂₃	1	2	yes	—
443	#391	C₂²×C₂₃	1	2	yes	—
444	#391	C₂²×C₂₃	1	2	yes	—
445	#391	C₂²×C₂₃	1	1	yes	characteristic
446	#391	C₂²×C₂₃	1	2	yes	—
447	#391	C₂²×C₂₃	1	2	yes	—
448	#391	C₂²×C₂₃	1	1	yes	characteristic
449	#389	C₂²×C₂₃	1	2	yes	—
450	#389	C₂²×C₂₃	1	2	yes	—
451	#389	C₂²×C₂₃	1	2	yes	—
452	#389	C₂²×C₂₃	1	1	yes	characteristic
453	#389	C₂²×C₂₃	1	2	yes	—
454	#389	C₂²×C₂₃	1	2	yes	—
455	#389	C₂²×C₂₃	1	1	yes	characteristic
456	#387	C₂²×C₂₃	1	2	yes	—
457	#387	C₂²×C₂₃	1	2	yes	—
458	#387	C₂²×C₂₃	1	2	yes	—
459	#387	C₂²×C₂₃	1	2	yes	—
460	#387	C₂²×C₂₃	1	2	yes	—
461	#387	C₂²×C₂₃	1	2	yes	—
462	#387	C₂²×C₂₃	1	2	yes	—
463	#387	C₂²×C₂₃	1	2	yes	—
464	#387	C₂²×C₂₃	1	2	yes	—
465	#387	C₂²×C₂₃	1	2	yes	—
466	#387	C₂²×C₂₃	1	2	yes	—
467	#387	C₂²×C₂₃	1	2	yes	—
468	#387	C₂²×C₂₃	1	2	yes	—
469	#387	C₂²×C₂₃	1	2	yes	—
470	#387	C₂²×C₂₃	1	2	yes	—
471	#387	C₂²×C₂₃	1	2	yes	—
472	#387	C₂²×C₂₃	1	2	yes	—
473	#387	C₂²×C₂₃	1	2	yes	—
474	#387	C₂²×C₂₃	1	2	yes	—
475	#387	C₂²×C₂₃	1	2	yes	—
476	#387	C₂²×C₂₃	1	2	yes	—
477	#387	C₂²×C₂₃	1	2	yes	—
478	#387	C₂²×C₂₃	1	2	yes	—
479	#387	C₂²×C₂₃	1	2	yes	—
480	#387	C₂²×C₂₃	1	2	yes	—
481	#387	C₂²×C₂₃	1	2	yes	—
482	#387	C₂²×C₂₃	1	2	yes	—
483	#387	C₂²×C₂₃	1	2	yes	—
484	#385	C₂²×C₂₃	1	2	yes	—
485	#385	C₂²×C₂₃	1	2	yes	—
486	#385	C₂²×C₂₃	1	2	yes	—
487	#385	C₂²×C₂₃	1	2	yes	—
488	#383	C₂²×C₂₃	1	2	yes	—
489	#383	C₂²×C₂₃	1	2	yes	—
490	#382	C₂²×C₂₃	1	2	yes	—
491	#382	C₂²×C₂₃	1	2	yes	—
492	#381	C₂²×C₂₃	1	2	yes	—
493	#380	C₂²×C₂₃	1	1	yes	characteristic
494	#380	C₂²×C₂₃	1	1	yes	characteristic
495	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
496	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
497	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
499	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
503	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
504	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
505	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
506	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
509	#376	C₂²×C₂₃	1	2	yes	—
510	#376	C₂²×C₂₃	1	2	yes	—
511	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
512	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
513	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
514	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
515	C₂×C₂₃	—	2	4	no	—
516	C₂×C₂₃	C₂×#519	1	1	yes	characteristic
517	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
518	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
519	C₂×C₂₃	#3535	1	1	yes	characteristic
520	C₂×C₂₃	#3538	1	1	yes	characteristic
521	C₂×C₂₃	#3563	1	1	yes	characteristic
522	C₂×C₂₃	#3564	1	1	yes	characteristic
523	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
524	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
525	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
527	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
528	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
533	C₄⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
534	C₄⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
535	#125	C₂×C₄×C₂₃	1	16	yes	complemented
536	#125	C₂×C₄×C₂₃	1	16	yes	complemented
537	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
538	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	—
539	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	—
540	C₄×Q₈	—	4	2	no	—
541	C₄×Q₈	—	4	2	no	—
542	C₄×Q₈	—	4	4	no	—
543	#117	C₂×C₄×C₂₃	1	16	yes	—
544	C₂×C₄⋊C₄	—	4	2	no	—
545	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	—
546	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
552	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
560	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
566	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
569	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
575	C₂×C₄²	—	4	2	no	—
576	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
578	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
579	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
580	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
581	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
582	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
583	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
584	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
585	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
587	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
588	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
591	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
592	#95	C₂³×C₂₃	1	2	yes	—
593	#95	C₂³×C₂₃	1	2	yes	—
594	#95	C₂³×C₂₃	1	2	yes	—
595	#95	C₂³×C₂₃	1	2	yes	—
596	#95	C₂³×C₂₃	1	2	yes	—
597	#95	C₂³×C₂₃	1	2	yes	—
598	#95	C₂³×C₂₃	1	2	yes	—
599	#95	C₂³×C₂₃	1	2	yes	—
600	#95	C₂³×C₂₃	1	2	yes	—
601	#95	C₂³×C₂₃	1	2	yes	—
602	#95	C₂³×C₂₃	1	2	yes	—
603	#95	C₂³×C₂₃	1	2	yes	—
604	#95	C₂³×C₂₃	1	2	yes	—
605	#95	C₂³×C₂₃	1	2	yes	—
606	#95	C₂³×C₂₃	1	2	yes	—
607	#95	C₂³×C₂₃	1	2	yes	—
608	#95	C₂³×C₂₃	1	2	yes	—
609	#95	C₂³×C₂₃	1	2	yes	—
610	#95	C₂³×C₂₃	1	2	yes	—
611	#95	C₂³×C₂₃	1	2	yes	—
612	#95	C₂³×C₂₃	1	2	yes	—
613	#95	C₂³×C₂₃	1	2	yes	—
614	#95	C₂³×C₂₃	1	2	yes	—
615	#95	C₂³×C₂₃	1	2	yes	—
616	#95	C₂³×C₂₃	1	2	yes	—
617	#95	C₂³×C₂₃	1	2	yes	—
618	#95	C₂³×C₂₃	1	2	yes	—
619	#95	C₂³×C₂₃	1	2	yes	—
620	#95	C₂³×C₂₃	1	2	yes	—
621	#95	C₂³×C₂₃	1	2	yes	—
622	#95	C₂³×C₂₃	1	2	yes	—
623	#95	C₂³×C₂₃	1	2	yes	—
624	C₂₃	#34432	1	1	yes	characteristic, direct product factor, Sylow
625	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
626	C₂×Q₈	—	4	1	no	—
627	C₂×Q₈	—	4	1	no	—
628	C₂×Q₈	—	4	2	no	—
629	C₂×Q₈	—	4	2	no	—
630	C₂×Q₈	—	4	1	no	—
631	C₂×Q₈	—	4	1	no	—
632	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
633	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
634	C₂×Q₈	C₂²×C₄×C₂₃	1	8	yes	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	—	4	1	no	—
645	C₂²×C₄	—	4	1	no	—
646	C₂²×C₄	—	4	1	no	—
647	C₂²×C₄	—	4	1	no	—
648	C₂²×C₄	—	4	1	no	—
649	C₂²×C₄	—	4	1	no	—
650	C₂²×C₄	—	4	1	no	—
651	C₂²×C₄	—	4	1	no	—
652	C₂²×C₄	—	4	1	no	—
653	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
654	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
655	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
656	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
664	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
670	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	2	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	2	no	—
683	C₄⋊C₄	—	4	2	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	—	4	1	no	—
686	C₄⋊C₄	—	4	1	no	—
687	C₄⋊C₄	—	4	2	no	—
688	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
689	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
690	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
691	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
692	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
693	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
694	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
695	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
696	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
697	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
698	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	4	no	—
701	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
702	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
703	C₄²	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	4	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	4	1	no	—
708	C₄²	—	4	1	no	—
709	C₄²	—	4	2	no	—
710	C₄²	—	4	2	no	—
711	C₄²	—	4	2	no	—
712	C₄²	—	4	2	no	—
713	C₄²	—	4	2	no	—
714	C₄²	—	4	2	no	—
715	C₄²	—	4	2	no	—
716	C₄²	—	4	2	no	—
717	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
718	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	—	2	1	no	—
723	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
724	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
725	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
726	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
727	Q₈	—	4	4	no	—
728	Q₈	—	4	4	no	—
729	Q₈	—	4	8	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	1	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	8	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	1	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	1	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	—	8	2	no	—
781	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
782	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
783	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
784	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
785	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
786	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
787	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
788	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
789	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
790	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	C₂₃×#519	1	4	yes	—
798	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
799	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
800	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
801	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
802	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
803	C₂²	C₂₃×#585	1	1	yes	characteristic
804	C₂²	C₂₃×#585	1	1	yes	characteristic
805	C₄	—	2	4	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	4	no	—
809	C₄	—	2	4	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	1	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	2	no	—
823	C₂	—	2	4	no	—
824	C₂	C₂×C₂₃×#519	1	1	yes	characteristic
825	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
827	C₂	C₂₃×#3535	1	1	yes	characteristic
828	C₂	C₂₃×#3538	1	1	yes	characteristic
829	C₂	C₂₃×#3563	1	1	yes	characteristic
830	C₂	C₂₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁴×C₂₃	C₂⁴
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×#2382	C₂	semidirect
3. C₂₃×#2381	C₂	semidirect
4. C₂₃×#2371	C₂	semidirect
6. C₂₃×#2365	C₂	semidirect
10. C₂₃×#2336	C₂	semidirect
11. C₂₃×#2336	C₂	semidirect
12. C₂₃×#2331	C₂	semidirect
15. C₂₃×#2327	C₂	semidirect
20. C₂₃×#544	C₄	semidirect
118. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
119. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
120. C₂₃×#125	C₂×C₄	semidirect
121. C₂₃×#125	C₂×C₄	semidirect
303. #34432	C₂₃	direct (N × H)
377. #2382	C₂×C₂₃	semidirect
378. #2381	C₂×C₂₃	semidirect
379. #2371	C₂×C₂₃	semidirect
381. #2365	C₂×C₂₃	semidirect
385. #2336	C₂×C₂₃	semidirect
386. #2336	C₂×C₂₃	semidirect
387. #2331	C₂×C₂₃	semidirect
390. #2327	C₂×C₂₃	semidirect
427. #544	C₄×C₂₃	semidirect
533. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
534. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
535. #125	C₂×C₄×C₂₃	semidirect
536. #125	C₂×C₄×C₂₃	semidirect
624. C₂₃	#34432	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×#544	2
C₂₃×#2382	2
C₂₃×#2381	2
C₂₃×#2371	2
C₂₃×#2368	2
C₂₃×#2365	2
C₂₃×#2360	2
C₂₃×#2343	2
C₂₃×#2336	2
C₂₃×#2331	2
C₂₃×#2329	2
C₂₃×#2327	2
C₂₃×#2313	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂×C₂₃×#387	2
#34432	23

Subgroups — C23×#34432 #19182058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34432 #19182058