Subgroups — C₂₃×#34333 #19181959

Order 5888.

2288 conjugacy classes of subgroups.

The subgroup lattice has 958 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×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2368	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2368	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2360	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic
10	C₂₃×#2349	C₂	1	1	yes	maximal, characteristic
11	D₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
12	C₂₃×#2345	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2329	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2329	C₂	1	2	yes	maximal, complemented
17	C₄×C₂₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#387	C₂	1	2	yes	maximal, complemented
21	C₂₃×#2275	C₂	1	1	yes	maximal, characteristic
22	C₂₃×#2275	C₂	1	1	yes	maximal, characteristic
23	C₄²×D₄×C₂₃	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×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
42	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
43	C₂₃×#391	C₂²	1	1	yes	characteristic
44	C₂₃×#391	C₂²	1	1	yes	characteristic
45	C₂₃×#391	C₂²	1	2	yes	—
46	C₂₃×#391	C₂²	1	2	yes	—
47	C₂₃×#391	C₂²	1	2	yes	—
48	C₂₃×#391	C₂²	1	2	yes	—
49	C₂₃×#389	C₂²	1	1	yes	characteristic
50	C₂₃×#389	C₂²	1	1	yes	characteristic
51	C₂₃×#389	C₂²	1	2	yes	—
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#389	C₂²	1	2	yes	—
55	C₂₃×#389	C₂²	1	2	yes	—
56	C₂₃×#389	C₂²	1	2	yes	—
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	1	yes	characteristic
61	C₂₃×#387	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
70	C₂₃×#387	C₂²	1	1	yes	characteristic
71	C₂₃×#387	C₂²	1	1	yes	characteristic
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×#387	C₂²	1	2	yes	—
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#385	C₂²	1	2	yes	—
80	C₂₃×#385	C₂²	1	2	yes	—
81	C₂₃×#385	C₂²	1	2	yes	—
82	C₂₃×#385	C₂²	1	2	yes	—
83	C₂₃×#385	C₂²	1	2	yes	—
84	C₂₃×#385	C₂²	1	2	yes	—
85	C₂₃×#384	C₂²	1	1	yes	characteristic
86	C₂₃×#382	C₂²	1	1	yes	characteristic
87	C₂₃×#382	C₂²	1	1	yes	characteristic
88	C₂₃×#380	C₂²	1	2	yes	—
89	C₂₃×#380	C₂²	1	2	yes	—
90	C₂₃×#380	C₂²	1	2	yes	—
91	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
92	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
93	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
95	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
96	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
98	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
99	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
100	C₄×C₄⋊C₄×C₂₃	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	2	yes	—
104	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
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×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
109	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
110	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
111	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
112	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
113	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
114	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
117	C₂₃×#376	C₂²	1	1	yes	characteristic
118	C₂₃×#376	C₂²	1	1	yes	characteristic
119	C₂×C₂₃×#95	C₂²	1	2	yes	—
120	C₂×C₂₃×#95	C₂²	1	2	yes	—
121	C₂×C₂₃×#95	C₂²	1	2	yes	—
122	C₂×C₂₃×#95	C₂²	1	2	yes	—
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×C₂₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
132	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂₃×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
135	C₂₃×#125	C₂×C₄	1	8	yes	complemented
136	C₂₃×#125	C₂×C₄	1	8	yes	complemented
137	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
138	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
139	C₂₃×C₂²⋊Q₈	C₂×C₄	1	16	yes	complemented
140	C₄×Q₈×C₂₃	—	4	4	no	—
141	C₄×Q₈×C₂₃	C₂×C₄	1	8	yes	complemented
142	C₄×D₄×C₂₃	—	2	4	no	—
143	C₄×D₄×C₂₃	—	2	4	no	—
144	C₄×D₄×C₂₃	—	2	4	no	—
145	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
146	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
147	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	—
148	C₄×D₄×C₂₃	Q₈	1	8	yes	complemented
149	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
150	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	16	yes	complemented
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	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	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄²×C₂₃	—	4	4	no	—
188	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₂₃	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	2	yes	—
213	C₂₃×#95	C₂³	1	2	yes	—
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	2	yes	—
219	C₂₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
226	C₂₃×#95	C₂³	1	1	yes	characteristic
227	C₂₃×#95	C₂³	1	1	yes	characteristic
228	C₂₃×#95	C₂³	1	1	yes	characteristic
229	C₂₃×#95	C₂³	1	1	yes	characteristic
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	2	yes	—
233	C₂₃×#95	C₂³	1	1	yes	characteristic
234	C₂₃×#95	C₂³	1	1	yes	characteristic
235	C₂₃×#95	C₂³	1	1	yes	characteristic
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂₃×#95	C₂³	1	2	yes	—
238	C₂₃×#95	C₂³	1	2	yes	—
239	C₂₃×#95	C₂³	1	2	yes	—
240	C₂₃×#95	C₂³	1	1	yes	characteristic
241	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
242	C₂×Q₈×C₂₃	—	4	2	no	—
243	C₂×Q₈×C₂₃	—	4	1	no	—
244	C₂×Q₈×C₂₃	—	4	1	no	—
245	C₂×Q₈×C₂₃	—	4	2	no	—
246	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
247	C₂×Q₈×C₂₃	C₂²×C₄	1	8	yes	—
248	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
249	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
250	C₂×D₄×C₂₃	#41	1	4	yes	—
251	C₂²×C₄×C₂₃	—	2	4	no	—
252	C₂²×C₄×C₂₃	—	2	4	no	—
253	C₂²×C₄×C₂₃	—	2	4	no	—
254	C₂²×C₄×C₂₃	—	2	4	no	—
255	C₂²×C₄×C₂₃	—	4	2	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	C₂²×C₄	1	8	yes	—
269	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
270	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
271	C₂²×C₄×C₂₃	C₂×Q₈	1	8	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
279	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	4	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	4	2	no	—
301	C₄⋊C₄×C₂₃	—	4	2	no	—
302	C₄⋊C₄×C₂₃	—	4	2	no	—
303	C₄⋊C₄×C₂₃	—	4	2	no	—
304	C₄⋊C₄×C₂₃	—	4	1	no	—
305	C₄⋊C₄×C₂₃	—	4	1	no	—
306	C₄⋊C₄×C₂₃	—	4	2	no	—
307	C₄⋊C₄×C₂₃	—	4	1	no	—
308	C₄⋊C₄×C₂₃	—	4	2	no	—
309	C₄⋊C₄×C₂₃	—	4	1	no	—
310	C₄⋊C₄×C₂₃	—	4	2	no	—
311	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
312	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
313	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
314	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
315	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
316	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
317	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
318	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
319	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
320	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
321	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
322	C₄⋊C₄×C₂₃	C₂×Q₈	1	4	yes	—
323	C₂²⋊C₄×C₂₃	—	2	4	no	—
324	C₂²⋊C₄×C₂₃	—	2	4	no	—
325	C₂²⋊C₄×C₂₃	—	2	4	no	—
326	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
327	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
328	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
329	C₂²⋊C₄×C₂₃	C₂×Q₈	1	8	yes	—
330	C₄²×C₂₃	—	2	2	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	—	2	2	no	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	2	4	no	—
335	C₄²×C₂₃	—	4	2	no	—
336	C₄²×C₂₃	—	4	2	no	—
337	C₄²×C₂₃	—	4	2	no	—
338	C₄²×C₂₃	—	4	1	no	—
339	C₄²×C₂₃	—	4	1	no	—
340	C₄²×C₂₃	—	4	2	no	—
341	C₄²×C₂₃	—	4	2	no	—
342	C₄²×C₂₃	—	4	2	no	—
343	C₄²×C₂₃	—	4	1	no	—
344	C₄²×C₂₃	—	4	2	no	—
345	C₄²×C₂₃	—	4	2	no	—
346	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
347	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
348	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
349	C₄²×C₂₃	C₂×Q₈	1	4	yes	—
350	#34333	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
351	C₂³×C₂₃	—	2	2	no	—
352	C₂³×C₂₃	—	2	2	no	—
353	C₂³×C₂₃	—	2	2	no	—
354	C₂³×C₂₃	—	2	2	no	—
355	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
356	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
357	C₂³×C₂₃	C₂×#41	1	4	yes	—
358	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
359	Q₈×C₂₃	—	4	4	no	—
360	Q₈×C₂₃	—	4	8	no	—
361	D₄×C₂₃	C₄×Q₈	1	16	yes	complemented
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	2	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	1	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	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	1	no	—
380	C₂×C₄×C₂₃	—	2	1	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	1	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	1	no	—
386	C₂×C₄×C₂₃	—	2	1	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	1	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	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	1	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	1	no	—
401	C₂×C₄×C₂₃	—	2	1	no	—
402	C₂×C₄×C₂₃	—	2	1	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	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	2	2	no	—
409	C₂×C₄×C₂₃	—	2	1	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	1	no	—
412	C₂×C₄×C₂₃	—	4	8	no	—
413	C₂×C₄×C₂₃	—	4	8	no	—
414	C₂×C₄×C₂₃	—	4	8	no	—
415	C₂×C₄×C₂₃	—	4	8	no	—
416	C₂×C₄×C₂₃	—	4	8	no	—
417	C₂×C₄×C₂₃	—	8	4	no	—
418	C₂×C₄×C₂₃	—	8	4	no	—
419	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
420	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
421	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
422	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
423	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
424	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
426	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
427	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
428	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
430	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
431	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
432	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
433	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
434	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
435	C₂×#554	C₂×C₂₃	1	1	yes	characteristic
436	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
437	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
438	#2368	C₂×C₂₃	1	2	yes	complemented
439	#2368	C₂×C₂₃	1	2	yes	complemented
440	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#2360	C₂×C₂₃	1	2	yes	complemented
442	#2355	C₂×C₂₃	1	1	yes	characteristic, complemented
443	#2349	C₂×C₂₃	1	1	yes	characteristic
444	#2349	C₂×C₂₃	1	1	yes	characteristic
445	D₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic
446	#2345	C₂×C₂₃	1	2	yes	complemented
447	#2331	C₂×C₂₃	1	1	yes	characteristic, complemented
448	#2330	C₂×C₂₃	1	1	yes	characteristic, complemented
449	#2329	C₂×C₂₃	1	2	yes	complemented
450	#2329	C₂×C₂₃	1	2	yes	complemented
451	C₄×#125	C₂×C₂₃	1	1	yes	characteristic, complemented
452	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
453	#2295	C₂×C₂₃	1	1	yes	characteristic, complemented
454	C₂×#387	C₂×C₂₃	1	2	yes	complemented
455	#2275	C₂×C₂₃	1	1	yes	characteristic
456	#2275	C₂×C₂₃	1	1	yes	characteristic
457	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic
458	C₂²×C₂₃	—	2	4	no	—
459	C₂²×C₂₃	—	2	4	no	—
460	C₂²×C₂₃	—	2	4	no	—
461	C₂²×C₂₃	—	2	4	no	—
462	C₂²×C₂₃	—	2	4	no	—
463	C₂²×C₂₃	—	2	4	no	—
464	C₂²×C₂₃	C₂×C₄×Q₈	1	8	yes	—
465	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
466	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
467	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
468	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂²×C₂₃	#585	1	1	yes	characteristic
470	C₂²×C₂₃	#585	1	1	yes	characteristic
471	C₂²×C₂₃	#585	1	1	yes	characteristic
472	C₄×C₂₃	—	2	2	no	—
473	C₄×C₂₃	—	2	4	no	—
474	C₄×C₂₃	—	2	2	no	—
475	C₄×C₂₃	—	2	2	no	—
476	C₄×C₂₃	—	2	2	no	—
477	C₄×C₂₃	—	2	2	no	—
478	C₄×C₂₃	—	2	4	no	—
479	C₄×C₂₃	—	2	4	no	—
480	C₄×C₂₃	—	2	2	no	—
481	C₄×C₂₃	—	2	2	no	—
482	C₄×C₂₃	—	2	4	no	—
483	C₄×C₂₃	—	2	2	no	—
484	C₄×C₂₃	—	2	2	no	—
485	C₄×C₂₃	—	4	1	no	—
486	C₄×C₂₃	—	4	2	no	—
487	C₄×C₂₃	—	4	2	no	—
488	C₄×C₂₃	—	4	1	no	—
489	C₄×C₂₃	—	4	1	no	—
490	C₄×C₂₃	—	4	1	no	—
491	C₄×C₂₃	—	4	2	no	—
492	C₄×C₂₃	—	4	1	no	—
493	C₄×C₂₃	C₂×C₄×Q₈	1	4	yes	—
494	#554	C₄×C₂₃	1	16	yes	complemented
495	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
496	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
498	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
499	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
500	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
501	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
502	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
503	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
504	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
505	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
506	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
507	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
510	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
511	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
512	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
513	#391	C₂²×C₂₃	1	1	yes	characteristic
514	#391	C₂²×C₂₃	1	2	yes	—
515	#391	C₂²×C₂₃	1	2	yes	—
516	#391	C₂²×C₂₃	1	2	yes	—
517	#391	C₂²×C₂₃	1	2	yes	—
518	#391	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	2	yes	—
524	#389	C₂²×C₂₃	1	2	yes	—
525	#389	C₂²×C₂₃	1	2	yes	—
526	#389	C₂²×C₂₃	1	1	yes	characteristic
527	#389	C₂²×C₂₃	1	1	yes	characteristic
528	#389	C₂²×C₂₃	1	1	yes	characteristic
529	#389	C₂²×C₂₃	1	1	yes	characteristic
530	#389	C₂²×C₂₃	1	1	yes	characteristic
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	2	yes	—
540	#387	C₂²×C₂₃	1	2	yes	—
541	#387	C₂²×C₂₃	1	1	yes	characteristic
542	#387	C₂²×C₂₃	1	2	yes	—
543	#387	C₂²×C₂₃	1	2	yes	—
544	#387	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	1	yes	characteristic
549	#385	C₂²×C₂₃	1	2	yes	—
550	#385	C₂²×C₂₃	1	2	yes	—
551	#385	C₂²×C₂₃	1	2	yes	—
552	#385	C₂²×C₂₃	1	2	yes	—
553	#385	C₂²×C₂₃	1	2	yes	—
554	#385	C₂²×C₂₃	1	2	yes	—
555	#384	C₂²×C₂₃	1	1	yes	characteristic
556	#382	C₂²×C₂₃	1	1	yes	characteristic
557	#382	C₂²×C₂₃	1	1	yes	characteristic
558	#380	C₂²×C₂₃	1	2	yes	—
559	#380	C₂²×C₂₃	1	2	yes	—
560	#380	C₂²×C₂₃	1	2	yes	—
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	2	yes	—
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	2	yes	—
567	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
575	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
576	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
577	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
578	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
579	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
580	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
581	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
583	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
584	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
585	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
586	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
587	#376	C₂²×C₂₃	1	1	yes	characteristic
588	#376	C₂²×C₂₃	1	1	yes	characteristic
589	C₂×#95	C₂²×C₂₃	1	2	yes	—
590	C₂×#95	C₂²×C₂₃	1	2	yes	—
591	C₂×#95	C₂²×C₂₃	1	2	yes	—
592	C₂×#95	C₂²×C₂₃	1	2	yes	—
593	C₄³	C₂²×C₂₃	1	1	yes	characteristic
594	C₂×C₂₃	—	2	8	no	—
595	C₂×C₂₃	C₂²×C₄×Q₈	1	1	yes	characteristic
596	C₂×C₂₃	#3428	1	1	yes	characteristic
597	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
598	C₂×C₂₃	#3501	1	1	yes	characteristic
599	C₂×C₂₃	#3504	1	1	yes	characteristic
600	C₂×C₂₃	#3513	1	1	yes	characteristic
601	C₂×C₂₃	#3521	1	1	yes	characteristic
602	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
603	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
604	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
605	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
606	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
607	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
608	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
609	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
610	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
611	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
612	C₄⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
613	#125	C₂×C₄×C₂₃	1	8	yes	complemented
614	#125	C₂×C₄×C₂₃	1	8	yes	complemented
615	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
616	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
617	C₂²⋊Q₈	C₂×C₄×C₂₃	1	16	yes	complemented
618	C₄×Q₈	—	4	4	no	—
619	C₄×Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	4	no	—
623	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
624	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
625	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	—
626	C₄×D₄	Q₈×C₂₃	1	8	yes	complemented
627	C₂×C₄⋊C₄	—	4	4	no	—
628	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	16	yes	complemented
629	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
665	C₂×C₄²	—	4	4	no	—
666	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
667	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
668	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
669	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
670	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
671	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
674	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
677	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
679	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
680	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
681	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
682	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
686	#95	C₂³×C₂₃	1	1	yes	characteristic
687	#95	C₂³×C₂₃	1	1	yes	characteristic
688	#95	C₂³×C₂₃	1	1	yes	characteristic
689	#95	C₂³×C₂₃	1	1	yes	characteristic
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	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	#95	C₂³×C₂₃	1	1	yes	characteristic
703	#95	C₂³×C₂₃	1	1	yes	characteristic
704	#95	C₂³×C₂₃	1	1	yes	characteristic
705	#95	C₂³×C₂₃	1	1	yes	characteristic
706	#95	C₂³×C₂₃	1	1	yes	characteristic
707	#95	C₂³×C₂₃	1	1	yes	characteristic
708	#95	C₂³×C₂₃	1	2	yes	—
709	#95	C₂³×C₂₃	1	2	yes	—
710	#95	C₂³×C₂₃	1	2	yes	—
711	#95	C₂³×C₂₃	1	1	yes	characteristic
712	#95	C₂³×C₂₃	1	1	yes	characteristic
713	#95	C₂³×C₂₃	1	1	yes	characteristic
714	#95	C₂³×C₂₃	1	2	yes	—
715	#95	C₂³×C₂₃	1	2	yes	—
716	#95	C₂³×C₂₃	1	2	yes	—
717	#95	C₂³×C₂₃	1	2	yes	—
718	#95	C₂³×C₂₃	1	1	yes	characteristic
719	C₂₃	#34333	1	1	yes	characteristic, direct product factor, Sylow
720	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
721	C₂×Q₈	—	4	2	no	—
722	C₂×Q₈	—	4	1	no	—
723	C₂×Q₈	—	4	1	no	—
724	C₂×Q₈	—	4	2	no	—
725	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
726	C₂×Q₈	C₂²×C₄×C₂₃	1	8	yes	—
727	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
728	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
729	C₂×D₄	#41×C₂₃	1	4	yes	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	4	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	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	C₂²×C₄×C₂₃	1	8	yes	—
748	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
749	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
750	C₂²×C₄	C₂×Q₈×C₂₃	1	8	yes	—
751	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
763	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
764	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
770	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	—	4	2	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	—	4	1	no	—
785	C₄⋊C₄	—	4	1	no	—
786	C₄⋊C₄	—	4	2	no	—
787	C₄⋊C₄	—	4	1	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	1	no	—
790	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
791	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
792	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
793	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
794	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
795	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
796	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
797	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
798	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
799	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
800	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
801	C₄⋊C₄	C₂×Q₈×C₂₃	1	4	yes	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
806	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
807	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
808	C₂²⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	4	no	—
814	C₄²	—	4	2	no	—
815	C₄²	—	4	2	no	—
816	C₄²	—	4	2	no	—
817	C₄²	—	4	2	no	—
818	C₄²	—	4	2	no	—
819	C₄²	—	4	1	no	—
820	C₄²	—	4	1	no	—
821	C₄²	—	4	2	no	—
822	C₄²	—	4	2	no	—
823	C₄²	—	4	2	no	—
824	C₄²	—	4	1	no	—
825	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
826	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
827	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
828	C₄²	C₂×Q₈×C₂₃	1	4	yes	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	2	no	—
832	C₂³	—	2	2	no	—
833	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
834	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
835	C₂³	C₂×#41×C₂₃	1	4	yes	—
836	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
837	Q₈	—	4	4	no	—
838	Q₈	—	4	8	no	—
839	D₄	C₄×Q₈×C₂₃	1	16	yes	complemented
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	2	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	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	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	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	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	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	4	8	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	8	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	4	8	no	—
895	C₂×C₄	—	8	4	no	—
896	C₂×C₄	—	8	4	no	—
897	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
898	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
899	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
900	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
901	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
902	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
903	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
904	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
905	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
906	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
907	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
908	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
909	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
910	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
911	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
912	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
913	C₂²	—	2	4	no	—
914	C₂²	—	2	4	no	—
915	C₂²	—	2	4	no	—
916	C₂²	—	2	4	no	—
917	C₂²	—	2	4	no	—
918	C₂²	—	2	4	no	—
919	C₂²	C₂×C₄×Q₈×C₂₃	1	8	yes	—
920	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
921	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
922	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
923	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
924	C₂²	C₂₃×#585	1	1	yes	characteristic
925	C₂²	C₂₃×#585	1	1	yes	characteristic
926	C₂²	C₂₃×#585	1	1	yes	characteristic
927	C₄	—	2	2	no	—
928	C₄	—	2	4	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	4	no	—
934	C₄	—	2	4	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	—	4	1	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	C₂×C₄×Q₈×C₂₃	1	4	yes	—
949	C₂	—	2	8	no	—
950	C₂	C₂²×C₄×Q₈×C₂₃	1	1	yes	characteristic
951	C₂	C₂₃×#3428	1	1	yes	characteristic
952	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
953	C₂	C₂₃×#3501	1	1	yes	characteristic
954	C₂	C₂₃×#3504	1	1	yes	characteristic
955	C₂	C₂₃×#3513	1	1	yes	characteristic
956	C₂	C₂₃×#3521	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×#2370	C₂	semidirect
3. C₂₃×#2370	C₂	semidirect
4. C₂₃×#2368	C₂	semidirect
5. C₂₃×#2368	C₂	semidirect
6. C₂₃×#2365	C₂	semidirect
7. C₂₃×#2360	C₂	semidirect
8. C₂₃×#2355	C₂	semidirect
12. C₂₃×#2345	C₂	semidirect
13. C₂₃×#2331	C₂	semidirect
14. C₂₃×#2330	C₂	semidirect
15. C₂₃×#2329	C₂	semidirect
16. C₂₃×#2329	C₂	semidirect
17. C₄×C₂₃×#125	C₂	semidirect
18. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
19. C₂₃×#2295	C₂	semidirect
20. C₂×C₂₃×#387	C₂	semidirect
24. C₂₃×#554	C₄	semidirect
134. C₂₃×C₄⋊Q₈	C₂×C₄	semidirect
135. C₂₃×#125	C₂×C₄	semidirect
136. C₂₃×#125	C₂×C₄	semidirect
137. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
138. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
139. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
141. C₄×Q₈×C₂₃	C₂×C₄	semidirect
148. C₄×D₄×C₂₃	Q₈	semidirect
150. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
350. #34333	C₂₃	direct (N × H)
361. D₄×C₂₃	C₄×Q₈	semidirect
436. #2370	C₂×C₂₃	semidirect
437. #2370	C₂×C₂₃	semidirect
438. #2368	C₂×C₂₃	semidirect
439. #2368	C₂×C₂₃	semidirect
440. #2365	C₂×C₂₃	semidirect
441. #2360	C₂×C₂₃	semidirect
442. #2355	C₂×C₂₃	semidirect
446. #2345	C₂×C₂₃	semidirect
447. #2331	C₂×C₂₃	semidirect
448. #2330	C₂×C₂₃	semidirect
449. #2329	C₂×C₂₃	semidirect
450. #2329	C₂×C₂₃	semidirect
451. C₄×#125	C₂×C₂₃	semidirect
452. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
453. #2295	C₂×C₂₃	semidirect
454. C₂×#387	C₂×C₂₃	semidirect
494. #554	C₄×C₂₃	semidirect
612. C₄⋊Q₈	C₂×C₄×C₂₃	semidirect
613. #125	C₂×C₄×C₂₃	semidirect
614. #125	C₂×C₄×C₂₃	semidirect
615. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
616. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
617. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
619. C₄×Q₈	C₂×C₄×C₂₃	semidirect
626. C₄×D₄	Q₈×C₂₃	semidirect
628. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
719. C₂₃	#34333	direct (N × H)
839. D₄	C₄×Q₈×C₂₃	semidirect

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×#2370	2
C₂₃×#2368	2
C₂₃×#2365	2
C₂₃×#2360	2
C₂₃×#2355	2
C₂₃×#2349	2
D₄×C₄⋊C₄×C₂₃	2
C₂₃×#2345	2
C₂₃×#2331	2
C₂₃×#2330	2
C₂₃×#2329	2
C₄×C₂₃×#125	2
C₄×C₂₃×C₂²⋊Q₈	2
C₂₃×#2295	2
C₂×C₂₃×#387	2
C₂₃×#2275	2
C₄²×D₄×C₂₃	2
#34333	23

Subgroups — C23×#34333 #19181959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34333 #19181959