Subgroups — C₂₃×#36561 #19184187

Order 5888.

2384 conjugacy classes of subgroups.

The subgroup lattice has 754 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	2	yes	maximal, complemented
2	C₂₃×#2857	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2564	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2556	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2551	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2506	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2492	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2452	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2417	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2365	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2360	C₂	1	2	yes	maximal, complemented
14	D₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic
16	C₄×C₂₃×#121	C₂	1	2	yes	maximal
17	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#554	—	2	16	no	—
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₂₃×#125	C₂²	1	4	yes	—
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	—
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
39	C₂₃×#400	C₂²	1	4	yes	—
40	C₂₃×#399	C₂²	1	4	yes	—
41	C₂₃×#398	C₂²	1	4	yes	—
42	C₂₃×#396	C₂²	1	4	yes	—
43	C₂₃×#395	C₂²	1	4	yes	—
44	C₂₃×#393	C₂²	1	4	yes	—
45	C₂₃×#391	C₂²	1	2	yes	—
46	C₂₃×#391	C₂²	1	4	yes	—
47	C₂₃×#391	C₂²	1	2	yes	—
48	C₂₃×#390	C₂²	1	1	yes	characteristic
49	C₂₃×#390	C₂²	1	2	yes	—
50	C₂₃×#389	C₂²	1	2	yes	—
51	C₂₃×#389	C₂²	1	2	yes	—
52	C₂₃×#389	C₂²	1	2	yes	—
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	4	yes	—
58	C₂₃×#388	C₂²	1	4	yes	—
59	C₂₃×#388	C₂²	1	2	yes	—
60	C₂₃×#387	C₂²	1	4	yes	—
61	C₂₃×#387	C₂²	1	4	yes	—
62	C₂₃×#386	C₂²	1	4	yes	—
63	C₂₃×#386	C₂²	1	2	yes	—
64	C₂₃×#385	C₂²	1	4	yes	—
65	C₂₃×#385	C₂²	1	4	yes	—
66	C₂₃×#384	C₂²	1	2	yes	—
67	C₂₃×#384	C₂²	1	1	yes	characteristic
68	C₂₃×#380	C₂²	1	2	yes	—
69	C₂₃×#380	C₂²	1	4	yes	—
70	C₂₃×#380	C₂²	1	2	yes	—
71	C₂₃×#380	C₂²	1	1	yes	characteristic
72	C₂₃×#380	C₂²	1	2	yes	—
73	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
75	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
76	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
77	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
79	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
81	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
82	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
83	C₂×C₂₃×#95	C₂²	1	2	yes	—
84	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
85	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
86	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
87	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
94	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
95	C₂₃×C₄⋊Q₈	—	2	8	no	—
96	C₂₃×C₄⋊Q₈	—	2	4	no	—
97	C₂₃×C₄⋊Q₈	—	4	4	no	—
98	C₂₃×#125	—	2	16	no	—
99	C₂₃×C₂²⋊Q₈	—	2	16	no	—
100	C₂₃×C₂²⋊Q₈	—	2	8	no	—
101	C₂₃×C₂²⋊Q₈	—	2	16	no	—
102	C₂₃×C₂²⋊Q₈	—	2	8	no	—
103	C₂₃×C₂²⋊Q₈	—	2	8	no	—
104	C₂₃×#121	Q₈	1	8	yes	complemented
105	C₄×Q₈×C₂₃	—	2	8	no	—
106	C₄×D₄×C₂₃	—	2	16	no	—
107	C₄×D₄×C₂₃	—	2	8	no	—
108	C₄×D₄×C₂₃	—	2	4	no	—
109	C₄×D₄×C₂₃	—	4	4	no	—
110	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
111	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
112	C₂×C₄⋊C₄×C₂₃	D₄	1	8	yes	complemented
113	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
144	C₂×C₄²×C₂₃	—	2	4	no	—
145	C₂×C₄²×C₂₃	—	4	4	no	—
146	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
148	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
149	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
151	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
155	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
156	C₂₃×#95	C₂³	1	2	yes	—
157	C₂₃×#95	C₂³	1	2	yes	—
158	C₂₃×#95	C₂³	1	2	yes	—
159	C₂₃×#95	C₂³	1	2	yes	—
160	C₂₃×#95	C₂³	1	4	yes	—
161	C₂₃×#95	C₂³	1	2	yes	—
162	C₂₃×#95	C₂³	1	2	yes	—
163	C₂₃×#95	C₂³	1	4	yes	—
164	C₂₃×#95	C₂³	1	2	yes	—
165	C₂₃×#95	C₂³	1	4	yes	—
166	C₂₃×#95	C₂³	1	4	yes	—
167	C₂₃×#95	C₂³	1	4	yes	—
168	C₂₃×#95	C₂³	1	4	yes	—
169	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
170	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₂₃	—	2	4	no	—
172	C₂×Q₈×C₂₃	—	2	8	no	—
173	C₂×Q₈×C₂₃	—	2	4	no	—
174	C₂×Q₈×C₂₃	—	2	4	no	—
175	C₂×Q₈×C₂₃	—	4	4	no	—
176	C₂×Q₈×C₂₃	—	4	4	no	—
177	C₂×D₄×C₂₃	—	2	4	no	—
178	C₂×D₄×C₂₃	—	2	4	no	—
179	C₂×D₄×C₂₃	—	2	2	no	—
180	C₂×D₄×C₂₃	—	2	2	no	—
181	C₂×D₄×C₂₃	C₂×Q₈	1	8	yes	—
182	C₂×D₄×C₂₃	C₂×Q₈	1	4	yes	—
183	C₂²×C₄×C₂₃	—	2	2	no	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	2	no	—
186	C₂²×C₄×C₂₃	—	2	2	no	—
187	C₂²×C₄×C₂₃	—	2	2	no	—
188	C₂²×C₄×C₂₃	—	2	4	no	—
189	C₂²×C₄×C₂₃	—	2	4	no	—
190	C₂²×C₄×C₂₃	—	2	2	no	—
191	C₂²×C₄×C₂₃	—	2	4	no	—
192	C₂²×C₄×C₂₃	—	2	4	no	—
193	C₂²×C₄×C₂₃	—	2	4	no	—
194	C₂²×C₄×C₂₃	—	2	8	no	—
195	C₂²×C₄×C₂₃	—	4	2	no	—
196	C₂²×C₄×C₂₃	—	4	2	no	—
197	C₂²×C₄×C₂₃	—	4	1	no	—
198	C₂²×C₄×C₂₃	—	4	2	no	—
199	C₂²×C₄×C₂₃	—	4	4	no	—
200	C₂²×C₄×C₂₃	—	4	4	no	—
201	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
202	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
203	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
204	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
206	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₄⋊C₄×C₂₃	—	2	8	no	—
220	C₄⋊C₄×C₂₃	—	2	4	no	—
221	C₄⋊C₄×C₂₃	—	2	4	no	—
222	C₄⋊C₄×C₂₃	—	2	8	no	—
223	C₄⋊C₄×C₂₃	—	2	8	no	—
224	C₄⋊C₄×C₂₃	—	2	8	no	—
225	C₄⋊C₄×C₂₃	—	2	8	no	—
226	C₄⋊C₄×C₂₃	—	2	4	no	—
227	C₄⋊C₄×C₂₃	—	2	2	no	—
228	C₄⋊C₄×C₂₃	—	2	2	no	—
229	C₄⋊C₄×C₂₃	—	2	8	no	—
230	C₄⋊C₄×C₂₃	—	2	4	no	—
231	C₄⋊C₄×C₂₃	—	2	4	no	—
232	C₄⋊C₄×C₂₃	—	2	4	no	—
233	C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₄⋊C₄×C₂₃	—	4	2	no	—
235	C₄⋊C₄×C₂₃	—	4	4	no	—
236	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
237	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
238	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
239	C₄⋊C₄×C₂₃	C₂×Q₈	1	4	yes	—
240	C₄⋊C₄×C₂₃	#41	1	4	yes	—
241	C₂²⋊C₄×C₂₃	—	2	8	no	—
242	C₂²⋊C₄×C₂₃	—	2	4	no	—
243	C₂²⋊C₄×C₂₃	—	2	8	no	—
244	C₂²⋊C₄×C₂₃	—	2	4	no	—
245	C₂²⋊C₄×C₂₃	—	2	4	no	—
246	C₂²⋊C₄×C₂₃	—	2	8	no	—
247	C₂²⋊C₄×C₂₃	—	4	2	no	—
248	C₂²⋊C₄×C₂₃	—	4	4	no	—
249	C₂²⋊C₄×C₂₃	C₂×Q₈	1	8	yes	—
250	C₄²×C₂₃	—	2	8	no	—
251	C₄²×C₂₃	—	2	4	no	—
252	C₄²×C₂₃	—	2	2	no	—
253	C₄²×C₂₃	—	2	2	no	—
254	C₄²×C₂₃	—	2	2	no	—
255	C₄²×C₂₃	—	2	4	no	—
256	C₄²×C₂₃	—	2	4	no	—
257	C₄²×C₂₃	—	4	2	no	—
258	C₄²×C₂₃	—	4	2	no	—
259	C₄²×C₂₃	#41	1	4	yes	—
260	#36561	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	1	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	2	no	—
270	C₂³×C₂₃	—	2	2	no	—
271	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
272	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
273	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
274	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
275	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
276	Q₈×C₂₃	—	4	8	no	—
277	Q₈×C₂₃	—	8	8	no	—
278	D₄×C₂₃	—	2	16	no	—
279	D₄×C₂₃	—	2	8	no	—
280	C₂×C₄×C₂₃	—	2	2	no	—
281	C₂×C₄×C₂₃	—	2	1	no	—
282	C₂×C₄×C₂₃	—	2	1	no	—
283	C₂×C₄×C₂₃	—	2	1	no	—
284	C₂×C₄×C₂₃	—	2	2	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	8	no	—
295	C₂×C₄×C₂₃	—	2	8	no	—
296	C₂×C₄×C₂₃	—	2	4	no	—
297	C₂×C₄×C₂₃	—	2	2	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	4	no	—
300	C₂×C₄×C₂₃	—	2	1	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	4	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	4	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	4	no	—
314	C₂×C₄×C₂₃	—	4	8	no	—
315	C₂×C₄×C₂₃	—	4	4	no	—
316	C₂×C₄×C₂₃	—	4	8	no	—
317	C₂×C₄×C₂₃	—	4	8	no	—
318	C₂×C₄×C₂₃	—	8	8	no	—
319	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
320	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
324	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
325	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
326	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
327	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
328	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
329	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
330	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
331	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
332	C₂×#554	C₂×C₂₃	1	2	yes	complemented
333	#2857	C₂×C₂₃	1	2	yes	complemented
334	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
335	#2564	C₂×C₂₃	1	4	yes	complemented
336	#2556	C₂×C₂₃	1	4	yes	complemented
337	#2551	C₂×C₂₃	1	1	yes	characteristic, complemented
338	#2542	C₂×C₂₃	1	1	yes	characteristic, complemented
339	#2506	C₂×C₂₃	1	2	yes	complemented
340	#2492	C₂×C₂₃	1	2	yes	complemented
341	#2452	C₂×C₂₃	1	2	yes	complemented
342	#2417	C₂×C₂₃	1	2	yes	complemented
343	#2365	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2360	C₂×C₂₃	1	2	yes	complemented
345	D₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₄×#121	C₂×C₂₃	1	2	yes	—
347	C₄×#121	C₂×C₂₃	1	1	yes	characteristic
348	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂²×C₂₃	—	2	2	no	—
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	2	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	2	2	no	—
355	C₂²×C₂₃	—	2	4	no	—
356	C₂²×C₂₃	—	2	4	no	—
357	C₂²×C₂₃	—	2	4	no	—
358	C₂²×C₂₃	—	4	2	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	D₄×Q₈	1	4	yes	—
363	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
364	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
365	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
366	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
367	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
369	C₂²×C₂₃	#585	1	1	yes	characteristic
370	C₄×C₂₃	—	2	2	no	—
371	C₄×C₂₃	—	2	4	no	—
372	C₄×C₂₃	—	2	2	no	—
373	C₄×C₂₃	—	2	2	no	—
374	C₄×C₂₃	—	2	4	no	—
375	C₄×C₂₃	—	2	4	no	—
376	C₄×C₂₃	—	2	4	no	—
377	C₄×C₂₃	—	4	2	no	—
378	C₄×C₂₃	—	4	4	no	—
379	C₄×C₂₃	—	4	1	no	—
380	C₄×C₂₃	—	4	4	no	—
381	C₄×C₂₃	—	4	2	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	#532	1	4	yes	—
384	C₄×C₂₃	#554	1	4	yes	complemented
385	#554	—	2	16	no	—
386	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
388	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
389	C₂×#125	C₂²×C₂₃	1	4	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
393	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
394	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
395	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
397	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
398	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
400	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
401	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
402	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
404	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
405	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
406	#400	C₂²×C₂₃	1	4	yes	—
407	#399	C₂²×C₂₃	1	4	yes	—
408	#398	C₂²×C₂₃	1	4	yes	—
409	#396	C₂²×C₂₃	1	4	yes	—
410	#395	C₂²×C₂₃	1	4	yes	—
411	#393	C₂²×C₂₃	1	4	yes	—
412	#391	C₂²×C₂₃	1	2	yes	—
413	#391	C₂²×C₂₃	1	4	yes	—
414	#391	C₂²×C₂₃	1	2	yes	—
415	#390	C₂²×C₂₃	1	1	yes	characteristic
416	#390	C₂²×C₂₃	1	2	yes	—
417	#389	C₂²×C₂₃	1	2	yes	—
418	#389	C₂²×C₂₃	1	4	yes	—
419	#389	C₂²×C₂₃	1	2	yes	—
420	#389	C₂²×C₂₃	1	2	yes	—
421	#389	C₂²×C₂₃	1	2	yes	—
422	#389	C₂²×C₂₃	1	2	yes	—
423	#389	C₂²×C₂₃	1	1	yes	characteristic
424	#389	C₂²×C₂₃	1	2	yes	—
425	#388	C₂²×C₂₃	1	4	yes	—
426	#388	C₂²×C₂₃	1	2	yes	—
427	#387	C₂²×C₂₃	1	4	yes	—
428	#387	C₂²×C₂₃	1	4	yes	—
429	#386	C₂²×C₂₃	1	2	yes	—
430	#386	C₂²×C₂₃	1	4	yes	—
431	#385	C₂²×C₂₃	1	4	yes	—
432	#385	C₂²×C₂₃	1	4	yes	—
433	#384	C₂²×C₂₃	1	1	yes	characteristic
434	#384	C₂²×C₂₃	1	2	yes	—
435	#380	C₂²×C₂₃	1	2	yes	—
436	#380	C₂²×C₂₃	1	4	yes	—
437	#380	C₂²×C₂₃	1	2	yes	—
438	#380	C₂²×C₂₃	1	1	yes	characteristic
439	#380	C₂²×C₂₃	1	2	yes	—
440	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
442	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
446	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
450	C₂×#95	C₂²×C₂₃	1	2	yes	—
451	C₂×C₂₃	—	2	4	no	—
452	C₂×C₂₃	—	4	4	no	—
453	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
454	C₂×C₂₃	C₂×D₄×Q₈	1	1	yes	characteristic
455	C₂×C₂₃	C₂×#554	1	1	yes	characteristic
456	C₂×C₂₃	Q₈×#41	1	1	yes	characteristic
457	C₂×C₂₃	#3495	1	1	yes	characteristic
458	C₂×C₂₃	#3496	1	1	yes	characteristic
459	C₂×C₂₃	#3520	1	1	yes	characteristic
460	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
461	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
462	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
463	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
465	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
466	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
467	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
470	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
471	C₄⋊Q₈	—	2	8	no	—
472	C₄⋊Q₈	—	2	4	no	—
473	C₄⋊Q₈	—	4	4	no	—
474	#125	—	2	16	no	—
475	C₂²⋊Q₈	—	2	16	no	—
476	C₂²⋊Q₈	—	2	8	no	—
477	C₂²⋊Q₈	—	2	16	no	—
478	C₂²⋊Q₈	—	2	8	no	—
479	C₂²⋊Q₈	—	2	8	no	—
480	#121	Q₈×C₂₃	1	8	yes	complemented
481	C₄×Q₈	—	2	8	no	—
482	C₄×D₄	—	2	16	no	—
483	C₄×D₄	—	2	8	no	—
484	C₄×D₄	—	2	4	no	—
485	C₄×D₄	—	4	4	no	—
486	C₂×C₄⋊C₄	—	2	8	no	—
487	C₂×C₄⋊C₄	—	2	4	no	—
488	C₂×C₄⋊C₄	D₄×C₂₃	1	8	yes	complemented
489	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
496	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
520	C₂×C₄²	—	2	4	no	—
521	C₂×C₄²	—	4	4	no	—
522	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
523	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
524	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
526	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
530	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
531	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
532	#95	C₂³×C₂₃	1	2	yes	—
533	#95	C₂³×C₂₃	1	2	yes	—
534	#95	C₂³×C₂₃	1	2	yes	—
535	#95	C₂³×C₂₃	1	2	yes	—
536	#95	C₂³×C₂₃	1	4	yes	—
537	#95	C₂³×C₂₃	1	2	yes	—
538	#95	C₂³×C₂₃	1	2	yes	—
539	#95	C₂³×C₂₃	1	4	yes	—
540	#95	C₂³×C₂₃	1	2	yes	—
541	#95	C₂³×C₂₃	1	4	yes	—
542	#95	C₂³×C₂₃	1	4	yes	—
543	#95	C₂³×C₂₃	1	4	yes	—
544	#95	C₂³×C₂₃	1	4	yes	—
545	C₂₃	#36561	1	1	yes	characteristic, direct product factor, Sylow
546	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
547	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
548	C₂×Q₈	—	2	4	no	—
549	C₂×Q₈	—	2	8	no	—
550	C₂×Q₈	—	2	4	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	—	4	4	no	—
553	C₂×Q₈	—	4	4	no	—
554	C₂×D₄	—	2	4	no	—
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	C₂×Q₈×C₂₃	1	8	yes	—
559	C₂×D₄	C₂×Q₈×C₂₃	1	4	yes	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	—	2	4	no	—
571	C₂²×C₄	—	2	8	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	1	no	—
575	C₂²×C₄	—	4	2	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	—	4	4	no	—
578	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
579	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
580	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
584	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
587	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
592	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
594	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
596	C₄⋊C₄	—	2	8	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	8	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	2	no	—
606	C₄⋊C₄	—	2	8	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	4	4	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
614	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
615	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
616	C₄⋊C₄	C₂×Q₈×C₂₃	1	4	yes	—
617	C₄⋊C₄	#41×C₂₃	1	4	yes	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	2	no	—
626	C₂²⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
627	C₄²	—	2	8	no	—
628	C₄²	—	2	4	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	2	4	no	—
634	C₄²	—	4	2	no	—
635	C₄²	—	4	2	no	—
636	C₄²	#41×C₂₃	1	4	yes	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
648	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
649	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
650	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
651	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
652	Q₈	—	4	8	no	—
653	Q₈	—	8	8	no	—
654	D₄	—	2	16	no	—
655	D₄	—	2	8	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	8	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	4	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	4	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	4	8	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	8	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	8	8	no	—
695	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
696	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
697	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
698	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
699	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
700	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
701	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
702	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
703	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
704	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
705	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
706	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
707	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	4	no	—
715	C₂²	—	2	4	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	D₄×Q₈×C₂₃	1	4	yes	—
722	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
723	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
724	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
725	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
726	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
727	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
728	C₂²	C₂₃×#585	1	1	yes	characteristic
729	C₄	—	2	2	no	—
730	C₄	—	2	4	no	—
731	C₄	—	2	2	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	4	no	—
734	C₄	—	2	4	no	—
735	C₄	—	2	4	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	4	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	4	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	C₂₃×#532	1	4	yes	—
743	C₄	C₂₃×#554	1	4	yes	complemented
744	C₂	—	2	4	no	—
745	C₂	—	4	4	no	—
746	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
747	C₂	C₂×D₄×Q₈×C₂₃	1	1	yes	characteristic
748	C₂	C₂×C₂₃×#554	1	1	yes	characteristic
749	C₂	Q₈×#41×C₂₃	1	1	yes	characteristic
750	C₂	C₂₃×#3495	1	1	yes	characteristic
751	C₂	C₂₃×#3496	1	1	yes	characteristic
752	C₂	C₂₃×#3520	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. C₂×C₂₃×#554	C₂	semidirect
2. C₂₃×#2857	C₂	semidirect
3. C₂₃×#2857	C₂	semidirect
4. C₂₃×#2564	C₂	semidirect
5. C₂₃×#2556	C₂	semidirect
6. C₂₃×#2551	C₂	semidirect
7. C₂₃×#2542	C₂	semidirect
8. C₂₃×#2506	C₂	semidirect
9. C₂₃×#2492	C₂	semidirect
10. C₂₃×#2452	C₂	semidirect
11. C₂₃×#2417	C₂	semidirect
12. C₂₃×#2365	C₂	semidirect
13. C₂₃×#2360	C₂	semidirect
14. D₄×C₄⋊C₄×C₂₃	C₂	semidirect
17. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
104. C₂₃×#121	Q₈	semidirect
112. C₂×C₄⋊C₄×C₂₃	D₄	semidirect
260. #36561	C₂₃	direct (N × H)
332. C₂×#554	C₂×C₂₃	semidirect
333. #2857	C₂×C₂₃	semidirect
334. #2857	C₂×C₂₃	semidirect
335. #2564	C₂×C₂₃	semidirect
336. #2556	C₂×C₂₃	semidirect
337. #2551	C₂×C₂₃	semidirect
338. #2542	C₂×C₂₃	semidirect
339. #2506	C₂×C₂₃	semidirect
340. #2492	C₂×C₂₃	semidirect
341. #2452	C₂×C₂₃	semidirect
342. #2417	C₂×C₂₃	semidirect
343. #2365	C₂×C₂₃	semidirect
344. #2360	C₂×C₂₃	semidirect
345. D₄×C₄⋊C₄	C₂×C₂₃	semidirect
348. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
384. C₄×C₂₃	#554	semidirect
480. #121	Q₈×C₂₃	semidirect
488. C₂×C₄⋊C₄	D₄×C₂₃	semidirect
545. C₂₃	#36561	direct (N × H)
743. C₄	C₂₃×#554	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×#2857	2
C₂₃×#2564	2
C₂₃×#2556	2
C₂₃×#2551	2
C₂₃×#2542	2
C₂₃×#2506	2
C₂₃×#2492	2
C₂₃×#2452	2
C₂₃×#2417	2
C₂₃×#2365	2
C₂₃×#2360	2
D₄×C₄⋊C₄×C₂₃	2
C₄×C₂₃×#121	2
C₂×C₄×C₄⋊C₄×C₂₃	2
#36561	23

Subgroups — C23×#36561 #19184187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36561 #19184187