Subgroups — C₂×C₂₃×#2395 #19182168

Order 5888.

3182 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2395	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#397	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#394	C₂	1	2	yes	maximal
10	C₂×C₄×C₄⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₂₃	—	2	8	no	—
17	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	—
18	C₂×C₂₃×#117	—	2	8	no	—
19	C₂×C₂₃×#117	C₂²	1	8	yes	complemented
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#400	C₂²	1	8	yes	complemented
35	C₂₃×#399	C₂²	1	8	yes	complemented
36	C₂₃×#398	C₂²	1	8	yes	complemented
37	C₂₃×#397	C₂²	1	8	yes	complemented
38	C₂₃×#397	C₂²	1	16	yes	complemented
39	C₂₃×#394	C₂²	1	16	yes	—
40	C₄×C₄⋊C₄×C₂₃	C₂²	1	16	yes	complemented
41	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
42	C₄×C₂²⋊C₄×C₂₃	C₂²	1	16	yes	complemented
43	C₂×C₂₃×#95	C₂²	1	2	yes	—
44	C₂×C₂₃×#95	C₂²	1	2	yes	—
45	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#95	C₂²	1	2	yes	—
48	C₂×C₂₃×#95	C₂²	1	2	yes	—
49	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
50	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₂₃	—	2	4	no	—
52	C₂²×D₄×C₂₃	—	2	4	no	—
53	C₂²×D₄×C₂₃	—	2	4	no	—
54	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₂₃	—	2	8	no	—
56	C₂³×C₄×C₂₃	—	2	4	no	—
57	C₂³×C₄×C₂₃	—	2	8	no	—
58	C₂³×C₄×C₂₃	D₄	1	8	yes	—
59	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
61	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₂₃	—	2	32	no	—
71	C₂₃×#117	—	2	32	no	—
72	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
73	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
74	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
75	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
76	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
77	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
83	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
85	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
88	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
90	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₂₃	—	2	8	no	—
95	C₂×C₄²×C₂₃	—	2	4	no	—
96	C₂×C₄²×C₂₃	—	2	8	no	—
97	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
98	C₂×C₄²×C₂₃	C₂³	1	8	yes	—
99	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
100	C₂₃×#95	C₂³	1	8	yes	—
101	C₂₃×#95	C₂³	1	8	yes	—
102	C₂₃×#95	C₂³	1	4	yes	—
103	C₂₃×#95	C₂³	1	4	yes	—
104	C₂₃×#95	C₂³	1	8	yes	—
105	C₂₃×#95	C₂³	1	8	yes	—
106	C₂⁴×C₂₃	—	2	2	no	—
107	C₂⁴×C₂₃	—	2	4	no	—
108	C₂⁴×C₂₃	—	2	4	no	—
109	C₂⁴×C₂₃	—	2	4	no	—
110	C₂⁴×C₂₃	—	2	4	no	—
111	C₂⁴×C₂₃	—	2	2	no	—
112	C₂⁴×C₂₃	—	2	2	no	—
113	C₂⁴×C₂₃	—	2	2	no	—
114	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
115	C₂⁴×C₂₃	#41	1	4	yes	—
116	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
117	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
118	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
119	C₂×D₄×C₂₃	—	2	32	no	—
120	C₂×D₄×C₂₃	—	2	8	no	—
121	C₂×D₄×C₂₃	—	2	8	no	—
122	C₂×D₄×C₂₃	—	2	8	no	—
123	C₂²×C₄×C₂₃	—	2	2	no	—
124	C₂²×C₄×C₂₃	—	2	4	no	—
125	C₂²×C₄×C₂₃	—	2	4	no	—
126	C₂²×C₄×C₂₃	—	2	4	no	—
127	C₂²×C₄×C₂₃	—	2	2	no	—
128	C₂²×C₄×C₂₃	—	2	32	no	—
129	C₂²×C₄×C₂₃	—	2	16	no	—
130	C₂²×C₄×C₂₃	—	2	2	no	—
131	C₂²×C₄×C₂₃	—	2	4	no	—
132	C₂²×C₄×C₂₃	—	2	4	no	—
133	C₂²×C₄×C₂₃	—	2	2	no	—
134	C₂²×C₄×C₂₃	—	2	4	no	—
135	C₂²×C₄×C₂₃	—	2	4	no	—
136	C₂²×C₄×C₂₃	—	2	4	no	—
137	C₂²×C₄×C₂₃	—	2	4	no	—
138	C₂²×C₄×C₂₃	—	2	4	no	—
139	C₂²×C₄×C₂₃	—	2	4	no	—
140	C₂²×C₄×C₂₃	—	2	4	no	—
141	C₂²×C₄×C₂₃	—	2	4	no	—
142	C₂²×C₄×C₂₃	—	2	4	no	—
143	C₂²×C₄×C₂₃	—	2	8	no	—
144	C₂²×C₄×C₂₃	—	2	16	no	—
145	C₂²×C₄×C₂₃	—	4	16	no	—
146	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₂₃	C₂×D₄	1	16	yes	—
148	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₂₃	#41	1	8	yes	—
150	C₂²×C₄×C₂₃	#41	1	4	yes	—
151	C₂²×C₄×C₂₃	#41	1	8	yes	—
152	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
161	C₄⋊C₄×C₂₃	—	2	8	no	—
162	C₄⋊C₄×C₂₃	—	2	8	no	—
163	C₄⋊C₄×C₂₃	—	2	8	no	—
164	C₄⋊C₄×C₂₃	—	2	16	no	—
165	C₄⋊C₄×C₂₃	—	2	16	no	—
166	C₂²⋊C₄×C₂₃	—	2	16	no	—
167	C₂²⋊C₄×C₂₃	—	2	8	no	—
168	C₂²⋊C₄×C₂₃	—	2	16	no	—
169	C₂²⋊C₄×C₂₃	—	2	8	no	—
170	C₂²⋊C₄×C₂₃	—	2	16	no	—
171	C₂²⋊C₄×C₂₃	—	2	16	no	—
172	C₄²×C₂₃	—	2	16	no	—
173	C₄²×C₂₃	—	2	8	no	—
174	C₄²×C₂₃	—	2	16	no	—
175	C₂×#2395	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₂₃	—	2	8	no	—
177	C₂³×C₂₃	—	2	8	no	—
178	C₂³×C₂₃	—	2	8	no	—
179	C₂³×C₂₃	—	2	16	no	—
180	C₂³×C₂₃	—	2	8	no	—
181	C₂³×C₂₃	—	2	2	no	—
182	C₂³×C₂₃	—	2	4	no	—
183	C₂³×C₂₃	—	2	4	no	—
184	C₂³×C₂₃	—	2	4	no	—
185	C₂³×C₂₃	—	2	4	no	—
186	C₂³×C₂₃	—	2	2	no	—
187	C₂³×C₂₃	—	2	2	no	—
188	C₂³×C₂₃	—	2	2	no	—
189	C₂³×C₂₃	—	4	4	no	—
190	C₂³×C₂₃	—	4	8	no	—
191	C₂³×C₂₃	—	4	8	no	—
192	C₂³×C₂₃	—	4	8	no	—
193	C₂³×C₂₃	—	4	4	no	—
194	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
195	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
196	C₂³×C₂₃	C₂×#41	1	4	yes	—
197	C₂³×C₂₃	C₂×#41	1	4	yes	—
198	C₂³×C₂₃	C₂×#41	1	2	yes	—
199	C₂³×C₂₃	C₂×#41	1	2	yes	—
200	C₂³×C₂₃	C₂×#41	1	4	yes	—
201	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
202	D₄×C₂₃	—	2	32	no	—
203	C₂×C₄×C₂₃	—	2	8	no	—
204	C₂×C₄×C₂₃	—	2	8	no	—
205	C₂×C₄×C₂₃	—	2	16	no	—
206	C₂×C₄×C₂₃	—	2	2	no	—
207	C₂×C₄×C₂₃	—	2	4	no	—
208	C₂×C₄×C₂₃	—	2	4	no	—
209	C₂×C₄×C₂₃	—	2	4	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	2	32	no	—
212	C₂×C₄×C₂₃	—	2	2	no	—
213	C₂×C₄×C₂₃	—	2	4	no	—
214	C₂×C₄×C₂₃	—	2	4	no	—
215	C₂×C₄×C₂₃	—	2	2	no	—
216	C₂×C₄×C₂₃	—	2	4	no	—
217	C₂×C₄×C₂₃	—	2	4	no	—
218	C₂×C₄×C₂₃	—	2	4	no	—
219	C₂×C₄×C₂₃	—	2	4	no	—
220	C₂×C₄×C₂₃	—	2	4	no	—
221	C₂×C₄×C₂₃	—	2	4	no	—
222	C₂×C₄×C₂₃	—	2	4	no	—
223	C₂×C₄×C₂₃	—	2	4	no	—
224	C₂×C₄×C₂₃	—	2	4	no	—
225	C₂×C₄×C₂₃	—	4	4	no	—
226	C₂×C₄×C₂₃	—	4	8	no	—
227	C₂×C₄×C₂₃	—	4	8	no	—
228	C₂×C₄×C₂₃	—	4	4	no	—
229	C₂×C₄×C₂₃	—	4	8	no	—
230	C₂×C₄×C₂₃	—	4	16	no	—
231	C₂×C₄×C₂₃	#123	1	16	yes	—
232	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
235	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
236	C₂×C₄×C₂₃	C₂×#41	1	8	yes	—
237	C₂²×C₄×D₄	C₂×C₂₃	1	1	yes	characteristic
238	C₂²×#117	C₂×C₂₃	1	1	yes	characteristic, complemented
239	#2395	C₂×C₂₃	1	16	yes	direct product factor
240	C₂×#400	C₂×C₂₃	1	1	yes	characteristic, complemented
241	C₂×#399	C₂×C₂₃	1	1	yes	characteristic, complemented
242	C₂×#398	C₂×C₂₃	1	1	yes	characteristic, complemented
243	C₂×#397	C₂×C₂₃	1	2	yes	complemented
244	C₂×#397	C₂×C₂₃	1	1	yes	characteristic, complemented
245	C₂×#394	C₂×C₂₃	1	2	yes	—
246	C₂×C₄×C₄⋊C₄	C₂×C₂₃	1	2	yes	complemented
247	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
248	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	2	yes	complemented
249	C₂²×C₂₃	—	2	4	no	—
250	C₂²×C₂₃	—	2	4	no	—
251	C₂²×C₂₃	—	2	4	no	—
252	C₂²×C₂₃	—	2	8	no	—
253	C₂²×C₂₃	—	2	4	no	—
254	C₂²×C₂₃	—	4	16	no	—
255	C₂²×C₂₃	—	4	16	no	—
256	C₂²×C₂₃	—	4	2	no	—
257	C₂²×C₂₃	—	4	4	no	—
258	C₂²×C₂₃	—	4	4	no	—
259	C₂²×C₂₃	—	4	4	no	—
260	C₂²×C₂₃	—	4	2	no	—
261	C₂²×C₂₃	C₂×#123	1	4	yes	—
262	C₂²×C₂₃	#525	1	4	yes	—
263	C₂²×C₂₃	#529	1	8	yes	—
264	C₂²×C₂₃	#529	1	8	yes	—
265	C₂²×C₂₃	#532	1	4	yes	—
266	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
267	C₂²×C₂₃	C₂²×#41	1	2	yes	—
268	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
269	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₂₃	C₂²×#41	1	2	yes	—
271	C₄×C₂₃	—	2	4	no	—
272	C₄×C₂₃	—	2	4	no	—
273	C₄×C₂₃	—	2	8	no	—
274	C₄×C₂₃	—	4	2	no	—
275	C₄×C₂₃	—	4	4	no	—
276	C₄×C₂₃	—	4	4	no	—
277	C₄×C₂₃	—	4	2	no	—
278	C₄×C₂₃	—	4	4	no	—
279	C₄×C₂₃	C₂×#123	1	8	yes	—
280	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
281	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
282	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
283	C₂×C₄×D₄	—	2	8	no	—
284	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	—
285	C₂×#117	—	2	8	no	—
286	C₂×#117	C₂²×C₂₃	1	8	yes	complemented
287	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
288	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
289	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
290	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
292	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
293	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
295	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
296	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
299	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
300	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
301	#400	C₂²×C₂₃	1	8	yes	complemented
302	#399	C₂²×C₂₃	1	8	yes	complemented
303	#398	C₂²×C₂₃	1	8	yes	complemented
304	#397	C₂²×C₂₃	1	16	yes	complemented
305	#397	C₂²×C₂₃	1	8	yes	complemented
306	#394	C₂²×C₂₃	1	16	yes	—
307	C₄×C₄⋊C₄	C₂²×C₂₃	1	16	yes	complemented
308	C₄×C₂²⋊C₄	C₂²×C₂₃	1	16	yes	complemented
309	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
310	C₂×#95	C₂²×C₂₃	1	2	yes	—
311	C₂×#95	C₂²×C₂₃	1	2	yes	—
312	C₂×#95	C₂²×C₂₃	1	2	yes	—
313	C₂×#95	C₂²×C₂₃	1	2	yes	—
314	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
315	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
316	C₂×C₂₃	—	4	4	no	—
317	C₂×C₂₃	—	4	4	no	—
318	C₂×C₂₃	#2395	1	8	yes	direct product factor
319	C₂×C₂₃	C₂²×#123	1	1	yes	characteristic
320	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
321	C₂×C₂₃	C₂×#529	1	2	yes	—
322	C₂×C₂₃	C₂×#529	1	2	yes	—
323	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
324	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
325	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
326	C₂²×D₄	—	2	4	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
330	C₂³×C₄	—	2	8	no	—
331	C₂³×C₄	—	2	4	no	—
332	C₂³×C₄	—	2	8	no	—
333	C₂³×C₄	D₄×C₂₃	1	8	yes	—
334	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
336	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
337	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
340	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
342	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
345	C₄×D₄	—	2	32	no	—
346	#117	—	2	32	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	8	no	—
351	C₂×C₄⋊C₄	—	2	8	no	—
352	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
354	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
356	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
357	C₂×C₂²⋊C₄	—	2	8	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₂²⋊C₄	—	2	8	no	—
360	C₂×C₂²⋊C₄	—	2	4	no	—
361	C₂×C₂²⋊C₄	—	2	8	no	—
362	C₂×C₂²⋊C₄	—	2	8	no	—
363	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
369	C₂×C₄²	—	2	8	no	—
370	C₂×C₄²	—	2	4	no	—
371	C₂×C₄²	—	2	8	no	—
372	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
373	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
374	C₂×C₄²	C₂³×C₂₃	1	8	yes	—
375	#95	C₂³×C₂₃	1	8	yes	—
376	#95	C₂³×C₂₃	1	4	yes	—
377	#95	C₂³×C₂₃	1	8	yes	—
378	#95	C₂³×C₂₃	1	4	yes	—
379	#95	C₂³×C₂₃	1	8	yes	—
380	#95	C₂³×C₂₃	1	8	yes	—
381	C₂₃	C₂×#2395	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	2	2	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	4	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
391	C₂⁴	#41×C₂₃	1	4	yes	—
392	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
393	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
394	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
395	C₂×D₄	—	2	32	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	8	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	32	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	8	no	—
420	C₂²×C₄	—	2	16	no	—
421	C₂²×C₄	—	4	16	no	—
422	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₂₃	1	16	yes	—
424	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
425	C₂²×C₄	#41×C₂₃	1	8	yes	—
426	C₂²×C₄	#41×C₂₃	1	4	yes	—
427	C₂²×C₄	#41×C₂₃	1	8	yes	—
428	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	16	no	—
441	C₄⋊C₄	—	2	16	no	—
442	C₂²⋊C₄	—	2	16	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	2	16	no	—
448	C₄²	—	2	16	no	—
449	C₄²	—	2	8	no	—
450	C₄²	—	2	16	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	8	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	2	16	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	4	4	no	—
465	C₂³	—	4	8	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	8	no	—
468	C₂³	—	4	4	no	—
469	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
470	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
471	C₂³	C₂×#41×C₂₃	1	4	yes	—
472	C₂³	C₂×#41×C₂₃	1	4	yes	—
473	C₂³	C₂×#41×C₂₃	1	2	yes	—
474	C₂³	C₂×#41×C₂₃	1	2	yes	—
475	C₂³	C₂×#41×C₂₃	1	4	yes	—
476	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
477	D₄	—	2	32	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	16	no	—
486	C₂×C₄	—	2	32	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	8	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	16	no	—
506	C₂×C₄	C₂₃×#123	1	16	yes	—
507	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
508	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
509	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
510	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
511	C₂×C₄	C₂×#41×C₂₃	1	8	yes	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	8	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	16	no	—
523	C₂²	—	4	16	no	—
524	C₂²	C₂×C₂₃×#123	1	4	yes	—
525	C₂²	C₂₃×#525	1	4	yes	—
526	C₂²	C₂₃×#529	1	8	yes	—
527	C₂²	C₂₃×#529	1	8	yes	—
528	C₂²	C₂₃×#532	1	4	yes	—
529	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
530	C₂²	C₂²×#41×C₂₃	1	2	yes	—
531	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
532	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
533	C₂²	C₂²×#41×C₂₃	1	2	yes	—
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	8	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	4	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	4	no	—
542	C₄	C₂×C₂₃×#123	1	8	yes	—
543	C₂	—	4	4	no	—
544	C₂	—	4	4	no	—
545	C₂	C₂₃×#2395	1	8	yes	direct product factor
546	C₂	C₂²×C₂₃×#123	1	1	yes	characteristic
547	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
548	C₂	C₂×C₂₃×#529	1	2	yes	—
549	C₂	C₂×C₂₃×#529	1	2	yes	—
550	C₂	C₂×C₂₃×#532	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₂₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
socle	C₂⁴×C₂₃	C₂⁴
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×C₂₃×#117	C₂	semidirect
3. C₂₃×#2395	C₂	direct (N × H)
4. C₂×C₂₃×#400	C₂	semidirect
5. C₂×C₂₃×#399	C₂	semidirect
6. C₂×C₂₃×#398	C₂	semidirect
7. C₂×C₂₃×#397	C₂	semidirect
8. C₂×C₂₃×#397	C₂	semidirect
10. C₂×C₄×C₄⋊C₄×C₂₃	C₂	semidirect
11. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
12. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
19. C₂×C₂₃×#117	C₂²	semidirect
34. C₂₃×#400	C₂²	semidirect
35. C₂₃×#399	C₂²	semidirect
36. C₂₃×#398	C₂²	semidirect
37. C₂₃×#397	C₂²	semidirect
38. C₂₃×#397	C₂²	semidirect
40. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
41. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
42. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
175. C₂×#2395	C₂₃	direct (N × H)
238. C₂²×#117	C₂×C₂₃	semidirect
239. #2395	C₂×C₂₃	direct (N × H)
240. C₂×#400	C₂×C₂₃	semidirect
241. C₂×#399	C₂×C₂₃	semidirect
242. C₂×#398	C₂×C₂₃	semidirect
243. C₂×#397	C₂×C₂₃	semidirect
244. C₂×#397	C₂×C₂₃	semidirect
246. C₂×C₄×C₄⋊C₄	C₂×C₂₃	semidirect
247. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
248. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
286. C₂×#117	C₂²×C₂₃	semidirect
301. #400	C₂²×C₂₃	semidirect
302. #399	C₂²×C₂₃	semidirect
303. #398	C₂²×C₂₃	semidirect
304. #397	C₂²×C₂₃	semidirect
305. #397	C₂²×C₂₃	semidirect
307. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
308. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
309. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
318. C₂×C₂₃	#2395	direct (N × H)
381. C₂₃	C₂×#2395	direct (N × H)
545. C₂	C₂₃×#2395	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×D₄×C₂₃	2
C₂²×C₂₃×#117	2
C₂₃×#2395	2
C₂×C₂₃×#400	2
C₂×C₂₃×#399	2
C₂×C₂₃×#398	2
C₂×C₂₃×#397	2
C₂×C₂₃×#394	2
C₂×C₄×C₄⋊C₄×C₂₃	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2395	23

Subgroups — C2×C23×#2395 #19182168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2395 #19182168