Subgroups — C₂×C₅×#4664 #14319873

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×C₃⋊#95	C₂	1	2	yes	maximal, complemented
6	C₅×#4664	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#381	—	3	1	no	maximal, Hall
8	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
12	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₅×D₃	—	2	8	no	—
14	C₂²×C₄×C₅×D₃	C₄	1	8	yes	complemented
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
18	C₃×C₅×#95	C₂²	1	4	yes	complemented
19	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
20	C₅×C₃⋊#95	C₂²	1	8	yes	complemented
21	C₂×#4664	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂⁴×C₄×C₅	—	3	1	no	—
23	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
24	C₅×#381	—	3	8	no	—
25	C₂×C₅×#95	—	3	2	no	—
26	C₂×C₅×#95	—	3	1	no	—
27	C₂×C₅×#95	D₃	1	1	yes	characteristic, complemented
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₂³×C₅×D₃	—	2	4	no	—
30	C₂³×C₅×D₃	—	2	2	no	—
31	C₂³×C₅×D₃	—	2	2	no	—
32	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
33	C₂³×C₅×D₃	D₄	1	8	yes	—
34	C₂³×C₅×D₃	C₂³	1	2	yes	—
35	C₂²×C₃×C₄×C₅	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	4	no	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₅×Dic₃	—	2	4	no	—
43	C₂²×C₅×Dic₃	—	2	4	no	—
44	C₂²×C₅×Dic₃	—	2	4	no	—
45	C₂²×C₅×Dic₃	—	2	4	no	—
46	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
47	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
48	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
49	C₂×C₄×C₅×D₃	—	2	32	no	—
50	C₂×C₄×C₅×D₃	—	2	16	no	—
51	C₂×C₄×C₅×D₃	C₂×C₄	1	16	yes	complemented
52	C₅×(C₂×D₃)⋊C₄	—	2	16	no	—
53	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
54	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	—
55	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×C₃⋊#95	C₂×C₅	1	2	yes	complemented
58	#4664	C₂×C₅	1	8	yes	direct product factor
59	C₂⁵×C₅	—	3	1	no	—
60	C₂³×C₄×C₅	—	3	1	no	—
61	C₂³×C₄×C₅	—	3	8	no	—
62	C₂³×C₄×C₅	—	3	4	no	—
63	C₂³×C₄×C₅	—	3	2	no	—
64	C₂³×C₄×C₅	—	6	8	no	—
65	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
66	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
68	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
69	C₅×#95	—	3	8	no	—
70	C₅×#95	—	3	4	no	—
71	C₅×#95	C₂×D₃	1	4	yes	complemented
72	C₂×#381	—	3	1	no	Sylow
73	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
74	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
75	C₂³×C₃×C₅	#41	1	4	yes	—
76	C₂³×C₃×C₅	#41	1	2	yes	—
77	C₂³×C₃×C₅	#41	1	2	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
79	C₂²×C₅×D₃	—	2	8	no	—
80	C₂²×C₅×D₃	—	2	8	no	—
81	C₂²×C₅×D₃	—	2	16	no	—
82	C₂²×C₅×D₃	—	2	16	no	—
83	C₂²×C₅×D₃	—	2	4	no	—
84	C₂²×C₅×D₃	—	2	2	no	—
85	C₂²×C₅×D₃	—	2	2	no	—
86	C₂²×C₅×D₃	C₂²⋊C₄	1	16	yes	—
87	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
89	C₂×C₃×C₄×C₅	—	2	8	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	4	8	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
96	C₂×C₅×Dic₃	—	2	8	no	—
97	C₂×C₅×Dic₃	—	2	4	no	—
98	C₂×C₅×Dic₃	—	2	4	no	—
99	C₂×C₅×Dic₃	—	2	4	no	—
100	C₂×C₅×Dic₃	—	2	4	no	—
101	C₂×C₅×Dic₃	—	4	8	no	—
102	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
103	C₄×C₅×D₃	—	2	32	no	—
104	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
106	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
107	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
108	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
109	C₂²×C₄×D₃	—	2	8	no	—
110	C₂²×C₄×D₃	C₄×C₅	1	8	yes	complemented
111	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
112	C₂×(C₂×D₃)⋊C₄	—	2	8	no	—
113	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	—
114	C₃×#95	C₂²×C₅	1	4	yes	complemented
115	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
116	C₃⋊#95	C₂²×C₅	1	8	yes	complemented
117	C₂⁴×C₅	—	3	4	no	—
118	C₂⁴×C₅	—	3	8	no	—
119	C₂⁴×C₅	—	3	2	no	—
120	C₂⁴×C₅	—	6	4	no	—
121	C₂⁴×C₅	—	6	2	no	—
122	C₂⁴×C₅	—	6	2	no	—
123	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	2	4	no	—
128	C₂²×C₄×C₅	—	3	4	no	—
129	C₂²×C₄×C₅	—	3	2	no	—
130	C₂²×C₄×C₅	—	3	16	no	—
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	—	6	32	no	—
133	C₂²×C₄×C₅	—	6	16	no	—
134	C₂²×C₄×C₅	—	6	4	no	—
135	C₂²×C₄×C₅	—	6	4	no	—
136	C₂²×C₄×C₅	—	6	4	no	—
137	C₂²×C₄×C₅	—	6	4	no	—
138	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
139	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
140	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
141	C₅×C₂²⋊C₄	—	6	16	no	—
142	C₂⁴×C₄	—	3	1	no	—
143	C₂²×C₂²⋊C₄	—	3	2	no	—
144	#381	—	3	8	no	—
145	C₂×#95	—	3	2	no	—
146	C₂×#95	—	3	1	no	—
147	C₂×#95	C₅×D₃	1	1	yes	characteristic, complemented
148	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
149	C₂²×C₃×C₅	#117	1	4	yes	—
150	C₂²×C₃×C₅	#117	1	4	yes	—
151	C₂²×C₃×C₅	#123	1	8	yes	—
152	C₂²×C₃×C₅	#123	1	8	yes	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
155	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
156	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
157	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
158	C₂×C₅×D₃	—	2	4	no	—
159	C₂×C₅×D₃	—	2	4	no	—
160	C₂×C₅×D₃	—	2	8	no	—
161	C₂×C₅×D₃	—	2	8	no	—
162	C₂×C₅×D₃	—	2	32	no	—
163	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	8	yes	—
164	C₃×C₄×C₅	—	2	4	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₅×Dic₃	—	2	4	no	—
167	C₅×Dic₃	—	4	4	no	—
168	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
169	C₂³×D₃	—	2	4	no	—
170	C₂³×D₃	—	2	2	no	—
171	C₂³×D₃	—	2	2	no	—
172	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
173	C₂³×D₃	C₅×D₄	1	8	yes	—
174	C₂³×D₃	C₂³×C₅	1	2	yes	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	2	4	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	4	no	—
179	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
180	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
182	C₂²×Dic₃	—	2	4	no	—
183	C₂²×Dic₃	—	2	4	no	—
184	C₂²×Dic₃	—	2	4	no	—
185	C₂²×Dic₃	—	2	4	no	—
186	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
187	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
188	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
189	C₂×C₄×D₃	—	2	32	no	—
190	C₂×C₄×D₃	—	2	16	no	—
191	C₂×C₄×D₃	C₂×C₄×C₅	1	16	yes	complemented
192	(C₂×D₃)⋊C₄	—	2	16	no	—
193	C₂³×C₅	—	3	16	no	—
194	C₂³×C₅	—	3	4	no	—
195	C₂³×C₅	—	3	8	no	—
196	C₂³×C₅	—	6	8	no	—
197	C₂³×C₅	—	6	16	no	—
198	C₂³×C₅	—	6	8	no	—
199	C₂³×C₅	—	6	16	no	—
200	C₂³×C₅	—	6	4	no	—
201	C₂³×C₅	—	6	2	no	—
202	C₂³×C₅	—	6	2	no	—
203	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
204	C₂³×C₅	#235	1	4	yes	—
205	C₂³×C₅	D₃×D₄	1	4	yes	—
206	C₂³×C₅	#237	1	2	yes	—
207	C₂³×C₅	#239	1	2	yes	—
208	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
209	C₂×C₄×C₅	—	2	8	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	4	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	3	4	no	—
215	C₂×C₄×C₅	—	4	8	no	—
216	C₂×C₄×C₅	—	6	32	no	—
217	C₂×C₄×C₅	—	6	8	no	—
218	C₂×C₄×C₅	—	6	4	no	—
219	C₂×C₄×C₅	—	6	4	no	—
220	C₂×C₄×C₅	—	6	4	no	—
221	C₂×C₄×C₅	—	6	4	no	—
222	C₂×C₄×C₅	—	12	8	no	—
223	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
224	C₂⁵	—	3	1	no	—
225	C₂³×C₄	—	3	1	no	—
226	C₂³×C₄	—	3	8	no	—
227	C₂³×C₄	—	3	4	no	—
228	C₂³×C₄	—	3	2	no	—
229	C₂³×C₄	—	6	8	no	—
230	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
231	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	—	3	8	no	—
233	C₂×C₂²⋊C₄	—	6	8	no	—
234	#95	—	3	8	no	—
235	#95	—	3	4	no	—
236	#95	C₂×C₅×D₃	1	4	yes	complemented
237	C₂×C₃×C₅	#381	1	8	yes	complemented
238	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
240	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
241	C₂×C₃×C₅	C₂×#123	1	2	yes	—
242	C₂×C₃×C₅	C₂×#123	1	2	yes	—
243	C₅×D₃	—	2	8	no	—
244	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
245	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
246	C₂³×C₃	C₅×#41	1	4	yes	—
247	C₂³×C₃	C₅×#41	1	2	yes	—
248	C₂³×C₃	C₅×#41	1	2	yes	—
249	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
250	C₂²×D₃	—	2	8	no	—
251	C₂²×D₃	—	2	8	no	—
252	C₂²×D₃	—	2	16	no	—
253	C₂²×D₃	—	2	16	no	—
254	C₂²×D₃	—	2	4	no	—
255	C₂²×D₃	—	2	2	no	—
256	C₂²×D₃	—	2	2	no	—
257	C₂²×D₃	C₅×C₂²⋊C₄	1	16	yes	—
258	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
259	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
260	C₂×C₃×C₄	—	2	8	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	4	8	no	—
266	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
267	C₂×Dic₃	—	2	8	no	—
268	C₂×Dic₃	—	2	4	no	—
269	C₂×Dic₃	—	2	4	no	—
270	C₂×Dic₃	—	2	4	no	—
271	C₂×Dic₃	—	2	4	no	—
272	C₂×Dic₃	—	4	8	no	—
273	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
274	C₄×D₃	—	2	32	no	—
275	C₂²×C₅	—	3	8	no	—
276	C₂²×C₅	—	6	32	no	—
277	C₂²×C₅	—	6	4	no	—
278	C₂²×C₅	—	6	8	no	—
279	C₂²×C₅	—	6	4	no	—
280	C₂²×C₅	—	6	8	no	—
281	C₂²×C₅	#872	1	4	yes	—
282	C₂²×C₅	D₃×C₂²⋊C₄	1	4	yes	—
283	C₂²×C₅	#883	1	8	yes	—
284	C₂²×C₅	#892	1	4	yes	—
285	C₂²×C₅	#894	1	8	yes	—
286	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
287	C₂²×C₅	C₂×#235	1	2	yes	—
288	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
289	C₂²×C₅	C₂×#237	1	1	yes	characteristic
290	C₂²×C₅	C₂×#239	1	1	yes	characteristic
291	C₄×C₅	—	2	4	no	—
292	C₄×C₅	—	4	4	no	—
293	C₄×C₅	—	6	4	no	—
294	C₄×C₅	—	12	4	no	—
295	C₂⁴	—	3	4	no	—
296	C₂⁴	—	3	8	no	—
297	C₂⁴	—	3	2	no	—
298	C₂⁴	—	6	4	no	—
299	C₂⁴	—	6	2	no	—
300	C₂⁴	—	6	2	no	—
301	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	3	4	no	—
307	C₂²×C₄	—	3	2	no	—
308	C₂²×C₄	—	3	16	no	—
309	C₂²×C₄	—	3	4	no	—
310	C₂²×C₄	—	6	32	no	—
311	C₂²×C₄	—	6	16	no	—
312	C₂²×C₄	—	6	4	no	—
313	C₂²×C₄	—	6	4	no	—
314	C₂²×C₄	—	6	4	no	—
315	C₂²×C₄	—	6	4	no	—
316	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
317	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
318	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
319	C₂²⋊C₄	—	6	16	no	—
320	C₃×C₅	C₂×#381	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
322	C₂²×C₃	C₅×#117	1	4	yes	—
323	C₂²×C₃	C₅×#117	1	4	yes	—
324	C₂²×C₃	C₅×#123	1	8	yes	—
325	C₂²×C₃	C₅×#123	1	8	yes	—
326	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
327	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
328	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
329	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
330	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
331	C₂×D₃	—	2	32	no	—
332	C₂×D₃	—	2	4	no	—
333	C₂×D₃	—	2	4	no	—
334	C₂×D₃	—	2	8	no	—
335	C₂×D₃	—	2	8	no	—
336	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
337	C₃×C₄	—	2	4	no	—
338	C₃×C₄	—	4	4	no	—
339	Dic₃	—	2	4	no	—
340	Dic₃	—	4	4	no	—
341	C₂×C₅	—	6	8	no	—
342	C₂×C₅	#4664	1	8	yes	direct product factor
343	C₂×C₅	C₂×#872	1	1	yes	characteristic
344	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
345	C₂×C₅	C₂×#883	1	2	yes	—
346	C₂×C₅	C₂×#892	1	1	yes	characteristic
347	C₂×C₅	C₂×#894	1	2	yes	—
348	C₂³	—	3	16	no	—
349	C₂³	—	3	4	no	—
350	C₂³	—	3	8	no	—
351	C₂³	—	6	8	no	—
352	C₂³	—	6	16	no	—
353	C₂³	—	6	8	no	—
354	C₂³	—	6	16	no	—
355	C₂³	—	6	4	no	—
356	C₂³	—	6	2	no	—
357	C₂³	—	6	2	no	—
358	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
359	C₂³	C₅×#235	1	4	yes	—
360	C₂³	C₅×D₃×D₄	1	4	yes	—
361	C₂³	C₅×#237	1	2	yes	—
362	C₂³	C₅×#239	1	2	yes	—
363	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	3	4	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	6	32	no	—
372	C₂×C₄	—	6	8	no	—
373	C₂×C₄	—	6	4	no	—
374	C₂×C₄	—	6	4	no	—
375	C₂×C₄	—	6	4	no	—
376	C₂×C₄	—	6	4	no	—
377	C₂×C₄	—	12	8	no	—
378	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
379	C₂×C₃	C₅×#381	1	8	yes	complemented
380	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
381	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
382	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
383	C₂×C₃	C₂×C₅×#123	1	2	yes	—
384	C₂×C₃	C₂×C₅×#123	1	2	yes	—
385	D₃	—	2	8	no	—
386	C₅	C₂×#4664	1	1	yes	characteristic, direct product factor, Sylow
387	C₂²	—	3	8	no	—
388	C₂²	—	6	32	no	—
389	C₂²	—	6	4	no	—
390	C₂²	—	6	8	no	—
391	C₂²	—	6	4	no	—
392	C₂²	—	6	8	no	—
393	C₂²	C₅×#872	1	4	yes	—
394	C₂²	C₅×D₃×C₂²⋊C₄	1	4	yes	—
395	C₂²	C₅×#883	1	8	yes	—
396	C₂²	C₅×#892	1	4	yes	—
397	C₂²	C₅×#894	1	8	yes	—
398	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
399	C₂²	C₂×C₅×#235	1	2	yes	—
400	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
401	C₂²	C₂×C₅×#237	1	1	yes	characteristic
402	C₂²	C₂×C₅×#239	1	1	yes	characteristic
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	6	4	no	—
406	C₄	—	12	4	no	—
407	C₃	C₂×C₅×#381	1	1	yes	characteristic, complemented, Sylow
408	C₂	—	6	8	no	—
409	C₂	C₅×#4664	1	8	yes	direct product factor
410	C₂	C₂×C₅×#872	1	1	yes	characteristic
411	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
412	C₂	C₂×C₅×#883	1	2	yes	—
413	C₂	C₂×C₅×#892	1	1	yes	characteristic
414	C₂	C₂×C₅×#894	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#95	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#95	D₃
hypocenter	C₃	C₂×C₅×#381
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂×C₅×#95

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×C₅×#95	C₂	semidirect
4. C₂×C₅×C₃⋊#95	C₂	semidirect
5. C₂×C₅×C₃⋊#95	C₂	semidirect
6. C₅×#4664	C₂	direct (N × H)
14. C₂²×C₄×C₅×D₃	C₄	semidirect
18. C₃×C₅×#95	C₂²	semidirect
19. C₅×C₃⋊#95	C₂²	semidirect
20. C₅×C₃⋊#95	C₂²	semidirect
21. C₂×#4664	C₅	direct (N × H)
27. C₂×C₅×#95	D₃	semidirect
51. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
55. C₂×C₃×#95	C₂×C₅	semidirect
56. C₂×C₃⋊#95	C₂×C₅	semidirect
57. C₂×C₃⋊#95	C₂×C₅	semidirect
58. #4664	C₂×C₅	direct (N × H)
71. C₅×#95	C₂×D₃	semidirect
110. C₂²×C₄×D₃	C₄×C₅	semidirect
114. C₃×#95	C₂²×C₅	semidirect
115. C₃⋊#95	C₂²×C₅	semidirect
116. C₃⋊#95	C₂²×C₅	semidirect
147. C₂×#95	C₅×D₃	semidirect
191. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
236. #95	C₂×C₅×D₃	semidirect
237. C₂×C₃×C₅	#381	semidirect
320. C₃×C₅	C₂×#381	semidirect
342. C₂×C₅	#4664	direct (N × H)
379. C₂×C₃	C₅×#381	semidirect
386. C₅	C₂×#4664	direct (N × H)
407. C₃	C₂×C₅×#381	semidirect
409. C₂	C₅×#4664	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₂×C₃×C₅×#95	2
C₂×C₅×C₃⋊#95	2
C₅×#4664	2
C₂×C₅×#381	3
C₂×#4664	5

Subgroups — C2×C5×#4664 #14319873

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4664 #14319873