Subgroups — C₃×C₅×#2092 #14275126

Order 1920.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×#102	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2092	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₃×C₅×#107	—	2	2	no	—
18	C₃×C₅×#106	—	2	2	no	—
19	C₃×C₅×#102	—	2	2	no	—
20	C₃×C₅×#102	—	2	2	no	—
21	C₃×C₅×#95	—	2	2	no	—
22	C₃×#2092	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic
26	C₂×C₅×#102	C₂×C₃	1	1	yes	characteristic
27	C₅×#390	C₂×C₃	1	1	yes	characteristic
28	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
29	C₅×#336	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂⁴×C₃×C₅	—	2	1	no	—
31	C₂×C₃×C₅×D₄	—	2	1	no	—
32	C₂×C₃×C₅×D₄	—	2	1	no	—
33	C₂×C₃×C₅×D₄	—	2	1	no	—
34	C₂×C₃×C₅×D₄	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂²×C₃×C₄×C₅	—	2	1	no	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₃×C₅×C₄⋊C₄	—	2	1	no	—
54	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic
60	C₂×C₃×#102	C₂×C₅	1	1	yes	characteristic
61	C₃×#390	C₂×C₅	1	1	yes	characteristic
62	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#336	C₂×C₅	1	1	yes	characteristic, complemented
64	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₅×#107	—	2	2	no	—
73	C₅×#106	—	2	2	no	—
74	C₅×#102	—	2	2	no	—
75	C₅×#102	—	2	2	no	—
76	C₅×#95	—	2	2	no	—
77	#2092	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	4	1	no	—
80	C₂³×C₃×C₅	—	4	1	no	—
81	C₂³×C₃×C₅	—	4	2	no	—
82	C₂³×C₃×C₅	—	4	2	no	—
83	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
84	C₃×C₅×D₄	—	2	2	no	—
85	C₃×C₅×D₄	—	2	2	no	—
86	C₃×C₅×D₄	—	4	1	no	—
87	C₃×C₅×D₄	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	4	1	no	—
93	C₂×C₃×C₄×C₅	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₃×C₅×C₈	—	2	2	no	—
104	C₃×C₅×C₈	—	2	2	no	—
105	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
106	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
113	C₃×#107	—	2	2	no	—
114	C₃×#106	—	2	2	no	—
115	C₃×#102	—	2	2	no	—
116	C₃×#102	—	2	2	no	—
117	C₃×#95	—	2	2	no	—
118	C₂⁴×C₅	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	2	1	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	C₃×Q₈	1	2	yes	—
125	C₂²×C₄×C₅	—	2	1	no	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
135	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	2	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	1	no	—
142	C₅×C₂²⋊C₄	—	4	4	no	—
143	C₄²×C₅	—	2	1	no	—
144	C₄²×C₅	—	2	1	no	—
145	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic
148	C₂×#102	C₂×C₃×C₅	1	1	yes	characteristic
149	#390	C₂×C₃×C₅	1	1	yes	characteristic
150	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
151	#336	C₂×C₃×C₅	1	1	yes	characteristic, complemented
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	4	no	—
154	C₂²×C₃×C₅	—	8	2	no	—
155	C₂²×C₃×C₅	—	8	1	no	—
156	C₂²×C₃×C₅	—	8	1	no	—
157	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂²×C₃×C₅	#123	1	1	yes	characteristic
159	C₂²×C₃×C₅	#127	1	1	yes	characteristic
160	C₂²×C₃×C₅	#135	1	2	yes	—
161	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	—
162	C₃×C₄×C₅	—	4	2	no	—
163	C₃×C₄×C₅	—	8	1	no	—
164	C₃×C₄×C₅	—	8	1	no	—
165	C₃×C₄×C₅	—	8	1	no	—
166	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
167	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
168	C₃×C₄×C₅	#123	1	1	yes	characteristic
169	C₃×C₄×C₅	#123	1	1	yes	characteristic
170	C₂⁴×C₃	—	2	1	no	—
171	C₂×C₃×D₄	—	2	1	no	—
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	—	2	1	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	—	2	1	no	—
176	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂×C₃×C₈	—	2	1	no	—
183	C₂×C₃×C₈	—	2	1	no	—
184	C₂×C₃×C₈	—	2	1	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
187	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
188	C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×C₄⋊C₄	—	2	1	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	—	2	1	no	—
192	C₃×C₄⋊C₄	—	2	1	no	—
193	C₃×C₄⋊C₄	—	2	1	no	—
194	C₃×C₂²⋊C₄	—	4	4	no	—
195	C₃×C₄²	—	2	1	no	—
196	C₃×C₄²	—	2	1	no	—
197	C₂³×C₅	—	2	2	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	4	1	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
203	C₅×D₄	—	2	2	no	—
204	C₅×D₄	—	2	2	no	—
205	C₅×D₄	—	4	1	no	—
206	C₅×D₄	—	4	1	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
220	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
222	C₅×C₈	—	2	2	no	—
223	C₅×C₈	—	2	2	no	—
224	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
225	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
226	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
232	#107	—	2	2	no	—
233	#106	—	2	2	no	—
234	#102	—	2	2	no	—
235	#102	—	2	2	no	—
236	#95	—	2	2	no	—
237	C₂×C₃×C₅	—	8	2	no	—
238	C₂×C₃×C₅	#399	1	1	yes	characteristic
239	C₂×C₃×C₅	#478	1	2	yes	—
240	C₂×C₃×C₅	#482	1	2	yes	—
241	C₂×C₃×C₅	#495	1	1	yes	characteristic
242	C₂×C₃×C₅	#496	1	1	yes	characteristic
243	C₂³×C₃	—	2	2	no	—
244	C₂³×C₃	—	4	1	no	—
245	C₂³×C₃	—	4	1	no	—
246	C₂³×C₃	—	4	2	no	—
247	C₂³×C₃	—	4	2	no	—
248	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
249	C₃×D₄	—	2	2	no	—
250	C₃×D₄	—	2	2	no	—
251	C₃×D₄	—	4	1	no	—
252	C₃×D₄	—	4	1	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	4	1	no	—
257	C₂×C₃×C₄	—	4	1	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	4	2	no	—
260	C₂×C₃×C₄	—	4	2	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
266	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
267	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
268	C₃×C₈	—	2	2	no	—
269	C₃×C₈	—	2	2	no	—
270	C₂²×C₅	—	4	2	no	—
271	C₂²×C₅	—	4	4	no	—
272	C₂²×C₅	—	8	2	no	—
273	C₂²×C₅	—	8	1	no	—
274	C₂²×C₅	—	8	1	no	—
275	C₂²×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
276	C₂²×C₅	C₃×#123	1	1	yes	characteristic
277	C₂²×C₅	C₃×#127	1	1	yes	characteristic
278	C₂²×C₅	C₃×#135	1	2	yes	—
279	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
280	C₄×C₅	—	4	2	no	—
281	C₄×C₅	—	8	1	no	—
282	C₄×C₅	—	8	1	no	—
283	C₄×C₅	—	8	1	no	—
284	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
285	C₄×C₅	C₃×C₂²⋊Q₈	1	1	yes	characteristic
286	C₄×C₅	C₃×#123	1	1	yes	characteristic
287	C₄×C₅	C₃×#123	1	1	yes	characteristic
288	C₂⁴	—	2	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	C₃×C₅×Q₈	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
299	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
305	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₃×C₅	#2092	1	1	yes	characteristic, direct product factor, Hall
316	C₂²×C₃	—	4	2	no	—
317	C₂²×C₃	—	4	4	no	—
318	C₂²×C₃	—	8	2	no	—
319	C₂²×C₃	—	8	1	no	—
320	C₂²×C₃	—	8	1	no	—
321	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
322	C₂²×C₃	C₅×#123	1	1	yes	characteristic
323	C₂²×C₃	C₅×#127	1	1	yes	characteristic
324	C₂²×C₃	C₅×#135	1	2	yes	—
325	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
326	C₃×C₄	—	4	2	no	—
327	C₃×C₄	—	8	1	no	—
328	C₃×C₄	—	8	1	no	—
329	C₃×C₄	—	8	1	no	—
330	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
331	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
332	C₃×C₄	C₅×#123	1	1	yes	characteristic
333	C₃×C₄	C₅×#123	1	1	yes	characteristic
334	C₂×C₅	—	8	2	no	—
335	C₂×C₅	C₃×#399	1	1	yes	characteristic
336	C₂×C₅	C₃×#478	1	2	yes	—
337	C₂×C₅	C₃×#482	1	2	yes	—
338	C₂×C₅	C₃×#495	1	1	yes	characteristic
339	C₂×C₅	C₃×#496	1	1	yes	characteristic
340	C₂³	—	2	2	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
361	C₂×C₄	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
362	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
363	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
364	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	2	2	no	—
367	C₂×C₃	—	8	2	no	—
368	C₂×C₃	C₅×#399	1	1	yes	characteristic
369	C₂×C₃	C₅×#478	1	2	yes	—
370	C₂×C₃	C₅×#482	1	2	yes	—
371	C₂×C₃	C₅×#495	1	1	yes	characteristic
372	C₂×C₃	C₅×#496	1	1	yes	characteristic
373	C₅	C₃×#2092	1	1	yes	characteristic, direct product factor, Sylow
374	C₂²	—	4	4	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂²	C₃×C₅×#123	1	1	yes	characteristic
381	C₂²	C₃×C₅×#127	1	1	yes	characteristic
382	C₂²	C₃×C₅×#135	1	2	yes	—
383	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
384	C₄	—	4	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
389	C₄	C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
390	C₄	C₃×C₅×#123	1	1	yes	characteristic
391	C₄	C₃×C₅×#123	1	1	yes	characteristic
392	C₃	C₅×#2092	1	1	yes	characteristic, direct product factor, Sylow
393	C₂	—	8	2	no	—
394	C₂	C₃×C₅×#399	1	1	yes	characteristic
395	C₂	C₃×C₅×#478	1	2	yes	—
396	C₂	C₃×C₅×#482	1	2	yes	—
397	C₂	C₃×C₅×#495	1	1	yes	characteristic
398	C₂	C₃×C₅×#496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#107	C₂	semidirect
2. C₂×C₃×C₅×#106	C₂	semidirect
6. C₃×C₅×#382	C₂	semidirect
7. C₃×C₅×#336	C₂	semidirect
8. C₅×#2092	C₃	direct (N × H)
22. C₃×#2092	C₅	direct (N × H)
23. C₂×C₅×#107	C₂×C₃	semidirect
24. C₂×C₅×#106	C₂×C₃	semidirect
28. C₅×#382	C₂×C₃	semidirect
29. C₅×#336	C₂×C₃	semidirect
57. C₂×C₃×#107	C₂×C₅	semidirect
58. C₂×C₃×#106	C₂×C₅	semidirect
62. C₃×#382	C₂×C₅	semidirect
63. C₃×#336	C₂×C₅	semidirect
77. #2092	C₃×C₅	direct (N × H)
145. C₂×#107	C₂×C₃×C₅	semidirect
146. C₂×#106	C₂×C₃×C₅	semidirect
150. #382	C₂×C₃×C₅	semidirect
151. #336	C₂×C₃×C₅	semidirect
315. C₃×C₅	#2092	direct (N × H)
373. C₅	C₃×#2092	direct (N × H)
392. C₃	C₅×#2092	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×C₃×C₅×#107	2
C₂×C₃×C₅×#106	2
C₂×C₃×C₅×#102	2
C₃×C₅×#390	2
C₃×C₅×#382	2
C₃×C₅×#336	2
C₅×#2092	3
C₃×#2092	5

Subgroups — C3×C5×#2092 #14275126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2092 #14275126