Subgroups — C₃×C₅×#1976 #14275010

Order 1920.

568 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#421	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#410	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1976	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
8	C₃×C₅×#135	—	2	1	no	—
9	C₃×C₅×#135	—	2	1	no	—
10	C₃×C₅×#135	—	2	1	no	—
11	C₃×C₅×#135	—	2	1	no	—
12	C₂×C₃×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×SD₁₆	C₄	1	2	yes	complemented
14	C₂×C₃×C₅×D₈	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₂²	1	2	yes	—
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	C₃×C₅×#107	—	2	1	no	—
20	C₃×C₅×#106	—	2	1	no	—
21	C₃×C₅×#104	—	2	4	no	—
22	C₃×C₅×#99	—	2	4	no	—
23	C₃×C₅×#97	—	2	1	no	—
24	C₃×C₄×C₅×C₈	—	2	1	no	—
25	C₃×#1976	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic
27	C₅×#427	C₂×C₃	1	1	yes	characteristic, complemented
28	C₅×#421	C₂×C₃	1	2	yes	complemented
29	C₅×#410	C₂×C₃	1	2	yes	complemented
30	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×C₅×#41	—	2	2	no	—
32	C₃×C₅×#41	—	2	2	no	—
33	C₃×C₅×#41	—	2	2	no	—
34	C₃×C₅×#41	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
38	C₂²×C₃×C₄×C₅	—	2	2	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₃×C₅×Q₁₆	—	2	1	no	—
41	C₃×C₅×Q₁₆	—	2	1	no	—
42	C₃×C₅×SD₁₆	—	2	2	no	—
43	C₃×C₅×SD₁₆	—	2	2	no	—
44	C₃×C₅×D₈	—	2	1	no	—
45	C₃×C₅×D₈	—	2	1	no	—
46	C₃×C₅×M₁₆	—	2	1	no	—
47	C₃×C₅×M₁₆	D₄	1	2	yes	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
55	C₃×C₅×C₄⋊C₄	—	2	1	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
58	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	C₃×C₄²×C₅	—	2	2	no	—
61	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
62	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×#421	C₂×C₅	1	2	yes	complemented
64	C₃×#410	C₂×C₅	1	2	yes	complemented
65	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
67	C₅×#135	—	2	1	no	—
68	C₅×#135	—	2	1	no	—
69	C₅×#135	—	2	1	no	—
70	C₅×#135	—	2	1	no	—
71	C₂×C₅×Q₁₆	C₃×C₄	1	1	yes	characteristic, complemented
72	C₂×C₅×SD₁₆	C₃×C₄	1	2	yes	complemented
73	C₂×C₅×D₈	C₃×C₄	1	1	yes	characteristic, complemented
74	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₅×#117	C₂²×C₃	1	2	yes	—
77	C₅×#117	C₂²×C₃	1	1	yes	characteristic
78	C₅×#107	—	2	1	no	—
79	C₅×#106	—	2	1	no	—
80	C₅×#104	—	2	4	no	—
81	C₅×#99	—	2	4	no	—
82	C₅×#97	—	2	1	no	—
83	C₄×C₅×C₈	—	2	1	no	—
84	#1976	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
85	C₂³×C₃×C₅	—	2	2	no	—
86	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
87	C₃×C₅×Q₈	—	2	2	no	—
88	C₃×C₅×Q₈	—	2	2	no	—
89	C₃×C₅×D₄	—	2	2	no	—
90	C₃×C₅×D₄	—	2	2	no	—
91	C₃×C₅×D₄	—	4	2	no	—
92	C₃×C₅×D₄	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	4	2	no	—
96	C₂×C₃×C₄×C₅	—	4	2	no	—
97	C₂×C₃×C₄×C₅	—	4	2	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
104	C₃×C₅×C₈	—	2	2	no	—
105	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
106	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
107	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
108	C₃×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
110	C₃×#135	—	2	1	no	—
111	C₃×#135	—	2	1	no	—
112	C₃×#135	—	2	1	no	—
113	C₃×#135	—	2	1	no	—
114	C₂×C₃×Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
115	C₂×C₃×SD₁₆	C₄×C₅	1	2	yes	complemented
116	C₂×C₃×D₈	C₄×C₅	1	1	yes	characteristic, complemented
117	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
118	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
119	C₃×#117	C₂²×C₅	1	2	yes	—
120	C₃×#117	C₂²×C₅	1	1	yes	characteristic
121	C₃×#107	—	2	1	no	—
122	C₃×#106	—	2	1	no	—
123	C₃×#104	—	2	4	no	—
124	C₃×#99	—	2	4	no	—
125	C₃×#97	—	2	1	no	—
126	C₃×C₄×C₈	—	2	1	no	—
127	C₅×#41	—	2	2	no	—
128	C₅×#41	—	2	2	no	—
129	C₅×#41	—	2	2	no	—
130	C₅×#41	—	2	2	no	—
131	C₂×C₅×Q₈	C₂×C₃×C₄	1	2	yes	—
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
136	C₅×Q₁₆	—	2	1	no	—
137	C₅×Q₁₆	—	2	1	no	—
138	C₅×SD₁₆	—	2	2	no	—
139	C₅×SD₁₆	—	2	2	no	—
140	C₅×D₈	—	2	1	no	—
141	C₅×D₈	—	2	1	no	—
142	C₅×M₁₆	—	2	1	no	—
143	C₅×M₁₆	C₃×D₄	1	2	yes	—
144	C₂×C₅×C₈	—	2	1	no	—
145	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
148	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
151	C₅×C₄⋊C₄	—	2	1	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
155	C₄²×C₅	—	2	1	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic
158	#427	C₂×C₃×C₅	1	1	yes	characteristic, complemented
159	#421	C₂×C₃×C₅	1	2	yes	complemented
160	#410	C₂×C₃×C₅	1	2	yes	complemented
161	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
162	C₂²×C₃×C₅	—	4	1	no	—
163	C₂²×C₃×C₅	—	4	2	no	—
164	C₂²×C₃×C₅	—	8	2	no	—
165	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	#121	1	1	yes	characteristic
167	C₂²×C₃×C₅	#127	1	1	yes	characteristic
168	C₃×C₄×C₅	—	4	2	no	—
169	C₃×C₄×C₅	—	4	2	no	—
170	C₃×C₄×C₅	—	8	2	no	—
171	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
173	C₃×C₄×C₅	#121	1	1	yes	characteristic
174	C₃×C₄×C₅	#124	1	1	yes	characteristic
175	C₃×#41	—	2	2	no	—
176	C₃×#41	—	2	2	no	—
177	C₃×#41	—	2	2	no	—
178	C₃×#41	—	2	2	no	—
179	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
180	C₂×C₃×D₄	—	2	2	no	—
181	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
182	C₂²×C₃×C₄	—	2	2	no	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₃×Q₁₆	—	2	1	no	—
185	C₃×Q₁₆	—	2	1	no	—
186	C₃×SD₁₆	—	2	2	no	—
187	C₃×SD₁₆	—	2	2	no	—
188	C₃×D₈	—	2	1	no	—
189	C₃×D₈	—	2	1	no	—
190	C₃×M₁₆	—	2	1	no	—
191	C₃×M₁₆	C₅×D₄	1	2	yes	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
194	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
195	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
196	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
197	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
198	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
199	C₃×C₄⋊C₄	—	2	1	no	—
200	C₃×C₄⋊C₄	—	2	2	no	—
201	C₃×C₂²⋊C₄	—	2	2	no	—
202	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
203	C₃×C₄²	—	2	1	no	—
204	C₃×C₄²	—	2	2	no	—
205	C₂³×C₅	—	2	2	no	—
206	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
207	C₅×Q₈	—	2	2	no	—
208	C₅×Q₈	—	2	2	no	—
209	C₅×D₄	—	2	2	no	—
210	C₅×D₄	—	2	2	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
223	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
226	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
227	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
228	C₅×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
230	#135	—	2	1	no	—
231	#135	—	2	1	no	—
232	#135	—	2	1	no	—
233	#135	—	2	1	no	—
234	C₂×Q₁₆	C₃×C₄×C₅	1	1	yes	characteristic, complemented
235	C₂×SD₁₆	C₃×C₄×C₅	1	2	yes	complemented
236	C₂×D₈	C₃×C₄×C₅	1	1	yes	characteristic, complemented
237	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
238	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
239	#117	C₂²×C₃×C₅	1	2	yes	—
240	#117	C₂²×C₃×C₅	1	1	yes	characteristic
241	#107	—	2	1	no	—
242	#106	—	2	1	no	—
243	#104	—	2	4	no	—
244	#99	—	2	4	no	—
245	#97	—	2	1	no	—
246	C₄×C₈	—	2	1	no	—
247	C₂×C₃×C₅	—	2	1	no	—
248	C₂×C₃×C₅	—	2	1	no	—
249	C₂×C₃×C₅	—	2	1	no	—
250	C₂×C₃×C₅	—	8	2	no	—
251	C₂×C₃×C₅	#390	1	1	yes	characteristic
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
254	C₃×Q₈	—	2	2	no	—
255	C₃×Q₈	—	2	2	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	2	2	no	—
258	C₃×D₄	—	4	2	no	—
259	C₃×D₄	—	4	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	—	4	2	no	—
264	C₂×C₃×C₄	—	4	2	no	—
265	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
269	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
270	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
271	C₃×C₈	—	2	2	no	—
272	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
274	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
275	C₃×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×C₅	—	4	1	no	—
277	C₂²×C₅	—	4	2	no	—
278	C₂²×C₅	—	8	2	no	—
279	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
280	C₂²×C₅	C₃×#121	1	1	yes	characteristic
281	C₂²×C₅	C₃×#127	1	1	yes	characteristic
282	C₄×C₅	—	4	2	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	8	2	no	—
285	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
287	C₄×C₅	C₃×#121	1	1	yes	characteristic
288	C₄×C₅	C₃×#124	1	1	yes	characteristic
289	#41	—	2	2	no	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	2	2	no	—
293	C₂×Q₈	C₂×C₃×C₄×C₅	1	2	yes	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
298	Q₁₆	—	2	1	no	—
299	Q₁₆	—	2	1	no	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	D₈	—	2	1	no	—
303	D₈	—	2	1	no	—
304	M₁₆	—	2	1	no	—
305	M₁₆	C₃×C₅×D₄	1	2	yes	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
308	C₂×C₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic
309	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
310	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
311	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
312	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	2	no	—
319	C₃×C₅	#1976	1	1	yes	characteristic, direct product factor, Hall
320	C₂²×C₃	—	4	1	no	—
321	C₂²×C₃	—	4	2	no	—
322	C₂²×C₃	—	8	2	no	—
323	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
324	C₂²×C₃	C₅×#121	1	1	yes	characteristic
325	C₂²×C₃	C₅×#127	1	1	yes	characteristic
326	C₃×C₄	—	4	2	no	—
327	C₃×C₄	—	4	2	no	—
328	C₃×C₄	—	8	2	no	—
329	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
330	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
331	C₃×C₄	C₅×#121	1	1	yes	characteristic
332	C₃×C₄	C₅×#124	1	1	yes	characteristic
333	C₂×C₅	—	2	1	no	—
334	C₂×C₅	—	2	1	no	—
335	C₂×C₅	—	2	1	no	—
336	C₂×C₅	—	8	2	no	—
337	C₂×C₅	C₃×#390	1	1	yes	characteristic
338	C₂³	—	2	2	no	—
339	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
340	Q₈	—	2	2	no	—
341	Q₈	—	2	2	no	—
342	D₄	—	2	2	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
352	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
353	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
355	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
356	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
359	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
360	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
361	C₈	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
362	C₂×C₃	—	2	1	no	—
363	C₂×C₃	—	2	1	no	—
364	C₂×C₃	—	2	1	no	—
365	C₂×C₃	—	8	2	no	—
366	C₂×C₃	C₅×#390	1	1	yes	characteristic
367	C₅	C₃×#1976	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	—	4	1	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
372	C₂²	C₃×C₅×#121	1	1	yes	characteristic
373	C₂²	C₃×C₅×#127	1	1	yes	characteristic
374	C₄	—	4	2	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
378	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
379	C₄	C₃×C₅×#121	1	1	yes	characteristic
380	C₄	C₃×C₅×#124	1	1	yes	characteristic
381	C₃	C₅×#1976	1	1	yes	characteristic, direct product factor, Sylow
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	—	8	2	no	—
386	C₂	C₃×C₅×#390	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄×C₅	#121
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂×C₃×C₅	#390
prime radical	C₂×C₃×C₅×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#427	C₂	semidirect
3. C₃×C₅×#421	C₂	semidirect
4. C₃×C₅×#410	C₂	semidirect
5. C₃×C₅×#405	C₂	semidirect
6. C₅×#1976	C₃	direct (N × H)
12. C₂×C₃×C₅×Q₁₆	C₄	semidirect
13. C₂×C₃×C₅×SD₁₆	C₄	semidirect
14. C₂×C₃×C₅×D₈	C₄	semidirect
25. C₃×#1976	C₅	direct (N × H)
27. C₅×#427	C₂×C₃	semidirect
28. C₅×#421	C₂×C₃	semidirect
29. C₅×#410	C₂×C₃	semidirect
30. C₅×#405	C₂×C₃	semidirect
62. C₃×#427	C₂×C₅	semidirect
63. C₃×#421	C₂×C₅	semidirect
64. C₃×#410	C₂×C₅	semidirect
65. C₃×#405	C₂×C₅	semidirect
71. C₂×C₅×Q₁₆	C₃×C₄	semidirect
72. C₂×C₅×SD₁₆	C₃×C₄	semidirect
73. C₂×C₅×D₈	C₃×C₄	semidirect
84. #1976	C₃×C₅	direct (N × H)
114. C₂×C₃×Q₁₆	C₄×C₅	semidirect
115. C₂×C₃×SD₁₆	C₄×C₅	semidirect
116. C₂×C₃×D₈	C₄×C₅	semidirect
158. #427	C₂×C₃×C₅	semidirect
159. #421	C₂×C₃×C₅	semidirect
160. #410	C₂×C₃×C₅	semidirect
161. #405	C₂×C₃×C₅	semidirect
234. C₂×Q₁₆	C₃×C₄×C₅	semidirect
235. C₂×SD₁₆	C₃×C₄×C₅	semidirect
236. C₂×D₈	C₃×C₄×C₅	semidirect
319. C₃×C₅	#1976	direct (N × H)
367. C₅	C₃×#1976	direct (N × H)
381. C₃	C₅×#1976	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×#135	2
C₃×C₅×#427	2
C₃×C₅×#421	2
C₃×C₅×#410	2
C₃×C₅×#405	2
C₅×#1976	3
C₃×#1976	5

Subgroups — C3×C5×#1976 #14275010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1976 #14275010