Subgroups — C₃×C₅×#1970 #14275004

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
6	C₅×#1970	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
8	C₂×C₃×C₅×D₈	—	2	2	no	—
9	C₂×C₃×C₅×D₈	—	2	2	no	—
10	C₂×C₃×C₅×D₈	C₄	1	4	yes	complemented
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#107	—	2	2	no	—
17	C₃×C₅×#102	—	2	4	no	—
18	C₃×C₄×C₅×C₈	—	2	2	no	—
19	C₃×#1970	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
23	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#390	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	—	2	2	no	—
26	C₂×C₃×C₅×D₄	—	2	2	no	—
27	C₂×C₃×C₅×D₄	—	2	2	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	—	2	2	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₃×C₅×D₈	—	2	8	no	—
36	C₂×C₃×C₅×C₈	—	2	1	no	—
37	C₂×C₃×C₅×C₈	—	2	1	no	—
38	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
40	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
41	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
45	C₃×C₄²×C₅	—	2	1	no	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic
48	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
49	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
50	C₂×C₃×C₄×C₈	C₂×C₅	1	1	yes	characteristic, complemented
51	C₃×#390	C₂×C₅	1	2	yes	complemented
52	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
53	C₂×C₅×D₈	—	2	2	no	—
54	C₂×C₅×D₈	—	2	2	no	—
55	C₂×C₅×D₈	C₃×C₄	1	4	yes	complemented
56	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
59	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₅×#107	—	2	2	no	—
62	C₅×#102	—	2	4	no	—
63	C₄×C₅×C₈	—	2	2	no	—
64	#1970	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₃×C₅	—	2	4	no	—
66	C₂³×C₃×C₅	—	4	2	no	—
67	C₂³×C₃×C₅	—	4	2	no	—
68	C₂³×C₃×C₅	—	4	4	no	—
69	C₂³×C₃×C₅	—	4	4	no	—
70	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
71	C₃×C₅×D₄	—	2	4	no	—
72	C₃×C₅×D₄	—	2	4	no	—
73	C₃×C₅×D₄	—	4	2	no	—
74	C₃×C₅×D₄	—	4	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	4	2	no	—
78	C₂×C₃×C₄×C₅	—	4	4	no	—
79	C₂×C₃×C₄×C₅	D₈	1	4	yes	complemented
80	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
86	C₃×C₅×C₈	—	2	2	no	—
87	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
88	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
89	C₂×C₃×D₈	—	2	2	no	—
90	C₂×C₃×D₈	—	2	2	no	—
91	C₂×C₃×D₈	C₄×C₅	1	4	yes	complemented
92	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
95	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
97	C₃×#107	—	2	2	no	—
98	C₃×#102	—	2	4	no	—
99	C₃×C₄×C₈	—	2	2	no	—
100	C₂⁴×C₅	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	2	no	—
106	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
109	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
110	C₅×D₈	—	2	8	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	—	2	1	no	—
113	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
114	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
115	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
116	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₄⋊C₄	—	2	2	no	—
119	C₅×C₂²⋊C₄	—	4	8	no	—
120	C₄²×C₅	—	2	1	no	—
121	C₄²×C₅	—	2	1	no	—
122	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic
123	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
124	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
125	C₂×C₄×C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
126	#390	C₂×C₃×C₅	1	2	yes	complemented
127	C₂²×C₃×C₅	—	4	4	no	—
128	C₂²×C₃×C₅	—	4	8	no	—
129	C₂²×C₃×C₅	—	8	4	no	—
130	C₂²×C₃×C₅	—	8	2	no	—
131	C₂²×C₃×C₅	—	8	2	no	—
132	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
133	C₂²×C₃×C₅	#121	1	1	yes	characteristic
134	C₂²×C₃×C₅	#127	1	1	yes	characteristic
135	C₂²×C₃×C₅	C₂×D₈	1	2	yes	—
136	C₂²×C₃×C₅	#135	1	2	yes	—
137	C₃×C₄×C₅	—	2	4	no	—
138	C₃×C₄×C₅	—	8	2	no	—
139	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
141	C₃×C₄×C₅	#121	1	1	yes	characteristic
142	C₃×C₄×C₅	#124	1	1	yes	characteristic
143	C₂⁴×C₃	—	2	2	no	—
144	C₂×C₃×D₄	—	2	2	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	—	2	2	no	—
147	C₂×C₃×D₄	—	2	2	no	—
148	C₂×C₃×D₄	—	2	2	no	—
149	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
150	C₂²×C₃×C₄	—	2	2	no	—
151	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₃×D₈	—	2	8	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
157	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
158	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
159	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
160	C₃×C₄⋊C₄	—	2	2	no	—
161	C₃×C₄⋊C₄	—	2	2	no	—
162	C₃×C₂²⋊C₄	—	4	8	no	—
163	C₃×C₄²	—	2	1	no	—
164	C₃×C₄²	—	2	1	no	—
165	C₂³×C₅	—	2	4	no	—
166	C₂³×C₅	—	4	2	no	—
167	C₂³×C₅	—	4	2	no	—
168	C₂³×C₅	—	4	4	no	—
169	C₂³×C₅	—	4	4	no	—
170	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
171	C₅×D₄	—	2	4	no	—
172	C₅×D₄	—	2	4	no	—
173	C₅×D₄	—	4	2	no	—
174	C₅×D₄	—	4	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	4	2	no	—
178	C₂×C₄×C₅	—	4	4	no	—
179	C₂×C₄×C₅	C₃×D₈	1	4	yes	complemented
180	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
185	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
186	C₅×C₈	—	2	2	no	—
187	C₅×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
188	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
189	C₂×D₈	—	2	2	no	—
190	C₂×D₈	—	2	2	no	—
191	C₂×D₈	C₃×C₄×C₅	1	4	yes	complemented
192	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
193	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
194	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
195	C₂×C₂²⋊C₄	—	2	4	no	—
196	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
197	#107	—	2	2	no	—
198	#102	—	2	4	no	—
199	C₄×C₈	—	2	2	no	—
200	C₂×C₃×C₅	—	8	4	no	—
201	C₂×C₃×C₅	#390	1	1	yes	characteristic
202	C₂×C₃×C₅	C₄×D₈	1	2	yes	—
203	C₂×C₃×C₅	#466	1	2	yes	—
204	C₂×C₃×C₅	#493	1	1	yes	characteristic
205	C₂×C₃×C₅	#495	1	1	yes	characteristic
206	C₂³×C₃	—	2	4	no	—
207	C₂³×C₃	—	4	2	no	—
208	C₂³×C₃	—	4	2	no	—
209	C₂³×C₃	—	4	4	no	—
210	C₂³×C₃	—	4	4	no	—
211	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
212	C₃×D₄	—	2	4	no	—
213	C₃×D₄	—	2	4	no	—
214	C₃×D₄	—	4	2	no	—
215	C₃×D₄	—	4	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	4	2	no	—
219	C₂×C₃×C₄	—	4	4	no	—
220	C₂×C₃×C₄	C₅×D₈	1	4	yes	complemented
221	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
226	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
227	C₃×C₈	—	2	2	no	—
228	C₃×C₈	C₅×C₂²⋊C₄	1	4	yes	complemented
229	C₂²×C₅	—	4	4	no	—
230	C₂²×C₅	—	4	8	no	—
231	C₂²×C₅	—	8	4	no	—
232	C₂²×C₅	—	8	2	no	—
233	C₂²×C₅	—	8	2	no	—
234	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₅	C₃×#121	1	1	yes	characteristic
236	C₂²×C₅	C₃×#127	1	1	yes	characteristic
237	C₂²×C₅	C₂×C₃×D₈	1	2	yes	—
238	C₂²×C₅	C₃×#135	1	2	yes	—
239	C₄×C₅	—	2	4	no	—
240	C₄×C₅	—	8	2	no	—
241	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
242	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
243	C₄×C₅	C₃×#121	1	1	yes	characteristic
244	C₄×C₅	C₃×#124	1	1	yes	characteristic
245	C₂⁴	—	2	2	no	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
254	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
255	D₈	—	2	8	no	—
256	C₂×C₈	—	2	1	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
259	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
260	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
261	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
262	C₄⋊C₄	—	2	2	no	—
263	C₄⋊C₄	—	2	2	no	—
264	C₂²⋊C₄	—	4	8	no	—
265	C₄²	—	2	1	no	—
266	C₄²	—	2	1	no	—
267	C₃×C₅	#1970	1	1	yes	characteristic, direct product factor, Hall
268	C₂²×C₃	—	4	4	no	—
269	C₂²×C₃	—	4	8	no	—
270	C₂²×C₃	—	8	4	no	—
271	C₂²×C₃	—	8	2	no	—
272	C₂²×C₃	—	8	2	no	—
273	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
274	C₂²×C₃	C₅×#121	1	1	yes	characteristic
275	C₂²×C₃	C₅×#127	1	1	yes	characteristic
276	C₂²×C₃	C₂×C₅×D₈	1	2	yes	—
277	C₂²×C₃	C₅×#135	1	2	yes	—
278	C₃×C₄	—	2	4	no	—
279	C₃×C₄	—	8	2	no	—
280	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
281	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
282	C₃×C₄	C₅×#121	1	1	yes	characteristic
283	C₃×C₄	C₅×#124	1	1	yes	characteristic
284	C₂×C₅	—	8	4	no	—
285	C₂×C₅	C₃×#390	1	1	yes	characteristic
286	C₂×C₅	C₃×C₄×D₈	1	2	yes	—
287	C₂×C₅	C₃×#466	1	2	yes	—
288	C₂×C₅	C₃×#493	1	1	yes	characteristic
289	C₂×C₅	C₃×#495	1	1	yes	characteristic
290	C₂³	—	2	4	no	—
291	C₂³	—	4	2	no	—
292	C₂³	—	4	2	no	—
293	C₂³	—	4	4	no	—
294	C₂³	—	4	4	no	—
295	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
296	D₄	—	2	4	no	—
297	D₄	—	2	4	no	—
298	D₄	—	4	2	no	—
299	D₄	—	4	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	4	4	no	—
304	C₂×C₄	C₃×C₅×D₈	1	4	yes	complemented
305	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
306	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
307	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
308	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
309	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
310	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
311	C₈	—	2	2	no	—
312	C₈	C₃×C₅×C₂²⋊C₄	1	4	yes	complemented
313	C₂×C₃	—	8	4	no	—
314	C₂×C₃	C₅×#390	1	1	yes	characteristic
315	C₂×C₃	C₄×C₅×D₈	1	2	yes	—
316	C₂×C₃	C₅×#466	1	2	yes	—
317	C₂×C₃	C₅×#493	1	1	yes	characteristic
318	C₂×C₃	C₅×#495	1	1	yes	characteristic
319	C₅	C₃×#1970	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²	—	4	4	no	—
321	C₂²	—	4	8	no	—
322	C₂²	—	8	4	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
326	C₂²	C₃×C₅×#121	1	1	yes	characteristic
327	C₂²	C₃×C₅×#127	1	1	yes	characteristic
328	C₂²	C₂×C₃×C₅×D₈	1	2	yes	—
329	C₂²	C₃×C₅×#135	1	2	yes	—
330	C₄	—	2	4	no	—
331	C₄	—	8	2	no	—
332	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
333	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
334	C₄	C₃×C₅×#121	1	1	yes	characteristic
335	C₄	C₃×C₅×#124	1	1	yes	characteristic
336	C₃	C₅×#1970	1	1	yes	characteristic, direct product factor, Sylow
337	C₂	—	8	4	no	—
338	C₂	C₃×C₅×#390	1	1	yes	characteristic
339	C₂	C₃×C₄×C₅×D₈	1	2	yes	—
340	C₂	C₃×C₅×#466	1	2	yes	—
341	C₂	C₃×C₅×#493	1	1	yes	characteristic
342	C₂	C₃×C₅×#495	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₈	C₂
LCS	G ▷ C₂×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
2. C₂×C₃×C₅×#107	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₅×#1970	C₃	direct (N × H)
10. C₂×C₃×C₅×D₈	C₄	semidirect
19. C₃×#1970	C₅	direct (N × H)
21. C₂×C₅×#107	C₂×C₃	semidirect
22. C₂×C₅×#102	C₂×C₃	semidirect
23. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
24. C₅×#390	C₂×C₃	semidirect
48. C₂×C₃×#107	C₂×C₅	semidirect
49. C₂×C₃×#102	C₂×C₅	semidirect
50. C₂×C₃×C₄×C₈	C₂×C₅	semidirect
51. C₃×#390	C₂×C₅	semidirect
55. C₂×C₅×D₈	C₃×C₄	semidirect
64. #1970	C₃×C₅	direct (N × H)
79. C₂×C₃×C₄×C₅	D₈	semidirect
87. C₃×C₅×C₈	C₂²⋊C₄	semidirect
91. C₂×C₃×D₈	C₄×C₅	semidirect
123. C₂×#107	C₂×C₃×C₅	semidirect
124. C₂×#102	C₂×C₃×C₅	semidirect
125. C₂×C₄×C₈	C₂×C₃×C₅	semidirect
126. #390	C₂×C₃×C₅	semidirect
179. C₂×C₄×C₅	C₃×D₈	semidirect
187. C₅×C₈	C₃×C₂²⋊C₄	semidirect
191. C₂×D₈	C₃×C₄×C₅	semidirect
220. C₂×C₃×C₄	C₅×D₈	semidirect
228. C₃×C₈	C₅×C₂²⋊C₄	semidirect
267. C₃×C₅	#1970	direct (N × H)
304. C₂×C₄	C₃×C₅×D₈	semidirect
312. C₈	C₃×C₅×C₂²⋊C₄	semidirect
319. C₅	C₃×#1970	direct (N × H)
336. C₃	C₅×#1970	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×C₃×C₅×D₈	2
C₂×C₃×C₅×#107	2
C₂×C₃×C₅×#102	2
C₂×C₃×C₄×C₅×C₈	2
C₃×C₅×#390	2
C₅×#1970	3
C₃×#1970	5

Subgroups — C3×C5×#1970 #14275004

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1970 #14275004