Subgroups — C₃×C₅×#2621 #14275655

Order 1920.

1056 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	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#397	C₂	1	4	yes	maximal
6	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2621	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
12	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
13	C₃×C₅×#117	—	2	4	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₃×C₅×#95	C₂²	1	4	yes	—
23	C₃×C₅×#95	C₂²	1	8	yes	—
24	C₃×#2621	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
27	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic
28	C₅×#398	C₂×C₃	1	4	yes	complemented
29	C₅×#397	C₂×C₃	1	4	yes	—
30	C₅×#391	C₂×C₃	1	2	yes	complemented
31	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	—	2	4	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	—	2	4	no	—
36	C₂²×C₃×C₄×C₅	—	2	2	no	—
37	C₂²×C₃×C₄×C₅	—	2	2	no	—
38	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₃×C₅×C₄⋊C₄	—	2	4	no	—
46	C₃×C₅×C₄⋊C₄	—	2	4	no	—
47	C₃×C₅×C₄⋊C₄	—	2	8	no	—
48	C₃×C₅×C₄⋊C₄	—	2	8	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₄²×C₅	—	2	2	no	—
52	C₃×C₄²×C₅	D₄	1	4	yes	—
53	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
55	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
56	C₃×#398	C₂×C₅	1	4	yes	complemented
57	C₃×#397	C₂×C₅	1	4	yes	—
58	C₃×#391	C₂×C₅	1	2	yes	complemented
59	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	—	2	4	no	—
63	C₅×C₂²⋊Q₈	—	2	8	no	—
64	C₅×#117	—	2	4	no	—
65	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₅×#95	C₂²×C₃	1	4	yes	—
74	C₅×#95	C₂²×C₃	1	8	yes	—
75	#2621	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂³×C₃×C₅	—	2	1	no	—
77	C₂³×C₃×C₅	—	2	1	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₃×C₅×Q₈	—	4	8	no	—
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	8	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	8	no	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	#41	1	2	yes	—
98	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
99	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
100	C₃×C₄⋊Q₈	—	2	4	no	—
101	C₃×C₂²⋊Q₈	—	2	8	no	—
102	C₃×#117	—	2	4	no	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
104	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
105	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
106	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₃×#95	C₂²×C₅	1	4	yes	—
112	C₃×#95	C₂²×C₅	1	8	yes	—
113	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	4	no	—
116	C₂×C₅×Q₈	—	2	4	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
120	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
121	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
122	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
123	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	8	no	—
129	C₅×C₄⋊C₄	—	2	8	no	—
130	C₅×C₂²⋊C₄	—	2	8	no	—
131	C₅×C₂²⋊C₄	—	2	4	no	—
132	C₄²×C₅	—	2	2	no	—
133	C₄²×C₅	C₃×D₄	1	4	yes	—
134	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
135	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	—
136	C₂×#117	C₂×C₃×C₅	1	1	yes	characteristic
137	#398	C₂×C₃×C₅	1	4	yes	complemented
138	#397	C₂×C₃×C₅	1	4	yes	—
139	#391	C₂×C₃×C₅	1	2	yes	complemented
140	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	C₂²×C₃×C₅	—	2	2	no	—
142	C₂²×C₃×C₅	—	2	4	no	—
143	C₂²×C₃×C₅	—	4	2	no	—
144	C₂²×C₃×C₅	—	4	2	no	—
145	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
146	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
147	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
148	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
149	C₃×C₄×C₅	—	2	2	no	—
150	C₃×C₄×C₅	—	2	4	no	—
151	C₃×C₄×C₅	—	4	4	no	—
152	C₃×C₄×C₅	—	4	2	no	—
153	C₃×C₄×C₅	—	4	4	no	—
154	C₃×C₄×C₅	#121	1	4	yes	—
155	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
156	C₂×C₃×Q₈	—	2	4	no	—
157	C₂×C₃×Q₈	—	2	4	no	—
158	C₂×C₃×Q₈	—	2	4	no	—
159	C₂²×C₃×C₄	—	2	2	no	—
160	C₂²×C₃×C₄	—	2	2	no	—
161	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
162	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
163	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₃×C₄⋊C₄	—	2	4	no	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	2	8	no	—
171	C₃×C₄⋊C₄	—	2	8	no	—
172	C₃×C₂²⋊C₄	—	2	8	no	—
173	C₃×C₂²⋊C₄	—	2	4	no	—
174	C₃×C₄²	—	2	2	no	—
175	C₃×C₄²	C₅×D₄	1	4	yes	—
176	C₂³×C₅	—	2	1	no	—
177	C₂³×C₅	—	2	1	no	—
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
180	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
181	C₅×Q₈	—	4	8	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	4	no	—
185	C₂×C₄×C₅	—	2	8	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	4	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	2	4	no	—
190	C₂×C₄×C₅	—	2	4	no	—
191	C₂×C₄×C₅	—	2	4	no	—
192	C₂×C₄×C₅	—	2	8	no	—
193	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
194	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
195	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
196	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
197	C₂×C₄×C₅	C₃×#41	1	2	yes	—
198	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
199	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
200	C₄⋊Q₈	—	2	4	no	—
201	C₂²⋊Q₈	—	2	8	no	—
202	#117	—	2	4	no	—
203	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
204	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
205	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
206	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
207	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
208	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
209	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
211	#95	C₂²×C₃×C₅	1	4	yes	—
212	#95	C₂²×C₃×C₅	1	8	yes	—
213	C₂×C₃×C₅	—	4	2	no	—
214	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
215	C₂×C₃×C₅	#536	1	2	yes	—
216	C₂×C₃×C₅	#536	1	2	yes	—
217	C₂×C₃×C₅	#541	1	2	yes	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	—	2	4	no	—
221	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
222	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
223	C₃×Q₈	—	4	8	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	4	no	—
227	C₂×C₃×C₄	—	2	8	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	2	4	no	—
233	C₂×C₃×C₄	—	2	4	no	—
234	C₂×C₃×C₄	—	2	8	no	—
235	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
236	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
237	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
238	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
239	C₂×C₃×C₄	C₅×#41	1	2	yes	—
240	C₂²×C₅	—	2	2	no	—
241	C₂²×C₅	—	2	4	no	—
242	C₂²×C₅	—	4	2	no	—
243	C₂²×C₅	—	4	2	no	—
244	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
245	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
246	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
247	C₂²×C₅	C₃×2₋¹⁺⁴	1	4	yes	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	2	4	no	—
250	C₄×C₅	—	4	4	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	—	4	4	no	—
253	C₄×C₅	C₃×#121	1	4	yes	—
254	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	C₃×C₅×D₄	1	4	yes	—
261	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
262	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
263	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
264	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
265	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
266	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
267	C₄⋊C₄	—	2	4	no	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	8	no	—
270	C₄⋊C₄	—	2	8	no	—
271	C₂²⋊C₄	—	2	8	no	—
272	C₂²⋊C₄	—	2	4	no	—
273	C₄²	—	2	2	no	—
274	C₄²	C₃×C₅×D₄	1	4	yes	—
275	C₃×C₅	#2621	1	1	yes	characteristic, direct product factor, Hall
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	2	4	no	—
278	C₂²×C₃	—	4	2	no	—
279	C₂²×C₃	—	4	2	no	—
280	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
282	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
283	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
284	C₃×C₄	—	2	2	no	—
285	C₃×C₄	—	2	4	no	—
286	C₃×C₄	—	4	4	no	—
287	C₃×C₄	—	4	2	no	—
288	C₃×C₄	—	4	4	no	—
289	C₃×C₄	C₅×#121	1	4	yes	—
290	C₂×C₅	—	4	2	no	—
291	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
292	C₂×C₅	C₃×#536	1	2	yes	—
293	C₂×C₅	C₃×#536	1	2	yes	—
294	C₂×C₅	C₃×#541	1	2	yes	—
295	C₂³	—	2	1	no	—
296	C₂³	—	2	1	no	—
297	C₂³	—	2	4	no	—
298	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
299	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
300	Q₈	—	4	8	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
313	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
314	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
315	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
316	C₂×C₄	C₃×C₅×#41	1	2	yes	—
317	C₂×C₃	—	4	2	no	—
318	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
319	C₂×C₃	C₅×#536	1	2	yes	—
320	C₂×C₃	C₅×#536	1	2	yes	—
321	C₂×C₃	C₅×#541	1	2	yes	—
322	C₅	C₃×#2621	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	4	2	no	—
326	C₂²	—	4	2	no	—
327	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
328	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
329	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
330	C₂²	C₃×C₅×2₋¹⁺⁴	1	4	yes	—
331	C₄	—	2	2	no	—
332	C₄	—	2	4	no	—
333	C₄	—	4	4	no	—
334	C₄	—	4	2	no	—
335	C₄	—	4	4	no	—
336	C₄	C₃×C₅×#121	1	4	yes	—
337	C₃	C₅×#2621	1	1	yes	characteristic, direct product factor, Sylow
338	C₂	—	4	2	no	—
339	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
340	C₂	C₃×C₅×#536	1	2	yes	—
341	C₂	C₃×C₅×#536	1	2	yes	—
342	C₂	C₃×C₅×#541	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
6. C₃×C₅×#391	C₂	semidirect
7. C₃×C₅×#382	C₂	semidirect
8. C₅×#2621	C₃	direct (N × H)
24. C₃×#2621	C₅	direct (N × H)
25. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
28. C₅×#398	C₂×C₃	semidirect
30. C₅×#391	C₂×C₃	semidirect
31. C₅×#382	C₂×C₃	semidirect
53. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
56. C₃×#398	C₂×C₅	semidirect
58. C₃×#391	C₂×C₅	semidirect
59. C₃×#382	C₂×C₅	semidirect
75. #2621	C₃×C₅	direct (N × H)
134. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
137. #398	C₂×C₃×C₅	semidirect
139. #391	C₂×C₃×C₅	semidirect
140. #382	C₂×C₃×C₅	semidirect
275. C₃×C₅	#2621	direct (N × H)
322. C₅	C₃×#2621	direct (N × H)
337. C₃	C₅×#2621	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×C₄⋊Q₈	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₅×#117	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#391	2
C₃×C₅×#382	2
C₅×#2621	3
C₃×#2621	5

Subgroups — C3×C5×#2621 #14275655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2621 #14275655