Subgroups — C₂×C₃×C₅×#562 #14276561

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#562	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#124	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#123	C₂	1	4	yes	maximal, complemented
5	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
6	C₂×C₃×C₅×#121	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#562	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	—
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
11	C₂³×C₃×C₄×C₅	C₂²	1	4	yes	—
12	C₃×C₅×#125	C₂²	1	8	yes	complemented
13	C₃×C₅×#124	C₂²	1	16	yes	complemented
14	C₃×C₅×#123	C₂²	1	32	yes	complemented
15	C₃×C₅×C₂²⋊Q₈	C₂²	1	32	yes	complemented
16	C₃×C₅×#121	C₂²	1	32	yes	complemented
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₃×#562	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#562	C₂×C₃	1	16	yes	direct product factor
26	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₅×#124	C₂×C₃	1	2	yes	complemented
28	C₂×C₅×#123	C₂×C₃	1	4	yes	complemented
29	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	4	yes	complemented
30	C₂×C₅×#121	C₂×C₃	1	4	yes	complemented
31	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
32	C₂×C₃×C₅×Q₈	—	4	4	no	—
33	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
34	C₂×C₃×C₅×D₄	—	4	8	no	—
35	C₂×C₃×C₅×D₄	—	4	4	no	—
36	C₂×C₃×C₅×D₄	C₂³	1	16	yes	—
37	C₂×C₃×C₅×D₄	C₂³	1	8	yes	—
38	C₂²×C₃×C₄×C₅	—	4	8	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	16	yes	—
44	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
45	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
46	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
47	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
48	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
49	C₃×C₅×C₂²⋊C₄	C₂³	1	16	yes	—
50	C₃×C₄²×C₅	C₂³	1	4	yes	—
51	C₃×#562	C₂×C₅	1	16	yes	direct product factor
52	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#124	C₂×C₅	1	2	yes	complemented
54	C₂×C₃×#123	C₂×C₅	1	4	yes	complemented
55	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	4	yes	complemented
56	C₂×C₃×#121	C₂×C₅	1	4	yes	complemented
57	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
58	C₂²×C₅×D₄	C₂²×C₃	1	4	yes	—
59	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
60	C₂³×C₄×C₅	C₂²×C₃	1	4	yes	—
61	C₅×#125	C₂²×C₃	1	8	yes	complemented
62	C₅×#124	C₂²×C₃	1	16	yes	complemented
63	C₅×#123	C₂²×C₃	1	32	yes	complemented
64	C₅×C₂²⋊Q₈	C₂²×C₃	1	32	yes	complemented
65	C₅×#121	C₂²×C₃	1	32	yes	complemented
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
71	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
72	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
73	C₂×#562	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	—	2	8	no	—
75	C₂³×C₃×C₅	—	2	8	no	—
76	C₂³×C₃×C₅	—	2	8	no	—
77	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
78	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
79	C₃×C₅×Q₈	—	4	8	no	—
80	C₃×C₅×D₄	—	4	16	no	—
81	C₃×C₅×D₄	—	4	8	no	—
82	C₂×C₃×C₄×C₅	—	2	8	no	—
83	C₂×C₃×C₄×C₅	—	2	8	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	4	16	no	—
87	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
89	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
91	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
92	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	—
93	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
94	C₂³×C₃×C₄	C₂²×C₅	1	4	yes	—
95	C₃×#125	C₂²×C₅	1	8	yes	complemented
96	C₃×#124	C₂²×C₅	1	16	yes	complemented
97	C₃×#123	C₂²×C₅	1	32	yes	complemented
98	C₃×C₂²⋊Q₈	C₂²×C₅	1	32	yes	complemented
99	C₃×#121	C₂²×C₅	1	32	yes	complemented
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
101	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
102	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
103	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
104	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
105	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
106	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
107	C₂⁴×C₅	C₂³×C₃	1	4	yes	—
108	C₂×C₅×Q₈	—	4	4	no	—
109	C₂×C₅×Q₈	C₂³×C₃	1	8	yes	—
110	C₂×C₅×D₄	—	4	8	no	—
111	C₂×C₅×D₄	—	4	4	no	—
112	C₂×C₅×D₄	C₂³×C₃	1	16	yes	—
113	C₂×C₅×D₄	C₂³×C₃	1	8	yes	—
114	C₂²×C₄×C₅	—	4	8	no	—
115	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
117	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
118	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	16	yes	—
120	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
121	C₅×C₄⋊C₄	C₂³×C₃	1	16	yes	—
122	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
123	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
124	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
125	C₅×C₂²⋊C₄	C₂³×C₃	1	16	yes	—
126	C₄²×C₅	C₂³×C₃	1	4	yes	—
127	#562	C₂×C₃×C₅	1	16	yes	direct product factor
128	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
129	C₂×#124	C₂×C₃×C₅	1	2	yes	complemented
130	C₂×#123	C₂×C₃×C₅	1	4	yes	complemented
131	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	4	yes	complemented
132	C₂×#121	C₂×C₃×C₅	1	4	yes	complemented
133	C₂²×C₃×C₅	—	2	8	no	—
134	C₂²×C₃×C₅	—	2	8	no	—
135	C₂²×C₃×C₅	—	2	8	no	—
136	C₂²×C₃×C₅	—	4	16	no	—
137	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
138	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
139	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
140	C₃×C₄×C₅	—	2	8	no	—
141	C₃×C₄×C₅	—	2	8	no	—
142	C₃×C₄×C₅	—	2	4	no	—
143	C₃×C₄×C₅	—	2	2	no	—
144	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
145	C₂×C₃×Q₈	—	4	4	no	—
146	C₂×C₃×Q₈	C₂³×C₅	1	8	yes	—
147	C₂×C₃×D₄	—	4	8	no	—
148	C₂×C₃×D₄	—	4	4	no	—
149	C₂×C₃×D₄	C₂³×C₅	1	16	yes	—
150	C₂×C₃×D₄	C₂³×C₅	1	8	yes	—
151	C₂²×C₃×C₄	—	4	8	no	—
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
154	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
155	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
156	C₂²×C₃×C₄	C₂³×C₅	1	16	yes	—
157	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
158	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
159	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
160	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
161	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
162	C₃×C₂²⋊C₄	C₂³×C₅	1	16	yes	—
163	C₃×C₄²	C₂³×C₅	1	4	yes	—
164	C₂³×C₅	—	2	8	no	—
165	C₂³×C₅	—	2	8	no	—
166	C₂³×C₅	—	2	8	no	—
167	C₂³×C₅	C₂⁴×C₃	1	8	yes	—
168	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
169	C₅×Q₈	—	4	8	no	—
170	C₅×D₄	—	4	16	no	—
171	C₅×D₄	—	4	8	no	—
172	C₂×C₄×C₅	—	2	8	no	—
173	C₂×C₄×C₅	—	2	8	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	4	16	no	—
177	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
178	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
179	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
180	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
181	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
182	C₂²×D₄	C₂²×C₃×C₅	1	4	yes	—
183	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
184	C₂³×C₄	C₂²×C₃×C₅	1	4	yes	—
185	#125	C₂²×C₃×C₅	1	8	yes	complemented
186	#124	C₂²×C₃×C₅	1	16	yes	complemented
187	#123	C₂²×C₃×C₅	1	32	yes	complemented
188	C₂²⋊Q₈	C₂²×C₃×C₅	1	32	yes	complemented
189	#121	C₂²×C₃×C₅	1	32	yes	complemented
190	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
191	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
192	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
193	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
194	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
195	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
196	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
197	C₂×C₃×C₅	—	4	8	no	—
198	C₂×C₃×C₅	#562	1	4	yes	direct product factor
199	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
200	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
201	C₂³×C₃	—	2	8	no	—
202	C₂³×C₃	—	2	8	no	—
203	C₂³×C₃	—	2	8	no	—
204	C₂³×C₃	C₂⁴×C₅	1	8	yes	—
205	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
206	C₃×Q₈	—	4	8	no	—
207	C₃×D₄	—	4	16	no	—
208	C₃×D₄	—	4	8	no	—
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	8	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	4	16	no	—
214	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
215	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
216	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
217	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
218	C₂²×C₅	—	2	8	no	—
219	C₂²×C₅	—	2	8	no	—
220	C₂²×C₅	—	2	8	no	—
221	C₂²×C₅	—	4	16	no	—
222	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
223	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
224	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
225	C₄×C₅	—	2	8	no	—
226	C₄×C₅	—	2	8	no	—
227	C₄×C₅	—	2	4	no	—
228	C₄×C₅	—	2	2	no	—
229	C₂⁴	C₂³×C₃×C₅	1	4	yes	—
230	C₂×Q₈	—	4	4	no	—
231	C₂×Q₈	C₂³×C₃×C₅	1	8	yes	—
232	C₂×D₄	—	4	8	no	—
233	C₂×D₄	—	4	4	no	—
234	C₂×D₄	C₂³×C₃×C₅	1	16	yes	—
235	C₂×D₄	C₂³×C₃×C₅	1	8	yes	—
236	C₂²×C₄	—	4	8	no	—
237	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
238	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
239	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
240	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
241	C₂²×C₄	C₂³×C₃×C₅	1	16	yes	—
242	C₄⋊C₄	C₂³×C₃×C₅	1	16	yes	—
243	C₄⋊C₄	C₂³×C₃×C₅	1	16	yes	—
244	C₄⋊C₄	C₂³×C₃×C₅	1	8	yes	—
245	C₂²⋊C₄	C₂³×C₃×C₅	1	16	yes	—
246	C₂²⋊C₄	C₂³×C₃×C₅	1	16	yes	—
247	C₂²⋊C₄	C₂³×C₃×C₅	1	16	yes	—
248	C₄²	C₂³×C₃×C₅	1	4	yes	—
249	C₃×C₅	C₂×#562	1	1	yes	characteristic, direct product factor, Hall
250	C₂²×C₃	—	2	8	no	—
251	C₂²×C₃	—	2	8	no	—
252	C₂²×C₃	—	2	8	no	—
253	C₂²×C₃	—	4	16	no	—
254	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
255	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
256	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
257	C₃×C₄	—	2	8	no	—
258	C₃×C₄	—	2	8	no	—
259	C₃×C₄	—	2	4	no	—
260	C₃×C₄	—	2	2	no	—
261	C₂×C₅	—	4	8	no	—
262	C₂×C₅	C₃×#562	1	4	yes	direct product factor
263	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
264	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
265	C₂³	—	2	8	no	—
266	C₂³	—	2	8	no	—
267	C₂³	—	2	8	no	—
268	C₂³	C₂⁴×C₃×C₅	1	8	yes	—
269	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
270	Q₈	—	4	8	no	—
271	D₄	—	4	16	no	—
272	D₄	—	4	8	no	—
273	C₂×C₄	—	2	8	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	4	16	no	—
278	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
279	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
280	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
281	C₂×C₄	C₂⁴×C₃×C₅	1	8	yes	—
282	C₂×C₃	—	4	8	no	—
283	C₂×C₃	C₅×#562	1	4	yes	direct product factor
284	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
285	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
286	C₅	C₂×C₃×#562	1	1	yes	characteristic, direct product factor, Sylow
287	C₂²	—	2	8	no	—
288	C₂²	—	2	8	no	—
289	C₂²	—	2	8	no	—
290	C₂²	—	4	16	no	—
291	C₂²	C₃×C₅×H(5,𝔽₂)	1	4	yes	—
292	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
293	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
294	C₄	—	2	8	no	—
295	C₄	—	2	8	no	—
296	C₄	—	2	4	no	—
297	C₄	—	2	2	no	—
298	C₃	C₂×C₅×#562	1	1	yes	characteristic, direct product factor, Sylow
299	C₂	—	4	8	no	—
300	C₂	C₃×C₅×#562	1	4	yes	direct product factor
301	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	2	yes	—
302	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#562	C₂	direct (N × H)
2. C₂×C₃×C₅×#125	C₂	semidirect
3. C₂×C₃×C₅×#124	C₂	semidirect
4. C₂×C₃×C₅×#123	C₂	semidirect
5. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
6. C₂×C₃×C₅×#121	C₂	semidirect
7. C₂×C₅×#562	C₃	direct (N × H)
12. C₃×C₅×#125	C₂²	semidirect
13. C₃×C₅×#124	C₂²	semidirect
14. C₃×C₅×#123	C₂²	semidirect
15. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
16. C₃×C₅×#121	C₂²	semidirect
24. C₂×C₃×#562	C₅	direct (N × H)
25. C₅×#562	C₂×C₃	direct (N × H)
26. C₂×C₅×#125	C₂×C₃	semidirect
27. C₂×C₅×#124	C₂×C₃	semidirect
28. C₂×C₅×#123	C₂×C₃	semidirect
29. C₂×C₅×C₂²⋊Q₈	C₂×C₃	semidirect
30. C₂×C₅×#121	C₂×C₃	semidirect
51. C₃×#562	C₂×C₅	direct (N × H)
52. C₂×C₃×#125	C₂×C₅	semidirect
53. C₂×C₃×#124	C₂×C₅	semidirect
54. C₂×C₃×#123	C₂×C₅	semidirect
55. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
56. C₂×C₃×#121	C₂×C₅	semidirect
61. C₅×#125	C₂²×C₃	semidirect
62. C₅×#124	C₂²×C₃	semidirect
63. C₅×#123	C₂²×C₃	semidirect
64. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
65. C₅×#121	C₂²×C₃	semidirect
73. C₂×#562	C₃×C₅	direct (N × H)
95. C₃×#125	C₂²×C₅	semidirect
96. C₃×#124	C₂²×C₅	semidirect
97. C₃×#123	C₂²×C₅	semidirect
98. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
99. C₃×#121	C₂²×C₅	semidirect
127. #562	C₂×C₃×C₅	direct (N × H)
128. C₂×#125	C₂×C₃×C₅	semidirect
129. C₂×#124	C₂×C₃×C₅	semidirect
130. C₂×#123	C₂×C₃×C₅	semidirect
131. C₂×C₂²⋊Q₈	C₂×C₃×C₅	semidirect
132. C₂×#121	C₂×C₃×C₅	semidirect
185. #125	C₂²×C₃×C₅	semidirect
186. #124	C₂²×C₃×C₅	semidirect
187. #123	C₂²×C₃×C₅	semidirect
188. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
189. #121	C₂²×C₃×C₅	semidirect
198. C₂×C₃×C₅	#562	direct (N × H)
249. C₃×C₅	C₂×#562	direct (N × H)
262. C₂×C₅	C₃×#562	direct (N × H)
283. C₂×C₃	C₅×#562	direct (N × H)
286. C₅	C₂×C₃×#562	direct (N × H)
298. C₃	C₂×C₅×#562	direct (N × H)
300. C₂	C₃×C₅×#562	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#562	2
C₂×C₃×C₅×#125	2
C₂×C₃×C₅×#124	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂×C₃×C₅×#121	2
C₂×C₅×#562	3
C₂×C₃×#562	5

Subgroups — C2×C3×C5×#562 #14276561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#562 #14276561