Subgroups — C₂×C₅×#4530 #14294748

Order 1920.

864 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	2	yes	maximal
3	C₅×#4530	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×#343	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₄×C₅	C₄	1	2	yes	—
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
8	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
9	C₂×C₃×C₅×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂×C₅×#208	—	2	4	no	—
12	C₂×C₅×#208	—	2	2	no	—
13	C₂×C₅×#208	C₄	1	8	yes	complemented
14	C₂×C₅×#208	C₂²	1	4	yes	—
15	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
16	C₂×#4530	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₅×M₁₆	—	3	2	no	—
18	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic
19	C₅×#343	—	3	4	no	—
20	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	—	2	2	no	—
22	C₂²×C₃×C₄×C₅	—	2	2	no	—
23	C₂²×C₃×C₄×C₅	—	4	4	no	—
24	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
25	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
27	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
28	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	Q₈	1	2	yes	—
31	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
32	C₃×C₅×C₄⋊C₄	—	2	4	no	—
33	C₃×C₅×C₄⋊C₄	—	2	4	no	—
34	C₅×#208	—	2	8	no	—
35	C₅×#208	—	2	4	no	—
36	C₅×#208	C₂×C₄	1	8	yes	complemented
37	C₂×C₅×C₃⋊C₈	—	2	8	no	—
38	C₂×C₅×C₃⋊C₈	—	2	4	no	—
39	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
40	C₂²×#208	C₂×C₅	1	2	yes	—
41	#4530	C₂×C₅	1	4	yes	direct product factor
42	C₂³×C₄×C₅	Dic₃	1	2	yes	—
43	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
44	C₂×C₅×M₁₆	—	3	8	no	—
45	C₂×C₅×M₁₆	—	3	4	no	—
46	C₂×C₅×M₁₆	—	6	4	no	—
47	C₂×C₅×M₁₆	—	6	2	no	—
48	C₂²×C₅×C₈	—	6	2	no	—
49	C₂×C₅×C₄⋊C₄	—	2	2	no	—
50	C₂×C₅×C₄⋊C₄	—	2	2	no	—
51	C₂×C₅×C₄⋊C₄	Dic₃	1	2	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
53	C₂×#343	—	3	1	no	Sylow
54	C₂³×C₃×C₅	—	2	2	no	—
55	C₂³×C₃×C₅	—	2	2	no	—
56	C₂³×C₃×C₅	C₄²	1	2	yes	—
57	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
58	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
59	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
60	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×C₅	—	2	4	no	—
62	C₂×C₃×C₄×C₅	—	4	4	no	—
63	C₂×C₃×C₄×C₅	—	4	4	no	—
64	C₂×C₃×C₄×C₅	—	4	4	no	—
65	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
66	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
67	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
68	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
69	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
70	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
71	C₂×C₃×C₄×C₅	C₄⋊C₄	1	4	yes	—
72	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
73	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
75	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
76	C₅×C₃⋊C₈	—	2	8	no	—
77	C₂³×C₃×C₄	C₄×C₅	1	2	yes	—
78	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
79	C₂×C₃×C₄⋊C₄	—	2	2	no	—
80	C₂×C₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₃×C₄⋊C₄	C₄×C₅	1	2	yes	—
82	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
83	C₂×#208	—	2	4	no	—
84	C₂×#208	—	2	2	no	—
85	C₂×#208	C₄×C₅	1	8	yes	complemented
86	C₂×#208	C₂²×C₅	1	4	yes	—
87	C₂²×C₃⋊C₈	—	2	2	no	—
88	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	4	4	no	—
92	C₂²×C₄×C₅	Dic₆	1	2	yes	—
93	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
94	C₂²×C₄×C₅	D₁₂	1	2	yes	—
95	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
96	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
97	C₂²×C₄×C₅	#67	1	2	yes	—
98	C₂²×C₄×C₅	#67	1	2	yes	—
99	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
100	C₅×M₁₆	—	3	8	no	—
101	C₅×M₁₆	—	6	8	no	—
102	C₅×M₁₆	—	6	4	no	—
103	C₂×C₅×C₈	—	6	8	no	—
104	C₂×C₅×C₈	—	6	4	no	—
105	C₅×C₄⋊C₄	—	2	4	no	—
106	C₅×C₄⋊C₄	—	2	4	no	—
107	C₂²×M₁₆	—	3	2	no	—
108	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic
109	#343	—	3	4	no	—
110	C₂²×C₃×C₅	—	2	4	no	—
111	C₂²×C₃×C₅	—	2	4	no	—
112	C₂²×C₃×C₅	—	2	1	no	—
113	C₂²×C₃×C₅	—	2	1	no	—
114	C₂²×C₃×C₅	—	2	1	no	—
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	#95	1	2	yes	—
117	C₂²×C₃×C₅	#95	1	2	yes	—
118	C₂²×C₃×C₅	#100	1	2	yes	—
119	C₂²×C₃×C₅	#101	1	2	yes	—
120	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
121	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
123	C₃×C₄×C₅	—	4	4	no	—
124	C₃×C₄×C₅	#95	1	4	yes	—
125	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
126	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
127	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
128	C₂²×C₃×C₄	—	2	2	no	—
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	4	4	no	—
131	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
132	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
133	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
135	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
136	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
137	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
138	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
139	C₃×C₄⋊C₄	—	2	4	no	—
140	C₃×C₄⋊C₄	—	2	4	no	—
141	#208	—	2	8	no	—
142	#208	—	2	4	no	—
143	#208	C₂×C₄×C₅	1	8	yes	complemented
144	C₂×C₃⋊C₈	—	2	8	no	—
145	C₂×C₃⋊C₈	—	2	4	no	—
146	C₂³×C₅	—	2	2	no	—
147	C₂³×C₅	—	2	2	no	—
148	C₂³×C₅	C₄×Dic₃	1	2	yes	—
149	C₂³×C₅	C₄⋊Dic₃	1	2	yes	—
150	C₂³×C₅	#217	1	1	yes	characteristic
151	C₂³×C₅	#217	1	1	yes	characteristic
152	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
153	C₂×C₄×C₅	—	2	4	no	—
154	C₂×C₄×C₅	—	4	4	no	—
155	C₂×C₄×C₅	—	4	4	no	—
156	C₂×C₄×C₅	—	4	4	no	—
157	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
158	C₂×C₄×C₅	Dic₃⋊C₄	1	4	yes	—
159	C₂×C₄×C₅	Dic₃⋊C₄	1	4	yes	—
160	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
161	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
162	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	4	yes	—
163	C₂×C₄×C₅	#217	1	2	yes	—
164	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
165	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
166	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂×#67	1	2	yes	—
168	C₅×C₈	—	6	8	no	—
169	C₂³×C₄	C₅×Dic₃	1	2	yes	—
170	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
171	C₂×M₁₆	—	3	8	no	—
172	C₂×M₁₆	—	3	4	no	—
173	C₂×M₁₆	—	6	4	no	—
174	C₂×M₁₆	—	6	2	no	—
175	C₂²×C₈	—	6	2	no	—
176	C₂×C₄⋊C₄	—	2	2	no	—
177	C₂×C₄⋊C₄	—	2	2	no	—
178	C₂×C₄⋊C₄	C₅×Dic₃	1	2	yes	—
179	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
180	C₂×C₃×C₅	—	2	2	no	—
181	C₂×C₃×C₅	—	2	1	no	—
182	C₂×C₃×C₅	—	2	1	no	—
183	C₂×C₃×C₅	#343	1	4	yes	complemented
184	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
185	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
186	C₂×C₃×C₅	C₂×#101	1	1	yes	characteristic
187	C₂³×C₃	—	2	2	no	—
188	C₂³×C₃	—	2	2	no	—
189	C₂³×C₃	C₄²×C₅	1	2	yes	—
190	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
193	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
194	C₂×C₃×C₄	—	2	4	no	—
195	C₂×C₃×C₄	—	4	4	no	—
196	C₂×C₃×C₄	—	4	4	no	—
197	C₂×C₃×C₄	—	4	4	no	—
198	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
199	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
200	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	4	yes	—
201	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
202	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
203	C₂×C₃×C₄	C₅×C₄⋊C₄	1	4	yes	—
204	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
205	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
206	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
207	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
208	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
209	C₃⋊C₈	—	2	8	no	—
210	C₂²×C₅	—	2	1	no	—
211	C₂²×C₅	—	2	1	no	—
212	C₂²×C₅	—	2	1	no	—
213	C₂²×C₅	—	2	1	no	—
214	C₂²×C₅	—	2	4	no	—
215	C₂²×C₅	—	2	4	no	—
216	C₂²×C₅	C₃⋊#95	1	2	yes	—
217	C₂²×C₅	C₃⋊#95	1	2	yes	—
218	C₂²×C₅	#833	1	2	yes	—
219	C₂²×C₅	#836	1	2	yes	—
220	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
221	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
222	C₂²×C₅	C₂×#217	1	1	yes	characteristic
223	C₄×C₅	—	4	4	no	—
224	C₄×C₅	C₃⋊#95	1	4	yes	—
225	C₄×C₅	C₂×Dic₃⋊C₄	1	2	yes	—
226	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
227	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
228	C₂²×C₄	—	2	2	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	C₅×Dic₆	1	2	yes	—
232	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
233	C₂²×C₄	C₅×D₁₂	1	2	yes	—
234	C₂²×C₄	C₂×C₅×Dic₃	1	4	yes	—
235	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
236	C₂²×C₄	C₅×#67	1	2	yes	—
237	C₂²×C₄	C₅×#67	1	2	yes	—
238	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
239	M₁₆	—	3	8	no	—
240	M₁₆	—	6	8	no	—
241	M₁₆	—	6	4	no	—
242	C₂×C₈	—	6	8	no	—
243	C₂×C₈	—	6	4	no	—
244	C₄⋊C₄	—	2	4	no	—
245	C₄⋊C₄	—	2	4	no	—
246	C₃×C₅	C₂×#343	1	1	yes	characteristic, complemented, Hall
247	C₂²×C₃	—	2	1	no	—
248	C₂²×C₃	—	2	1	no	—
249	C₂²×C₃	—	2	1	no	—
250	C₂²×C₃	—	2	1	no	—
251	C₂²×C₃	—	2	4	no	—
252	C₂²×C₃	—	2	4	no	—
253	C₂²×C₃	C₅×#95	1	2	yes	—
254	C₂²×C₃	C₅×#95	1	2	yes	—
255	C₂²×C₃	C₅×#100	1	2	yes	—
256	C₂²×C₃	C₅×#101	1	2	yes	—
257	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
258	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
260	C₃×C₄	—	4	4	no	—
261	C₃×C₄	C₅×#95	1	4	yes	—
262	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
263	C₃×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
264	C₂×C₅	—	2	2	no	—
265	C₂×C₅	—	2	1	no	—
266	C₂×C₅	—	2	1	no	—
267	C₂×C₅	#4530	1	4	yes	direct product factor
268	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
269	C₂×C₅	C₂×#833	1	1	yes	characteristic
270	C₂×C₅	C₂×#836	1	1	yes	characteristic
271	C₂³	—	2	2	no	—
272	C₂³	—	2	2	no	—
273	C₂³	C₄×C₅×Dic₃	1	2	yes	—
274	C₂³	C₅×C₄⋊Dic₃	1	2	yes	—
275	C₂³	C₅×#217	1	1	yes	characteristic
276	C₂³	C₅×#217	1	1	yes	characteristic
277	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	4	4	no	—
280	C₂×C₄	—	4	4	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
283	C₂×C₄	C₅×Dic₃⋊C₄	1	4	yes	—
284	C₂×C₄	C₅×Dic₃⋊C₄	1	4	yes	—
285	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
286	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
287	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	4	yes	—
288	C₂×C₄	C₅×#217	1	2	yes	—
289	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
290	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
291	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
292	C₂×C₄	C₂×C₅×#67	1	2	yes	—
293	C₈	—	6	8	no	—
294	C₂×C₃	—	2	1	no	—
295	C₂×C₃	—	2	1	no	—
296	C₂×C₃	—	2	2	no	—
297	C₂×C₃	C₅×#343	1	4	yes	complemented
298	C₂×C₃	C₂×C₅×#95	1	1	yes	characteristic
299	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
300	C₂×C₃	C₂×C₅×#101	1	1	yes	characteristic
301	C₅	C₂×#4530	1	1	yes	characteristic, direct product factor, Sylow
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	C₅×C₃⋊#95	1	2	yes	—
309	C₂²	C₅×C₃⋊#95	1	2	yes	—
310	C₂²	C₅×#833	1	2	yes	—
311	C₂²	C₅×#836	1	2	yes	—
312	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
313	C₂²	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
314	C₂²	C₂×C₅×#217	1	1	yes	characteristic
315	C₄	—	4	4	no	—
316	C₄	C₅×C₃⋊#95	1	4	yes	—
317	C₄	C₂×C₅×Dic₃⋊C₄	1	2	yes	—
318	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	2	yes	—
319	C₃	C₂×C₅×#343	1	1	yes	characteristic, complemented, Sylow
320	C₂	—	2	1	no	—
321	C₂	—	2	1	no	—
322	C₂	—	2	2	no	—
323	C₂	C₅×#4530	1	4	yes	direct product factor
324	C₂	C₂×C₅×C₃⋊#95	1	1	yes	characteristic
325	C₂	C₂×C₅×#833	1	1	yes	characteristic
326	C₂	C₂×C₅×#836	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	#217
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#343
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₅×#4530	C₂	direct (N × H)
13. C₂×C₅×#208	C₄	semidirect
16. C₂×#4530	C₅	direct (N × H)
36. C₅×#208	C₂×C₄	semidirect
41. #4530	C₂×C₅	direct (N × H)
85. C₂×#208	C₄×C₅	semidirect
143. #208	C₂×C₄×C₅	semidirect
183. C₂×C₃×C₅	#343	semidirect
246. C₃×C₅	C₂×#343	semidirect
267. C₂×C₅	#4530	direct (N × H)
297. C₂×C₃	C₅×#343	semidirect
301. C₅	C₂×#4530	direct (N × H)
319. C₃	C₂×C₅×#343	semidirect
323. C₂	C₅×#4530	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×C₄⋊C₄	2
C₂²×C₅×#208	2
C₅×#4530	2
C₂×C₅×#343	3
C₂×#4530	5

Subgroups — C2×C5×#4530 #14294748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4530 #14294748