Subgroups — C₂×C₃×C₅×(C₂×D₃)⋊C₄ #13087938

Order 1440.

582 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₃×C₅×C₂²⋊C₄	—	3	1	no	maximal
6	C₂×C₅×(C₂×D₃)⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃²×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×D₃	—	2	2	no	—
9	C₂²×C₃×C₅×D₃	—	2	2	no	—
10	C₂²×C₃×C₅×D₃	C₄	1	4	yes	complemented
11	C₂²×C₃×C₅×D₃	C₂²	1	2	yes	—
12	C₂×C₃²×C₄×C₅	—	2	2	no	—
13	C₂×C₃²×C₄×C₅	C₂²	1	2	yes	complemented
14	C₂×C₃×C₅×Dic₃	—	2	2	no	—
15	C₂×C₃×C₅×Dic₃	C₂²	1	2	yes	complemented
16	C₂×C₃×(C₂×D₃)⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂⁴×C₃×C₅	—	3	1	no	—
18	C₂³×C₅×D₃	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₃×C₄×C₅	—	2	1	no	—
20	C₂²×C₃×C₄×C₅	—	3	1	no	—
21	C₂²×C₃×C₄×C₅	D₃	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₄×C₅	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂²×C₅×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
24	C₃×C₅×C₂²⋊C₄	—	3	4	no	—
25	C₅×(C₂×D₃)⋊C₄	C₂×C₃	1	4	yes	direct product factor
26	C₂²×C₃²×C₅	C₂×C₄	1	2	yes	—
27	C₂²×C₃²×C₅	D₄	1	2	yes	—
28	C₂²×C₃²×C₅	D₄	1	2	yes	—
29	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
30	C₂×C₃×C₅×D₃	—	2	8	no	—
31	C₂×C₃×C₅×D₃	—	2	2	no	—
32	C₂×C₃×C₅×D₃	—	2	2	no	—
33	C₂×C₃×C₅×D₃	C₂×C₄	1	4	yes	complemented
34	C₃²×C₄×C₅	—	2	2	no	—
35	C₃×C₅×Dic₃	—	2	2	no	—
36	C₂×C₅×C₂²⋊C₄	—	3	1	no	Hall
37	C₂³×C₃×D₃	C₂×C₅	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂×C₅	1	1	yes	characteristic, complemented
39	C₂²×C₃×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
40	C₃×(C₂×D₃)⋊C₄	C₂×C₅	1	4	yes	direct product factor
41	C₂³×C₃×C₅	—	2	1	no	—
42	C₂³×C₃×C₅	—	3	4	no	—
43	C₂³×C₃×C₅	—	3	2	no	—
44	C₂³×C₃×C₅	—	6	2	no	—
45	C₂³×C₃×C₅	—	6	2	no	—
46	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
47	C₂³×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
48	C₂²×C₅×D₃	—	2	2	no	—
49	C₂²×C₅×D₃	—	2	2	no	—
50	C₂²×C₅×D₃	C₃×C₄	1	4	yes	complemented
51	C₂²×C₅×D₃	C₂²×C₃	1	2	yes	—
52	C₂×C₃×C₄×C₅	—	2	4	no	—
53	C₂×C₃×C₄×C₅	—	2	2	no	—
54	C₂×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₃×C₄×C₅	—	2	2	no	—
56	C₂×C₃×C₄×C₅	—	3	2	no	—
57	C₂×C₃×C₄×C₅	—	6	2	no	—
58	C₂×C₃×C₄×C₅	C₂×D₃	1	2	yes	complemented
59	C₂×C₃×C₄×C₅	C₂²×C₃	1	2	yes	complemented
60	C₂×C₅×Dic₃	—	2	2	no	—
61	C₂×C₅×Dic₃	C₂²×C₃	1	2	yes	complemented
62	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
63	C₂×(C₂×D₃)⋊C₄	C₃×C₅	1	1	yes	characteristic, direct product factor
64	C₂×C₃²×C₅	C₂²⋊C₄	1	4	yes	complemented
65	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
68	C₃×C₅×D₃	—	2	4	no	—
69	C₂⁴×C₅	—	3	1	no	—
70	C₂²×C₄×C₅	—	3	1	no	—
71	C₂²×C₄×C₅	C₃×D₃	1	1	yes	characteristic, complemented
72	C₅×C₂²⋊C₄	—	3	4	no	—
73	C₂³×C₃²	C₂²×C₅	1	1	yes	characteristic
74	C₂²×C₃×D₃	—	2	2	no	—
75	C₂²×C₃×D₃	—	2	2	no	—
76	C₂²×C₃×D₃	C₄×C₅	1	4	yes	complemented
77	C₂²×C₃×D₃	C₂²×C₅	1	2	yes	—
78	C₂×C₃²×C₄	—	2	2	no	—
79	C₂×C₃²×C₄	C₂²×C₅	1	2	yes	complemented
80	C₂×C₃×Dic₃	—	2	2	no	—
81	C₂×C₃×Dic₃	C₂²×C₅	1	2	yes	complemented
82	C₂²×C₃×C₅	—	2	2	no	—
83	C₂²×C₃×C₅	—	2	2	no	—
84	C₂²×C₃×C₅	—	2	2	no	—
85	C₂²×C₃×C₅	—	2	1	no	—
86	C₂²×C₃×C₅	—	3	4	no	—
87	C₂²×C₃×C₅	—	6	8	no	—
88	C₂²×C₃×C₅	—	6	2	no	—
89	C₂²×C₃×C₅	—	6	2	no	—
90	C₂²×C₃×C₅	C₄×D₃	1	2	yes	—
91	C₂²×C₃×C₅	D₁₂	1	2	yes	—
92	C₂²×C₃×C₅	#67	1	2	yes	—
93	C₂²×C₃×C₅	C₂×C₃×C₄	1	2	yes	—
94	C₂²×C₃×C₅	C₃×D₄	1	2	yes	—
95	C₂²×C₃×C₅	C₃×D₄	1	2	yes	—
96	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
97	C₂²×C₃×C₅	C₂³×C₃	1	1	yes	characteristic
98	C₂×C₅×D₃	—	2	8	no	—
99	C₂×C₅×D₃	—	2	2	no	—
100	C₂×C₅×D₃	—	2	2	no	—
101	C₂×C₅×D₃	C₂×C₃×C₄	1	4	yes	complemented
102	C₃×C₄×C₅	—	2	4	no	—
103	C₃×C₄×C₅	—	2	2	no	—
104	C₃×C₄×C₅	—	2	2	no	—
105	C₃×C₄×C₅	—	6	2	no	—
106	C₅×Dic₃	—	2	2	no	—
107	C₂⁴×C₃	—	3	1	no	—
108	C₂³×D₃	C₂×C₃×C₅	1	1	yes	characteristic
109	C₂²×C₃×C₄	—	2	1	no	—
110	C₂²×C₃×C₄	—	3	1	no	—
111	C₂²×C₃×C₄	C₅×D₃	1	1	yes	characteristic, complemented
112	C₂²×C₃×C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
113	C₂²×Dic₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
114	C₃×C₂²⋊C₄	—	3	4	no	—
115	(C₂×D₃)⋊C₄	C₂×C₃×C₅	1	4	yes	direct product factor
116	C₃²×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
117	C₂³×C₅	—	3	4	no	—
118	C₂³×C₅	—	3	2	no	—
119	C₂³×C₅	—	6	2	no	—
120	C₂³×C₅	—	6	2	no	—
121	C₂³×C₅	C₂×C₃×D₃	1	1	yes	characteristic
122	C₂×C₄×C₅	—	2	2	no	—
123	C₂×C₄×C₅	—	3	2	no	—
124	C₂×C₄×C₅	—	6	2	no	—
125	C₂×C₄×C₅	C₂×C₃×D₃	1	2	yes	complemented
126	C₂²×C₃²	C₂×C₄×C₅	1	2	yes	—
127	C₂²×C₃²	C₅×D₄	1	2	yes	—
128	C₂²×C₃²	C₅×D₄	1	2	yes	—
129	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
130	C₂×C₃×D₃	—	2	8	no	—
131	C₂×C₃×D₃	—	2	2	no	—
132	C₂×C₃×D₃	—	2	2	no	—
133	C₂×C₃×D₃	C₂×C₄×C₅	1	4	yes	complemented
134	C₃²×C₄	—	2	2	no	—
135	C₃×Dic₃	—	2	2	no	—
136	C₂×C₂²⋊C₄	—	3	1	no	Sylow
137	C₂×C₃×C₅	—	2	4	no	—
138	C₂×C₃×C₅	—	2	1	no	—
139	C₂×C₃×C₅	—	2	1	no	—
140	C₂×C₃×C₅	—	2	1	no	—
141	C₂×C₃×C₅	—	6	4	no	—
142	C₂×C₃×C₅	(C₂×D₃)⋊C₄	1	4	yes	direct product factor
143	C₂×C₃×C₅	C₃×C₂²⋊C₄	1	4	yes	complemented
144	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
145	C₂×C₃×C₅	C₂×D₁₂	1	1	yes	characteristic
146	C₂×C₃×C₅	C₂×#67	1	1	yes	characteristic
147	C₂×C₃×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
148	C₂×C₃×C₅	C₂×C₃×D₄	1	1	yes	characteristic
149	C₂×C₃×C₅	C₂×C₃×D₄	1	1	yes	characteristic
150	C₅×D₃	—	2	4	no	—
151	C₂³×C₃	—	2	1	no	—
152	C₂³×C₃	—	3	4	no	—
153	C₂³×C₃	—	3	2	no	—
154	C₂³×C₃	—	6	2	no	—
155	C₂³×C₃	—	6	2	no	—
156	C₂³×C₃	C₂×C₅×D₃	1	1	yes	characteristic
157	C₂³×C₃	C₂²×C₃×C₅	1	1	yes	characteristic
158	C₂²×D₃	—	2	2	no	—
159	C₂²×D₃	—	2	2	no	—
160	C₂²×D₃	C₃×C₄×C₅	1	4	yes	complemented
161	C₂²×D₃	C₂²×C₃×C₅	1	2	yes	—
162	C₂×C₃×C₄	—	2	4	no	—
163	C₂×C₃×C₄	—	2	2	no	—
164	C₂×C₃×C₄	—	2	2	no	—
165	C₂×C₃×C₄	—	2	2	no	—
166	C₂×C₃×C₄	—	3	2	no	—
167	C₂×C₃×C₄	—	6	2	no	—
168	C₂×C₃×C₄	C₂×C₅×D₃	1	2	yes	complemented
169	C₂×C₃×C₄	C₂²×C₃×C₅	1	2	yes	complemented
170	C₂×Dic₃	—	2	2	no	—
171	C₂×Dic₃	C₂²×C₃×C₅	1	2	yes	complemented
172	C₂²×C₅	—	3	4	no	—
173	C₂²×C₅	—	6	8	no	—
174	C₂²×C₅	—	6	2	no	—
175	C₂²×C₅	—	6	2	no	—
176	C₂²×C₅	C₃×C₄×D₃	1	2	yes	—
177	C₂²×C₅	C₃×D₁₂	1	2	yes	—
178	C₂²×C₅	C₃×#67	1	2	yes	—
179	C₂²×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
180	C₄×C₅	—	2	2	no	—
181	C₄×C₅	—	6	2	no	—
182	C₂×C₃²	C₅×C₂²⋊C₄	1	4	yes	complemented
183	C₂×C₃²	C₂²×C₄×C₅	1	1	yes	characteristic
184	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
185	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
186	C₃×D₃	—	2	4	no	—
187	C₂⁴	—	3	1	no	—
188	C₂²×C₄	—	3	1	no	—
189	C₂²×C₄	C₃×C₅×D₃	1	1	yes	characteristic, complemented
190	C₂²⋊C₄	—	3	4	no	—
191	C₃×C₅	—	2	1	no	—
192	C₃×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor
193	C₃×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
194	C₂²×C₃	—	2	2	no	—
195	C₂²×C₃	—	2	2	no	—
196	C₂²×C₃	—	2	2	no	—
197	C₂²×C₃	—	2	1	no	—
198	C₂²×C₃	—	3	4	no	—
199	C₂²×C₃	—	6	8	no	—
200	C₂²×C₃	—	6	2	no	—
201	C₂²×C₃	—	6	2	no	—
202	C₂²×C₃	C₄×C₅×D₃	1	2	yes	—
203	C₂²×C₃	C₅×D₁₂	1	2	yes	—
204	C₂²×C₃	C₅×#67	1	2	yes	—
205	C₂²×C₃	C₂×C₃×C₄×C₅	1	2	yes	—
206	C₂²×C₃	C₃×C₅×D₄	1	2	yes	—
207	C₂²×C₃	C₃×C₅×D₄	1	2	yes	—
208	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
209	C₂²×C₃	C₂³×C₃×C₅	1	1	yes	characteristic
210	C₂×D₃	—	2	8	no	—
211	C₂×D₃	—	2	2	no	—
212	C₂×D₃	—	2	2	no	—
213	C₂×D₃	C₂×C₃×C₄×C₅	1	4	yes	complemented
214	C₃×C₄	—	2	4	no	—
215	C₃×C₄	—	2	2	no	—
216	C₃×C₄	—	2	2	no	—
217	C₃×C₄	—	6	2	no	—
218	Dic₃	—	2	2	no	—
219	C₂×C₅	—	6	4	no	—
220	C₂×C₅	C₃×(C₂×D₃)⋊C₄	1	4	yes	direct product factor
221	C₂×C₅	C₂×C₃×C₄×D₃	1	1	yes	characteristic
222	C₂×C₅	C₂×C₃×D₁₂	1	1	yes	characteristic
223	C₂×C₅	C₂×C₃×#67	1	1	yes	characteristic
224	C₃²	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
225	C₂³	—	3	4	no	—
226	C₂³	—	3	2	no	—
227	C₂³	—	6	2	no	—
228	C₂³	—	6	2	no	—
229	C₂³	C₂×C₃×C₅×D₃	1	1	yes	characteristic
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	3	2	no	—
232	C₂×C₄	—	6	2	no	—
233	C₂×C₄	C₂×C₃×C₅×D₃	1	2	yes	complemented
234	C₂×C₃	—	2	1	no	—
235	C₂×C₃	—	2	4	no	—
236	C₂×C₃	—	2	1	no	—
237	C₂×C₃	—	2	1	no	—
238	C₂×C₃	—	6	4	no	—
239	C₂×C₃	C₅×(C₂×D₃)⋊C₄	1	4	yes	direct product factor
240	C₂×C₃	C₃×C₅×C₂²⋊C₄	1	4	yes	complemented
241	C₂×C₃	C₂×C₄×C₅×D₃	1	1	yes	characteristic
242	C₂×C₃	C₂×C₅×D₁₂	1	1	yes	characteristic
243	C₂×C₃	C₂×C₅×#67	1	1	yes	characteristic
244	C₂×C₃	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
245	C₂×C₃	C₂×C₃×C₅×D₄	1	1	yes	characteristic
246	C₂×C₃	C₂×C₃×C₅×D₄	1	1	yes	characteristic
247	D₃	—	2	4	no	—
248	C₅	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
249	C₂²	—	3	4	no	—
250	C₂²	—	6	2	no	—
251	C₂²	—	6	8	no	—
252	C₂²	—	6	2	no	—
253	C₂²	C₃×C₄×C₅×D₃	1	2	yes	—
254	C₂²	C₃×C₅×D₁₂	1	2	yes	—
255	C₂²	C₃×C₅×#67	1	2	yes	—
256	C₂²	C₂²×C₃×C₅×D₃	1	1	yes	characteristic
257	C₄	—	2	2	no	—
258	C₄	—	6	2	no	—
259	C₃	—	2	1	no	—
260	C₃	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor
261	C₃	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented
262	C₂	—	6	4	no	—
263	C₂	C₃×C₅×(C₂×D₃)⋊C₄	1	4	yes	direct product factor
264	C₂	C₂×C₃×C₄×C₅×D₃	1	1	yes	characteristic
265	C₂	C₂×C₃×C₅×D₁₂	1	1	yes	characteristic
266	C₂	C₂×C₃×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃×C₅	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄×C₅
Frattini	C₂²	C₂²×C₃×C₅×D₃
Fitting	C₂²×C₃²×C₄×C₅	C₂
socle	C₂³×C₃²×C₅	C₂²
prime radical	C₂³×C₃×C₅×D₃	C₂
cosocle	C₂²×C₃	C₂³×C₃×C₅
hypercenter	C₂²×C₃×C₄×C₅	D₃
hypocenter	C₃	C₂×C₃×C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂²×C₃×C₄×C₅

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×C₄×C₅	C₂	semidirect
3. C₂²×C₃×C₅×Dic₃	C₂	semidirect
4. C₃×C₅×(C₂×D₃)⋊C₄	C₂	direct (N × H)
6. C₂×C₅×(C₂×D₃)⋊C₄	C₃	direct (N × H)
10. C₂²×C₃×C₅×D₃	C₄	semidirect
13. C₂×C₃²×C₄×C₅	C₂²	semidirect
15. C₂×C₃×C₅×Dic₃	C₂²	semidirect
16. C₂×C₃×(C₂×D₃)⋊C₄	C₅	direct (N × H)
21. C₂²×C₃×C₄×C₅	D₃	semidirect
22. C₂²×C₃×C₄×C₅	C₂×C₃	semidirect
23. C₂²×C₅×Dic₃	C₂×C₃	semidirect
25. C₅×(C₂×D₃)⋊C₄	C₂×C₃	direct (N × H)
33. C₂×C₃×C₅×D₃	C₂×C₄	semidirect
38. C₂²×C₃²×C₄	C₂×C₅	semidirect
39. C₂²×C₃×Dic₃	C₂×C₅	semidirect
40. C₃×(C₂×D₃)⋊C₄	C₂×C₅	direct (N × H)
50. C₂²×C₅×D₃	C₃×C₄	semidirect
58. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
59. C₂×C₃×C₄×C₅	C₂²×C₃	semidirect
61. C₂×C₅×Dic₃	C₂²×C₃	semidirect
63. C₂×(C₂×D₃)⋊C₄	C₃×C₅	direct (N × H)
64. C₂×C₃²×C₅	C₂²⋊C₄	semidirect
71. C₂²×C₄×C₅	C₃×D₃	semidirect
76. C₂²×C₃×D₃	C₄×C₅	semidirect
79. C₂×C₃²×C₄	C₂²×C₅	semidirect
81. C₂×C₃×Dic₃	C₂²×C₅	semidirect
101. C₂×C₅×D₃	C₂×C₃×C₄	semidirect
111. C₂²×C₃×C₄	C₅×D₃	semidirect
112. C₂²×C₃×C₄	C₂×C₃×C₅	semidirect
113. C₂²×Dic₃	C₂×C₃×C₅	semidirect
115. (C₂×D₃)⋊C₄	C₂×C₃×C₅	direct (N × H)
116. C₃²×C₅	C₂×C₂²⋊C₄	semidirect
125. C₂×C₄×C₅	C₂×C₃×D₃	semidirect
133. C₂×C₃×D₃	C₂×C₄×C₅	semidirect
142. C₂×C₃×C₅	(C₂×D₃)⋊C₄	direct (N × H)
143. C₂×C₃×C₅	C₃×C₂²⋊C₄	semidirect
160. C₂²×D₃	C₃×C₄×C₅	semidirect
168. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
169. C₂×C₃×C₄	C₂²×C₃×C₅	semidirect
171. C₂×Dic₃	C₂²×C₃×C₅	semidirect
182. C₂×C₃²	C₅×C₂²⋊C₄	semidirect
189. C₂²×C₄	C₃×C₅×D₃	semidirect
192. C₃×C₅	C₂×(C₂×D₃)⋊C₄	direct (N × H)
193. C₃×C₅	C₂×C₃×C₂²⋊C₄	semidirect
213. C₂×D₃	C₂×C₃×C₄×C₅	semidirect
220. C₂×C₅	C₃×(C₂×D₃)⋊C₄	direct (N × H)
224. C₃²	C₂×C₅×C₂²⋊C₄	semidirect
233. C₂×C₄	C₂×C₃×C₅×D₃	semidirect
239. C₂×C₃	C₅×(C₂×D₃)⋊C₄	direct (N × H)
240. C₂×C₃	C₃×C₅×C₂²⋊C₄	semidirect
248. C₅	C₂×C₃×(C₂×D₃)⋊C₄	direct (N × H)
260. C₃	C₂×C₅×(C₂×D₃)⋊C₄	direct (N × H)
261. C₃	C₂×C₃×C₅×C₂²⋊C₄	semidirect
263. C₂	C₃×C₅×(C₂×D₃)⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₃	2
C₂²×C₃²×C₄×C₅	2
C₂²×C₃×C₅×Dic₃	2
C₃×C₅×(C₂×D₃)⋊C₄	2
C₂×C₃×C₅×C₂²⋊C₄	3
C₂×C₅×(C₂×D₃)⋊C₄	3
C₂×C₃×(C₂×D₃)⋊C₄	5

Subgroups — C2×C3×C5×(C2×D3)⋊C4 #13087938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×(C₂×D₃)⋊C₄ #13087938