Subgroups — C₂×C₅×D₃×D₁₂ #13089316

Order 1440.

998 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃²	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#626	C₂	1	2	yes	maximal, complemented
6	C₅×D₃×D₁₂	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×D₃×D₄	—	3	1	no	maximal
8	C₂²×C₅×D₁₂	—	3	1	no	maximal
9	C₂²×C₅×C₃⋊D₃	C₂²	1	2	yes	complemented
10	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₃	C₂²	1	2	yes	complemented
12	C₂×C₅×D₃²	—	2	8	no	—
13	C₂×C₅×D₃²	C₂²	1	8	yes	complemented
14	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
15	C₅×C₄⋊(C₃⋊D₃)	C₂²	1	4	yes	complemented
16	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×D₁₂	C₂²	1	4	yes	complemented
18	C₃×C₄×C₅×D₃	C₂²	1	4	yes	complemented
19	C₅×#626	C₂²	1	8	yes	complemented
20	C₂×D₃×D₁₂	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂³×C₅×D₃	—	3	2	no	—
22	C₂³×C₅×D₃	—	3	2	no	—
23	C₂×C₃×C₅×D₄	—	3	1	no	—
24	C₂²×C₃×C₄×C₅	—	3	1	no	—
25	C₂×C₅×#67	—	3	2	no	—
26	C₅×D₃×D₄	—	3	8	no	—
27	C₂×C₅×D₁₂	—	3	2	no	—
28	C₂×C₅×D₁₂	—	3	1	no	—
29	C₂×C₅×D₁₂	—	3	1	no	—
30	C₂×C₅×D₁₂	—	3	8	no	—
31	C₂×C₅×D₁₂	—	6	1	no	—
32	C₂×C₅×D₁₂	D₃	1	1	yes	characteristic, direct product factor
33	C₂×C₄×C₅×D₃	D₃	1	1	yes	characteristic, complemented
34	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×C₃⋊D₃	—	2	4	no	—
36	C₂×C₅×C₃⋊D₃	C₂³	1	4	yes	complemented
37	C₂×C₃×C₅×D₃	—	2	4	no	—
38	C₂×C₃×C₅×D₃	D₄	1	4	yes	complemented
39	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
40	C₂×C₃×C₅×D₃	C₂³	1	4	yes	complemented
41	C₅×D₃²	—	2	16	no	—
42	C₃²×C₄×C₅	C₂³	1	2	yes	complemented
43	C₃×C₅×Dic₃	C₂³	1	2	yes	complemented
44	C₂²×C₅×D₄	—	9	1	no	Hall
45	C₂²×D₃²	C₂×C₅	1	2	yes	complemented
46	C₂×C₄⋊(C₃⋊D₃)	C₂×C₅	1	1	yes	characteristic, complemented
47	C₂×C₃×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
48	C₂×C₃×C₄×D₃	C₂×C₅	1	1	yes	characteristic, complemented
49	C₂×#626	C₂×C₅	1	2	yes	complemented
50	D₃×D₁₂	C₂×C₅	1	8	yes	direct product factor
51	C₂³×C₃×C₅	—	3	1	no	—
52	C₂³×C₃×C₅	—	3	2	no	—
53	C₂²×C₅×D₃	—	3	2	no	—
54	C₂²×C₅×D₃	—	3	2	no	—
55	C₂²×C₅×D₃	—	3	8	no	—
56	C₂²×C₅×D₃	—	3	8	no	—
57	C₂²×C₅×D₃	—	6	8	no	—
58	C₂²×C₅×D₃	—	6	8	no	—
59	C₂²×C₅×D₃	—	6	2	no	—
60	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₅×D₃	C₂×D₃	1	2	yes	complemented
62	C₃×C₅×D₄	—	3	4	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	3	1	no	—
65	C₂×C₃×C₄×C₅	—	3	4	no	—
66	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
67	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
68	C₅×#67	—	3	8	no	—
69	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
70	C₅×D₁₂	—	3	8	no	—
71	C₅×D₁₂	—	3	4	no	—
72	C₅×D₁₂	—	3	4	no	—
73	C₅×D₁₂	—	6	4	no	—
74	C₅×D₁₂	C₂×D₃	1	4	yes	direct product factor
75	C₄×C₅×D₃	C₂×D₃	1	4	yes	complemented
76	C₂×D₃×D₄	—	3	1	no	—
77	C₂²×D₁₂	—	3	1	no	—
78	C₂×C₃²×C₅	C₂×D₄	1	2	yes	complemented
79	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
80	C₅×C₃⋊D₃	—	2	4	no	—
81	C₃×C₅×D₃	—	2	4	no	—
82	C₃×C₅×D₃	C₂×D₄	1	4	yes	complemented
83	C₂⁴×C₅	—	9	2	no	—
84	C₂×C₅×D₄	—	3	1	no	—
85	C₂×C₅×D₄	—	9	8	no	—
86	C₂×C₅×D₄	—	9	2	no	—
87	C₂×C₅×D₄	—	9	1	no	—
88	C₂²×C₄×C₅	—	3	1	no	—
89	C₂²×C₃⋊D₃	C₂²×C₅	1	2	yes	complemented
90	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
91	C₂²×C₃×D₃	C₂²×C₅	1	2	yes	complemented
92	C₂×D₃²	—	2	8	no	—
93	C₂×D₃²	C₂²×C₅	1	8	yes	complemented
94	C₂×C₃²×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
95	C₄⋊(C₃⋊D₃)	C₂²×C₅	1	4	yes	complemented
96	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
97	C₃×D₁₂	C₂²×C₅	1	4	yes	complemented
98	C₃×C₄×D₃	C₂²×C₅	1	4	yes	complemented
99	#626	C₂²×C₅	1	8	yes	complemented
100	C₂²×C₃×C₅	—	2	1	no	—
101	C₂²×C₃×C₅	—	3	4	no	—
102	C₂²×C₃×C₅	—	3	2	no	—
103	C₂²×C₃×C₅	—	3	4	no	—
104	C₂²×C₃×C₅	—	6	4	no	—
105	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
106	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
107	C₂×C₅×D₃	—	2	4	no	—
108	C₂×C₅×D₃	—	3	4	no	—
109	C₂×C₅×D₃	—	3	4	no	—
110	C₂×C₅×D₃	—	6	4	no	—
111	C₂×C₅×D₃	—	6	16	no	—
112	C₂×C₅×D₃	—	6	4	no	—
113	C₂×C₅×D₃	—	6	4	no	—
114	C₂×C₅×D₃	—	6	16	no	—
115	C₂×C₅×D₃	—	12	4	no	—
116	C₂×C₅×D₃	D₁₂	1	4	yes	direct product factor
117	C₂×C₅×D₃	C₂²×D₃	1	2	yes	—
118	C₂×C₅×D₃	C₂²×D₃	1	4	yes	complemented
119	C₃×C₄×C₅	—	2	2	no	—
120	C₃×C₄×C₅	—	3	2	no	—
121	C₃×C₄×C₅	C₂²×D₃	1	2	yes	complemented
122	C₃×C₄×C₅	C₂²×D₃	1	2	yes	complemented
123	C₅×Dic₃	C₂²×D₃	1	2	yes	complemented
124	C₂³×D₃	—	3	2	no	—
125	C₂³×D₃	—	3	2	no	—
126	C₂×C₃×D₄	—	3	1	no	—
127	C₂²×C₃×C₄	—	3	1	no	—
128	C₂×#67	—	3	2	no	—
129	D₃×D₄	—	3	8	no	—
130	C₂×D₁₂	—	3	2	no	—
131	C₂×D₁₂	—	3	1	no	—
132	C₂×D₁₂	—	3	1	no	—
133	C₂×D₁₂	—	3	8	no	—
134	C₂×D₁₂	—	6	1	no	—
135	C₂×D₁₂	C₅×D₃	1	1	yes	characteristic, direct product factor
136	C₂×C₄×D₃	C₅×D₃	1	1	yes	characteristic, complemented
137	C₃²×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
138	C₂³×C₅	—	3	1	no	—
139	C₂³×C₅	—	3	2	no	—
140	C₂³×C₅	—	9	8	no	—
141	C₂³×C₅	—	9	2	no	—
142	C₂³×C₅	—	18	8	no	—
143	C₅×D₄	—	3	4	no	—
144	C₅×D₄	—	9	8	no	—
145	C₅×D₄	—	9	4	no	—
146	C₂×C₄×C₅	—	3	1	no	—
147	C₂×C₄×C₅	—	3	4	no	—
148	C₂×C₄×C₅	D₃²	1	1	yes	characteristic, complemented
149	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
150	C₂×C₃⋊D₃	—	2	4	no	—
151	C₂×C₃⋊D₃	C₂³×C₅	1	4	yes	complemented
152	C₂×C₃×D₃	—	2	4	no	—
153	C₂×C₃×D₃	C₅×D₄	1	4	yes	complemented
154	C₂×C₃×D₃	C₂³×C₅	1	2	yes	—
155	C₂×C₃×D₃	C₂³×C₅	1	4	yes	complemented
156	D₃²	—	2	16	no	—
157	C₃²×C₄	C₂³×C₅	1	2	yes	complemented
158	C₃×Dic₃	C₂³×C₅	1	2	yes	complemented
159	C₂²×D₄	—	9	1	no	Sylow
160	C₂×C₃×C₅	—	2	1	no	—
161	C₂×C₃×C₅	—	2	2	no	—
162	C₂×C₃×C₅	—	3	4	no	—
163	C₂×C₃×C₅	—	6	4	no	—
164	C₂×C₃×C₅	C₂×D₁₂	1	2	yes	complemented
165	C₂×C₃×C₅	D₃×D₄	1	2	yes	complemented
166	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
167	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
168	C₅×D₃	—	2	4	no	—
169	C₅×D₃	—	6	4	no	—
170	C₅×D₃	—	6	4	no	—
171	C₅×D₃	—	12	4	no	—
172	C₅×D₃	C₂×D₁₂	1	4	yes	direct product factor
173	C₂³×C₃	—	3	1	no	—
174	C₂³×C₃	—	3	2	no	—
175	C₂²×D₃	—	3	2	no	—
176	C₂²×D₃	—	3	2	no	—
177	C₂²×D₃	—	3	8	no	—
178	C₂²×D₃	—	3	8	no	—
179	C₂²×D₃	—	6	2	no	—
180	C₂²×D₃	—	6	8	no	—
181	C₂²×D₃	—	6	8	no	—
182	C₂²×D₃	C₂×C₅×D₃	1	1	yes	characteristic
183	C₂²×D₃	C₂×C₅×D₃	1	2	yes	complemented
184	C₃×D₄	—	3	4	no	—
185	C₂×C₃×C₄	—	2	1	no	—
186	C₂×C₃×C₄	—	3	1	no	—
187	C₂×C₃×C₄	—	3	4	no	—
188	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
189	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
190	#67	—	3	8	no	—
191	C₂×Dic₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
192	D₁₂	—	3	8	no	—
193	D₁₂	—	3	4	no	—
194	D₁₂	—	3	4	no	—
195	D₁₂	—	6	4	no	—
196	D₁₂	C₂×C₅×D₃	1	4	yes	direct product factor
197	C₄×D₃	C₂×C₅×D₃	1	4	yes	complemented
198	C₂²×C₅	—	3	2	no	—
199	C₂²×C₅	—	3	4	no	—
200	C₂²×C₅	—	3	4	no	—
201	C₂²×C₅	—	6	4	no	—
202	C₂²×C₅	—	9	4	no	—
203	C₂²×C₅	—	18	16	no	—
204	C₂²×C₅	—	18	4	no	—
205	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
206	C₄×C₅	—	3	2	no	—
207	C₄×C₅	C₂×D₃²	1	2	yes	complemented
208	C₂×C₃²	C₂×C₅×D₄	1	2	yes	complemented
209	C₂×C₃²	C₂⁴×C₅	1	1	yes	characteristic
210	C₃⋊D₃	—	2	4	no	—
211	C₃×D₃	—	2	4	no	—
212	C₃×D₃	C₂×C₅×D₄	1	4	yes	complemented
213	C₂⁴	—	9	2	no	—
214	C₂×D₄	—	3	1	no	—
215	C₂×D₄	—	9	8	no	—
216	C₂×D₄	—	9	2	no	—
217	C₂×D₄	—	9	1	no	—
218	C₂²×C₄	—	3	1	no	—
219	C₃×C₅	—	2	1	no	—
220	C₃×C₅	C₂²×D₁₂	1	1	yes	characteristic, complemented
221	C₃×C₅	C₂×D₃×D₄	1	1	yes	characteristic, complemented
222	C₂²×C₃	—	2	1	no	—
223	C₂²×C₃	—	3	4	no	—
224	C₂²×C₃	—	3	2	no	—
225	C₂²×C₃	—	3	4	no	—
226	C₂²×C₃	—	6	4	no	—
227	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
228	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
229	C₂×D₃	—	2	4	no	—
230	C₂×D₃	—	3	4	no	—
231	C₂×D₃	—	3	4	no	—
232	C₂×D₃	—	6	4	no	—
233	C₂×D₃	—	6	16	no	—
234	C₂×D₃	—	6	4	no	—
235	C₂×D₃	—	6	4	no	—
236	C₂×D₃	—	6	16	no	—
237	C₂×D₃	—	12	4	no	—
238	C₂×D₃	C₅×D₁₂	1	4	yes	direct product factor
239	C₂×D₃	C₂²×C₅×D₃	1	2	yes	—
240	C₂×D₃	C₂²×C₅×D₃	1	4	yes	complemented
241	C₃×C₄	—	2	2	no	—
242	C₃×C₄	—	3	2	no	—
243	C₃×C₄	C₂²×C₅×D₃	1	2	yes	complemented
244	C₃×C₄	C₂²×C₅×D₃	1	2	yes	complemented
245	Dic₃	C₂²×C₅×D₃	1	2	yes	complemented
246	C₂×C₅	—	3	4	no	—
247	C₂×C₅	—	6	4	no	—
248	C₂×C₅	—	18	4	no	—
249	C₂×C₅	D₃×D₁₂	1	2	yes	direct product factor
250	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
251	C₃²	C₂²×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
252	C₂³	—	3	1	no	—
253	C₂³	—	3	2	no	—
254	C₂³	—	9	8	no	—
255	C₂³	—	9	2	no	—
256	C₂³	—	18	8	no	—
257	D₄	—	3	4	no	—
258	D₄	—	9	8	no	—
259	D₄	—	9	4	no	—
260	C₂×C₄	—	3	1	no	—
261	C₂×C₄	—	3	4	no	—
262	C₂×C₄	C₅×D₃²	1	1	yes	characteristic, complemented
263	C₂×C₃	—	2	1	no	—
264	C₂×C₃	—	2	2	no	—
265	C₂×C₃	—	3	4	no	—
266	C₂×C₃	—	6	4	no	—
267	C₂×C₃	C₂×C₅×D₁₂	1	2	yes	complemented
268	C₂×C₃	C₅×D₃×D₄	1	2	yes	complemented
269	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
270	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
271	D₃	—	2	4	no	—
272	D₃	—	6	4	no	—
273	D₃	—	6	4	no	—
274	D₃	—	12	4	no	—
275	D₃	C₂×C₅×D₁₂	1	4	yes	direct product factor
276	C₅	C₂×D₃×D₁₂	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²	—	3	2	no	—
278	C₂²	—	3	4	no	—
279	C₂²	—	3	4	no	—
280	C₂²	—	6	4	no	—
281	C₂²	—	9	4	no	—
282	C₂²	—	18	16	no	—
283	C₂²	—	18	4	no	—
284	C₂²	C₂×C₅×D₃²	1	1	yes	characteristic
285	C₄	—	3	2	no	—
286	C₄	C₂×C₅×D₃²	1	2	yes	complemented
287	C₃	—	2	1	no	—
288	C₃	C₂²×C₅×D₁₂	1	1	yes	characteristic, complemented
289	C₃	C₂×C₅×D₃×D₄	1	1	yes	characteristic, complemented
290	C₂	—	3	4	no	—
291	C₂	—	6	4	no	—
292	C₂	—	18	4	no	—
293	C₂	C₅×D₃×D₁₂	1	2	yes	direct product factor
294	C₂	C₂²×C₅×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃²
Fitting	C₂×C₃²×C₄×C₅	C₂²
socle	C₂²×C₃²×C₅	C₂³
hypercenter	C₂×C₄×C₅	D₃²
hypocenter	C₃²	C₂²×C₅×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃²	C₂	semidirect
2. C₂×C₅×C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₂×C₃×C₅×D₁₂	C₂	semidirect
4. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
5. C₂×C₅×#626	C₂	semidirect
6. C₅×D₃×D₁₂	C₂	direct (N × H)
9. C₂²×C₅×C₃⋊D₃	C₂²	semidirect
11. C₂²×C₃×C₅×D₃	C₂²	semidirect
13. C₂×C₅×D₃²	C₂²	semidirect
14. C₂×C₃²×C₄×C₅	C₂²	semidirect
15. C₅×C₄⋊(C₃⋊D₃)	C₂²	semidirect
16. C₂×C₃×C₅×Dic₃	C₂²	semidirect
17. C₃×C₅×D₁₂	C₂²	semidirect
18. C₃×C₄×C₅×D₃	C₂²	semidirect
19. C₅×#626	C₂²	semidirect
20. C₂×D₃×D₁₂	C₅	direct (N × H)
32. C₂×C₅×D₁₂	D₃	direct (N × H)
33. C₂×C₄×C₅×D₃	D₃	semidirect
36. C₂×C₅×C₃⋊D₃	C₂³	semidirect
38. C₂×C₃×C₅×D₃	D₄	semidirect
40. C₂×C₃×C₅×D₃	C₂³	semidirect
42. C₃²×C₄×C₅	C₂³	semidirect
43. C₃×C₅×Dic₃	C₂³	semidirect
45. C₂²×D₃²	C₂×C₅	semidirect
46. C₂×C₄⋊(C₃⋊D₃)	C₂×C₅	semidirect
47. C₂×C₃×D₁₂	C₂×C₅	semidirect
48. C₂×C₃×C₄×D₃	C₂×C₅	semidirect
49. C₂×#626	C₂×C₅	semidirect
50. D₃×D₁₂	C₂×C₅	direct (N × H)
61. C₂²×C₅×D₃	C₂×D₃	semidirect
66. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
67. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
69. C₂×C₅×Dic₃	C₂×D₃	semidirect
74. C₅×D₁₂	C₂×D₃	direct (N × H)
75. C₄×C₅×D₃	C₂×D₃	semidirect
78. C₂×C₃²×C₅	C₂×D₄	semidirect
82. C₃×C₅×D₃	C₂×D₄	semidirect
89. C₂²×C₃⋊D₃	C₂²×C₅	semidirect
91. C₂²×C₃×D₃	C₂²×C₅	semidirect
93. C₂×D₃²	C₂²×C₅	semidirect
94. C₂×C₃²×C₄	C₂²×C₅	semidirect
95. C₄⋊(C₃⋊D₃)	C₂²×C₅	semidirect
96. C₂×C₃×Dic₃	C₂²×C₅	semidirect
97. C₃×D₁₂	C₂²×C₅	semidirect
98. C₃×C₄×D₃	C₂²×C₅	semidirect
99. #626	C₂²×C₅	semidirect
116. C₂×C₅×D₃	D₁₂	direct (N × H)
118. C₂×C₅×D₃	C₂²×D₃	semidirect
121. C₃×C₄×C₅	C₂²×D₃	semidirect
122. C₃×C₄×C₅	C₂²×D₃	semidirect
123. C₅×Dic₃	C₂²×D₃	semidirect
135. C₂×D₁₂	C₅×D₃	direct (N × H)
136. C₂×C₄×D₃	C₅×D₃	semidirect
137. C₃²×C₅	C₂²×D₄	semidirect
148. C₂×C₄×C₅	D₃²	semidirect
151. C₂×C₃⋊D₃	C₂³×C₅	semidirect
153. C₂×C₃×D₃	C₅×D₄	semidirect
155. C₂×C₃×D₃	C₂³×C₅	semidirect
157. C₃²×C₄	C₂³×C₅	semidirect
158. C₃×Dic₃	C₂³×C₅	semidirect
164. C₂×C₃×C₅	C₂×D₁₂	semidirect
165. C₂×C₃×C₅	D₃×D₄	semidirect
172. C₅×D₃	C₂×D₁₂	direct (N × H)
183. C₂²×D₃	C₂×C₅×D₃	semidirect
188. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
189. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
191. C₂×Dic₃	C₂×C₅×D₃	semidirect
196. D₁₂	C₂×C₅×D₃	direct (N × H)
197. C₄×D₃	C₂×C₅×D₃	semidirect
207. C₄×C₅	C₂×D₃²	semidirect
208. C₂×C₃²	C₂×C₅×D₄	semidirect
212. C₃×D₃	C₂×C₅×D₄	semidirect
220. C₃×C₅	C₂²×D₁₂	semidirect
221. C₃×C₅	C₂×D₃×D₄	semidirect
238. C₂×D₃	C₅×D₁₂	direct (N × H)
240. C₂×D₃	C₂²×C₅×D₃	semidirect
243. C₃×C₄	C₂²×C₅×D₃	semidirect
244. C₃×C₄	C₂²×C₅×D₃	semidirect
245. Dic₃	C₂²×C₅×D₃	semidirect
249. C₂×C₅	D₃×D₁₂	direct (N × H)
251. C₃²	C₂²×C₅×D₄	semidirect
262. C₂×C₄	C₅×D₃²	semidirect
267. C₂×C₃	C₂×C₅×D₁₂	semidirect
268. C₂×C₃	C₅×D₃×D₄	semidirect
275. D₃	C₂×C₅×D₁₂	direct (N × H)
276. C₅	C₂×D₃×D₁₂	direct (N × H)
286. C₄	C₂×C₅×D₃²	semidirect
288. C₃	C₂²×C₅×D₁₂	semidirect
289. C₃	C₂×C₅×D₃×D₄	semidirect
293. C₂	C₅×D₃×D₁₂	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×C₅×D₃²	2
C₂×C₅×C₄⋊(C₃⋊D₃)	2
C₂×C₃×C₅×D₁₂	2
C₂×C₃×C₄×C₅×D₃	2
C₂×C₅×#626	2
C₅×D₃×D₁₂	2
C₂×C₅×D₃×D₄	3
C₂²×C₅×D₁₂	3
C₂×D₃×D₁₂	5

Subgroups — C2×C5×D3×D12 #13089316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×D₃×D₁₂ #13089316