Subgroups — C₅×D₃×(C₂×D₃)⋊C₄ #13087192

Order 1440.

562 conjugacy classes of subgroups.

The subgroup lattice has 366 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	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3752	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#3722	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×(C₂×D₃)⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×(C₂×D₃)⋊C₄	—	3	1	no	maximal
9	C₅×D₃×C₂²⋊C₄	—	3	1	no	maximal
10	C₂²×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₂×C₅×D₃²	—	2	2	no	—
14	C₂×C₅×D₃²	—	2	2	no	—
15	C₂×C₅×D₃²	C₄	1	4	yes	complemented
16	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₄×C₅×D₃	—	2	2	no	—
21	C₅×D₃×Dic₃	—	2	2	no	—
22	D₃×(C₂×D₃)⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂³×C₅×D₃	—	3	1	no	—
24	C₂³×C₅×D₃	—	3	1	no	—
25	C₂²×C₃×C₄×C₅	—	3	1	no	—
26	C₂²×C₅×Dic₃	—	3	1	no	—
27	C₂×C₄×C₅×D₃	—	3	1	no	—
28	C₂×C₄×C₅×D₃	D₃	1	1	yes	characteristic, complemented
29	C₃×C₅×C₂²⋊C₄	—	3	1	no	—
30	C₅×#217	—	3	1	no	—
31	C₅×(C₂×D₃)⋊C₄	—	3	1	no	—
32	C₅×(C₂×D₃)⋊C₄	—	3	1	no	—
33	C₅×(C₂×D₃)⋊C₄	—	3	1	no	—
34	C₅×(C₂×D₃)⋊C₄	—	3	1	no	—
35	C₅×(C₂×D₃)⋊C₄	—	3	1	no	—
36	C₅×(C₂×D₃)⋊C₄	—	6	1	no	—
37	C₅×(C₂×D₃)⋊C₄	D₃	1	1	yes	characteristic, direct product factor
38	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
39	C₂×C₅×C₃⋊D₃	—	2	1	no	—
40	C₂×C₅×C₃⋊D₃	—	2	1	no	—
41	C₂×C₅×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
42	C₂×C₃×C₅×D₃	—	2	1	no	—
43	C₂×C₃×C₅×D₃	—	2	1	no	—
44	C₂×C₃×C₅×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×D₃	C₂×C₄	1	2	yes	complemented
46	C₂×C₃×C₅×D₃	D₄	1	2	yes	—
47	C₂×C₃×C₅×D₃	D₄	1	2	yes	—
48	C₅×D₃²	—	2	8	no	—
49	C₃²×C₄×C₅	—	2	1	no	—
50	C₅×C₃⋊Dic₃	—	2	1	no	—
51	C₃×C₅×Dic₃	—	2	1	no	—
52	C₃×C₅×Dic₃	—	2	1	no	—
53	C₂×C₅×C₂²⋊C₄	—	9	1	no	Hall
54	C₂²×D₃²	C₂×C₅	1	1	yes	characteristic
55	C₂×C₃×C₄×D₃	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×D₃×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
57	#3752	C₂×C₅	1	1	yes	characteristic, complemented
58	C₃×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
59	#3722	C₂×C₅	1	1	yes	characteristic, complemented
60	(C₂×D₃)⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂³×C₃×C₅	—	3	1	no	—
62	C₂³×C₃×C₅	—	3	1	no	—
63	C₂²×C₅×D₃	—	3	1	no	—
64	C₂²×C₅×D₃	—	3	1	no	—
65	C₂²×C₅×D₃	—	3	4	no	—
66	C₂²×C₅×D₃	—	3	4	no	—
67	C₂²×C₅×D₃	—	6	2	no	—
68	C₂²×C₅×D₃	—	6	2	no	—
69	C₂²×C₅×D₃	—	6	2	no	—
70	C₂²×C₅×D₃	—	6	2	no	—
71	C₂²×C₅×D₃	—	6	1	no	—
72	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
73	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	—	2	1	no	—
75	C₂×C₃×C₄×C₅	—	3	1	no	—
76	C₂×C₃×C₄×C₅	—	3	1	no	—
77	C₂×C₃×C₄×C₅	—	6	2	no	—
78	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
79	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
80	C₂×C₅×Dic₃	—	3	1	no	—
81	C₂×C₅×Dic₃	—	3	1	no	—
82	C₂×C₅×Dic₃	—	6	2	no	—
83	C₂×C₅×Dic₃	—	6	1	no	—
84	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
85	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
86	C₄×C₅×D₃	—	2	2	no	—
87	C₄×C₅×D₃	—	6	2	no	—
88	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
89	D₃×C₂²⋊C₄	—	3	1	no	—
90	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
93	C₅×C₃⋊D₃	—	2	2	no	—
94	C₃×C₅×D₃	—	2	2	no	—
95	C₃×C₅×D₃	C₂²⋊C₄	1	4	yes	complemented
96	C₂⁴×C₅	—	9	1	no	—
97	C₂²×C₄×C₅	—	3	1	no	—
98	C₂²×C₄×C₅	—	9	1	no	—
99	C₅×C₂²⋊C₄	—	3	1	no	—
100	C₅×C₂²⋊C₄	—	9	1	no	—
101	C₅×C₂²⋊C₄	—	9	1	no	—
102	C₅×C₂²⋊C₄	—	9	1	no	—
103	C₂²×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
104	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
105	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
106	C₂×D₃²	—	2	2	no	—
107	C₂×D₃²	—	2	2	no	—
108	C₂×D₃²	C₄×C₅	1	4	yes	complemented
109	C₂×C₃²×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
110	C₂×C₃⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
111	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
113	C₃×C₄×D₃	—	2	2	no	—
114	D₃×Dic₃	—	2	2	no	—
115	C₂²×C₃×C₅	—	2	1	no	—
116	C₂²×C₃×C₅	—	3	2	no	—
117	C₂²×C₃×C₅	—	3	2	no	—
118	C₂²×C₃×C₅	—	3	2	no	—
119	C₂²×C₃×C₅	—	3	2	no	—
120	C₂²×C₃×C₅	—	6	1	no	—
121	C₂²×C₃×C₅	—	6	1	no	—
122	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
123	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₂×C₅×D₃	—	2	1	no	—
125	C₂×C₅×D₃	—	2	1	no	—
126	C₂×C₅×D₃	—	3	2	no	—
127	C₂×C₅×D₃	—	3	2	no	—
128	C₂×C₅×D₃	—	6	2	no	—
129	C₂×C₅×D₃	—	6	8	no	—
130	C₂×C₅×D₃	—	6	1	no	—
131	C₂×C₅×D₃	—	6	1	no	—
132	C₂×C₅×D₃	—	6	1	no	—
133	C₂×C₅×D₃	—	6	1	no	—
134	C₂×C₅×D₃	—	6	8	no	—
135	C₂×C₅×D₃	—	12	1	no	—
136	C₂×C₅×D₃	—	12	1	no	—
137	C₂×C₅×D₃	C₄×D₃	1	2	yes	—
138	C₂×C₅×D₃	C₄×D₃	1	2	yes	complemented
139	C₂×C₅×D₃	D₁₂	1	2	yes	—
140	C₂×C₅×D₃	#67	1	2	yes	—
141	C₃×C₄×C₅	—	2	1	no	—
142	C₃×C₄×C₅	—	2	1	no	—
143	C₃×C₄×C₅	—	4	1	no	—
144	C₃×C₄×C₅	—	6	1	no	—
145	C₃×C₄×C₅	—	6	1	no	—
146	C₅×Dic₃	—	2	1	no	—
147	C₅×Dic₃	—	2	1	no	—
148	C₅×Dic₃	—	6	1	no	—
149	C₅×Dic₃	—	6	1	no	—
150	C₅×Dic₃	—	12	1	no	—
151	C₂³×D₃	—	3	1	no	—
152	C₂³×D₃	—	3	1	no	—
153	C₂²×C₃×C₄	—	3	1	no	—
154	C₂²×Dic₃	—	3	1	no	—
155	C₂×C₄×D₃	—	3	1	no	—
156	C₂×C₄×D₃	C₅×D₃	1	1	yes	characteristic, complemented
157	C₃×C₂²⋊C₄	—	3	1	no	—
158	#217	—	3	1	no	—
159	(C₂×D₃)⋊C₄	—	3	1	no	—
160	(C₂×D₃)⋊C₄	—	3	1	no	—
161	(C₂×D₃)⋊C₄	—	3	1	no	—
162	(C₂×D₃)⋊C₄	—	3	1	no	—
163	(C₂×D₃)⋊C₄	—	3	1	no	—
164	(C₂×D₃)⋊C₄	—	6	1	no	—
165	(C₂×D₃)⋊C₄	C₅×D₃	1	1	yes	characteristic, direct product factor
166	C₃²×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
167	C₂³×C₅	—	3	1	no	—
168	C₂³×C₅	—	3	1	no	—
169	C₂³×C₅	—	9	4	no	—
170	C₂³×C₅	—	9	1	no	—
171	C₂³×C₅	—	18	2	no	—
172	C₂³×C₅	—	18	2	no	—
173	C₂×C₄×C₅	—	3	1	no	—
174	C₂×C₄×C₅	—	3	1	no	—
175	C₂×C₄×C₅	—	6	2	no	—
176	C₂×C₄×C₅	—	9	1	no	—
177	C₂×C₄×C₅	—	18	2	no	—
178	C₂×C₄×C₅	D₃²	1	1	yes	characteristic, complemented
179	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
180	C₂×C₃⋊D₃	—	2	1	no	—
181	C₂×C₃⋊D₃	—	2	1	no	—
182	C₂×C₃⋊D₃	C₂×C₄×C₅	1	2	yes	complemented
183	C₂×C₃×D₃	—	2	1	no	—
184	C₂×C₃×D₃	—	2	1	no	—
185	C₂×C₃×D₃	C₂×C₄×C₅	1	2	yes	—
186	C₂×C₃×D₃	C₂×C₄×C₅	1	2	yes	complemented
187	C₂×C₃×D₃	C₅×D₄	1	2	yes	—
188	C₂×C₃×D₃	C₅×D₄	1	2	yes	—
189	D₃²	—	2	8	no	—
190	C₃²×C₄	—	2	1	no	—
191	C₃⋊Dic₃	—	2	1	no	—
192	C₃×Dic₃	—	2	1	no	—
193	C₃×Dic₃	—	2	1	no	—
194	C₂×C₂²⋊C₄	—	9	1	no	Sylow
195	C₂×C₃×C₅	—	2	1	no	—
196	C₂×C₃×C₅	—	2	1	no	—
197	C₂×C₃×C₅	—	2	1	no	—
198	C₂×C₃×C₅	—	3	4	no	—
199	C₂×C₃×C₅	—	6	2	no	—
200	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
202	C₂×C₃×C₅	C₂×D₁₂	1	1	yes	characteristic
203	C₂×C₃×C₅	D₃×D₄	1	1	yes	characteristic
204	C₂×C₃×C₅	D₃×D₄	1	1	yes	characteristic
205	C₂×C₃×C₅	C₂×#67	1	1	yes	characteristic
206	C₅×D₃	—	2	2	no	—
207	C₅×D₃	—	6	2	no	—
208	C₅×D₃	—	6	2	no	—
209	C₅×D₃	—	12	2	no	—
210	C₅×D₃	(C₂×D₃)⋊C₄	1	4	yes	direct product factor
211	C₂³×C₃	—	3	1	no	—
212	C₂³×C₃	—	3	1	no	—
213	C₂²×D₃	—	3	1	no	—
214	C₂²×D₃	—	3	1	no	—
215	C₂²×D₃	—	3	4	no	—
216	C₂²×D₃	—	3	4	no	—
217	C₂²×D₃	—	6	1	no	—
218	C₂²×D₃	—	6	2	no	—
219	C₂²×D₃	—	6	2	no	—
220	C₂²×D₃	—	6	2	no	—
221	C₂²×D₃	—	6	2	no	—
222	C₂²×D₃	C₂×C₅×D₃	1	1	yes	characteristic
223	C₂²×D₃	C₂×C₅×D₃	1	1	yes	characteristic
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	3	1	no	—
226	C₂×C₃×C₄	—	3	1	no	—
227	C₂×C₃×C₄	—	6	2	no	—
228	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
229	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
230	C₂×Dic₃	—	3	1	no	—
231	C₂×Dic₃	—	3	1	no	—
232	C₂×Dic₃	—	6	1	no	—
233	C₂×Dic₃	—	6	2	no	—
234	C₂×Dic₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
235	C₂×Dic₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
236	C₄×D₃	—	2	2	no	—
237	C₄×D₃	—	6	2	no	—
238	C₂²×C₅	—	3	2	no	—
239	C₂²×C₅	—	3	2	no	—
240	C₂²×C₅	—	3	2	no	—
241	C₂²×C₅	—	3	2	no	—
242	C₂²×C₅	—	6	1	no	—
243	C₂²×C₅	—	6	1	no	—
244	C₂²×C₅	—	9	2	no	—
245	C₂²×C₅	—	18	8	no	—
246	C₂²×C₅	—	18	1	no	—
247	C₂²×C₅	—	18	1	no	—
248	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
249	C₄×C₅	—	2	1	no	—
250	C₄×C₅	—	6	1	no	—
251	C₄×C₅	—	6	1	no	—
252	C₄×C₅	—	18	1	no	—
253	C₂×C₃²	C₂²×C₄×C₅	1	1	yes	characteristic
254	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
256	C₃⋊D₃	—	2	2	no	—
257	C₃×D₃	—	2	2	no	—
258	C₃×D₃	C₅×C₂²⋊C₄	1	4	yes	complemented
259	C₂⁴	—	9	1	no	—
260	C₂²×C₄	—	3	1	no	—
261	C₂²×C₄	—	9	1	no	—
262	C₂²⋊C₄	—	3	1	no	—
263	C₂²⋊C₄	—	9	1	no	—
264	C₂²⋊C₄	—	9	1	no	—
265	C₂²⋊C₄	—	9	1	no	—
266	C₃×C₅	—	2	1	no	—
267	C₃×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
268	C₃×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic, complemented
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	3	2	no	—
271	C₂²×C₃	—	3	2	no	—
272	C₂²×C₃	—	3	2	no	—
273	C₂²×C₃	—	3	2	no	—
274	C₂²×C₃	—	6	1	no	—
275	C₂²×C₃	—	6	1	no	—
276	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
277	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
278	C₂×D₃	—	2	1	no	—
279	C₂×D₃	—	2	1	no	—
280	C₂×D₃	—	3	2	no	—
281	C₂×D₃	—	3	2	no	—
282	C₂×D₃	—	6	2	no	—
283	C₂×D₃	—	6	8	no	—
284	C₂×D₃	—	6	1	no	—
285	C₂×D₃	—	6	1	no	—
286	C₂×D₃	—	6	1	no	—
287	C₂×D₃	—	6	1	no	—
288	C₂×D₃	—	6	8	no	—
289	C₂×D₃	—	12	1	no	—
290	C₂×D₃	—	12	1	no	—
291	C₂×D₃	C₄×C₅×D₃	1	2	yes	—
292	C₂×D₃	C₄×C₅×D₃	1	2	yes	complemented
293	C₂×D₃	C₅×D₁₂	1	2	yes	—
294	C₂×D₃	C₅×#67	1	2	yes	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	4	1	no	—
298	C₃×C₄	—	6	1	no	—
299	C₃×C₄	—	6	1	no	—
300	Dic₃	—	2	1	no	—
301	Dic₃	—	2	1	no	—
302	Dic₃	—	6	1	no	—
303	Dic₃	—	6	1	no	—
304	Dic₃	—	12	1	no	—
305	C₂×C₅	—	3	4	no	—
306	C₂×C₅	—	6	2	no	—
307	C₂×C₅	—	18	2	no	—
308	C₂×C₅	C₄×D₃²	1	1	yes	characteristic
309	C₂×C₅	D₃×D₁₂	1	1	yes	characteristic
310	C₂×C₅	D₃×#67	1	1	yes	characteristic
311	C₃²	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
312	C₂³	—	3	1	no	—
313	C₂³	—	3	1	no	—
314	C₂³	—	9	4	no	—
315	C₂³	—	9	1	no	—
316	C₂³	—	18	2	no	—
317	C₂³	—	18	2	no	—
318	C₂×C₄	—	3	1	no	—
319	C₂×C₄	—	3	1	no	—
320	C₂×C₄	—	6	2	no	—
321	C₂×C₄	—	9	1	no	—
322	C₂×C₄	—	18	2	no	—
323	C₂×C₄	C₅×D₃²	1	1	yes	characteristic, complemented
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	3	4	no	—
328	C₂×C₃	—	6	2	no	—
329	C₂×C₃	C₂×C₄×C₅×D₃	1	1	yes	characteristic
330	C₂×C₃	C₂×C₄×C₅×D₃	1	1	yes	characteristic
331	C₂×C₃	C₂×C₅×D₁₂	1	1	yes	characteristic
332	C₂×C₃	C₅×D₃×D₄	1	1	yes	characteristic
333	C₂×C₃	C₅×D₃×D₄	1	1	yes	characteristic
334	C₂×C₃	C₂×C₅×#67	1	1	yes	characteristic
335	D₃	—	2	2	no	—
336	D₃	—	6	2	no	—
337	D₃	—	6	2	no	—
338	D₃	—	12	2	no	—
339	D₃	C₅×(C₂×D₃)⋊C₄	1	4	yes	direct product factor
340	C₅	D₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
341	C₂²	—	3	2	no	—
342	C₂²	—	3	2	no	—
343	C₂²	—	3	2	no	—
344	C₂²	—	3	2	no	—
345	C₂²	—	6	1	no	—
346	C₂²	—	6	1	no	—
347	C₂²	—	9	2	no	—
348	C₂²	—	18	8	no	—
349	C₂²	—	18	1	no	—
350	C₂²	—	18	1	no	—
351	C₂²	C₂×C₅×D₃²	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	6	1	no	—
354	C₄	—	6	1	no	—
355	C₄	—	18	1	no	—
356	C₃	—	2	1	no	—
357	C₃	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
358	C₃	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic, complemented
359	C₂	—	3	4	no	—
360	C₂	—	6	2	no	—
361	C₂	—	18	2	no	—
362	C₂	C₄×C₅×D₃²	1	1	yes	characteristic
363	C₂	C₅×D₃×D₁₂	1	1	yes	characteristic
364	C₂	C₅×D₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃²
commutator	C₂×C₃²	C₂²×C₄×C₅
Frattini	C₂²	C₂×C₅×D₃²
Fitting	C₂×C₃²×C₄×C₅	C₂²
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂²×C₅×D₃²	C₂
cosocle	C₂²×C₃²	C₂³×C₅
hypercenter	C₂×C₄×C₅	D₃²
hypocenter	C₃²	C₂×C₅×C₂²⋊C₄
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
2. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
3. C₂×C₅×D₃×Dic₃	C₂	semidirect
4. C₅×#3752	C₂	semidirect
5. C₃×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₅×#3722	C₂	semidirect
7. C₅×(C₂×D₃)⋊Dic₃	C₂	semidirect
15. C₂×C₅×D₃²	C₄	semidirect
16. C₂×C₃²×C₄×C₅	C₂²	semidirect
17. C₂×C₅×C₃⋊Dic₃	C₂²	semidirect
18. C₂×C₃×C₅×Dic₃	C₂²	semidirect
19. C₂×C₃×C₅×Dic₃	C₂²	semidirect
22. D₃×(C₂×D₃)⋊C₄	C₅	direct (N × H)
28. C₂×C₄×C₅×D₃	D₃	semidirect
37. C₅×(C₂×D₃)⋊C₄	D₃	direct (N × H)
41. C₂×C₅×C₃⋊D₃	C₂×C₄	semidirect
45. C₂×C₃×C₅×D₃	C₂×C₄	semidirect
55. C₂×C₃×C₄×D₃	C₂×C₅	semidirect
56. C₂×D₃×Dic₃	C₂×C₅	semidirect
57. #3752	C₂×C₅	semidirect
58. C₃×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
59. #3722	C₂×C₅	semidirect
60. (C₂×D₃)⋊Dic₃	C₂×C₅	semidirect
78. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
79. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
84. C₂×C₅×Dic₃	C₂×D₃	semidirect
85. C₂×C₅×Dic₃	C₂×D₃	semidirect
95. C₃×C₅×D₃	C₂²⋊C₄	semidirect
108. C₂×D₃²	C₄×C₅	semidirect
109. C₂×C₃²×C₄	C₂²×C₅	semidirect
110. C₂×C₃⋊Dic₃	C₂²×C₅	semidirect
111. C₂×C₃×Dic₃	C₂²×C₅	semidirect
112. C₂×C₃×Dic₃	C₂²×C₅	semidirect
138. C₂×C₅×D₃	C₄×D₃	semidirect
156. C₂×C₄×D₃	C₅×D₃	semidirect
165. (C₂×D₃)⋊C₄	C₅×D₃	direct (N × H)
166. C₃²×C₅	C₂×C₂²⋊C₄	semidirect
178. C₂×C₄×C₅	D₃²	semidirect
182. C₂×C₃⋊D₃	C₂×C₄×C₅	semidirect
186. C₂×C₃×D₃	C₂×C₄×C₅	semidirect
210. C₅×D₃	(C₂×D₃)⋊C₄	direct (N × H)
228. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
229. C₂×C₃×C₄	C₂×C₅×D₃	semidirect
234. C₂×Dic₃	C₂×C₅×D₃	semidirect
235. C₂×Dic₃	C₂×C₅×D₃	semidirect
258. C₃×D₃	C₅×C₂²⋊C₄	semidirect
267. C₃×C₅	D₃×C₂²⋊C₄	semidirect
268. C₃×C₅	C₂×(C₂×D₃)⋊C₄	semidirect
292. C₂×D₃	C₄×C₅×D₃	semidirect
311. C₃²	C₂×C₅×C₂²⋊C₄	semidirect
323. C₂×C₄	C₅×D₃²	semidirect
339. D₃	C₅×(C₂×D₃)⋊C₄	direct (N × H)
340. C₅	D₃×(C₂×D₃)⋊C₄	direct (N × H)
357. C₃	C₅×D₃×C₂²⋊C₄	semidirect
358. C₃	C₂×C₅×(C₂×D₃)⋊C₄	semidirect

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×C₃×C₄×C₅×D₃	2
C₂×C₅×D₃×Dic₃	2
C₅×#3752	2
C₃×C₅×(C₂×D₃)⋊C₄	2
C₅×#3722	2
C₅×(C₂×D₃)⋊Dic₃	2
C₂×C₅×(C₂×D₃)⋊C₄	3
C₅×D₃×C₂²⋊C₄	3
D₃×(C₂×D₃)⋊C₄	5

Subgroups — C5×D3×(C2×D3)⋊C4 #13087192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×(C₂×D₃)⋊C₄ #13087192