Subgroups — C₅×D₃²×D₄ #13089323

Order 1440.

998 conjugacy classes of subgroups.

The subgroup lattice has 344 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	C₅×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃×D₄	C₂	1	2	yes	maximal, complemented
4	C₅×#3811	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×#67	C₂	1	4	yes	maximal, complemented
6	C₅×#3802	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₃×D₁₂	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×D₃²	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×D₃×D₄	—	3	2	no	maximal
10	C₂²×C₅×C₃⋊D₃	C₂²	1	2	yes	complemented
11	C₂²×C₃×C₅×D₃	C₂²	1	4	yes	complemented
12	C₂×C₅×D₃²	—	2	8	no	—
13	C₂×C₅×D₃²	C₂²	1	1	yes	characteristic
14	C₂×C₅×D₃²	C₂²	1	4	yes	complemented
15	C₂×C₅×D₃²	C₂²	1	2	yes	complemented
16	C₃²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₅×#638	C₂²	1	2	yes	complemented
18	C₅×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
19	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#67	C₂²	1	4	yes	complemented
21	C₃×C₅×D₁₂	C₂²	1	2	yes	complemented
22	C₃×C₄×C₅×D₃	C₂²	1	2	yes	complemented
23	C₅×#626	C₂²	1	4	yes	complemented
24	C₅×#625	C₂²	1	2	yes	complemented
25	C₅×#624	C₂²	1	1	yes	characteristic, complemented
26	C₅×D₃×Dic₃	C₂²	1	2	yes	complemented
27	D₃²×D₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂³×C₅×D₃	—	3	4	no	—
29	C₂×C₃×C₅×D₄	—	3	2	no	—
30	C₂×C₅×#67	—	3	4	no	—
31	C₅×D₃×D₄	—	3	4	no	—
32	C₅×D₃×D₄	—	3	2	no	—
33	C₅×D₃×D₄	—	3	4	no	—
34	C₅×D₃×D₄	—	3	2	no	—
35	C₅×D₃×D₄	—	3	2	no	—
36	C₅×D₃×D₄	—	6	1	no	—
37	C₅×D₃×D₄	D₃	1	2	yes	direct product factor
38	C₂×C₅×D₁₂	—	3	2	no	—
39	C₂×C₄×C₅×D₃	—	3	2	no	—
40	C₂²×C₃²×C₅	C₂³	1	2	yes	complemented
41	C₂×C₅×C₃⋊D₃	—	2	4	no	—
42	C₂×C₅×C₃⋊D₃	C₂³	1	1	yes	characteristic
43	C₂×C₅×C₃⋊D₃	C₂³	1	2	yes	complemented
44	C₂×C₃×C₅×D₃	—	2	8	no	—
45	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₃	C₂³	1	4	yes	complemented
47	C₅×D₃²	—	2	4	no	—
48	C₅×D₃²	—	2	8	no	—
49	C₅×D₃²	D₄	1	4	yes	direct product factor
50	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic, complemented
51	C₅×C₃⋊Dic₃	C₂³	1	1	yes	characteristic, complemented
52	C₃×C₅×Dic₃	C₂³	1	2	yes	complemented
53	C₂²×C₅×D₄	—	9	1	no	Hall
54	C₂²×D₃²	C₂×C₅	1	2	yes	complemented
55	D₄×C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
56	C₃×D₃×D₄	C₂×C₅	1	2	yes	complemented
57	#3811	C₂×C₅	1	2	yes	complemented
58	D₃×#67	C₂×C₅	1	4	yes	complemented
59	#3802	C₂×C₅	1	1	yes	characteristic, complemented
60	D₃×D₁₂	C₂×C₅	1	2	yes	complemented
61	C₄×D₃²	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂³×C₃×C₅	—	3	4	no	—
63	C₂²×C₅×D₃	—	3	2	no	—
64	C₂²×C₅×D₃	—	3	4	no	—
65	C₂²×C₅×D₃	—	3	4	no	—
66	C₂²×C₅×D₃	—	3	4	no	—
67	C₂²×C₅×D₃	—	3	4	no	—
68	C₂²×C₅×D₃	—	6	16	no	—
69	C₂²×C₅×D₃	—	6	2	no	—
70	C₂²×C₅×D₃	C₂×D₃	1	4	yes	complemented
71	C₃×C₅×D₄	—	2	1	no	—
72	C₃×C₅×D₄	—	3	4	no	—
73	C₃×C₅×D₄	—	3	2	no	—
74	C₃×C₅×D₄	C₂×D₃	1	2	yes	complemented
75	C₂×C₃×C₄×C₅	—	3	2	no	—
76	C₅×#67	—	3	4	no	—
77	C₅×#67	—	3	4	no	—
78	C₅×#67	—	3	4	no	—
79	C₅×#67	—	6	2	no	—
80	C₅×#67	C₂×D₃	1	4	yes	complemented
81	C₂×C₅×Dic₃	—	3	2	no	—
82	C₅×D₁₂	—	3	4	no	—
83	C₅×D₁₂	—	3	2	no	—
84	C₅×D₁₂	—	6	1	no	—
85	C₅×D₁₂	C₂×D₃	1	2	yes	complemented
86	C₄×C₅×D₃	—	3	2	no	—
87	C₄×C₅×D₃	—	3	2	no	—
88	C₄×C₅×D₃	—	3	2	no	—
89	C₄×C₅×D₃	—	6	1	no	—
90	C₄×C₅×D₃	C₂×D₃	1	2	yes	complemented
91	C₂×D₃×D₄	—	3	2	no	—
92	C₂×C₃²×C₅	—	2	2	no	—
93	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
94	C₅×C₃⋊D₃	—	2	2	no	—
95	C₅×C₃⋊D₃	C₂×D₄	1	2	yes	complemented
96	C₃×C₅×D₃	—	2	4	no	—
97	C₃×C₅×D₃	C₂×D₄	1	4	yes	complemented
98	C₂⁴×C₅	—	9	2	no	—
99	C₂×C₅×D₄	—	3	2	no	—
100	C₂×C₅×D₄	—	9	2	no	—
101	C₂×C₅×D₄	—	9	2	no	—
102	C₂×C₅×D₄	—	9	1	no	—
103	C₂×C₅×D₄	—	9	4	no	—
104	C₂×C₅×D₄	—	9	1	no	—
105	C₂²×C₄×C₅	—	9	1	no	—
106	C₂²×C₃⋊D₃	C₂²×C₅	1	2	yes	complemented
107	C₂²×C₃×D₃	C₂²×C₅	1	4	yes	complemented
108	C₂×D₃²	—	2	8	no	—
109	C₂×D₃²	C₂²×C₅	1	1	yes	characteristic
110	C₂×D₃²	C₂²×C₅	1	4	yes	complemented
111	C₂×D₃²	C₂²×C₅	1	2	yes	complemented
112	C₃²×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
113	#638	C₂²×C₅	1	2	yes	complemented
114	C₄⋊(C₃⋊D₃)	C₂²×C₅	1	1	yes	characteristic, complemented
115	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic, complemented
116	C₃×#67	C₂²×C₅	1	4	yes	complemented
117	C₃×D₁₂	C₂²×C₅	1	2	yes	complemented
118	C₃×C₄×D₃	C₂²×C₅	1	2	yes	complemented
119	#626	C₂²×C₅	1	4	yes	complemented
120	#625	C₂²×C₅	1	2	yes	complemented
121	#624	C₂²×C₅	1	1	yes	characteristic, complemented
122	D₃×Dic₃	C₂²×C₅	1	2	yes	complemented
123	C₂²×C₃×C₅	—	2	2	no	—
124	C₂²×C₃×C₅	—	3	2	no	—
125	C₂²×C₃×C₅	—	3	4	no	—
126	C₂²×C₃×C₅	—	6	8	no	—
127	C₂²×C₃×C₅	C₂²×D₃	1	4	yes	complemented
128	C₂×C₅×D₃	—	2	8	no	—
129	C₂×C₅×D₃	—	3	2	no	—
130	C₂×C₅×D₃	—	3	8	no	—
131	C₂×C₅×D₃	—	3	4	no	—
132	C₂×C₅×D₃	—	6	1	no	—
133	C₂×C₅×D₃	—	6	2	no	—
134	C₂×C₅×D₃	—	6	8	no	—
135	C₂×C₅×D₃	—	6	8	no	—
136	C₂×C₅×D₃	—	6	8	no	—
137	C₂×C₅×D₃	—	6	8	no	—
138	C₂×C₅×D₃	—	12	4	no	—
139	C₂×C₅×D₃	C₂²×D₃	1	2	yes	—
140	C₂×C₅×D₃	C₂²×D₃	1	4	yes	complemented
141	C₃×C₄×C₅	—	2	1	no	—
142	C₃×C₄×C₅	—	3	2	no	—
143	C₃×C₄×C₅	C₂²×D₃	1	2	yes	complemented
144	C₅×Dic₃	—	3	2	no	—
145	C₅×Dic₃	—	6	1	no	—
146	C₅×Dic₃	C₂²×D₃	1	2	yes	complemented
147	C₂³×D₃	—	3	4	no	—
148	C₂×C₃×D₄	—	3	2	no	—
149	C₂×#67	—	3	4	no	—
150	D₃×D₄	—	3	4	no	—
151	D₃×D₄	—	3	2	no	—
152	D₃×D₄	—	3	4	no	—
153	D₃×D₄	—	3	2	no	—
154	D₃×D₄	—	3	2	no	—
155	D₃×D₄	—	6	1	no	—
156	D₃×D₄	C₅×D₃	1	2	yes	direct product factor
157	C₂×D₁₂	—	3	2	no	—
158	C₂×C₄×D₃	—	3	2	no	—
159	C₃²×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
160	C₂³×C₅	—	3	4	no	—
161	C₂³×C₅	—	9	1	no	—
162	C₂³×C₅	—	9	4	no	—
163	C₂³×C₅	—	9	2	no	—
164	C₂³×C₅	—	9	2	no	—
165	C₂³×C₅	—	18	8	no	—
166	C₅×D₄	—	3	4	no	—
167	C₅×D₄	—	3	2	no	—
168	C₅×D₄	—	9	4	no	—
169	C₅×D₄	—	9	2	no	—
170	C₅×D₄	—	9	2	no	—
171	C₅×D₄	—	9	1	no	—
172	C₅×D₄	D₃²	1	1	yes	characteristic, direct product factor
173	C₂×C₄×C₅	—	3	2	no	—
174	C₂×C₄×C₅	—	9	1	no	—
175	C₂×C₄×C₅	—	9	2	no	—
176	C₂×C₄×C₅	—	9	1	no	—
177	C₂²×C₃²	C₂³×C₅	1	2	yes	complemented
178	C₂×C₃⋊D₃	—	2	4	no	—
179	C₂×C₃⋊D₃	C₂³×C₅	1	1	yes	characteristic
180	C₂×C₃⋊D₃	C₂³×C₅	1	2	yes	complemented
181	C₂×C₃×D₃	—	2	8	no	—
182	C₂×C₃×D₃	C₂³×C₅	1	2	yes	—
183	C₂×C₃×D₃	C₂³×C₅	1	4	yes	complemented
184	D₃²	—	2	4	no	—
185	D₃²	—	2	8	no	—
186	D₃²	C₅×D₄	1	4	yes	direct product factor
187	C₃²×C₄	C₂³×C₅	1	1	yes	characteristic, complemented
188	C₃⋊Dic₃	C₂³×C₅	1	1	yes	characteristic, complemented
189	C₃×Dic₃	C₂³×C₅	1	2	yes	complemented
190	C₂²×D₄	—	9	1	no	Sylow
191	C₂×C₃×C₅	—	2	4	no	—
192	C₂×C₃×C₅	—	2	1	no	—
193	C₂×C₃×C₅	—	3	4	no	—
194	C₂×C₃×C₅	—	4	2	no	—
195	C₂×C₃×C₅	—	6	4	no	—
196	C₂×C₃×C₅	C₂³×D₃	1	2	yes	—
197	C₅×D₃	—	2	4	no	—
198	C₅×D₃	—	3	4	no	—
199	C₅×D₃	—	6	2	no	—
200	C₅×D₃	—	6	4	no	—
201	C₅×D₃	—	12	2	no	—
202	C₅×D₃	D₃×D₄	1	4	yes	direct product factor
203	C₂³×C₃	—	3	4	no	—
204	C₂²×D₃	—	3	2	no	—
205	C₂²×D₃	—	3	4	no	—
206	C₂²×D₃	—	3	4	no	—
207	C₂²×D₃	—	3	4	no	—
208	C₂²×D₃	—	3	4	no	—
209	C₂²×D₃	—	6	2	no	—
210	C₂²×D₃	—	6	16	no	—
211	C₂²×D₃	C₂×C₅×D₃	1	4	yes	complemented
212	C₃×D₄	—	2	1	no	—
213	C₃×D₄	—	3	4	no	—
214	C₃×D₄	—	3	2	no	—
215	C₃×D₄	C₂×C₅×D₃	1	2	yes	complemented
216	C₂×C₃×C₄	—	3	2	no	—
217	#67	—	3	4	no	—
218	#67	—	3	4	no	—
219	#67	—	3	4	no	—
220	#67	—	6	2	no	—
221	#67	C₂×C₅×D₃	1	4	yes	complemented
222	C₂×Dic₃	—	3	2	no	—
223	D₁₂	—	3	4	no	—
224	D₁₂	—	3	2	no	—
225	D₁₂	—	6	1	no	—
226	D₁₂	C₂×C₅×D₃	1	2	yes	complemented
227	C₄×D₃	—	3	2	no	—
228	C₄×D₃	—	3	2	no	—
229	C₄×D₃	—	3	2	no	—
230	C₄×D₃	—	6	1	no	—
231	C₄×D₃	C₂×C₅×D₃	1	2	yes	complemented
232	C₂²×C₅	—	3	2	no	—
233	C₂²×C₅	—	3	4	no	—
234	C₂²×C₅	—	6	8	no	—
235	C₂²×C₅	—	9	4	no	—
236	C₂²×C₅	—	9	1	no	—
237	C₂²×C₅	—	9	2	no	—
238	C₂²×C₅	—	18	4	no	—
239	C₂²×C₅	—	18	8	no	—
240	C₂²×C₅	—	18	4	no	—
241	C₂²×C₅	C₂×D₃²	1	2	yes	complemented
242	C₄×C₅	—	3	2	no	—
243	C₄×C₅	—	9	1	no	—
244	C₄×C₅	C₂×D₃²	1	1	yes	characteristic, complemented
245	C₂×C₃²	—	2	2	no	—
246	C₂×C₃²	C₂⁴×C₅	1	1	yes	characteristic
247	C₃⋊D₃	—	2	2	no	—
248	C₃⋊D₃	C₂×C₅×D₄	1	2	yes	complemented
249	C₃×D₃	—	2	4	no	—
250	C₃×D₃	C₂×C₅×D₄	1	4	yes	complemented
251	C₂⁴	—	9	2	no	—
252	C₂×D₄	—	3	2	no	—
253	C₂×D₄	—	9	2	no	—
254	C₂×D₄	—	9	2	no	—
255	C₂×D₄	—	9	1	no	—
256	C₂×D₄	—	9	4	no	—
257	C₂×D₄	—	9	1	no	—
258	C₂²×C₄	—	9	1	no	—
259	C₃×C₅	—	2	1	no	—
260	C₃×C₅	C₂×D₃×D₄	1	2	yes	complemented
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	3	2	no	—
263	C₂²×C₃	—	3	4	no	—
264	C₂²×C₃	—	6	8	no	—
265	C₂²×C₃	C₂²×C₅×D₃	1	4	yes	complemented
266	C₂×D₃	—	2	8	no	—
267	C₂×D₃	—	3	2	no	—
268	C₂×D₃	—	3	8	no	—
269	C₂×D₃	—	3	4	no	—
270	C₂×D₃	—	6	1	no	—
271	C₂×D₃	—	6	2	no	—
272	C₂×D₃	—	6	8	no	—
273	C₂×D₃	—	6	8	no	—
274	C₂×D₃	—	6	8	no	—
275	C₂×D₃	—	6	8	no	—
276	C₂×D₃	—	12	4	no	—
277	C₂×D₃	C₂²×C₅×D₃	1	2	yes	—
278	C₂×D₃	C₂²×C₅×D₃	1	4	yes	complemented
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	3	2	no	—
281	C₃×C₄	C₂²×C₅×D₃	1	2	yes	complemented
282	Dic₃	—	3	2	no	—
283	Dic₃	—	6	1	no	—
284	Dic₃	C₂²×C₅×D₃	1	2	yes	complemented
285	C₂×C₅	—	2	2	no	—
286	C₂×C₅	—	3	4	no	—
287	C₂×C₅	—	6	4	no	—
288	C₂×C₅	—	9	2	no	—
289	C₂×C₅	—	18	2	no	—
290	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
291	C₃²	C₂²×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
292	C₂³	—	3	4	no	—
293	C₂³	—	9	1	no	—
294	C₂³	—	9	4	no	—
295	C₂³	—	9	2	no	—
296	C₂³	—	9	2	no	—
297	C₂³	—	18	8	no	—
298	D₄	—	3	4	no	—
299	D₄	—	3	2	no	—
300	D₄	—	9	4	no	—
301	D₄	—	9	2	no	—
302	D₄	—	9	2	no	—
303	D₄	—	9	1	no	—
304	D₄	C₅×D₃²	1	1	yes	characteristic, direct product factor
305	C₂×C₄	—	3	2	no	—
306	C₂×C₄	—	9	1	no	—
307	C₂×C₄	—	9	2	no	—
308	C₂×C₄	—	9	1	no	—
309	C₂×C₃	—	2	4	no	—
310	C₂×C₃	—	2	1	no	—
311	C₂×C₃	—	3	4	no	—
312	C₂×C₃	—	4	2	no	—
313	C₂×C₃	—	6	4	no	—
314	C₂×C₃	C₂³×C₅×D₃	1	2	yes	—
315	D₃	—	2	4	no	—
316	D₃	—	3	4	no	—
317	D₃	—	6	2	no	—
318	D₃	—	6	4	no	—
319	D₃	—	12	2	no	—
320	D₃	C₅×D₃×D₄	1	4	yes	direct product factor
321	C₅	D₃²×D₄	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	—	3	2	no	—
323	C₂²	—	3	4	no	—
324	C₂²	—	6	8	no	—
325	C₂²	—	9	4	no	—
326	C₂²	—	9	1	no	—
327	C₂²	—	9	2	no	—
328	C₂²	—	18	4	no	—
329	C₂²	—	18	8	no	—
330	C₂²	—	18	4	no	—
331	C₂²	C₂×C₅×D₃²	1	2	yes	complemented
332	C₄	—	3	2	no	—
333	C₄	—	9	1	no	—
334	C₄	C₂×C₅×D₃²	1	1	yes	characteristic, complemented
335	C₃	—	2	1	no	—
336	C₃	C₂×C₅×D₃×D₄	1	2	yes	complemented
337	C₂	—	2	2	no	—
338	C₂	—	3	4	no	—
339	C₂	—	6	4	no	—
340	C₂	—	9	2	no	—
341	C₂	—	18	2	no	—
342	C₂	C₂²×C₅×D₃²	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃²	C₂	semidirect
2. C₅×D₄×C₃⋊D₃	C₂	semidirect
3. C₃×C₅×D₃×D₄	C₂	semidirect
4. C₅×#3811	C₂	semidirect
5. C₅×D₃×#67	C₂	semidirect
6. C₅×#3802	C₂	semidirect
7. C₅×D₃×D₁₂	C₂	semidirect
8. C₄×C₅×D₃²	C₂	semidirect
10. C₂²×C₅×C₃⋊D₃	C₂²	semidirect
11. C₂²×C₃×C₅×D₃	C₂²	semidirect
14. C₂×C₅×D₃²	C₂²	semidirect
15. C₂×C₅×D₃²	C₂²	semidirect
16. C₃²×C₅×D₄	C₂²	semidirect
17. C₅×#638	C₂²	semidirect
18. C₅×C₄⋊(C₃⋊D₃)	C₂²	semidirect
19. C₄×C₅×C₃⋊D₃	C₂²	semidirect
20. C₃×C₅×#67	C₂²	semidirect
21. C₃×C₅×D₁₂	C₂²	semidirect
22. C₃×C₄×C₅×D₃	C₂²	semidirect
23. C₅×#626	C₂²	semidirect
24. C₅×#625	C₂²	semidirect
25. C₅×#624	C₂²	semidirect
26. C₅×D₃×Dic₃	C₂²	semidirect
27. D₃²×D₄	C₅	direct (N × H)
37. C₅×D₃×D₄	D₃	direct (N × H)
40. C₂²×C₃²×C₅	C₂³	semidirect
43. C₂×C₅×C₃⋊D₃	C₂³	semidirect
46. C₂×C₃×C₅×D₃	C₂³	semidirect
49. C₅×D₃²	D₄	direct (N × H)
50. C₃²×C₄×C₅	C₂³	semidirect
51. C₅×C₃⋊Dic₃	C₂³	semidirect
52. C₃×C₅×Dic₃	C₂³	semidirect
54. C₂²×D₃²	C₂×C₅	semidirect
55. D₄×C₃⋊D₃	C₂×C₅	semidirect
56. C₃×D₃×D₄	C₂×C₅	semidirect
57. #3811	C₂×C₅	semidirect
58. D₃×#67	C₂×C₅	semidirect
59. #3802	C₂×C₅	semidirect
60. D₃×D₁₂	C₂×C₅	semidirect
61. C₄×D₃²	C₂×C₅	semidirect
70. C₂²×C₅×D₃	C₂×D₃	semidirect
74. C₃×C₅×D₄	C₂×D₃	semidirect
80. C₅×#67	C₂×D₃	semidirect
85. C₅×D₁₂	C₂×D₃	semidirect
90. C₄×C₅×D₃	C₂×D₃	semidirect
95. C₅×C₃⋊D₃	C₂×D₄	semidirect
97. C₃×C₅×D₃	C₂×D₄	semidirect
106. C₂²×C₃⋊D₃	C₂²×C₅	semidirect
107. C₂²×C₃×D₃	C₂²×C₅	semidirect
110. C₂×D₃²	C₂²×C₅	semidirect
111. C₂×D₃²	C₂²×C₅	semidirect
112. C₃²×D₄	C₂²×C₅	semidirect
113. #638	C₂²×C₅	semidirect
114. C₄⋊(C₃⋊D₃)	C₂²×C₅	semidirect
115. C₄×C₃⋊D₃	C₂²×C₅	semidirect
116. C₃×#67	C₂²×C₅	semidirect
117. C₃×D₁₂	C₂²×C₅	semidirect
118. C₃×C₄×D₃	C₂²×C₅	semidirect
119. #626	C₂²×C₅	semidirect
120. #625	C₂²×C₅	semidirect
121. #624	C₂²×C₅	semidirect
122. D₃×Dic₃	C₂²×C₅	semidirect
127. C₂²×C₃×C₅	C₂²×D₃	semidirect
140. C₂×C₅×D₃	C₂²×D₃	semidirect
143. C₃×C₄×C₅	C₂²×D₃	semidirect
146. C₅×Dic₃	C₂²×D₃	semidirect
156. D₃×D₄	C₅×D₃	direct (N × H)
159. C₃²×C₅	C₂²×D₄	semidirect
172. C₅×D₄	D₃²	direct (N × H)
177. C₂²×C₃²	C₂³×C₅	semidirect
180. C₂×C₃⋊D₃	C₂³×C₅	semidirect
183. C₂×C₃×D₃	C₂³×C₅	semidirect
186. D₃²	C₅×D₄	direct (N × H)
187. C₃²×C₄	C₂³×C₅	semidirect
188. C₃⋊Dic₃	C₂³×C₅	semidirect
189. C₃×Dic₃	C₂³×C₅	semidirect
202. C₅×D₃	D₃×D₄	direct (N × H)
211. C₂²×D₃	C₂×C₅×D₃	semidirect
215. C₃×D₄	C₂×C₅×D₃	semidirect
221. #67	C₂×C₅×D₃	semidirect
226. D₁₂	C₂×C₅×D₃	semidirect
231. C₄×D₃	C₂×C₅×D₃	semidirect
241. C₂²×C₅	C₂×D₃²	semidirect
244. C₄×C₅	C₂×D₃²	semidirect
248. C₃⋊D₃	C₂×C₅×D₄	semidirect
250. C₃×D₃	C₂×C₅×D₄	semidirect
260. C₃×C₅	C₂×D₃×D₄	semidirect
265. C₂²×C₃	C₂²×C₅×D₃	semidirect
278. C₂×D₃	C₂²×C₅×D₃	semidirect
281. C₃×C₄	C₂²×C₅×D₃	semidirect
284. Dic₃	C₂²×C₅×D₃	semidirect
291. C₃²	C₂²×C₅×D₄	semidirect
304. D₄	C₅×D₃²	direct (N × H)
320. D₃	C₅×D₃×D₄	direct (N × H)
321. C₅	D₃²×D₄	direct (N × H)
331. C₂²	C₂×C₅×D₃²	semidirect
334. C₄	C₂×C₅×D₃²	semidirect
336. C₃	C₂×C₅×D₃×D₄	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
C₅×D₄×C₃⋊D₃	2
C₃×C₅×D₃×D₄	2
C₅×#3811	2
C₅×D₃×#67	2
C₅×#3802	2
C₅×D₃×D₁₂	2
C₄×C₅×D₃²	2
C₂×C₅×D₃×D₄	3
D₃²×D₄	5

Subgroups — C5×D32×D4 #13089323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃²×D₄ #13089323