Subgroups — C₅×#5586 #11755971

Order 960.

660 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#953	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#939	C₂	1	2	yes	maximal, complemented
6	C₅×#935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄×Dic₃	C₂	1	2	yes	maximal, complemented
8	C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#67⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#878	C₂	1	2	yes	maximal, complemented
11	C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#525	—	3	1	no	maximal, Hall
13	C₂⁴×C₃×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₅×#67	C₂²	1	2	yes	—
17	C₂×C₅×#67	C₂²	1	1	yes	characteristic
18	C₂×C₅×#67	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₅×Dic₃	—	2	4	no	—
20	C₂²×C₅×Dic₃	C₂²	1	2	yes	—
21	C₂²×C₅×Dic₃	C₂²	1	2	yes	—
22	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
23	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₅×#237	—	2	4	no	—
26	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₅×#217	C₂²	1	1	yes	characteristic
31	C₅×#217	C₂²	1	2	yes	—
32	C₅×#217	C₂²	1	2	yes	complemented
33	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
35	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
36	C₅×Dic₃⋊C₄	C₂²	1	2	yes	complemented
37	C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
38	#5586	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×#41	—	3	1	no	—
40	C₂³×C₄×C₅	—	3	1	no	—
41	C₅×#123	—	3	1	no	—
42	C₅×#123	—	3	1	no	—
43	C₅×C₂²⋊Q₈	—	3	2	no	—
44	C₅×#121	—	3	2	no	—
45	C₅×#120	—	3	1	no	—
46	C₅×#120	D₃	1	1	yes	characteristic, complemented
47	C₄×C₅×D₄	—	3	2	no	—
48	C₄×C₅×D₄	—	3	2	no	—
49	C₅×#117	—	3	1	no	—
50	C₂³×C₃×C₅	—	2	2	no	—
51	C₂³×C₃×C₅	—	2	4	no	—
52	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
54	C₂³×C₃×C₅	C₂³	1	2	yes	—
55	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
56	C₃×C₅×D₄	—	2	2	no	—
57	C₃×C₅×D₄	—	2	4	no	—
58	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
60	C₅×#67	—	2	2	no	—
61	C₅×#67	—	2	4	no	—
62	C₅×#67	—	2	2	no	—
63	C₂×C₅×Dic₃	—	2	2	no	—
64	C₂×C₅×Dic₃	—	2	2	no	—
65	C₂×C₅×Dic₃	—	2	4	no	—
66	C₂×C₅×Dic₃	—	2	4	no	—
67	C₂×C₅×Dic₃	D₄	1	4	yes	complemented
68	C₂×C₅×Dic₃	C₂³	1	2	yes	—
69	C₂×C₅×Dic₃	C₂³	1	2	yes	—
70	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₃	—	2	2	no	—
74	C₅×Dic₆	—	2	2	no	—
75	C₂³×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#237	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
78	#953	C₂×C₅	1	1	yes	characteristic, complemented
79	#939	C₂×C₅	1	2	yes	complemented
80	#935	C₂×C₅	1	1	yes	characteristic, complemented
81	D₄×Dic₃	C₂×C₅	1	2	yes	complemented
82	#886	C₂×C₅	1	1	yes	characteristic, complemented
83	#67⋊C₄	C₂×C₅	1	2	yes	complemented
84	#878	C₂×C₅	1	2	yes	complemented
85	#877	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂⁴×C₅	C₂×D₃	1	1	yes	characteristic
87	C₅×#41	—	6	4	no	—
88	C₂×C₅×Q₈	—	3	1	no	—
89	C₂×C₅×D₄	—	3	2	no	—
90	C₂×C₅×D₄	—	3	1	no	—
91	C₂×C₅×D₄	—	3	1	no	—
92	C₂×C₅×D₄	C₂×D₃	1	2	yes	—
93	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₄×C₅	—	3	1	no	—
95	C₂²×C₄×C₅	—	3	2	no	—
96	C₂²×C₄×C₅	—	3	1	no	—
97	C₂²×C₄×C₅	—	3	2	no	—
98	C₂²×C₄×C₅	—	3	1	no	—
99	C₂²×C₄×C₅	—	3	1	no	—
100	C₂²×C₄×C₅	—	6	4	no	—
101	C₅×C₄⋊C₄	—	3	2	no	—
102	C₅×C₄⋊C₄	—	3	2	no	—
103	C₅×C₄⋊C₄	—	3	2	no	—
104	C₅×C₂²⋊C₄	—	3	1	no	—
105	C₅×C₂²⋊C₄	—	3	2	no	—
106	C₅×C₂²⋊C₄	—	3	2	no	—
107	C₅×C₂²⋊C₄	—	3	2	no	—
108	C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
109	C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
110	C₄²×C₅	—	3	2	no	—
111	#525	—	3	1	no	Sylow
112	C₂²×C₃×C₅	—	2	8	no	—
113	C₂²×C₃×C₅	—	2	2	no	—
114	C₂²×C₃×C₅	—	2	2	no	—
115	C₂²×C₃×C₅	—	2	2	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	—	2	2	no	—
118	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
119	C₂²×C₃×C₅	#41	1	4	yes	complemented
120	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
121	C₂×C₅×D₃	—	2	1	no	—
122	C₂×C₅×D₃	—	2	2	no	—
123	C₃×C₄×C₅	—	2	1	no	—
124	C₃×C₄×C₅	—	2	2	no	—
125	C₅×Dic₃	—	2	1	no	—
126	C₅×Dic₃	—	2	2	no	—
127	C₅×Dic₃	—	2	2	no	—
128	C₅×Dic₃	C₂×D₄	1	2	yes	—
129	C₅×Dic₃	C₂×D₄	1	2	yes	—
130	C₂⁴×C₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×D₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
133	C₂×#67	C₂²×C₅	1	2	yes	—
134	C₂×#67	C₂²×C₅	1	1	yes	characteristic
135	C₂×#67	C₂²×C₅	1	1	yes	characteristic, complemented
136	C₂²×Dic₃	—	2	4	no	—
137	C₂²×Dic₃	C₂²×C₅	1	2	yes	—
138	C₂²×Dic₃	C₂²×C₅	1	2	yes	—
139	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
140	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic
141	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
142	#237	—	2	4	no	—
143	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
144	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
147	#217	C₂²×C₅	1	1	yes	characteristic
148	#217	C₂²×C₅	1	2	yes	—
149	#217	C₂²×C₅	1	2	yes	complemented
150	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	complemented
151	C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
152	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
153	Dic₃⋊C₄	C₂²×C₅	1	2	yes	complemented
154	C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
155	C₂³×C₅	—	2	2	no	—
156	C₂³×C₅	—	2	4	no	—
157	C₂³×C₅	—	3	1	no	—
158	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂³×C₅	C₂²×D₃	1	2	yes	—
161	C₅×Q₈	—	6	2	no	—
162	C₅×D₄	—	2	2	no	—
163	C₅×D₄	—	2	4	no	—
164	C₅×D₄	—	6	2	no	—
165	C₅×D₄	—	6	2	no	—
166	C₅×D₄	—	6	4	no	—
167	C₂×C₄×C₅	—	3	4	no	—
168	C₂×C₄×C₅	—	3	1	no	—
169	C₂×C₄×C₅	—	3	1	no	—
170	C₂×C₄×C₅	—	3	2	no	—
171	C₂×C₄×C₅	—	3	2	no	—
172	C₂×C₄×C₅	—	3	1	no	—
173	C₂×C₄×C₅	—	6	2	no	—
174	C₂×C₄×C₅	—	6	4	no	—
175	C₂×C₄×C₅	—	6	4	no	—
176	C₂×C₄×C₅	—	6	2	no	—
177	C₂×C₄×C₅	—	6	2	no	—
178	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
179	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂×#41	—	3	1	no	—
181	C₂³×C₄	—	3	1	no	—
182	#123	—	3	1	no	—
183	#123	—	3	1	no	—
184	C₂²⋊Q₈	—	3	2	no	—
185	#121	—	3	2	no	—
186	#120	—	3	1	no	—
187	#120	C₅×D₃	1	1	yes	characteristic, complemented
188	C₄×D₄	—	3	2	no	—
189	C₄×D₄	—	3	2	no	—
190	#117	—	3	1	no	—
191	C₂×C₃×C₅	—	2	2	no	—
192	C₂×C₃×C₅	—	2	4	no	—
193	C₂×C₃×C₅	—	4	1	no	—
194	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₃×C₅	C₂×#41	1	2	yes	—
196	C₅×D₃	—	4	1	no	—
197	C₂³×C₃	—	2	2	no	—
198	C₂³×C₃	—	2	4	no	—
199	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
200	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
201	C₂³×C₃	C₂³×C₅	1	2	yes	—
202	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
203	C₃×D₄	—	2	2	no	—
204	C₃×D₄	—	2	4	no	—
205	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	#67	—	2	2	no	—
208	#67	—	2	4	no	—
209	#67	—	2	2	no	—
210	C₂×Dic₃	—	2	2	no	—
211	C₂×Dic₃	—	2	2	no	—
212	C₂×Dic₃	—	2	4	no	—
213	C₂×Dic₃	—	2	4	no	—
214	C₂×Dic₃	C₅×D₄	1	4	yes	complemented
215	C₂×Dic₃	C₂³×C₅	1	2	yes	—
216	C₂×Dic₃	C₂³×C₅	1	2	yes	—
217	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
218	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
219	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
220	C₄×D₃	—	2	2	no	—
221	Dic₆	—	2	2	no	—
222	C₂²×C₅	—	2	8	no	—
223	C₂²×C₅	—	2	2	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	2	2	no	—
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	6	1	no	—
229	C₂²×C₅	—	6	2	no	—
230	C₂²×C₅	D₃×D₄	1	2	yes	—
231	C₂²×C₅	#237	1	4	yes	complemented
232	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
233	C₄×C₅	—	2	1	no	—
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	3	2	no	—
236	C₄×C₅	—	3	2	no	—
237	C₄×C₅	—	6	2	no	—
238	C₄×C₅	—	6	1	no	—
239	C₄×C₅	—	6	2	no	—
240	C₂⁴	C₂×C₅×D₃	1	1	yes	characteristic
241	#41	—	6	4	no	—
242	C₂×Q₈	—	3	1	no	—
243	C₂×D₄	—	3	2	no	—
244	C₂×D₄	—	3	1	no	—
245	C₂×D₄	—	3	1	no	—
246	C₂×D₄	C₂×C₅×D₃	1	2	yes	—
247	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
248	C₂²×C₄	—	3	1	no	—
249	C₂²×C₄	—	3	2	no	—
250	C₂²×C₄	—	3	1	no	—
251	C₂²×C₄	—	3	2	no	—
252	C₂²×C₄	—	3	1	no	—
253	C₂²×C₄	—	3	1	no	—
254	C₂²×C₄	—	6	4	no	—
255	C₄⋊C₄	—	3	2	no	—
256	C₄⋊C₄	—	3	2	no	—
257	C₄⋊C₄	—	3	2	no	—
258	C₂²⋊C₄	—	3	1	no	—
259	C₂²⋊C₄	—	3	2	no	—
260	C₂²⋊C₄	—	3	2	no	—
261	C₂²⋊C₄	—	3	2	no	—
262	C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
264	C₄²	—	3	2	no	—
265	C₃×C₅	#525	1	1	yes	characteristic, complemented, Hall
266	C₂²×C₃	—	2	8	no	—
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	2	no	—
272	C₂²×C₃	C₂×C₅×D₄	1	2	yes	—
273	C₂²×C₃	C₅×#41	1	4	yes	complemented
274	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
275	C₂×D₃	—	2	1	no	—
276	C₂×D₃	—	2	2	no	—
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	2	no	—
279	Dic₃	—	2	1	no	—
280	Dic₃	—	2	2	no	—
281	Dic₃	—	2	2	no	—
282	Dic₃	C₂×C₅×D₄	1	2	yes	—
283	Dic₃	C₂×C₅×D₄	1	2	yes	—
284	C₂×C₅	—	2	2	no	—
285	C₂×C₅	—	2	4	no	—
286	C₂×C₅	—	4	1	no	—
287	C₂×C₅	—	12	1	no	—
288	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
289	C₂×C₅	C₂×#237	1	2	yes	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	3	1	no	—
293	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
294	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₂³	C₂²×C₅×D₃	1	2	yes	—
296	Q₈	—	6	2	no	—
297	D₄	—	2	2	no	—
298	D₄	—	2	4	no	—
299	D₄	—	6	2	no	—
300	D₄	—	6	2	no	—
301	D₄	—	6	4	no	—
302	C₂×C₄	—	3	4	no	—
303	C₂×C₄	—	3	1	no	—
304	C₂×C₄	—	3	1	no	—
305	C₂×C₄	—	3	2	no	—
306	C₂×C₄	—	3	2	no	—
307	C₂×C₄	—	3	1	no	—
308	C₂×C₄	—	6	2	no	—
309	C₂×C₄	—	6	4	no	—
310	C₂×C₄	—	6	4	no	—
311	C₂×C₄	—	6	2	no	—
312	C₂×C₄	—	6	2	no	—
313	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
314	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
315	C₂×C₃	—	2	2	no	—
316	C₂×C₃	—	2	4	no	—
317	C₂×C₃	—	4	1	no	—
318	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
319	C₂×C₃	C₂×C₅×#41	1	2	yes	—
320	D₃	—	4	1	no	—
321	C₅	#5586	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	—	2	8	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	6	1	no	—
329	C₂²	—	6	2	no	—
330	C₂²	C₅×D₃×D₄	1	2	yes	—
331	C₂²	C₅×#237	1	4	yes	complemented
332	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	3	2	no	—
336	C₄	—	3	2	no	—
337	C₄	—	6	2	no	—
338	C₄	—	6	1	no	—
339	C₄	—	6	2	no	—
340	C₃	C₅×#525	1	1	yes	characteristic, complemented, Sylow
341	C₂	—	2	2	no	—
342	C₂	—	2	4	no	—
343	C₂	—	4	1	no	—
344	C₂	—	12	1	no	—
345	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
346	C₂	C₂×C₅×#237	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₅
Frattini	C₂²	C₂³×C₅×D₃
Fitting	C₃×C₅×#120	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#120	D₃
hypocenter	C₃	C₅×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#120

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×Dic₃	C₂	semidirect
2. C₂×C₅×#237	C₂	semidirect
3. C₃×C₅×#120	C₂	semidirect
4. C₅×#953	C₂	semidirect
5. C₅×#939	C₂	semidirect
6. C₅×#935	C₂	semidirect
7. C₅×D₄×Dic₃	C₂	semidirect
8. C₅×#886	C₂	semidirect
9. C₅×#67⋊C₄	C₂	semidirect
10. C₅×#878	C₂	semidirect
11. C₅×#877	C₂	semidirect
18. C₂×C₅×#67	C₂²	semidirect
24. C₂²×C₅×Dic₃	C₂²	semidirect
26. C₂×C₄×C₅×D₃	C₂²	semidirect
27. C₂×C₅×Dic₆	C₂²	semidirect
32. C₅×#217	C₂²	semidirect
33. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₅×C₄⋊Dic₃	C₂²	semidirect
35. C₅×Dic₃⋊C₄	C₂²	semidirect
36. C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₄×C₅×Dic₃	C₂²	semidirect
38. #5586	C₅	direct (N × H)
46. C₅×#120	D₃	semidirect
67. C₂×C₅×Dic₃	D₄	semidirect
75. C₂³×Dic₃	C₂×C₅	semidirect
76. C₂×#237	C₂×C₅	semidirect
77. C₃×#120	C₂×C₅	semidirect
78. #953	C₂×C₅	semidirect
79. #939	C₂×C₅	semidirect
80. #935	C₂×C₅	semidirect
81. D₄×Dic₃	C₂×C₅	semidirect
82. #886	C₂×C₅	semidirect
83. #67⋊C₄	C₂×C₅	semidirect
84. #878	C₂×C₅	semidirect
85. #877	C₂×C₅	semidirect
119. C₂²×C₃×C₅	#41	semidirect
135. C₂×#67	C₂²×C₅	semidirect
141. C₂²×Dic₃	C₂²×C₅	semidirect
143. C₂×C₄×D₃	C₂²×C₅	semidirect
144. C₂×Dic₆	C₂²×C₅	semidirect
149. #217	C₂²×C₅	semidirect
150. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
151. C₄⋊Dic₃	C₂²×C₅	semidirect
152. Dic₃⋊C₄	C₂²×C₅	semidirect
153. Dic₃⋊C₄	C₂²×C₅	semidirect
154. C₄×Dic₃	C₂²×C₅	semidirect
187. #120	C₅×D₃	semidirect
214. C₂×Dic₃	C₅×D₄	semidirect
231. C₂²×C₅	#237	semidirect
265. C₃×C₅	#525	semidirect
273. C₂²×C₃	C₅×#41	semidirect
321. C₅	#5586	direct (N × H)
331. C₂²	C₅×#237	semidirect
340. C₃	C₅×#525	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×Dic₃	2
C₂×C₅×#237	2
C₃×C₅×#120	2
C₅×#953	2
C₅×#939	2
C₅×#935	2
C₅×D₄×Dic₃	2
C₅×#886	2
C₅×#67⋊C₄	2
C₅×#878	2
C₅×#877	2
C₅×#525	3
#5586	5

Subgroups — C5×#5586 #11755971

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5586 #11755971