Subgroups — C₅×#5656 #11756041

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	C₂×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#929	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#896	C₂	1	2	yes	maximal, complemented
7	C₅×#893	C₂	1	2	yes	maximal, complemented
8	C₅×#884	C₂	1	2	yes	maximal, complemented
9	C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#67⋊C₄	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	C₂³×C₅×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₄×C₅	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	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
21	C₅×#237	—	2	4	no	—
22	C₂×C₅×D₁₂	C₂²	1	2	yes	—
23	C₂×C₄×C₅×D₃	—	2	4	no	—
24	C₂×C₄×C₅×D₃	C₂²	1	2	yes	—
25	C₂×C₄×C₅×D₃	C₂²	1	2	yes	—
26	C₂×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
31	C₅×#217	C₂²	1	1	yes	characteristic
32	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
33	C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₅×(C₂×D₃)⋊C₄	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	#5656	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	D₃	1	1	yes	characteristic, complemented
43	C₅×C₂²⋊Q₈	—	3	2	no	—
44	C₅×#121	—	3	2	no	—
45	C₅×#120	—	3	1	no	—
46	C₅×#120	—	3	1	no	—
47	C₄×C₅×D₄	—	3	2	no	—
48	C₄×C₅×D₄	—	3	2	no	—
49	C₅×#117	—	3	1	no	—
50	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₅×D₃	—	2	2	no	—
53	C₂²×C₅×D₃	—	2	4	no	—
54	C₂²×C₅×D₃	C₂³	1	1	yes	characteristic
55	C₂²×C₅×D₃	C₂³	1	2	yes	—
56	C₃×C₅×D₄	—	2	2	no	—
57	C₂×C₃×C₄×C₅	—	2	2	no	—
58	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₅×#67	—	2	2	no	—
62	C₅×#67	—	2	4	no	—
63	C₅×#67	—	2	2	no	—
64	C₂×C₅×Dic₃	—	2	2	no	—
65	C₂×C₅×Dic₃	D₄	1	4	yes	complemented
66	C₂×C₅×Dic₃	C₂³	1	2	yes	—
67	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₅×D₁₂	—	2	4	no	—
71	C₄×C₅×D₃	—	2	4	no	—
72	C₄×C₅×D₃	—	2	4	no	—
73	C₄×C₅×D₃	—	2	2	no	—
74	C₅×Dic₆	—	2	2	no	—
75	C₂×#237	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂²×C₄×D₃	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
78	#937	C₂×C₅	1	1	yes	characteristic, complemented
79	#929	C₂×C₅	1	1	yes	characteristic, complemented
80	#896	C₂×C₅	1	2	yes	complemented
81	#893	C₂×C₅	1	2	yes	complemented
82	#884	C₂×C₅	1	2	yes	complemented
83	#882	C₂×C₅	1	1	yes	characteristic, complemented
84	#67⋊C₄	C₂×C₅	1	2	yes	complemented
85	#877	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂⁴×C₅	—	3	1	no	—
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	—	3	2	no	—
93	C₂×C₅×D₄	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₄×C₅	—	3	1	no	—
95	C₂²×C₄×C₅	—	3	1	no	—
96	C₂²×C₄×C₅	—	3	2	no	—
97	C₂²×C₄×C₅	—	3	1	no	—
98	C₂²×C₄×C₅	—	3	2	no	—
99	C₂²×C₄×C₅	—	6	4	no	—
100	C₂²×C₄×C₅	C₂×D₃	1	1	yes	characteristic
101	C₅×C₄⋊C₄	—	3	2	no	—
102	C₅×C₄⋊C₄	—	3	2	no	—
103	C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
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	complemented
110	C₄²×C₅	—	3	2	no	—
111	#525	—	3	1	no	Sylow
112	C₂²×C₃×C₅	—	2	2	no	—
113	C₂²×C₃×C₅	—	2	1	no	—
114	C₂²×C₃×C₅	—	2	2	no	—
115	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
116	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
117	C₂×C₅×D₃	—	2	8	no	—
118	C₂×C₅×D₃	—	2	2	no	—
119	C₂×C₅×D₃	—	2	2	no	—
120	C₂×C₅×D₃	—	2	1	no	—
121	C₂×C₅×D₃	—	2	2	no	—
122	C₂×C₅×D₃	#41	1	4	yes	complemented
123	C₃×C₄×C₅	—	2	1	no	—
124	C₃×C₄×C₅	—	2	2	no	—
125	C₃×C₄×C₅	—	2	2	no	—
126	C₅×Dic₃	—	2	1	no	—
127	C₅×Dic₃	—	2	2	no	—
128	C₅×Dic₃	C₂×D₄	1	2	yes	—
129	C₅×Dic₃	C₂×D₄	1	2	yes	—
130	C₂³×D₃	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
132	C₂²×C₃×C₄	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	C₂²×C₅	1	1	yes	characteristic
137	C₂²×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
138	#237	—	2	4	no	—
139	C₂×D₁₂	C₂²×C₅	1	2	yes	—
140	C₂×C₄×D₃	—	2	4	no	—
141	C₂×C₄×D₃	C₂²×C₅	1	2	yes	—
142	C₂×C₄×D₃	C₂²×C₅	1	2	yes	—
143	C₂×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
144	C₂×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
145	C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
146	C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
147	C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
148	#217	C₂²×C₅	1	1	yes	characteristic
149	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
150	(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
151	(C₂×D₃)⋊C₄	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	—	3	2	no	—
156	C₂³×C₅	—	3	1	no	—
157	C₂³×C₅	—	6	4	no	—
158	C₂³×C₅	—	6	2	no	—
159	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂³×C₅	C₂²×D₃	1	1	yes	characteristic
161	C₅×Q₈	—	6	2	no	—
162	C₅×D₄	—	2	2	no	—
163	C₅×D₄	—	6	4	no	—
164	C₅×D₄	—	6	2	no	—
165	C₅×D₄	—	6	4	no	—
166	C₅×D₄	—	6	2	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	3	4	no	—
169	C₂×C₄×C₅	—	3	1	no	—
170	C₂×C₄×C₅	—	3	1	no	—
171	C₂×C₄×C₅	—	3	2	no	—
172	C₂×C₄×C₅	—	3	1	no	—
173	C₂×C₄×C₅	—	6	4	no	—
174	C₂×C₄×C₅	—	6	4	no	—
175	C₂×C₄×C₅	—	6	2	no	—
176	C₂×C₄×C₅	—	6	2	no	—
177	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
178	C₂×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂²×D₃	1	2	yes	—
180	C₂×#41	—	3	1	no	—
181	C₂³×C₄	—	3	1	no	—
182	#123	—	3	1	no	—
183	#123	C₅×D₃	1	1	yes	characteristic, complemented
184	C₂²⋊Q₈	—	3	2	no	—
185	#121	—	3	2	no	—
186	#120	—	3	1	no	—
187	#120	—	3	1	no	—
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	—	4	1	no	—
193	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₃×C₅	C₂×#41	1	2	yes	—
195	C₅×D₃	—	2	4	no	—
196	C₅×D₃	—	4	1	no	—
197	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
198	C₂³×C₃	C₂³×C₅	1	1	yes	characteristic
199	C₂²×D₃	—	2	2	no	—
200	C₂²×D₃	—	2	4	no	—
201	C₂²×D₃	C₂³×C₅	1	1	yes	characteristic
202	C₂²×D₃	C₂³×C₅	1	2	yes	—
203	C₃×D₄	—	2	2	no	—
204	C₂×C₃×C₄	—	2	2	no	—
205	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	#67	—	2	2	no	—
209	#67	—	2	4	no	—
210	#67	—	2	2	no	—
211	C₂×Dic₃	—	2	2	no	—
212	C₂×Dic₃	C₅×D₄	1	4	yes	complemented
213	C₂×Dic₃	C₂³×C₅	1	2	yes	—
214	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
215	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
216	C₂×Dic₃	C₂³×C₅	1	1	yes	characteristic
217	D₁₂	—	2	4	no	—
218	C₄×D₃	—	2	4	no	—
219	C₄×D₃	—	2	4	no	—
220	C₄×D₃	—	2	2	no	—
221	Dic₆	—	2	2	no	—
222	C₂²×C₅	—	2	2	no	—
223	C₂²×C₅	—	2	1	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	3	4	no	—
226	C₂²×C₅	—	6	8	no	—
227	C₂²×C₅	—	6	2	no	—
228	C₂²×C₅	—	6	2	no	—
229	C₂²×C₅	—	6	1	no	—
230	C₂²×C₅	—	6	2	no	—
231	C₂²×C₅	D₃×D₄	1	2	yes	—
232	C₂²×C₅	C₂³×D₃	1	1	yes	characteristic
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	2	no	—
236	C₄×C₅	—	3	2	no	—
237	C₄×C₅	—	3	2	no	—
238	C₄×C₅	—	6	1	no	—
239	C₄×C₅	—	6	2	no	—
240	C₂⁴	—	3	1	no	—
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	—	3	2	no	—
247	C₂×D₄	C₂×C₅×D₃	1	1	yes	characteristic
248	C₂²×C₄	—	3	1	no	—
249	C₂²×C₄	—	3	1	no	—
250	C₂²×C₄	—	3	2	no	—
251	C₂²×C₄	—	3	1	no	—
252	C₂²×C₄	—	3	2	no	—
253	C₂²×C₄	—	6	4	no	—
254	C₂²×C₄	C₂×C₅×D₃	1	1	yes	characteristic
255	C₄⋊C₄	—	3	2	no	—
256	C₄⋊C₄	—	3	2	no	—
257	C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
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	complemented
264	C₄²	—	3	2	no	—
265	C₃×C₅	#525	1	1	yes	characteristic, complemented, Hall
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	C₂×C₅×D₄	1	2	yes	—
270	C₂²×C₃	C₂⁴×C₅	1	1	yes	characteristic
271	C₂×D₃	—	2	8	no	—
272	C₂×D₃	—	2	2	no	—
273	C₂×D₃	—	2	2	no	—
274	C₂×D₃	—	2	1	no	—
275	C₂×D₃	—	2	2	no	—
276	C₂×D₃	C₅×#41	1	4	yes	complemented
277	C₃×C₄	—	2	1	no	—
278	C₃×C₄	—	2	2	no	—
279	C₃×C₄	—	2	2	no	—
280	Dic₃	—	2	1	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	—	4	1	no	—
286	C₂×C₅	—	6	4	no	—
287	C₂×C₅	—	12	1	no	—
288	C₂×C₅	C₂×D₃×D₄	1	1	yes	characteristic
289	C₂×C₅	D₃×#41	1	2	yes	—
290	C₂³	—	3	2	no	—
291	C₂³	—	3	1	no	—
292	C₂³	—	6	4	no	—
293	C₂³	—	6	2	no	—
294	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₂³	C₂²×C₅×D₃	1	1	yes	characteristic
296	Q₈	—	6	2	no	—
297	D₄	—	2	2	no	—
298	D₄	—	6	4	no	—
299	D₄	—	6	2	no	—
300	D₄	—	6	4	no	—
301	D₄	—	6	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	3	4	no	—
304	C₂×C₄	—	3	1	no	—
305	C₂×C₄	—	3	1	no	—
306	C₂×C₄	—	3	2	no	—
307	C₂×C₄	—	3	1	no	—
308	C₂×C₄	—	6	4	no	—
309	C₂×C₄	—	6	4	no	—
310	C₂×C₄	—	6	2	no	—
311	C₂×C₄	—	6	2	no	—
312	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
313	C₂×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
314	C₂×C₄	C₂²×C₅×D₃	1	2	yes	—
315	C₂×C₃	—	2	2	no	—
316	C₂×C₃	—	4	1	no	—
317	C₂×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
318	C₂×C₃	C₂×C₅×#41	1	2	yes	—
319	D₃	—	2	4	no	—
320	D₃	—	4	1	no	—
321	C₅	#5656	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	—	2	2	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	3	4	no	—
326	C₂²	—	6	8	no	—
327	C₂²	—	6	2	no	—
328	C₂²	—	6	2	no	—
329	C₂²	—	6	1	no	—
330	C₂²	—	6	2	no	—
331	C₂²	C₅×D₃×D₄	1	2	yes	—
332	C₂²	C₂³×C₅×D₃	1	1	yes	characteristic
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	2	2	no	—
336	C₄	—	3	2	no	—
337	C₄	—	3	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	—	4	1	no	—
343	C₂	—	6	4	no	—
344	C₂	—	12	1	no	—
345	C₂	C₂×C₅×D₃×D₄	1	1	yes	characteristic
346	C₂	C₅×D₃×#41	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×#123	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₅×#123	D₃
hypocenter	C₃	C₅×#525
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#237	C₂	semidirect
2. C₂²×C₄×C₅×D₃	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₅×#937	C₂	semidirect
5. C₅×#929	C₂	semidirect
6. C₅×#896	C₂	semidirect
7. C₅×#893	C₂	semidirect
8. C₅×#884	C₂	semidirect
9. C₅×#882	C₂	semidirect
10. C₅×#67⋊C₄	C₂	semidirect
11. C₅×#877	C₂	semidirect
18. C₂×C₅×#67	C₂²	semidirect
20. C₂²×C₅×Dic₃	C₂²	semidirect
26. C₂×C₄×C₅×D₃	C₂²	semidirect
27. C₂×C₅×Dic₆	C₂²	semidirect
28. C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₃×C₅×C₂²⋊C₄	C₂²	semidirect
34. C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₅×Dic₃⋊C₄	C₂²	semidirect
36. C₅×Dic₃⋊C₄	C₂²	semidirect
37. C₄×C₅×Dic₃	C₂²	semidirect
38. #5656	C₅	direct (N × H)
42. C₅×#123	D₃	semidirect
65. C₂×C₅×Dic₃	D₄	semidirect
75. C₂×#237	C₂×C₅	semidirect
76. C₂²×C₄×D₃	C₂×C₅	semidirect
77. C₃×#123	C₂×C₅	semidirect
78. #937	C₂×C₅	semidirect
79. #929	C₂×C₅	semidirect
80. #896	C₂×C₅	semidirect
81. #893	C₂×C₅	semidirect
82. #884	C₂×C₅	semidirect
83. #882	C₂×C₅	semidirect
84. #67⋊C₄	C₂×C₅	semidirect
85. #877	C₂×C₅	semidirect
103. C₅×C₄⋊C₄	C₂×D₃	semidirect
109. C₅×C₂²⋊C₄	C₂×D₃	semidirect
122. C₂×C₅×D₃	#41	semidirect
135. C₂×#67	C₂²×C₅	semidirect
137. C₂²×Dic₃	C₂²×C₅	semidirect
143. C₂×C₄×D₃	C₂²×C₅	semidirect
144. C₂×Dic₆	C₂²×C₅	semidirect
145. C₃×C₄⋊C₄	C₂²×C₅	semidirect
147. C₃×C₂²⋊C₄	C₂²×C₅	semidirect
151. (C₂×D₃)⋊C₄	C₂²×C₅	semidirect
152. Dic₃⋊C₄	C₂²×C₅	semidirect
153. Dic₃⋊C₄	C₂²×C₅	semidirect
154. C₄×Dic₃	C₂²×C₅	semidirect
183. #123	C₅×D₃	semidirect
212. C₂×Dic₃	C₅×D₄	semidirect
257. C₄⋊C₄	C₂×C₅×D₃	semidirect
263. C₂²⋊C₄	C₂×C₅×D₃	semidirect
265. C₃×C₅	#525	semidirect
276. C₂×D₃	C₅×#41	semidirect
321. C₅	#5656	direct (N × H)
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
C₂×C₅×#237	2
C₂²×C₄×C₅×D₃	2
C₃×C₅×#123	2
C₅×#937	2
C₅×#929	2
C₅×#896	2
C₅×#893	2
C₅×#884	2
C₅×#882	2
C₅×#67⋊C₄	2
C₅×#877	2
C₅×#525	3
#5656	5

Subgroups — C5×#5656 #11756041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#5656 #11756041