Subgroups — C₅×#63978 #13087247

Order 1440.

430 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#638	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#626	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃⋊Dic₃	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	C₅×#939	—	3	1	no	maximal
9	C₅×#930	—	3	1	no	maximal
10	C₂³×C₃²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
13	C₅×#638	—	2	2	no	—
14	C₂×C₅×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
15	C₃×C₅×#67	—	2	2	no	—
16	C₂×C₃×C₅×Dic₃	—	2	2	no	—
17	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₅×#626	—	2	2	no	—
21	#63978	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₃×C₅×D₄	—	3	1	no	—
23	C₂²×C₃×C₄×C₅	—	3	1	no	—
24	C₂×C₅×#67	—	3	1	no	—
25	C₂×C₅×#67	—	3	1	no	—
26	C₂×C₅×#67	—	3	1	no	—
27	C₂×C₅×#67	—	6	1	no	—
28	C₂×C₅×#67	D₃	1	1	yes	characteristic, complemented
29	C₂²×C₅×Dic₃	D₃	1	1	yes	characteristic, complemented
30	C₂×C₅×D₁₂	—	3	1	no	—
31	C₅×#217	—	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×C₄⋊Dic₃	—	3	1	no	—
36	C₅×Dic₃⋊C₄	—	3	1	no	—
37	C₂²×C₃²×C₅	—	2	1	no	—
38	C₂²×C₃²×C₅	—	2	1	no	—
39	C₂²×C₃²×C₅	D₄	1	2	yes	complemented
40	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₅×C₃⋊D₃	—	2	1	no	—
42	C₂×C₅×C₃⋊D₃	—	2	1	no	—
43	C₂×C₅×C₃⋊D₃	—	2	1	no	—
44	C₂×C₃×C₅×D₃	—	2	1	no	—
45	C₂×C₃×C₅×D₃	—	2	1	no	—
46	C₂×C₃×C₅×D₃	—	2	1	no	—
47	C₅×C₃⋊Dic₃	—	2	1	no	—
48	C₃×C₅×Dic₃	—	2	1	no	—
49	C₃×C₅×Dic₃	—	2	1	no	—
50	C₃×C₅×Dic₃	D₄	1	2	yes	complemented
51	C₅×#121	—	9	1	no	Hall
52	C₂×#638	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₃×#67	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂²×C₃×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#626	C₂×C₅	1	1	yes	characteristic, complemented
56	Dic₃⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
57	#3722	C₂×C₅	1	1	yes	characteristic, complemented
58	(C₂×D₃)⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂³×C₃×C₅	—	2	1	no	—
60	C₂³×C₃×C₅	—	3	1	no	—
61	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₅×D₃	—	3	1	no	—
64	C₂²×C₅×D₃	—	3	1	no	—
65	C₂²×C₅×D₃	—	6	1	no	—
66	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
67	C₃×C₅×D₄	—	6	2	no	—
68	C₂×C₃×C₄×C₅	—	3	1	no	—
69	C₂×C₃×C₄×C₅	—	3	1	no	—
70	C₂×C₃×C₄×C₅	—	3	1	no	—
71	C₂×C₃×C₄×C₅	—	6	2	no	—
72	C₅×#67	—	2	2	no	—
73	C₅×#67	—	6	4	no	—
74	C₅×#67	—	6	2	no	—
75	C₅×#67	—	6	2	no	—
76	C₅×#67	—	6	2	no	—
77	C₂×C₅×Dic₃	—	2	2	no	—
78	C₂×C₅×Dic₃	—	3	1	no	—
79	C₂×C₅×Dic₃	—	3	1	no	—
80	C₂×C₅×Dic₃	—	6	1	no	—
81	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic
82	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic
83	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic
84	C₅×D₁₂	—	6	2	no	—
85	#939	—	3	1	no	—
86	#930	—	3	1	no	—
87	C₂×C₃²×C₅	—	2	2	no	—
88	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃²×C₅	#41	1	1	yes	characteristic
91	C₅×C₃⋊D₃	—	4	1	no	—
92	C₃×C₅×D₃	—	4	1	no	—
93	C₂×C₅×D₄	—	3	1	no	—
94	C₂×C₅×D₄	—	9	1	no	—
95	C₂×C₅×D₄	—	9	1	no	—
96	C₂²×C₄×C₅	—	3	1	no	—
97	C₅×C₄⋊C₄	—	9	1	no	—
98	C₅×C₂²⋊C₄	—	9	1	no	—
99	C₅×C₂²⋊C₄	—	9	1	no	—
100	C₂³×C₃²	C₂²×C₅	1	1	yes	characteristic
101	C₂²×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
103	#638	—	2	2	no	—
104	C₂×C₃⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
105	C₃×#67	—	2	2	no	—
106	C₂×C₃×Dic₃	—	2	2	no	—
107	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
108	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
110	#626	—	2	2	no	—
111	C₂²×C₃×C₅	—	2	1	no	—
112	C₂²×C₃×C₅	—	2	1	no	—
113	C₂²×C₃×C₅	—	2	1	no	—
114	C₂²×C₃×C₅	—	2	1	no	—
115	C₂²×C₃×C₅	—	2	2	no	—
116	C₂²×C₃×C₅	—	2	1	no	—
117	C₂²×C₃×C₅	—	4	1	no	—
118	C₂²×C₃×C₅	—	4	1	no	—
119	C₂²×C₃×C₅	—	6	1	no	—
120	C₂²×C₃×C₅	—	6	1	no	—
121	C₂²×C₃×C₅	—	6	1	no	—
122	C₂²×C₃×C₅	D₁₂	1	2	yes	complemented
123	C₂²×C₃×C₅	#67	1	2	yes	complemented
124	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
125	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₅×D₃	—	2	1	no	—
127	C₂×C₅×D₃	—	2	1	no	—
128	C₂×C₅×D₃	—	2	1	no	—
129	C₂×C₅×D₃	—	6	2	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	1	no	—
135	C₂×C₅×D₃	—	6	1	no	—
136	C₂×C₅×D₃	—	12	1	no	—
137	C₂×C₅×D₃	—	12	1	no	—
138	C₃×C₄×C₅	—	3	2	no	—
139	C₃×C₄×C₅	—	6	1	no	—
140	C₃×C₄×C₅	—	6	1	no	—
141	C₅×Dic₃	—	2	1	no	—
142	C₅×Dic₃	—	2	1	no	—
143	C₅×Dic₃	—	6	2	no	—
144	C₅×Dic₃	—	6	1	no	—
145	C₅×Dic₃	—	6	1	no	—
146	C₅×Dic₃	#67	1	2	yes	complemented
147	C₂×C₃×D₄	—	3	1	no	—
148	C₂²×C₃×C₄	—	3	1	no	—
149	C₂×#67	—	3	1	no	—
150	C₂×#67	—	3	1	no	—
151	C₂×#67	—	3	1	no	—
152	C₂×#67	—	6	1	no	—
153	C₂×#67	C₅×D₃	1	1	yes	characteristic, complemented
154	C₂²×Dic₃	C₅×D₃	1	1	yes	characteristic, complemented
155	C₂×D₁₂	—	3	1	no	—
156	#217	—	3	1	no	—
157	(C₂×D₃)⋊C₄	—	3	1	no	—
158	(C₂×D₃)⋊C₄	—	3	1	no	—
159	(C₂×D₃)⋊C₄	—	3	1	no	—
160	C₄⋊Dic₃	—	3	1	no	—
161	Dic₃⋊C₄	—	3	1	no	—
162	C₃²×C₅	#121	1	1	yes	characteristic, complemented, Hall
163	C₂³×C₅	—	3	1	no	—
164	C₂³×C₅	—	9	1	no	—
165	C₂³×C₅	D₃²	1	1	yes	characteristic
166	C₅×D₄	—	6	2	no	—
167	C₅×D₄	—	18	2	no	—
168	C₅×D₄	—	18	2	no	—
169	C₂×C₄×C₅	—	3	1	no	—
170	C₂×C₄×C₅	—	3	1	no	—
171	C₂×C₄×C₅	—	3	1	no	—
172	C₂×C₄×C₅	—	6	2	no	—
173	C₂×C₄×C₅	—	9	1	no	—
174	C₂²×C₃²	—	2	1	no	—
175	C₂²×C₃²	—	2	1	no	—
176	C₂²×C₃²	C₅×D₄	1	2	yes	complemented
177	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
178	C₂×C₃⋊D₃	—	2	1	no	—
179	C₂×C₃⋊D₃	—	2	1	no	—
180	C₂×C₃⋊D₃	—	2	1	no	—
181	C₂×C₃×D₃	—	2	1	no	—
182	C₂×C₃×D₃	—	2	1	no	—
183	C₂×C₃×D₃	—	2	1	no	—
184	C₃⋊Dic₃	—	2	1	no	—
185	C₃×Dic₃	—	2	1	no	—
186	C₃×Dic₃	—	2	1	no	—
187	C₃×Dic₃	C₅×D₄	1	2	yes	complemented
188	#121	—	9	1	no	Sylow
189	C₂×C₃×C₅	—	2	2	no	—
190	C₂×C₃×C₅	—	2	2	no	—
191	C₂×C₃×C₅	—	2	1	no	—
192	C₂×C₃×C₅	—	2	1	no	—
193	C₂×C₃×C₅	—	2	1	no	—
194	C₂×C₃×C₅	—	4	2	no	—
195	C₂×C₃×C₅	—	12	1	no	—
196	C₂×C₃×C₅	C₂×D₁₂	1	1	yes	characteristic
197	C₂×C₃×C₅	#235	1	1	yes	characteristic
198	C₂×C₃×C₅	D₃×D₄	1	1	yes	characteristic
199	C₂×C₃×C₅	#237	1	1	yes	characteristic
200	C₂×C₃×C₅	C₂×#67	1	1	yes	characteristic
201	C₂×C₃×C₅	C₂×#67	1	1	yes	characteristic
202	C₅×D₃	—	4	1	no	—
203	C₅×D₃	—	12	2	no	—
204	C₅×D₃	—	12	1	no	—
205	C₅×D₃	—	12	1	no	—
206	C₂³×C₃	—	2	1	no	—
207	C₂³×C₃	—	3	1	no	—
208	C₂³×C₃	C₂×C₅×D₃	1	1	yes	characteristic
209	C₂³×C₃	C₂×C₅×D₃	1	1	yes	characteristic
210	C₂²×D₃	—	3	1	no	—
211	C₂²×D₃	—	3	1	no	—
212	C₂²×D₃	—	6	1	no	—
213	C₂²×D₃	C₂×C₅×D₃	1	1	yes	characteristic
214	C₃×D₄	—	6	2	no	—
215	C₂×C₃×C₄	—	3	1	no	—
216	C₂×C₃×C₄	—	3	1	no	—
217	C₂×C₃×C₄	—	3	1	no	—
218	C₂×C₃×C₄	—	6	2	no	—
219	#67	—	2	2	no	—
220	#67	—	6	4	no	—
221	#67	—	6	2	no	—
222	#67	—	6	2	no	—
223	#67	—	6	2	no	—
224	C₂×Dic₃	—	2	2	no	—
225	C₂×Dic₃	—	3	1	no	—
226	C₂×Dic₃	—	3	1	no	—
227	C₂×Dic₃	—	6	1	no	—
228	C₂×Dic₃	C₂×C₅×D₃	1	1	yes	characteristic
229	C₂×Dic₃	C₂×C₅×D₃	1	1	yes	characteristic
230	C₂×Dic₃	C₂×C₅×D₃	1	1	yes	characteristic
231	D₁₂	—	6	2	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	—	6	1	no	—
235	C₂²×C₅	—	6	1	no	—
236	C₂²×C₅	—	6	1	no	—
237	C₂²×C₅	—	18	1	no	—
238	C₂²×C₅	—	18	1	no	—
239	C₂²×C₅	—	18	1	no	—
240	C₂²×C₅	#626	1	2	yes	complemented
241	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
242	C₄×C₅	—	3	2	no	—
243	C₄×C₅	—	6	1	no	—
244	C₄×C₅	—	6	1	no	—
245	C₄×C₅	—	18	1	no	—
246	C₂×C₃²	—	2	2	no	—
247	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
249	C₂×C₃²	C₅×#41	1	1	yes	characteristic
250	C₃⋊D₃	—	4	1	no	—
251	C₃×D₃	—	4	1	no	—
252	C₂×D₄	—	3	1	no	—
253	C₂×D₄	—	9	1	no	—
254	C₂×D₄	—	9	1	no	—
255	C₂²×C₄	—	3	1	no	—
256	C₄⋊C₄	—	9	1	no	—
257	C₂²⋊C₄	—	9	1	no	—
258	C₂²⋊C₄	—	9	1	no	—
259	C₃×C₅	—	2	1	no	—
260	C₃×C₅	#930	1	1	yes	characteristic, complemented
261	C₃×C₅	#939	1	1	yes	characteristic, complemented
262	C₂²×C₃	—	2	1	no	—
263	C₂²×C₃	—	2	1	no	—
264	C₂²×C₃	—	2	1	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	4	1	no	—
269	C₂²×C₃	—	4	1	no	—
270	C₂²×C₃	—	6	1	no	—
271	C₂²×C₃	—	6	1	no	—
272	C₂²×C₃	—	6	1	no	—
273	C₂²×C₃	C₅×D₁₂	1	2	yes	complemented
274	C₂²×C₃	C₅×#67	1	2	yes	complemented
275	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
276	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
277	C₂×D₃	—	2	1	no	—
278	C₂×D₃	—	2	1	no	—
279	C₂×D₃	—	2	1	no	—
280	C₂×D₃	—	6	2	no	—
281	C₂×D₃	—	6	1	no	—
282	C₂×D₃	—	6	1	no	—
283	C₂×D₃	—	6	1	no	—
284	C₂×D₃	—	6	1	no	—
285	C₂×D₃	—	6	1	no	—
286	C₂×D₃	—	6	1	no	—
287	C₂×D₃	—	12	1	no	—
288	C₂×D₃	—	12	1	no	—
289	C₃×C₄	—	3	2	no	—
290	C₃×C₄	—	6	1	no	—
291	C₃×C₄	—	6	1	no	—
292	Dic₃	—	2	1	no	—
293	Dic₃	—	2	1	no	—
294	Dic₃	—	6	2	no	—
295	Dic₃	—	6	1	no	—
296	Dic₃	—	6	1	no	—
297	Dic₃	C₅×#67	1	2	yes	complemented
298	C₂×C₅	—	2	2	no	—
299	C₂×C₅	—	12	1	no	—
300	C₂×C₅	—	36	1	no	—
301	C₂×C₅	#3804	1	1	yes	characteristic
302	C₂×C₅	C₂×#626	1	1	yes	characteristic
303	C₂×C₅	D₃×#67	1	1	yes	characteristic
304	C₃²	C₅×#121	1	1	yes	characteristic, complemented, Sylow
305	C₂³	—	3	1	no	—
306	C₂³	—	9	1	no	—
307	C₂³	C₅×D₃²	1	1	yes	characteristic
308	D₄	—	6	2	no	—
309	D₄	—	18	2	no	—
310	D₄	—	18	2	no	—
311	C₂×C₄	—	3	1	no	—
312	C₂×C₄	—	3	1	no	—
313	C₂×C₄	—	3	1	no	—
314	C₂×C₄	—	6	2	no	—
315	C₂×C₄	—	9	1	no	—
316	C₂×C₃	—	2	2	no	—
317	C₂×C₃	—	2	2	no	—
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	1	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	—	4	2	no	—
322	C₂×C₃	—	12	1	no	—
323	C₂×C₃	C₂×C₅×D₁₂	1	1	yes	characteristic
324	C₂×C₃	C₅×#235	1	1	yes	characteristic
325	C₂×C₃	C₅×D₃×D₄	1	1	yes	characteristic
326	C₂×C₃	C₅×#237	1	1	yes	characteristic
327	C₂×C₃	C₂×C₅×#67	1	1	yes	characteristic
328	C₂×C₃	C₂×C₅×#67	1	1	yes	characteristic
329	D₃	—	4	1	no	—
330	D₃	—	12	2	no	—
331	D₃	—	12	1	no	—
332	D₃	—	12	1	no	—
333	C₅	#63978	1	1	yes	characteristic, direct product factor, Sylow
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	6	1	no	—
337	C₂²	—	6	1	no	—
338	C₂²	—	6	1	no	—
339	C₂²	—	18	1	no	—
340	C₂²	—	18	1	no	—
341	C₂²	—	18	1	no	—
342	C₂²	C₅×#626	1	2	yes	complemented
343	C₂²	C₂×C₅×D₃²	1	1	yes	characteristic
344	C₄	—	3	2	no	—
345	C₄	—	6	1	no	—
346	C₄	—	6	1	no	—
347	C₄	—	18	1	no	—
348	C₃	—	2	1	no	—
349	C₃	C₅×#930	1	1	yes	characteristic, complemented
350	C₃	C₅×#939	1	1	yes	characteristic, complemented
351	C₂	—	2	2	no	—
352	C₂	—	12	1	no	—
353	C₂	—	36	1	no	—
354	C₂	C₅×#3804	1	1	yes	characteristic
355	C₂	C₂×C₅×#626	1	1	yes	characteristic
356	C₂	C₅×D₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃²
commutator, cosocle	C₂²×C₃²	C₂³×C₅
Frattini	C₂²	C₂×C₅×D₃²
Fitting	C₂³×C₃²×C₅	C₂²
socle	C₂²×C₃²×C₅	C₂³
hypercenter	C₂³×C₅	D₃²
hypocenter	C₃²	C₅×#121
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#638	C₂	semidirect
2. C₂×C₃×C₅×#67	C₂	semidirect
3. C₂²×C₃×C₅×Dic₃	C₂	semidirect
4. C₂×C₅×#626	C₂	semidirect
5. C₅×Dic₃⋊Dic₃	C₂	semidirect
6. C₅×#3722	C₂	semidirect
7. C₅×(C₂×D₃)⋊Dic₃	C₂	semidirect
21. #63978	C₅	direct (N × H)
28. C₂×C₅×#67	D₃	semidirect
29. C₂²×C₅×Dic₃	D₃	semidirect
39. C₂²×C₃²×C₅	D₄	semidirect
50. C₃×C₅×Dic₃	D₄	semidirect
52. C₂×#638	C₂×C₅	semidirect
53. C₂×C₃×#67	C₂×C₅	semidirect
54. C₂²×C₃×Dic₃	C₂×C₅	semidirect
55. C₂×#626	C₂×C₅	semidirect
56. Dic₃⋊Dic₃	C₂×C₅	semidirect
57. #3722	C₂×C₅	semidirect
58. (C₂×D₃)⋊Dic₃	C₂×C₅	semidirect
122. C₂²×C₃×C₅	D₁₂	semidirect
123. C₂²×C₃×C₅	#67	semidirect
146. C₅×Dic₃	#67	semidirect
153. C₂×#67	C₅×D₃	semidirect
154. C₂²×Dic₃	C₅×D₃	semidirect
162. C₃²×C₅	#121	semidirect
176. C₂²×C₃²	C₅×D₄	semidirect
187. C₃×Dic₃	C₅×D₄	semidirect
240. C₂²×C₅	#626	semidirect
260. C₃×C₅	#930	semidirect
261. C₃×C₅	#939	semidirect
273. C₂²×C₃	C₅×D₁₂	semidirect
274. C₂²×C₃	C₅×#67	semidirect
297. Dic₃	C₅×#67	semidirect
304. C₃²	C₅×#121	semidirect
333. C₅	#63978	direct (N × H)
342. C₂²	C₅×#626	semidirect
349. C₃	C₅×#930	semidirect
350. C₃	C₅×#939	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#638	2
C₂×C₃×C₅×#67	2
C₂²×C₃×C₅×Dic₃	2
C₂×C₅×#626	2
C₅×Dic₃⋊Dic₃	2
C₅×#3722	2
C₅×(C₂×D₃)⋊Dic₃	2
C₅×#939	3
C₅×#930	3
#63978	5

Subgroups — C5×#63978 #13087247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#63978 #13087247