Subgroups — C₅×#68258 #14288854

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4695	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1620	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₅×#947	—	2	1	no	—
11	C₂×C₅×#215	—	2	1	no	—
12	C₂×C₅×D₂₄	—	2	2	no	—
13	C₂×C₅×#204	—	2	1	no	—
14	C₅×#894	—	2	2	no	—
15	C₅×#893	—	2	1	no	—
16	C₅×#875	—	2	1	no	—
17	C₅×#874	C₂²	1	1	yes	characteristic
18	C₅×#874	C₂²	1	1	yes	characteristic
19	C₄×C₅×D₁₂	—	2	1	no	—
20	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₅×#821	—	2	1	no	—
24	C₅×#809	—	2	1	no	—
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#68258	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#559	—	3	1	no	—
28	C₅×#493	—	3	1	no	—
29	C₅×#460	—	3	1	no	—
30	C₅×#460	—	3	1	no	—
31	C₅×#331	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
35	C₂×C₅×D₁₂	—	2	1	no	—
36	C₂×C₅×D₁₂	—	2	1	no	—
37	C₂×C₅×D₁₂	—	2	1	no	—
38	C₂×C₅×D₁₂	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	D₄	1	2	yes	—
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
47	C₃×C₄²×C₅	—	2	1	no	—
48	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
49	C₅×#215	—	4	2	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
53	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
54	C₅×Dic₃⋊C₄	—	2	1	no	—
55	C₄×C₅×Dic₃	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₅×D₂₄	—	4	4	no	—
58	C₅×#204	—	4	2	no	—
59	#5585	C₂×C₅	1	1	yes	characteristic, complemented
60	#5027	C₂×C₅	1	1	yes	characteristic, complemented
61	#4848	C₂×C₅	1	1	yes	characteristic, complemented
62	#4695	C₂×C₅	1	1	yes	characteristic
63	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
64	#4485	C₂×C₅	1	1	yes	characteristic, complemented
65	#4456	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×SD₁₆	—	6	1	no	—
67	C₂×C₅×SD₁₆	—	6	1	no	—
68	C₂×C₅×D₈	—	6	2	no	—
69	C₅×#127	—	3	1	no	—
70	C₅×#127	—	3	1	no	—
71	C₅×#124	—	6	1	no	—
72	C₅×#124	—	6	1	no	—
73	C₅×#123	—	6	2	no	—
74	C₄×C₅×Q₈	—	3	1	no	—
75	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	6	1	no	—
77	C₄×C₅×D₄	—	6	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
83	#1620	—	3	1	no	Sylow
84	C₂²×C₅×D₃	—	2	2	no	—
85	C₂²×C₅×D₃	—	4	1	no	—
86	C₃×C₅×Q₈	—	2	1	no	—
87	C₃×C₅×Q₈	—	2	1	no	—
88	C₂×C₃×C₄×C₅	—	2	1	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₅×Dic₃	—	2	1	no	—
94	C₂×C₅×Dic₃	—	2	1	no	—
95	C₅×D₁₂	—	4	2	no	—
96	C₅×D₁₂	—	4	2	no	—
97	C₅×D₁₂	—	4	1	no	—
98	C₅×D₁₂	—	4	1	no	—
99	C₅×D₁₂	—	4	1	no	—
100	C₅×D₁₂	—	4	1	no	—
101	C₅×D₁₂	—	4	1	no	—
102	C₅×D₁₂	—	4	1	no	—
103	C₅×D₁₂	—	4	1	no	—
104	C₅×D₁₂	—	4	1	no	—
105	C₄×C₅×D₃	—	8	2	no	—
106	C₅×Dic₆	—	2	1	no	—
107	C₅×Dic₆	—	2	1	no	—
108	C₃×C₅×C₈	—	2	2	no	—
109	C₃×C₅×C₈	—	4	1	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
112	#947	—	2	1	no	—
113	C₂×#215	—	2	1	no	—
114	C₂×D₂₄	—	2	2	no	—
115	C₂×#204	—	2	1	no	—
116	#894	—	2	2	no	—
117	#893	—	2	1	no	—
118	#875	—	2	1	no	—
119	#874	C₂²×C₅	1	1	yes	characteristic
120	#874	C₂²×C₅	1	1	yes	characteristic
121	C₄×D₁₂	—	2	1	no	—
122	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
123	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
125	#821	—	2	1	no	—
126	#809	—	2	1	no	—
127	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₅×Q₈	—	3	1	no	—
129	C₂×C₅×Q₈	D₁₂	1	1	yes	characteristic
130	C₂×C₅×D₄	—	3	2	no	—
131	C₂×C₅×D₄	—	6	1	no	—
132	C₂×C₅×D₄	—	6	1	no	—
133	C₂×C₅×D₄	—	6	1	no	—
134	C₂×C₅×D₄	—	6	1	no	—
135	C₂×C₅×D₄	—	6	1	no	—
136	C₂²×C₄×C₅	—	6	2	no	—
137	C₅×SD₁₆	—	12	2	no	—
138	C₅×SD₁₆	—	12	2	no	—
139	C₅×D₈	—	12	4	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	6	1	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	3	1	no	—
145	C₅×C₄⋊C₄	—	6	1	no	—
146	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
147	C₅×C₂²⋊C₄	—	6	2	no	—
148	C₅×C₂²⋊C₄	—	6	2	no	—
149	C₅×C₂²⋊C₄	—	6	2	no	—
150	C₄²×C₅	—	2	1	no	—
151	C₄²×C₅	—	6	1	no	—
152	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
153	#559	—	3	1	no	—
154	#493	—	3	1	no	—
155	#460	—	3	1	no	—
156	#460	—	3	1	no	—
157	#331	—	3	1	no	—
158	Q₈⋊C₈	—	3	1	no	—
159	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
160	C₂²×C₃×C₅	#120	1	1	yes	characteristic
161	C₂×C₅×D₃	—	4	2	no	—
162	C₂×C₅×D₃	—	4	2	no	—
163	C₂×C₅×D₃	—	4	2	no	—
164	C₂×C₅×D₃	—	8	1	no	—
165	C₂×C₅×D₃	—	8	1	no	—
166	C₂×C₅×D₃	—	8	1	no	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	4	1	no	—
169	C₃×C₄×C₅	—	4	1	no	—
170	C₃×C₄×C₅	#135	1	1	yes	characteristic
171	C₃×C₄×C₅	#135	1	1	yes	characteristic
172	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₅×Dic₃	—	4	1	no	—
175	C₅×Dic₃	—	4	1	no	—
176	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
177	C₂×D₁₂	—	2	1	no	—
178	C₂×D₁₂	—	2	1	no	—
179	C₂×D₁₂	—	2	1	no	—
180	C₂×D₁₂	—	2	1	no	—
181	C₂×D₁₂	—	2	1	no	—
182	C₂×D₁₂	C₅×D₄	1	2	yes	—
183	C₂×C₄×D₃	—	2	2	no	—
184	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₃×C₄⋊C₄	—	2	1	no	—
188	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
189	C₃×C₄²	—	2	1	no	—
190	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
191	#215	—	4	2	no	—
192	(C₂×D₃)⋊C₄	—	2	2	no	—
193	(C₂×D₃)⋊C₄	—	2	2	no	—
194	(C₂×D₃)⋊C₄	—	2	2	no	—
195	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
196	Dic₃⋊C₄	—	2	1	no	—
197	C₄×Dic₃	—	2	1	no	—
198	C₂×C₃⋊C₈	—	2	1	no	—
199	D₂₄	—	4	4	no	—
200	#204	—	4	2	no	—
201	C₂³×C₅	—	6	2	no	—
202	C₂³×C₅	—	12	1	no	—
203	C₅×Q₈	—	2	1	no	—
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	6	1	no	—
206	C₅×Q₈	—	6	1	no	—
207	C₅×D₄	—	12	2	no	—
208	C₅×D₄	—	12	2	no	—
209	C₅×D₄	—	12	1	no	—
210	C₅×D₄	—	12	1	no	—
211	C₅×D₄	—	12	1	no	—
212	C₅×D₄	—	12	1	no	—
213	C₅×D₄	—	12	1	no	—
214	C₅×D₄	—	12	1	no	—
215	C₅×D₄	—	12	1	no	—
216	C₅×D₄	—	12	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	6	1	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	24	2	no	—
222	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
223	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	4	1	no	—
227	C₅×C₈	—	12	1	no	—
228	C₂×SD₁₆	—	6	1	no	—
229	C₂×SD₁₆	—	6	1	no	—
230	C₂×D₈	—	6	2	no	—
231	#127	—	3	1	no	—
232	#127	—	3	1	no	—
233	#124	—	6	1	no	—
234	#124	—	6	1	no	—
235	#123	—	6	2	no	—
236	C₄×Q₈	—	3	1	no	—
237	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
238	C₄×D₄	—	6	1	no	—
239	C₄×D₄	—	6	1	no	—
240	C₄⋊C₈	—	3	1	no	—
241	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
242	#102	—	6	1	no	—
243	#102	—	6	1	no	—
244	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
245	C₂×C₃×C₅	#449	1	1	yes	characteristic
246	C₂×C₃×C₅	#449	1	1	yes	characteristic
247	C₂×C₃×C₅	#453	1	1	yes	characteristic
248	C₅×D₃	—	8	2	no	—
249	C₅×D₃	—	16	1	no	—
250	C₂²×D₃	—	2	2	no	—
251	C₂²×D₃	—	4	1	no	—
252	C₃×Q₈	—	2	1	no	—
253	C₃×Q₈	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂×Dic₃	—	2	1	no	—
260	C₂×Dic₃	—	2	1	no	—
261	D₁₂	—	4	2	no	—
262	D₁₂	—	4	2	no	—
263	D₁₂	—	4	1	no	—
264	D₁₂	—	4	1	no	—
265	D₁₂	—	4	1	no	—
266	D₁₂	—	4	1	no	—
267	D₁₂	—	4	1	no	—
268	D₁₂	—	4	1	no	—
269	D₁₂	—	4	1	no	—
270	D₁₂	—	4	1	no	—
271	C₄×D₃	—	8	2	no	—
272	Dic₆	—	2	1	no	—
273	Dic₆	—	2	1	no	—
274	C₃×C₈	—	2	2	no	—
275	C₃×C₈	—	4	1	no	—
276	C₃⋊C₈	—	4	1	no	—
277	C₂²×C₅	—	12	2	no	—
278	C₂²×C₅	—	12	2	no	—
279	C₂²×C₅	—	12	2	no	—
280	C₂²×C₅	—	24	1	no	—
281	C₂²×C₅	—	24	1	no	—
282	C₂²×C₅	—	24	1	no	—
283	C₂²×C₅	#882	1	1	yes	characteristic
284	C₄×C₅	—	2	1	no	—
285	C₄×C₅	—	4	1	no	—
286	C₄×C₅	—	4	1	no	—
287	C₄×C₅	—	12	1	no	—
288	C₄×C₅	—	12	1	no	—
289	C₄×C₅	#904	1	1	yes	characteristic
290	C₄×C₅	#908	1	1	yes	characteristic
291	C₄×C₅	#914	1	1	yes	characteristic
292	C₄×C₅	#919	1	1	yes	characteristic
293	C₂×Q₈	—	3	1	no	—
294	C₂×Q₈	C₅×D₁₂	1	1	yes	characteristic
295	C₂×D₄	—	3	2	no	—
296	C₂×D₄	—	6	1	no	—
297	C₂×D₄	—	6	1	no	—
298	C₂×D₄	—	6	1	no	—
299	C₂×D₄	—	6	1	no	—
300	C₂×D₄	—	6	1	no	—
301	C₂²×C₄	—	6	2	no	—
302	SD₁₆	—	12	2	no	—
303	SD₁₆	—	12	2	no	—
304	D₈	—	12	4	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	6	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	3	1	no	—
310	C₄⋊C₄	—	6	1	no	—
311	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
312	C₂²⋊C₄	—	6	2	no	—
313	C₂²⋊C₄	—	6	2	no	—
314	C₂²⋊C₄	—	6	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	6	1	no	—
317	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
318	C₃×C₅	#1620	1	1	yes	characteristic, complemented, Hall
319	C₂²×C₃	C₅×#120	1	1	yes	characteristic
320	C₂×D₃	—	4	2	no	—
321	C₂×D₃	—	4	2	no	—
322	C₂×D₃	—	4	2	no	—
323	C₂×D₃	—	8	1	no	—
324	C₂×D₃	—	8	1	no	—
325	C₂×D₃	—	8	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	4	1	no	—
328	C₃×C₄	—	4	1	no	—
329	C₃×C₄	C₅×#135	1	1	yes	characteristic
330	C₃×C₄	C₅×#135	1	1	yes	characteristic
331	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
332	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
333	Dic₃	—	4	1	no	—
334	Dic₃	—	4	1	no	—
335	C₂×C₅	—	24	2	no	—
336	C₂×C₅	—	48	1	no	—
337	C₂×C₅	#4734	1	1	yes	characteristic
338	C₂×C₅	#4810	1	1	yes	characteristic
339	C₂×C₅	#4822	1	1	yes	characteristic
340	C₂³	—	6	2	no	—
341	C₂³	—	12	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	6	1	no	—
345	Q₈	—	6	1	no	—
346	D₄	—	12	2	no	—
347	D₄	—	12	2	no	—
348	D₄	—	12	1	no	—
349	D₄	—	12	1	no	—
350	D₄	—	12	1	no	—
351	D₄	—	12	1	no	—
352	D₄	—	12	1	no	—
353	D₄	—	12	1	no	—
354	D₄	—	12	1	no	—
355	D₄	—	12	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	6	1	no	—
359	C₂×C₄	—	6	1	no	—
360	C₂×C₄	—	24	2	no	—
361	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
362	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
363	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	4	1	no	—
366	C₈	—	12	1	no	—
367	C₂×C₃	C₅×#449	1	1	yes	characteristic
368	C₂×C₃	C₅×#449	1	1	yes	characteristic
369	C₂×C₃	C₅×#453	1	1	yes	characteristic
370	D₃	—	8	2	no	—
371	D₃	—	16	1	no	—
372	C₅	#68258	1	1	yes	characteristic, direct product factor, Sylow
373	C₂²	—	12	2	no	—
374	C₂²	—	12	2	no	—
375	C₂²	—	12	2	no	—
376	C₂²	—	24	1	no	—
377	C₂²	—	24	1	no	—
378	C₂²	—	24	1	no	—
379	C₂²	C₅×#882	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	12	1	no	—
384	C₄	—	12	1	no	—
385	C₄	C₅×#904	1	1	yes	characteristic
386	C₄	C₅×#908	1	1	yes	characteristic
387	C₄	C₅×#914	1	1	yes	characteristic
388	C₄	C₅×#919	1	1	yes	characteristic
389	C₃	C₅×#1620	1	1	yes	characteristic, complemented, Sylow
390	C₂	—	24	2	no	—
391	C₂	—	48	1	no	—
392	C₂	C₅×#4734	1	1	yes	characteristic
393	C₂	C₅×#4810	1	1	yes	characteristic
394	C₂	C₅×#4822	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#882
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×Q₈⋊C₈	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#4695	C₂
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1620
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₅×#5585	C₂	semidirect
2. C₅×#5027	C₂	semidirect
3. C₅×#4848	C₂	semidirect
5. C₃×C₅×Q₈⋊C₈	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4456	C₂	semidirect
26. #68258	C₅	direct (N × H)
33. C₅×Q₈⋊C₈	D₃	semidirect
59. #5585	C₂×C₅	semidirect
60. #5027	C₂×C₅	semidirect
61. #4848	C₂×C₅	semidirect
63. C₃×Q₈⋊C₈	C₂×C₅	semidirect
64. #4485	C₂×C₅	semidirect
65. #4456	C₂×C₅	semidirect
159. Q₈⋊C₈	C₅×D₃	semidirect
318. C₃×C₅	#1620	semidirect
372. C₅	#68258	direct (N × H)
389. C₃	C₅×#1620	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5585	2
C₅×#5027	2
C₅×#4848	2
C₅×#4695	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4485	2
C₅×#4456	2
C₅×#1620	3
#68258	5

Subgroups — C5×#68258 #14288854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68258 #14288854