Subgroups — C₅×#68244 #14288962

Order 1920.

472 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5579	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4843	C₂	1	1	yes	maximal, characteristic
4	C₅×#4693	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4481	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1622	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₅×#946	—	2	1	no	—
11	C₂×C₅×#215	—	2	1	no	—
12	C₂×C₅×D₂₄	—	2	1	no	—
13	C₂×C₅×#204	—	2	2	no	—
14	C₅×#896	—	2	2	no	—
15	C₅×D₃×C₄⋊C₄	—	2	1	no	—
16	C₅×#874	C₂²	1	1	yes	characteristic
17	C₄×C₅×D₁₂	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₅×#870	—	2	1	no	—
20	C₅×#869	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	#68244	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#554	—	3	1	no	—
28	C₅×#492	—	3	1	no	—
29	C₅×#460	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#333	—	3	1	no	—
32	C₅×Q₈⋊C₈	D₃	1	1	yes	characteristic, complemented
33	C₅×D₄⋊C₈	—	3	1	no	—
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	D₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	—	2	1	no	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₅×Dic₆	D₄	1	2	yes	—
42	C₂×C₃×C₅×C₈	—	2	1	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₃×C₅×C₄⋊C₄	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×#215	—	4	2	no	—
49	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
51	C₅×C₄⋊Dic₃	—	2	1	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
54	C₅×Dic₃⋊C₄	—	2	2	no	—
55	C₅×Dic₃⋊C₄	—	2	2	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₅×D₂₄	—	4	2	no	—
58	C₅×#204	—	4	4	no	—
59	#5579	C₂×C₅	1	1	yes	characteristic, complemented
60	#5027	C₂×C₅	1	1	yes	characteristic, complemented
61	#4843	C₂×C₅	1	1	yes	characteristic
62	#4693	C₂×C₅	1	1	yes	characteristic, complemented
63	C₃×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
64	#4481	C₂×C₅	1	1	yes	characteristic, complemented
65	#4459	C₂×C₅	1	1	yes	characteristic, complemented
66	C₂×C₅×SD₁₆	—	6	2	no	—
67	C₂×C₅×SD₁₆	—	6	1	no	—
68	C₂×C₅×D₈	—	6	1	no	—
69	C₅×C₄⋊Q₈	—	3	1	no	—
70	C₅×#127	—	3	1	no	—
71	C₅×#125	—	6	1	no	—
72	C₅×C₂²⋊Q₈	—	6	2	no	—
73	C₅×C₂²⋊Q₈	—	6	1	no	—
74	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
75	C₄×C₅×D₄	—	3	1	no	—
76	C₄×C₅×D₄	—	6	1	no	—
77	C₂×C₅×C₄⋊C₄	—	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	#1622	—	3	1	no	Sylow
84	C₂²×C₅×D₃	—	2	1	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	2	no	—
95	C₅×D₁₂	—	2	1	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	SD₁₆	1	2	yes	complemented
102	C₄×C₅×D₃	—	4	1	no	—
103	C₄×C₅×D₃	—	4	1	no	—
104	C₄×C₅×D₃	—	8	2	no	—
105	C₅×Dic₆	—	4	2	no	—
106	C₃×C₅×C₈	—	2	2	no	—
107	C₃×C₅×C₈	—	4	1	no	—
108	C₅×C₃⋊C₈	—	4	1	no	—
109	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
110	#946	—	2	1	no	—
111	C₂×#215	—	2	1	no	—
112	C₂×D₂₄	—	2	1	no	—
113	C₂×#204	—	2	2	no	—
114	#896	—	2	2	no	—
115	D₃×C₄⋊C₄	—	2	1	no	—
116	#874	C₂²×C₅	1	1	yes	characteristic
117	C₄×D₁₂	—	2	1	no	—
118	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
119	#870	—	2	1	no	—
120	#869	C₂²×C₅	1	1	yes	characteristic
121	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
122	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
123	#821	—	2	1	no	—
124	#809	—	2	1	no	—
125	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₅×Q₈	—	3	2	no	—
127	C₂×C₅×Q₈	D₁₂	1	1	yes	characteristic
128	C₂×C₅×D₄	—	3	1	no	—
129	C₂×C₅×D₄	—	6	1	no	—
130	C₂×C₅×D₄	—	6	1	no	—
131	C₂×C₅×D₄	—	6	1	no	—
132	C₂²×C₄×C₅	—	6	2	no	—
133	C₂²×C₄×C₅	—	6	1	no	—
134	C₅×SD₁₆	—	12	4	no	—
135	C₅×SD₁₆	—	12	2	no	—
136	C₅×D₈	—	12	2	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	6	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	3	1	no	—
142	C₅×C₄⋊C₄	—	6	2	no	—
143	C₅×C₄⋊C₄	—	6	2	no	—
144	C₅×C₄⋊C₄	—	6	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	1	no	—
149	C₄²×C₅	—	2	1	no	—
150	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
151	#554	—	3	1	no	—
152	#492	—	3	1	no	—
153	#460	—	3	1	no	—
154	#459	—	3	1	no	—
155	#333	—	3	1	no	—
156	Q₈⋊C₈	C₅×D₃	1	1	yes	characteristic, complemented
157	D₄⋊C₈	—	3	1	no	—
158	C₂²×C₃×C₅	#120	1	1	yes	characteristic
159	C₂×C₅×D₃	—	2	2	no	—
160	C₂×C₅×D₃	—	4	1	no	—
161	C₂×C₅×D₃	—	4	1	no	—
162	C₂×C₅×D₃	—	8	1	no	—
163	C₂×C₅×D₃	—	8	1	no	—
164	C₂×C₅×D₃	—	8	1	no	—
165	C₃×C₄×C₅	—	2	1	no	—
166	C₃×C₄×C₅	—	4	1	no	—
167	C₃×C₄×C₅	—	4	1	no	—
168	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
169	C₃×C₄×C₅	#135	1	1	yes	characteristic
170	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₃×C₄×C₅	#137	1	1	yes	characteristic
172	C₅×Dic₃	—	4	1	no	—
173	C₅×Dic₃	—	4	2	no	—
174	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
175	C₂×D₁₂	—	2	1	no	—
176	C₂×D₁₂	—	2	1	no	—
177	C₂×D₁₂	—	2	1	no	—
178	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
179	C₂×C₄×D₃	—	2	1	no	—
180	C₂×C₄×D₃	—	2	2	no	—
181	C₂×Dic₆	C₅×D₄	1	2	yes	—
182	C₂×C₃×C₈	—	2	1	no	—
183	C₂×C₃×C₈	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	1	no	—
185	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
188	#215	—	4	2	no	—
189	(C₂×D₃)⋊C₄	—	2	2	no	—
190	(C₂×D₃)⋊C₄	—	2	1	no	—
191	C₄⋊Dic₃	—	2	1	no	—
192	C₄⋊Dic₃	—	2	1	no	—
193	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
194	Dic₃⋊C₄	—	2	2	no	—
195	Dic₃⋊C₄	—	2	2	no	—
196	C₂×C₃⋊C₈	—	2	1	no	—
197	D₂₄	—	4	2	no	—
198	#204	—	4	4	no	—
199	C₂³×C₅	—	6	1	no	—
200	C₂³×C₅	—	12	1	no	—
201	C₅×Q₈	—	2	1	no	—
202	C₅×Q₈	—	2	1	no	—
203	C₅×Q₈	—	12	2	no	—
204	C₅×D₄	—	3	2	no	—
205	C₅×D₄	—	6	1	no	—
206	C₅×D₄	—	12	2	no	—
207	C₅×D₄	—	12	1	no	—
208	C₅×D₄	—	12	1	no	—
209	C₅×D₄	—	12	1	no	—
210	C₅×D₄	—	12	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	6	1	no	—
214	C₂×C₄×C₅	—	6	2	no	—
215	C₂×C₄×C₅	—	12	1	no	—
216	C₂×C₄×C₅	—	12	1	no	—
217	C₂×C₄×C₅	—	24	2	no	—
218	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
219	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
220	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
221	C₅×C₈	—	2	2	no	—
222	C₅×C₈	—	4	1	no	—
223	C₅×C₈	—	12	1	no	—
224	C₂×SD₁₆	—	6	2	no	—
225	C₂×SD₁₆	—	6	1	no	—
226	C₂×D₈	—	6	1	no	—
227	C₄⋊Q₈	—	3	1	no	—
228	#127	—	3	1	no	—
229	#125	—	6	1	no	—
230	C₂²⋊Q₈	—	6	2	no	—
231	C₂²⋊Q₈	—	6	1	no	—
232	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
233	C₄×D₄	—	3	1	no	—
234	C₄×D₄	—	6	1	no	—
235	C₂×C₄⋊C₄	—	6	1	no	—
236	C₄⋊C₈	—	3	1	no	—
237	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
238	#102	—	6	1	no	—
239	#102	—	6	1	no	—
240	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
241	C₂×C₃×C₅	#448	1	1	yes	characteristic
242	C₂×C₃×C₅	#449	1	1	yes	characteristic
243	C₂×C₃×C₅	#453	1	1	yes	characteristic
244	C₅×D₃	—	4	2	no	—
245	C₅×D₃	—	16	1	no	—
246	C₂²×D₃	—	2	1	no	—
247	C₂²×D₃	—	4	1	no	—
248	C₃×Q₈	—	2	1	no	—
249	C₃×Q₈	—	2	1	no	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×Dic₃	—	2	1	no	—
256	C₂×Dic₃	—	2	2	no	—
257	D₁₂	—	2	1	no	—
258	D₁₂	—	4	2	no	—
259	D₁₂	—	4	1	no	—
260	D₁₂	—	4	1	no	—
261	D₁₂	—	4	1	no	—
262	D₁₂	—	4	1	no	—
263	D₁₂	C₅×SD₁₆	1	2	yes	complemented
264	C₄×D₃	—	4	1	no	—
265	C₄×D₃	—	4	1	no	—
266	C₄×D₃	—	8	2	no	—
267	Dic₆	—	4	2	no	—
268	C₃×C₈	—	2	2	no	—
269	C₃×C₈	—	4	1	no	—
270	C₃⋊C₈	—	4	1	no	—
271	C₂²×C₅	—	6	2	no	—
272	C₂²×C₅	—	12	1	no	—
273	C₂²×C₅	—	12	1	no	—
274	C₂²×C₅	—	24	1	no	—
275	C₂²×C₅	—	24	1	no	—
276	C₂²×C₅	—	24	1	no	—
277	C₂²×C₅	#882	1	1	yes	characteristic
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	4	1	no	—
280	C₄×C₅	—	4	1	no	—
281	C₄×C₅	—	12	1	no	—
282	C₄×C₅	—	12	2	no	—
283	C₄×C₅	#904	1	1	yes	characteristic
284	C₄×C₅	#908	1	1	yes	characteristic
285	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
286	C₄×C₅	#918	1	1	yes	characteristic
287	C₂×Q₈	—	3	2	no	—
288	C₂×Q₈	C₅×D₁₂	1	1	yes	characteristic
289	C₂×D₄	—	3	1	no	—
290	C₂×D₄	—	6	1	no	—
291	C₂×D₄	—	6	1	no	—
292	C₂×D₄	—	6	1	no	—
293	C₂²×C₄	—	6	2	no	—
294	C₂²×C₄	—	6	1	no	—
295	SD₁₆	—	12	4	no	—
296	SD₁₆	—	12	2	no	—
297	D₈	—	12	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	6	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	3	1	no	—
303	C₄⋊C₄	—	6	2	no	—
304	C₄⋊C₄	—	6	2	no	—
305	C₄⋊C₄	—	6	1	no	—
306	C₄⋊C₄	—	6	1	no	—
307	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
308	C₂²⋊C₄	—	6	2	no	—
309	C₂²⋊C₄	—	6	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
312	C₃×C₅	#1622	1	1	yes	characteristic, complemented, Hall
313	C₂²×C₃	C₅×#120	1	1	yes	characteristic
314	C₂×D₃	—	2	2	no	—
315	C₂×D₃	—	4	1	no	—
316	C₂×D₃	—	4	1	no	—
317	C₂×D₃	—	8	1	no	—
318	C₂×D₃	—	8	1	no	—
319	C₂×D₃	—	8	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	—	4	1	no	—
323	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
324	C₃×C₄	C₅×#135	1	1	yes	characteristic
325	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₃×C₄	C₅×#137	1	1	yes	characteristic
327	Dic₃	—	4	1	no	—
328	Dic₃	—	4	2	no	—
329	C₂×C₅	—	12	2	no	—
330	C₂×C₅	—	48	1	no	—
331	C₂×C₅	#4734	1	1	yes	characteristic
332	C₂×C₅	#4806	1	1	yes	characteristic
333	C₂×C₅	#4822	1	1	yes	characteristic
334	C₂³	—	6	1	no	—
335	C₂³	—	12	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	12	2	no	—
339	D₄	—	3	2	no	—
340	D₄	—	6	1	no	—
341	D₄	—	12	2	no	—
342	D₄	—	12	1	no	—
343	D₄	—	12	1	no	—
344	D₄	—	12	1	no	—
345	D₄	—	12	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	6	1	no	—
349	C₂×C₄	—	6	2	no	—
350	C₂×C₄	—	12	1	no	—
351	C₂×C₄	—	12	1	no	—
352	C₂×C₄	—	24	2	no	—
353	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
354	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
355	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
356	C₈	—	2	2	no	—
357	C₈	—	4	1	no	—
358	C₈	—	12	1	no	—
359	C₂×C₃	C₅×#448	1	1	yes	characteristic
360	C₂×C₃	C₅×#449	1	1	yes	characteristic
361	C₂×C₃	C₅×#453	1	1	yes	characteristic
362	D₃	—	4	2	no	—
363	D₃	—	16	1	no	—
364	C₅	#68244	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	6	2	no	—
366	C₂²	—	12	1	no	—
367	C₂²	—	12	1	no	—
368	C₂²	—	24	1	no	—
369	C₂²	—	24	1	no	—
370	C₂²	—	24	1	no	—
371	C₂²	C₅×#882	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	12	1	no	—
376	C₄	—	12	2	no	—
377	C₄	C₅×#904	1	1	yes	characteristic
378	C₄	C₅×#908	1	1	yes	characteristic
379	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
380	C₄	C₅×#918	1	1	yes	characteristic
381	C₃	C₅×#1622	1	1	yes	characteristic, complemented, Sylow
382	C₂	—	12	2	no	—
383	C₂	—	48	1	no	—
384	C₂	C₅×#4734	1	1	yes	characteristic
385	C₂	C₅×#4806	1	1	yes	characteristic
386	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×#4843	C₂
hypercenter	C₅×Q₈⋊C₈	D₃
hypocenter	C₃	C₅×#1622
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×#5579	C₂	semidirect
2. C₅×#5027	C₂	semidirect
4. C₅×#4693	C₂	semidirect
5. C₃×C₅×Q₈⋊C₈	C₂	semidirect
6. C₅×#4481	C₂	semidirect
7. C₅×#4459	C₂	semidirect
26. #68244	C₅	direct (N × H)
32. C₅×Q₈⋊C₈	D₃	semidirect
59. #5579	C₂×C₅	semidirect
60. #5027	C₂×C₅	semidirect
62. #4693	C₂×C₅	semidirect
63. C₃×Q₈⋊C₈	C₂×C₅	semidirect
64. #4481	C₂×C₅	semidirect
65. #4459	C₂×C₅	semidirect
101. C₅×D₁₂	SD₁₆	semidirect
156. Q₈⋊C₈	C₅×D₃	semidirect
263. D₁₂	C₅×SD₁₆	semidirect
312. C₃×C₅	#1622	semidirect
364. C₅	#68244	direct (N × H)
381. C₃	C₅×#1622	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5579	2
C₅×#5027	2
C₅×#4843	2
C₅×#4693	2
C₃×C₅×Q₈⋊C₈	2
C₅×#4481	2
C₅×#4459	2
C₅×#1622	3
#68244	5

Subgroups — C5×#68244 #14288962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68244 #14288962