Subgroups — C₅×#71205 #14289211

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5727	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5075	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5072	C₂	1	1	yes	maximal, characteristic
5	C₅×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4459	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4456	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1627	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#127	C₂²	1	1	yes	characteristic
12	C₅×#946	—	2	1	no	—
13	C₂×C₅×#214	—	2	1	no	—
14	C₂×C₅×#213	—	2	1	no	—
15	C₅×#896	—	2	2	no	—
16	C₅×#893	—	2	1	no	—
17	C₅×#888	—	2	1	no	—
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₃×C₅×#102	—	2	2	no	—
21	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×#832	—	2	1	no	—
23	C₅×#832	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#71205	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄×Q₈	—	3	1	no	—
28	C₅×#486	D₃	1	1	yes	characteristic, complemented
29	C₅×#460	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×Q₈⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₅×D₃×Q₈	—	4	2	no	—
39	C₅×D₃×Q₈	—	4	2	no	—
40	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₅×Dic₆	—	2	2	no	—
44	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
48	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
49	C₅×#214	—	4	2	no	—
50	C₅×#213	—	4	2	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
53	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
54	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
55	C₅×Dic₃⋊C₄	—	2	2	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	#5727	C₂×C₅	1	1	yes	characteristic, complemented
61	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
62	#5075	C₂×C₅	1	1	yes	characteristic, complemented
63	#5072	C₂×C₅	1	1	yes	characteristic
64	#4547	C₂×C₅	1	1	yes	characteristic, complemented
65	#4459	C₂×C₅	1	1	yes	characteristic, complemented
66	#4456	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂²×C₅×Q₈	—	6	1	no	—
68	C₂×C₅×SD₁₆	—	6	1	no	—
69	C₂×C₅×D₈	—	6	1	no	—
70	C₅×C₄⋊Q₈	—	6	1	no	—
71	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
72	C₅×#127	C₂×D₃	1	1	yes	characteristic
73	C₅×C₂²⋊Q₈	—	6	1	no	—
74	C₅×C₂²⋊Q₈	—	6	2	no	—
75	C₄×C₅×Q₈	—	3	1	no	—
76	C₄×C₅×D₄	—	3	1	no	—
77	C₄×C₅×D₄	—	6	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×#102	—	2	2	no	—
81	C₅×#102	—	6	1	no	—
82	C₅×#102	—	6	1	no	—
83	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	#1627	—	3	1	no	Sylow
85	C₂³×C₃×C₅	—	4	1	no	—
86	C₂²×C₅×D₃	—	2	1	no	—
87	C₃×C₅×Q₈	—	4	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×D₄	—	4	2	no	—
90	C₃×C₅×D₄	—	4	1	no	—
91	C₃×C₅×D₄	—	4	1	no	—
92	C₃×C₅×D₄	—	4	1	no	—
93	C₃×C₅×D₄	—	4	1	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂×C₅×Dic₃	—	2	1	no	—
99	C₂×C₅×Dic₃	—	2	1	no	—
100	C₂×C₅×Dic₃	—	2	1	no	—
101	C₅×D₁₂	—	2	1	no	—
102	C₅×D₁₂	SD₁₆	1	2	yes	complemented
103	C₄×C₅×D₃	—	4	4	no	—
104	C₄×C₅×D₃	—	4	1	no	—
105	C₄×C₅×D₃	—	4	1	no	—
106	C₅×Dic₆	—	2	1	no	—
107	C₅×Dic₆	—	4	4	no	—
108	C₅×Dic₆	D₈	1	2	yes	complemented
109	C₃×C₅×C₈	—	4	1	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₅×C₃⋊C₈	—	4	1	no	—
112	C₂×D₃×Q₈	—	2	1	no	—
113	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
114	C₃×#127	C₂²×C₅	1	1	yes	characteristic
115	#946	—	2	1	no	—
116	C₂×#214	—	2	1	no	—
117	C₂×#213	—	2	1	no	—
118	#896	—	2	2	no	—
119	#893	—	2	1	no	—
120	#888	—	2	1	no	—
121	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
122	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
123	C₃×#102	—	2	2	no	—
124	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
125	#832	—	2	1	no	—
126	#832	—	2	1	no	—
127	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
128	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	3	1	no	—
131	C₂×C₅×Q₈	—	6	2	no	—
132	C₂×C₅×Q₈	—	12	2	no	—
133	C₂×C₅×Q₈	—	12	2	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	3	1	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₂²×C₄×C₅	—	6	1	no	—
140	C₅×SD₁₆	—	12	2	no	—
141	C₅×D₈	—	12	2	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₂×C₅×C₈	—	6	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	3	1	no	—
147	C₅×C₄⋊C₄	—	3	1	no	—
148	C₅×C₄⋊C₄	—	6	2	no	—
149	C₅×C₄⋊C₄	—	6	1	no	—
150	C₅×C₄⋊C₄	#67	1	2	yes	—
151	C₅×C₂²⋊C₄	—	6	2	no	—
152	C₅×C₂²⋊C₄	—	6	1	no	—
153	C₄²×C₅	—	6	1	no	—
154	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
155	D₄×Q₈	—	3	1	no	—
156	#486	C₅×D₃	1	1	yes	characteristic, complemented
157	#460	—	3	1	no	—
158	#459	—	3	1	no	—
159	#332	—	3	1	no	—
160	Q₈⋊C₈	—	3	1	no	—
161	D₄⋊C₈	—	3	1	no	—
162	C₂²×C₃×C₅	—	8	1	no	—
163	C₂²×C₃×C₅	—	8	1	no	—
164	C₂²×C₃×C₅	—	8	1	no	—
165	C₂²×C₃×C₅	#120	1	1	yes	characteristic
166	C₂×C₅×D₃	—	2	2	no	—
167	C₂×C₅×D₃	—	4	1	no	—
168	C₂×C₅×D₃	—	4	1	no	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	—	4	2	no	—
171	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
173	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
174	C₃×C₄×C₅	#137	1	1	yes	characteristic
175	C₅×Dic₃	—	2	2	no	—
176	C₅×Dic₃	—	4	1	no	—
177	C₅×Dic₃	—	4	1	no	—
178	C₂×C₃×Q₈	—	2	1	no	—
179	C₂×C₃×D₄	—	2	1	no	—
180	C₂×C₃×D₄	—	2	1	no	—
181	C₂×C₃×D₄	—	2	1	no	—
182	D₃×Q₈	—	4	2	no	—
183	D₃×Q₈	—	4	2	no	—
184	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
185	C₂×C₄×D₃	—	2	2	no	—
186	C₂×C₄×D₃	—	2	1	no	—
187	C₂×Dic₆	—	2	2	no	—
188	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
189	C₂×C₃×C₈	—	2	1	no	—
190	C₃×C₄⋊C₄	—	2	1	no	—
191	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
192	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
193	#214	—	4	2	no	—
194	#213	—	4	2	no	—
195	(C₂×D₃)⋊C₄	—	2	2	no	—
196	(C₂×D₃)⋊C₄	—	2	1	no	—
197	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
198	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
199	Dic₃⋊C₄	—	2	2	no	—
200	Dic₃⋊C₄	—	2	1	no	—
201	C₄×Dic₃	—	2	1	no	—
202	C₂×C₃⋊C₈	—	2	1	no	—
203	C₂×C₃⋊C₈	—	2	1	no	—
204	C₂³×C₅	—	4	1	no	—
205	C₂³×C₅	—	6	1	no	—
206	C₅×Q₈	—	3	2	no	—
207	C₅×Q₈	—	4	1	no	—
208	C₅×Q₈	—	4	1	no	—
209	C₅×Q₈	—	6	1	no	—
210	C₅×Q₈	—	12	4	no	—
211	C₅×D₄	—	3	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	1	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	4	1	no	—
216	C₅×D₄	—	4	1	no	—
217	C₅×D₄	—	6	1	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	6	1	no	—
220	C₂×C₄×C₅	—	6	1	no	—
221	C₂×C₄×C₅	—	6	1	no	—
222	C₂×C₄×C₅	—	12	4	no	—
223	C₂×C₄×C₅	—	12	1	no	—
224	C₂×C₄×C₅	—	12	1	no	—
225	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
226	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
228	C₅×C₈	—	4	1	no	—
229	C₅×C₈	—	12	1	no	—
230	C₅×C₈	—	12	1	no	—
231	C₂²×Q₈	—	6	1	no	—
232	C₂×SD₁₆	—	6	1	no	—
233	C₂×D₈	—	6	1	no	—
234	C₄⋊Q₈	—	6	1	no	—
235	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
236	#127	C₂×C₅×D₃	1	1	yes	characteristic
237	C₂²⋊Q₈	—	6	1	no	—
238	C₂²⋊Q₈	—	6	2	no	—
239	C₄×Q₈	—	3	1	no	—
240	C₄×D₄	—	3	1	no	—
241	C₄×D₄	—	6	1	no	—
242	C₄⋊C₈	—	3	1	no	—
243	C₄⋊C₈	—	3	1	no	—
244	#102	—	2	2	no	—
245	#102	—	6	1	no	—
246	#102	—	6	1	no	—
247	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
248	C₂×C₃×C₅	—	16	1	no	—
249	C₂×C₃×C₅	#447	1	1	yes	characteristic
250	C₂×C₃×C₅	#448	1	1	yes	characteristic
251	C₂×C₃×C₅	#454	1	1	yes	characteristic
252	C₅×D₃	—	4	2	no	—
253	C₂³×C₃	—	4	1	no	—
254	C₂²×D₃	—	2	1	no	—
255	C₃×Q₈	—	4	1	no	—
256	C₃×Q₈	—	4	1	no	—
257	C₃×D₄	—	4	2	no	—
258	C₃×D₄	—	4	1	no	—
259	C₃×D₄	—	4	1	no	—
260	C₃×D₄	—	4	1	no	—
261	C₃×D₄	—	4	1	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
266	C₂×Dic₃	—	2	1	no	—
267	C₂×Dic₃	—	2	1	no	—
268	C₂×Dic₃	—	2	1	no	—
269	D₁₂	—	2	1	no	—
270	D₁₂	C₅×SD₁₆	1	2	yes	complemented
271	C₄×D₃	—	4	4	no	—
272	C₄×D₃	—	4	1	no	—
273	C₄×D₃	—	4	1	no	—
274	Dic₆	—	2	1	no	—
275	Dic₆	—	4	4	no	—
276	Dic₆	C₅×D₈	1	2	yes	complemented
277	C₃×C₈	—	4	1	no	—
278	C₃⋊C₈	—	4	1	no	—
279	C₃⋊C₈	—	4	1	no	—
280	C₂²×C₅	—	6	2	no	—
281	C₂²×C₅	—	8	1	no	—
282	C₂²×C₅	—	8	1	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	12	1	no	—
285	C₂²×C₅	—	12	1	no	—
286	C₂²×C₅	#937	1	1	yes	characteristic
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	6	2	no	—
290	C₄×C₅	—	12	1	no	—
291	C₄×C₅	—	12	1	no	—
292	C₄×C₅	D₃×D₈	1	1	yes	characteristic
293	C₄×C₅	#911	1	1	yes	characteristic
294	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
295	C₄×C₅	#915	1	1	yes	characteristic
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	3	1	no	—
298	C₂×Q₈	—	6	2	no	—
299	C₂×Q₈	—	12	2	no	—
300	C₂×Q₈	—	12	2	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	3	1	no	—
305	C₂²×C₄	—	6	2	no	—
306	C₂²×C₄	—	6	1	no	—
307	SD₁₆	—	12	2	no	—
308	D₈	—	12	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	6	1	no	—
311	C₂×C₈	—	6	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	3	1	no	—
314	C₄⋊C₄	—	3	1	no	—
315	C₄⋊C₄	—	6	2	no	—
316	C₄⋊C₄	—	6	1	no	—
317	C₄⋊C₄	C₅×#67	1	2	yes	—
318	C₂²⋊C₄	—	6	2	no	—
319	C₂²⋊C₄	—	6	1	no	—
320	C₄²	—	6	1	no	—
321	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
322	C₃×C₅	#1627	1	1	yes	characteristic, complemented, Hall
323	C₂²×C₃	—	8	1	no	—
324	C₂²×C₃	—	8	1	no	—
325	C₂²×C₃	—	8	1	no	—
326	C₂²×C₃	C₅×#120	1	1	yes	characteristic
327	C₂×D₃	—	2	2	no	—
328	C₂×D₃	—	4	1	no	—
329	C₂×D₃	—	4	1	no	—
330	C₃×C₄	—	2	1	no	—
331	C₃×C₄	—	4	2	no	—
332	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
333	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
334	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₃×C₄	C₅×#137	1	1	yes	characteristic
336	Dic₃	—	2	2	no	—
337	Dic₃	—	4	1	no	—
338	Dic₃	—	4	1	no	—
339	C₂×C₅	—	12	2	no	—
340	C₂×C₅	—	16	1	no	—
341	C₂×C₅	#5062	1	1	yes	characteristic
342	C₂×C₅	#5156	1	1	yes	characteristic
343	C₂×C₅	#5170	1	1	yes	characteristic
344	C₂³	—	4	1	no	—
345	C₂³	—	6	1	no	—
346	Q₈	—	3	2	no	—
347	Q₈	—	4	1	no	—
348	Q₈	—	4	1	no	—
349	Q₈	—	6	1	no	—
350	Q₈	—	12	4	no	—
351	D₄	—	3	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	1	no	—
357	D₄	—	6	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	6	1	no	—
360	C₂×C₄	—	6	1	no	—
361	C₂×C₄	—	6	1	no	—
362	C₂×C₄	—	12	4	no	—
363	C₂×C₄	—	12	1	no	—
364	C₂×C₄	—	12	1	no	—
365	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
366	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
367	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	12	1	no	—
370	C₈	—	12	1	no	—
371	C₂×C₃	—	16	1	no	—
372	C₂×C₃	C₅×#447	1	1	yes	characteristic
373	C₂×C₃	C₅×#448	1	1	yes	characteristic
374	C₂×C₃	C₅×#454	1	1	yes	characteristic
375	D₃	—	4	2	no	—
376	C₅	#71205	1	1	yes	characteristic, direct product factor, Sylow
377	C₂²	—	6	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	8	1	no	—
380	C₂²	—	8	1	no	—
381	C₂²	—	12	1	no	—
382	C₂²	—	12	1	no	—
383	C₂²	C₅×#937	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	6	2	no	—
387	C₄	—	12	1	no	—
388	C₄	—	12	1	no	—
389	C₄	C₅×D₃×D₈	1	1	yes	characteristic
390	C₄	C₅×#911	1	1	yes	characteristic
391	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
392	C₄	C₅×#915	1	1	yes	characteristic
393	C₃	C₅×#1627	1	1	yes	characteristic, complemented, Sylow
394	C₂	—	12	2	no	—
395	C₂	—	16	1	no	—
396	C₂	C₅×#5062	1	1	yes	characteristic
397	C₂	C₅×#5156	1	1	yes	characteristic
398	C₂	C₅×#5170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#486	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×#5072	C₂
hypercenter	C₅×#486	D₃
hypocenter	C₃	C₅×#1627
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#486

Complements

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

N	H ≅ G/N	type
1. C₅×#5727	C₂	semidirect
2. C₃×C₅×#486	C₂	semidirect
3. C₅×#5075	C₂	semidirect
5. C₅×#4547	C₂	semidirect
6. C₅×#4459	C₂	semidirect
7. C₅×#4456	C₂	semidirect
26. #71205	C₅	direct (N × H)
28. C₅×#486	D₃	semidirect
60. #5727	C₂×C₅	semidirect
61. C₃×#486	C₂×C₅	semidirect
62. #5075	C₂×C₅	semidirect
64. #4547	C₂×C₅	semidirect
65. #4459	C₂×C₅	semidirect
66. #4456	C₂×C₅	semidirect
102. C₅×D₁₂	SD₁₆	semidirect
108. C₅×Dic₆	D₈	semidirect
156. #486	C₅×D₃	semidirect
270. D₁₂	C₅×SD₁₆	semidirect
276. Dic₆	C₅×D₈	semidirect
322. C₃×C₅	#1627	semidirect
376. C₅	#71205	direct (N × H)
393. C₃	C₅×#1627	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5727	2
C₃×C₅×#486	2
C₅×#5075	2
C₅×#5072	2
C₅×#4547	2
C₅×#4459	2
C₅×#4456	2
C₅×#1627	3
#71205	5

Subgroups — C5×#71205 #14289211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71205 #14289211