Subgroups — C₅×#71842 #14309015

Order 1920.

488 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5006	C₂	1	1	yes	maximal, characteristic
3	C₅×#5005	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic
5	C₅×#4533	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4531	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2031	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
11	C₃×C₅×#125	—	2	1	no	—
12	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
13	C₃×C₄×C₅×Q₈	—	2	2	no	—
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₅×#926	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	C₂²	1	1	yes	characteristic
19	C₂×C₅×#208	C₂²	1	1	yes	characteristic
20	C₅×#806	—	2	2	no	—
21	C₅×#805	—	2	1	no	—
22	C₅×#805	—	2	1	no	—
23	C₅×#805	—	2	2	no	—
24	#71842	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#533	D₃	1	1	yes	characteristic, complemented
26	C₅×#421	—	3	1	no	—
27	C₂×C₅×#104	—	3	1	no	—
28	C₅×#410	—	3	1	no	—
29	C₅×#344	—	3	1	no	—
30	C₅×#339	—	3	1	no	—
31	C₅×H(3,ℤ/4)	—	3	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₅×#67	—	2	1	no	—
36	C₅×#235	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₂×C₅×D₁₂	Q₈	1	1	yes	characteristic, complemented
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₅×Dic₆	Q₈	1	1	yes	characteristic, complemented
43	C₃×C₅×C₄⋊C₄	—	2	4	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
48	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	—	2	1	no	—
51	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
52	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
53	C₃×C₄²×C₅	D₄	1	2	yes	—
54	C₅×#217	—	2	1	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₄×C₅×Dic₃	—	2	1	no	—
57	C₅×#208	—	2	1	no	—
58	C₅×#208	—	2	1	no	—
59	C₅×#208	—	2	1	no	—
60	C₅×#208	—	2	1	no	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
64	#5006	C₂×C₅	1	1	yes	characteristic
65	#5005	C₂×C₅	1	1	yes	characteristic
66	C₂×#805	C₂×C₅	1	1	yes	characteristic
67	#4533	C₂×C₅	1	1	yes	characteristic, complemented
68	#4531	C₂×C₅	1	1	yes	characteristic, complemented
69	#4523	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×C₅×#41	—	3	1	no	—
71	C₂×C₅×M₁₆	—	3	1	no	—
72	C₂×C₅×M₁₆	—	3	1	no	—
73	C₅×C₄⋊Q₈	—	2	1	no	—
74	C₅×#125	—	2	1	no	—
75	C₅×C₂²⋊Q₈	—	2	2	no	—
76	C₄×C₅×Q₈	—	2	2	no	—
77	C₅×#117	—	3	1	no	—
78	C₅×#117	C₂×D₃	1	1	yes	characteristic
79	C₅×#117	C₂×D₃	1	1	yes	characteristic
80	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
81	C₅×#104	—	6	1	no	—
82	C₅×#104	—	6	1	no	—
83	C₅×#104	—	6	2	no	—
84	C₅×#99	—	6	2	no	—
85	#2031	—	3	1	no	Sylow
86	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₃×C₅×Q₈	—	4	4	no	—
89	C₂×C₃×C₄×C₅	—	2	1	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	2	2	no	—
92	C₂×C₃×C₄×C₅	—	2	2	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₅×#67	—	4	1	no	—
101	C₅×#67	—	4	1	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	—	4	1	no	—
104	C₅×D₁₂	—	2	1	no	—
105	C₅×D₁₂	—	2	1	no	—
106	C₄×C₅×D₃	—	4	1	no	—
107	C₄×C₅×D₃	—	4	1	no	—
108	C₅×Dic₆	—	2	1	no	—
109	C₅×Dic₆	—	2	1	no	—
110	C₅×C₃⋊C₈	—	4	1	no	—
111	C₅×C₃⋊C₈	—	4	1	no	—
112	C₂×#235	C₂²×C₅	1	1	yes	characteristic
113	C₃×C₄⋊Q₈	—	2	1	no	—
114	C₃×#125	—	2	1	no	—
115	C₃×C₂²⋊Q₈	—	2	2	no	—
116	C₃×C₄×Q₈	—	2	2	no	—
117	C₃×#117	C₂²×C₅	1	1	yes	characteristic
118	C₃×#117	C₂²×C₅	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
120	#926	C₂²×C₅	1	1	yes	characteristic
121	C₂×#208	C₂²×C₅	1	1	yes	characteristic
122	C₂×#208	C₂²×C₅	1	1	yes	characteristic
123	#806	—	2	2	no	—
124	#805	—	2	1	no	—
125	#805	—	2	1	no	—
126	#805	—	2	2	no	—
127	C₅×#41	—	6	1	no	—
128	C₅×#41	—	6	1	no	—
129	C₅×#41	—	6	1	no	—
130	C₅×#41	—	6	1	no	—
131	C₂×C₅×Q₈	—	2	2	no	—
132	C₂×C₅×Q₈	—	3	1	no	—
133	C₂×C₅×D₄	—	3	1	no	—
134	C₂×C₅×D₄	—	6	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	6	1	no	—
137	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₅×M₁₆	—	6	1	no	—
139	C₅×M₁₆	—	6	1	no	—
140	C₅×M₁₆	—	6	1	no	—
141	C₅×M₁₆	—	6	1	no	—
142	C₂×C₅×C₈	—	6	1	no	—
143	C₂×C₅×C₈	—	6	1	no	—
144	C₅×C₄⋊C₄	—	2	4	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₂²⋊C₄	—	2	1	no	—
150	C₅×C₂²⋊C₄	—	6	1	no	—
151	C₅×C₂²⋊C₄	#67	1	2	yes	—
152	C₄²×C₅	—	2	1	no	—
153	C₄²×C₅	—	2	1	no	—
154	C₄²×C₅	—	6	1	no	—
155	C₄²×C₅	#67	1	1	yes	characteristic
156	C₄²×C₅	#67	1	1	yes	characteristic
157	C₄²×C₅	#67	1	2	yes	—
158	#533	C₅×D₃	1	1	yes	characteristic, complemented
159	#421	—	3	1	no	—
160	C₂×#104	—	3	1	no	—
161	#410	—	3	1	no	—
162	#344	—	3	1	no	—
163	#339	—	3	1	no	—
164	H(3,ℤ/4)	—	3	1	no	—
165	C₂²×C₃×C₅	—	4	1	no	—
166	C₂²×C₃×C₅	#120	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂²×C₃×C₅	#124	1	1	yes	characteristic
169	C₂×C₅×D₃	—	4	1	no	—
170	C₂×C₅×D₃	—	8	1	no	—
171	C₃×C₄×C₅	—	2	2	no	—
172	C₃×C₄×C₅	—	4	1	no	—
173	C₃×C₄×C₅	—	4	2	no	—
174	C₃×C₄×C₅	—	4	2	no	—
175	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
176	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
177	C₃×C₄×C₅	#124	1	1	yes	characteristic
178	C₃×C₄×C₅	#124	1	1	yes	characteristic
179	C₅×Dic₃	—	4	1	no	—
180	C₅×Dic₃	—	8	1	no	—
181	C₂×C₃×Q₈	—	2	2	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
184	C₂×#67	—	2	1	no	—
185	#235	—	2	1	no	—
186	#235	—	2	1	no	—
187	#235	—	2	1	no	—
188	#235	—	2	1	no	—
189	C₂×D₁₂	C₅×Q₈	1	1	yes	characteristic, complemented
190	C₂×C₄×D₃	—	2	1	no	—
191	C₂×Dic₆	C₅×Q₈	1	1	yes	characteristic, complemented
192	C₃×C₄⋊C₄	—	2	4	no	—
193	C₃×C₄⋊C₄	—	2	2	no	—
194	C₃×C₄⋊C₄	—	2	1	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₂²⋊C₄	—	2	1	no	—
197	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
198	C₃×C₄²	—	2	1	no	—
199	C₃×C₄²	—	2	1	no	—
200	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
201	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
202	C₃×C₄²	C₅×D₄	1	2	yes	—
203	#217	—	2	1	no	—
204	C₄⋊Dic₃	—	2	1	no	—
205	C₄×Dic₃	—	2	1	no	—
206	#208	—	2	1	no	—
207	#208	—	2	1	no	—
208	#208	—	2	1	no	—
209	#208	—	2	1	no	—
210	C₂×C₃⋊C₈	—	2	1	no	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	C₂³×C₅	—	6	1	no	—
213	C₂³×C₅	C₂×#67	1	1	yes	characteristic
214	C₅×Q₈	—	4	4	no	—
215	C₅×Q₈	—	6	1	no	—
216	C₅×Q₈	—	6	1	no	—
217	C₅×D₄	—	6	1	no	—
218	C₅×D₄	—	6	1	no	—
219	C₅×D₄	—	12	1	no	—
220	C₅×D₄	—	12	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	6	1	no	—
227	C₂×C₄×C₅	—	12	1	no	—
228	C₂×C₄×C₅	—	12	1	no	—
229	C₂×C₄×C₅	—	12	1	no	—
230	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
231	C₂×C₄×C₅	#239	1	1	yes	characteristic
232	C₂×C₄×C₅	#239	1	1	yes	characteristic
233	C₂×C₄×C₅	#239	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
236	C₅×C₈	—	12	1	no	—
237	C₅×C₈	—	12	1	no	—
238	C₂×#41	—	3	1	no	—
239	C₂×M₁₆	—	3	1	no	—
240	C₂×M₁₆	—	3	1	no	—
241	C₄⋊Q₈	—	2	1	no	—
242	#125	—	2	1	no	—
243	C₂²⋊Q₈	—	2	2	no	—
244	C₄×Q₈	—	2	2	no	—
245	#117	—	3	1	no	—
246	#117	C₂×C₅×D₃	1	1	yes	characteristic
247	#117	C₂×C₅×D₃	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
249	#104	—	6	1	no	—
250	#104	—	6	1	no	—
251	#104	—	6	2	no	—
252	#99	—	6	2	no	—
253	C₂×C₃×C₅	—	2	1	no	—
254	C₂×C₃×C₅	—	2	1	no	—
255	C₂×C₃×C₅	—	2	1	no	—
256	C₂×C₃×C₅	#393	1	1	yes	characteristic
257	C₅×D₃	—	8	1	no	—
258	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂²×D₃	—	2	1	no	—
260	C₃×Q₈	—	4	4	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	2	2	no	—
265	C₂×C₃×C₄	—	4	2	no	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
268	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
269	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
270	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
271	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
272	#67	—	4	1	no	—
273	#67	—	4	1	no	—
274	C₂×Dic₃	—	2	1	no	—
275	C₂×Dic₃	—	4	1	no	—
276	D₁₂	—	2	1	no	—
277	D₁₂	—	2	1	no	—
278	C₄×D₃	—	4	1	no	—
279	C₄×D₃	—	4	1	no	—
280	Dic₆	—	2	1	no	—
281	Dic₆	—	2	1	no	—
282	C₃⋊C₈	—	4	1	no	—
283	C₃⋊C₈	—	4	1	no	—
284	C₂²×C₅	—	4	1	no	—
285	C₂²×C₅	—	12	1	no	—
286	C₂²×C₅	—	24	1	no	—
287	C₂²×C₅	#946	1	1	yes	characteristic
288	C₂²×C₅	#947	1	1	yes	characteristic
289	C₂²×C₅	#953	1	1	yes	characteristic
290	C₄×C₅	—	2	2	no	—
291	C₄×C₅	—	4	1	no	—
292	C₄×C₅	—	4	2	no	—
293	C₄×C₅	—	4	2	no	—
294	C₄×C₅	—	12	1	no	—
295	C₄×C₅	—	24	1	no	—
296	C₄×C₅	#946	1	1	yes	characteristic
297	C₄×C₅	#946	1	1	yes	characteristic
298	C₄×C₅	#947	1	1	yes	characteristic
299	C₄×C₅	#947	1	1	yes	characteristic
300	#41	—	6	1	no	—
301	#41	—	6	1	no	—
302	#41	—	6	1	no	—
303	#41	—	6	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	3	1	no	—
306	C₂×D₄	—	3	1	no	—
307	C₂×D₄	—	6	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	6	1	no	—
310	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
311	M₁₆	—	6	1	no	—
312	M₁₆	—	6	1	no	—
313	M₁₆	—	6	1	no	—
314	M₁₆	—	6	1	no	—
315	C₂×C₈	—	6	1	no	—
316	C₂×C₈	—	6	1	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	6	1	no	—
322	C₂²⋊C₄	—	2	1	no	—
323	C₂²⋊C₄	—	6	1	no	—
324	C₂²⋊C₄	C₅×#67	1	2	yes	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	6	1	no	—
328	C₄²	C₅×#67	1	1	yes	characteristic
329	C₄²	C₅×#67	1	1	yes	characteristic
330	C₄²	C₅×#67	1	2	yes	—
331	C₃×C₅	#2031	1	1	yes	characteristic, complemented, Hall
332	C₂²×C₃	—	4	1	no	—
333	C₂²×C₃	C₅×#120	1	1	yes	characteristic
334	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
335	C₂²×C₃	C₅×#124	1	1	yes	characteristic
336	C₂×D₃	—	4	1	no	—
337	C₂×D₃	—	8	1	no	—
338	C₃×C₄	—	2	2	no	—
339	C₃×C₄	—	4	1	no	—
340	C₃×C₄	—	4	2	no	—
341	C₃×C₄	—	4	2	no	—
342	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
343	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
344	C₃×C₄	C₅×#124	1	1	yes	characteristic
345	C₃×C₄	C₅×#124	1	1	yes	characteristic
346	Dic₃	—	4	1	no	—
347	Dic₃	—	8	1	no	—
348	C₂×C₅	—	2	1	no	—
349	C₂×C₅	—	2	1	no	—
350	C₂×C₅	—	2	1	no	—
351	C₂×C₅	—	24	1	no	—
352	C₂×C₅	#5231	1	1	yes	characteristic
353	C₂³	—	6	1	no	—
354	C₂³	C₂×C₅×#67	1	1	yes	characteristic
355	Q₈	—	4	4	no	—
356	Q₈	—	6	1	no	—
357	Q₈	—	6	1	no	—
358	D₄	—	6	1	no	—
359	D₄	—	6	1	no	—
360	D₄	—	12	1	no	—
361	D₄	—	12	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	6	1	no	—
368	C₂×C₄	—	12	1	no	—
369	C₂×C₄	—	12	1	no	—
370	C₂×C₄	—	12	1	no	—
371	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
372	C₂×C₄	C₅×#239	1	1	yes	characteristic
373	C₂×C₄	C₅×#239	1	1	yes	characteristic
374	C₂×C₄	C₅×#239	1	1	yes	characteristic
375	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
376	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
377	C₈	—	12	1	no	—
378	C₈	—	12	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	C₅×#393	1	1	yes	characteristic
383	D₃	—	8	1	no	—
384	C₅	#71842	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	4	1	no	—
386	C₂²	—	12	1	no	—
387	C₂²	—	24	1	no	—
388	C₂²	C₅×#946	1	1	yes	characteristic
389	C₂²	C₅×#947	1	1	yes	characteristic
390	C₂²	C₅×#953	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	12	1	no	—
396	C₄	—	24	1	no	—
397	C₄	C₅×#946	1	1	yes	characteristic
398	C₄	C₅×#946	1	1	yes	characteristic
399	C₄	C₅×#947	1	1	yes	characteristic
400	C₄	C₅×#947	1	1	yes	characteristic
401	C₃	C₅×#2031	1	1	yes	characteristic, complemented, Sylow
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	24	1	no	—
406	C₂	C₅×#5231	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#947
commutator, cosocle	C₂²×C₃×C₄	C₂³×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#533	C₂
socle	C₂×C₃×C₅	#393
prime radical	C₂×C₅×#235	C₂²
hypercenter	C₅×#533	D₃
hypocenter	C₃	C₅×#2031
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#533

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
5. C₅×#4533	C₂	semidirect
6. C₅×#4531	C₂	semidirect
7. C₅×#4523	C₂	semidirect
24. #71842	C₅	direct (N × H)
25. C₅×#533	D₃	semidirect
40. C₂×C₅×D₁₂	Q₈	semidirect
42. C₂×C₅×Dic₆	Q₈	semidirect
63. C₃×#533	C₂×C₅	semidirect
67. #4533	C₂×C₅	semidirect
68. #4531	C₂×C₅	semidirect
69. #4523	C₂×C₅	semidirect
158. #533	C₅×D₃	semidirect
189. C₂×D₁₂	C₅×Q₈	semidirect
191. C₂×Dic₆	C₅×Q₈	semidirect
331. C₃×C₅	#2031	semidirect
384. C₅	#71842	direct (N × H)
401. C₃	C₅×#2031	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#533	2
C₅×#5006	2
C₅×#5005	2
C₂×C₅×#805	2
C₅×#4533	2
C₅×#4531	2
C₅×#4523	2
C₅×#2031	3
#71842	5

Subgroups — C5×#71842 #14309015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71842 #14309015