Subgroups — C₅×#70577 #14297867

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4987	C₂	1	2	yes	maximal
5	C₅×#4529	C₂	1	2	yes	maximal, complemented
6	C₅×#1807	—	3	1	no	maximal, Hall
7	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
11	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×D₃×C₈	—	2	2	no	—
14	C₂×C₅×D₃×C₈	—	2	2	no	—
15	C₂×C₅×D₃×C₈	C₄	1	4	yes	complemented
16	C₃×C₅×#106	—	2	2	no	—
17	C₅×C₃⋊#95	—	2	2	no	—
18	C₅×#817	—	2	2	no	—
19	#70577	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂³×C₅×C₈	—	3	1	no	—
21	C₂×C₅×#106	—	3	1	no	—
22	C₂×C₅×#106	D₃	1	1	yes	characteristic, complemented
23	C₅×#380	—	3	2	no	—
24	C₅×#340	—	3	2	no	—
25	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
28	C₂²×C₅×Dic₃	—	2	2	no	—
29	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
30	C₂×C₄×C₅×D₃	—	2	1	no	—
31	C₂×C₄×C₅×D₃	—	2	1	no	—
32	C₂×C₄×C₅×D₃	—	2	1	no	—
33	C₂×C₄×C₅×D₃	—	2	1	no	—
34	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
35	C₂×C₄×C₅×D₃	Q₈	1	2	yes	—
36	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
38	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
39	C₃×C₅×C₄⋊C₄	—	2	2	no	—
40	C₃×C₅×C₄⋊C₄	—	2	2	no	—
41	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
42	C₅×C₄⋊Dic₃	—	2	2	no	—
43	C₅×C₄⋊Dic₃	—	2	2	no	—
44	C₂×C₅×C₃⋊C₈	—	2	1	no	—
45	C₂×C₅×C₃⋊C₈	—	2	1	no	—
46	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
47	C₅×D₃×C₈	—	2	8	no	—
48	C₂²×D₃×C₈	C₂×C₅	1	1	yes	characteristic
49	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
50	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
51	#4987	C₂×C₅	1	2	yes	—
52	#4529	C₂×C₅	1	2	yes	complemented
53	C₂³×C₄×C₅	—	3	1	no	—
54	C₂²×C₅×C₈	—	3	1	no	—
55	C₂²×C₅×C₈	—	3	4	no	—
56	C₂²×C₅×C₈	—	6	2	no	—
57	C₂²×C₅×C₈	—	6	2	no	—
58	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	—	3	2	no	—
60	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
62	C₅×#106	—	2	2	no	—
63	C₅×#106	—	6	2	no	—
64	C₅×#95	—	6	2	no	—
65	#1807	—	3	1	no	Sylow
66	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₅×D₃	—	2	1	no	—
68	C₂²×C₅×D₃	—	2	1	no	—
69	C₂²×C₅×D₃	—	2	2	no	—
70	C₂²×C₅×D₃	C₄⋊C₄	1	2	yes	—
71	C₂²×C₅×D₃	SD₁₆	1	4	yes	—
72	C₂×C₃×C₄×C₅	—	4	2	no	—
73	C₂×C₃×C₄×C₅	—	4	2	no	—
74	C₂×C₃×C₄×C₅	—	4	2	no	—
75	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
81	C₂×C₅×Dic₃	—	2	1	no	—
82	C₂×C₅×Dic₃	—	2	1	no	—
83	C₂×C₅×Dic₃	—	4	2	no	—
84	C₂×C₅×Dic₃	—	4	2	no	—
85	C₂×C₅×Dic₃	—	4	2	no	—
86	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
87	C₄×C₅×D₃	—	2	2	no	—
88	C₄×C₅×D₃	—	2	2	no	—
89	C₄×C₅×D₃	—	2	2	no	—
90	C₄×C₅×D₃	—	2	2	no	—
91	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
92	C₅×C₃⋊C₈	—	2	2	no	—
93	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
94	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
96	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
97	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
98	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
99	C₂×D₃×C₈	—	2	2	no	—
100	C₂×D₃×C₈	—	2	2	no	—
101	C₂×D₃×C₈	C₄×C₅	1	4	yes	complemented
102	C₃×#106	—	2	2	no	—
103	C₃⋊#95	—	2	2	no	—
104	#817	—	2	2	no	—
105	C₂⁴×C₅	—	3	1	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	3	1	no	—
108	C₂²×C₄×C₅	—	3	2	no	—
109	C₂²×C₄×C₅	—	3	2	no	—
110	C₂²×C₄×C₅	—	6	1	no	—
111	C₂²×C₄×C₅	—	6	1	no	—
112	C₂²×C₄×C₅	—	6	1	no	—
113	C₂²×C₄×C₅	—	6	1	no	—
114	C₂²×C₄×C₅	—	6	2	no	—
115	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
116	C₂×C₅×C₈	—	3	2	no	—
117	C₂×C₅×C₈	—	6	1	no	—
118	C₂×C₅×C₈	—	6	1	no	—
119	C₂×C₅×C₈	—	6	8	no	—
120	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
121	C₂×C₅×C₈	D₁₂	1	2	yes	—
122	C₂×C₅×C₈	#67	1	2	yes	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	6	2	no	—
126	C₅×C₄⋊C₄	—	6	2	no	—
127	C₅×C₂²⋊C₄	—	12	4	no	—
128	C₂³×C₈	—	3	1	no	—
129	C₂×#106	—	3	1	no	—
130	C₂×#106	C₅×D₃	1	1	yes	characteristic, complemented
131	#380	—	3	2	no	—
132	#340	—	3	2	no	—
133	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂²×C₃×C₅	#121	1	1	yes	characteristic
135	C₂²×C₃×C₅	#121	1	1	yes	characteristic
136	C₂²×C₃×C₅	C₂×SD₁₆	1	2	yes	—
137	C₂²×C₃×C₅	#135	1	2	yes	—
138	C₂×C₅×D₃	—	2	2	no	—
139	C₂×C₅×D₃	—	2	2	no	—
140	C₂×C₅×D₃	—	2	4	no	—
141	C₂×C₅×D₃	—	2	4	no	—
142	C₂×C₅×D₃	#106	1	4	yes	complemented
143	C₃×C₄×C₅	—	8	2	no	—
144	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₃×C₄×C₅	#117	1	1	yes	characteristic
146	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
147	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
148	C₅×Dic₃	—	2	2	no	—
149	C₅×Dic₃	—	8	2	no	—
150	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	—	2	2	no	—
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₂²×Dic₃	—	2	2	no	—
154	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
155	C₂×C₄×D₃	—	2	1	no	—
156	C₂×C₄×D₃	—	2	1	no	—
157	C₂×C₄×D₃	—	2	1	no	—
158	C₂×C₄×D₃	—	2	1	no	—
159	C₂×C₄×D₃	C₂×C₄×C₅	1	2	yes	—
160	C₂×C₄×D₃	C₅×Q₈	1	2	yes	—
161	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
162	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
163	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
164	C₃×C₄⋊C₄	—	2	2	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	(C₂×D₃)⋊C₄	—	4	4	no	—
167	C₄⋊Dic₃	—	2	2	no	—
168	C₄⋊Dic₃	—	2	2	no	—
169	C₂×C₃⋊C₈	—	2	1	no	—
170	C₂×C₃⋊C₈	—	2	1	no	—
171	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
172	D₃×C₈	—	2	8	no	—
173	C₂³×C₅	—	3	2	no	—
174	C₂³×C₅	—	3	4	no	—
175	C₂³×C₅	—	6	1	no	—
176	C₂³×C₅	—	6	2	no	—
177	C₂³×C₅	—	6	1	no	—
178	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅	—	3	2	no	—
180	C₂×C₄×C₅	—	4	2	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	—	6	1	no	—
184	C₂×C₄×C₅	—	6	1	no	—
185	C₂×C₄×C₅	—	6	2	no	—
186	C₂×C₄×C₅	—	6	2	no	—
187	C₂×C₄×C₅	—	6	2	no	—
188	C₂×C₄×C₅	—	6	2	no	—
189	C₂×C₄×C₅	—	12	2	no	—
190	C₂×C₄×C₅	—	12	2	no	—
191	C₂×C₄×C₅	—	12	2	no	—
192	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
194	C₂×C₄×C₅	#237	1	1	yes	characteristic
195	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₅	#239	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
198	C₅×C₈	—	6	2	no	—
199	C₅×C₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
200	C₂³×C₄	—	3	1	no	—
201	C₂²×C₈	—	3	1	no	—
202	C₂²×C₈	—	3	4	no	—
203	C₂²×C₈	—	6	2	no	—
204	C₂²×C₈	—	6	2	no	—
205	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	—	3	2	no	—
207	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
208	C₂×C₂²⋊C₄	—	6	2	no	—
209	#106	—	2	2	no	—
210	#106	—	6	2	no	—
211	#95	—	6	2	no	—
212	C₂×C₃×C₅	#380	1	1	yes	characteristic
213	C₂×C₃×C₅	C₂×#106	1	1	yes	characteristic
214	C₂×C₃×C₅	#427	1	1	yes	characteristic
215	C₂×C₃×C₅	#465	1	2	yes	—
216	C₂×C₃×C₅	#465	1	2	yes	—
217	C₅×D₃	—	2	4	no	—
218	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
219	C₂²×D₃	—	2	1	no	—
220	C₂²×D₃	—	2	1	no	—
221	C₂²×D₃	—	2	2	no	—
222	C₂²×D₃	C₅×C₄⋊C₄	1	2	yes	—
223	C₂²×D₃	C₅×SD₁₆	1	4	yes	—
224	C₂×C₃×C₄	—	4	2	no	—
225	C₂×C₃×C₄	—	4	2	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
231	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
232	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
233	C₂×Dic₃	—	2	1	no	—
234	C₂×Dic₃	—	2	1	no	—
235	C₂×Dic₃	—	4	2	no	—
236	C₂×Dic₃	—	4	2	no	—
237	C₂×Dic₃	—	4	2	no	—
238	C₂×Dic₃	C₅×C₄⋊C₄	1	2	yes	—
239	C₄×D₃	—	2	2	no	—
240	C₄×D₃	—	2	2	no	—
241	C₄×D₃	—	2	2	no	—
242	C₄×D₃	—	2	2	no	—
243	C₃×C₈	C₅×C₂²⋊C₄	1	4	yes	complemented
244	C₃⋊C₈	—	2	2	no	—
245	C₂²×C₅	—	3	4	no	—
246	C₂²×C₅	—	6	4	no	—
247	C₂²×C₅	—	6	4	no	—
248	C₂²×C₅	—	6	2	no	—
249	C₂²×C₅	—	6	2	no	—
250	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
251	C₂²×C₅	#895	1	1	yes	characteristic
252	C₂²×C₅	D₃×SD₁₆	1	2	yes	—
253	C₂²×C₅	#916	1	2	yes	—
254	C₂²×C₅	#938	1	1	yes	characteristic
255	C₄×C₅	—	6	2	no	—
256	C₄×C₅	—	8	2	no	—
257	C₄×C₅	—	24	2	no	—
258	C₄×C₅	#892	1	1	yes	characteristic
259	C₄×C₅	#897	1	1	yes	characteristic
260	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
261	C₄×C₅	#946	1	1	yes	characteristic
262	C₂⁴	—	3	1	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	3	1	no	—
265	C₂²×C₄	—	3	2	no	—
266	C₂²×C₄	—	3	2	no	—
267	C₂²×C₄	—	6	1	no	—
268	C₂²×C₄	—	6	1	no	—
269	C₂²×C₄	—	6	1	no	—
270	C₂²×C₄	—	6	1	no	—
271	C₂²×C₄	—	6	2	no	—
272	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
273	C₂×C₈	—	3	2	no	—
274	C₂×C₈	—	6	1	no	—
275	C₂×C₈	—	6	1	no	—
276	C₂×C₈	—	6	8	no	—
277	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
278	C₂×C₈	C₅×D₁₂	1	2	yes	—
279	C₂×C₈	C₅×#67	1	2	yes	—
280	C₄⋊C₄	—	2	2	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	6	2	no	—
283	C₄⋊C₄	—	6	2	no	—
284	C₂²⋊C₄	—	12	4	no	—
285	C₃×C₅	#1807	1	1	yes	characteristic, complemented, Hall
286	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
287	C₂²×C₃	C₅×#121	1	1	yes	characteristic
288	C₂²×C₃	C₅×#121	1	1	yes	characteristic
289	C₂²×C₃	C₂×C₅×SD₁₆	1	2	yes	—
290	C₂²×C₃	C₅×#135	1	2	yes	—
291	C₂×D₃	—	2	2	no	—
292	C₂×D₃	—	2	2	no	—
293	C₂×D₃	—	2	4	no	—
294	C₂×D₃	—	2	4	no	—
295	C₂×D₃	C₅×#106	1	4	yes	complemented
296	C₃×C₄	—	8	2	no	—
297	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
298	C₃×C₄	C₅×#117	1	1	yes	characteristic
299	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
300	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
301	Dic₃	—	2	2	no	—
302	Dic₃	—	8	2	no	—
303	C₂×C₅	—	6	4	no	—
304	C₂×C₅	D₃×#106	1	1	yes	characteristic
305	C₂×C₅	#4860	1	1	yes	characteristic
306	C₂×C₅	#4864	1	2	yes	—
307	C₂×C₅	#4987	1	1	yes	characteristic
308	C₂×C₅	#5171	1	2	yes	—
309	C₂³	—	3	2	no	—
310	C₂³	—	3	4	no	—
311	C₂³	—	6	1	no	—
312	C₂³	—	6	2	no	—
313	C₂³	—	6	1	no	—
314	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
315	C₂×C₄	—	3	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	6	1	no	—
320	C₂×C₄	—	6	1	no	—
321	C₂×C₄	—	6	2	no	—
322	C₂×C₄	—	6	2	no	—
323	C₂×C₄	—	6	2	no	—
324	C₂×C₄	—	6	2	no	—
325	C₂×C₄	—	12	2	no	—
326	C₂×C₄	—	12	2	no	—
327	C₂×C₄	—	12	2	no	—
328	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
329	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
330	C₂×C₄	C₅×#237	1	1	yes	characteristic
331	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
332	C₂×C₄	C₅×#239	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
334	C₈	—	6	2	no	—
335	C₈	C₅×(C₂×D₃)⋊C₄	1	4	yes	complemented
336	C₂×C₃	C₅×#380	1	1	yes	characteristic
337	C₂×C₃	C₂×C₅×#106	1	1	yes	characteristic
338	C₂×C₃	C₅×#427	1	1	yes	characteristic
339	C₂×C₃	C₅×#465	1	2	yes	—
340	C₂×C₃	C₅×#465	1	2	yes	—
341	D₃	—	2	4	no	—
342	C₅	#70577	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²	—	3	4	no	—
344	C₂²	—	6	4	no	—
345	C₂²	—	6	2	no	—
346	C₂²	—	6	2	no	—
347	C₂²	—	6	4	no	—
348	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
349	C₂²	C₅×#895	1	1	yes	characteristic
350	C₂²	C₅×D₃×SD₁₆	1	2	yes	—
351	C₂²	C₅×#916	1	2	yes	—
352	C₂²	C₅×#938	1	1	yes	characteristic
353	C₄	—	6	2	no	—
354	C₄	—	8	2	no	—
355	C₄	—	24	2	no	—
356	C₄	C₅×#892	1	1	yes	characteristic
357	C₄	C₅×#897	1	1	yes	characteristic
358	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
359	C₄	C₅×#946	1	1	yes	characteristic
360	C₃	C₅×#1807	1	1	yes	characteristic, complemented, Sylow
361	C₂	—	6	4	no	—
362	C₂	C₅×D₃×#106	1	1	yes	characteristic
363	C₂	C₅×#4860	1	1	yes	characteristic
364	C₂	C₅×#4864	1	2	yes	—
365	C₂	C₅×#4987	1	1	yes	characteristic
366	C₂	C₅×#5171	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#106	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂³×C₅×D₃	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#106	D₃
hypocenter	C₃	C₅×#1807
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#106

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#106	C₂	semidirect
3. C₂×C₅×#817	C₂	semidirect
5. C₅×#4529	C₂	semidirect
15. C₂×C₅×D₃×C₈	C₄	semidirect
19. #70577	C₅	direct (N × H)
22. C₂×C₅×#106	D₃	semidirect
49. C₂×C₃×#106	C₂×C₅	semidirect
50. C₂×#817	C₂×C₅	semidirect
52. #4529	C₂×C₅	semidirect
91. C₃×C₅×C₈	C₂²⋊C₄	semidirect
101. C₂×D₃×C₈	C₄×C₅	semidirect
130. C₂×#106	C₅×D₃	semidirect
142. C₂×C₅×D₃	#106	semidirect
199. C₅×C₈	(C₂×D₃)⋊C₄	semidirect
243. C₃×C₈	C₅×C₂²⋊C₄	semidirect
285. C₃×C₅	#1807	semidirect
295. C₂×D₃	C₅×#106	semidirect
335. C₈	C₅×(C₂×D₃)⋊C₄	semidirect
342. C₅	#70577	direct (N × H)
360. C₃	C₅×#1807	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×D₃×C₈	2
C₂×C₃×C₅×#106	2
C₂×C₅×#817	2
C₅×#4987	2
C₅×#4529	2
C₅×#1807	3
#70577	5

Subgroups — C5×#70577 #14297867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70577 #14297867