Subgroups — C₅×#69484 #14304931

Order 1920.

520 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	2	yes	maximal
4	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₅×#4524	C₂	1	2	yes	maximal
6	C₅×#1939	—	3	1	no	maximal, Hall
7	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
8	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
9	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
10	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
12	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#95	C₄	1	2	yes	—
15	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
16	C₅×C₄⋊(C₃⋊C₈)	—	2	4	no	—
17	C₄×C₅×C₃⋊C₈	—	2	2	no	—
18	#69484	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₅×C₄⋊C₈	—	3	2	no	—
20	C₂×C₅×C₄⋊C₈	—	3	1	no	—
21	C₂×C₄×C₅×C₈	—	3	1	no	—
22	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic
23	C₅×#336	—	3	2	no	—
24	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
25	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₄	—	2	2	no	—
30	C₃×C₅×C₄⋊C₄	C₈	1	4	yes	complemented
31	C₃×C₄²×C₅	—	2	2	no	—
32	C₃×C₄²×C₅	—	2	2	no	—
33	C₃×C₄²×C₅	D₄	1	2	yes	—
34	C₃×C₄²×C₅	Q₈	1	2	yes	—
35	C₂×C₅×C₃⋊C₈	—	2	1	no	—
36	C₂×C₅×C₃⋊C₈	—	2	1	no	—
37	C₂×C₅×C₃⋊C₈	—	2	1	no	—
38	C₂×C₅×C₃⋊C₈	—	2	1	no	—
39	C₂×C₅×C₃⋊C₈	—	2	2	no	—
40	C₂×C₅×C₃⋊C₈	—	2	2	no	—
41	C₂×C₅×C₃⋊C₈	—	2	2	no	—
42	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
43	C₂×C₅×C₃⋊C₈	Q₈	1	2	yes	—
44	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
45	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic
46	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	2	yes	—
47	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic
48	#4524	C₂×C₅	1	2	yes	—
49	C₂²×C₅×C₈	—	3	1	no	—
50	C₂²×C₅×C₈	—	3	1	no	—
51	C₂²×C₅×C₈	—	3	2	no	—
52	C₂×C₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
53	C₂×C₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic
54	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
55	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
56	C₅×C₄⋊C₈	—	6	4	no	—
57	C₅×C₄⋊C₈	—	6	2	no	—
58	C₄×C₅×C₈	—	6	2	no	—
59	C₅×#95	Dic₃	1	2	yes	—
60	#1939	—	3	1	no	Sylow
61	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×C₅	—	2	2	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	2	1	no	—
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	—	2	2	no	—
67	C₂×C₃×C₄×C₅	—	2	2	no	—
68	C₂×C₃×C₄×C₅	—	2	2	no	—
69	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
70	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
71	C₂×C₃×C₄×C₅	C₂×C₈	1	4	yes	—
72	C₂×C₃×C₄×C₅	C₂×C₈	1	2	yes	—
73	C₂×C₃×C₄×C₅	M₁₆	1	2	yes	—
74	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
80	C₅×C₃⋊C₈	—	2	2	no	—
81	C₅×C₃⋊C₈	—	2	2	no	—
82	C₅×C₃⋊C₈	—	4	2	no	—
83	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
84	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
85	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
86	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
87	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
88	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
89	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
90	C₃×#95	C₄×C₅	1	2	yes	—
91	C₄⋊(C₃⋊C₈)	—	2	2	no	—
92	C₄⋊(C₃⋊C₈)	—	2	4	no	—
93	C₄×C₃⋊C₈	—	2	2	no	—
94	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
95	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
96	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
99	C₂×C₅×C₈	—	3	2	no	—
100	C₂×C₅×C₈	—	3	2	no	—
101	C₂×C₅×C₈	—	6	1	no	—
102	C₂×C₅×C₈	—	6	1	no	—
103	C₂×C₅×C₈	—	6	1	no	—
104	C₂×C₅×C₈	—	6	1	no	—
105	C₂×C₅×C₈	—	6	2	no	—
106	C₂×C₅×C₈	—	6	2	no	—
107	C₂×C₅×C₈	—	6	2	no	—
108	C₅×C₄⋊C₄	—	2	2	no	—
109	C₅×C₄⋊C₄	C₃⋊C₈	1	4	yes	complemented
110	C₄²×C₅	—	2	2	no	—
111	C₄²×C₅	—	2	2	no	—
112	C₄²×C₅	Dic₆	1	2	yes	—
113	C₄²×C₅	D₁₂	1	2	yes	—
114	C₂×C₄⋊C₈	—	3	2	no	—
115	C₂×C₄⋊C₈	—	3	1	no	—
116	C₂×C₄×C₈	—	3	1	no	—
117	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic
118	#336	—	3	2	no	—
119	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
121	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
122	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
123	C₂²×C₃×C₅	C₂×M₁₆	1	1	yes	characteristic
124	C₂²×C₃×C₅	#131	1	1	yes	characteristic
125	C₂²×C₃×C₅	#131	1	1	yes	characteristic
126	C₃×C₄×C₅	—	2	2	no	—
127	C₃×C₄×C₅	—	2	4	no	—
128	C₃×C₄×C₅	—	4	2	no	—
129	C₃×C₄×C₅	C₄⋊C₈	1	4	yes	complemented
130	C₃×C₄×C₅	#121	1	1	yes	characteristic
131	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
132	C₃×C₄×C₅	#125	1	1	yes	characteristic
133	C₃×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
135	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
137	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
138	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
139	C₃×C₄⋊C₄	—	2	2	no	—
140	C₃×C₄⋊C₄	C₅×C₈	1	4	yes	complemented
141	C₃×C₄²	—	2	2	no	—
142	C₃×C₄²	—	2	2	no	—
143	C₃×C₄²	C₅×D₄	1	2	yes	—
144	C₃×C₄²	C₅×Q₈	1	2	yes	—
145	C₂×C₃⋊C₈	—	2	1	no	—
146	C₂×C₃⋊C₈	—	2	1	no	—
147	C₂×C₃⋊C₈	—	2	1	no	—
148	C₂×C₃⋊C₈	—	2	1	no	—
149	C₂×C₃⋊C₈	—	2	2	no	—
150	C₂×C₃⋊C₈	—	2	2	no	—
151	C₂×C₃⋊C₈	—	2	2	no	—
152	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
153	C₂×C₃⋊C₈	C₅×Q₈	1	2	yes	—
154	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
155	C₂×C₄×C₅	—	2	2	no	—
156	C₂×C₄×C₅	—	2	1	no	—
157	C₂×C₄×C₅	—	2	1	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	C₂×C₃⋊C₈	1	4	yes	—
163	C₂×C₄×C₅	C₂×C₃⋊C₈	1	2	yes	—
164	C₂×C₄×C₅	#208	1	2	yes	—
165	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
166	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
167	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
168	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
169	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅	#237	1	1	yes	characteristic
171	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₅	#239	1	1	yes	characteristic
173	C₅×C₈	—	6	2	no	—
174	C₅×C₈	—	6	2	no	—
175	C₅×C₈	—	12	2	no	—
176	C₂²×C₈	—	3	1	no	—
177	C₂²×C₈	—	3	1	no	—
178	C₂²×C₈	—	3	2	no	—
179	C₂×C₄⋊C₄	C₅×Dic₃	1	1	yes	characteristic
180	C₂×C₄⋊C₄	C₅×Dic₃	1	1	yes	characteristic
181	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
182	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
183	C₄⋊C₈	—	6	4	no	—
184	C₄⋊C₈	—	6	2	no	—
185	C₄×C₈	—	6	2	no	—
186	#95	C₅×Dic₃	1	2	yes	—
187	C₂×C₃×C₅	#389	1	1	yes	characteristic
188	C₂×C₃×C₅	C₂×C₄⋊C₈	1	1	yes	characteristic
189	C₂×C₃×C₅	#424	1	1	yes	characteristic
190	C₂×C₃×C₅	C₈×D₄	1	1	yes	characteristic
191	C₂×C₃×C₅	#436	1	1	yes	characteristic
192	C₂×C₃×C₅	C₈×Q₈	1	1	yes	characteristic
193	C₂×C₃×C₅	#446	1	1	yes	characteristic
194	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	2	no	—
201	C₂×C₃×C₄	—	2	2	no	—
202	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
203	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
204	C₂×C₃×C₄	C₂×C₅×C₈	1	4	yes	—
205	C₂×C₃×C₄	C₂×C₅×C₈	1	2	yes	—
206	C₂×C₃×C₄	C₅×M₁₆	1	2	yes	—
207	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
208	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
210	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
211	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
212	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
213	C₃⋊C₈	—	2	2	no	—
214	C₃⋊C₈	—	2	2	no	—
215	C₃⋊C₈	—	4	2	no	—
216	C₂²×C₅	C₂²×C₃⋊C₈	1	1	yes	characteristic
217	C₂²×C₅	C₂×#208	1	1	yes	characteristic
218	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
219	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
220	C₂²×C₅	Q₈×Dic₃	1	1	yes	characteristic
221	C₂²×C₅	#948	1	1	yes	characteristic
222	C₂²×C₅	#948	1	1	yes	characteristic
223	C₄×C₅	—	2	2	no	—
224	C₄×C₅	—	2	4	no	—
225	C₄×C₅	—	4	2	no	—
226	C₄×C₅	C₄⋊(C₃⋊C₈)	1	4	yes	complemented
227	C₄×C₅	#888	1	1	yes	characteristic
228	C₄×C₅	#890	1	1	yes	characteristic
229	C₄×C₅	#895	1	1	yes	characteristic
230	C₄×C₅	#897	1	1	yes	characteristic
231	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
232	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
233	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
234	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
236	C₂×C₈	—	3	2	no	—
237	C₂×C₈	—	3	2	no	—
238	C₂×C₈	—	6	1	no	—
239	C₂×C₈	—	6	1	no	—
240	C₂×C₈	—	6	1	no	—
241	C₂×C₈	—	6	1	no	—
242	C₂×C₈	—	6	2	no	—
243	C₂×C₈	—	6	2	no	—
244	C₂×C₈	—	6	2	no	—
245	C₄⋊C₄	—	2	2	no	—
246	C₄⋊C₄	C₅×C₃⋊C₈	1	4	yes	complemented
247	C₄²	—	2	2	no	—
248	C₄²	—	2	2	no	—
249	C₄²	C₅×Dic₆	1	2	yes	—
250	C₄²	C₅×D₁₂	1	2	yes	—
251	C₃×C₅	#1939	1	1	yes	characteristic, complemented, Hall
252	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
253	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
254	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
255	C₂²×C₃	C₂²×C₅×C₈	1	1	yes	characteristic
256	C₂²×C₃	C₂×C₅×M₁₆	1	1	yes	characteristic
257	C₂²×C₃	C₅×#131	1	1	yes	characteristic
258	C₂²×C₃	C₅×#131	1	1	yes	characteristic
259	C₃×C₄	—	2	2	no	—
260	C₃×C₄	—	2	4	no	—
261	C₃×C₄	—	4	2	no	—
262	C₃×C₄	C₅×C₄⋊C₈	1	4	yes	complemented
263	C₃×C₄	C₅×#121	1	1	yes	characteristic
264	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
265	C₃×C₄	C₅×#125	1	1	yes	characteristic
266	C₃×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
267	C₂×C₅	C₂×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
268	C₂×C₅	#4984	1	1	yes	characteristic
269	C₂×C₅	#4999	1	1	yes	characteristic
270	C₂×C₅	D₄×C₃⋊C₈	1	1	yes	characteristic
271	C₂×C₅	#5012	1	1	yes	characteristic
272	C₂×C₅	Q₈×C₃⋊C₈	1	1	yes	characteristic
273	C₂×C₅	#5024	1	1	yes	characteristic
274	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	C₂×C₅×C₃⋊C₈	1	4	yes	—
283	C₂×C₄	C₂×C₅×C₃⋊C₈	1	2	yes	—
284	C₂×C₄	C₅×#208	1	2	yes	—
285	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
286	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
287	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
288	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
289	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
290	C₂×C₄	C₅×#237	1	1	yes	characteristic
291	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
292	C₂×C₄	C₅×#239	1	1	yes	characteristic
293	C₈	—	6	2	no	—
294	C₈	—	6	2	no	—
295	C₈	—	12	2	no	—
296	C₂×C₃	C₅×#389	1	1	yes	characteristic
297	C₂×C₃	C₂×C₅×C₄⋊C₈	1	1	yes	characteristic
298	C₂×C₃	C₅×#424	1	1	yes	characteristic
299	C₂×C₃	C₅×C₈×D₄	1	1	yes	characteristic
300	C₂×C₃	C₅×#436	1	1	yes	characteristic
301	C₂×C₃	C₅×C₈×Q₈	1	1	yes	characteristic
302	C₂×C₃	C₅×#446	1	1	yes	characteristic
303	C₅	#69484	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²	C₂²×C₅×C₃⋊C₈	1	1	yes	characteristic
305	C₂²	C₂×C₅×#208	1	1	yes	characteristic
306	C₂²	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
307	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
308	C₂²	C₅×Q₈×Dic₃	1	1	yes	characteristic
309	C₂²	C₅×#948	1	1	yes	characteristic
310	C₂²	C₅×#948	1	1	yes	characteristic
311	C₄	—	2	2	no	—
312	C₄	—	2	4	no	—
313	C₄	—	4	2	no	—
314	C₄	C₅×C₄⋊(C₃⋊C₈)	1	4	yes	complemented
315	C₄	C₅×#888	1	1	yes	characteristic
316	C₄	C₅×#890	1	1	yes	characteristic
317	C₄	C₅×#895	1	1	yes	characteristic
318	C₄	C₅×#897	1	1	yes	characteristic
319	C₃	C₅×#1939	1	1	yes	characteristic, complemented, Sylow
320	C₂	C₂×C₅×C₄⋊(C₃⋊C₈)	1	1	yes	characteristic
321	C₂	C₅×#4984	1	1	yes	characteristic
322	C₂	C₅×#4999	1	1	yes	characteristic
323	C₂	C₅×D₄×C₃⋊C₈	1	1	yes	characteristic
324	C₂	C₅×#5012	1	1	yes	characteristic
325	C₂	C₅×Q₈×C₃⋊C₈	1	1	yes	characteristic
326	C₂	C₅×#5024	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₅×C₈
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#1939
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
18. #69484	C₅	direct (N × H)
30. C₃×C₅×C₄⋊C₄	C₈	semidirect
109. C₅×C₄⋊C₄	C₃⋊C₈	semidirect
129. C₃×C₄×C₅	C₄⋊C₈	semidirect
140. C₃×C₄⋊C₄	C₅×C₈	semidirect
226. C₄×C₅	C₄⋊(C₃⋊C₈)	semidirect
246. C₄⋊C₄	C₅×C₃⋊C₈	semidirect
251. C₃×C₅	#1939	semidirect
262. C₃×C₄	C₅×C₄⋊C₈	semidirect
303. C₅	#69484	direct (N × H)
314. C₄	C₅×C₄⋊(C₃⋊C₈)	semidirect
319. C₃	C₅×#1939	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×C₄⋊C₄	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4524	2
C₅×#1939	3
#69484	5

Subgroups — C5×#69484 #14304931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69484 #14304931