Subgroups — C₅×#69906 #14295046

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#830	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#815	C₂	1	2	yes	maximal, complemented
5	C₅×#4550	C₂	1	2	yes	maximal, complemented
6	C₅×#1749	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₅×Dic₃	C₄	1	2	yes	—
9	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₅×Dic₃	—	2	4	no	—
11	C₂×C₄×C₅×Dic₃	C₄	1	2	yes	—
12	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
15	C₃×C₅×C₂²⋊C₈	C₄	1	4	yes	complemented
16	C₅×#830	C₄	1	4	yes	complemented
17	C₅×#815	—	2	4	no	—
18	#69906	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₄²×C₅	—	3	1	no	—
20	C₂×C₅×C₂²⋊C₈	—	3	1	no	—
21	C₂×C₅×C₂²⋊C₈	D₃	1	1	yes	characteristic
22	C₂×C₅×#97	—	3	2	no	—
23	C₅×#336	—	3	2	no	—
24	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₅×Dic₃	—	2	4	no	—
32	C₂²×C₅×Dic₃	—	2	4	no	—
33	C₂²×C₅×Dic₃	—	2	4	no	—
34	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
35	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
36	C₂×C₃×C₅×C₈	—	2	2	no	—
37	C₂×C₃×C₅×C₈	—	2	2	no	—
38	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
39	C₄×C₅×Dic₃	—	2	2	no	—
40	C₄×C₅×Dic₃	—	2	4	no	—
41	C₄×C₅×Dic₃	D₄	1	4	yes	—
42	C₂×C₅×C₃⋊C₈	—	2	2	no	—
43	C₂×C₅×C₃⋊C₈	—	2	2	no	—
44	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
45	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
47	C₂×#830	C₂×C₅	1	1	yes	characteristic
48	C₂×#815	C₂×C₅	1	2	yes	complemented
49	#4550	C₂×C₅	1	2	yes	complemented
50	C₂³×C₄×C₅	—	3	2	no	—
51	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
52	C₂²×C₅×C₈	—	3	2	no	—
53	C₂²×C₅×C₈	C₂×D₃	1	2	yes	—
54	C₂×C₄²×C₅	—	3	1	no	—
55	C₂×C₄²×C₅	—	3	2	no	—
56	C₂×C₄²×C₅	—	3	1	no	—
57	C₂×C₄²×C₅	—	6	4	no	—
58	C₅×C₂²⋊C₈	—	3	4	no	—
59	C₅×C₂²⋊C₈	Dic₃	1	4	yes	complemented
60	C₅×#97	—	6	4	no	—
61	#1749	—	3	1	no	Sylow
62	C₂³×C₃×C₅	—	2	1	no	—
63	C₂³×C₃×C₅	—	2	1	no	—
64	C₂³×C₃×C₅	—	2	2	no	—
65	C₂³×C₃×C₅	C₄²	1	2	yes	—
66	C₂³×C₃×C₅	M₁₆	1	4	yes	—
67	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×C₅	—	2	1	no	—
69	C₂×C₃×C₄×C₅	—	2	1	no	—
70	C₂×C₃×C₄×C₅	—	2	4	no	—
71	C₂×C₃×C₄×C₅	—	2	4	no	—
72	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
73	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
76	C₂×C₃×C₄×C₅	#41	1	2	yes	—
77	C₂×C₅×Dic₃	—	2	16	no	—
78	C₂×C₅×Dic₃	—	2	2	no	—
79	C₂×C₅×Dic₃	—	2	2	no	—
80	C₂×C₅×Dic₃	—	2	2	no	—
81	C₂×C₅×Dic₃	—	2	2	no	—
82	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
83	C₂×C₅×Dic₃	M₁₆	1	4	yes	—
84	C₃×C₅×C₈	—	2	4	no	—
85	C₅×C₃⋊C₈	—	2	4	no	—
86	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
87	C₂³×Dic₃	C₄×C₅	1	2	yes	—
88	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
89	C₂×C₄×Dic₃	—	2	4	no	—
90	C₂×C₄×Dic₃	C₄×C₅	1	2	yes	—
91	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
92	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
93	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
94	C₃×C₂²⋊C₈	C₄×C₅	1	4	yes	complemented
95	#830	C₄×C₅	1	4	yes	complemented
96	#815	—	2	4	no	—
97	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	—	2	2	no	—
100	C₂²×C₄×C₅	—	3	2	no	—
101	C₂²×C₄×C₅	—	3	2	no	—
102	C₂²×C₄×C₅	—	6	4	no	—
103	C₂²×C₄×C₅	—	6	4	no	—
104	C₂²×C₄×C₅	—	6	4	no	—
105	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
107	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
108	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	—	3	4	no	—
112	C₂×C₅×C₈	—	6	2	no	—
113	C₂×C₅×C₈	—	6	2	no	—
114	C₂×C₅×C₈	C₂×Dic₃	1	4	yes	complemented
115	C₄²×C₅	—	3	4	no	—
116	C₄²×C₅	—	6	4	no	—
117	C₄²×C₅	—	6	2	no	—
118	C₂²×C₄²	—	3	1	no	—
119	C₂×C₂²⋊C₈	—	3	1	no	—
120	C₂×C₂²⋊C₈	C₅×D₃	1	1	yes	characteristic
121	C₂×#97	—	3	2	no	—
122	#336	—	3	2	no	—
123	C₂²×C₃×C₅	—	2	2	no	—
124	C₂²×C₃×C₅	—	2	2	no	—
125	C₂²×C₃×C₅	—	2	4	no	—
126	C₂²×C₃×C₅	—	2	4	no	—
127	C₂²×C₃×C₅	#97	1	4	yes	complemented
128	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
129	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₃×C₅	#117	1	1	yes	characteristic
131	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
132	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
133	C₃×C₄×C₅	—	2	2	no	—
134	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
135	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
136	C₅×Dic₃	—	2	4	no	—
137	C₅×Dic₃	—	2	4	no	—
138	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
139	C₂²×C₃×C₄	—	2	2	no	—
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
143	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
144	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
145	C₂²×Dic₃	—	2	4	no	—
146	C₂²×Dic₃	—	2	4	no	—
147	C₂²×Dic₃	—	2	4	no	—
148	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
149	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
153	C₄×Dic₃	—	2	2	no	—
154	C₄×Dic₃	—	2	4	no	—
155	C₄×Dic₃	C₅×D₄	1	4	yes	—
156	C₂×C₃⋊C₈	—	2	2	no	—
157	C₂×C₃⋊C₈	—	2	2	no	—
158	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
159	C₂³×C₅	—	2	1	no	—
160	C₂³×C₅	—	2	1	no	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	ΓL(1,𝔽₂₅)	1	4	yes	—
163	C₂³×C₅	C₄×Dic₃	1	2	yes	—
164	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	3	4	no	—
170	C₂×C₄×C₅	—	3	4	no	—
171	C₂×C₄×C₅	—	6	16	no	—
172	C₂×C₄×C₅	—	6	2	no	—
173	C₂×C₄×C₅	—	6	2	no	—
174	C₂×C₄×C₅	—	6	2	no	—
175	C₂×C₄×C₅	—	6	2	no	—
176	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
177	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
178	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
179	C₂×C₄×C₅	#237	1	2	yes	—
180	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
181	C₅×C₈	—	2	4	no	—
182	C₅×C₈	—	6	4	no	—
183	C₂³×C₄	—	3	2	no	—
184	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
185	C₂²×C₈	—	3	2	no	—
186	C₂²×C₈	C₂×C₅×D₃	1	2	yes	—
187	C₂×C₄²	—	3	1	no	—
188	C₂×C₄²	—	3	2	no	—
189	C₂×C₄²	—	3	1	no	—
190	C₂×C₄²	—	6	4	no	—
191	C₂²⋊C₈	—	3	4	no	—
192	C₂²⋊C₈	C₅×Dic₃	1	4	yes	complemented
193	#97	—	6	4	no	—
194	C₂×C₃×C₅	—	2	4	no	—
195	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₃×C₅	C₂×#97	1	1	yes	characteristic
197	C₂×C₃×C₅	C₄×M₁₆	1	1	yes	characteristic
198	C₂×C₃×C₅	#407	1	2	yes	—
199	C₂×C₃×C₅	#432	1	2	yes	—
200	C₂³×C₃	—	2	1	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	2	2	no	—
203	C₂³×C₃	C₄²×C₅	1	2	yes	—
204	C₂³×C₃	C₅×M₁₆	1	4	yes	—
205	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
206	C₂×C₃×C₄	—	2	1	no	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	4	no	—
210	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
211	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
212	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
214	C₂×C₃×C₄	C₅×#41	1	2	yes	—
215	C₂×Dic₃	—	2	16	no	—
216	C₂×Dic₃	—	2	2	no	—
217	C₂×Dic₃	—	2	2	no	—
218	C₂×Dic₃	—	2	2	no	—
219	C₂×Dic₃	—	2	2	no	—
220	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
221	C₂×Dic₃	C₅×M₁₆	1	4	yes	—
222	C₃×C₈	—	2	4	no	—
223	C₃⋊C₈	—	2	4	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	2	4	no	—
226	C₂²×C₅	—	2	4	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	#815	1	4	yes	complemented
229	C₂²×C₅	#877	1	1	yes	characteristic
230	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
231	C₂²×C₅	C₂×ΓL(1,𝔽₂₅)	1	2	yes	—
232	C₂²×C₅	D₃×M₁₆	1	2	yes	—
233	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	6	4	no	—
236	C₄×C₅	—	6	4	no	—
237	C₄×C₅	#67⋊C₄	1	2	yes	—
238	C₄×C₅	D₄×Dic₃	1	2	yes	—
239	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	3	2	no	—
243	C₂²×C₄	—	3	2	no	—
244	C₂²×C₄	—	6	4	no	—
245	C₂²×C₄	—	6	4	no	—
246	C₂²×C₄	—	6	4	no	—
247	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
248	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
249	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
250	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	3	4	no	—
254	C₂×C₈	—	6	2	no	—
255	C₂×C₈	—	6	2	no	—
256	C₂×C₈	C₂×C₅×Dic₃	1	4	yes	complemented
257	C₄²	—	3	4	no	—
258	C₄²	—	6	4	no	—
259	C₄²	—	6	2	no	—
260	C₃×C₅	#1749	1	1	yes	characteristic, complemented, Hall
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	2	4	no	—
264	C₂²×C₃	—	2	4	no	—
265	C₂²×C₃	C₅×#97	1	4	yes	complemented
266	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
267	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×C₃	C₅×#117	1	1	yes	characteristic
269	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
270	C₂²×C₃	C₂×C₅×M₁₆	1	2	yes	—
271	C₃×C₄	—	2	2	no	—
272	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
273	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
274	Dic₃	—	2	4	no	—
275	Dic₃	—	2	4	no	—
276	C₂×C₅	—	2	4	no	—
277	C₂×C₅	#4719	1	2	yes	—
278	C₂×C₅	#4726	1	2	yes	—
279	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₅	C₂×#815	1	1	yes	characteristic
281	C₂×C₅	Dic₃×M₁₆	1	1	yes	characteristic
282	C₂³	—	2	1	no	—
283	C₂³	—	2	1	no	—
284	C₂³	—	2	2	no	—
285	C₂³	C₅×ΓL(1,𝔽₂₅)	1	4	yes	—
286	C₂³	C₄×C₅×Dic₃	1	2	yes	—
287	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	3	4	no	—
293	C₂×C₄	—	3	4	no	—
294	C₂×C₄	—	6	16	no	—
295	C₂×C₄	—	6	2	no	—
296	C₂×C₄	—	6	2	no	—
297	C₂×C₄	—	6	2	no	—
298	C₂×C₄	—	6	2	no	—
299	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
300	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
301	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
302	C₂×C₄	C₅×#237	1	2	yes	—
303	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
304	C₈	—	2	4	no	—
305	C₈	—	6	4	no	—
306	C₂×C₃	—	2	4	no	—
307	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₃	C₂×C₅×#97	1	1	yes	characteristic
309	C₂×C₃	C₄×C₅×M₁₆	1	1	yes	characteristic
310	C₂×C₃	C₅×#407	1	2	yes	—
311	C₂×C₃	C₅×#432	1	2	yes	—
312	C₅	#69906	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²	—	2	2	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	2	no	—
317	C₂²	C₅×#815	1	4	yes	complemented
318	C₂²	C₅×#877	1	1	yes	characteristic
319	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
320	C₂²	C₂×C₅×ΓL(1,𝔽₂₅)	1	2	yes	—
321	C₂²	C₅×D₃×M₁₆	1	2	yes	—
322	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
323	C₄	—	2	2	no	—
324	C₄	—	6	4	no	—
325	C₄	—	6	4	no	—
326	C₄	C₅×#67⋊C₄	1	2	yes	—
327	C₄	C₅×D₄×Dic₃	1	2	yes	—
328	C₃	C₅×#1749	1	1	yes	characteristic, complemented, Sylow
329	C₂	—	2	4	no	—
330	C₂	C₅×#4719	1	2	yes	—
331	C₂	C₅×#4726	1	2	yes	—
332	C₂	C₅×Dic₃×C₂²⋊C₄	1	1	yes	characteristic
333	C₂	C₂×C₅×#815	1	1	yes	characteristic
334	C₂	C₅×Dic₃×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊C₈	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂⁴×C₃×C₅	C₂×C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₂²⋊C₈	D₃
hypocenter	C₃	C₅×#1749
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×C₅×#815	C₂	semidirect
5. C₅×#4550	C₂	semidirect
15. C₃×C₅×C₂²⋊C₈	C₄	semidirect
16. C₅×#830	C₄	semidirect
18. #69906	C₅	direct (N × H)
38. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
44. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
48. C₂×#815	C₂×C₅	semidirect
49. #4550	C₂×C₅	semidirect
59. C₅×C₂²⋊C₈	Dic₃	semidirect
94. C₃×C₂²⋊C₈	C₄×C₅	semidirect
95. #830	C₄×C₅	semidirect
114. C₂×C₅×C₈	C₂×Dic₃	semidirect
127. C₂²×C₃×C₅	#97	semidirect
152. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
158. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
192. C₂²⋊C₈	C₅×Dic₃	semidirect
228. C₂²×C₅	#815	semidirect
256. C₂×C₈	C₂×C₅×Dic₃	semidirect
260. C₃×C₅	#1749	semidirect
265. C₂²×C₃	C₅×#97	semidirect
312. C₅	#69906	direct (N × H)
317. C₂²	C₅×#815	semidirect
328. C₃	C₅×#1749	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×Dic₃	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₂×C₅×#830	2
C₂×C₅×#815	2
C₅×#4550	2
C₅×#1749	3
#69906	5

Subgroups — C5×#69906 #14295046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69906 #14295046