Subgroups — C₂×C₃×C₅×#353 #14275158

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#99	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#353	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₅×#353	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×C₅×D₄	—	2	2	no	—
6	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic, complemented
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₃×C₅×#127	—	2	2	no	—
9	C₃×C₅×#127	C₄	1	2	yes	complemented
10	C₃×C₅×#127	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
12	C₂×C₃×C₄²×C₅	C₄	1	1	yes	characteristic, complemented
13	C₃×C₅×#99	—	2	2	no	—
14	C₃×C₅×#99	C₂²	1	4	yes	complemented
15	C₂×C₃×#353	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₅×#127	C₂×C₃	1	1	yes	characteristic
17	C₂×C₅×#99	C₂×C₃	1	2	yes	complemented
18	C₅×#353	C₂×C₃	1	4	yes	direct product factor
19	C₂⁴×C₃×C₅	—	2	1	no	—
20	C₂⁴×C₃×C₅	D₄	1	2	yes	—
21	C₂×C₃×C₅×D₄	—	2	4	no	—
22	C₂×C₃×C₅×D₄	—	2	4	no	—
23	C₂×C₃×C₅×D₄	—	2	1	no	—
24	C₂×C₃×C₅×D₄	—	4	1	no	—
25	C₂×C₃×C₅×D₄	—	4	1	no	—
26	C₂×C₃×C₅×D₄	—	4	8	no	—
27	C₂×C₃×C₅×D₄	—	4	1	no	—
28	C₂×C₃×C₅×D₄	—	4	1	no	—
29	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	complemented
31	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
32	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	4	2	no	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
37	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
38	C₃×C₄²×C₅	—	2	1	no	—
39	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
40	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic
41	C₂×C₃×#99	C₂×C₅	1	2	yes	complemented
42	C₃×#353	C₂×C₅	1	4	yes	direct product factor
43	C₂²×C₅×D₄	—	2	2	no	—
44	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic, complemented
45	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
46	C₅×#127	—	2	2	no	—
47	C₅×#127	C₃×C₄	1	2	yes	complemented
48	C₅×#127	C₂²×C₃	1	2	yes	—
49	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
50	C₂×C₄²×C₅	C₃×C₄	1	1	yes	characteristic, complemented
51	C₅×#99	—	2	2	no	—
52	C₅×#99	C₂²×C₃	1	4	yes	complemented
53	C₂×#353	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³×C₃×C₅	—	2	2	no	—
55	C₂³×C₃×C₅	—	2	2	no	—
56	C₂³×C₃×C₅	—	2	2	no	—
57	C₂³×C₃×C₅	—	4	4	no	—
58	C₂³×C₃×C₅	—	4	4	no	—
59	C₂³×C₃×C₅	—	4	1	no	—
60	C₂³×C₃×C₅	—	4	1	no	—
61	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
62	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
63	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
64	C₃×C₅×D₄	—	4	1	no	—
65	C₃×C₅×D₄	—	4	2	no	—
66	C₃×C₅×D₄	—	4	1	no	—
67	C₃×C₅×D₄	—	4	8	no	—
68	C₃×C₅×D₄	—	4	8	no	—
69	C₃×C₅×D₄	—	4	2	no	—
70	C₃×C₅×D₄	—	4	2	no	—
71	C₂×C₃×C₄×C₅	—	2	4	no	—
72	C₂×C₃×C₄×C₅	—	2	1	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	4	4	no	—
76	C₂×C₃×C₄×C₅	—	8	4	no	—
77	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₃×D₄	—	2	2	no	—
80	C₂²×C₃×D₄	C₄×C₅	1	1	yes	characteristic, complemented
81	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
82	C₃×#127	—	2	2	no	—
83	C₃×#127	C₄×C₅	1	2	yes	complemented
84	C₃×#127	C₂²×C₅	1	2	yes	—
85	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₃×C₄²	C₄×C₅	1	1	yes	characteristic, complemented
87	C₃×#99	—	2	2	no	—
88	C₃×#99	C₂²×C₅	1	4	yes	complemented
89	C₂⁴×C₅	—	2	1	no	—
90	C₂⁴×C₅	C₃×D₄	1	2	yes	—
91	C₂×C₅×D₄	—	2	4	no	—
92	C₂×C₅×D₄	—	2	4	no	—
93	C₂×C₅×D₄	—	2	1	no	—
94	C₂×C₅×D₄	—	4	1	no	—
95	C₂×C₅×D₄	—	4	1	no	—
96	C₂×C₅×D₄	—	4	1	no	—
97	C₂×C₅×D₄	—	4	1	no	—
98	C₂×C₅×D₄	—	4	8	no	—
99	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
100	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	complemented
101	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
102	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
103	C₂²×C₄×C₅	—	2	1	no	—
104	C₂²×C₄×C₅	—	4	2	no	—
105	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
106	C₅×C₂²⋊C₄	—	2	4	no	—
107	C₅×C₂²⋊C₄	—	4	2	no	—
108	C₄²×C₅	—	2	1	no	—
109	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
110	C₂×#127	C₂×C₃×C₅	1	1	yes	characteristic
111	C₂×#99	C₂×C₃×C₅	1	2	yes	complemented
112	#353	C₂×C₃×C₅	1	4	yes	direct product factor
113	C₂²×C₃×C₅	—	2	2	no	—
114	C₂²×C₃×C₅	—	2	2	no	—
115	C₂²×C₃×C₅	—	2	2	no	—
116	C₂²×C₃×C₅	—	4	2	no	—
117	C₂²×C₃×C₅	—	4	2	no	—
118	C₂²×C₃×C₅	—	4	4	no	—
119	C₂²×C₃×C₅	—	4	4	no	—
120	C₂²×C₃×C₅	—	4	2	no	—
121	C₂²×C₃×C₅	—	8	2	no	—
122	C₂²×C₃×C₅	—	8	2	no	—
123	C₂²×C₃×C₅	—	8	2	no	—
124	C₂²×C₃×C₅	#99	1	1	yes	characteristic
125	C₂²×C₃×C₅	#99	1	1	yes	characteristic
126	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₃×C₄×C₅	—	2	4	no	—
128	C₃×C₄×C₅	—	2	1	no	—
129	C₃×C₄×C₅	—	2	1	no	—
130	C₃×C₄×C₅	—	8	4	no	—
131	C₂⁴×C₃	—	2	1	no	—
132	C₂⁴×C₃	C₅×D₄	1	2	yes	—
133	C₂×C₃×D₄	—	2	4	no	—
134	C₂×C₃×D₄	—	2	4	no	—
135	C₂×C₃×D₄	—	2	1	no	—
136	C₂×C₃×D₄	—	4	1	no	—
137	C₂×C₃×D₄	—	4	1	no	—
138	C₂×C₃×D₄	—	4	1	no	—
139	C₂×C₃×D₄	—	4	1	no	—
140	C₂×C₃×D₄	—	4	8	no	—
141	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
142	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	complemented
143	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
144	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
145	C₂²×C₃×C₄	—	2	1	no	—
146	C₂²×C₃×C₄	—	4	2	no	—
147	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
148	C₃×C₂²⋊C₄	—	2	4	no	—
149	C₃×C₂²⋊C₄	—	4	2	no	—
150	C₃×C₄²	—	2	1	no	—
151	C₃×C₄²	C₂×C₄×C₅	1	2	yes	complemented
152	C₂³×C₅	—	2	2	no	—
153	C₂³×C₅	—	2	2	no	—
154	C₂³×C₅	—	2	2	no	—
155	C₂³×C₅	—	4	4	no	—
156	C₂³×C₅	—	4	4	no	—
157	C₂³×C₅	—	4	1	no	—
158	C₂³×C₅	—	4	1	no	—
159	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
161	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
162	C₅×D₄	—	4	1	no	—
163	C₅×D₄	—	4	2	no	—
164	C₅×D₄	—	4	1	no	—
165	C₅×D₄	—	4	2	no	—
166	C₅×D₄	—	4	8	no	—
167	C₅×D₄	—	4	8	no	—
168	C₅×D₄	—	4	2	no	—
169	C₂×C₄×C₅	—	2	4	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	4	4	no	—
174	C₂×C₄×C₅	—	8	4	no	—
175	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
177	C₂²×D₄	—	2	2	no	—
178	C₂²×D₄	C₃×C₄×C₅	1	1	yes	characteristic, complemented
179	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
180	#127	—	2	2	no	—
181	#127	C₃×C₄×C₅	1	2	yes	complemented
182	#127	C₂²×C₃×C₅	1	2	yes	—
183	C₂×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₄²	C₃×C₄×C₅	1	1	yes	characteristic, complemented
185	#99	—	2	2	no	—
186	#99	C₂²×C₃×C₅	1	4	yes	complemented
187	C₂×C₃×C₅	—	2	1	no	—
188	C₂×C₃×C₅	—	2	1	no	—
189	C₂×C₃×C₅	—	4	2	no	—
190	C₂×C₃×C₅	—	4	2	no	—
191	C₂×C₃×C₅	—	8	2	no	—
192	C₂×C₃×C₅	#353	1	2	yes	direct product factor
193	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
194	C₂³×C₃	—	2	2	no	—
195	C₂³×C₃	—	2	2	no	—
196	C₂³×C₃	—	2	2	no	—
197	C₂³×C₃	—	4	4	no	—
198	C₂³×C₃	—	4	4	no	—
199	C₂³×C₃	—	4	1	no	—
200	C₂³×C₃	—	4	1	no	—
201	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
202	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
203	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
204	C₃×D₄	—	4	1	no	—
205	C₃×D₄	—	4	2	no	—
206	C₃×D₄	—	4	1	no	—
207	C₃×D₄	—	4	2	no	—
208	C₃×D₄	—	4	8	no	—
209	C₃×D₄	—	4	8	no	—
210	C₃×D₄	—	4	2	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	4	4	no	—
216	C₂×C₃×C₄	—	8	4	no	—
217	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
219	C₂²×C₅	—	2	2	no	—
220	C₂²×C₅	—	2	2	no	—
221	C₂²×C₅	—	2	2	no	—
222	C₂²×C₅	—	4	2	no	—
223	C₂²×C₅	—	4	2	no	—
224	C₂²×C₅	—	4	4	no	—
225	C₂²×C₅	—	4	4	no	—
226	C₂²×C₅	—	4	2	no	—
227	C₂²×C₅	—	8	2	no	—
228	C₂²×C₅	—	8	2	no	—
229	C₂²×C₅	—	8	2	no	—
230	C₂²×C₅	C₃×#99	1	1	yes	characteristic
231	C₂²×C₅	C₃×#99	1	1	yes	characteristic
232	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
233	C₄×C₅	—	2	4	no	—
234	C₄×C₅	—	2	1	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	8	4	no	—
237	C₂⁴	—	2	1	no	—
238	C₂⁴	C₃×C₅×D₄	1	2	yes	—
239	C₂×D₄	—	2	4	no	—
240	C₂×D₄	—	2	4	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	—	4	1	no	—
243	C₂×D₄	—	4	1	no	—
244	C₂×D₄	—	4	1	no	—
245	C₂×D₄	—	4	1	no	—
246	C₂×D₄	—	4	8	no	—
247	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
248	C₂×D₄	C₂×C₃×C₄×C₅	1	2	yes	complemented
249	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
250	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
251	C₂²×C₄	—	2	1	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
254	C₂²⋊C₄	—	2	4	no	—
255	C₂²⋊C₄	—	4	2	no	—
256	C₄²	—	2	1	no	—
257	C₄²	C₂×C₃×C₄×C₅	1	2	yes	complemented
258	C₃×C₅	C₂×#353	1	1	yes	characteristic, direct product factor, Hall
259	C₂²×C₃	—	2	2	no	—
260	C₂²×C₃	—	2	2	no	—
261	C₂²×C₃	—	2	2	no	—
262	C₂²×C₃	—	4	2	no	—
263	C₂²×C₃	—	4	2	no	—
264	C₂²×C₃	—	4	4	no	—
265	C₂²×C₃	—	4	4	no	—
266	C₂²×C₃	—	4	2	no	—
267	C₂²×C₃	—	8	2	no	—
268	C₂²×C₃	—	8	2	no	—
269	C₂²×C₃	—	8	2	no	—
270	C₂²×C₃	C₅×#99	1	1	yes	characteristic
271	C₂²×C₃	C₅×#99	1	1	yes	characteristic
272	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	2	1	no	—
275	C₃×C₄	—	2	1	no	—
276	C₃×C₄	—	8	4	no	—
277	C₂×C₅	—	2	1	no	—
278	C₂×C₅	—	2	1	no	—
279	C₂×C₅	—	4	2	no	—
280	C₂×C₅	—	4	2	no	—
281	C₂×C₅	—	8	2	no	—
282	C₂×C₅	C₃×#353	1	2	yes	direct product factor
283	C₂×C₅	C₂×C₃×#99	1	1	yes	characteristic
284	C₂³	—	2	2	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	—	4	4	no	—
288	C₂³	—	4	4	no	—
289	C₂³	—	4	1	no	—
290	C₂³	—	4	1	no	—
291	C₂³	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
292	C₂³	C₃×C₅×C₂²⋊C₄	1	2	yes	—
293	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
294	D₄	—	4	1	no	—
295	D₄	—	4	2	no	—
296	D₄	—	4	1	no	—
297	D₄	—	4	2	no	—
298	D₄	—	4	8	no	—
299	D₄	—	4	8	no	—
300	D₄	—	4	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	4	4	no	—
306	C₂×C₄	—	8	4	no	—
307	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
309	C₂×C₃	—	2	1	no	—
310	C₂×C₃	—	2	1	no	—
311	C₂×C₃	—	4	2	no	—
312	C₂×C₃	—	4	2	no	—
313	C₂×C₃	—	8	2	no	—
314	C₂×C₃	C₅×#353	1	2	yes	direct product factor
315	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
316	C₅	C₂×C₃×#353	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	4	2	no	—
321	C₂²	—	4	2	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	8	2	no	—
328	C₂²	C₃×C₅×#99	1	1	yes	characteristic
329	C₂²	C₃×C₅×#99	1	1	yes	characteristic
330	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
331	C₄	—	2	4	no	—
332	C₄	—	2	1	no	—
333	C₄	—	2	1	no	—
334	C₄	—	8	4	no	—
335	C₃	C₂×C₅×#353	1	1	yes	characteristic, direct product factor, Sylow
336	C₂	—	2	1	no	—
337	C₂	—	2	1	no	—
338	C₂	—	4	2	no	—
339	C₂	—	4	2	no	—
340	C₂	—	8	2	no	—
341	C₂	C₃×C₅×#353	1	2	yes	direct product factor
342	C₂	C₂×C₃×C₅×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#99
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂×D₄	C₂³×C₃×C₅
prime radical	C₂×C₃×C₅×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂³×C₃×C₅ ◁ C₂²×C₃×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#99	C₂	semidirect
3. C₃×C₅×#353	C₂	direct (N × H)
4. C₂×C₅×#353	C₃	direct (N × H)
6. C₂²×C₃×C₅×D₄	C₄	semidirect
9. C₃×C₅×#127	C₄	semidirect
12. C₂×C₃×C₄²×C₅	C₄	semidirect
14. C₃×C₅×#99	C₂²	semidirect
15. C₂×C₃×#353	C₅	direct (N × H)
17. C₂×C₅×#99	C₂×C₃	semidirect
18. C₅×#353	C₂×C₃	direct (N × H)
30. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
39. C₃×C₄²×C₅	C₂×C₄	semidirect
41. C₂×C₃×#99	C₂×C₅	semidirect
42. C₃×#353	C₂×C₅	direct (N × H)
44. C₂²×C₅×D₄	C₃×C₄	semidirect
47. C₅×#127	C₃×C₄	semidirect
50. C₂×C₄²×C₅	C₃×C₄	semidirect
52. C₅×#99	C₂²×C₃	semidirect
53. C₂×#353	C₃×C₅	direct (N × H)
80. C₂²×C₃×D₄	C₄×C₅	semidirect
83. C₃×#127	C₄×C₅	semidirect
86. C₂×C₃×C₄²	C₄×C₅	semidirect
88. C₃×#99	C₂²×C₅	semidirect
100. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
109. C₄²×C₅	C₂×C₃×C₄	semidirect
111. C₂×#99	C₂×C₃×C₅	semidirect
112. #353	C₂×C₃×C₅	direct (N × H)
142. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
151. C₃×C₄²	C₂×C₄×C₅	semidirect
178. C₂²×D₄	C₃×C₄×C₅	semidirect
181. #127	C₃×C₄×C₅	semidirect
184. C₂×C₄²	C₃×C₄×C₅	semidirect
186. #99	C₂²×C₃×C₅	semidirect
192. C₂×C₃×C₅	#353	direct (N × H)
248. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
257. C₄²	C₂×C₃×C₄×C₅	semidirect
258. C₃×C₅	C₂×#353	direct (N × H)
282. C₂×C₅	C₃×#353	direct (N × H)
314. C₂×C₃	C₅×#353	direct (N × H)
316. C₅	C₂×C₃×#353	direct (N × H)
335. C₃	C₂×C₅×#353	direct (N × H)
341. C₂	C₃×C₅×#353	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#127	2
C₂×C₃×C₅×#99	2
C₃×C₅×#353	2
C₂×C₅×#353	3
C₂×C₃×#353	5

Subgroups — C2×C3×C5×#353 #14275158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#353 #14275158