Subgroups — C₂×C₅×#5058 #14438970

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#215	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×#213	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#874	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5058	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#496	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	—	2	2	no	—
11	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
12	C₃×C₅×#124	—	2	2	no	—
13	C₃×C₅×#124	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₅×#215	—	2	8	no	—
17	C₂×C₅×#215	C₂²	1	8	yes	complemented
18	C₂×C₅×#213	—	2	8	no	—
19	C₂×C₅×#213	C₂²	1	8	yes	complemented
20	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
21	C₅×#874	—	2	2	no	—
22	C₅×#874	C₂²	1	4	yes	complemented
23	C₅×#803	C₂²	1	4	yes	complemented
24	C₂×#5058	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×SD₁₆	—	3	2	no	—
26	C₂²×C₅×D₈	—	3	2	no	—
27	C₂×C₅×#127	—	3	1	no	—
28	C₂×C₅×#124	D₃	1	1	yes	characteristic, complemented
29	C₅×#496	—	3	8	no	—
30	C₂×C₅×#97	—	3	1	no	—
31	C₂⁴×C₃×C₅	—	2	1	no	—
32	C₂³×C₅×D₃	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	—	2	1	no	—
34	C₂×C₃×C₅×Q₈	—	2	4	no	—
35	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₂×C₅×D₁₂	—	2	4	no	—
43	C₂×C₅×D₁₂	—	2	4	no	—
44	C₂×C₅×D₁₂	—	2	2	no	—
45	C₂×C₅×D₁₂	—	2	8	no	—
46	C₂×C₅×D₁₂	—	4	8	no	—
47	C₂×C₅×D₁₂	C₂³	1	4	yes	—
48	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
49	C₃×C₄²×C₅	D₄	1	2	yes	—
50	C₃×C₄²×C₅	C₂³	1	2	yes	—
51	C₅×#215	—	2	16	no	—
52	C₅×#213	—	2	16	no	—
53	C₂×C₅×C₃⋊C₈	D₄	1	8	yes	complemented
54	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
55	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂²×#215	C₂×C₅	1	2	yes	complemented
57	C₂²×#213	C₂×C₅	1	2	yes	complemented
58	C₂×#874	C₂×C₅	1	1	yes	characteristic, complemented
59	#5058	C₂×C₅	1	8	yes	direct product factor
60	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	—	3	2	no	—
63	C₂²×C₅×D₄	—	6	2	no	—
64	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
65	C₂×C₅×SD₁₆	—	3	8	no	—
66	C₂×C₅×SD₁₆	—	6	8	no	—
67	C₂×C₅×D₈	—	3	8	no	—
68	C₂×C₅×D₈	—	6	8	no	—
69	C₂²×C₅×C₈	—	3	2	no	—
70	C₅×#127	—	3	4	no	—
71	C₅×#127	—	6	2	no	—
72	C₅×#124	—	2	2	no	—
73	C₅×#124	C₂×D₃	1	4	yes	complemented
74	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
76	C₅×#97	—	3	4	no	—
77	C₂×#496	—	3	1	no	Sylow
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	—	4	2	no	—
80	C₂³×C₃×C₅	—	4	4	no	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₅×D₃	—	2	4	no	—
83	C₂²×C₅×D₃	—	4	4	no	—
84	C₂²×C₅×D₃	—	4	8	no	—
85	C₃×C₅×Q₈	—	2	4	no	—
86	C₃×C₅×Q₈	—	4	2	no	—
87	C₃×C₅×D₄	—	2	4	no	—
88	C₃×C₅×D₄	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
95	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
96	C₅×D₁₂	—	2	4	no	—
97	C₅×D₁₂	—	2	4	no	—
98	C₅×D₁₂	—	4	16	no	—
99	C₅×D₁₂	—	4	4	no	—
100	C₅×C₃⋊C₈	C₂×D₄	1	8	yes	complemented
101	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
102	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
103	C₂²×D₁₂	—	2	2	no	—
104	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
105	C₃×#124	—	2	2	no	—
106	C₃×#124	C₂²×C₅	1	4	yes	complemented
107	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
109	C₂×#215	—	2	8	no	—
110	C₂×#215	C₂²×C₅	1	8	yes	complemented
111	C₂×#213	—	2	8	no	—
112	C₂×#213	C₂²×C₅	1	8	yes	complemented
113	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
114	#874	—	2	2	no	—
115	#874	C₂²×C₅	1	4	yes	complemented
116	#803	C₂²×C₅	1	4	yes	complemented
117	C₂⁴×C₅	—	2	1	no	—
118	C₂⁴×C₅	—	6	2	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	4	no	—
121	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
122	C₂×C₅×D₄	—	2	4	no	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	3	4	no	—
125	C₂×C₅×D₄	—	6	4	no	—
126	C₂×C₅×D₄	—	6	4	no	—
127	C₂×C₅×D₄	—	6	8	no	—
128	C₂×C₅×D₄	—	6	2	no	—
129	C₂×C₅×D₄	—	12	8	no	—
130	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
131	C₂²×C₄×C₅	—	2	1	no	—
132	C₂²×C₄×C₅	#67	1	2	yes	—
133	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₅×SD₁₆	—	6	16	no	—
135	C₅×D₈	—	6	16	no	—
136	C₂×C₅×C₈	—	3	8	no	—
137	C₂×C₅×C₈	—	3	4	no	—
138	C₅×C₂²⋊C₄	—	2	8	no	—
139	C₄²×C₅	#67	1	2	yes	—
140	C₄²×C₅	C₂²×D₃	1	2	yes	—
141	C₂²×SD₁₆	—	3	2	no	—
142	C₂²×D₈	—	3	2	no	—
143	C₂×#127	—	3	1	no	—
144	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
145	#496	—	3	8	no	—
146	C₂×#97	—	3	1	no	—
147	C₂²×C₃×C₅	—	4	2	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	8	4	no	—
150	C₂²×C₃×C₅	#127	1	2	yes	—
151	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
152	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₅×D₃	—	4	4	no	—
154	C₂×C₅×D₃	—	4	8	no	—
155	C₂×C₅×D₃	—	8	8	no	—
156	C₃×C₄×C₅	—	2	4	no	—
157	C₃×C₄×C₅	—	4	2	no	—
158	C₃×C₄×C₅	#127	1	2	yes	—
159	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
160	C₂⁴×C₃	—	2	1	no	—
161	C₂³×D₃	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	1	no	—
163	C₂×C₃×Q₈	—	2	4	no	—
164	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
165	C₂×C₃×D₄	—	2	4	no	—
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
171	C₂×D₁₂	—	2	4	no	—
172	C₂×D₁₂	—	2	4	no	—
173	C₂×D₁₂	—	2	2	no	—
174	C₂×D₁₂	—	2	8	no	—
175	C₂×D₁₂	—	4	8	no	—
176	C₂×D₁₂	C₂³×C₅	1	4	yes	—
177	C₃×C₂²⋊C₄	—	2	8	no	—
178	C₃×C₄²	C₅×D₄	1	2	yes	—
179	C₃×C₄²	C₂³×C₅	1	2	yes	—
180	#215	—	2	16	no	—
181	#213	—	2	16	no	—
182	C₂×C₃⋊C₈	C₅×D₄	1	8	yes	complemented
183	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	4	2	no	—
186	C₂³×C₅	—	4	4	no	—
187	C₂³×C₅	—	6	4	no	—
188	C₂³×C₅	—	12	4	no	—
189	C₂³×C₅	—	12	8	no	—
190	C₂³×C₅	C₂×#67	1	1	yes	characteristic
191	C₅×Q₈	—	2	4	no	—
192	C₅×Q₈	—	4	2	no	—
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	6	4	no	—
196	C₅×D₄	—	6	4	no	—
197	C₅×D₄	—	12	16	no	—
198	C₅×D₄	—	12	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	4	2	no	—
202	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
203	C₂×C₄×C₅	C₂×#67	1	4	yes	—
204	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
206	C₅×C₈	—	3	8	no	—
207	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
208	C₂²×D₄	—	3	2	no	—
209	C₂²×D₄	—	6	2	no	—
210	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
211	C₂×SD₁₆	—	3	8	no	—
212	C₂×SD₁₆	—	6	8	no	—
213	C₂×D₈	—	3	8	no	—
214	C₂×D₈	—	6	8	no	—
215	C₂²×C₈	—	3	2	no	—
216	#127	—	3	4	no	—
217	#127	—	6	2	no	—
218	#124	—	2	2	no	—
219	#124	C₂×C₅×D₃	1	4	yes	complemented
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
222	#97	—	3	4	no	—
223	C₂×C₃×C₅	—	8	2	no	—
224	C₂×C₃×C₅	#496	1	4	yes	complemented
225	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
226	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
227	C₅×D₃	—	8	4	no	—
228	C₂³×C₃	—	2	2	no	—
229	C₂³×C₃	—	4	2	no	—
230	C₂³×C₃	—	4	4	no	—
231	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
232	C₂²×D₃	—	2	4	no	—
233	C₂²×D₃	—	4	4	no	—
234	C₂²×D₃	—	4	8	no	—
235	C₃×Q₈	—	2	4	no	—
236	C₃×Q₈	—	4	2	no	—
237	C₃×D₄	—	2	4	no	—
238	C₃×D₄	—	4	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
243	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
244	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
246	D₁₂	—	2	4	no	—
247	D₁₂	—	2	4	no	—
248	D₁₂	—	4	16	no	—
249	D₁₂	—	4	4	no	—
250	C₃⋊C₈	C₂×C₅×D₄	1	8	yes	complemented
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	—	4	4	no	—
253	C₂²×C₅	—	8	4	no	—
254	C₂²×C₅	—	12	4	no	—
255	C₂²×C₅	—	12	8	no	—
256	C₂²×C₅	—	24	8	no	—
257	C₂²×C₅	#940	1	2	yes	—
258	C₂²×C₅	#949	1	4	yes	—
259	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	4	2	no	—
262	C₄×C₅	#940	1	2	yes	—
263	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
264	C₂⁴	—	2	1	no	—
265	C₂⁴	—	6	2	no	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	3	4	no	—
272	C₂×D₄	—	6	4	no	—
273	C₂×D₄	—	6	4	no	—
274	C₂×D₄	—	6	8	no	—
275	C₂×D₄	—	6	2	no	—
276	C₂×D₄	—	12	8	no	—
277	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	C₅×#67	1	2	yes	—
280	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
281	SD₁₆	—	6	16	no	—
282	D₈	—	6	16	no	—
283	C₂×C₈	—	3	8	no	—
284	C₂×C₈	—	3	4	no	—
285	C₂²⋊C₄	—	2	8	no	—
286	C₄²	C₅×#67	1	2	yes	—
287	C₄²	C₂²×C₅×D₃	1	2	yes	—
288	C₃×C₅	C₂×#496	1	1	yes	characteristic, complemented, Hall
289	C₂²×C₃	—	4	2	no	—
290	C₂²×C₃	—	4	4	no	—
291	C₂²×C₃	—	8	4	no	—
292	C₂²×C₃	C₅×#127	1	2	yes	—
293	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
294	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
295	C₂×D₃	—	4	4	no	—
296	C₂×D₃	—	4	8	no	—
297	C₂×D₃	—	8	8	no	—
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	4	2	no	—
300	C₃×C₄	C₅×#127	1	2	yes	—
301	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
302	C₂×C₅	—	8	2	no	—
303	C₂×C₅	—	24	4	no	—
304	C₂×C₅	#5058	1	4	yes	direct product factor
305	C₂×C₅	C₂×#940	1	1	yes	characteristic
306	C₂×C₅	C₂×#949	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	4	2	no	—
309	C₂³	—	4	4	no	—
310	C₂³	—	6	4	no	—
311	C₂³	—	12	4	no	—
312	C₂³	—	12	8	no	—
313	C₂³	C₂×C₅×#67	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	4	2	no	—
316	D₄	—	2	4	no	—
317	D₄	—	4	2	no	—
318	D₄	—	6	4	no	—
319	D₄	—	6	4	no	—
320	D₄	—	12	16	no	—
321	D₄	—	12	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
326	C₂×C₄	C₂×C₅×#67	1	4	yes	—
327	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
328	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
329	C₈	—	3	8	no	—
330	C₂×C₃	—	8	2	no	—
331	C₂×C₃	C₅×#496	1	4	yes	complemented
332	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
333	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
334	D₃	—	8	4	no	—
335	C₅	C₂×#5058	1	1	yes	characteristic, direct product factor, Sylow
336	C₂²	—	4	2	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	12	4	no	—
340	C₂²	—	12	8	no	—
341	C₂²	—	24	8	no	—
342	C₂²	C₅×#940	1	2	yes	—
343	C₂²	C₅×#949	1	4	yes	—
344	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
345	C₄	—	2	4	no	—
346	C₄	—	4	2	no	—
347	C₄	C₅×#940	1	2	yes	—
348	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
349	C₃	C₂×C₅×#496	1	1	yes	characteristic, complemented, Sylow
350	C₂	—	8	2	no	—
351	C₂	—	24	4	no	—
352	C₂	C₅×#5058	1	4	yes	direct product factor
353	C₂	C₂×C₅×#940	1	1	yes	characteristic
354	C₂	C₂×C₅×#949	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#496
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂²×C₅×#215	C₂	semidirect
3. C₂²×C₅×#213	C₂	semidirect
4. C₂×C₅×#874	C₂	semidirect
5. C₅×#5058	C₂	direct (N × H)
6. C₂×C₅×#803	C₂	semidirect
13. C₃×C₅×#124	C₂²	semidirect
17. C₂×C₅×#215	C₂²	semidirect
19. C₂×C₅×#213	C₂²	semidirect
22. C₅×#874	C₂²	semidirect
23. C₅×#803	C₂²	semidirect
24. C₂×#5058	C₅	direct (N × H)
28. C₂×C₅×#124	D₃	semidirect
53. C₂×C₅×C₃⋊C₈	D₄	semidirect
55. C₂×C₃×#124	C₂×C₅	semidirect
56. C₂²×#215	C₂×C₅	semidirect
57. C₂²×#213	C₂×C₅	semidirect
58. C₂×#874	C₂×C₅	semidirect
59. #5058	C₂×C₅	direct (N × H)
60. C₂×#803	C₂×C₅	semidirect
73. C₅×#124	C₂×D₃	semidirect
100. C₅×C₃⋊C₈	C₂×D₄	semidirect
106. C₃×#124	C₂²×C₅	semidirect
110. C₂×#215	C₂²×C₅	semidirect
112. C₂×#213	C₂²×C₅	semidirect
115. #874	C₂²×C₅	semidirect
116. #803	C₂²×C₅	semidirect
144. C₂×#124	C₅×D₃	semidirect
182. C₂×C₃⋊C₈	C₅×D₄	semidirect
219. #124	C₂×C₅×D₃	semidirect
224. C₂×C₃×C₅	#496	semidirect
250. C₃⋊C₈	C₂×C₅×D₄	semidirect
288. C₃×C₅	C₂×#496	semidirect
304. C₂×C₅	#5058	direct (N × H)
331. C₂×C₃	C₅×#496	semidirect
335. C₅	C₂×#5058	direct (N × H)
349. C₃	C₂×C₅×#496	semidirect
352. C₂	C₅×#5058	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×#124	2
C₂²×C₅×#215	2
C₂²×C₅×#213	2
C₂×C₅×#874	2
C₅×#5058	2
C₂×C₅×#803	2
C₂×C₅×#496	3
C₂×#5058	5

Subgroups — C2×C5×#5058 #14438970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5058 #14438970