Subgroups — C₂×C₅×#5518 #14481205

Order 1920.

2008 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×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#924	C₂	1	2	yes	maximal
3	C₅×#5518	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#889	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#879	C₂	1	4	yes	maximal
6	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#869	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₅×Dic₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#541	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
12	C₃×C₅×#117	C₂²	1	8	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×#217	C₂²	1	4	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
20	C₅×#924	C₂²	1	16	yes	—
21	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
22	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
23	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
25	C₅×#889	C₂²	1	32	yes	complemented
26	C₅×#879	C₂²	1	32	yes	—
27	C₅×#870	C₂²	1	8	yes	complemented
28	C₅×#869	C₂²	1	8	yes	complemented
29	C₄×C₅×Dic₆	C₂²	1	16	yes	complemented
30	C₂×#5518	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#541	—	3	16	no	—
32	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
33	C₂×C₅×#126	—	3	4	no	—
34	C₂×C₅×#125	—	3	4	no	—
35	C₂×C₅×#125	—	3	1	no	—
36	C₂×C₅×C₂²⋊Q₈	—	3	2	no	—
37	C₂×C₄×C₅×Q₈	—	3	2	no	—
38	C₂×C₅×#117	D₃	1	1	yes	characteristic
39	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
47	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
48	C₂×C₅×Dic₆	—	2	8	no	—
49	C₂×C₅×Dic₆	C₂³	1	8	yes	—
50	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
51	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
52	C₃×C₄²×C₅	C₂³	1	4	yes	—
53	C₃×C₄²×C₅	C₂³	1	4	yes	—
54	C₅×#217	C₂³	1	16	yes	—
55	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
56	C₅×C₄⋊Dic₃	C₂³	1	16	yes	—
57	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
58	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
59	C₅×Dic₃⋊C₄	C₂³	1	16	yes	—
60	C₄×C₅×Dic₃	C₂³	1	16	yes	—
61	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
62	C₂×#924	C₂×C₅	1	2	yes	—
63	#5518	C₂×C₅	1	16	yes	direct product factor
64	C₂×#889	C₂×C₅	1	4	yes	complemented
65	C₂×#879	C₂×C₅	1	4	yes	—
66	C₂×#870	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×#869	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₄×Dic₆	C₂×C₅	1	2	yes	complemented
69	C₂²×C₅×Q₈	—	3	2	no	—
70	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
71	C₅×C₄⋊Q₈	—	3	8	no	—
72	C₅×#126	—	3	32	no	—
73	C₅×#125	—	3	32	no	—
74	C₅×#125	—	3	8	no	—
75	C₅×C₂²⋊Q₈	—	3	16	no	—
76	C₄×C₅×Q₈	—	3	16	no	—
77	C₅×#117	C₂×D₃	1	8	yes	—
78	C₂×C₅×C₄⋊C₄	—	3	4	no	—
79	C₂×C₅×C₄⋊C₄	—	3	4	no	—
80	C₂×C₅×C₄⋊C₄	—	3	4	no	—
81	C₂×C₅×C₄⋊C₄	—	3	2	no	—
82	C₂×C₅×C₄⋊C₄	—	3	4	no	—
83	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
84	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
85	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
86	C₂×C₄²×C₅	—	3	4	no	—
87	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
89	C₂×#541	—	3	1	no	Sylow
90	C₂³×C₃×C₅	—	2	2	no	—
91	C₂³×C₃×C₅	—	2	4	no	—
92	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
93	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	2	4	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	—	2	8	no	—
98	C₂×C₃×C₄×C₅	#41	1	4	yes	—
99	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
101	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
102	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
103	C₂×C₅×Dic₃	—	2	8	no	—
104	C₂×C₅×Dic₃	—	2	8	no	—
105	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
106	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
107	C₅×Dic₆	—	2	16	no	—
108	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
109	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
110	C₃×#117	C₂²×C₅	1	8	yes	—
111	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
114	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
115	C₂×#217	C₂²×C₅	1	4	yes	—
116	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
117	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
118	#924	C₂²×C₅	1	16	yes	—
119	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
120	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
121	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	—
122	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
123	#889	C₂²×C₅	1	32	yes	complemented
124	#879	C₂²×C₅	1	32	yes	—
125	#870	C₂²×C₅	1	8	yes	complemented
126	#869	C₂²×C₅	1	8	yes	complemented
127	C₄×Dic₆	C₂²×C₅	1	16	yes	complemented
128	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₅×Q₈	—	3	8	no	—
130	C₂×C₅×Q₈	—	6	8	no	—
131	C₂²×C₄×C₅	—	2	4	no	—
132	C₂²×C₄×C₅	—	3	4	no	—
133	C₂²×C₄×C₅	—	3	4	no	—
134	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
136	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
137	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
139	C₅×C₄⋊C₄	—	3	8	no	—
140	C₅×C₄⋊C₄	—	3	16	no	—
141	C₅×C₄⋊C₄	—	3	16	no	—
142	C₅×C₄⋊C₄	—	3	16	no	—
143	C₅×C₄⋊C₄	—	3	16	no	—
144	C₅×C₄⋊C₄	C₂²×D₃	1	8	yes	—
145	C₅×C₂²⋊C₄	—	3	16	no	—
146	C₅×C₂²⋊C₄	C₂²×D₃	1	8	yes	—
147	C₄²×C₅	—	3	16	no	—
148	C₄²×C₅	C₂²×D₃	1	4	yes	—
149	C₄²×C₅	C₂²×D₃	1	4	yes	—
150	#541	—	3	16	no	—
151	C₂×C₄⋊Q₈	—	3	1	no	—
152	C₂×#126	—	3	4	no	—
153	C₂×#125	—	3	4	no	—
154	C₂×#125	—	3	1	no	—
155	C₂×C₂²⋊Q₈	—	3	2	no	—
156	C₂×C₄×Q₈	—	3	2	no	—
157	C₂×#117	C₅×D₃	1	1	yes	characteristic
158	C₂²×C₃×C₅	—	2	2	no	—
159	C₂²×C₃×C₅	—	2	4	no	—
160	C₂²×C₃×C₅	—	4	4	no	—
161	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
162	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
163	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	2	4	no	—
166	C₃×C₄×C₅	—	2	4	no	—
167	C₃×C₄×C₅	C₂×#41	1	4	yes	—
168	C₅×Dic₃	—	2	8	no	—
169	C₅×Dic₃	—	2	8	no	—
170	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
177	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
178	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
179	C₂×Dic₆	—	2	8	no	—
180	C₂×Dic₆	C₂³×C₅	1	8	yes	—
181	C₃×C₄⋊C₄	C₂³×C₅	1	8	yes	—
182	C₃×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
183	C₃×C₄²	C₂³×C₅	1	4	yes	—
184	C₃×C₄²	C₂³×C₅	1	4	yes	—
185	#217	C₂³×C₅	1	16	yes	—
186	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
187	C₄⋊Dic₃	C₂³×C₅	1	16	yes	—
188	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
189	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
190	Dic₃⋊C₄	C₂³×C₅	1	16	yes	—
191	C₄×Dic₃	C₂³×C₅	1	16	yes	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	C₂³×D₃	1	2	yes	—
195	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
196	C₅×Q₈	—	6	16	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	4	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	8	no	—
201	C₂×C₄×C₅	—	3	8	no	—
202	C₂×C₄×C₅	—	3	8	no	—
203	C₂×C₄×C₅	—	6	8	no	—
204	C₂×C₄×C₅	—	6	8	no	—
205	C₂×C₄×C₅	#235	1	4	yes	—
206	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
207	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
208	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
209	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
210	C₂²×Q₈	—	3	2	no	—
211	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
212	C₄⋊Q₈	—	3	8	no	—
213	#126	—	3	32	no	—
214	#125	—	3	32	no	—
215	#125	—	3	8	no	—
216	C₂²⋊Q₈	—	3	16	no	—
217	C₄×Q₈	—	3	16	no	—
218	#117	C₂×C₅×D₃	1	8	yes	—
219	C₂×C₄⋊C₄	—	3	2	no	—
220	C₂×C₄⋊C₄	—	3	4	no	—
221	C₂×C₄⋊C₄	—	3	4	no	—
222	C₂×C₄⋊C₄	—	3	4	no	—
223	C₂×C₄⋊C₄	—	3	4	no	—
224	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
225	C₂×C₂²⋊C₄	—	3	4	no	—
226	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
227	C₂×C₄²	—	3	4	no	—
228	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
229	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
230	C₂×C₃×C₅	—	4	2	no	—
231	C₂×C₃×C₅	#541	1	4	yes	complemented
232	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
233	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
234	C₂³×C₃	—	2	2	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
237	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	8	no	—
242	C₂×C₃×C₄	C₅×#41	1	4	yes	—
243	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
244	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
245	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
246	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
247	C₂×Dic₃	—	2	8	no	—
248	C₂×Dic₃	—	2	8	no	—
249	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
250	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
251	Dic₆	—	2	16	no	—
252	C₂²×C₅	—	2	2	no	—
253	C₂²×C₅	—	2	4	no	—
254	C₂²×C₅	—	4	4	no	—
255	C₂²×C₅	C₂×#235	1	2	yes	—
256	C₂²×C₅	#1010	1	4	yes	—
257	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
258	C₄×C₅	—	2	2	no	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	6	8	no	—
262	C₄×C₅	—	6	8	no	—
263	C₄×C₅	C₂×#235	1	4	yes	—
264	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
265	C₂×Q₈	—	3	8	no	—
266	C₂×Q₈	—	6	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	3	4	no	—
269	C₂²×C₄	—	3	4	no	—
270	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
271	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
272	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
274	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
275	C₄⋊C₄	—	3	8	no	—
276	C₄⋊C₄	—	3	16	no	—
277	C₄⋊C₄	—	3	16	no	—
278	C₄⋊C₄	—	3	16	no	—
279	C₄⋊C₄	—	3	16	no	—
280	C₄⋊C₄	C₂²×C₅×D₃	1	8	yes	—
281	C₂²⋊C₄	—	3	16	no	—
282	C₂²⋊C₄	C₂²×C₅×D₃	1	8	yes	—
283	C₄²	—	3	16	no	—
284	C₄²	C₂²×C₅×D₃	1	4	yes	—
285	C₄²	C₂²×C₅×D₃	1	4	yes	—
286	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	4	no	—
289	C₂²×C₃	—	4	4	no	—
290	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
291	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
292	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	C₂×C₅×#41	1	4	yes	—
297	Dic₃	—	2	8	no	—
298	Dic₃	—	2	8	no	—
299	C₂×C₅	—	4	2	no	—
300	C₂×C₅	#5518	1	4	yes	direct product factor
301	C₂×C₅	C₂²×#235	1	1	yes	characteristic
302	C₂×C₅	C₂×#1010	1	2	yes	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	4	no	—
305	C₂³	C₂³×C₅×D₃	1	2	yes	—
306	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
307	Q₈	—	6	16	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	3	8	no	—
313	C₂×C₄	—	3	8	no	—
314	C₂×C₄	—	6	8	no	—
315	C₂×C₄	—	6	8	no	—
316	C₂×C₄	C₅×#235	1	4	yes	—
317	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
318	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
319	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
320	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
321	C₂×C₃	—	4	2	no	—
322	C₂×C₃	C₅×#541	1	4	yes	complemented
323	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
324	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
325	C₅	C₂×#5518	1	1	yes	characteristic, direct product factor, Sylow
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	4	4	no	—
329	C₂²	C₂×C₅×#235	1	2	yes	—
330	C₂²	C₅×#1010	1	4	yes	—
331	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	2	4	no	—
334	C₄	—	2	4	no	—
335	C₄	—	6	8	no	—
336	C₄	—	6	8	no	—
337	C₄	C₂×C₅×#235	1	4	yes	—
338	C₃	C₂×C₅×#541	1	1	yes	characteristic, complemented, Sylow
339	C₂	—	4	2	no	—
340	C₂	C₅×#5518	1	4	yes	direct product factor
341	C₂	C₂²×C₅×#235	1	1	yes	characteristic
342	C₂	C₂×C₅×#1010	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₂×C₅×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
3. C₅×#5518	C₂	direct (N × H)
4. C₂×C₅×#889	C₂	semidirect
6. C₂×C₅×#870	C₂	semidirect
7. C₂×C₅×#869	C₂	semidirect
8. C₂×C₄×C₅×Dic₆	C₂	semidirect
25. C₅×#889	C₂²	semidirect
27. C₅×#870	C₂²	semidirect
28. C₅×#869	C₂²	semidirect
29. C₄×C₅×Dic₆	C₂²	semidirect
30. C₂×#5518	C₅	direct (N × H)
63. #5518	C₂×C₅	direct (N × H)
64. C₂×#889	C₂×C₅	semidirect
66. C₂×#870	C₂×C₅	semidirect
67. C₂×#869	C₂×C₅	semidirect
68. C₂×C₄×Dic₆	C₂×C₅	semidirect
123. #889	C₂²×C₅	semidirect
125. #870	C₂²×C₅	semidirect
126. #869	C₂²×C₅	semidirect
127. C₄×Dic₆	C₂²×C₅	semidirect
231. C₂×C₃×C₅	#541	semidirect
286. C₃×C₅	C₂×#541	semidirect
300. C₂×C₅	#5518	direct (N × H)
322. C₂×C₃	C₅×#541	semidirect
325. C₅	C₂×#5518	direct (N × H)
338. C₃	C₂×C₅×#541	semidirect
340. C₂	C₅×#5518	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×#117	2
C₂×C₅×#924	2
C₅×#5518	2
C₂×C₅×#889	2
C₂×C₅×#879	2
C₂×C₅×#870	2
C₂×C₅×#869	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#541	3
C₂×#5518	5

Subgroups — C2×C5×#5518 #14481205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5518 #14481205