Subgroups — C₂×C₅×#5510 #14480572

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#930	C₂	1	4	yes	maximal, complemented
4	C₅×#5510	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#897	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#895	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#537	—	3	1	no	maximal, Hall
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	C₂²	1	4	yes	—
11	C₂×C₅×#235	—	2	16	no	—
12	C₂×C₅×#235	C₂²	1	16	yes	complemented
13	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
14	C₂²×C₅×D₁₂	C₂²	1	4	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
16	C₂²×C₅×Dic₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	8	yes	complemented
19	C₅×#930	C₂²	1	32	yes	complemented
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
21	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
22	C₅×#897	C₂²	1	32	yes	complemented
23	C₅×#895	C₂²	1	32	yes	complemented
24	C₂×#5510	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×#41	—	3	2	no	—
26	C₅×#537	—	3	16	no	—
27	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
28	C₂×C₅×#121	—	3	4	no	—
29	C₂×C₅×#121	—	3	4	no	—
30	C₂²×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂³×C₅×D₃	C₂³	1	4	yes	—
33	C₂²×C₃×C₄×C₅	—	4	4	no	—
34	C₂²×C₃×C₄×C₅	D₄	1	8	yes	complemented
35	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂×C₅×#67	—	2	16	no	—
40	C₂×C₅×#67	C₂³	1	16	yes	—
41	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
42	C₅×#235	—	2	64	no	—
43	C₂×C₅×D₁₂	—	2	8	no	—
44	C₂×C₅×D₁₂	—	4	8	no	—
45	C₂×C₅×D₁₂	C₂³	1	8	yes	—
46	C₂×C₅×D₁₂	C₂³	1	16	yes	—
47	C₂×C₄×C₅×D₃	—	2	16	no	—
48	C₂×C₄×C₅×D₃	C₂³	1	16	yes	—
49	C₂×C₅×Dic₆	—	2	8	no	—
50	C₂×C₅×Dic₆	C₂³	1	8	yes	—
51	C₃×C₅×C₄⋊C₄	C₂³	1	16	yes	—
52	C₅×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
53	C₅×C₄⋊Dic₃	C₂³	1	16	yes	—
54	C₂²×#235	C₂×C₅	1	2	yes	complemented
55	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×#930	C₂×C₅	1	4	yes	complemented
57	#5510	C₂×C₅	1	16	yes	direct product factor
58	C₂×#897	C₂×C₅	1	4	yes	complemented
59	C₂×#895	C₂×C₅	1	4	yes	complemented
60	C₂×C₅×#41	—	3	16	no	—
61	C₂×C₅×#41	—	6	16	no	—
62	C₂²×C₅×Q₈	—	3	2	no	—
63	C₂²×C₅×D₄	—	3	4	no	—
64	C₂²×C₅×D₄	—	3	2	no	—
65	C₂²×C₅×D₄	—	3	4	no	—
66	C₂³×C₄×C₅	—	3	4	no	—
67	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
68	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
69	C₅×C₂²⋊Q₈	—	3	32	no	—
70	C₅×#121	—	3	32	no	—
71	C₅×#121	—	3	32	no	—
72	C₂×C₅×C₄⋊C₄	—	3	4	no	—
73	C₂×C₅×C₄⋊C₄	C₂×D₃	1	4	yes	—
74	C₂×C₅×C₄⋊C₄	C₂×D₃	1	8	yes	complemented
75	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
76	C₂×#537	—	3	1	no	Sylow
77	C₂³×C₃×C₅	—	2	2	no	—
78	C₂³×C₃×C₅	—	2	2	no	—
79	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
81	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
82	C₂²×C₅×D₃	—	2	8	no	—
83	C₂²×C₅×D₃	—	2	8	no	—
84	C₂²×C₅×D₃	—	2	8	no	—
85	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
86	C₂×C₃×C₄×C₅	—	2	8	no	—
87	C₂×C₃×C₄×C₅	—	4	8	no	—
88	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	complemented
90	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
91	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
92	C₅×#67	—	2	32	no	—
93	C₂×C₅×Dic₃	—	2	8	no	—
94	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
95	C₅×D₁₂	—	2	16	no	—
96	C₅×D₁₂	—	4	16	no	—
97	C₄×C₅×D₃	—	2	32	no	—
98	C₅×Dic₆	—	2	16	no	—
99	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
100	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
101	C₂²×#67	C₂²×C₅	1	4	yes	—
102	C₂×#235	—	2	16	no	—
103	C₂×#235	C₂²×C₅	1	16	yes	complemented
104	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
105	C₂²×D₁₂	C₂²×C₅	1	4	yes	—
106	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
107	C₂²×Dic₆	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
110	#930	C₂²×C₅	1	32	yes	complemented
111	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	—
112	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
113	#897	C₂²×C₅	1	32	yes	complemented
114	#895	C₂²×C₅	1	32	yes	complemented
115	C₂⁴×C₅	—	3	4	no	—
116	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₅×#41	—	6	64	no	—
118	C₂×C₅×Q₈	—	3	8	no	—
119	C₂×C₅×Q₈	—	6	8	no	—
120	C₂×C₅×D₄	—	3	16	no	—
121	C₂×C₅×D₄	—	3	8	no	—
122	C₂×C₅×D₄	—	3	16	no	—
123	C₂×C₅×D₄	—	6	16	no	—
124	C₂×C₅×D₄	—	6	8	no	—
125	C₂×C₅×D₄	—	12	8	no	—
126	C₂²×C₄×C₅	—	3	4	no	—
127	C₂²×C₄×C₅	—	3	16	no	—
128	C₂²×C₄×C₅	—	4	4	no	—
129	C₂²×C₄×C₅	—	6	16	no	—
130	C₂²×C₄×C₅	D₁₂	1	8	yes	complemented
131	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
132	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
133	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
134	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
135	C₅×C₄⋊C₄	—	3	16	no	—
136	C₅×C₄⋊C₄	C₂²×D₃	1	16	yes	—
137	C₅×C₂²⋊C₄	—	3	32	no	—
138	C₂²×#41	—	3	2	no	—
139	#537	—	3	16	no	—
140	C₂×C₂²⋊Q₈	—	3	4	no	—
141	C₂×#121	—	3	4	no	—
142	C₂×#121	—	3	4	no	—
143	C₂²×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
144	C₂²×C₃×C₅	—	2	8	no	—
145	C₂²×C₃×C₅	—	2	2	no	—
146	C₂²×C₃×C₅	—	2	2	no	—
147	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
148	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
149	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
150	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
151	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
152	C₂×C₅×D₃	—	2	8	no	—
153	C₂×C₅×D₃	—	2	8	no	—
154	C₂×C₅×D₃	—	2	8	no	—
155	C₂×C₅×D₃	—	4	16	no	—
156	C₃×C₄×C₅	—	2	8	no	—
157	C₃×C₄×C₅	C₂²×D₄	1	8	yes	—
158	C₅×Dic₃	—	2	8	no	—
159	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
160	C₂³×D₃	C₂³×C₅	1	4	yes	—
161	C₂²×C₃×C₄	—	4	4	no	—
162	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
163	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
164	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
165	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
167	C₂×#67	—	2	16	no	—
168	C₂×#67	C₂³×C₅	1	16	yes	—
169	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
170	#235	—	2	64	no	—
171	C₂×D₁₂	—	2	8	no	—
172	C₂×D₁₂	—	4	8	no	—
173	C₂×D₁₂	C₂³×C₅	1	8	yes	—
174	C₂×D₁₂	C₂³×C₅	1	16	yes	—
175	C₂×C₄×D₃	—	2	16	no	—
176	C₂×C₄×D₃	C₂³×C₅	1	16	yes	—
177	C₂×Dic₆	—	2	8	no	—
178	C₂×Dic₆	C₂³×C₅	1	8	yes	—
179	C₃×C₄⋊C₄	C₂³×C₅	1	16	yes	—
180	(C₂×D₃)⋊C₄	C₂³×C₅	1	32	yes	—
181	C₄⋊Dic₃	C₂³×C₅	1	16	yes	—
182	C₂³×C₅	—	2	2	no	—
183	C₂³×C₅	—	2	2	no	—
184	C₂³×C₅	—	3	8	no	—
185	C₂³×C₅	—	6	8	no	—
186	C₂³×C₅	—	6	8	no	—
187	C₂³×C₅	—	6	8	no	—
188	C₂³×C₅	C₂×D₁₂	1	4	yes	—
189	C₂³×C₅	C₂³×D₃	1	2	yes	—
190	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
191	C₅×Q₈	—	6	16	no	—
192	C₅×D₄	—	6	32	no	—
193	C₅×D₄	—	6	16	no	—
194	C₅×D₄	—	12	16	no	—
195	C₂×C₄×C₅	—	2	8	no	—
196	C₂×C₄×C₅	—	3	8	no	—
197	C₂×C₄×C₅	—	4	8	no	—
198	C₂×C₄×C₅	—	6	8	no	—
199	C₂×C₄×C₅	—	6	32	no	—
200	C₂×C₄×C₅	C₂×D₁₂	1	8	yes	—
201	C₂×C₄×C₅	C₂×D₁₂	1	16	yes	complemented
202	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
203	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
204	C₂×#41	—	3	16	no	—
205	C₂×#41	—	6	16	no	—
206	C₂²×Q₈	—	3	2	no	—
207	C₂²×D₄	—	3	4	no	—
208	C₂²×D₄	—	3	2	no	—
209	C₂²×D₄	—	3	4	no	—
210	C₂³×C₄	—	3	4	no	—
211	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
212	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
213	C₂²⋊Q₈	—	3	32	no	—
214	#121	—	3	32	no	—
215	#121	—	3	32	no	—
216	C₂×C₄⋊C₄	—	3	4	no	—
217	C₂×C₄⋊C₄	C₂×C₅×D₃	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×C₅×D₃	1	8	yes	complemented
219	C₂×C₂²⋊C₄	—	3	8	no	—
220	C₂×C₃×C₅	—	2	4	no	—
221	C₂×C₃×C₅	#537	1	4	yes	complemented
222	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
223	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
225	C₅×D₃	—	4	8	no	—
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	—	2	2	no	—
228	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
229	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
230	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
231	C₂²×D₃	—	2	8	no	—
232	C₂²×D₃	—	2	8	no	—
233	C₂²×D₃	—	2	8	no	—
234	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
235	C₂×C₃×C₄	—	2	8	no	—
236	C₂×C₃×C₄	—	4	8	no	—
237	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	—
238	C₂×C₃×C₄	C₂×C₅×D₄	1	16	yes	complemented
239	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
240	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
241	#67	—	2	32	no	—
242	C₂×Dic₃	—	2	8	no	—
243	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
244	D₁₂	—	2	16	no	—
245	D₁₂	—	4	16	no	—
246	C₄×D₃	—	2	32	no	—
247	Dic₆	—	2	16	no	—
248	C₂²×C₅	—	2	2	no	—
249	C₂²×C₅	—	2	2	no	—
250	C₂²×C₅	—	2	8	no	—
251	C₂²×C₅	—	6	8	no	—
252	C₂²×C₅	—	6	8	no	—
253	C₂²×C₅	—	6	8	no	—
254	C₂²×C₅	—	12	16	no	—
255	C₂²×C₅	C₂²×D₁₂	1	4	yes	—
256	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
257	C₂²×C₅	#1004	1	2	yes	—
258	C₂²×C₅	#1007	1	2	yes	—
259	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
260	C₄×C₅	—	2	8	no	—
261	C₄×C₅	—	6	8	no	—
262	C₄×C₅	C₂²×D₁₂	1	8	yes	—
263	C₂⁴	—	3	4	no	—
264	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
265	#41	—	6	64	no	—
266	C₂×Q₈	—	3	8	no	—
267	C₂×Q₈	—	6	8	no	—
268	C₂×D₄	—	3	16	no	—
269	C₂×D₄	—	3	8	no	—
270	C₂×D₄	—	3	16	no	—
271	C₂×D₄	—	6	16	no	—
272	C₂×D₄	—	6	8	no	—
273	C₂×D₄	—	12	8	no	—
274	C₂²×C₄	—	3	4	no	—
275	C₂²×C₄	—	3	16	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	6	16	no	—
278	C₂²×C₄	C₅×D₁₂	1	8	yes	complemented
279	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
280	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
281	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
282	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
283	C₄⋊C₄	—	3	16	no	—
284	C₄⋊C₄	C₂²×C₅×D₃	1	16	yes	—
285	C₂²⋊C₄	—	3	32	no	—
286	C₃×C₅	C₂×#537	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	8	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
291	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
292	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
293	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
294	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
295	C₂×D₃	—	2	8	no	—
296	C₂×D₃	—	2	8	no	—
297	C₂×D₃	—	2	8	no	—
298	C₂×D₃	—	4	16	no	—
299	C₃×C₄	—	2	8	no	—
300	C₃×C₄	C₂²×C₅×D₄	1	8	yes	—
301	Dic₃	—	2	8	no	—
302	C₂×C₅	—	2	4	no	—
303	C₂×C₅	—	12	8	no	—
304	C₂×C₅	#5510	1	4	yes	direct product factor
305	C₂×C₅	C₂³×D₁₂	1	1	yes	characteristic
306	C₂×C₅	C₂×#1004	1	1	yes	characteristic
307	C₂×C₅	C₂×#1007	1	1	yes	characteristic
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	3	8	no	—
311	C₂³	—	6	8	no	—
312	C₂³	—	6	8	no	—
313	C₂³	—	6	8	no	—
314	C₂³	C₂×C₅×D₁₂	1	4	yes	—
315	C₂³	C₂³×C₅×D₃	1	2	yes	—
316	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
317	Q₈	—	6	16	no	—
318	D₄	—	6	32	no	—
319	D₄	—	6	16	no	—
320	D₄	—	12	16	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	3	8	no	—
323	C₂×C₄	—	4	8	no	—
324	C₂×C₄	—	6	8	no	—
325	C₂×C₄	—	6	32	no	—
326	C₂×C₄	C₂×C₅×D₁₂	1	8	yes	—
327	C₂×C₄	C₂×C₅×D₁₂	1	16	yes	complemented
328	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
329	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	C₅×#537	1	4	yes	complemented
332	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
333	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
335	D₃	—	4	8	no	—
336	C₅	C₂×#5510	1	1	yes	characteristic, direct product factor, Sylow
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	6	8	no	—
341	C₂²	—	6	8	no	—
342	C₂²	—	6	8	no	—
343	C₂²	—	12	16	no	—
344	C₂²	C₂²×C₅×D₁₂	1	4	yes	—
345	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
346	C₂²	C₅×#1004	1	2	yes	—
347	C₂²	C₅×#1007	1	2	yes	—
348	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
349	C₄	—	2	8	no	—
350	C₄	—	6	8	no	—
351	C₄	C₂²×C₅×D₁₂	1	8	yes	—
352	C₃	C₂×C₅×#537	1	1	yes	characteristic, complemented, Sylow
353	C₂	—	2	4	no	—
354	C₂	—	12	8	no	—
355	C₂	C₅×#5510	1	4	yes	direct product factor
356	C₂	C₂³×C₅×D₁₂	1	1	yes	characteristic
357	C₂	C₂×C₅×#1004	1	1	yes	characteristic
358	C₂	C₂×C₅×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂²×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₂×C₅×#537
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#235	C₂	semidirect
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂×C₅×#930	C₂	semidirect
4. C₅×#5510	C₂	direct (N × H)
5. C₂×C₅×#897	C₂	semidirect
6. C₂×C₅×#895	C₂	semidirect
12. C₂×C₅×#235	C₂²	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
19. C₅×#930	C₂²	semidirect
22. C₅×#897	C₂²	semidirect
23. C₅×#895	C₂²	semidirect
24. C₂×#5510	C₅	direct (N × H)
30. C₂²×C₅×C₄⋊C₄	D₃	semidirect
34. C₂²×C₃×C₄×C₅	D₄	semidirect
54. C₂²×#235	C₂×C₅	semidirect
55. C₂²×C₃×C₄⋊C₄	C₂×C₅	semidirect
56. C₂×#930	C₂×C₅	semidirect
57. #5510	C₂×C₅	direct (N × H)
58. C₂×#897	C₂×C₅	semidirect
59. C₂×#895	C₂×C₅	semidirect
74. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
89. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
103. C₂×#235	C₂²×C₅	semidirect
109. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
110. #930	C₂²×C₅	semidirect
113. #897	C₂²×C₅	semidirect
114. #895	C₂²×C₅	semidirect
130. C₂²×C₄×C₅	D₁₂	semidirect
143. C₂²×C₄⋊C₄	C₅×D₃	semidirect
162. C₂²×C₃×C₄	C₅×D₄	semidirect
201. C₂×C₄×C₅	C₂×D₁₂	semidirect
218. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
221. C₂×C₃×C₅	#537	semidirect
238. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
278. C₂²×C₄	C₅×D₁₂	semidirect
286. C₃×C₅	C₂×#537	semidirect
304. C₂×C₅	#5510	direct (N × H)
327. C₂×C₄	C₂×C₅×D₁₂	semidirect
331. C₂×C₃	C₅×#537	semidirect
336. C₅	C₂×#5510	direct (N × H)
352. C₃	C₂×C₅×#537	semidirect
355. C₂	C₅×#5510	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₅×#930	2
C₅×#5510	2
C₂×C₅×#897	2
C₂×C₅×#895	2
C₂×C₅×#537	3
C₂×#5510	5

Subgroups — C2×C5×#5510 #14480572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5510 #14480572