Subgroups — C₂×C₅×#5717 #14482412

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃×D₄	C₂	1	4	yes	maximal, complemented
2	C₂×C₃×C₅×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#938	C₂	1	4	yes	maximal, complemented
4	C₂×C₅×#937	C₂	1	4	yes	maximal, complemented
5	C₅×#5717	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×D₄²	—	3	1	no	maximal, Hall
8	C₂⁴×C₅×D₃	C₂²	1	4	yes	complemented
9	C₂²×C₃×C₅×D₄	C₂²	1	4	yes	complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
11	C₂²×C₅×#67	C₂²	1	8	yes	complemented
12	C₂×C₅×D₃×D₄	—	2	32	no	—
13	C₂×C₅×D₃×D₄	C₂²	1	32	yes	complemented
14	C₂²×C₅×D₁₂	C₂²	1	2	yes	—
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	complemented
16	C₃×C₅×#127	C₂²	1	8	yes	complemented
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₅×#217	C₂²	1	4	yes	complemented
19	C₅×#938	C₂²	1	32	yes	complemented
20	C₅×#937	C₂²	1	32	yes	complemented
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
23	C₄×C₅×D₁₂	C₂²	1	16	yes	complemented
24	C₂×#5717	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂³×C₅×D₄	—	3	4	no	—
26	C₅×D₄²	—	3	16	no	—
27	C₂×C₅×#127	D₃	1	1	yes	characteristic, complemented
28	C₂×C₅×#121	—	3	4	no	—
29	C₂×C₅×#120	—	3	4	no	—
30	C₂×C₄×C₅×D₄	—	3	2	no	—
31	C₂⁴×C₃×C₅	C₂³	1	4	yes	—
32	C₂³×C₅×D₃	—	2	32	no	—
33	C₂³×C₅×D₃	—	4	8	no	—
34	C₂³×C₅×D₃	C₂³	1	4	yes	—
35	C₂³×C₅×D₃	C₂³	1	16	yes	complemented
36	C₂×C₃×C₅×D₄	—	2	16	no	—
37	C₂×C₃×C₅×D₄	—	4	4	no	—
38	C₂×C₃×C₅×D₄	C₂³	1	16	yes	complemented
39	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂×C₅×#67	—	2	32	no	—
43	C₂×C₅×#67	C₂³	1	32	yes	complemented
44	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
45	C₅×D₃×D₄	—	2	128	no	—
46	C₂×C₅×D₁₂	D₄	1	16	yes	complemented
47	C₂×C₅×D₁₂	C₂³	1	8	yes	—
48	C₂×C₄×C₅×D₃	—	2	16	no	—
49	C₂×C₄×C₅×D₃	C₂³	1	16	yes	complemented
50	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
51	C₅×#217	C₂³	1	16	yes	complemented
52	C₅×(C₂×D₃)⋊C₄	C₂³	1	16	yes	complemented
53	C₅×C₄⋊Dic₃	C₂³	1	8	yes	complemented
54	C₂²×D₃×D₄	C₂×C₅	1	4	yes	complemented
55	C₂×C₃×#127	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×#938	C₂×C₅	1	4	yes	complemented
57	C₂×#937	C₂×C₅	1	4	yes	complemented
58	#5717	C₂×C₅	1	16	yes	direct product factor
59	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	complemented
60	C₂⁵×C₅	—	3	4	no	—
61	C₂²×C₅×D₄	—	3	8	no	—
62	C₂²×C₅×D₄	—	3	32	no	—
63	C₂²×C₅×D₄	—	3	2	no	—
64	C₂²×C₅×D₄	—	6	32	no	—
65	C₂²×C₅×D₄	C₂×D₃	1	4	yes	complemented
66	C₂²×C₅×D₄	C₂×D₃	1	2	yes	complemented
67	C₂³×C₄×C₅	—	3	4	no	—
68	C₅×#127	C₂×D₃	1	8	yes	complemented
69	C₅×#121	—	3	32	no	—
70	C₅×#120	—	3	32	no	—
71	C₄×C₅×D₄	—	3	16	no	—
72	C₂×C₅×C₄⋊C₄	—	3	2	no	—
73	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
74	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
75	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
76	C₂×D₄²	—	3	1	no	Sylow
77	C₂³×C₃×C₅	—	2	16	no	—
78	C₂³×C₃×C₅	—	2	8	no	—
79	C₂³×C₃×C₅	C₂⁴	1	8	yes	—
80	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	8	no	—
82	C₂²×C₅×D₃	—	2	8	no	—
83	C₂²×C₅×D₃	—	2	64	no	—
84	C₂²×C₅×D₃	—	4	16	no	—
85	C₂²×C₅×D₃	—	4	64	no	—
86	C₂²×C₅×D₃	C₂×D₄	1	16	yes	complemented
87	C₂²×C₅×D₃	C₂⁴	1	8	yes	—
88	C₃×C₅×D₄	—	2	32	no	—
89	C₃×C₅×D₄	—	4	8	no	—
90	C₂×C₃×C₄×C₅	—	2	2	no	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	8	yes	complemented
92	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
94	C₅×#67	—	2	64	no	—
95	C₂×C₅×Dic₃	—	2	8	no	—
96	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
97	C₅×D₁₂	C₂×D₄	1	32	yes	complemented
98	C₄×C₅×D₃	—	2	32	no	—
99	C₂⁴×D₃	C₂²×C₅	1	4	yes	complemented
100	C₂²×C₃×D₄	C₂²×C₅	1	4	yes	complemented
101	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
102	C₂²×#67	C₂²×C₅	1	8	yes	complemented
103	C₂×D₃×D₄	—	2	32	no	—
104	C₂×D₃×D₄	C₂²×C₅	1	32	yes	complemented
105	C₂²×D₁₂	C₂²×C₅	1	2	yes	—
106	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	complemented
107	C₃×#127	C₂²×C₅	1	8	yes	complemented
108	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
109	C₂×#217	C₂²×C₅	1	4	yes	complemented
110	#938	C₂²×C₅	1	32	yes	complemented
111	#937	C₂²×C₅	1	32	yes	complemented
112	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	complemented
113	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
114	C₄×D₁₂	C₂²×C₅	1	16	yes	complemented
115	C₂⁴×C₅	—	3	4	no	—
116	C₂⁴×C₅	—	3	16	no	—
117	C₂⁴×C₅	—	6	32	no	—
118	C₂⁴×C₅	—	12	8	no	—
119	C₂⁴×C₅	C₂²×D₃	1	4	yes	—
120	C₂×C₅×D₄	—	2	16	no	—
121	C₂×C₅×D₄	—	3	32	no	—
122	C₂×C₅×D₄	—	3	16	no	—
123	C₂×C₅×D₄	—	3	8	no	—
124	C₂×C₅×D₄	—	4	4	no	—
125	C₂×C₅×D₄	—	6	128	no	—
126	C₂×C₅×D₄	—	6	32	no	—
127	C₂×C₅×D₄	C₂²×D₃	1	16	yes	complemented
128	C₂×C₅×D₄	C₂²×D₃	1	8	yes	complemented
129	C₂²×C₄×C₅	—	3	4	no	—
130	C₂²×C₄×C₅	—	3	16	no	—
131	C₂²×C₄×C₅	—	6	16	no	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
134	C₅×C₄⋊C₄	—	3	8	no	—
135	C₅×C₂²⋊C₄	—	3	16	no	—
136	C₅×C₂²⋊C₄	—	3	16	no	—
137	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
138	C₂³×D₄	—	3	4	no	—
139	D₄²	—	3	16	no	—
140	C₂×#127	C₅×D₃	1	1	yes	characteristic, complemented
141	C₂×#121	—	3	4	no	—
142	C₂×#120	—	3	4	no	—
143	C₂×C₄×D₄	—	3	2	no	—
144	C₂²×C₃×C₅	—	2	16	no	—
145	C₂²×C₃×C₅	—	2	8	no	—
146	C₂²×C₃×C₅	—	4	16	no	—
147	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
148	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
149	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
150	C₂×C₅×D₃	—	2	32	no	—
151	C₂×C₅×D₃	—	2	8	no	—
152	C₂×C₅×D₃	—	2	8	no	—
153	C₂×C₅×D₃	—	4	64	no	—
154	C₂×C₅×D₃	C₂²×D₄	1	16	yes	complemented
155	C₃×C₄×C₅	—	2	2	no	—
156	C₃×C₄×C₅	C₂²×D₄	1	8	yes	complemented
157	C₅×Dic₃	—	2	8	no	—
158	C₂⁴×C₃	C₂³×C₅	1	4	yes	—
159	C₂³×D₃	—	2	32	no	—
160	C₂³×D₃	—	4	8	no	—
161	C₂³×D₃	C₂³×C₅	1	4	yes	—
162	C₂³×D₃	C₂³×C₅	1	16	yes	complemented
163	C₂×C₃×D₄	—	2	16	no	—
164	C₂×C₃×D₄	—	4	4	no	—
165	C₂×C₃×D₄	C₂³×C₅	1	16	yes	complemented
166	C₂×C₃×D₄	C₂³×C₅	1	8	yes	complemented
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
169	C₂×#67	—	2	32	no	—
170	C₂×#67	C₂³×C₅	1	32	yes	complemented
171	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
172	D₃×D₄	—	2	128	no	—
173	C₂×D₁₂	C₅×D₄	1	16	yes	complemented
174	C₂×D₁₂	C₂³×C₅	1	8	yes	—
175	C₂×C₄×D₃	—	2	16	no	—
176	C₂×C₄×D₃	C₂³×C₅	1	16	yes	complemented
177	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
178	#217	C₂³×C₅	1	16	yes	complemented
179	(C₂×D₃)⋊C₄	C₂³×C₅	1	16	yes	complemented
180	C₄⋊Dic₃	C₂³×C₅	1	8	yes	complemented
181	C₂³×C₅	—	2	16	no	—
182	C₂³×C₅	—	2	8	no	—
183	C₂³×C₅	—	3	16	no	—
184	C₂³×C₅	—	3	8	no	—
185	C₂³×C₅	—	6	64	no	—
186	C₂³×C₅	—	6	8	no	—
187	C₂³×C₅	—	6	8	no	—
188	C₂³×C₅	—	12	16	no	—
189	C₂³×C₅	—	12	64	no	—
190	C₂³×C₅	C₂³×D₃	1	8	yes	—
191	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
192	C₅×D₄	—	2	32	no	—
193	C₅×D₄	—	3	32	no	—
194	C₅×D₄	—	4	8	no	—
195	C₅×D₄	—	6	64	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	3	8	no	—
198	C₂×C₄×C₅	—	6	8	no	—
199	C₂×C₄×C₅	—	6	32	no	—
200	C₂×C₄×C₅	D₃×D₄	1	8	yes	complemented
201	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
202	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
203	C₂⁵	—	3	4	no	—
204	C₂²×D₄	—	3	8	no	—
205	C₂²×D₄	—	3	32	no	—
206	C₂²×D₄	—	3	2	no	—
207	C₂²×D₄	—	6	32	no	—
208	C₂²×D₄	C₂×C₅×D₃	1	4	yes	complemented
209	C₂²×D₄	C₂×C₅×D₃	1	2	yes	complemented
210	C₂³×C₄	—	3	4	no	—
211	#127	C₂×C₅×D₃	1	8	yes	complemented
212	#121	—	3	32	no	—
213	#120	—	3	32	no	—
214	C₄×D₄	—	3	16	no	—
215	C₂×C₄⋊C₄	—	3	2	no	—
216	C₂×C₂²⋊C₄	—	3	4	no	—
217	C₂×C₂²⋊C₄	—	3	4	no	—
218	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
219	C₂×C₃×C₅	—	4	8	no	—
220	C₂×C₃×C₅	D₄²	1	4	yes	complemented
221	C₂×C₃×C₅	C₂³×D₄	1	2	yes	—
222	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
223	C₅×D₃	—	2	16	no	—
224	C₂³×C₃	—	2	16	no	—
225	C₂³×C₃	—	2	8	no	—
226	C₂³×C₃	C₂⁴×C₅	1	8	yes	—
227	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
228	C₂²×D₃	—	2	8	no	—
229	C₂²×D₃	—	2	8	no	—
230	C₂²×D₃	—	2	64	no	—
231	C₂²×D₃	—	4	16	no	—
232	C₂²×D₃	—	4	64	no	—
233	C₂²×D₃	C₂×C₅×D₄	1	16	yes	complemented
234	C₂²×D₃	C₂⁴×C₅	1	8	yes	—
235	C₃×D₄	—	2	32	no	—
236	C₃×D₄	—	4	8	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	complemented
239	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
240	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
241	#67	—	2	64	no	—
242	C₂×Dic₃	—	2	8	no	—
243	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
244	D₁₂	C₂×C₅×D₄	1	32	yes	complemented
245	C₄×D₃	—	2	32	no	—
246	C₂²×C₅	—	2	16	no	—
247	C₂²×C₅	—	2	8	no	—
248	C₂²×C₅	—	3	16	no	—
249	C₂²×C₅	—	4	16	no	—
250	C₂²×C₅	—	6	8	no	—
251	C₂²×C₅	—	6	8	no	—
252	C₂²×C₅	—	6	32	no	—
253	C₂²×C₅	—	12	64	no	—
254	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
255	C₂²×C₅	#1004	1	2	yes	—
256	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	6	8	no	—
259	C₄×C₅	C₂×D₃×D₄	1	8	yes	complemented
260	C₂⁴	—	3	4	no	—
261	C₂⁴	—	3	16	no	—
262	C₂⁴	—	6	32	no	—
263	C₂⁴	—	12	8	no	—
264	C₂⁴	C₂²×C₅×D₃	1	4	yes	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	3	32	no	—
267	C₂×D₄	—	3	16	no	—
268	C₂×D₄	—	3	8	no	—
269	C₂×D₄	—	4	4	no	—
270	C₂×D₄	—	6	128	no	—
271	C₂×D₄	—	6	32	no	—
272	C₂×D₄	C₂²×C₅×D₃	1	16	yes	complemented
273	C₂×D₄	C₂²×C₅×D₃	1	8	yes	complemented
274	C₂²×C₄	—	3	4	no	—
275	C₂²×C₄	—	3	16	no	—
276	C₂²×C₄	—	6	16	no	—
277	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
279	C₄⋊C₄	—	3	8	no	—
280	C₂²⋊C₄	—	3	16	no	—
281	C₂²⋊C₄	—	3	16	no	—
282	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
283	C₃×C₅	C₂×D₄²	1	1	yes	characteristic, complemented, Hall
284	C₂²×C₃	—	2	16	no	—
285	C₂²×C₃	—	2	8	no	—
286	C₂²×C₃	—	4	16	no	—
287	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
288	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
289	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
290	C₂×D₃	—	2	32	no	—
291	C₂×D₃	—	2	8	no	—
292	C₂×D₃	—	2	8	no	—
293	C₂×D₃	—	4	64	no	—
294	C₂×D₃	C₂²×C₅×D₄	1	16	yes	complemented
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	C₂²×C₅×D₄	1	8	yes	complemented
297	Dic₃	—	2	8	no	—
298	C₂×C₅	—	4	8	no	—
299	C₂×C₅	—	6	16	no	—
300	C₂×C₅	#5717	1	4	yes	direct product factor
301	C₂×C₅	C₂²×D₃×D₄	1	2	yes	—
302	C₂×C₅	C₂×#1004	1	1	yes	characteristic
303	C₂³	—	2	16	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	3	16	no	—
306	C₂³	—	3	8	no	—
307	C₂³	—	6	64	no	—
308	C₂³	—	6	8	no	—
309	C₂³	—	6	8	no	—
310	C₂³	—	12	16	no	—
311	C₂³	—	12	64	no	—
312	C₂³	C₂³×C₅×D₃	1	8	yes	—
313	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
314	D₄	—	2	32	no	—
315	D₄	—	3	32	no	—
316	D₄	—	4	8	no	—
317	D₄	—	6	64	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	3	8	no	—
320	C₂×C₄	—	6	8	no	—
321	C₂×C₄	—	6	32	no	—
322	C₂×C₄	C₅×D₃×D₄	1	8	yes	complemented
323	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
324	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
325	C₂×C₃	—	4	8	no	—
326	C₂×C₃	C₅×D₄²	1	4	yes	complemented
327	C₂×C₃	C₂³×C₅×D₄	1	2	yes	—
328	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
329	D₃	—	2	16	no	—
330	C₅	C₂×#5717	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²	—	2	16	no	—
332	C₂²	—	2	8	no	—
333	C₂²	—	3	16	no	—
334	C₂²	—	4	16	no	—
335	C₂²	—	6	8	no	—
336	C₂²	—	6	8	no	—
337	C₂²	—	6	32	no	—
338	C₂²	—	12	64	no	—
339	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
340	C₂²	C₅×#1004	1	2	yes	—
341	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	6	8	no	—
344	C₄	C₂×C₅×D₃×D₄	1	8	yes	complemented
345	C₃	C₂×C₅×D₄²	1	1	yes	characteristic, complemented, Sylow
346	C₂	—	4	8	no	—
347	C₂	—	6	16	no	—
348	C₂	C₅×#5717	1	4	yes	direct product factor
349	C₂	C₂²×C₅×D₃×D₄	1	2	yes	—
350	C₂	C₂×C₅×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#127	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#127	D₃
hypocenter	C₃	C₂×C₅×D₄²
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#127

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃×D₄	C₂	semidirect
2. C₂×C₃×C₅×#127	C₂	semidirect
3. C₂×C₅×#938	C₂	semidirect
4. C₂×C₅×#937	C₂	semidirect
5. C₅×#5717	C₂	direct (N × H)
6. C₂×C₄×C₅×D₁₂	C₂	semidirect
8. C₂⁴×C₅×D₃	C₂²	semidirect
9. C₂²×C₃×C₅×D₄	C₂²	semidirect
10. C₂²×C₃×C₅×D₄	C₂²	semidirect
11. C₂²×C₅×#67	C₂²	semidirect
13. C₂×C₅×D₃×D₄	C₂²	semidirect
15. C₂²×C₄×C₅×D₃	C₂²	semidirect
16. C₃×C₅×#127	C₂²	semidirect
17. C₂×C₃×C₄²×C₅	C₂²	semidirect
18. C₂×C₅×#217	C₂²	semidirect
19. C₅×#938	C₂²	semidirect
20. C₅×#937	C₂²	semidirect
21. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
22. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
23. C₄×C₅×D₁₂	C₂²	semidirect
24. C₂×#5717	C₅	direct (N × H)
27. C₂×C₅×#127	D₃	semidirect
35. C₂³×C₅×D₃	C₂³	semidirect
38. C₂×C₃×C₅×D₄	C₂³	semidirect
39. C₂×C₃×C₅×D₄	C₂³	semidirect
43. C₂×C₅×#67	C₂³	semidirect
46. C₂×C₅×D₁₂	D₄	semidirect
49. C₂×C₄×C₅×D₃	C₂³	semidirect
50. C₃×C₄²×C₅	C₂³	semidirect
51. C₅×#217	C₂³	semidirect
52. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
53. C₅×C₄⋊Dic₃	C₂³	semidirect
54. C₂²×D₃×D₄	C₂×C₅	semidirect
55. C₂×C₃×#127	C₂×C₅	semidirect
56. C₂×#938	C₂×C₅	semidirect
57. C₂×#937	C₂×C₅	semidirect
58. #5717	C₂×C₅	direct (N × H)
59. C₂×C₄×D₁₂	C₂×C₅	semidirect
65. C₂²×C₅×D₄	C₂×D₃	semidirect
66. C₂²×C₅×D₄	C₂×D₃	semidirect
68. C₅×#127	C₂×D₃	semidirect
75. C₂×C₄²×C₅	C₂×D₃	semidirect
86. C₂²×C₅×D₃	C₂×D₄	semidirect
91. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
97. C₅×D₁₂	C₂×D₄	semidirect
99. C₂⁴×D₃	C₂²×C₅	semidirect
100. C₂²×C₃×D₄	C₂²×C₅	semidirect
101. C₂²×C₃×D₄	C₂²×C₅	semidirect
102. C₂²×#67	C₂²×C₅	semidirect
104. C₂×D₃×D₄	C₂²×C₅	semidirect
106. C₂²×C₄×D₃	C₂²×C₅	semidirect
107. C₃×#127	C₂²×C₅	semidirect
108. C₂×C₃×C₄²	C₂²×C₅	semidirect
109. C₂×#217	C₂²×C₅	semidirect
110. #938	C₂²×C₅	semidirect
111. #937	C₂²×C₅	semidirect
112. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
113. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
114. C₄×D₁₂	C₂²×C₅	semidirect
127. C₂×C₅×D₄	C₂²×D₃	semidirect
128. C₂×C₅×D₄	C₂²×D₃	semidirect
137. C₄²×C₅	C₂²×D₃	semidirect
140. C₂×#127	C₅×D₃	semidirect
154. C₂×C₅×D₃	C₂²×D₄	semidirect
156. C₃×C₄×C₅	C₂²×D₄	semidirect
162. C₂³×D₃	C₂³×C₅	semidirect
165. C₂×C₃×D₄	C₂³×C₅	semidirect
166. C₂×C₃×D₄	C₂³×C₅	semidirect
170. C₂×#67	C₂³×C₅	semidirect
173. C₂×D₁₂	C₅×D₄	semidirect
176. C₂×C₄×D₃	C₂³×C₅	semidirect
177. C₃×C₄²	C₂³×C₅	semidirect
178. #217	C₂³×C₅	semidirect
179. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
180. C₄⋊Dic₃	C₂³×C₅	semidirect
200. C₂×C₄×C₅	D₃×D₄	semidirect
208. C₂²×D₄	C₂×C₅×D₃	semidirect
209. C₂²×D₄	C₂×C₅×D₃	semidirect
211. #127	C₂×C₅×D₃	semidirect
218. C₂×C₄²	C₂×C₅×D₃	semidirect
220. C₂×C₃×C₅	D₄²	semidirect
233. C₂²×D₃	C₂×C₅×D₄	semidirect
238. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
244. D₁₂	C₂×C₅×D₄	semidirect
259. C₄×C₅	C₂×D₃×D₄	semidirect
272. C₂×D₄	C₂²×C₅×D₃	semidirect
273. C₂×D₄	C₂²×C₅×D₃	semidirect
282. C₄²	C₂²×C₅×D₃	semidirect
283. C₃×C₅	C₂×D₄²	semidirect
294. C₂×D₃	C₂²×C₅×D₄	semidirect
296. C₃×C₄	C₂²×C₅×D₄	semidirect
300. C₂×C₅	#5717	direct (N × H)
322. C₂×C₄	C₅×D₃×D₄	semidirect
326. C₂×C₃	C₅×D₄²	semidirect
330. C₅	C₂×#5717	direct (N × H)
344. C₄	C₂×C₅×D₃×D₄	semidirect
345. C₃	C₂×C₅×D₄²	semidirect
348. C₂	C₅×#5717	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×D₃×D₄	2
C₂×C₃×C₅×#127	2
C₂×C₅×#938	2
C₂×C₅×#937	2
C₅×#5717	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×D₄²	3
C₂×#5717	5

Subgroups — C2×C5×#5717 #14482412

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5717 #14482412