Subgroups — C₂×C₅×#5159 #14427975

Order 1920.

1192 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#938	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#832	C₂	1	2	yes	maximal, complemented
5	C₅×#5159	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#817	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#469	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
9	C₂²×C₅×#67	—	2	2	no	—
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×D₈	—	2	4	no	—
12	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
13	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₅×#217	—	2	2	no	—
15	C₅×#938	—	2	4	no	—
16	C₅×#938	C₂²	1	8	yes	complemented
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	complemented
21	C₅×#832	C₂²	1	8	yes	complemented
22	C₅×#817	C₂²	1	4	yes	complemented
23	C₂×#5159	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂²×C₅×D₈	D₃	1	1	yes	characteristic, complemented
25	C₂²×C₅×M₁₆	—	3	1	no	—
26	C₂×C₅×#121	—	3	2	no	—
27	C₅×#469	—	3	8	no	—
28	C₂×C₅×#106	—	3	1	no	—
29	C₂×C₅×#102	—	3	2	no	—
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
32	C₂×C₃×C₅×D₄	—	2	4	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	4	no	—
35	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	—	2	8	no	—
38	C₂×C₅×#67	—	4	8	no	—
39	C₂²×C₅×Dic₃	—	2	2	no	—
40	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	2	no	—
42	C₂×C₄×C₅×D₃	—	2	2	no	—
43	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
44	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
45	C₃×C₅×D₈	—	2	8	no	—
46	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₅×#217	—	2	8	no	—
49	C₅×C₄⋊Dic₃	—	2	2	no	—
50	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
53	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
54	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
55	C₂×#938	C₂×C₅	1	2	yes	complemented
56	C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	1	1	yes	characteristic, complemented
57	C₂×#832	C₂×C₅	1	2	yes	complemented
58	#5159	C₂×C₅	1	8	yes	direct product factor
59	C₂×#817	C₂×C₅	1	1	yes	characteristic, complemented
60	C₂²×C₅×D₄	—	6	2	no	—
61	C₂²×C₅×D₄	C₂×D₃	1	2	yes	—
62	C₂³×C₄×C₅	—	3	1	no	—
63	C₂×C₅×D₈	—	2	4	no	—
64	C₂×C₅×D₈	C₂×D₃	1	4	yes	complemented
65	C₂×C₅×M₁₆	—	3	4	no	—
66	C₂×C₅×M₁₆	—	6	4	no	—
67	C₂²×C₅×C₈	—	3	1	no	—
68	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
69	C₅×#121	—	3	8	no	—
70	C₅×#121	—	6	4	no	—
71	C₂×C₅×C₄⋊C₄	—	3	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
73	C₅×#106	—	3	4	no	—
74	C₅×#102	—	3	8	no	—
75	C₂×#469	—	3	1	no	Sylow
76	C₂³×C₃×C₅	—	2	4	no	—
77	C₂³×C₃×C₅	—	4	4	no	—
78	C₂³×C₃×C₅	—	4	4	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₅×D₃	—	2	2	no	—
82	C₂²×C₅×D₃	—	2	4	no	—
83	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
84	C₃×C₅×D₄	—	2	4	no	—
85	C₃×C₅×D₄	—	2	4	no	—
86	C₃×C₅×D₄	—	4	4	no	—
87	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
91	C₅×#67	—	4	16	no	—
92	C₂×C₅×Dic₃	—	2	2	no	—
93	C₂×C₅×Dic₃	—	2	4	no	—
94	C₂×C₅×Dic₃	—	4	4	no	—
95	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
96	C₄×C₅×D₃	—	2	4	no	—
97	C₄×C₅×D₃	—	2	2	no	—
98	C₄×C₅×D₃	—	2	2	no	—
99	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
100	C₅×C₃⋊C₈	—	2	2	no	—
101	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
102	C₂²×#67	—	2	2	no	—
103	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×D₈	—	2	4	no	—
105	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
106	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
107	C₂×#217	—	2	2	no	—
108	#938	—	2	4	no	—
109	#938	C₂²×C₅	1	8	yes	complemented
110	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
111	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
112	C₂×ΓL(1,𝔽₂₅)	—	2	4	no	—
113	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	4	yes	complemented
114	#832	C₂²×C₅	1	8	yes	complemented
115	#817	C₂²×C₅	1	4	yes	complemented
116	C₂⁴×C₅	—	2	2	no	—
117	C₂⁴×C₅	—	3	1	no	—
118	C₂×C₅×D₄	—	2	2	no	—
119	C₂×C₅×D₄	—	2	4	no	—
120	C₂×C₅×D₄	—	2	4	no	—
121	C₂×C₅×D₄	—	6	8	no	—
122	C₂×C₅×D₄	—	12	8	no	—
123	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
124	C₂²×C₄×C₅	—	3	1	no	—
125	C₂²×C₄×C₅	—	3	2	no	—
126	C₂²×C₄×C₅	—	3	2	no	—
127	C₂²×C₄×C₅	—	6	2	no	—
128	C₂²×C₄×C₅	—	6	2	no	—
129	C₂²×C₄×C₅	—	6	2	no	—
130	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
131	C₅×D₈	—	2	8	no	—
132	C₅×M₁₆	—	6	8	no	—
133	C₂×C₅×C₈	—	3	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₂×C₅×C₈	#67	1	4	yes	complemented
136	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
137	C₅×C₄⋊C₄	—	3	4	no	—
138	C₅×C₄⋊C₄	—	6	2	no	—
139	C₅×C₂²⋊C₄	—	6	8	no	—
140	C₂²×D₈	C₅×D₃	1	1	yes	characteristic, complemented
141	C₂²×M₁₆	—	3	1	no	—
142	C₂×#121	—	3	2	no	—
143	#469	—	3	8	no	—
144	C₂×#106	—	3	1	no	—
145	C₂×#102	—	3	2	no	—
146	C₂²×C₃×C₅	—	4	4	no	—
147	C₂²×C₃×C₅	—	4	4	no	—
148	C₂²×C₃×C₅	—	4	4	no	—
149	C₂²×C₃×C₅	—	8	8	no	—
150	C₂²×C₃×C₅	#121	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	—	2	2	no	—
154	C₂×C₅×D₃	—	2	4	no	—
155	C₂×C₅×D₃	—	4	4	no	—
156	C₃×C₄×C₅	#121	1	2	yes	—
157	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
158	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
159	C₅×Dic₃	—	2	2	no	—
160	C₅×Dic₃	—	4	4	no	—
161	C₂⁴×C₃	—	2	2	no	—
162	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
163	C₂×C₃×D₄	—	2	4	no	—
164	C₂×C₃×D₄	—	2	2	no	—
165	C₂×C₃×D₄	—	2	4	no	—
166	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
168	C₂×#67	—	2	8	no	—
169	C₂×#67	—	4	8	no	—
170	C₂²×Dic₃	—	2	2	no	—
171	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
172	C₂×C₄×D₃	—	2	2	no	—
173	C₂×C₄×D₃	—	2	2	no	—
174	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
175	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
176	C₃×D₈	—	2	8	no	—
177	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
178	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
179	#217	—	2	8	no	—
180	C₄⋊Dic₃	—	2	2	no	—
181	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
182	C₂×C₃⋊C₈	—	2	2	no	—
183	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
184	ΓL(1,𝔽₂₅)	—	2	8	no	—
185	C₂³×C₅	—	2	4	no	—
186	C₂³×C₅	—	3	2	no	—
187	C₂³×C₅	—	4	4	no	—
188	C₂³×C₅	—	4	4	no	—
189	C₂³×C₅	—	4	4	no	—
190	C₂³×C₅	—	6	4	no	—
191	C₂³×C₅	—	6	2	no	—
192	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
193	C₅×D₄	—	2	4	no	—
194	C₅×D₄	—	2	4	no	—
195	C₅×D₄	—	4	4	no	—
196	C₅×D₄	—	12	16	no	—
197	C₂×C₄×C₅	—	3	2	no	—
198	C₂×C₄×C₅	—	6	2	no	—
199	C₂×C₄×C₅	—	6	4	no	—
200	C₂×C₄×C₅	—	6	2	no	—
201	C₂×C₄×C₅	—	6	2	no	—
202	C₂×C₄×C₅	—	6	4	no	—
203	C₂×C₄×C₅	—	12	4	no	—
204	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	#237	1	2	yes	—
206	C₂×C₄×C₅	C₂×#67	1	2	yes	—
207	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
208	C₅×C₈	—	6	2	no	—
209	C₅×C₈	C₂×#67	1	4	yes	complemented
210	C₂²×D₄	—	6	2	no	—
211	C₂²×D₄	C₂×C₅×D₃	1	2	yes	—
212	C₂³×C₄	—	3	1	no	—
213	C₂×D₈	—	2	4	no	—
214	C₂×D₈	C₂×C₅×D₃	1	4	yes	complemented
215	C₂×M₁₆	—	3	4	no	—
216	C₂×M₁₆	—	6	4	no	—
217	C₂²×C₈	—	3	1	no	—
218	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
219	#121	—	3	8	no	—
220	#121	—	6	4	no	—
221	C₂×C₄⋊C₄	—	3	2	no	—
222	C₂×C₂²⋊C₄	—	6	2	no	—
223	#106	—	3	4	no	—
224	#102	—	3	8	no	—
225	C₂×C₃×C₅	—	8	4	no	—
226	C₂×C₃×C₅	#469	1	4	yes	complemented
227	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
228	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
229	C₅×D₃	—	4	2	no	—
230	C₂³×C₃	—	2	4	no	—
231	C₂³×C₃	—	4	4	no	—
232	C₂³×C₃	—	4	4	no	—
233	C₂³×C₃	—	4	4	no	—
234	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
235	C₂²×D₃	—	2	2	no	—
236	C₂²×D₃	—	2	4	no	—
237	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
238	C₃×D₄	—	2	4	no	—
239	C₃×D₄	—	2	4	no	—
240	C₃×D₄	—	4	4	no	—
241	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
243	C₂×C₃×C₄	C₅×#41	1	2	yes	—
244	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
245	#67	—	4	16	no	—
246	C₂×Dic₃	—	2	2	no	—
247	C₂×Dic₃	—	2	4	no	—
248	C₂×Dic₃	—	4	4	no	—
249	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
250	C₄×D₃	—	2	4	no	—
251	C₄×D₃	—	2	2	no	—
252	C₄×D₃	—	2	2	no	—
253	C₃×C₈	C₂×C₅×D₄	1	4	yes	complemented
254	C₃⋊C₈	—	2	2	no	—
255	C₂²×C₅	—	4	4	no	—
256	C₂²×C₅	—	4	4	no	—
257	C₂²×C₅	—	4	4	no	—
258	C₂²×C₅	—	6	4	no	—
259	C₂²×C₅	—	6	2	no	—
260	C₂²×C₅	—	8	8	no	—
261	C₂²×C₅	—	12	4	no	—
262	C₂²×C₅	#911	1	4	yes	—
263	C₂²×C₅	#938	1	2	yes	—
264	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
265	C₄×C₅	—	6	2	no	—
266	C₄×C₅	—	12	4	no	—
267	C₄×C₅	#938	1	2	yes	—
268	C₄×C₅	C₂×#237	1	1	yes	characteristic
269	C₄×C₅	C₂²×#67	1	1	yes	characteristic
270	C₂⁴	—	2	2	no	—
271	C₂⁴	—	3	1	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	6	8	no	—
276	C₂×D₄	—	12	8	no	—
277	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
278	C₂²×C₄	—	3	1	no	—
279	C₂²×C₄	—	3	2	no	—
280	C₂²×C₄	—	3	2	no	—
281	C₂²×C₄	—	6	2	no	—
282	C₂²×C₄	—	6	2	no	—
283	C₂²×C₄	—	6	2	no	—
284	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
285	D₈	—	2	8	no	—
286	M₁₆	—	6	8	no	—
287	C₂×C₈	—	3	2	no	—
288	C₂×C₈	—	6	2	no	—
289	C₂×C₈	C₅×#67	1	4	yes	complemented
290	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
291	C₄⋊C₄	—	3	4	no	—
292	C₄⋊C₄	—	6	2	no	—
293	C₂²⋊C₄	—	6	8	no	—
294	C₃×C₅	C₂×#469	1	1	yes	characteristic, complemented, Hall
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	—	4	4	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	—	8	8	no	—
299	C₂²×C₃	C₅×#121	1	2	yes	—
300	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
301	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
302	C₂×D₃	—	2	2	no	—
303	C₂×D₃	—	2	4	no	—
304	C₂×D₃	—	4	4	no	—
305	C₃×C₄	C₅×#121	1	2	yes	—
306	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
307	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
308	Dic₃	—	2	2	no	—
309	Dic₃	—	4	4	no	—
310	C₂×C₅	—	8	4	no	—
311	C₂×C₅	—	12	2	no	—
312	C₂×C₅	#5159	1	4	yes	direct product factor
313	C₂×C₅	C₂×#911	1	2	yes	—
314	C₂×C₅	C₂×#938	1	1	yes	characteristic
315	C₂³	—	2	4	no	—
316	C₂³	—	3	2	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	6	4	no	—
321	C₂³	—	6	2	no	—
322	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	4	no	—
326	D₄	—	12	16	no	—
327	C₂×C₄	—	3	2	no	—
328	C₂×C₄	—	6	2	no	—
329	C₂×C₄	—	6	4	no	—
330	C₂×C₄	—	6	2	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	6	4	no	—
333	C₂×C₄	—	12	4	no	—
334	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
335	C₂×C₄	C₅×#237	1	2	yes	—
336	C₂×C₄	C₂×C₅×#67	1	2	yes	—
337	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
338	C₈	—	6	2	no	—
339	C₈	C₂×C₅×#67	1	4	yes	complemented
340	C₂×C₃	—	8	4	no	—
341	C₂×C₃	C₅×#469	1	4	yes	complemented
342	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
343	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
344	D₃	—	4	2	no	—
345	C₅	C₂×#5159	1	1	yes	characteristic, direct product factor, Sylow
346	C₂²	—	4	4	no	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	6	4	no	—
350	C₂²	—	6	2	no	—
351	C₂²	—	8	8	no	—
352	C₂²	—	12	4	no	—
353	C₂²	C₅×#911	1	4	yes	—
354	C₂²	C₅×#938	1	2	yes	—
355	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
356	C₄	—	6	2	no	—
357	C₄	—	12	4	no	—
358	C₄	C₅×#938	1	2	yes	—
359	C₄	C₂×C₅×#237	1	1	yes	characteristic
360	C₄	C₂²×C₅×#67	1	1	yes	characteristic
361	C₃	C₂×C₅×#469	1	1	yes	characteristic, complemented, Sylow
362	C₂	—	8	4	no	—
363	C₂	—	12	2	no	—
364	C₂	C₅×#5159	1	4	yes	direct product factor
365	C₂	C₂×C₅×#911	1	2	yes	—
366	C₂	C₂×C₅×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×D₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂²×C₅×D₈	D₃
hypocenter	C₃	C₂×C₅×#469
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×D₈	C₂	semidirect
2. C₂×C₅×#938	C₂	semidirect
3. C₂²×C₅×ΓL(1,𝔽₂₅)	C₂	semidirect
4. C₂×C₅×#832	C₂	semidirect
5. C₅×#5159	C₂	direct (N × H)
6. C₂×C₅×#817	C₂	semidirect
12. C₂×C₃×C₅×D₈	C₂²	semidirect
16. C₅×#938	C₂²	semidirect
20. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
21. C₅×#832	C₂²	semidirect
22. C₅×#817	C₂²	semidirect
23. C₂×#5159	C₅	direct (N × H)
24. C₂²×C₅×D₈	D₃	semidirect
46. C₂×C₃×C₅×C₈	D₄	semidirect
54. C₂²×C₃×D₈	C₂×C₅	semidirect
55. C₂×#938	C₂×C₅	semidirect
56. C₂²×ΓL(1,𝔽₂₅)	C₂×C₅	semidirect
57. C₂×#832	C₂×C₅	semidirect
58. #5159	C₂×C₅	direct (N × H)
59. C₂×#817	C₂×C₅	semidirect
64. C₂×C₅×D₈	C₂×D₃	semidirect
99. C₃×C₅×C₈	C₂×D₄	semidirect
105. C₂×C₃×D₈	C₂²×C₅	semidirect
109. #938	C₂²×C₅	semidirect
113. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
114. #832	C₂²×C₅	semidirect
115. #817	C₂²×C₅	semidirect
135. C₂×C₅×C₈	#67	semidirect
140. C₂²×D₈	C₅×D₃	semidirect
177. C₂×C₃×C₈	C₅×D₄	semidirect
209. C₅×C₈	C₂×#67	semidirect
214. C₂×D₈	C₂×C₅×D₃	semidirect
226. C₂×C₃×C₅	#469	semidirect
253. C₃×C₈	C₂×C₅×D₄	semidirect
289. C₂×C₈	C₅×#67	semidirect
294. C₃×C₅	C₂×#469	semidirect
312. C₂×C₅	#5159	direct (N × H)
339. C₈	C₂×C₅×#67	semidirect
341. C₂×C₃	C₅×#469	semidirect
345. C₅	C₂×#5159	direct (N × H)
361. C₃	C₂×C₅×#469	semidirect
364. C₂	C₅×#5159	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×C₃×C₅×D₈	2
C₂×C₅×#938	2
C₂²×C₅×ΓL(1,𝔽₂₅)	2
C₂×C₅×#832	2
C₅×#5159	2
C₂×C₅×#817	2
C₂×C₅×#469	3
C₂×#5159	5

Subgroups — C2×C5×#5159 #14427975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5159 #14427975