Subgroups — C₂×C₅×#4717 #14417931

Order 1920.

928 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	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#901	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#805	C₂	1	2	yes	maximal, complemented
6	C₅×#4717	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#444	—	3	1	no	maximal, Hall
8	C₂×C₅×#235	C₂²	1	2	yes	—
9	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×#208	C₂²	1	2	yes	—
13	C₂×C₅×Dic₁₂	C₄	1	1	yes	characteristic, complemented
14	C₅×#904	C₄	1	4	yes	complemented
15	C₅×#904	C₂²	1	4	yes	—
16	C₂×C₅×D₂₄	C₄	1	1	yes	characteristic, complemented
17	C₂×C₅×#204	C₄	1	2	yes	complemented
18	C₅×#901	—	2	4	no	—
19	C₅×#901	C₂²	1	8	yes	complemented
20	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
21	C₂×C₅×D₃×C₈	—	2	2	no	—
22	C₃×C₅×#97	C₂²	1	4	yes	complemented
23	C₅×#819	C₂²	1	4	yes	complemented
24	C₅×#805	C₂²	1	8	yes	complemented
25	C₂×#4717	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×#135	—	3	1	no	—
27	C₂×C₅×#131	—	3	2	no	—
28	C₅×#444	—	3	8	no	—
29	C₂×C₅×#108	—	3	1	no	—
30	C₂×C₅×#104	—	3	2	no	—
31	C₂×C₅×#97	D₃	1	1	yes	characteristic, complemented
32	C₂²×C₃×C₄×C₅	—	2	1	no	—
33	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₅×#67	—	2	2	no	—
35	C₅×#235	—	2	2	no	—
36	C₅×#235	—	2	2	no	—
37	C₅×#235	C₂×C₄	1	4	yes	—
38	C₅×#235	C₂³	1	4	yes	—
39	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
40	C₂×C₄×C₅×D₃	—	2	2	no	—
41	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
46	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
47	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂³	1	2	yes	—
51	C₅×#208	—	2	2	no	—
52	C₅×#208	C₂³	1	4	yes	—
53	C₂×C₅×C₃⋊C₈	—	2	2	no	—
54	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
55	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
56	C₅×#204	C₂×C₄	1	8	yes	complemented
57	C₅×ΓL(1,𝔽₂₅)	—	2	8	no	—
58	C₅×D₃×C₈	—	2	8	no	—
59	C₂×#904	C₂×C₅	1	1	yes	characteristic
60	C₂×#901	C₂×C₅	1	2	yes	complemented
61	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×#819	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#805	C₂×C₅	1	2	yes	complemented
64	#4717	C₂×C₅	1	8	yes	direct product factor
65	C₂×C₅×#41	—	3	2	no	—
66	C₅×#135	—	3	4	no	—
67	C₅×#135	—	3	4	no	—
68	C₂×C₅×Q₁₆	—	3	1	no	—
69	C₂×C₅×SD₁₆	—	3	2	no	—
70	C₂×C₅×D₈	—	3	1	no	—
71	C₅×#131	—	3	8	no	—
72	C₅×#131	—	6	4	no	—
73	C₂×C₅×M₁₆	—	3	2	no	—
74	C₂×C₅×M₁₆	—	6	2	no	—
75	C₂²×C₅×C₈	—	6	2	no	—
76	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
79	C₅×#108	—	3	4	no	—
80	C₅×#104	—	3	8	no	—
81	C₅×#97	C₂×D₃	1	4	yes	complemented
82	C₂×#444	—	3	1	no	Sylow
83	C₂³×C₃×C₅	#41	1	1	yes	characteristic
84	C₂²×C₅×D₃	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	4	2	no	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
93	C₅×#67	—	2	4	no	—
94	C₅×#67	—	2	4	no	—
95	C₂×C₅×Dic₃	—	2	2	no	—
96	C₅×D₁₂	—	2	2	no	—
97	C₅×D₁₂	C₂²×C₄	1	4	yes	—
98	C₄×C₅×D₃	—	2	4	no	—
99	C₄×C₅×D₃	—	2	4	no	—
100	C₅×Dic₆	—	2	2	no	—
101	C₅×Dic₆	C₂²×C₄	1	4	yes	—
102	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
103	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
104	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
105	C₅×C₃⋊C₈	—	2	4	no	—
106	C₂×#235	C₂²×C₅	1	2	yes	—
107	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
108	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
110	C₂×#208	C₂²×C₅	1	2	yes	—
111	C₂×Dic₁₂	C₄×C₅	1	1	yes	characteristic, complemented
112	#904	C₄×C₅	1	4	yes	complemented
113	#904	C₂²×C₅	1	4	yes	—
114	C₂×D₂₄	C₄×C₅	1	1	yes	characteristic, complemented
115	C₂×#204	C₄×C₅	1	2	yes	complemented
116	#901	—	2	4	no	—
117	#901	C₂²×C₅	1	8	yes	complemented
118	C₂×ΓL(1,𝔽₂₅)	—	2	2	no	—
119	C₂×D₃×C₈	—	2	2	no	—
120	C₃×#97	C₂²×C₅	1	4	yes	complemented
121	#819	C₂²×C₅	1	4	yes	complemented
122	#805	C₂²×C₅	1	8	yes	complemented
123	C₅×#41	—	3	4	no	—
124	C₅×#41	—	3	4	no	—
125	C₅×#41	—	6	2	no	—
126	C₅×#41	—	6	2	no	—
127	C₂×C₅×Q₈	—	3	2	no	—
128	C₂×C₅×D₄	—	3	2	no	—
129	C₂×C₅×D₄	—	6	2	no	—
130	C₂²×C₄×C₅	—	2	1	no	—
131	C₂²×C₄×C₅	—	6	2	no	—
132	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
133	C₅×Q₁₆	—	3	4	no	—
134	C₅×SD₁₆	—	3	8	no	—
135	C₅×D₈	—	3	4	no	—
136	C₅×M₁₆	—	3	4	no	—
137	C₅×M₁₆	—	6	2	no	—
138	C₅×M₁₆	—	6	8	no	—
139	C₂×C₅×C₈	—	6	2	no	—
140	C₂×C₅×C₈	—	6	8	no	—
141	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
142	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
143	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
144	C₂×C₅×C₈	D₁₂	1	2	yes	—
145	C₂×C₅×C₈	D₁₂	1	2	yes	—
146	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
147	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
148	C₄²×C₅	—	2	1	no	—
149	C₄²×C₅	C₂²×D₃	1	2	yes	—
150	C₂×#135	—	3	1	no	—
151	C₂×#131	—	3	2	no	—
152	#444	—	3	8	no	—
153	C₂×#108	—	3	1	no	—
154	C₂×#104	—	3	2	no	—
155	C₂×#97	C₅×D₃	1	1	yes	characteristic, complemented
156	C₂²×C₃×C₅	—	2	2	no	—
157	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
160	C₂×C₅×D₃	—	2	4	no	—
161	C₂×C₅×D₃	—	4	4	no	—
162	C₃×C₄×C₅	—	4	2	no	—
163	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
164	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
165	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₅×Dic₃	—	2	4	no	—
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₂×#67	—	2	2	no	—
171	#235	—	2	2	no	—
172	#235	—	2	2	no	—
173	#235	C₂×C₄×C₅	1	4	yes	—
174	#235	C₂³×C₅	1	4	yes	—
175	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
176	C₂×C₄×D₃	—	2	2	no	—
177	C₂×Dic₆	C₂×C₄×C₅	1	2	yes	—
178	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂×C₄×C₅	1	1	yes	characteristic
180	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
181	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
182	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
183	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
184	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	C₂³×C₅	1	2	yes	—
187	#208	—	2	2	no	—
188	#208	C₂³×C₅	1	4	yes	—
189	C₂×C₃⋊C₈	—	2	2	no	—
190	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
191	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
192	#204	C₂×C₄×C₅	1	8	yes	complemented
193	ΓL(1,𝔽₂₅)	—	2	8	no	—
194	D₃×C₈	—	2	8	no	—
195	C₂³×C₅	—	6	2	no	—
196	C₂³×C₅	#235	1	1	yes	characteristic
197	C₅×Q₈	—	3	4	no	—
198	C₅×Q₈	—	6	2	no	—
199	C₅×D₄	—	3	4	no	—
200	C₅×D₄	—	6	4	no	—
201	C₅×D₄	—	6	4	no	—
202	C₅×D₄	—	6	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	6	2	no	—
206	C₂×C₄×C₅	—	6	4	no	—
207	C₂×C₄×C₅	—	6	4	no	—
208	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
212	C₂×C₄×C₅	#235	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
214	C₅×C₈	—	6	4	no	—
215	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
216	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
217	C₅×C₈	C₂×D₁₂	1	4	yes	—
218	C₂×#41	—	3	2	no	—
219	#135	—	3	4	no	—
220	#135	—	3	4	no	—
221	C₂×Q₁₆	—	3	1	no	—
222	C₂×SD₁₆	—	3	2	no	—
223	C₂×D₈	—	3	1	no	—
224	#131	—	3	8	no	—
225	#131	—	6	4	no	—
226	C₂×M₁₆	—	3	2	no	—
227	C₂×M₁₆	—	6	2	no	—
228	C₂²×C₈	—	6	2	no	—
229	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
230	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
232	#108	—	3	4	no	—
233	#104	—	3	8	no	—
234	#97	C₂×C₅×D₃	1	4	yes	complemented
235	C₂×C₃×C₅	—	2	1	no	—
236	C₂×C₃×C₅	—	2	1	no	—
237	C₂×C₃×C₅	#444	1	2	yes	complemented
238	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
239	C₅×D₃	—	4	4	no	—
240	C₂³×C₃	C₅×#41	1	1	yes	characteristic
241	C₂²×D₃	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	4	2	no	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
250	#67	—	2	4	no	—
251	#67	—	2	4	no	—
252	C₂×Dic₃	—	2	2	no	—
253	D₁₂	—	2	2	no	—
254	D₁₂	C₂²×C₄×C₅	1	4	yes	—
255	C₄×D₃	—	2	4	no	—
256	C₄×D₃	—	2	4	no	—
257	Dic₆	—	2	2	no	—
258	Dic₆	C₂²×C₄×C₅	1	4	yes	—
259	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
260	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
261	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
262	C₃⋊C₈	—	2	4	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	6	4	no	—
265	C₂²×C₅	—	12	4	no	—
266	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
267	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
268	C₂²×C₅	C₂×#235	1	1	yes	characteristic
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	6	4	no	—
271	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
272	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
273	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
274	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
275	#41	—	3	4	no	—
276	#41	—	3	4	no	—
277	#41	—	6	2	no	—
278	#41	—	6	2	no	—
279	C₂×Q₈	—	3	2	no	—
280	C₂×D₄	—	3	2	no	—
281	C₂×D₄	—	6	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	6	2	no	—
284	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
285	Q₁₆	—	3	4	no	—
286	SD₁₆	—	3	8	no	—
287	D₈	—	3	4	no	—
288	M₁₆	—	3	4	no	—
289	M₁₆	—	6	2	no	—
290	M₁₆	—	6	8	no	—
291	C₂×C₈	—	6	2	no	—
292	C₂×C₈	—	6	8	no	—
293	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
294	C₂×C₈	C₄×C₅×D₃	1	1	yes	characteristic
295	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
296	C₂×C₈	C₅×D₁₂	1	2	yes	—
297	C₂×C₈	C₅×D₁₂	1	2	yes	—
298	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
299	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
300	C₄²	—	2	1	no	—
301	C₄²	C₂²×C₅×D₃	1	2	yes	—
302	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
303	C₂²×C₃	—	2	2	no	—
304	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
307	C₂×D₃	—	2	4	no	—
308	C₂×D₃	—	4	4	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
311	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
312	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
313	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
314	Dic₃	—	2	4	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	2	1	no	—
317	C₂×C₅	—	12	4	no	—
318	C₂×C₅	#4717	1	2	yes	direct product factor
319	C₂×C₅	C₂×C₄×D₁₂	1	1	yes	characteristic
320	C₂³	—	6	2	no	—
321	C₂³	C₅×#235	1	1	yes	characteristic
322	Q₈	—	3	4	no	—
323	Q₈	—	6	2	no	—
324	D₄	—	3	4	no	—
325	D₄	—	6	4	no	—
326	D₄	—	6	4	no	—
327	D₄	—	6	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	6	2	no	—
331	C₂×C₄	—	6	4	no	—
332	C₂×C₄	—	6	4	no	—
333	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
335	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
336	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
337	C₂×C₄	C₅×#235	1	1	yes	characteristic
338	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
339	C₈	—	6	4	no	—
340	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
341	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
342	C₈	C₂×C₅×D₁₂	1	4	yes	—
343	C₂×C₃	—	2	1	no	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	C₅×#444	1	2	yes	complemented
346	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
347	D₃	—	4	4	no	—
348	C₅	C₂×#4717	1	1	yes	characteristic, direct product factor, Sylow
349	C₂²	—	2	2	no	—
350	C₂²	—	6	4	no	—
351	C₂²	—	12	4	no	—
352	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
353	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
354	C₂²	C₂×C₅×#235	1	1	yes	characteristic
355	C₄	—	4	2	no	—
356	C₄	—	6	4	no	—
357	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
358	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
359	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
360	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
361	C₃	C₂×C₅×#444	1	1	yes	characteristic, complemented, Sylow
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	12	4	no	—
365	C₂	C₅×#4717	1	2	yes	direct product factor
366	C₂	C₂×C₄×C₅×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#97	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#97	D₃
hypocenter	C₃	C₂×C₅×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₂×C₅×#97

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#901	C₂	semidirect
3. C₂×C₃×C₅×#97	C₂	semidirect
4. C₂×C₅×#819	C₂	semidirect
5. C₂×C₅×#805	C₂	semidirect
6. C₅×#4717	C₂	direct (N × H)
13. C₂×C₅×Dic₁₂	C₄	semidirect
14. C₅×#904	C₄	semidirect
16. C₂×C₅×D₂₄	C₄	semidirect
17. C₂×C₅×#204	C₄	semidirect
19. C₅×#901	C₂²	semidirect
22. C₃×C₅×#97	C₂²	semidirect
23. C₅×#819	C₂²	semidirect
24. C₅×#805	C₂²	semidirect
25. C₂×#4717	C₅	direct (N × H)
31. C₂×C₅×#97	D₃	semidirect
54. C₅×Dic₁₂	C₂×C₄	semidirect
55. C₅×D₂₄	C₂×C₄	semidirect
56. C₅×#204	C₂×C₄	semidirect
60. C₂×#901	C₂×C₅	semidirect
61. C₂×C₃×#97	C₂×C₅	semidirect
62. C₂×#819	C₂×C₅	semidirect
63. C₂×#805	C₂×C₅	semidirect
64. #4717	C₂×C₅	direct (N × H)
81. C₅×#97	C₂×D₃	semidirect
111. C₂×Dic₁₂	C₄×C₅	semidirect
112. #904	C₄×C₅	semidirect
114. C₂×D₂₄	C₄×C₅	semidirect
115. C₂×#204	C₄×C₅	semidirect
117. #901	C₂²×C₅	semidirect
120. C₃×#97	C₂²×C₅	semidirect
121. #819	C₂²×C₅	semidirect
122. #805	C₂²×C₅	semidirect
155. C₂×#97	C₅×D₃	semidirect
190. Dic₁₂	C₂×C₄×C₅	semidirect
191. D₂₄	C₂×C₄×C₅	semidirect
192. #204	C₂×C₄×C₅	semidirect
234. #97	C₂×C₅×D₃	semidirect
237. C₂×C₃×C₅	#444	semidirect
302. C₃×C₅	C₂×#444	semidirect
318. C₂×C₅	#4717	direct (N × H)
345. C₂×C₃	C₅×#444	semidirect
348. C₅	C₂×#4717	direct (N × H)
361. C₃	C₂×C₅×#444	semidirect
365. C₂	C₅×#4717	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×C₅×#904	2
C₂×C₅×#901	2
C₂×C₃×C₅×#97	2
C₂×C₅×#819	2
C₂×C₅×#805	2
C₅×#4717	2
C₂×C₅×#444	3
C₂×#4717	5

Subgroups — C2×C5×#4717 #14417931

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4717 #14417931