Subgroups — C₅×#92018 #72260140

Order 2400.

772 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#6817	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
5	C₅×#6777	C₂	1	2	yes	maximal, complemented
6	C₅×D₅×D₁₂	C₂	1	2	yes	maximal, complemented
7	C₅×#6772	C₂	1	2	yes	maximal, complemented
8	C₅×#6768	C₂	1	2	yes	maximal, complemented
9	C₅×#4144	—	3	1	no	maximal, Hall
10	C₂²×C₅²×D₃	C₂²	1	2	yes	complemented
11	C₂×C₅×D₃×D₅	C₂²	1	4	yes	complemented
12	C₂×C₃×C₄×C₅²	C₂²	1	1	yes	characteristic, complemented
13	C₅×#1220	C₂²	1	2	yes	complemented
14	C₅×D₆₀	C₂²	1	1	yes	characteristic, complemented
15	C₄×C₅×D₁₅	C₂²	1	2	yes	complemented
16	C₅×Dic₃₀	C₂²	1	1	yes	characteristic, complemented
17	C₅²×D₁₂	C₂²	1	2	yes	complemented
18	C₅²×D₁₂	C₂²	1	2	yes	complemented
19	C₃×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
20	C₃×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₄×C₅×D₅	C₂²	1	2	yes	complemented
22	C₃×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
23	C₅×#1203	C₂²	1	4	yes	complemented
24	C₅×#1201	C₂²	1	4	yes	complemented
25	C₅×D₃×Dic₅	C₂²	1	4	yes	complemented
26	C₅×#1009	—	5	1	no	maximal
27	#92018	C₅	1	1	yes	maximal, characteristic, direct product factor
28	C₂×C₅²×D₄	—	3	1	no	—
29	C₂×C₅×C₂²⋊D₅	—	3	4	no	—
30	C₅×#711	—	3	2	no	—
31	C₅×#711	—	3	2	no	—
32	C₅×D₄×D₅	—	3	2	no	—
33	C₅×D₄×D₅	—	3	2	no	—
34	C₅×#709	—	3	1	no	—
35	C₅×#709	D₃	1	1	yes	characteristic, complemented
36	C₂²×C₃×C₅²	C₂³	1	1	yes	characteristic
37	C₂×C₅×D₁₅	C₂³	1	2	yes	—
38	C₂×C₅²×D₃	—	4	2	no	—
39	C₂×C₅²×D₃	C₂³	1	4	yes	—
40	C₂×C₃×C₅×D₅	C₂³	1	2	yes	—
41	C₅×D₃×D₅	—	4	4	no	—
42	C₃×C₄×C₅²	C₂³	1	1	yes	characteristic
43	C₃×C₄×C₅²	C₂³	1	1	yes	characteristic
44	C₅×Dic₁₅	C₂³	1	2	yes	—
45	C₃×C₅×Dic₅	C₂³	1	2	yes	—
46	C₃×C₅×#41	—	5	1	no	—
47	#6817	C₂×C₅	1	1	yes	characteristic, complemented
48	C₅×#239	—	5	2	no	—
49	C₅×D₃×D₄	—	5	4	no	—
50	C₅×D₃×D₄	—	5	2	no	—
51	C₅×#235	—	5	1	no	—
52	C₅×#235	—	5	2	no	—
53	C₂×C₅×D₁₂	—	2	2	no	—
54	C₂×C₅×D₁₂	—	5	2	no	—
55	C₂×C₅×D₁₂	D₅	1	1	yes	characteristic, complemented
56	C₂×C₅×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
57	C₃×#709	C₂×C₅	1	1	yes	characteristic, complemented
58	D₃×C₂²⋊D₅	C₂×C₅	1	4	yes	complemented
59	#6777	C₂×C₅	1	2	yes	complemented
60	D₅×D₁₂	C₂×C₅	1	2	yes	complemented
61	#6772	C₂×C₅	1	2	yes	complemented
62	#6768	C₂×C₅	1	2	yes	complemented
63	C₂³×C₅²	—	3	2	no	—
64	C₂²×C₅×D₅	—	3	4	no	—
65	C₅²×D₄	—	3	2	no	—
66	C₅²×D₄	—	3	2	no	—
67	C₂×C₄×C₅²	C₂×D₃	1	1	yes	characteristic, complemented
68	C₅×C₂²⋊D₅	—	3	2	no	—
69	C₅×C₂²⋊D₅	—	3	4	no	—
70	C₅×C₂²⋊D₅	—	3	4	no	—
71	C₅×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
72	C₂×C₅×Dic₅	—	3	4	no	—
73	C₅×D₂₀	—	3	1	no	—
74	C₅×D₂₀	C₂×D₃	1	1	yes	characteristic, complemented
75	C₄×C₅×D₅	—	3	2	no	—
76	C₄×C₅×D₅	C₂×D₃	1	2	yes	complemented
77	C₅×Dic₁₀	—	3	1	no	—
78	C₅×Dic₁₀	C₂×D₃	1	1	yes	characteristic, complemented
79	C₅×H(5,𝔽₂)	—	15	1	no	—
80	#4144	—	3	1	no	—
81	C₂×C₃×C₅²	—	2	1	no	—
82	C₂×C₃×C₅²	C₂⁴	1	1	yes	characteristic
83	C₅×D₁₅	—	2	2	no	—
84	C₅²×D₃	—	2	4	no	—
85	C₃×C₅×D₅	—	2	2	no	—
86	C₂²×C₅×D₃	—	2	4	no	—
87	C₂²×C₅×D₃	—	5	4	no	—
88	C₂²×C₅×D₃	C₂×D₅	1	2	yes	complemented
89	C₂²×C₅×D₃	C₂²×C₅	1	2	yes	complemented
90	C₂×D₃×D₅	C₂²×C₅	1	4	yes	complemented
91	C₃×C₅×Q₈	—	5	1	no	—
92	C₃×C₅×D₄	—	5	2	no	—
93	C₃×C₅×D₄	—	5	1	no	—
94	C₂×C₃×C₄×C₅	—	2	2	no	—
95	C₂×C₃×C₄×C₅	—	5	2	no	—
96	C₂×C₃×C₄×C₅	C₂×D₅	1	1	yes	characteristic, complemented
97	C₂×C₃×C₄×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
98	#1220	C₂²×C₅	1	2	yes	complemented
99	D₆₀	C₂²×C₅	1	1	yes	characteristic, complemented
100	C₄×D₁₅	C₂²×C₅	1	2	yes	complemented
101	Dic₃₀	C₂²×C₅	1	1	yes	characteristic, complemented
102	C₅×#67	—	5	2	no	—
103	C₅×#67	—	5	4	no	—
104	C₅×D₁₂	—	2	4	no	—
105	C₅×D₁₂	—	2	4	no	—
106	C₅×D₁₂	—	5	4	no	—
107	C₅×D₁₂	—	5	1	no	—
108	C₅×D₁₂	C₂×D₅	1	2	yes	complemented
109	C₅×D₁₂	C₂×D₅	1	2	yes	complemented
110	C₅×D₁₂	C₂²×C₅	1	2	yes	complemented
111	C₅×D₁₂	C₂²×C₅	1	2	yes	complemented
112	C₄×C₅×D₃	—	5	4	no	—
113	C₄×C₅×D₃	—	5	2	no	—
114	C₅×Dic₆	—	5	1	no	—
115	C₃×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
116	C₃×D₂₀	C₂²×C₅	1	1	yes	characteristic, complemented
117	C₃×C₄×D₅	C₂²×C₅	1	2	yes	complemented
118	C₃×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
119	#1203	C₂²×C₅	1	4	yes	complemented
120	#1201	C₂²×C₅	1	4	yes	complemented
121	D₃×Dic₅	C₂²×C₅	1	4	yes	complemented
122	C₂²×C₅²	—	3	4	no	—
123	C₂²×C₅²	—	12	2	no	—
124	C₂²×C₅²	C₂²×D₃	1	1	yes	characteristic
125	C₂×C₅×D₅	—	3	2	no	—
126	C₂×C₅×D₅	—	12	4	no	—
127	C₂×C₅×D₅	C₂²×D₃	1	2	yes	—
128	C₄×C₅²	C₂²×D₃	1	1	yes	characteristic
129	C₄×C₅²	C₂²×D₃	1	1	yes	characteristic
130	C₅×Dic₅	—	3	2	no	—
131	C₅×Dic₅	C₂²×D₃	1	2	yes	—
132	#1009	—	5	1	no	Hall
133	C₅×#41	—	5	1	no	—
134	C₅×#41	—	15	2	no	—
135	C₅×#41	—	15	2	no	—
136	C₅×#41	—	15	1	no	—
137	C₂×C₅×D₄	—	3	1	no	—
138	C₂×C₅×D₄	—	3	1	no	—
139	C₂×C₅×D₄	—	6	2	no	—
140	C₂×C₅×D₄	—	15	2	no	—
141	C₂×C₅×D₄	—	15	2	no	—
142	C₂×C₅×D₄	—	15	4	no	—
143	C₂×C₂²⋊D₅	—	3	4	no	—
144	#711	—	3	2	no	—
145	#711	—	3	2	no	—
146	D₄×D₅	—	3	2	no	—
147	D₄×D₅	—	3	2	no	—
148	#709	—	3	1	no	—
149	#709	C₅×D₃	1	1	yes	characteristic, complemented
150	C₃×C₅²	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	5	2	no	—
153	C₂²×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
155	C₂×D₁₅	C₂³×C₅	1	2	yes	—
156	C₂×C₅×D₃	—	2	8	no	—
157	C₂×C₅×D₃	—	4	2	no	—
158	C₂×C₅×D₃	—	4	2	no	—
159	C₂×C₅×D₃	—	4	8	no	—
160	C₂×C₅×D₃	—	5	2	no	—
161	C₂×C₅×D₃	—	20	4	no	—
162	C₂×C₅×D₃	C₂²×D₅	1	4	yes	—
163	C₂×C₅×D₃	C₂³×C₅	1	4	yes	—
164	C₂×C₃×D₅	C₂³×C₅	1	2	yes	—
165	D₃×D₅	—	4	4	no	—
166	C₃×C₄×C₅	—	2	2	no	—
167	C₃×C₄×C₅	—	2	2	no	—
168	C₃×C₄×C₅	—	5	2	no	—
169	C₃×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
170	C₃×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
171	C₃×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
172	C₃×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
173	Dic₁₅	C₂³×C₅	1	2	yes	—
174	C₃×Dic₅	C₂³×C₅	1	2	yes	—
175	C₅×Dic₃	—	5	2	no	—
176	C₂×C₅²	—	2	1	no	—
177	C₂×C₅²	—	6	4	no	—
178	C₂×C₅²	C₂³×D₃	1	1	yes	characteristic
179	C₅×D₅	—	2	2	no	—
180	C₅×D₅	—	6	2	no	—
181	C₃×#41	—	5	1	no	—
182	#239	—	5	2	no	—
183	D₃×D₄	—	5	4	no	—
184	D₃×D₄	—	5	2	no	—
185	#235	—	5	1	no	—
186	#235	—	5	2	no	—
187	C₂×D₁₂	—	5	2	no	—
188	C₂×D₁₂	C₅×D₅	1	1	yes	characteristic, complemented
189	C₂³×C₅	—	3	2	no	—
190	C₂³×C₅	—	3	2	no	—
191	C₂³×C₅	—	6	4	no	—
192	C₂³×C₅	—	15	4	no	—
193	C₂²×D₅	—	3	4	no	—
194	C₅×Q₈	—	5	1	no	—
195	C₅×Q₈	—	15	1	no	—
196	C₅×D₄	—	3	2	no	—
197	C₅×D₄	—	3	2	no	—
198	C₅×D₄	—	3	2	no	—
199	C₅×D₄	—	3	2	no	—
200	C₅×D₄	—	5	2	no	—
201	C₅×D₄	—	5	1	no	—
202	C₅×D₄	—	6	4	no	—
203	C₅×D₄	—	6	4	no	—
204	C₅×D₄	—	15	4	no	—
205	C₅×D₄	—	15	4	no	—
206	C₅×D₄	—	15	2	no	—
207	C₅×D₄	—	15	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	5	2	no	—
210	C₂×C₄×C₅	—	15	4	no	—
211	C₂×C₄×C₅	—	15	2	no	—
212	C₂×C₄×C₅	D₃×D₅	1	1	yes	characteristic, complemented
213	C₂×C₄×C₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
214	C₂²⋊D₅	—	3	2	no	—
215	C₂²⋊D₅	—	3	4	no	—
216	C₂²⋊D₅	—	3	4	no	—
217	C₂²⋊D₅	C₂×C₅×D₃	1	2	yes	complemented
218	C₂×Dic₅	—	3	4	no	—
219	D₂₀	—	3	1	no	—
220	D₂₀	C₂×C₅×D₃	1	1	yes	characteristic, complemented
221	C₄×D₅	—	3	2	no	—
222	C₄×D₅	C₂×C₅×D₃	1	2	yes	complemented
223	Dic₁₀	—	3	1	no	—
224	Dic₁₀	C₂×C₅×D₃	1	1	yes	characteristic, complemented
225	H(5,𝔽₂)	—	15	1	no	Sylow
226	C₂×C₃×C₅	—	2	4	no	—
227	C₂×C₃×C₅	—	2	1	no	—
228	C₂×C₃×C₅	—	2	1	no	—
229	C₂×C₃×C₅	—	2	2	no	—
230	C₂×C₃×C₅	—	10	2	no	—
231	C₂×C₃×C₅	C₂³×D₅	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂⁴×C₅	1	1	yes	characteristic
233	D₁₅	—	2	2	no	—
234	C₃×D₅	—	2	2	no	—
235	C₅×D₃	—	2	4	no	—
236	C₅×D₃	—	2	4	no	—
237	C₅×D₃	—	4	8	no	—
238	C₅×D₃	—	10	2	no	—
239	C₅²	#1009	1	1	yes	characteristic, complemented, Sylow
240	C₂²×D₃	—	5	4	no	—
241	C₂²×D₃	C₂×C₅×D₅	1	2	yes	complemented
242	C₃×Q₈	—	5	1	no	—
243	C₃×D₄	—	5	2	no	—
244	C₃×D₄	—	5	1	no	—
245	C₂×C₃×C₄	—	5	2	no	—
246	C₂×C₃×C₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
247	#67	—	5	2	no	—
248	#67	—	5	4	no	—
249	D₁₂	—	5	4	no	—
250	D₁₂	—	5	1	no	—
251	D₁₂	C₂×C₅×D₅	1	2	yes	complemented
252	D₁₂	C₂×C₅×D₅	1	2	yes	complemented
253	C₄×D₃	—	5	4	no	—
254	C₄×D₃	—	5	2	no	—
255	Dic₆	—	5	1	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	3	4	no	—
258	C₂²×C₅	—	3	4	no	—
259	C₂²×C₅	—	5	2	no	—
260	C₂²×C₅	—	6	8	no	—
261	C₂²×C₅	—	12	2	no	—
262	C₂²×C₅	—	12	2	no	—
263	C₂²×C₅	—	12	8	no	—
264	C₂²×C₅	—	15	2	no	—
265	C₂²×C₅	—	60	4	no	—
266	C₂²×C₅	C₂×D₃×D₅	1	1	yes	characteristic
267	C₂²×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
268	C₂×D₅	—	3	2	no	—
269	C₂×D₅	—	12	4	no	—
270	C₂×D₅	C₂²×C₅×D₃	1	2	yes	—
271	C₄×C₅	—	2	2	no	—
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	5	2	no	—
274	C₄×C₅	—	15	2	no	—
275	C₄×C₅	C₂×D₃×D₅	1	1	yes	characteristic
276	C₄×C₅	C₂×D₃×D₅	1	1	yes	characteristic
277	C₄×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
278	C₄×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
279	Dic₅	—	3	2	no	—
280	Dic₅	C₂²×C₅×D₃	1	2	yes	—
281	#41	—	5	1	no	—
282	#41	—	15	2	no	—
283	#41	—	15	2	no	—
284	#41	—	15	1	no	—
285	C₂×D₄	—	3	1	no	—
286	C₂×D₄	—	15	2	no	—
287	C₂×D₄	—	15	2	no	—
288	C₂×D₄	—	15	4	no	—
289	C₃×C₅	—	2	2	no	—
290	C₃×C₅	#4144	1	1	yes	characteristic, complemented
291	C₃×C₅	C₅×H(5,𝔽₂)	1	1	yes	characteristic, complemented
292	C₂²×C₃	—	5	2	no	—
293	C₂²×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
294	C₂×D₃	—	4	2	no	—
295	C₂×D₃	—	5	2	no	—
296	C₂×D₃	—	20	4	no	—
297	C₂×D₃	C₂²×C₅×D₅	1	4	yes	—
298	C₃×C₄	—	5	2	no	—
299	C₃×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
300	C₃×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
301	Dic₃	—	5	2	no	—
302	C₂×C₅	—	2	4	no	—
303	C₂×C₅	—	2	1	no	—
304	C₂×C₅	—	2	1	no	—
305	C₂×C₅	—	2	2	no	—
306	C₂×C₅	—	6	4	no	—
307	C₂×C₅	—	6	4	no	—
308	C₂×C₅	—	10	2	no	—
309	C₂×C₅	—	12	8	no	—
310	C₂×C₅	—	30	2	no	—
311	C₂×C₅	C₂²×D₃×D₅	1	1	yes	characteristic
312	C₂×C₅	C₂³×C₅×D₃	1	1	yes	characteristic
313	D₅	—	2	2	no	—
314	D₅	—	6	2	no	—
315	C₂³	—	3	2	no	—
316	C₂³	—	15	4	no	—
317	Q₈	—	5	1	no	—
318	Q₈	—	15	1	no	—
319	D₄	—	3	2	no	—
320	D₄	—	3	2	no	—
321	D₄	—	5	2	no	—
322	D₄	—	5	1	no	—
323	D₄	—	15	4	no	—
324	D₄	—	15	4	no	—
325	D₄	—	15	2	no	—
326	D₄	—	15	1	no	—
327	C₂×C₄	—	5	2	no	—
328	C₂×C₄	—	15	4	no	—
329	C₂×C₄	—	15	2	no	—
330	C₂×C₄	C₅×D₃×D₅	1	1	yes	characteristic, complemented
331	C₂×C₃	—	2	1	no	—
332	C₂×C₃	—	10	2	no	—
333	C₂×C₃	C₂³×C₅×D₅	1	1	yes	characteristic
334	D₃	—	2	4	no	—
335	D₃	—	10	2	no	—
336	C₅	—	2	2	no	—
337	C₅	#92018	1	1	yes	characteristic, direct product factor
338	C₅	C₅×#1009	1	1	yes	characteristic, complemented
339	C₂²	—	3	4	no	—
340	C₂²	—	5	2	no	—
341	C₂²	—	12	2	no	—
342	C₂²	—	15	2	no	—
343	C₂²	—	60	4	no	—
344	C₂²	C₂×C₅×D₃×D₅	1	1	yes	characteristic
345	C₄	—	5	2	no	—
346	C₄	—	15	2	no	—
347	C₄	C₂×C₅×D₃×D₅	1	1	yes	characteristic
348	C₄	C₂×C₅×D₃×D₅	1	1	yes	characteristic
349	C₃	C₅×#4144	1	1	yes	characteristic, complemented, Sylow
350	C₂	—	2	1	no	—
351	C₂	—	6	4	no	—
352	C₂	—	10	2	no	—
353	C₂	—	30	2	no	—
354	C₂	C₂²×C₅×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃×D₅
Fitting	C₂×C₃×C₄×C₅²	C₂²
socle	C₂×C₃×C₅²	C₂⁴
hypercenter	C₂×C₄×C₅	D₃×D₅
hypocenter	C₃×C₅	C₅×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#6817	C₂	semidirect
2. C₂×C₅²×D₁₂	C₂	semidirect
3. C₃×C₅×#709	C₂	semidirect
4. C₅×D₃×C₂²⋊D₅	C₂	semidirect
5. C₅×#6777	C₂	semidirect
6. C₅×D₅×D₁₂	C₂	semidirect
7. C₅×#6772	C₂	semidirect
8. C₅×#6768	C₂	semidirect
10. C₂²×C₅²×D₃	C₂²	semidirect
11. C₂×C₅×D₃×D₅	C₂²	semidirect
12. C₂×C₃×C₄×C₅²	C₂²	semidirect
13. C₅×#1220	C₂²	semidirect
14. C₅×D₆₀	C₂²	semidirect
15. C₄×C₅×D₁₅	C₂²	semidirect
16. C₅×Dic₃₀	C₂²	semidirect
17. C₅²×D₁₂	C₂²	semidirect
18. C₅²×D₁₂	C₂²	semidirect
19. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
20. C₃×C₅×D₂₀	C₂²	semidirect
21. C₃×C₄×C₅×D₅	C₂²	semidirect
22. C₃×C₅×Dic₁₀	C₂²	semidirect
23. C₅×#1203	C₂²	semidirect
24. C₅×#1201	C₂²	semidirect
25. C₅×D₃×Dic₅	C₂²	semidirect
27. #92018	C₅	direct (N × H)
35. C₅×#709	D₃	semidirect
47. #6817	C₂×C₅	semidirect
55. C₂×C₅×D₁₂	D₅	semidirect
56. C₂×C₅×D₁₂	C₂×C₅	semidirect
57. C₃×#709	C₂×C₅	semidirect
58. D₃×C₂²⋊D₅	C₂×C₅	semidirect
59. #6777	C₂×C₅	semidirect
60. D₅×D₁₂	C₂×C₅	semidirect
61. #6772	C₂×C₅	semidirect
62. #6768	C₂×C₅	semidirect
67. C₂×C₄×C₅²	C₂×D₃	semidirect
71. C₅×C₂²⋊D₅	C₂×D₃	semidirect
74. C₅×D₂₀	C₂×D₃	semidirect
76. C₄×C₅×D₅	C₂×D₃	semidirect
78. C₅×Dic₁₀	C₂×D₃	semidirect
88. C₂²×C₅×D₃	C₂×D₅	semidirect
89. C₂²×C₅×D₃	C₂²×C₅	semidirect
90. C₂×D₃×D₅	C₂²×C₅	semidirect
96. C₂×C₃×C₄×C₅	C₂×D₅	semidirect
97. C₂×C₃×C₄×C₅	C₂²×C₅	semidirect
98. #1220	C₂²×C₅	semidirect
99. D₆₀	C₂²×C₅	semidirect
100. C₄×D₁₅	C₂²×C₅	semidirect
101. Dic₃₀	C₂²×C₅	semidirect
108. C₅×D₁₂	C₂×D₅	semidirect
109. C₅×D₁₂	C₂×D₅	semidirect
110. C₅×D₁₂	C₂²×C₅	semidirect
111. C₅×D₁₂	C₂²×C₅	semidirect
115. C₃×C₂²⋊D₅	C₂²×C₅	semidirect
116. C₃×D₂₀	C₂²×C₅	semidirect
117. C₃×C₄×D₅	C₂²×C₅	semidirect
118. C₃×Dic₁₀	C₂²×C₅	semidirect
119. #1203	C₂²×C₅	semidirect
120. #1201	C₂²×C₅	semidirect
121. D₃×Dic₅	C₂²×C₅	semidirect
149. #709	C₅×D₃	semidirect
150. C₃×C₅²	H(5,𝔽₂)	semidirect
188. C₂×D₁₂	C₅×D₅	semidirect
212. C₂×C₄×C₅	D₃×D₅	semidirect
213. C₂×C₄×C₅	C₂×C₅×D₃	semidirect
217. C₂²⋊D₅	C₂×C₅×D₃	semidirect
220. D₂₀	C₂×C₅×D₃	semidirect
222. C₄×D₅	C₂×C₅×D₃	semidirect
224. Dic₁₀	C₂×C₅×D₃	semidirect
239. C₅²	#1009	semidirect
241. C₂²×D₃	C₂×C₅×D₅	semidirect
246. C₂×C₃×C₄	C₂×C₅×D₅	semidirect
251. D₁₂	C₂×C₅×D₅	semidirect
252. D₁₂	C₂×C₅×D₅	semidirect
290. C₃×C₅	#4144	semidirect
291. C₃×C₅	C₅×H(5,𝔽₂)	semidirect
330. C₂×C₄	C₅×D₃×D₅	semidirect
337. C₅	#92018	direct (N × H)
338. C₅	C₅×#1009	semidirect
349. C₃	C₅×#4144	semidirect

Maximal subgroups

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

subgroup	index
C₅×#6817	2
C₂×C₅²×D₁₂	2
C₃×C₅×#709	2
C₅×D₃×C₂²⋊D₅	2
C₅×#6777	2
C₅×D₅×D₁₂	2
C₅×#6772	2
C₅×#6768	2
C₅×#4144	3
C₅×#1009	5
#92018	5

Subgroups — C5×#92018 #72260140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#92018 #72260140