Subgroups — C₅×#73851 #14330631

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#953	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5247	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4957	C₂	1	3	yes	maximal, complemented
5	C₅×#4956	C₂	1	3	yes	maximal, complemented
6	C₅×#4945	C₂	1	3	yes	maximal, complemented
7	C₅×#4944	C₂	1	3	yes	maximal, complemented
8	C₅×#2375	—	3	1	no	maximal, Hall
9	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	C₂²	1	3	yes	—
11	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
14	C₅×#953	C₄	1	8	yes	complemented
15	C₂×C₅×#217	C₂²	1	3	yes	—
16	C₂×C₅×#217	C₂²	1	3	yes	—
17	C₂×C₅×#217	C₂²	1	3	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	3	yes	complemented
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	3	yes	complemented
20	C₂×C₄×C₅×Dic₃	C₂²	1	3	yes	complemented
21	C₅×C₃⋊#95	C₂²	1	3	yes	complemented
22	C₅×C₃⋊#95	C₂²	1	3	yes	complemented
23	#73851	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#120	—	3	1	no	—
25	C₅×#390	—	3	3	no	—
26	C₅×#388	—	3	3	no	—
27	C₅×#388	—	3	3	no	—
28	C₅×#386	—	3	3	no	—
29	C₅×#379	—	3	1	no	—
30	C₅×#379	D₃	1	1	yes	characteristic, complemented
31	C₂⁴×C₃×C₅	—	4	3	no	—
32	C₂⁴×C₃×C₅	—	4	3	no	—
33	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
34	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
35	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₅×#67	—	4	3	no	—
39	C₂×C₅×#67	—	4	3	no	—
40	C₂×C₅×#67	C₂×C₄	1	12	yes	—
41	C₂²×C₅×Dic₃	C₂³	1	3	yes	—
42	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	C₂³	1	3	yes	—
44	C₂×C₄×C₅×D₃	—	4	3	no	—
45	C₃×C₅×C₂²⋊C₄	—	4	3	no	—
46	C₃×C₅×C₂²⋊C₄	—	4	3	no	—
47	C₅×#217	—	4	3	no	—
48	C₅×#217	—	4	3	no	—
49	C₅×#217	C₂×C₄	1	12	yes	complemented
50	C₅×(C₂×D₃)⋊C₄	—	4	3	no	—
51	C₅×Dic₃⋊C₄	—	4	3	no	—
52	C₄×C₅×Dic₃	—	4	3	no	—
53	C₂×#953	C₂×C₅	1	1	yes	characteristic
54	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
55	#5247	C₂×C₅	1	1	yes	characteristic, complemented
56	#4957	C₂×C₅	1	3	yes	complemented
57	#4956	C₂×C₅	1	3	yes	complemented
58	#4945	C₂×C₅	1	3	yes	complemented
59	#4944	C₂×C₅	1	3	yes	complemented
60	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
61	C₂²×C₅×D₄	—	3	3	no	—
62	C₂³×C₄×C₅	—	3	1	no	—
63	C₅×#120	—	3	8	no	—
64	C₂×C₅×C₄⋊C₄	—	3	3	no	—
65	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
66	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
67	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
68	C₂×C₅×C₂²⋊C₄	—	3	3	no	—
69	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	3	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	3	yes	—
71	C₂×C₄²×C₅	—	3	3	no	—
72	C₅×#95	—	3	3	no	—
73	C₅×#95	—	3	3	no	—
74	#2375	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	3	no	—
76	C₂³×C₃×C₅	—	2	3	no	—
77	C₂³×C₃×C₅	—	2	3	no	—
78	C₂³×C₃×C₅	—	2	3	no	—
79	C₂³×C₃×C₅	—	2	3	no	—
80	C₂³×C₃×C₅	—	2	3	no	—
81	C₂³×C₃×C₅	—	4	12	no	—
82	C₂³×C₃×C₅	—	4	12	no	—
83	C₂³×C₃×C₅	—	4	4	no	—
84	C₂³×C₃×C₅	C₂²×C₄	1	6	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₂²×C₅×D₃	—	2	3	no	—
87	C₂²×C₅×D₃	—	2	3	no	—
88	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	—	2	3	no	—
90	C₂×C₃×C₄×C₅	—	2	3	no	—
91	C₂×C₃×C₄×C₅	—	2	3	no	—
92	C₂×C₃×C₄×C₅	—	2	3	no	—
93	C₅×#67	—	4	12	no	—
94	C₂×C₅×Dic₃	—	2	3	no	—
95	C₂×C₅×Dic₃	—	2	3	no	—
96	C₂×C₅×Dic₃	—	2	3	no	—
97	C₂×C₅×Dic₃	—	2	3	no	—
98	C₂×C₅×Dic₃	—	2	3	no	—
99	C₂×C₅×Dic₃	—	2	3	no	—
100	C₂×C₅×Dic₃	C₂²×C₄	1	6	yes	—
101	C₄×C₅×D₃	—	4	4	no	—
102	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
103	C₂²×#67	C₂²×C₅	1	3	yes	—
104	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
105	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
106	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	3	yes	—
107	#953	C₄×C₅	1	8	yes	complemented
108	C₂×#217	C₂²×C₅	1	3	yes	—
109	C₂×#217	C₂²×C₅	1	3	yes	—
110	C₂×#217	C₂²×C₅	1	3	yes	—
111	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	3	yes	complemented
112	C₂×Dic₃⋊C₄	C₂²×C₅	1	3	yes	complemented
113	C₂×C₄×Dic₃	C₂²×C₅	1	3	yes	complemented
114	C₃⋊#95	C₂²×C₅	1	3	yes	complemented
115	C₃⋊#95	C₂²×C₅	1	3	yes	complemented
116	C₂⁴×C₅	—	3	1	no	—
117	C₂⁴×C₅	—	4	3	no	—
118	C₂⁴×C₅	—	4	3	no	—
119	C₂⁴×C₅	C₄×D₃	1	4	yes	complemented
120	C₂⁴×C₅	C₂²×D₃	1	3	yes	—
121	C₂×C₅×D₄	—	3	12	no	—
122	C₂×C₅×D₄	—	12	3	no	—
123	C₂×C₅×D₄	—	12	3	no	—
124	C₂²×C₄×C₅	—	3	3	no	—
125	C₂²×C₄×C₅	—	3	3	no	—
126	C₂²×C₄×C₅	—	3	1	no	—
127	C₂²×C₄×C₅	—	12	3	no	—
128	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
129	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
130	C₅×C₄⋊C₄	—	12	3	no	—
131	C₅×C₂²⋊C₄	—	3	12	no	—
132	C₅×C₂²⋊C₄	—	4	3	no	—
133	C₅×C₂²⋊C₄	—	4	3	no	—
134	C₅×C₂²⋊C₄	—	12	3	no	—
135	C₅×C₂²⋊C₄	—	12	3	no	—
136	C₅×C₂²⋊C₄	—	12	3	no	—
137	C₄²×C₅	—	12	3	no	—
138	C₂×#120	—	3	1	no	—
139	#390	—	3	3	no	—
140	#388	—	3	3	no	—
141	#388	—	3	3	no	—
142	#386	—	3	3	no	—
143	#379	—	3	1	no	—
144	#379	C₅×D₃	1	1	yes	characteristic, complemented
145	C₂²×C₃×C₅	—	2	6	no	—
146	C₂²×C₃×C₅	—	2	6	no	—
147	C₂²×C₃×C₅	—	2	6	no	—
148	C₂²×C₃×C₅	—	4	16	no	—
149	C₂²×C₃×C₅	—	4	3	no	—
150	C₂²×C₃×C₅	—	4	3	no	—
151	C₂²×C₃×C₅	—	4	3	no	—
152	C₂²×C₃×C₅	—	4	3	no	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	H(5,𝔽₂)	1	3	yes	—
155	C₂²×C₃×C₅	H(5,𝔽₂)	1	3	yes	—
156	C₂×C₅×D₃	—	2	6	no	—
157	C₂×C₅×D₃	—	4	3	no	—
158	C₂×C₅×D₃	—	4	1	no	—
159	C₃×C₄×C₅	—	4	3	no	—
160	C₃×C₄×C₅	—	4	1	no	—
161	C₅×Dic₃	—	2	6	no	—
162	C₅×Dic₃	—	4	3	no	—
163	C₅×Dic₃	—	4	1	no	—
164	C₂⁴×C₃	—	4	3	no	—
165	C₂⁴×C₃	—	4	3	no	—
166	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	complemented
167	C₂⁴×C₃	C₂³×C₅	1	3	yes	—
168	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
171	C₂×#67	—	4	3	no	—
172	C₂×#67	—	4	3	no	—
173	C₂×#67	C₂×C₄×C₅	1	12	yes	—
174	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
175	C₂²×Dic₃	C₂³×C₅	1	3	yes	—
176	C₂²×Dic₃	C₂³×C₅	1	3	yes	—
177	C₂×C₄×D₃	—	4	3	no	—
178	C₃×C₂²⋊C₄	—	4	3	no	—
179	C₃×C₂²⋊C₄	—	4	3	no	—
180	#217	—	4	3	no	—
181	#217	—	4	3	no	—
182	#217	C₂×C₄×C₅	1	12	yes	complemented
183	(C₂×D₃)⋊C₄	—	4	3	no	—
184	Dic₃⋊C₄	—	4	3	no	—
185	C₄×Dic₃	—	4	3	no	—
186	C₂³×C₅	—	2	3	no	—
187	C₂³×C₅	—	2	3	no	—
188	C₂³×C₅	—	2	3	no	—
189	C₂³×C₅	—	2	3	no	—
190	C₂³×C₅	—	2	3	no	—
191	C₂³×C₅	—	2	3	no	—
192	C₂³×C₅	—	3	2	no	—
193	C₂³×C₅	—	4	12	no	—
194	C₂³×C₅	—	4	4	no	—
195	C₂³×C₅	—	4	12	no	—
196	C₂³×C₅	—	6	3	no	—
197	C₂³×C₅	—	6	3	no	—
198	C₂³×C₅	C₂×C₄×D₃	1	6	yes	—
199	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
200	C₅×D₄	—	12	12	no	—
201	C₂×C₄×C₅	—	2	3	no	—
202	C₂×C₄×C₅	—	2	3	no	—
203	C₂×C₄×C₅	—	2	3	no	—
204	C₂×C₄×C₅	—	2	3	no	—
205	C₂×C₄×C₅	—	3	6	no	—
206	C₂×C₄×C₅	—	6	3	no	—
207	C₂×C₄×C₅	—	6	3	no	—
208	C₂×C₄×C₅	—	6	3	no	—
209	C₂×C₄×C₅	—	6	3	no	—
210	C₂×C₄×C₅	—	6	3	no	—
211	C₂×C₄×C₅	—	6	3	no	—
212	C₂×C₄×C₅	—	12	4	no	—
213	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
214	C₂²×D₄	—	3	3	no	—
215	C₂³×C₄	—	3	1	no	—
216	#120	—	3	8	no	—
217	C₂×C₄⋊C₄	—	3	3	no	—
218	C₂×C₂²⋊C₄	—	3	3	no	—
219	C₂×C₂²⋊C₄	—	3	3	no	—
220	C₂×C₂²⋊C₄	—	3	3	no	—
221	C₂×C₂²⋊C₄	—	3	3	no	—
222	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	3	yes	—
223	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	3	yes	—
224	C₂×C₄²	—	3	3	no	—
225	#95	—	3	3	no	—
226	#95	—	3	3	no	—
227	C₂×C₃×C₅	—	4	6	no	—
228	C₂×C₃×C₅	#518	1	3	yes	—
229	C₂×C₃×C₅	#560	1	3	yes	—
230	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
231	C₅×D₃	—	4	2	no	—
232	C₂³×C₃	—	2	3	no	—
233	C₂³×C₃	—	2	3	no	—
234	C₂³×C₃	—	2	3	no	—
235	C₂³×C₃	—	2	3	no	—
236	C₂³×C₃	—	2	3	no	—
237	C₂³×C₃	—	2	3	no	—
238	C₂³×C₃	—	4	12	no	—
239	C₂³×C₃	—	4	12	no	—
240	C₂³×C₃	—	4	4	no	—
241	C₂³×C₃	C₂²×C₄×C₅	1	6	yes	—
242	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
243	C₂²×D₃	—	2	3	no	—
244	C₂²×D₃	—	2	3	no	—
245	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
246	C₂×C₃×C₄	—	2	3	no	—
247	C₂×C₃×C₄	—	2	3	no	—
248	C₂×C₃×C₄	—	2	3	no	—
249	C₂×C₃×C₄	—	2	3	no	—
250	#67	—	4	12	no	—
251	C₂×Dic₃	—	2	3	no	—
252	C₂×Dic₃	—	2	3	no	—
253	C₂×Dic₃	—	2	3	no	—
254	C₂×Dic₃	—	2	3	no	—
255	C₂×Dic₃	—	2	3	no	—
256	C₂×Dic₃	—	2	3	no	—
257	C₂×Dic₃	C₂²×C₄×C₅	1	6	yes	—
258	C₄×D₃	—	4	4	no	—
259	C₂²×C₅	—	2	6	no	—
260	C₂²×C₅	—	2	6	no	—
261	C₂²×C₅	—	2	6	no	—
262	C₂²×C₅	—	4	16	no	—
263	C₂²×C₅	—	4	3	no	—
264	C₂²×C₅	—	4	3	no	—
265	C₂²×C₅	—	4	3	no	—
266	C₂²×C₅	—	4	3	no	—
267	C₂²×C₅	—	6	6	no	—
268	C₂²×C₅	—	12	1	no	—
269	C₂²×C₅	—	12	3	no	—
270	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
271	C₂²×C₅	#1004	1	3	yes	—
272	C₂²×C₅	#1004	1	3	yes	—
273	C₄×C₅	—	4	1	no	—
274	C₄×C₅	—	4	3	no	—
275	C₄×C₅	—	6	6	no	—
276	C₄×C₅	—	12	1	no	—
277	C₄×C₅	—	12	3	no	—
278	C₂⁴	—	3	1	no	—
279	C₂⁴	—	4	3	no	—
280	C₂⁴	—	4	3	no	—
281	C₂⁴	C₄×C₅×D₃	1	4	yes	complemented
282	C₂⁴	C₂²×C₅×D₃	1	3	yes	—
283	C₂×D₄	—	3	12	no	—
284	C₂×D₄	—	12	3	no	—
285	C₂×D₄	—	12	3	no	—
286	C₂²×C₄	—	3	3	no	—
287	C₂²×C₄	—	3	1	no	—
288	C₂²×C₄	—	3	3	no	—
289	C₂²×C₄	—	12	3	no	—
290	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
292	C₄⋊C₄	—	12	3	no	—
293	C₂²⋊C₄	—	3	12	no	—
294	C₂²⋊C₄	—	4	3	no	—
295	C₂²⋊C₄	—	4	3	no	—
296	C₂²⋊C₄	—	12	3	no	—
297	C₂²⋊C₄	—	12	3	no	—
298	C₂²⋊C₄	—	12	3	no	—
299	C₄²	—	12	3	no	—
300	C₃×C₅	#2375	1	1	yes	characteristic, complemented, Hall
301	C₂²×C₃	—	2	6	no	—
302	C₂²×C₃	—	2	6	no	—
303	C₂²×C₃	—	2	6	no	—
304	C₂²×C₃	—	4	16	no	—
305	C₂²×C₃	—	4	3	no	—
306	C₂²×C₃	—	4	3	no	—
307	C₂²×C₃	—	4	3	no	—
308	C₂²×C₃	—	4	3	no	—
309	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
310	C₂²×C₃	C₅×H(5,𝔽₂)	1	3	yes	—
311	C₂²×C₃	C₅×H(5,𝔽₂)	1	3	yes	—
312	C₂×D₃	—	2	6	no	—
313	C₂×D₃	—	4	3	no	—
314	C₂×D₃	—	4	1	no	—
315	C₃×C₄	—	4	3	no	—
316	C₃×C₄	—	4	1	no	—
317	Dic₃	—	2	6	no	—
318	Dic₃	—	4	3	no	—
319	Dic₃	—	4	1	no	—
320	C₂×C₅	—	4	6	no	—
321	C₂×C₅	—	12	2	no	—
322	C₂×C₅	#5486	1	3	yes	—
323	C₂×C₅	#5594	1	1	yes	characteristic
324	C₂×C₅	#5595	1	3	yes	—
325	C₂³	—	2	3	no	—
326	C₂³	—	2	3	no	—
327	C₂³	—	2	3	no	—
328	C₂³	—	2	3	no	—
329	C₂³	—	2	3	no	—
330	C₂³	—	2	3	no	—
331	C₂³	—	3	2	no	—
332	C₂³	—	4	12	no	—
333	C₂³	—	4	4	no	—
334	C₂³	—	4	12	no	—
335	C₂³	—	6	3	no	—
336	C₂³	—	6	3	no	—
337	C₂³	C₂×C₄×C₅×D₃	1	6	yes	—
338	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
339	D₄	—	12	12	no	—
340	C₂×C₄	—	2	3	no	—
341	C₂×C₄	—	2	3	no	—
342	C₂×C₄	—	2	3	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	3	6	no	—
345	C₂×C₄	—	6	3	no	—
346	C₂×C₄	—	6	3	no	—
347	C₂×C₄	—	6	3	no	—
348	C₂×C₄	—	6	3	no	—
349	C₂×C₄	—	6	3	no	—
350	C₂×C₄	—	6	3	no	—
351	C₂×C₄	—	12	4	no	—
352	C₂×C₃	—	4	6	no	—
353	C₂×C₃	C₅×#518	1	3	yes	—
354	C₂×C₃	C₅×#560	1	3	yes	—
355	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
356	D₃	—	4	2	no	—
357	C₅	#73851	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	—	2	6	no	—
359	C₂²	—	2	6	no	—
360	C₂²	—	2	6	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	4	3	no	—
363	C₂²	—	4	3	no	—
364	C₂²	—	4	3	no	—
365	C₂²	—	4	3	no	—
366	C₂²	—	6	6	no	—
367	C₂²	—	12	1	no	—
368	C₂²	—	12	3	no	—
369	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
370	C₂²	C₅×#1004	1	3	yes	—
371	C₂²	C₅×#1004	1	3	yes	—
372	C₄	—	4	1	no	—
373	C₄	—	4	3	no	—
374	C₄	—	6	6	no	—
375	C₄	—	12	1	no	—
376	C₄	—	12	3	no	—
377	C₃	C₅×#2375	1	1	yes	characteristic, complemented, Sylow
378	C₂	—	4	6	no	—
379	C₂	—	12	2	no	—
380	C₂	C₅×#5486	1	3	yes	—
381	C₂	C₅×#5594	1	1	yes	characteristic
382	C₂	C₅×#5595	1	3	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#379	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#953	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#379	D₃
hypocenter	C₃	C₅×#2375
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#379

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#379	C₂	semidirect
3. C₅×#5247	C₂	semidirect
4. C₅×#4957	C₂	semidirect
5. C₅×#4956	C₂	semidirect
6. C₅×#4945	C₂	semidirect
7. C₅×#4944	C₂	semidirect
11. C₂²×C₄×C₅×D₃	C₂²	semidirect
14. C₅×#953	C₄	semidirect
18. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
19. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
20. C₂×C₄×C₅×Dic₃	C₂²	semidirect
21. C₅×C₃⋊#95	C₂²	semidirect
22. C₅×C₃⋊#95	C₂²	semidirect
23. #73851	C₅	direct (N × H)
30. C₅×#379	D₃	semidirect
33. C₂⁴×C₃×C₅	C₂×C₄	semidirect
49. C₅×#217	C₂×C₄	semidirect
54. C₃×#379	C₂×C₅	semidirect
55. #5247	C₂×C₅	semidirect
56. #4957	C₂×C₅	semidirect
57. #4956	C₂×C₅	semidirect
58. #4945	C₂×C₅	semidirect
59. #4944	C₂×C₅	semidirect
104. C₂²×C₄×D₃	C₂²×C₅	semidirect
107. #953	C₄×C₅	semidirect
111. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
112. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
113. C₂×C₄×Dic₃	C₂²×C₅	semidirect
114. C₃⋊#95	C₂²×C₅	semidirect
115. C₃⋊#95	C₂²×C₅	semidirect
119. C₂⁴×C₅	C₄×D₃	semidirect
144. #379	C₅×D₃	semidirect
166. C₂⁴×C₃	C₂×C₄×C₅	semidirect
182. #217	C₂×C₄×C₅	semidirect
281. C₂⁴	C₄×C₅×D₃	semidirect
300. C₃×C₅	#2375	semidirect
357. C₅	#73851	direct (N × H)
377. C₃	C₅×#2375	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#953	2
C₃×C₅×#379	2
C₅×#5247	2
C₅×#4957	2
C₅×#4956	2
C₅×#4945	2
C₅×#4944	2
C₅×#2375	3
#73851	5

Subgroups — C5×#73851 #14330631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73851 #14330631