Subgroups — C₅×#73819 #14322431

Order 1920.

2208 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#877	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5247	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4957	C₂	1	8	yes	maximal, complemented
6	C₅×#4955	C₂	1	2	yes	maximal, complemented
7	C₅×#2309	—	3	1	no	maximal, Hall
8	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂²×C₅×#67	—	2	8	no	—
11	C₂²×C₅×#67	C₄	1	8	yes	complemented
12	C₂²×C₅×#67	C₂²	1	4	yes	—
13	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
16	C₂×C₅×#217	C₂²	1	2	yes	—
17	C₂×C₅×#217	C₂²	1	4	yes	complemented
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	complemented
20	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
21	C₅×#877	—	2	8	no	—
22	#73819	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂³×C₅×D₄	—	3	1	no	—
24	C₂×C₅×#117	—	3	2	no	—
25	C₅×#390	—	3	8	no	—
26	C₅×#379	—	3	1	no	—
27	C₅×#379	—	3	2	no	—
28	C₅×#379	D₃	1	1	yes	characteristic, complemented
29	C₂⁴×C₃×C₅	—	2	4	no	—
30	C₂⁴×C₃×C₅	—	4	4	no	—
31	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	—
32	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂³×C₅×D₃	—	2	4	no	—
35	C₂³×C₅×D₃	—	4	4	no	—
36	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
37	C₂³×C₅×D₃	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
39	C₂×C₅×#67	—	2	32	no	—
40	C₂×C₅×#67	—	2	8	no	—
41	C₂×C₅×#67	—	2	8	no	—
42	C₂×C₅×#67	C₂×C₄	1	16	yes	—
43	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
44	C₂²×C₅×Dic₃	D₄	1	8	yes	—
45	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
46	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
49	C₅×#217	—	2	4	no	—
50	C₅×#217	—	4	4	no	—
51	C₅×(C₂×D₃)⋊C₄	—	4	8	no	—
52	C₅×Dic₃⋊C₄	—	2	8	no	—
53	C₄×C₅×Dic₃	—	2	8	no	—
54	C₂³×#67	C₂×C₅	1	1	yes	characteristic
55	C₂×#877	C₂×C₅	1	2	yes	complemented
56	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
57	#5247	C₂×C₅	1	1	yes	characteristic, complemented
58	#4957	C₂×C₅	1	8	yes	complemented
59	#4955	C₂×C₅	1	2	yes	complemented
60	C₂⁵×C₅	—	3	1	no	—
61	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₅×D₄	—	3	8	no	—
63	C₂²×C₅×D₄	—	3	4	no	—
64	C₂²×C₅×D₄	—	6	8	no	—
65	C₂³×C₄×C₅	—	3	1	no	—
66	C₅×#117	—	6	8	no	—
67	C₂×C₅×C₄⋊C₄	—	3	4	no	—
68	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
69	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
70	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
71	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
72	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
73	C₂×C₄²×C₅	—	3	4	no	—
74	#2309	—	3	1	no	Sylow
75	C₂³×C₃×C₅	—	2	4	no	—
76	C₂³×C₃×C₅	—	2	8	no	—
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	—	4	8	no	—
81	C₂³×C₃×C₅	—	4	16	no	—
82	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
83	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
84	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₂²×C₅×D₃	—	2	8	no	—
87	C₂²×C₅×D₃	—	2	4	no	—
88	C₂²×C₅×D₃	—	2	8	no	—
89	C₂²×C₅×D₃	—	4	8	no	—
90	C₂²×C₅×D₃	—	4	16	no	—
91	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	8	no	—
94	C₅×#67	—	2	32	no	—
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	8	no	—
97	C₂×C₅×Dic₃	C₂²⋊C₄	1	16	yes	complemented
98	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
99	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
100	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
101	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
102	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
103	C₂²×#67	—	2	8	no	—
104	C₂²×#67	C₄×C₅	1	8	yes	complemented
105	C₂²×#67	C₂²×C₅	1	4	yes	—
106	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
107	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
109	C₂×#217	C₂²×C₅	1	2	yes	—
110	C₂×#217	C₂²×C₅	1	4	yes	complemented
111	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
112	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	complemented
113	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
114	#877	—	2	8	no	—
115	C₂⁴×C₅	—	2	4	no	—
116	C₂⁴×C₅	—	3	2	no	—
117	C₂⁴×C₅	—	3	4	no	—
118	C₂⁴×C₅	—	4	4	no	—
119	C₂⁴×C₅	—	6	4	no	—
120	C₂⁴×C₅	—	12	4	no	—
121	C₂⁴×C₅	C₄×D₃	1	4	yes	—
122	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
123	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₂×C₅×D₄	—	3	16	no	—
125	C₂×C₅×D₄	—	6	32	no	—
126	C₂×C₅×D₄	—	6	8	no	—
127	C₂×C₅×D₄	—	6	8	no	—
128	C₂²×C₄×C₅	—	3	4	no	—
129	C₂²×C₄×C₅	—	3	8	no	—
130	C₂²×C₄×C₅	—	3	2	no	—
131	C₂²×C₄×C₅	—	3	4	no	—
132	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
133	C₅×C₄⋊C₄	—	6	8	no	—
134	C₅×C₂²⋊C₄	—	2	4	no	—
135	C₅×C₂²⋊C₄	—	4	4	no	—
136	C₅×C₂²⋊C₄	—	6	4	no	—
137	C₅×C₂²⋊C₄	—	12	8	no	—
138	C₅×C₂²⋊C₄	—	12	4	no	—
139	C₄²×C₅	—	6	8	no	—
140	C₂³×D₄	—	3	1	no	—
141	C₂×#117	—	3	2	no	—
142	#390	—	3	8	no	—
143	#379	—	3	1	no	—
144	#379	—	3	2	no	—
145	#379	C₅×D₃	1	1	yes	characteristic, complemented
146	C₂²×C₃×C₅	—	2	4	no	—
147	C₂²×C₃×C₅	—	2	8	no	—
148	C₂²×C₃×C₅	—	2	4	no	—
149	C₂²×C₃×C₅	—	2	4	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	4	16	no	—
152	C₂²×C₃×C₅	—	4	8	no	—
153	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
154	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
155	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
156	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
157	C₂×C₅×D₃	—	2	4	no	—
158	C₂×C₅×D₃	—	2	8	no	—
159	C₂×C₅×D₃	—	4	16	no	—
160	C₂×C₅×D₃	—	4	8	no	—
161	C₃×C₄×C₅	—	4	4	no	—
162	C₅×Dic₃	—	4	4	no	—
163	C₅×Dic₃	C₂×C₂²⋊C₄	1	8	yes	—
164	C₂⁴×C₃	—	2	4	no	—
165	C₂⁴×C₃	—	4	4	no	—
166	C₂⁴×C₃	C₂×C₄×C₅	1	4	yes	—
167	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
168	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
169	C₂³×D₃	—	2	4	no	—
170	C₂³×D₃	—	4	4	no	—
171	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
172	C₂³×D₃	C₂³×C₅	1	2	yes	—
173	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
174	C₂×#67	—	2	32	no	—
175	C₂×#67	—	2	8	no	—
176	C₂×#67	—	2	8	no	—
177	C₂×#67	C₂×C₄×C₅	1	16	yes	—
178	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
179	C₂²×Dic₃	C₅×D₄	1	8	yes	—
180	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
181	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
182	C₃×C₂²⋊C₄	—	2	4	no	—
183	C₃×C₂²⋊C₄	—	4	4	no	—
184	#217	—	2	4	no	—
185	#217	—	4	4	no	—
186	(C₂×D₃)⋊C₄	—	4	8	no	—
187	Dic₃⋊C₄	—	2	8	no	—
188	C₄×Dic₃	—	2	8	no	—
189	C₂³×C₅	—	2	4	no	—
190	C₂³×C₅	—	2	8	no	—
191	C₂³×C₅	—	2	4	no	—
192	C₂³×C₅	—	2	4	no	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	3	4	no	—
195	C₂³×C₅	—	4	8	no	—
196	C₂³×C₅	—	4	16	no	—
197	C₂³×C₅	—	6	8	no	—
198	C₂³×C₅	—	6	4	no	—
199	C₂³×C₅	—	6	8	no	—
200	C₂³×C₅	—	12	8	no	—
201	C₂³×C₅	—	12	16	no	—
202	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
203	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
204	C₂³×C₅	D₃×D₄	1	4	yes	—
205	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
206	C₅×D₄	—	6	32	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	8	no	—
209	C₂×C₄×C₅	—	3	16	no	—
210	C₂×C₄×C₅	—	3	4	no	—
211	C₂×C₄×C₅	—	3	4	no	—
212	C₂×C₄×C₅	—	3	4	no	—
213	C₂×C₄×C₅	—	6	4	no	—
214	C₂×C₄×C₅	—	6	8	no	—
215	C₂⁵	—	3	1	no	—
216	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
217	C₂²×D₄	—	3	8	no	—
218	C₂²×D₄	—	3	4	no	—
219	C₂²×D₄	—	6	8	no	—
220	C₂³×C₄	—	3	1	no	—
221	#117	—	6	8	no	—
222	C₂×C₄⋊C₄	—	3	4	no	—
223	C₂×C₂²⋊C₄	—	3	2	no	—
224	C₂×C₂²⋊C₄	—	3	4	no	—
225	C₂×C₂²⋊C₄	—	3	8	no	—
226	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
227	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	4	yes	complemented
228	C₂×C₄²	—	3	4	no	—
229	C₂×C₃×C₅	—	2	4	no	—
230	C₂×C₃×C₅	—	4	4	no	—
231	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₅	#518	1	2	yes	—
233	C₂×C₃×C₅	#535	1	4	yes	—
234	C₅×D₃	—	4	4	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	2	8	no	—
237	C₂³×C₃	—	2	4	no	—
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	4	8	no	—
241	C₂³×C₃	—	4	16	no	—
242	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
243	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
244	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
245	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
246	C₂²×D₃	—	2	8	no	—
247	C₂²×D₃	—	2	4	no	—
248	C₂²×D₃	—	2	8	no	—
249	C₂²×D₃	—	4	8	no	—
250	C₂²×D₃	—	4	16	no	—
251	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	8	no	—
254	#67	—	2	32	no	—
255	C₂×Dic₃	—	2	4	no	—
256	C₂×Dic₃	—	2	8	no	—
257	C₂×Dic₃	C₅×C₂²⋊C₄	1	16	yes	complemented
258	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
259	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
260	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
261	C₂²×C₅	—	2	4	no	—
262	C₂²×C₅	—	2	8	no	—
263	C₂²×C₅	—	2	4	no	—
264	C₂²×C₅	—	2	4	no	—
265	C₂²×C₅	—	2	4	no	—
266	C₂²×C₅	—	4	16	no	—
267	C₂²×C₅	—	4	8	no	—
268	C₂²×C₅	—	6	4	no	—
269	C₂²×C₅	—	6	8	no	—
270	C₂²×C₅	—	12	16	no	—
271	C₂²×C₅	—	12	8	no	—
272	C₂²×C₅	D₃×C₂²⋊C₄	1	4	yes	—
273	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
274	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
275	C₂²×C₅	#1004	1	4	yes	—
276	C₄×C₅	—	3	8	no	—
277	C₄×C₅	—	4	4	no	—
278	C₄×C₅	—	12	4	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	3	2	no	—
281	C₂⁴	—	3	4	no	—
282	C₂⁴	—	4	4	no	—
283	C₂⁴	—	6	4	no	—
284	C₂⁴	—	12	4	no	—
285	C₂⁴	C₄×C₅×D₃	1	4	yes	—
286	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
287	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
288	C₂×D₄	—	3	16	no	—
289	C₂×D₄	—	6	32	no	—
290	C₂×D₄	—	6	8	no	—
291	C₂×D₄	—	6	8	no	—
292	C₂²×C₄	—	3	4	no	—
293	C₂²×C₄	—	3	8	no	—
294	C₂²×C₄	—	3	2	no	—
295	C₂²×C₄	—	3	4	no	—
296	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
297	C₄⋊C₄	—	6	8	no	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	6	4	no	—
301	C₂²⋊C₄	—	12	8	no	—
302	C₂²⋊C₄	—	12	4	no	—
303	C₄²	—	6	8	no	—
304	C₃×C₅	#2309	1	1	yes	characteristic, complemented, Hall
305	C₂²×C₃	—	2	4	no	—
306	C₂²×C₃	—	2	8	no	—
307	C₂²×C₃	—	2	4	no	—
308	C₂²×C₃	—	2	4	no	—
309	C₂²×C₃	—	2	4	no	—
310	C₂²×C₃	—	4	16	no	—
311	C₂²×C₃	—	4	8	no	—
312	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
313	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
314	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
315	C₂²×C₃	C₅×H(5,𝔽₂)	1	4	yes	—
316	C₂×D₃	—	2	4	no	—
317	C₂×D₃	—	2	8	no	—
318	C₂×D₃	—	4	16	no	—
319	C₂×D₃	—	4	8	no	—
320	C₃×C₄	—	4	4	no	—
321	Dic₃	—	4	4	no	—
322	Dic₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
323	C₂×C₅	—	2	4	no	—
324	C₂×C₅	—	4	4	no	—
325	C₂×C₅	—	12	4	no	—
326	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
327	C₂×C₅	#5486	1	2	yes	—
328	C₂×C₅	#5592	1	4	yes	—
329	C₂³	—	2	4	no	—
330	C₂³	—	2	8	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	3	4	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	4	16	no	—
337	C₂³	—	6	8	no	—
338	C₂³	—	6	4	no	—
339	C₂³	—	6	8	no	—
340	C₂³	—	12	8	no	—
341	C₂³	—	12	16	no	—
342	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
343	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
344	C₂³	C₅×D₃×D₄	1	4	yes	—
345	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
346	D₄	—	6	32	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	3	16	no	—
350	C₂×C₄	—	3	4	no	—
351	C₂×C₄	—	3	4	no	—
352	C₂×C₄	—	3	4	no	—
353	C₂×C₄	—	6	4	no	—
354	C₂×C₄	—	6	8	no	—
355	C₂×C₃	—	2	4	no	—
356	C₂×C₃	—	4	4	no	—
357	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
358	C₂×C₃	C₅×#518	1	2	yes	—
359	C₂×C₃	C₅×#535	1	4	yes	—
360	D₃	—	4	4	no	—
361	C₅	#73819	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	—	2	4	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	4	16	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	6	4	no	—
370	C₂²	—	6	8	no	—
371	C₂²	—	12	16	no	—
372	C₂²	—	12	8	no	—
373	C₂²	C₅×D₃×C₂²⋊C₄	1	4	yes	—
374	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
375	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
376	C₂²	C₅×#1004	1	4	yes	—
377	C₄	—	3	8	no	—
378	C₄	—	4	4	no	—
379	C₄	—	12	4	no	—
380	C₃	C₅×#2309	1	1	yes	characteristic, complemented, Sylow
381	C₂	—	2	4	no	—
382	C₂	—	4	4	no	—
383	C₂	—	12	4	no	—
384	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
385	C₂	C₅×#5486	1	2	yes	—
386	C₂	C₅×#5592	1	4	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	C₂³×C₅×#67	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#379	D₃
hypocenter	C₃	C₅×#2309
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. C₂×C₅×#877	C₂	semidirect
3. C₃×C₅×#379	C₂	semidirect
4. C₅×#5247	C₂	semidirect
5. C₅×#4957	C₂	semidirect
6. C₅×#4955	C₂	semidirect
11. C₂²×C₅×#67	C₄	semidirect
15. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
17. C₂×C₅×#217	C₂²	semidirect
18. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
19. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
20. C₂×C₄×C₅×Dic₃	C₂²	semidirect
22. #73819	C₅	direct (N × H)
28. C₅×#379	D₃	semidirect
55. C₂×#877	C₂×C₅	semidirect
56. C₃×#379	C₂×C₅	semidirect
57. #5247	C₂×C₅	semidirect
58. #4957	C₂×C₅	semidirect
59. #4955	C₂×C₅	semidirect
72. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
97. C₂×C₅×Dic₃	C₂²⋊C₄	semidirect
104. C₂²×#67	C₄×C₅	semidirect
108. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
110. C₂×#217	C₂²×C₅	semidirect
111. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
112. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
113. C₂×C₄×Dic₃	C₂²×C₅	semidirect
145. #379	C₅×D₃	semidirect
227. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
257. C₂×Dic₃	C₅×C₂²⋊C₄	semidirect
304. C₃×C₅	#2309	semidirect
361. C₅	#73819	direct (N × H)
380. C₃	C₅×#2309	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₅×#67	2
C₂×C₅×#877	2
C₃×C₅×#379	2
C₅×#5247	2
C₅×#4957	2
C₅×#4955	2
C₅×#2309	3
#73819	5

Subgroups — C5×#73819 #14322431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73819 #14322431