Subgroups — C₅×#22227 #11944947

Order 1280.

774 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#488	C₂	1	1	yes	maximal, characteristic
2	C₅×#2330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2326	C₂	1	1	yes	maximal, characteristic
4	C₅×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1959	C₂	1	1	yes	maximal, characteristic
6	C₅×#1927	C₂	1	2	yes	maximal, complemented
7	C₅×#1926	C₂	1	2	yes	maximal
8	C₅×#1865	C₂	1	2	yes	maximal, complemented
9	C₅×#1864	C₂	1	2	yes	maximal
10	C₅×#1844	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#125	C₂²	1	1	yes	characteristic
13	C₂×C₅×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₅×#488	C₄	1	8	yes	complemented
17	C₂×C₅×#106	C₂²	1	2	yes	—
18	C₂×C₅×#106	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#102	C₂²	1	2	yes	—
22	C₂×C₅×#102	C₂²	1	2	yes	—
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#391	C₂²	1	1	yes	characteristic
26	C₅×#390	C₂²	1	1	yes	characteristic
27	C₅×#389	—	2	2	no	—
28	C₅×#389	C₂²	1	2	yes	—
29	C₅×#388	—	2	2	no	—
30	C₅×#387	—	2	2	no	—
31	C₅×#385	—	2	2	no	—
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
35	C₅×#376	C₂²	1	1	yes	characteristic
36	C₅×#340	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	#22227	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
42	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₅	—	2	1	no	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₅×#125	—	2	2	no	—
47	C₅×#125	C₂×C₄	1	4	yes	complemented
48	C₅×#124	—	2	2	no	—
49	C₅×#124	C₂×C₄	1	4	yes	—
50	C₄×C₅×Q₈	—	4	2	no	—
51	C₄×C₅×D₄	—	4	2	no	—
52	C₂×C₅×C₄⋊C₄	—	2	2	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	—	2	2	no	—
57	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	—	2	2	no	—
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#106	—	4	2	no	—
70	C₅×#106	—	4	2	no	—
71	C₅×#103	—	4	2	no	—
72	C₅×#103	C₂×C₄	1	8	yes	complemented
73	C₅×#102	—	4	2	no	—
74	C₅×#102	C₂×C₄	1	8	yes	—
75	C₅×#97	—	2	2	no	—
76	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
77	C₅×#95	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₅×#95	—	2	2	no	—
80	C₅×#95	D₄	1	2	yes	—
81	C₅×#95	D₄	1	2	yes	—
82	C₂×#488	C₂×C₅	1	1	yes	characteristic
83	#2330	C₂×C₅	1	1	yes	characteristic, complemented
84	#2326	C₂×C₅	1	1	yes	characteristic
85	#1992	C₂×C₅	1	1	yes	characteristic, complemented
86	#1959	C₂×C₅	1	1	yes	characteristic
87	#1927	C₂×C₅	1	2	yes	complemented
88	#1926	C₂×C₅	1	2	yes	—
89	#1865	C₂×C₅	1	2	yes	complemented
90	#1864	C₂×C₅	1	2	yes	—
91	#1844	C₂×C₅	1	1	yes	characteristic, complemented
92	#1746	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂⁴×C₅	—	2	1	no	—
94	C₂×C₅×Q₈	—	2	1	no	—
95	C₂×C₅×Q₈	—	2	2	no	—
96	C₂×C₅×Q₈	—	2	2	no	—
97	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
98	C₂×C₅×D₄	—	2	1	no	—
99	C₂×C₅×D₄	—	2	2	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	—	2	1	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	1	no	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	1	no	—
107	C₂²×C₄×C₅	—	4	2	no	—
108	C₂²×C₄×C₅	—	8	2	no	—
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
120	C₅×C₄⋊C₄	—	2	8	no	—
121	C₅×C₄⋊C₄	—	2	2	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	2	no	—
124	C₅×C₄⋊C₄	—	2	2	no	—
125	C₅×C₄⋊C₄	—	2	2	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₄⋊C₄	—	8	2	no	—
128	C₅×C₄⋊C₄	—	8	2	no	—
129	C₅×C₄⋊C₄	—	8	2	no	—
130	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
131	C₅×C₂²⋊C₄	—	2	8	no	—
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₅×C₂²⋊C₄	—	8	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	4	2	no	—
137	C₄²×C₅	—	8	2	no	—
138	C₄²×C₅	C₂²×C₄	1	2	yes	—
139	C₄²×C₅	#41	1	2	yes	—
140	C₂×#125	C₂²×C₅	1	1	yes	characteristic
141	C₂×#124	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
144	#488	C₄×C₅	1	8	yes	complemented
145	C₂×#106	C₂²×C₅	1	2	yes	—
146	C₂×#106	C₂²×C₅	1	2	yes	—
147	C₂×#103	C₂²×C₅	1	2	yes	—
148	C₂×#103	C₂²×C₅	1	2	yes	—
149	C₂×#102	C₂²×C₅	1	2	yes	—
150	C₂×#102	C₂²×C₅	1	2	yes	—
151	C₂×#97	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
153	#391	C₂²×C₅	1	1	yes	characteristic
154	#390	C₂²×C₅	1	1	yes	characteristic
155	#389	—	2	2	no	—
156	#389	C₂²×C₅	1	2	yes	—
157	#388	—	2	2	no	—
158	#387	—	2	2	no	—
159	#385	—	2	2	no	—
160	#384	C₂²×C₅	1	1	yes	characteristic
161	#384	C₂²×C₅	1	1	yes	characteristic
162	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
163	#376	C₂²×C₅	1	1	yes	characteristic
164	#340	C₂²×C₅	1	2	yes	—
165	#340	C₂²×C₅	1	2	yes	—
166	#336	C₂²×C₅	1	2	yes	—
167	#336	C₂²×C₅	1	2	yes	—
168	C₂³×C₅	—	2	2	no	—
169	C₂³×C₅	—	4	1	no	—
170	C₂³×C₅	—	4	1	no	—
171	C₂³×C₅	—	4	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₅×Q₈	—	2	4	no	—
175	C₅×Q₈	—	4	2	no	—
176	C₅×D₄	—	2	4	no	—
177	C₅×D₄	—	4	2	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	4	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	4	1	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	8	4	no	—
201	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
202	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
205	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
206	C₅×C₈	—	2	4	no	—
207	C₅×C₈	—	4	2	no	—
208	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
209	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
210	C₂³×C₄	—	2	1	no	—
211	C₂²×C₈	C₂³×C₅	1	2	yes	—
212	C₂²×C₈	C₂³×C₅	1	2	yes	—
213	#125	—	2	2	no	—
214	#125	C₂×C₄×C₅	1	4	yes	complemented
215	#124	—	2	2	no	—
216	#124	C₂×C₄×C₅	1	4	yes	—
217	C₄×Q₈	—	4	2	no	—
218	C₄×D₄	—	4	2	no	—
219	C₂×C₄⋊C₄	—	2	2	no	—
220	C₂×C₄⋊C₄	—	2	1	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
236	#106	—	4	2	no	—
237	#106	—	4	2	no	—
238	#103	—	4	2	no	—
239	#103	C₂×C₄×C₅	1	8	yes	complemented
240	#102	—	4	2	no	—
241	#102	C₂×C₄×C₅	1	8	yes	—
242	#97	—	2	2	no	—
243	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	#95	C₅×D₄	1	2	yes	—
248	#95	C₅×D₄	1	2	yes	—
249	C₂²×C₅	—	4	2	no	—
250	C₂²×C₅	—	4	4	no	—
251	C₂²×C₅	—	8	1	no	—
252	C₂²×C₅	—	8	1	no	—
253	C₂²×C₅	—	8	2	no	—
254	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
255	C₂²×C₅	#535	1	1	yes	characteristic
256	C₂²×C₅	#536	1	1	yes	characteristic
257	C₂²×C₅	#577	1	2	yes	—
258	C₂²×C₅	#577	1	2	yes	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	—	4	2	no	—
261	C₄×C₅	—	4	4	no	—
262	C₄×C₅	—	4	1	no	—
263	C₄×C₅	—	4	1	no	—
264	C₄×C₅	—	4	2	no	—
265	C₄×C₅	—	8	2	no	—
266	C₄×C₅	—	8	1	no	—
267	C₄×C₅	—	8	1	no	—
268	C₄×C₅	#520	1	2	yes	—
269	C₄×C₅	#542	1	2	yes	—
270	C₂⁴	—	2	1	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	8	2	no	—
286	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
287	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	8	2	no	—
305	C₄⋊C₄	—	8	2	no	—
306	C₄⋊C₄	—	8	2	no	—
307	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	8	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	4	2	no	—
314	C₄²	—	8	2	no	—
315	C₄²	C₂²×C₄×C₅	1	2	yes	—
316	C₄²	C₅×#41	1	2	yes	—
317	C₂×C₅	—	8	2	no	—
318	C₂×C₅	#2326	1	1	yes	characteristic
319	C₂×C₅	#2952	1	2	yes	—
320	C₂×C₅	#3221	1	1	yes	characteristic
321	C₂×C₅	#3222	1	1	yes	characteristic
322	C₂×C₅	#3244	1	2	yes	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	4	1	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
329	Q₈	—	2	4	no	—
330	Q₈	—	4	2	no	—
331	D₄	—	2	4	no	—
332	D₄	—	4	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
357	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
358	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
359	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₅	#22227	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²	—	4	2	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
370	C₂²	C₅×#535	1	1	yes	characteristic
371	C₂²	C₅×#536	1	1	yes	characteristic
372	C₂²	C₅×#577	1	2	yes	—
373	C₂²	C₅×#577	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	4	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	1	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	1	no	—
383	C₄	C₅×#520	1	2	yes	—
384	C₄	C₅×#542	1	2	yes	—
385	C₂	—	8	2	no	—
386	C₂	C₅×#2326	1	1	yes	characteristic
387	C₂	C₅×#2952	1	2	yes	—
388	C₂	C₅×#3221	1	1	yes	characteristic
389	C₂	C₅×#3222	1	1	yes	characteristic
390	C₂	C₅×#3244	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2330	C₂	semidirect
4. C₅×#1992	C₂	semidirect
6. C₅×#1927	C₂	semidirect
8. C₅×#1865	C₂	semidirect
10. C₅×#1844	C₂	semidirect
11. C₅×#1746	C₂	semidirect
16. C₅×#488	C₄	semidirect
40. #22227	C₅	direct (N × H)
47. C₅×#125	C₂×C₄	semidirect
72. C₅×#103	C₂×C₄	semidirect
76. C₄×C₅×C₈	C₂×C₄	semidirect
83. #2330	C₂×C₅	semidirect
85. #1992	C₂×C₅	semidirect
87. #1927	C₂×C₅	semidirect
89. #1865	C₂×C₅	semidirect
91. #1844	C₂×C₅	semidirect
92. #1746	C₂×C₅	semidirect
144. #488	C₄×C₅	semidirect
214. #125	C₂×C₄×C₅	semidirect
239. #103	C₂×C₄×C₅	semidirect
243. C₄×C₈	C₂×C₄×C₅	semidirect
363. C₅	#22227	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×#488	2
C₅×#2330	2
C₅×#2326	2
C₅×#1992	2
C₅×#1959	2
C₅×#1927	2
C₅×#1926	2
C₅×#1865	2
C₅×#1864	2
C₅×#1844	2
C₅×#1746	2
#22227	5

Subgroups — C5×#22227 #11944947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22227 #11944947