Subgroups — C₅×#72146 #14297270

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#585	C₂	1	1	yes	maximal, characteristic
2	C₅×#5240	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5236	C₂	1	2	yes	maximal, complemented
4	C₅×#5234	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5233	C₂	1	2	yes	maximal, complemented
6	C₅×#1794	—	3	1	no	maximal, Hall
7	C₃×C₅×2₋¹⁺⁴	—	2	2	no	—
8	C₃×C₅×2₋¹⁺⁴	C₄	1	2	yes	complemented
9	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
10	C₃×C₅×H(5,𝔽₂)	—	2	2	no	—
11	C₃×C₅×H(5,𝔽₂)	C₄	1	2	yes	complemented
12	C₂×C₃×C₅×#41	—	2	4	no	—
13	C₂×C₃×C₅×#41	—	2	2	no	—
14	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
15	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#926	C₂²	1	2	yes	complemented
17	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
19	C₅×#837	—	2	4	no	—
20	C₅×#835	—	2	2	no	—
21	C₅×#834	—	2	2	no	—
22	C₅×#832	—	2	2	no	—
23	C₅×#830	—	2	2	no	—
24	#72146	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₅×#585	D₃	1	1	yes	characteristic
26	C₅×#421	—	3	2	no	—
27	C₅×#416	—	3	2	no	—
28	C₅×#410	—	3	1	no	—
29	C₅×#408	—	3	1	no	—
30	C₃×C₅×#41	—	2	4	no	—
31	C₃×C₅×#41	—	2	8	no	—
32	C₃×C₅×#41	—	2	4	no	—
33	C₃×C₅×#41	—	2	4	no	—
34	C₃×C₅×#41	—	2	4	no	—
35	C₃×C₅×#41	—	2	4	no	—
36	C₃×C₅×#41	—	2	2	no	—
37	C₃×C₅×#41	—	2	2	no	—
38	C₃×C₅×#41	—	2	2	no	—
39	C₃×C₅×#41	—	2	2	no	—
40	C₃×C₅×#41	C₂×C₄	1	4	yes	—
41	C₃×C₅×#41	D₄	1	4	yes	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	8	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	—	2	4	no	—
49	C₂×C₃×C₅×D₄	—	2	2	no	—
50	C₂×C₃×C₅×D₄	—	2	4	no	—
51	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
53	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	4	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₅×#217	—	2	2	no	—
59	C₅×C₄⋊Dic₃	—	2	2	no	—
60	C₄×C₅×Dic₃	—	2	2	no	—
61	C₅×#208	—	2	2	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	2	no	—
64	C₂×C₅×C₃⋊C₈	—	2	1	no	—
65	C₃×#585	C₂×C₅	1	1	yes	characteristic
66	#5240	C₂×C₅	1	1	yes	characteristic, complemented
67	#5236	C₂×C₅	1	2	yes	complemented
68	#5234	C₂×C₅	1	1	yes	characteristic, complemented
69	#5233	C₂×C₅	1	2	yes	complemented
70	C₅×2₋¹⁺⁴	—	2	2	no	—
71	C₅×2₋¹⁺⁴	Dic₃	1	2	yes	complemented
72	C₅×H(5,𝔽₂)	—	2	2	no	—
73	C₅×H(5,𝔽₂)	—	2	2	no	—
74	C₅×H(5,𝔽₂)	Dic₃	1	2	yes	complemented
75	C₂×C₅×#41	—	2	4	no	—
76	C₂×C₅×#41	—	2	2	no	—
77	C₂×C₅×#41	C₂×D₃	1	2	yes	—
78	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	—	3	1	no	—
80	C₂²×C₅×C₈	—	3	1	no	—
81	C₅×#117	—	3	2	no	—
82	C₅×#104	—	6	4	no	—
83	C₅×#103	—	6	2	no	—
84	C₅×#102	—	6	2	no	—
85	C₅×#99	—	6	2	no	—
86	C₅×C₂²⋊C₈	—	6	2	no	—
87	#1794	—	3	1	no	Sylow
88	C₂³×C₃×C₅	—	2	4	no	—
89	C₂³×C₃×C₅	—	2	2	no	—
90	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
91	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
92	C₃×C₅×Q₈	—	2	4	no	—
93	C₃×C₅×Q₈	—	2	2	no	—
94	C₃×C₅×Q₈	—	2	2	no	—
95	C₃×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
96	C₃×C₅×D₄	—	2	8	no	—
97	C₃×C₅×D₄	—	2	4	no	—
98	C₃×C₅×D₄	—	2	4	no	—
99	C₃×C₅×D₄	—	2	4	no	—
100	C₃×C₅×D₄	—	2	4	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	C₂²⋊C₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	8	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂×C₅×Dic₃	—	4	2	no	—
117	C₅×C₃⋊C₈	—	4	1	no	—
118	C₅×C₃⋊C₈	—	4	1	no	—
119	C₃×2₋¹⁺⁴	—	2	2	no	—
120	C₃×2₋¹⁺⁴	C₄×C₅	1	2	yes	complemented
121	C₃×H(5,𝔽₂)	—	2	2	no	—
122	C₃×H(5,𝔽₂)	—	2	2	no	—
123	C₃×H(5,𝔽₂)	C₄×C₅	1	2	yes	complemented
124	C₂×C₃×#41	—	2	4	no	—
125	C₂×C₃×#41	—	2	2	no	—
126	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
127	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
128	#926	C₂²×C₅	1	2	yes	complemented
129	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
131	#837	—	2	4	no	—
132	#835	—	2	2	no	—
133	#834	—	2	2	no	—
134	#832	—	2	2	no	—
135	#830	—	2	2	no	—
136	C₅×#41	—	2	4	no	—
137	C₅×#41	—	2	8	no	—
138	C₅×#41	—	2	4	no	—
139	C₅×#41	—	2	4	no	—
140	C₅×#41	—	2	4	no	—
141	C₅×#41	—	2	4	no	—
142	C₅×#41	—	2	2	no	—
143	C₅×#41	—	2	2	no	—
144	C₅×#41	—	2	2	no	—
145	C₅×#41	—	2	2	no	—
146	C₅×#41	C₂×Dic₃	1	4	yes	—
147	C₅×#41	#67	1	4	yes	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	4	no	—
150	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
151	C₂×C₅×Q₈	#67	1	2	yes	—
152	C₂×C₅×D₄	—	2	8	no	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	—	2	2	no	—
156	C₂×C₅×D₄	—	2	4	no	—
157	C₂×C₅×D₄	C₂×Dic₃	1	1	yes	characteristic
158	C₂×C₅×D₄	#67	1	2	yes	—
159	C₂×C₅×D₄	#67	1	2	yes	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	2	2	no	—
162	C₂²×C₄×C₅	#67	1	2	yes	—
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₅×M₁₆	—	6	2	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₂×C₅×C₈	—	6	2	no	—
167	C₂×C₅×C₈	—	6	1	no	—
168	C₅×C₄⋊C₄	—	6	2	no	—
169	C₅×C₂²⋊C₄	—	6	2	no	—
170	C₄²×C₅	—	6	2	no	—
171	#585	C₅×D₃	1	1	yes	characteristic
172	#421	—	3	2	no	—
173	#416	—	3	2	no	—
174	#410	—	3	1	no	—
175	#408	—	3	1	no	—
176	C₂²×C₃×C₅	—	2	2	no	—
177	C₂²×C₃×C₅	—	2	4	no	—
178	C₂²×C₃×C₅	—	4	1	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	—	8	2	no	—
181	C₂²×C₃×C₅	—	8	4	no	—
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₃×C₅	#120	1	2	yes	—
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
187	C₃×C₄×C₅	#120	1	1	yes	characteristic
188	C₃×C₄×C₅	#120	1	1	yes	characteristic
189	C₅×Dic₃	—	8	2	no	—
190	C₃×#41	—	2	4	no	—
191	C₃×#41	—	2	8	no	—
192	C₃×#41	—	2	4	no	—
193	C₃×#41	—	2	4	no	—
194	C₃×#41	—	2	4	no	—
195	C₃×#41	—	2	4	no	—
196	C₃×#41	—	2	2	no	—
197	C₃×#41	—	2	2	no	—
198	C₃×#41	—	2	2	no	—
199	C₃×#41	—	2	2	no	—
200	C₃×#41	C₂×C₄×C₅	1	4	yes	—
201	C₃×#41	C₅×D₄	1	4	yes	—
202	C₂×C₃×Q₈	—	2	2	no	—
203	C₂×C₃×Q₈	—	2	4	no	—
204	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
206	C₂×C₃×D₄	—	2	8	no	—
207	C₂×C₃×D₄	—	2	2	no	—
208	C₂×C₃×D₄	—	2	4	no	—
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	—	2	4	no	—
211	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
213	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
214	C₂²×C₃×C₄	—	2	4	no	—
215	C₂²×C₃×C₄	—	2	2	no	—
216	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
218	#217	—	2	2	no	—
219	C₄⋊Dic₃	—	2	2	no	—
220	C₄×Dic₃	—	2	2	no	—
221	#208	—	2	2	no	—
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂×C₃⋊C₈	—	2	1	no	—
224	C₂×C₃⋊C₈	—	2	2	no	—
225	C₂³×C₅	—	2	4	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	#217	1	2	yes	—
228	C₂³×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×Q₈	—	2	4	no	—
230	C₅×Q₈	—	2	2	no	—
231	C₅×Q₈	—	2	2	no	—
232	C₅×Q₈	#217	1	4	yes	—
233	C₅×D₄	—	2	8	no	—
234	C₅×D₄	—	2	4	no	—
235	C₅×D₄	—	2	4	no	—
236	C₅×D₄	—	2	4	no	—
237	C₅×D₄	—	2	4	no	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	2	2	no	—
240	C₅×D₄	#217	1	4	yes	—
241	C₂×C₄×C₅	—	2	4	no	—
242	C₂×C₄×C₅	—	2	8	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	4	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	12	2	no	—
249	C₂×C₄×C₅	#217	1	2	yes	—
250	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×#67	1	2	yes	—
252	C₂×C₄×C₅	C₂×#67	1	2	yes	—
253	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
254	C₅×C₈	—	12	1	no	—
255	C₅×C₈	—	12	1	no	—
256	2₋¹⁺⁴	—	2	2	no	—
257	2₋¹⁺⁴	C₅×Dic₃	1	2	yes	complemented
258	H(5,𝔽₂)	—	2	2	no	—
259	H(5,𝔽₂)	—	2	2	no	—
260	H(5,𝔽₂)	C₅×Dic₃	1	2	yes	complemented
261	C₂×#41	—	2	4	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	C₂×C₅×D₃	1	2	yes	—
264	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂×M₁₆	—	3	1	no	—
266	C₂²×C₈	—	3	1	no	—
267	#117	—	3	2	no	—
268	#104	—	6	4	no	—
269	#103	—	6	2	no	—
270	#102	—	6	2	no	—
271	#99	—	6	2	no	—
272	C₂²⋊C₈	—	6	2	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	4	2	no	—
276	C₂×C₃×C₅	—	4	4	no	—
277	C₂×C₃×C₅	#379	1	1	yes	characteristic
278	C₂³×C₃	—	2	4	no	—
279	C₂³×C₃	—	2	2	no	—
280	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
281	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
282	C₃×Q₈	—	2	4	no	—
283	C₃×Q₈	—	2	2	no	—
284	C₃×Q₈	—	2	2	no	—
285	C₃×Q₈	C₅×C₂²⋊C₄	1	4	yes	—
286	C₃×D₄	—	2	8	no	—
287	C₃×D₄	—	2	4	no	—
288	C₃×D₄	—	2	4	no	—
289	C₃×D₄	—	2	4	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	C₅×C₂²⋊C₄	1	4	yes	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	8	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×Dic₃	—	4	2	no	—
307	C₃⋊C₈	—	4	1	no	—
308	C₃⋊C₈	—	4	1	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	2	4	no	—
311	C₂²×C₅	—	4	1	no	—
312	C₂²×C₅	—	4	2	no	—
313	C₂²×C₅	—	8	2	no	—
314	C₂²×C₅	—	8	4	no	—
315	C₂²×C₅	C₂×#217	1	1	yes	characteristic
316	C₂²×C₅	#953	1	2	yes	—
317	C₄×C₅	—	2	4	no	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	24	2	no	—
320	C₄×C₅	C₂×#217	1	2	yes	—
321	C₄×C₅	#953	1	1	yes	characteristic
322	C₄×C₅	#953	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	2	8	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	C₂×C₅×Dic₃	1	4	yes	—
334	#41	C₅×#67	1	4	yes	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	C₂×C₅×Dic₃	1	1	yes	characteristic
338	C₂×Q₈	C₅×#67	1	2	yes	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	4	no	—
344	C₂×D₄	C₂×C₅×Dic₃	1	1	yes	characteristic
345	C₂×D₄	C₅×#67	1	2	yes	—
346	C₂×D₄	C₅×#67	1	2	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₅×#67	1	2	yes	—
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	M₁₆	—	6	2	no	—
352	C₂×C₈	—	6	1	no	—
353	C₂×C₈	—	6	1	no	—
354	C₂×C₈	—	6	2	no	—
355	C₄⋊C₄	—	6	2	no	—
356	C₂²⋊C₄	—	6	2	no	—
357	C₄²	—	6	2	no	—
358	C₃×C₅	#1794	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	2	4	no	—
361	C₂²×C₃	—	4	1	no	—
362	C₂²×C₃	—	4	2	no	—
363	C₂²×C₃	—	8	2	no	—
364	C₂²×C₃	—	8	4	no	—
365	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₂²×C₃	C₅×#120	1	2	yes	—
367	C₃×C₄	—	2	4	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
370	C₃×C₄	C₅×#120	1	1	yes	characteristic
371	C₃×C₄	C₅×#120	1	1	yes	characteristic
372	Dic₃	—	8	2	no	—
373	C₂×C₅	—	2	2	no	—
374	C₂×C₅	—	2	1	no	—
375	C₂×C₅	—	4	2	no	—
376	C₂×C₅	—	4	4	no	—
377	C₂×C₅	#5247	1	1	yes	characteristic
378	C₂³	—	2	4	no	—
379	C₂³	—	2	2	no	—
380	C₂³	C₅×#217	1	2	yes	—
381	C₂³	C₂×C₅×#67	1	1	yes	characteristic
382	Q₈	—	2	4	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	C₅×#217	1	4	yes	—
386	D₄	—	2	8	no	—
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	C₅×#217	1	4	yes	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	12	2	no	—
402	C₂×C₄	C₅×#217	1	2	yes	—
403	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
404	C₂×C₄	C₂×C₅×#67	1	2	yes	—
405	C₂×C₄	C₂×C₅×#67	1	2	yes	—
406	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
407	C₈	—	12	1	no	—
408	C₈	—	12	1	no	—
409	C₂×C₃	—	2	2	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	4	2	no	—
412	C₂×C₃	—	4	4	no	—
413	C₂×C₃	C₅×#379	1	1	yes	characteristic
414	C₅	#72146	1	1	yes	characteristic, direct product factor, Sylow
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	4	no	—
421	C₂²	C₂×C₅×#217	1	1	yes	characteristic
422	C₂²	C₅×#953	1	2	yes	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	24	2	no	—
426	C₄	C₂×C₅×#217	1	2	yes	—
427	C₄	C₅×#953	1	1	yes	characteristic
428	C₄	C₅×#953	1	1	yes	characteristic
429	C₃	C₅×#1794	1	1	yes	characteristic, complemented, Sylow
430	C₂	—	2	2	no	—
431	C₂	—	2	1	no	—
432	C₂	—	4	2	no	—
433	C₂	—	4	4	no	—
434	C₂	C₅×#5247	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#953
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₃×C₅×#585	C₂
socle	C₂×C₃×C₅	#379
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#585	D₃
hypocenter	C₃	C₅×#1794
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#585

Complements

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

N	H ≅ G/N	type
2. C₅×#5240	C₂	semidirect
3. C₅×#5236	C₂	semidirect
4. C₅×#5234	C₂	semidirect
5. C₅×#5233	C₂	semidirect
8. C₃×C₅×2₋¹⁺⁴	C₄	semidirect
11. C₃×C₅×H(5,𝔽₂)	C₄	semidirect
16. C₅×#926	C₂²	semidirect
17. C₂×C₅×#208	C₂²	semidirect
18. C₂²×C₅×C₃⋊C₈	C₂²	semidirect
24. #72146	C₅	direct (N × H)
66. #5240	C₂×C₅	semidirect
67. #5236	C₂×C₅	semidirect
68. #5234	C₂×C₅	semidirect
69. #5233	C₂×C₅	semidirect
71. C₅×2₋¹⁺⁴	Dic₃	semidirect
74. C₅×H(5,𝔽₂)	Dic₃	semidirect
120. C₃×2₋¹⁺⁴	C₄×C₅	semidirect
123. C₃×H(5,𝔽₂)	C₄×C₅	semidirect
128. #926	C₂²×C₅	semidirect
129. C₂×#208	C₂²×C₅	semidirect
130. C₂²×C₃⋊C₈	C₂²×C₅	semidirect
257. 2₋¹⁺⁴	C₅×Dic₃	semidirect
260. H(5,𝔽₂)	C₅×Dic₃	semidirect
358. C₃×C₅	#1794	semidirect
414. C₅	#72146	direct (N × H)
429. C₃	C₅×#1794	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#585	2
C₅×#5240	2
C₅×#5236	2
C₅×#5234	2
C₅×#5233	2
C₅×#1794	3
#72146	5

Subgroups — C5×#72146 #14297270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#72146 #14297270