Subgroups — C₅×#71910 #14289094

Order 1920.

512 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5088	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1625	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₅×#123	—	2	2	no	—
12	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
13	C₃×C₅×#121	—	2	1	no	—
14	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
17	C₂×C₅×#213	—	2	1	no	—
18	C₂×C₅×#213	—	2	1	no	—
19	C₅×#874	C₂²	1	1	yes	characteristic
20	C₅×#809	—	2	1	no	—
21	C₅×#809	—	2	1	no	—
22	C₅×#809	—	2	2	no	—
23	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
26	#71910	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#547	D₃	1	1	yes	characteristic, complemented
28	C₅×#486	—	3	1	no	—
29	C₅×#459	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₃×C₅×#41	—	4	2	no	—
35	C₃×C₅×#41	—	4	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
39	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	—	2	2	no	—
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₅×#213	—	4	2	no	—
56	C₅×#213	—	4	2	no	—
57	C₂×C₅×C₃⋊C₈	—	2	1	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₃×#547	C₂×C₅	1	1	yes	characteristic, complemented
61	#5088	C₂×C₅	1	1	yes	characteristic, complemented
62	#5015	C₂×C₅	1	1	yes	characteristic, complemented
63	#5015	C₂×C₅	1	1	yes	characteristic, complemented
64	#4547	C₂×C₅	1	1	yes	characteristic, complemented
65	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
66	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
67	C₂×C₅×#41	—	2	1	no	—
68	C₂×C₅×D₈	—	6	1	no	—
69	C₂×C₅×D₈	—	6	1	no	—
70	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
71	C₅×#127	—	3	1	no	—
72	C₅×#123	—	2	2	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₅×C₄⋊C₈	—	3	1	no	—
79	C₅×C₄⋊C₈	—	3	1	no	—
80	C₅×#102	—	6	1	no	—
81	C₅×#102	—	6	1	no	—
82	C₅×#102	—	6	2	no	—
83	C₄×C₅×C₈	—	3	1	no	—
84	#1625	—	3	1	no	Sylow
85	C₂³×C₃×C₅	—	2	1	no	—
86	C₂³×C₃×C₅	—	2	1	no	—
87	C₂²×C₅×D₃	—	4	1	no	—
88	C₃×C₅×Q₈	—	4	1	no	—
89	C₃×C₅×Q₈	—	4	1	no	—
90	C₃×C₅×D₄	—	2	1	no	—
91	C₃×C₅×D₄	—	2	1	no	—
92	C₃×C₅×D₄	—	2	1	no	—
93	C₃×C₅×D₄	—	4	4	no	—
94	C₃×C₅×D₄	D₈	1	2	yes	complemented
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	4	4	no	—
99	C₂×C₃×C₄×C₅	—	4	1	no	—
100	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	—	4	1	no	—
102	C₂×C₃×C₄×C₅	—	4	1	no	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₅×D₁₂	—	4	2	no	—
107	C₅×D₁₂	—	4	1	no	—
108	C₅×D₁₂	—	4	1	no	—
109	C₅×D₁₂	—	4	1	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₅×C₃⋊C₈	—	4	1	no	—
112	C₅×C₃⋊C₈	—	4	1	no	—
113	C₅×C₃⋊C₈	—	4	1	no	—
114	C₂×C₃×#41	—	2	1	no	—
115	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
116	C₃×#123	—	2	2	no	—
117	C₃×C₂²⋊Q₈	—	2	1	no	—
118	C₃×#121	—	2	1	no	—
119	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
120	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	—	2	1	no	—
122	C₂×#213	—	2	1	no	—
123	C₂×#213	—	2	1	no	—
124	#874	C₂²×C₅	1	1	yes	characteristic
125	#809	—	2	1	no	—
126	#809	—	2	1	no	—
127	#809	—	2	2	no	—
128	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
129	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
130	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
131	C₅×#41	—	4	2	no	—
132	C₅×#41	—	4	2	no	—
133	C₂×C₅×Q₈	—	2	1	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	6	1	no	—
136	C₂×C₅×D₄	—	6	1	no	—
137	C₂×C₅×D₄	—	6	1	no	—
138	C₂×C₅×D₄	#67	1	1	yes	characteristic
139	C₂×C₅×D₄	#67	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₅×D₈	—	12	2	no	—
144	C₅×D₈	—	12	2	no	—
145	C₂×C₅×C₈	—	6	1	no	—
146	C₂×C₅×C₈	—	6	1	no	—
147	C₂×C₅×C₈	—	6	1	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
151	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
152	C₅×C₄⋊C₄	#67	1	2	yes	—
153	C₅×C₂²⋊C₄	—	2	2	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
157	#547	C₅×D₃	1	1	yes	characteristic, complemented
158	#486	—	3	1	no	—
159	#459	—	3	1	no	—
160	#459	—	3	1	no	—
161	#332	—	3	1	no	—
162	D₄⋊C₈	—	3	1	no	—
163	D₄⋊C₈	—	3	1	no	—
164	C₂²×C₃×C₅	—	2	2	no	—
165	C₂²×C₃×C₅	—	4	1	no	—
166	C₂²×C₃×C₅	—	4	1	no	—
167	C₂²×C₃×C₅	—	4	1	no	—
168	C₂²×C₃×C₅	—	4	1	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	#120	1	1	yes	characteristic
171	C₂×C₅×D₃	—	8	1	no	—
172	C₂×C₅×D₃	—	8	1	no	—
173	C₂×C₅×D₃	—	8	1	no	—
174	C₃×C₄×C₅	—	2	1	no	—
175	C₃×C₄×C₅	—	4	1	no	—
176	C₃×C₄×C₅	—	4	2	no	—
177	C₃×C₄×C₅	—	4	1	no	—
178	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
179	C₃×C₄×C₅	#135	1	1	yes	characteristic
180	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₃×#41	—	4	2	no	—
183	C₃×#41	—	4	2	no	—
184	C₂×C₃×Q₈	—	2	1	no	—
185	C₂×C₃×D₄	—	2	2	no	—
186	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
187	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	2	1	no	—
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂×D₁₂	—	2	1	no	—
192	C₂×D₁₂	—	2	1	no	—
193	C₂×D₁₂	—	2	1	no	—
194	C₃×C₄⋊C₄	—	2	2	no	—
195	C₃×C₄⋊C₄	—	2	1	no	—
196	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
197	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
198	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
199	C₃×C₂²⋊C₄	—	2	2	no	—
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₂²⋊C₄	—	2	1	no	—
202	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
203	#213	—	4	2	no	—
204	#213	—	4	2	no	—
205	C₂×C₃⋊C₈	—	2	1	no	—
206	C₂×C₃⋊C₈	—	2	1	no	—
207	C₂×C₃⋊C₈	—	2	1	no	—
208	C₂³×C₅	—	2	1	no	—
209	C₂³×C₅	—	2	1	no	—
210	C₂³×C₅	—	12	1	no	—
211	C₅×Q₈	—	4	1	no	—
212	C₅×Q₈	—	4	1	no	—
213	C₅×D₄	—	2	1	no	—
214	C₅×D₄	—	2	1	no	—
215	C₅×D₄	—	2	1	no	—
216	C₅×D₄	—	4	4	no	—
217	C₅×D₄	—	12	2	no	—
218	C₅×D₄	—	12	1	no	—
219	C₅×D₄	—	12	1	no	—
220	C₅×D₄	—	12	1	no	—
221	C₅×D₄	—	12	1	no	—
222	C₅×D₄	#213	1	2	yes	complemented
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	2	2	no	—
226	C₂×C₄×C₅	—	4	4	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
234	C₅×C₈	—	12	1	no	—
235	C₅×C₈	—	12	1	no	—
236	C₅×C₈	—	12	1	no	—
237	C₂×#41	—	2	1	no	—
238	C₂×D₈	—	6	1	no	—
239	C₂×D₈	—	6	1	no	—
240	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
241	#127	—	3	1	no	—
242	#123	—	2	2	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	#121	—	2	1	no	—
245	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
246	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₄⋊C₈	—	3	1	no	—
249	C₄⋊C₈	—	3	1	no	—
250	#102	—	6	1	no	—
251	#102	—	6	1	no	—
252	#102	—	6	2	no	—
253	C₄×C₈	—	3	1	no	—
254	C₂×C₃×C₅	—	4	2	no	—
255	C₂×C₃×C₅	—	8	1	no	—
256	C₂×C₃×C₅	#447	1	1	yes	characteristic
257	C₂×C₃×C₅	#449	1	1	yes	characteristic
258	C₂×C₃×C₅	#454	1	1	yes	characteristic
259	C₅×D₃	—	16	1	no	—
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	2	1	no	—
262	C₂²×D₃	—	4	1	no	—
263	C₃×Q₈	—	4	1	no	—
264	C₃×Q₈	—	4	1	no	—
265	C₃×D₄	—	2	1	no	—
266	C₃×D₄	—	2	1	no	—
267	C₃×D₄	—	2	1	no	—
268	C₃×D₄	—	4	4	no	—
269	C₃×D₄	C₅×D₈	1	2	yes	complemented
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	4	4	no	—
274	C₂×C₃×C₄	—	4	1	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	—	4	1	no	—
277	C₂×C₃×C₄	—	4	1	no	—
278	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	D₁₂	—	4	2	no	—
282	D₁₂	—	4	1	no	—
283	D₁₂	—	4	1	no	—
284	D₁₂	—	4	1	no	—
285	D₁₂	—	4	1	no	—
286	C₃⋊C₈	—	4	1	no	—
287	C₃⋊C₈	—	4	1	no	—
288	C₃⋊C₈	—	4	1	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	4	1	no	—
291	C₂²×C₅	—	4	1	no	—
292	C₂²×C₅	—	4	1	no	—
293	C₂²×C₅	—	4	1	no	—
294	C₂²×C₅	—	4	1	no	—
295	C₂²×C₅	—	24	1	no	—
296	C₂²×C₅	—	24	1	no	—
297	C₂²×C₅	—	24	1	no	—
298	C₂²×C₅	#953	1	1	yes	characteristic
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	4	1	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	4	1	no	—
303	C₄×C₅	C₂×#213	1	1	yes	characteristic
304	C₄×C₅	#932	1	1	yes	characteristic
305	C₄×C₅	#949	1	1	yes	characteristic
306	C₄×C₅	#950	1	1	yes	characteristic
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	6	1	no	—
312	C₂×D₄	—	6	1	no	—
313	C₂×D₄	—	6	1	no	—
314	C₂×D₄	C₅×#67	1	1	yes	characteristic
315	C₂×D₄	C₅×#67	1	1	yes	characteristic
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	D₈	—	12	2	no	—
320	D₈	—	12	2	no	—
321	C₂×C₈	—	6	1	no	—
322	C₂×C₈	—	6	1	no	—
323	C₂×C₈	—	6	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
327	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
328	C₄⋊C₄	C₅×#67	1	2	yes	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
333	C₃×C₅	#1625	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	4	1	no	—
336	C₂²×C₃	—	4	1	no	—
337	C₂²×C₃	—	4	1	no	—
338	C₂²×C₃	—	4	1	no	—
339	C₂²×C₃	—	4	1	no	—
340	C₂²×C₃	C₅×#120	1	1	yes	characteristic
341	C₂×D₃	—	8	1	no	—
342	C₂×D₃	—	8	1	no	—
343	C₂×D₃	—	8	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	4	1	no	—
346	C₃×C₄	—	4	2	no	—
347	C₃×C₄	—	4	1	no	—
348	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
349	C₃×C₄	C₅×#135	1	1	yes	characteristic
350	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂×C₅	—	4	2	no	—
353	C₂×C₅	—	8	1	no	—
354	C₂×C₅	—	48	1	no	—
355	C₂×C₅	#5217	1	1	yes	characteristic
356	C₂×C₅	#5238	1	1	yes	characteristic
357	C₂×C₅	#5245	1	1	yes	characteristic
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	12	1	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	4	4	no	—
367	D₄	—	12	2	no	—
368	D₄	—	12	1	no	—
369	D₄	—	12	1	no	—
370	D₄	—	12	1	no	—
371	D₄	—	12	1	no	—
372	D₄	C₅×#213	1	2	yes	complemented
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
382	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
383	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
384	C₈	—	12	1	no	—
385	C₈	—	12	1	no	—
386	C₈	—	12	1	no	—
387	C₂×C₃	—	4	2	no	—
388	C₂×C₃	—	8	1	no	—
389	C₂×C₃	C₅×#447	1	1	yes	characteristic
390	C₂×C₃	C₅×#449	1	1	yes	characteristic
391	C₂×C₃	C₅×#454	1	1	yes	characteristic
392	D₃	—	16	1	no	—
393	C₅	#71910	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	24	1	no	—
401	C₂²	—	24	1	no	—
402	C₂²	—	24	1	no	—
403	C₂²	C₅×#953	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	C₂×C₅×#213	1	1	yes	characteristic
409	C₄	C₅×#932	1	1	yes	characteristic
410	C₄	C₅×#949	1	1	yes	characteristic
411	C₄	C₅×#950	1	1	yes	characteristic
412	C₃	C₅×#1625	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	4	2	no	—
414	C₂	—	8	1	no	—
415	C₂	—	48	1	no	—
416	C₂	C₅×#5217	1	1	yes	characteristic
417	C₂	C₅×#5238	1	1	yes	characteristic
418	C₂	C₅×#5245	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#953
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#547	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₅×#547	D₃
hypocenter	C₃	C₅×#1625
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#547

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#547	C₂	semidirect
2. C₅×#5088	C₂	semidirect
3. C₅×#5015	C₂	semidirect
4. C₅×#5015	C₂	semidirect
5. C₅×#4547	C₂	semidirect
6. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
7. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
26. #71910	C₅	direct (N × H)
27. C₅×#547	D₃	semidirect
60. C₃×#547	C₂×C₅	semidirect
61. #5088	C₂×C₅	semidirect
62. #5015	C₂×C₅	semidirect
63. #5015	C₂×C₅	semidirect
64. #4547	C₂×C₅	semidirect
65. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
66. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
94. C₃×C₅×D₄	D₈	semidirect
157. #547	C₅×D₃	semidirect
222. C₅×D₄	#213	semidirect
269. C₃×D₄	C₅×D₈	semidirect
333. C₃×C₅	#1625	semidirect
372. D₄	C₅×#213	semidirect
393. C₅	#71910	direct (N × H)
412. C₃	C₅×#1625	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#547	2
C₅×#5088	2
C₅×#5015	2
C₅×#4547	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1625	3
#71910	5

Subgroups — C5×#71910 #14289094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71910 #14289094