Subgroups — C₅×#71918 #14288890

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5073	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5027	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5015	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4544	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1621	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	—	2	1	no	—
10	C₃×C₅×#127	—	2	1	no	—
11	C₃×C₅×#127	C₂²	1	1	yes	characteristic
12	C₃×C₅×#121	—	2	2	no	—
13	C₃×C₅×#121	—	2	1	no	—
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	—	2	1	no	—
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₅×#215	—	2	1	no	—
18	C₂×C₅×#213	—	2	1	no	—
19	C₂×C₅×#213	—	2	2	no	—
20	C₅×#874	C₂²	1	1	yes	characteristic
21	C₅×#809	—	2	1	no	—
22	C₅×#809	—	2	1	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	#71918	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×#550	D₃	1	1	yes	characteristic, complemented
28	C₅×#493	—	3	1	no	—
29	C₅×#460	—	3	1	no	—
30	C₅×#459	—	3	1	no	—
31	C₅×#331	—	3	1	no	—
32	C₅×Q₈⋊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	D₄	1	1	yes	characteristic
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
42	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₅×#215	—	4	2	no	—
56	C₅×#213	—	4	4	no	—
57	C₅×#213	—	4	2	no	—
58	C₂×C₅×C₃⋊C₈	—	2	1	no	—
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
62	#5073	C₂×C₅	1	1	yes	characteristic, complemented
63	#5027	C₂×C₅	1	1	yes	characteristic, complemented
64	#5015	C₂×C₅	1	1	yes	characteristic, complemented
65	#4544	C₂×C₅	1	1	yes	characteristic, complemented
66	#4535	C₂×C₅	1	1	yes	characteristic, complemented
67	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₅×#41	—	2	1	no	—
69	C₂×C₅×SD₁₆	—	6	1	no	—
70	C₂×C₅×D₈	—	6	1	no	—
71	C₂×C₅×D₈	—	6	2	no	—
72	C₅×#127	—	2	1	no	—
73	C₅×#127	—	3	1	no	—
74	C₅×#127	C₂×D₃	1	1	yes	characteristic
75	C₅×#121	—	2	2	no	—
76	C₅×#121	—	2	1	no	—
77	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
80	C₅×C₄⋊C₈	—	3	1	no	—
81	C₅×C₄⋊C₈	—	3	1	no	—
82	C₅×#102	—	6	1	no	—
83	C₅×#102	—	6	1	no	—
84	C₄×C₅×C₈	—	3	1	no	—
85	#1621	—	3	1	no	Sylow
86	C₂³×C₃×C₅	—	2	1	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂²×C₅×D₃	—	4	1	no	—
89	C₃×C₅×Q₈	—	2	1	no	—
90	C₃×C₅×Q₈	D₈	1	2	yes	complemented
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	—	4	2	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	1	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₃×C₅×D₄	—	4	1	no	—
99	C₃×C₅×D₄	—	8	2	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₅×D₁₂	—	4	2	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₅×D₁₂	—	4	1	no	—
112	C₅×D₁₂	—	4	1	no	—
113	C₅×D₁₂	—	4	1	no	—
114	C₅×C₃⋊C₈	—	2	2	no	—
115	C₅×C₃⋊C₈	—	4	1	no	—
116	C₅×C₃⋊C₈	—	4	1	no	—
117	C₂×C₃×#41	—	2	1	no	—
118	C₃×#127	—	2	1	no	—
119	C₃×#127	C₂²×C₅	1	1	yes	characteristic
120	C₃×#121	—	2	2	no	—
121	C₃×#121	—	2	1	no	—
122	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
123	C₃×C₄×D₄	—	2	1	no	—
124	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
125	C₂×#215	—	2	1	no	—
126	C₂×#213	—	2	1	no	—
127	C₂×#213	—	2	2	no	—
128	#874	C₂²×C₅	1	1	yes	characteristic
129	#809	—	2	1	no	—
130	#809	—	2	1	no	—
131	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
132	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
133	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
134	C₅×#41	—	4	2	no	—
135	C₅×#41	—	4	2	no	—
136	C₂×C₅×Q₈	#67	1	1	yes	characteristic
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	6	1	no	—
142	C₂×C₅×D₄	—	6	1	no	—
143	C₂×C₅×D₄	—	6	1	no	—
144	C₂×C₅×D₄	#67	1	1	yes	characteristic
145	C₂×C₅×D₄	#67	1	2	yes	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₅×SD₁₆	—	12	2	no	—
149	C₅×D₈	—	12	4	no	—
150	C₅×D₈	—	12	2	no	—
151	C₂×C₅×C₈	—	6	1	no	—
152	C₂×C₅×C₈	—	6	1	no	—
153	C₂×C₅×C₈	—	6	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
156	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	2	2	no	—
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
161	#550	C₅×D₃	1	1	yes	characteristic, complemented
162	#493	—	3	1	no	—
163	#460	—	3	1	no	—
164	#459	—	3	1	no	—
165	#331	—	3	1	no	—
166	Q₈⋊C₈	—	3	1	no	—
167	D₄⋊C₈	—	3	1	no	—
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	—	4	1	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	2	no	—
173	C₂²×C₃×C₅	—	4	1	no	—
174	C₂²×C₃×C₅	#120	1	1	yes	characteristic
175	C₂×C₅×D₃	—	8	1	no	—
176	C₂×C₅×D₃	—	8	1	no	—
177	C₂×C₅×D₃	—	8	1	no	—
178	C₃×C₄×C₅	—	2	2	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	—	4	1	no	—
182	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
183	C₃×C₄×C₅	#135	1	1	yes	characteristic
184	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₃×#41	—	4	2	no	—
187	C₃×#41	—	4	2	no	—
188	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
189	C₂×C₃×D₄	—	2	2	no	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	1	no	—
192	C₂×C₃×D₄	—	2	1	no	—
193	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
194	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	—	2	1	no	—
197	C₂×D₁₂	—	2	1	no	—
198	C₂×D₁₂	—	2	1	no	—
199	C₂×D₁₂	—	2	1	no	—
200	C₃×C₄⋊C₄	—	2	1	no	—
201	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
202	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
203	C₃×C₂²⋊C₄	—	2	2	no	—
204	C₃×C₂²⋊C₄	—	2	1	no	—
205	C₃×C₄²	—	2	1	no	—
206	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
207	#215	—	4	2	no	—
208	#213	—	4	4	no	—
209	#213	—	4	2	no	—
210	C₂×C₃⋊C₈	—	2	1	no	—
211	C₂×C₃⋊C₈	—	2	1	no	—
212	C₂×C₃⋊C₈	—	2	1	no	—
213	C₂³×C₅	—	2	1	no	—
214	C₂³×C₅	—	2	2	no	—
215	C₂³×C₅	—	12	1	no	—
216	C₅×Q₈	—	2	1	no	—
217	C₅×Q₈	#213	1	2	yes	complemented
218	C₅×D₄	—	2	1	no	—
219	C₅×D₄	—	2	1	no	—
220	C₅×D₄	—	4	2	no	—
221	C₅×D₄	—	4	4	no	—
222	C₅×D₄	—	4	1	no	—
223	C₅×D₄	—	4	1	no	—
224	C₅×D₄	—	4	1	no	—
225	C₅×D₄	—	4	1	no	—
226	C₅×D₄	—	8	2	no	—
227	C₅×D₄	—	12	2	no	—
228	C₅×D₄	—	12	1	no	—
229	C₅×D₄	—	12	1	no	—
230	C₅×D₄	—	12	1	no	—
231	C₅×D₄	—	12	1	no	—
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	4	4	no	—
236	C₂×C₄×C₅	—	4	1	no	—
237	C₂×C₄×C₅	—	4	1	no	—
238	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
239	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
241	C₅×C₈	—	6	2	no	—
242	C₅×C₈	—	12	1	no	—
243	C₅×C₈	—	12	1	no	—
244	C₂×#41	—	2	1	no	—
245	C₂×SD₁₆	—	6	1	no	—
246	C₂×D₈	—	6	1	no	—
247	C₂×D₈	—	6	2	no	—
248	#127	—	2	1	no	—
249	#127	—	3	1	no	—
250	#127	C₂×C₅×D₃	1	1	yes	characteristic
251	#121	—	2	2	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
256	C₄⋊C₈	—	3	1	no	—
257	C₄⋊C₈	—	3	1	no	—
258	#102	—	6	1	no	—
259	#102	—	6	1	no	—
260	C₄×C₈	—	3	1	no	—
261	C₂×C₃×C₅	—	8	1	no	—
262	C₂×C₃×C₅	—	8	2	no	—
263	C₂×C₃×C₅	#447	1	1	yes	characteristic
264	C₂×C₃×C₅	#449	1	1	yes	characteristic
265	C₂×C₃×C₅	#453	1	1	yes	characteristic
266	C₅×D₃	—	16	1	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂²×D₃	—	4	1	no	—
270	C₃×Q₈	—	2	1	no	—
271	C₃×Q₈	C₅×D₈	1	2	yes	complemented
272	C₃×D₄	—	2	1	no	—
273	C₃×D₄	—	2	1	no	—
274	C₃×D₄	—	4	2	no	—
275	C₃×D₄	—	4	4	no	—
276	C₃×D₄	—	4	1	no	—
277	C₃×D₄	—	4	1	no	—
278	C₃×D₄	—	4	1	no	—
279	C₃×D₄	—	4	1	no	—
280	C₃×D₄	—	8	2	no	—
281	C₂×C₃×C₄	—	2	1	no	—
282	C₂×C₃×C₄	—	2	1	no	—
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	4	4	no	—
285	C₂×C₃×C₄	—	4	1	no	—
286	C₂×C₃×C₄	—	4	1	no	—
287	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
290	D₁₂	—	4	2	no	—
291	D₁₂	—	4	1	no	—
292	D₁₂	—	4	1	no	—
293	D₁₂	—	4	1	no	—
294	D₁₂	—	4	1	no	—
295	C₃⋊C₈	—	2	2	no	—
296	C₃⋊C₈	—	4	1	no	—
297	C₃⋊C₈	—	4	1	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	—	4	1	no	—
301	C₂²×C₅	—	4	2	no	—
302	C₂²×C₅	—	4	2	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	24	1	no	—
305	C₂²×C₅	—	24	1	no	—
306	C₂²×C₅	—	24	1	no	—
307	C₂²×C₅	#953	1	1	yes	characteristic
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	4	1	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	C₂×#213	1	1	yes	characteristic
313	C₄×C₅	#932	1	1	yes	characteristic
314	C₄×C₅	#949	1	1	yes	characteristic
315	C₄×C₅	#950	1	1	yes	characteristic
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	C₅×#67	1	1	yes	characteristic
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	6	1	no	—
324	C₂×D₄	—	6	1	no	—
325	C₂×D₄	—	6	1	no	—
326	C₂×D₄	C₅×#67	1	1	yes	characteristic
327	C₂×D₄	C₅×#67	1	2	yes	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	SD₁₆	—	12	2	no	—
331	D₈	—	12	4	no	—
332	D₈	—	12	2	no	—
333	C₂×C₈	—	6	1	no	—
334	C₂×C₈	—	6	1	no	—
335	C₂×C₈	—	6	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
338	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
343	C₃×C₅	#1621	1	1	yes	characteristic, complemented, Hall
344	C₂²×C₃	—	4	2	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	—	4	1	no	—
347	C₂²×C₃	—	4	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	C₅×#120	1	1	yes	characteristic
351	C₂×D₃	—	8	1	no	—
352	C₂×D₃	—	8	1	no	—
353	C₂×D₃	—	8	1	no	—
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	4	1	no	—
357	C₃×C₄	—	4	1	no	—
358	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
359	C₃×C₄	C₅×#135	1	1	yes	characteristic
360	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
361	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
362	C₂×C₅	—	8	1	no	—
363	C₂×C₅	—	8	2	no	—
364	C₂×C₅	—	48	1	no	—
365	C₂×C₅	#5217	1	1	yes	characteristic
366	C₂×C₅	#5238	1	1	yes	characteristic
367	C₂×C₅	#5241	1	1	yes	characteristic
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	12	1	no	—
371	Q₈	—	2	1	no	—
372	Q₈	C₅×#213	1	2	yes	complemented
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	—	4	1	no	—
381	D₄	—	8	2	no	—
382	D₄	—	12	2	no	—
383	D₄	—	12	1	no	—
384	D₄	—	12	1	no	—
385	D₄	—	12	1	no	—
386	D₄	—	12	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
394	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
395	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
396	C₈	—	6	2	no	—
397	C₈	—	12	1	no	—
398	C₈	—	12	1	no	—
399	C₂×C₃	—	8	1	no	—
400	C₂×C₃	—	8	2	no	—
401	C₂×C₃	C₅×#447	1	1	yes	characteristic
402	C₂×C₃	C₅×#449	1	1	yes	characteristic
403	C₂×C₃	C₅×#453	1	1	yes	characteristic
404	D₃	—	16	1	no	—
405	C₅	#71918	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	4	2	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	24	1	no	—
413	C₂²	—	24	1	no	—
414	C₂²	—	24	1	no	—
415	C₂²	C₅×#953	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	C₂×C₅×#213	1	1	yes	characteristic
421	C₄	C₅×#932	1	1	yes	characteristic
422	C₄	C₅×#949	1	1	yes	characteristic
423	C₄	C₅×#950	1	1	yes	characteristic
424	C₃	C₅×#1621	1	1	yes	characteristic, complemented, Sylow
425	C₂	—	8	1	no	—
426	C₂	—	8	2	no	—
427	C₂	—	48	1	no	—
428	C₂	C₅×#5217	1	1	yes	characteristic
429	C₂	C₅×#5238	1	1	yes	characteristic
430	C₂	C₅×#5241	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×#550	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₅×#550	D₃
hypocenter	C₃	C₅×#1621
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#550

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#550	C₂	semidirect
2. C₅×#5073	C₂	semidirect
3. C₅×#5027	C₂	semidirect
4. C₅×#5015	C₂	semidirect
5. C₅×#4544	C₂	semidirect
6. C₅×#4535	C₂	semidirect
7. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
26. #71918	C₅	direct (N × H)
27. C₅×#550	D₃	semidirect
61. C₃×#550	C₂×C₅	semidirect
62. #5073	C₂×C₅	semidirect
63. #5027	C₂×C₅	semidirect
64. #5015	C₂×C₅	semidirect
65. #4544	C₂×C₅	semidirect
66. #4535	C₂×C₅	semidirect
67. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
90. C₃×C₅×Q₈	D₈	semidirect
161. #550	C₅×D₃	semidirect
217. C₅×Q₈	#213	semidirect
271. C₃×Q₈	C₅×D₈	semidirect
343. C₃×C₅	#1621	semidirect
372. Q₈	C₅×#213	semidirect
405. C₅	#71918	direct (N × H)
424. C₃	C₅×#1621	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#550	2
C₅×#5073	2
C₅×#5027	2
C₅×#5015	2
C₅×#4544	2
C₅×#4535	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#1621	3
#71918	5

Subgroups — C5×#71918 #14288890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71918 #14288890