Subgroups — C₅×#71143 #14289340

Order 1920.

628 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	C₅×D₄×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5085	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×D₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4483	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1629	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×D₄	—	2	1	no	—
10	C₂²×C₅×D₁₂	—	2	1	no	—
11	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
12	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂×C₅×#215	—	2	2	no	—
14	C₅×#930	—	2	1	no	—
15	C₅×#895	—	2	1	no	—
16	C₅×#882	—	2	2	no	—
17	C₅×#874	C₂²	1	1	yes	characteristic
18	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
19	C₃×C₅×#106	—	2	1	no	—
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#102	—	2	1	no	—
22	C₅×#809	—	2	1	no	—
23	C₅×#808	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
25	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
26	#71143	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₅×D₄²	—	3	1	no	—
28	C₅×#492	—	3	1	no	—
29	C₅×#476	—	3	1	no	—
30	C₅×#476	D₃	1	1	yes	characteristic, complemented
31	C₅×#331	—	3	1	no	—
32	C₅×D₄⋊C₈	—	3	1	no	—
33	C₅×D₄⋊C₈	—	3	1	no	—
34	C₂³×C₅×D₃	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	—	2	1	no	—
36	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂×C₅×#67	—	2	2	no	—
39	C₅×D₃×D₄	—	4	2	no	—
40	C₅×D₃×D₄	—	4	2	no	—
41	C₂×C₅×D₁₂	—	2	2	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	4	2	no	—
45	C₂×C₅×D₁₂	—	4	2	no	—
46	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
47	C₂×C₅×D₁₂	D₄	1	2	yes	—
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
53	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
54	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
55	C₅×#215	—	4	4	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
58	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
59	C₂×C₅×C₃⋊C₈	—	2	1	no	—
60	C₂×C₅×C₃⋊C₈	—	2	1	no	—
61	D₄×D₁₂	C₂×C₅	1	1	yes	characteristic
62	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
63	#5085	C₂×C₅	1	1	yes	characteristic, complemented
64	#5084	C₂×C₅	1	1	yes	characteristic, complemented
65	D₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
66	#4485	C₂×C₅	1	1	yes	characteristic, complemented
67	#4483	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂²×C₅×D₄	—	6	1	no	—
69	C₂²×C₅×D₄	—	6	1	no	—
70	C₂×C₅×SD₁₆	—	6	2	no	—
71	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
72	C₅×#127	—	3	1	no	—
73	C₅×#121	—	6	1	no	—
74	C₅×#121	—	6	1	no	—
75	C₅×#120	—	6	2	no	—
76	C₄×C₅×D₄	—	3	1	no	—
77	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
78	C₅×#106	—	2	1	no	—
79	C₅×#106	—	6	1	no	—
80	C₅×C₄⋊C₈	—	3	1	no	—
81	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic, complemented
82	C₅×#102	—	2	1	no	—
83	C₅×#102	—	6	1	no	—
84	C₄×C₅×C₈	—	3	1	no	—
85	#1629	—	3	1	no	Sylow
86	C₂³×C₃×C₅	—	2	1	no	—
87	C₂²×C₅×D₃	—	2	1	no	—
88	C₂²×C₅×D₃	—	2	2	no	—
89	C₂²×C₅×D₃	—	4	4	no	—
90	C₂²×C₅×D₃	—	4	4	no	—
91	C₂²×C₅×D₃	—	8	2	no	—
92	C₃×C₅×Q₈	—	4	2	no	—
93	C₃×C₅×D₄	—	2	1	no	—
94	C₃×C₅×D₄	SD₁₆	1	2	yes	complemented
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	4	1	no	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₅×#67	—	4	4	no	—
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₅×D₁₂	—	2	1	no	—
105	C₅×D₁₂	—	4	2	no	—
106	C₅×D₁₂	—	4	4	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×D₁₂	SD₁₆	1	2	yes	complemented
112	C₄×C₅×D₃	—	4	1	no	—
113	C₄×C₅×D₃	—	4	1	no	—
114	C₃×C₅×C₈	—	4	1	no	—
115	C₅×C₃⋊C₈	—	2	2	no	—
116	C₅×C₃⋊C₈	—	4	1	no	—
117	C₂×D₃×D₄	—	2	1	no	—
118	C₂²×D₁₂	—	2	1	no	—
119	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
120	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
121	C₂×#215	—	2	2	no	—
122	#930	—	2	1	no	—
123	#895	—	2	1	no	—
124	#882	—	2	2	no	—
125	#874	C₂²×C₅	1	1	yes	characteristic
126	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
127	C₃×#106	—	2	1	no	—
128	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
129	C₃×#102	—	2	1	no	—
130	#809	—	2	1	no	—
131	#808	—	2	1	no	—
132	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic, complemented
133	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₂⁴×C₅	—	6	2	no	—
135	C₂×C₅×Q₈	—	2	1	no	—
136	C₂×C₅×D₄	—	3	1	no	—
137	C₂×C₅×D₄	—	3	2	no	—
138	C₂×C₅×D₄	—	6	2	no	—
139	C₂×C₅×D₄	—	6	2	no	—
140	C₂×C₅×D₄	—	6	1	no	—
141	C₂×C₅×D₄	—	6	1	no	—
142	C₂×C₅×D₄	—	12	2	no	—
143	C₂×C₅×D₄	—	12	2	no	—
144	C₂×C₅×D₄	—	12	2	no	—
145	C₂×C₅×D₄	—	12	2	no	—
146	C₂×C₅×D₄	#67	1	1	yes	characteristic
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	6	1	no	—
149	C₅×SD₁₆	—	12	4	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	6	1	no	—
152	C₂×C₅×C₈	—	6	1	no	—
153	C₅×C₄⋊C₄	—	2	1	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	3	1	no	—
156	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	6	2	no	—
159	C₅×C₂²⋊C₄	—	6	1	no	—
160	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
161	D₄²	—	3	1	no	—
162	#492	—	3	1	no	—
163	#476	—	3	1	no	—
164	#476	C₅×D₃	1	1	yes	characteristic, complemented
165	#331	—	3	1	no	—
166	D₄⋊C₈	—	3	1	no	—
167	D₄⋊C₈	—	3	1	no	—
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	—	4	1	no	—
171	C₂²×C₃×C₅	#120	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	2	no	—
173	C₂×C₅×D₃	—	4	1	no	—
174	C₂×C₅×D₃	—	4	1	no	—
175	C₂×C₅×D₃	—	4	2	no	—
176	C₂×C₅×D₃	—	4	2	no	—
177	C₂×C₅×D₃	—	4	2	no	—
178	C₂×C₅×D₃	—	8	8	no	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	—	8	1	no	—
182	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
183	C₃×C₄×C₅	C₂×SD₁₆	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	C₅×Dic₃	—	4	1	no	—
187	C₂³×D₃	—	2	2	no	—
188	C₂×C₃×Q₈	—	2	1	no	—
189	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
190	C₂²×C₃×C₄	—	2	1	no	—
191	C₂×#67	—	2	2	no	—
192	D₃×D₄	—	4	2	no	—
193	D₃×D₄	—	4	2	no	—
194	C₂×D₁₂	—	2	2	no	—
195	C₂×D₁₂	—	2	1	no	—
196	C₂×D₁₂	—	2	1	no	—
197	C₂×D₁₂	—	4	2	no	—
198	C₂×D₁₂	—	4	2	no	—
199	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
200	C₂×D₁₂	C₅×D₄	1	2	yes	—
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₃×C₈	—	2	1	no	—
203	C₃×C₄⋊C₄	—	2	1	no	—
204	C₃×C₄⋊C₄	—	2	1	no	—
205	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
206	C₃×C₂²⋊C₄	—	2	1	no	—
207	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
208	#215	—	4	4	no	—
209	(C₂×D₃)⋊C₄	—	2	2	no	—
210	(C₂×D₃)⋊C₄	—	2	1	no	—
211	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
212	C₂×C₃⋊C₈	—	2	1	no	—
213	C₂×C₃⋊C₈	—	2	1	no	—
214	C₂³×C₅	—	2	1	no	—
215	C₂³×C₅	—	6	1	no	—
216	C₂³×C₅	—	6	2	no	—
217	C₂³×C₅	—	12	4	no	—
218	C₂³×C₅	—	12	4	no	—
219	C₂³×C₅	—	24	2	no	—
220	C₅×Q₈	—	4	2	no	—
221	C₅×D₄	—	2	1	no	—
222	C₅×D₄	—	3	2	no	—
223	C₅×D₄	—	6	1	no	—
224	C₅×D₄	—	12	2	no	—
225	C₅×D₄	—	12	4	no	—
226	C₅×D₄	—	12	4	no	—
227	C₅×D₄	—	12	1	no	—
228	C₅×D₄	—	12	1	no	—
229	C₅×D₄	—	12	1	no	—
230	C₅×D₄	—	12	1	no	—
231	C₅×D₄	#215	1	2	yes	complemented
232	C₂×C₄×C₅	—	2	1	no	—
233	C₂×C₄×C₅	—	4	1	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	12	1	no	—
238	C₂×C₄×C₅	—	12	1	no	—
239	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
242	C₅×C₈	—	4	1	no	—
243	C₅×C₈	—	6	2	no	—
244	C₅×C₈	—	12	1	no	—
245	C₂²×D₄	—	6	1	no	—
246	C₂²×D₄	—	6	1	no	—
247	C₂×SD₁₆	—	6	2	no	—
248	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
249	#127	—	3	1	no	—
250	#121	—	6	1	no	—
251	#121	—	6	1	no	—
252	#120	—	6	2	no	—
253	C₄×D₄	—	3	1	no	—
254	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
255	#106	—	2	1	no	—
256	#106	—	6	1	no	—
257	C₄⋊C₈	—	3	1	no	—
258	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
259	#102	—	2	1	no	—
260	#102	—	6	1	no	—
261	C₄×C₈	—	3	1	no	—
262	C₂×C₃×C₅	—	4	2	no	—
263	C₂×C₃×C₅	#450	1	1	yes	characteristic
264	C₂×C₃×C₅	#450	1	1	yes	characteristic
265	C₂×C₃×C₅	#453	1	1	yes	characteristic
266	C₅×D₃	—	4	2	no	—
267	C₅×D₃	—	8	2	no	—
268	C₂³×C₃	—	2	1	no	—
269	C₂²×D₃	—	2	1	no	—
270	C₂²×D₃	—	2	2	no	—
271	C₂²×D₃	—	4	4	no	—
272	C₂²×D₃	—	4	4	no	—
273	C₂²×D₃	—	8	2	no	—
274	C₃×Q₈	—	4	2	no	—
275	C₃×D₄	—	2	1	no	—
276	C₃×D₄	C₅×SD₁₆	1	2	yes	complemented
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	4	1	no	—
279	C₂×C₃×C₄	—	4	1	no	—
280	C₂×C₃×C₄	—	4	1	no	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	#67	—	4	4	no	—
285	C₂×Dic₃	—	2	1	no	—
286	D₁₂	—	2	1	no	—
287	D₁₂	—	4	2	no	—
288	D₁₂	—	4	4	no	—
289	D₁₂	—	4	1	no	—
290	D₁₂	—	4	1	no	—
291	D₁₂	—	4	1	no	—
292	D₁₂	—	4	1	no	—
293	D₁₂	C₅×SD₁₆	1	2	yes	complemented
294	C₄×D₃	—	4	1	no	—
295	C₄×D₃	—	4	1	no	—
296	C₃×C₈	—	4	1	no	—
297	C₃⋊C₈	—	2	2	no	—
298	C₃⋊C₈	—	4	1	no	—
299	C₂²×C₅	—	2	2	no	—
300	C₂²×C₅	—	4	1	no	—
301	C₂²×C₅	—	4	1	no	—
302	C₂²×C₅	—	6	2	no	—
303	C₂²×C₅	—	12	1	no	—
304	C₂²×C₅	—	12	1	no	—
305	C₂²×C₅	—	12	2	no	—
306	C₂²×C₅	—	12	2	no	—
307	C₂²×C₅	—	12	2	no	—
308	C₂²×C₅	—	24	8	no	—
309	C₂²×C₅	#937	1	1	yes	characteristic
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	4	1	no	—
312	C₄×C₅	—	8	1	no	—
313	C₄×C₅	—	12	1	no	—
314	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
315	C₄×C₅	#914	1	1	yes	characteristic
316	C₄×C₅	C₂×#215	1	1	yes	characteristic
317	C₄×C₅	#949	1	1	yes	characteristic
318	C₂⁴	—	6	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×D₄	—	3	1	no	—
321	C₂×D₄	—	3	2	no	—
322	C₂×D₄	—	6	2	no	—
323	C₂×D₄	—	6	2	no	—
324	C₂×D₄	—	6	1	no	—
325	C₂×D₄	—	6	1	no	—
326	C₂×D₄	—	12	2	no	—
327	C₂×D₄	—	12	2	no	—
328	C₂×D₄	—	12	2	no	—
329	C₂×D₄	—	12	2	no	—
330	C₂×D₄	C₅×#67	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	6	1	no	—
333	SD₁₆	—	12	4	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	6	1	no	—
336	C₂×C₈	—	6	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	3	1	no	—
340	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	6	2	no	—
343	C₂²⋊C₄	—	6	1	no	—
344	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₃×C₅	#1629	1	1	yes	characteristic, complemented, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	4	1	no	—
348	C₂²×C₃	—	4	1	no	—
349	C₂²×C₃	C₅×#120	1	1	yes	characteristic
350	C₂×D₃	—	2	2	no	—
351	C₂×D₃	—	4	1	no	—
352	C₂×D₃	—	4	1	no	—
353	C₂×D₃	—	4	2	no	—
354	C₂×D₃	—	4	2	no	—
355	C₂×D₃	—	4	2	no	—
356	C₂×D₃	—	8	8	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	4	1	no	—
359	C₃×C₄	—	8	1	no	—
360	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
361	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
362	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₃×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
364	Dic₃	—	4	1	no	—
365	C₂×C₅	—	4	2	no	—
366	C₂×C₅	—	12	2	no	—
367	C₂×C₅	—	24	2	no	—
368	C₂×C₅	#5046	1	1	yes	characteristic
369	C₂×C₅	#5169	1	1	yes	characteristic
370	C₂×C₅	#5198	1	1	yes	characteristic
371	C₂³	—	2	1	no	—
372	C₂³	—	6	1	no	—
373	C₂³	—	6	2	no	—
374	C₂³	—	12	4	no	—
375	C₂³	—	12	4	no	—
376	C₂³	—	24	2	no	—
377	Q₈	—	4	2	no	—
378	D₄	—	2	1	no	—
379	D₄	—	3	2	no	—
380	D₄	—	6	1	no	—
381	D₄	—	12	2	no	—
382	D₄	—	12	4	no	—
383	D₄	—	12	4	no	—
384	D₄	—	12	1	no	—
385	D₄	—	12	1	no	—
386	D₄	—	12	1	no	—
387	D₄	—	12	1	no	—
388	D₄	C₅×#215	1	2	yes	complemented
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	6	1	no	—
394	C₂×C₄	—	12	1	no	—
395	C₂×C₄	—	12	1	no	—
396	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
397	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
398	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
399	C₈	—	4	1	no	—
400	C₈	—	6	2	no	—
401	C₈	—	12	1	no	—
402	C₂×C₃	—	4	2	no	—
403	C₂×C₃	C₅×#450	1	1	yes	characteristic
404	C₂×C₃	C₅×#450	1	1	yes	characteristic
405	C₂×C₃	C₅×#453	1	1	yes	characteristic
406	D₃	—	4	2	no	—
407	D₃	—	8	2	no	—
408	C₅	#71143	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	6	2	no	—
413	C₂²	—	12	1	no	—
414	C₂²	—	12	1	no	—
415	C₂²	—	12	2	no	—
416	C₂²	—	12	2	no	—
417	C₂²	—	12	2	no	—
418	C₂²	—	24	8	no	—
419	C₂²	C₅×#937	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	12	1	no	—
424	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
425	C₄	C₅×#914	1	1	yes	characteristic
426	C₄	C₂×C₅×#215	1	1	yes	characteristic
427	C₄	C₅×#949	1	1	yes	characteristic
428	C₃	C₅×#1629	1	1	yes	characteristic, complemented, Sylow
429	C₂	—	4	2	no	—
430	C₂	—	12	2	no	—
431	C₂	—	24	2	no	—
432	C₂	C₅×#5046	1	1	yes	characteristic
433	C₂	C₅×#5169	1	1	yes	characteristic
434	C₂	C₅×#5198	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator, cosocle	C₃×C₄²	C₂³×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#476	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₅×D₄×D₁₂	C₂
hypercenter	C₅×#476	D₃
hypocenter	C₃	C₅×#1629
LCS	G ▷ C₃×C₄² ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#476

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#476	C₂	semidirect
3. C₅×#5085	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×D₄⋊(C₃⋊C₈)	C₂	semidirect
6. C₅×#4485	C₂	semidirect
7. C₅×#4483	C₂	semidirect
11. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×C₄⋊C₈	C₂²	semidirect
24. C₅×C₄⋊(C₃⋊C₈)	C₂²	semidirect
25. C₄×C₅×C₃⋊C₈	C₂²	semidirect
26. #71143	C₅	direct (N × H)
30. C₅×#476	D₃	semidirect
62. C₃×#476	C₂×C₅	semidirect
63. #5085	C₂×C₅	semidirect
64. #5084	C₂×C₅	semidirect
65. D₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
66. #4485	C₂×C₅	semidirect
67. #4483	C₂×C₅	semidirect
71. C₅×C₄⋊Q₈	C₂×D₃	semidirect
81. C₅×C₄⋊C₈	C₂×D₃	semidirect
94. C₃×C₅×D₄	SD₁₆	semidirect
111. C₅×D₁₂	SD₁₆	semidirect
119. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
128. C₃×C₄⋊C₈	C₂²×C₅	semidirect
132. C₄⋊(C₃⋊C₈)	C₂²×C₅	semidirect
133. C₄×C₃⋊C₈	C₂²×C₅	semidirect
164. #476	C₅×D₃	semidirect
231. C₅×D₄	#215	semidirect
248. C₄⋊Q₈	C₂×C₅×D₃	semidirect
258. C₄⋊C₈	C₂×C₅×D₃	semidirect
276. C₃×D₄	C₅×SD₁₆	semidirect
293. D₁₂	C₅×SD₁₆	semidirect
345. C₃×C₅	#1629	semidirect
388. D₄	C₅×#215	semidirect
408. C₅	#71143	direct (N × H)
428. C₃	C₅×#1629	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×D₁₂	2
C₃×C₅×#476	2
C₅×#5085	2
C₅×#5084	2
C₅×D₄⋊(C₃⋊C₈)	2
C₅×#4485	2
C₅×#4483	2
C₅×#1629	3
#71143	5

Subgroups — C5×#71143 #14289340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71143 #14289340