Subgroups — C₅×#71645 #14302561

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5822	C₂	1	1	yes	maximal, characteristic
3	C₅×#5236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5006	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4533	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1906	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₅×#235	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	—	2	1	no	—
12	C₃×C₄×C₅×D₄	—	2	1	no	—
13	C₃×C₄×C₅×D₄	—	2	2	no	—
14	C₃×C₅×#117	—	2	1	no	—
15	C₃×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	—	2	1	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#951	C₄	1	2	yes	complemented
19	C₅×#950	—	2	2	no	—
20	C₅×#949	C₄	1	2	yes	complemented
21	C₅×#942	—	2	1	no	—
22	C₅×#932	—	2	1	no	—
23	C₅×#926	C₂²	1	1	yes	characteristic
24	C₂×C₅×#208	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₅×#837	—	2	2	no	—
27	C₅×#806	—	2	2	no	—
28	C₅×#805	—	2	1	no	—
29	C₅×#805	—	2	1	no	—
30	#71645	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#575	—	3	1	no	—
32	C₄×C₅×#41	D₃	1	1	yes	characteristic, complemented
33	C₅×#421	—	3	1	no	—
34	C₂×C₅×#104	—	3	1	no	—
35	C₅×#410	—	3	1	no	—
36	C₅×#344	—	3	1	no	—
37	C₅×#339	—	3	1	no	—
38	C₃×C₅×#41	—	2	1	no	—
39	C₃×C₅×#41	—	2	1	no	—
40	C₃×C₅×#41	C₂×C₄	1	2	yes	—
41	C₃×C₅×#41	D₄	1	2	yes	—
42	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	—	2	1	no	—
44	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	—	2	1	no	—
46	C₂²×C₃×C₄×C₅	—	2	2	no	—
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×#67	—	2	1	no	—
50	C₅×#235	—	2	1	no	—
51	C₅×#235	—	2	1	no	—
52	C₅×#235	—	2	1	no	—
53	C₅×#235	—	2	1	no	—
54	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
55	C₂×C₄×C₅×D₃	—	2	1	no	—
56	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
60	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
61	C₃×C₄²×C₅	—	2	2	no	—
62	C₃×C₄²×C₅	—	2	1	no	—
63	C₃×C₄²×C₅	—	2	1	no	—
64	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
66	C₅×#217	—	2	1	no	—
67	C₅×#216	—	2	2	no	—
68	C₅×#215	—	2	2	no	—
69	C₅×#214	—	2	2	no	—
70	C₅×#213	—	2	2	no	—
71	C₅×C₄⋊Dic₃	—	2	1	no	—
72	C₄×C₅×Dic₃	—	2	1	no	—
73	C₅×#208	—	2	1	no	—
74	C₅×#208	—	2	1	no	—
75	C₅×#208	—	2	1	no	—
76	C₅×#208	C₂×C₄	1	2	yes	complemented
77	C₂×C₅×C₃⋊C₈	—	2	1	no	—
78	C₂×C₅×C₃⋊C₈	—	2	1	no	—
79	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
80	#5822	C₂×C₅	1	1	yes	characteristic
81	#5236	C₂×C₅	1	1	yes	characteristic, complemented
82	#5006	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂×#805	C₂×C₅	1	1	yes	characteristic, complemented
84	#4533	C₂×C₅	1	1	yes	characteristic, complemented
85	#4523	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂×C₅×#41	—	3	1	no	—
87	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
88	C₅×#137	—	3	2	no	—
89	C₅×#137	—	6	1	no	—
90	C₅×AGL(1,ℤ/8)	—	3	2	no	—
91	C₅×AGL(1,ℤ/8)	—	6	1	no	—
92	C₅×#135	—	6	2	no	—
93	C₂×C₅×M₁₆	—	3	1	no	—
94	C₂×C₅×M₁₆	—	3	1	no	—
95	C₄×C₅×Q₈	—	2	1	no	—
96	C₄×C₅×D₄	—	2	1	no	—
97	C₄×C₅×D₄	—	2	2	no	—
98	C₅×#117	—	2	1	no	—
99	C₅×#117	—	3	1	no	—
100	C₅×#117	C₂×D₃	1	1	yes	characteristic
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
103	C₅×#104	—	6	2	no	—
104	C₅×#104	—	6	1	no	—
105	C₅×#104	—	6	1	no	—
106	C₅×#99	—	6	2	no	—
107	#1906	—	3	1	no	Sylow
108	C₂³×C₃×C₅	—	2	1	no	—
109	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₅×D₃	—	2	1	no	—
111	C₃×C₅×Q₈	—	2	1	no	—
112	C₃×C₅×Q₈	C₂²⋊C₄	1	2	yes	—
113	C₃×C₅×D₄	—	2	2	no	—
114	C₃×C₅×D₄	—	2	2	no	—
115	C₃×C₅×D₄	—	2	1	no	—
116	C₃×C₅×D₄	C₂²⋊C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	1	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	1	no	—
123	C₂×C₃×C₄×C₅	—	4	2	no	—
124	C₂×C₃×C₄×C₅	—	4	4	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
131	C₅×#67	—	4	1	no	—
132	C₅×#67	—	4	1	no	—
133	C₂×C₅×Dic₃	—	2	1	no	—
134	C₂×C₅×Dic₃	—	4	1	no	—
135	C₅×D₁₂	—	2	1	no	—
136	C₅×D₁₂	—	2	1	no	—
137	C₄×C₅×D₃	—	4	1	no	—
138	C₄×C₅×D₃	—	4	1	no	—
139	C₅×Dic₆	—	2	1	no	—
140	C₅×Dic₆	—	2	1	no	—
141	C₅×C₃⋊C₈	—	2	2	no	—
142	C₅×C₃⋊C₈	—	4	1	no	—
143	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
144	C₂×#235	C₂²×C₅	1	1	yes	characteristic
145	C₃×C₄×Q₈	—	2	1	no	—
146	C₃×C₄×D₄	—	2	1	no	—
147	C₃×C₄×D₄	—	2	2	no	—
148	C₃×#117	—	2	1	no	—
149	C₃×#117	C₂²×C₅	1	1	yes	characteristic
150	C₂×C₃×C₄²	—	2	1	no	—
151	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
152	#951	C₄×C₅	1	2	yes	complemented
153	#950	—	2	2	no	—
154	#949	C₄×C₅	1	2	yes	complemented
155	#942	—	2	1	no	—
156	#932	—	2	1	no	—
157	#926	C₂²×C₅	1	1	yes	characteristic
158	C₂×#208	C₂²×C₅	1	1	yes	characteristic
159	C₂×#208	C₂²×C₅	1	1	yes	characteristic
160	#837	—	2	2	no	—
161	#806	—	2	2	no	—
162	#805	—	2	1	no	—
163	#805	—	2	1	no	—
164	C₅×#41	—	2	1	no	—
165	C₅×#41	—	2	1	no	—
166	C₅×#41	—	6	1	no	—
167	C₅×#41	—	6	1	no	—
168	C₅×#41	—	6	1	no	—
169	C₅×#41	—	6	1	no	—
170	C₅×#41	C₄×D₃	1	2	yes	—
171	C₅×#41	D₁₂	1	2	yes	—
172	C₂×C₅×Q₈	—	3	1	no	—
173	C₂×C₅×Q₈	#67	1	1	yes	characteristic
174	C₂×C₅×D₄	—	2	1	no	—
175	C₂×C₅×D₄	—	3	1	no	—
176	C₂×C₅×D₄	—	6	1	no	—
177	C₂×C₅×D₄	#67	1	1	yes	characteristic
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	2	no	—
180	C₂²×C₄×C₅	—	2	1	no	—
181	C₂²×C₄×C₅	—	6	1	no	—
182	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
183	C₅×Q₁₆	—	6	2	no	—
184	C₅×SD₁₆	—	6	2	no	—
185	C₅×SD₁₆	—	6	2	no	—
186	C₅×D₈	—	6	2	no	—
187	C₅×M₁₆	—	3	2	no	—
188	C₅×M₁₆	—	6	1	no	—
189	C₅×M₁₆	—	6	1	no	—
190	C₅×M₁₆	—	6	1	no	—
191	C₂×C₅×C₈	—	6	1	no	—
192	C₂×C₅×C₈	—	6	1	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	1	no	—
195	C₅×C₄⋊C₄	—	6	1	no	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	6	1	no	—
198	C₅×C₂²⋊C₄	#67	1	2	yes	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	6	1	no	—
203	C₄²×C₅	#67	1	1	yes	characteristic
204	C₄²×C₅	#67	1	1	yes	characteristic
205	#575	—	3	1	no	—
206	C₄×#41	C₅×D₃	1	1	yes	characteristic, complemented
207	#421	—	3	1	no	—
208	C₂×#104	—	3	1	no	—
209	#410	—	3	1	no	—
210	#344	—	3	1	no	—
211	#339	—	3	1	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	4	1	no	—
214	C₂²×C₃×C₅	—	4	2	no	—
215	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
216	C₂²×C₃×C₅	#120	1	1	yes	characteristic
217	C₂²×C₃×C₅	#121	1	1	yes	characteristic
218	C₂×C₅×D₃	—	4	1	no	—
219	C₂×C₅×D₃	—	8	1	no	—
220	C₃×C₄×C₅	—	2	2	no	—
221	C₃×C₄×C₅	—	2	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	—	4	1	no	—
224	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
226	C₃×C₄×C₅	#121	1	1	yes	characteristic
227	C₃×C₄×C₅	#123	1	1	yes	characteristic
228	C₅×Dic₃	—	4	1	no	—
229	C₅×Dic₃	—	8	1	no	—
230	C₃×#41	—	2	1	no	—
231	C₃×#41	—	2	1	no	—
232	C₃×#41	C₂×C₄×C₅	1	2	yes	—
233	C₃×#41	C₅×D₄	1	2	yes	—
234	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
235	C₂×C₃×D₄	—	2	1	no	—
236	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
237	C₂²×C₃×C₄	—	2	1	no	—
238	C₂²×C₃×C₄	—	2	2	no	—
239	C₂²×C₃×C₄	—	2	1	no	—
240	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
241	C₂×#67	—	2	1	no	—
242	#235	—	2	1	no	—
243	#235	—	2	1	no	—
244	#235	—	2	1	no	—
245	#235	—	2	1	no	—
246	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic, complemented
247	C₂×C₄×D₃	—	2	1	no	—
248	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₂²⋊C₄	—	2	2	no	—
252	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
253	C₃×C₄²	—	2	2	no	—
254	C₃×C₄²	—	2	1	no	—
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
257	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
258	#217	—	2	1	no	—
259	#216	—	2	2	no	—
260	#215	—	2	2	no	—
261	#214	—	2	2	no	—
262	#213	—	2	2	no	—
263	C₄⋊Dic₃	—	2	1	no	—
264	C₄×Dic₃	—	2	1	no	—
265	#208	—	2	1	no	—
266	#208	—	2	1	no	—
267	#208	—	2	1	no	—
268	#208	C₂×C₄×C₅	1	2	yes	complemented
269	C₂×C₃⋊C₈	—	2	1	no	—
270	C₂×C₃⋊C₈	—	2	1	no	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	—	6	1	no	—
273	C₂³×C₅	C₂×#67	1	1	yes	characteristic
274	C₅×Q₈	—	2	1	no	—
275	C₅×Q₈	—	6	1	no	—
276	C₅×Q₈	—	6	1	no	—
277	C₅×Q₈	(C₂×D₃)⋊C₄	1	2	yes	—
278	C₅×D₄	—	2	2	no	—
279	C₅×D₄	—	2	2	no	—
280	C₅×D₄	—	2	1	no	—
281	C₅×D₄	—	6	1	no	—
282	C₅×D₄	—	6	1	no	—
283	C₅×D₄	—	12	1	no	—
284	C₅×D₄	—	12	1	no	—
285	C₅×D₄	(C₂×D₃)⋊C₄	1	2	yes	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	4	2	no	—
293	C₂×C₄×C₅	—	4	4	no	—
294	C₂×C₄×C₅	—	6	1	no	—
295	C₂×C₄×C₅	—	12	1	no	—
296	C₂×C₄×C₅	—	12	1	no	—
297	C₂×C₄×C₅	—	12	1	no	—
298	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
300	C₂×C₄×C₅	#235	1	1	yes	characteristic
301	C₂×C₄×C₅	#235	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
304	C₅×C₈	—	6	2	no	—
305	C₅×C₈	—	12	1	no	—
306	C₂×#41	—	3	1	no	—
307	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
308	#137	—	3	2	no	—
309	#137	—	6	1	no	—
310	AGL(1,ℤ/8)	—	3	2	no	—
311	AGL(1,ℤ/8)	—	6	1	no	—
312	#135	—	6	2	no	—
313	C₂×M₁₆	—	3	1	no	—
314	C₂×M₁₆	—	3	1	no	—
315	C₄×Q₈	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	2	no	—
318	#117	—	2	1	no	—
319	#117	—	3	1	no	—
320	#117	C₂×C₅×D₃	1	1	yes	characteristic
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
323	#104	—	6	2	no	—
324	#104	—	6	1	no	—
325	#104	—	6	1	no	—
326	#99	—	6	2	no	—
327	C₂×C₃×C₅	—	2	1	no	—
328	C₂×C₃×C₅	—	2	1	no	—
329	C₂×C₃×C₅	—	2	1	no	—
330	C₂×C₃×C₅	—	4	2	no	—
331	C₂×C₃×C₅	#386	1	1	yes	characteristic
332	C₅×D₃	—	8	1	no	—
333	C₂³×C₃	—	2	1	no	—
334	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×D₃	—	2	1	no	—
336	C₃×Q₈	—	2	1	no	—
337	C₃×Q₈	C₅×C₂²⋊C₄	1	2	yes	—
338	C₃×D₄	—	2	2	no	—
339	C₃×D₄	—	2	2	no	—
340	C₃×D₄	—	2	1	no	—
341	C₃×D₄	C₅×C₂²⋊C₄	1	2	yes	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	4	2	no	—
349	C₂×C₃×C₄	—	4	4	no	—
350	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
355	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
356	#67	—	4	1	no	—
357	#67	—	4	1	no	—
358	C₂×Dic₃	—	2	1	no	—
359	C₂×Dic₃	—	4	1	no	—
360	D₁₂	—	2	1	no	—
361	D₁₂	—	2	1	no	—
362	C₄×D₃	—	4	1	no	—
363	C₄×D₃	—	4	1	no	—
364	Dic₆	—	2	1	no	—
365	Dic₆	—	2	1	no	—
366	C₃⋊C₈	—	2	2	no	—
367	C₃⋊C₈	—	4	1	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	4	1	no	—
370	C₂²×C₅	—	4	2	no	—
371	C₂²×C₅	—	12	1	no	—
372	C₂²×C₅	—	24	1	no	—
373	C₂²×C₅	C₄×#67	1	1	yes	characteristic
374	C₂²×C₅	#930	1	1	yes	characteristic
375	C₂²×C₅	#953	1	1	yes	characteristic
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	2	2	no	—
378	C₄×C₅	—	4	2	no	—
379	C₄×C₅	—	4	1	no	—
380	C₄×C₅	—	12	1	no	—
381	C₄×C₅	—	24	1	no	—
382	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
383	C₄×C₅	C₄×#67	1	1	yes	characteristic
384	C₄×C₅	#929	1	1	yes	characteristic
385	C₄×C₅	#930	1	1	yes	characteristic
386	#41	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	6	1	no	—
389	#41	—	6	1	no	—
390	#41	—	6	1	no	—
391	#41	—	6	1	no	—
392	#41	C₄×C₅×D₃	1	2	yes	—
393	#41	C₅×D₁₂	1	2	yes	—
394	C₂×Q₈	—	3	1	no	—
395	C₂×Q₈	C₅×#67	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	3	1	no	—
398	C₂×D₄	—	6	1	no	—
399	C₂×D₄	C₅×#67	1	1	yes	characteristic
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	6	1	no	—
404	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
405	Q₁₆	—	6	2	no	—
406	SD₁₆	—	6	2	no	—
407	SD₁₆	—	6	2	no	—
408	D₈	—	6	2	no	—
409	M₁₆	—	3	2	no	—
410	M₁₆	—	6	1	no	—
411	M₁₆	—	6	1	no	—
412	M₁₆	—	6	1	no	—
413	C₂×C₈	—	6	1	no	—
414	C₂×C₈	—	6	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	6	1	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	6	1	no	—
420	C₂²⋊C₄	C₅×#67	1	2	yes	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	6	1	no	—
425	C₄²	C₅×#67	1	1	yes	characteristic
426	C₄²	C₅×#67	1	1	yes	characteristic
427	C₃×C₅	#1906	1	1	yes	characteristic, complemented, Hall
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	4	1	no	—
430	C₂²×C₃	—	4	2	no	—
431	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₃	C₅×#120	1	1	yes	characteristic
433	C₂²×C₃	C₅×#121	1	1	yes	characteristic
434	C₂×D₃	—	4	1	no	—
435	C₂×D₃	—	8	1	no	—
436	C₃×C₄	—	2	2	no	—
437	C₃×C₄	—	2	2	no	—
438	C₃×C₄	—	4	2	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
441	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
442	C₃×C₄	C₅×#121	1	1	yes	characteristic
443	C₃×C₄	C₅×#123	1	1	yes	characteristic
444	Dic₃	—	4	1	no	—
445	Dic₃	—	8	1	no	—
446	C₂×C₅	—	2	1	no	—
447	C₂×C₅	—	2	1	no	—
448	C₂×C₅	—	2	1	no	—
449	C₂×C₅	—	4	2	no	—
450	C₂×C₅	—	24	1	no	—
451	C₂×C₅	#5213	1	1	yes	characteristic
452	C₂³	—	2	1	no	—
453	C₂³	—	6	1	no	—
454	C₂³	C₂×C₅×#67	1	1	yes	characteristic
455	Q₈	—	2	1	no	—
456	Q₈	—	6	1	no	—
457	Q₈	—	6	1	no	—
458	Q₈	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
459	D₄	—	2	2	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	1	no	—
462	D₄	—	6	1	no	—
463	D₄	—	6	1	no	—
464	D₄	—	12	1	no	—
465	D₄	—	12	1	no	—
466	D₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	—	6	1	no	—
476	C₂×C₄	—	12	1	no	—
477	C₂×C₄	—	12	1	no	—
478	C₂×C₄	—	12	1	no	—
479	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
480	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
481	C₂×C₄	C₅×#235	1	1	yes	characteristic
482	C₂×C₄	C₅×#235	1	1	yes	characteristic
483	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
484	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
485	C₈	—	6	2	no	—
486	C₈	—	12	1	no	—
487	C₂×C₃	—	2	1	no	—
488	C₂×C₃	—	2	1	no	—
489	C₂×C₃	—	2	1	no	—
490	C₂×C₃	—	4	2	no	—
491	C₂×C₃	C₅×#386	1	1	yes	characteristic
492	D₃	—	8	1	no	—
493	C₅	#71645	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	12	1	no	—
498	C₂²	—	24	1	no	—
499	C₂²	C₄×C₅×#67	1	1	yes	characteristic
500	C₂²	C₅×#930	1	1	yes	characteristic
501	C₂²	C₅×#953	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	—	12	1	no	—
507	C₄	—	24	1	no	—
508	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
509	C₄	C₄×C₅×#67	1	1	yes	characteristic
510	C₄	C₅×#929	1	1	yes	characteristic
511	C₄	C₅×#930	1	1	yes	characteristic
512	C₃	C₅×#1906	1	1	yes	characteristic, complemented, Sylow
513	C₂	—	2	1	no	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	4	2	no	—
517	C₂	—	24	1	no	—
518	C₂	C₅×#5213	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#930
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₅×#5822	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#1906
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
3. C₅×#5236	C₂	semidirect
4. C₅×#5006	C₂	semidirect
5. C₂×C₅×#805	C₂	semidirect
6. C₅×#4533	C₂	semidirect
7. C₅×#4523	C₂	semidirect
18. C₅×#951	C₄	semidirect
20. C₅×#949	C₄	semidirect
30. #71645	C₅	direct (N × H)
32. C₄×C₅×#41	D₃	semidirect
54. C₂×C₅×D₁₂	C₂×C₄	semidirect
56. C₂×C₅×Dic₆	C₂×C₄	semidirect
76. C₅×#208	C₂×C₄	semidirect
79. C₃×C₄×#41	C₂×C₅	semidirect
81. #5236	C₂×C₅	semidirect
82. #5006	C₂×C₅	semidirect
83. C₂×#805	C₂×C₅	semidirect
84. #4533	C₂×C₅	semidirect
85. #4523	C₂×C₅	semidirect
152. #951	C₄×C₅	semidirect
154. #949	C₄×C₅	semidirect
206. C₄×#41	C₅×D₃	semidirect
246. C₂×D₁₂	C₂×C₄×C₅	semidirect
248. C₂×Dic₆	C₂×C₄×C₅	semidirect
268. #208	C₂×C₄×C₅	semidirect
427. C₃×C₅	#1906	semidirect
493. C₅	#71645	direct (N × H)
512. C₃	C₅×#1906	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#5822	2
C₅×#5236	2
C₅×#5006	2
C₂×C₅×#805	2
C₅×#4533	2
C₅×#4523	2
C₅×#1906	3
#71645	5

Subgroups — C5×#71645 #14302561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71645 #14302561