Subgroups — C₅×#79897 #14418011

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5768	C₂	1	1	yes	maximal, characteristic
2	C₅×D₃×#131	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5196	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5145	C₂	1	2	yes	maximal, complemented
6	C₅×#4895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4824	C₂	1	2	yes	maximal, complemented
9	C₅×#4821	C₂	1	2	yes	maximal, complemented
10	C₅×#4717	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4708	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2955	—	3	1	no	maximal, Hall
13	C₅×D₃×#41	C₂²	1	2	yes	—
14	C₃×C₅×#135	C₂²	1	1	yes	characteristic
15	C₃×C₅×#131	C₂²	1	2	yes	complemented
16	C₅×#950	C₂²	1	2	yes	—
17	C₅×#948	C₂²	1	2	yes	complemented
18	C₅×#918	C₄	1	2	yes	complemented
19	C₅×#915	C₄	1	2	yes	complemented
20	C₅×#914	C₄	1	2	yes	complemented
21	C₅×#911	C₄	1	2	yes	complemented
22	C₅×#907	—	2	2	no	—
23	C₅×#907	C₂²	1	2	yes	complemented
24	C₅×D₃×M₁₆	—	2	2	no	—
25	C₅×D₃×M₁₆	C₂²	1	2	yes	—
26	C₅×#904	C₂²	1	1	yes	characteristic
27	C₅×#901	—	2	2	no	—
28	C₅×#901	C₂²	1	2	yes	complemented
29	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic
30	C₂×C₅×D₃×C₈	—	2	2	no	—
31	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
32	C₅×#872	C₂²	1	1	yes	characteristic
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#104	C₂²	1	2	yes	complemented
35	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
36	C₅×#837	C₂²	1	2	yes	complemented
37	C₅×#825	C₂²	1	2	yes	complemented
38	C₅×#822	C₂²	1	2	yes	complemented
39	C₅×#819	C₂²	1	1	yes	characteristic, complemented
40	C₅×#815	C₂²	1	1	yes	characteristic, complemented
41	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic, complemented
42	C₅×#805	C₂²	1	2	yes	complemented
43	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
44	#79897	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#575	—	3	1	no	—
46	C₂×C₅×#131	—	3	2	no	—
47	C₅×#444	—	3	1	no	—
48	C₅×#444	—	3	2	no	—
49	C₅×#444	D₃	1	1	yes	characteristic, complemented
50	C₅×#443	—	3	1	no	—
51	C₅×#443	—	3	2	no	—
52	C₅×#443	—	3	1	no	—
53	C₅×#430	—	3	1	no	—
54	C₅×#421	—	3	2	no	—
55	C₅×#405	—	3	1	no	—
56	C₃×C₅×#41	C₂³	1	2	yes	—
57	C₅×#239	C₂×C₄	1	2	yes	—
58	C₅×D₃×Q₈	C₂×C₄	1	2	yes	—
59	C₅×#237	—	2	2	no	—
60	C₅×#237	C₂×C₄	1	2	yes	—
61	C₅×D₃×D₄	—	2	2	no	—
62	C₅×D₃×D₄	C₂×C₄	1	2	yes	—
63	C₅×#235	—	2	2	no	—
64	C₅×#235	C₂³	1	2	yes	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
68	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	—
69	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic
70	C₃×C₅×M₁₆	—	2	2	no	—
71	C₃×C₅×M₁₆	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₅×#216	C₂×C₄	1	2	yes	—
77	C₅×#215	C₂×C₄	1	2	yes	—
78	C₅×#214	C₂×C₄	1	2	yes	—
79	C₅×#213	C₂×C₄	1	2	yes	—
80	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
81	C₅×Dic₃⋊C₄	—	2	1	no	—
82	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₅×#208	—	2	2	no	—
84	C₅×#208	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	—	2	2	no	—
86	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×Dic₁₂	C₂×C₄	1	1	yes	characteristic
89	C₅×D₂₄	C₂×C₄	1	1	yes	characteristic
90	C₅×#204	C₂×C₄	1	2	yes	—
91	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
92	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
93	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
94	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
95	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
96	C₅×D₃×C₈	—	2	2	no	—
97	C₅×D₃×C₈	—	2	2	no	—
98	C₅×D₃×C₈	—	2	2	no	—
99	C₅×D₃×C₈	D₄	1	2	yes	—
100	C₅×D₃×C₈	D₄	1	2	yes	—
101	#5768	C₂×C₅	1	1	yes	characteristic
102	D₃×#131	C₂×C₅	1	2	yes	complemented
103	C₃×#444	C₂×C₅	1	1	yes	characteristic, complemented
104	#5196	C₂×C₅	1	1	yes	characteristic, complemented
105	#5145	C₂×C₅	1	2	yes	complemented
106	#4895	C₂×C₅	1	1	yes	characteristic, complemented
107	#4893	C₂×C₅	1	1	yes	characteristic, complemented
108	#4824	C₂×C₅	1	2	yes	complemented
109	#4821	C₂×C₅	1	2	yes	complemented
110	#4717	C₂×C₅	1	1	yes	characteristic, complemented
111	#4708	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	2	no	—
113	C₅×#137	—	3	2	no	—
114	C₅×#137	—	3	2	no	—
115	C₅×AGL(1,ℤ/8)	—	3	2	no	—
116	C₅×AGL(1,ℤ/8)	—	3	2	no	—
117	C₅×#135	—	3	2	no	—
118	C₅×#135	—	3	1	no	—
119	C₅×#135	C₂×D₃	1	1	yes	characteristic
120	C₅×#131	—	3	2	no	—
121	C₅×#131	—	3	2	no	—
122	C₅×#131	—	3	2	no	—
123	C₅×#131	—	6	2	no	—
124	C₅×#131	—	6	2	no	—
125	C₅×#131	C₂×D₃	1	2	yes	complemented
126	C₂×C₅×M₁₆	—	3	1	no	—
127	C₂×C₅×M₁₆	—	3	2	no	—
128	C₂×C₅×M₁₆	—	6	2	no	—
129	C₂²×C₅×C₈	—	3	1	no	—
130	C₂²×C₅×C₈	—	6	2	no	—
131	C₅×#117	—	3	1	no	—
132	C₅×#108	—	3	2	no	—
133	C₅×#108	—	3	1	no	—
134	C₅×#108	C₂×D₃	1	1	yes	characteristic, complemented
135	C₅×#104	—	3	2	no	—
136	C₅×#104	—	3	2	no	—
137	C₅×#104	—	3	2	no	—
138	C₅×#104	C₂×D₃	1	2	yes	complemented
139	C₅×#97	—	3	1	no	—
140	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
141	C₄×C₅×C₈	—	3	1	no	—
142	C₄×C₅×C₈	—	3	1	no	—
143	#2955	—	3	1	no	Sylow
144	C₂²×C₅×D₃	—	2	2	no	—
145	C₂²×C₅×D₃	#41	1	1	yes	characteristic
146	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
147	C₃×C₅×D₄	—	2	2	no	—
148	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
152	C₅×#67	—	2	2	no	—
153	C₅×#67	—	2	2	no	—
154	C₅×#67	—	2	2	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	#41	1	1	yes	characteristic
158	C₅×D₁₂	—	2	2	no	—
159	C₅×D₁₂	C₂²×C₄	1	2	yes	—
160	C₄×C₅×D₃	—	2	2	no	—
161	C₄×C₅×D₃	—	2	2	no	—
162	C₄×C₅×D₃	—	2	2	no	—
163	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
164	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
165	C₅×Dic₆	—	2	2	no	—
166	C₅×Dic₆	C₂²×C₄	1	2	yes	—
167	C₃×C₅×C₈	—	2	2	no	—
168	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
171	C₅×C₃⋊C₈	—	2	2	no	—
172	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
173	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
175	D₃×#41	C₂²×C₅	1	2	yes	—
176	C₃×#135	C₂²×C₅	1	1	yes	characteristic
177	C₃×#131	C₂²×C₅	1	2	yes	complemented
178	#950	C₂²×C₅	1	2	yes	—
179	#948	C₂²×C₅	1	2	yes	complemented
180	#918	C₄×C₅	1	2	yes	complemented
181	#915	C₄×C₅	1	2	yes	complemented
182	#914	C₄×C₅	1	2	yes	complemented
183	#911	C₄×C₅	1	2	yes	complemented
184	#907	—	2	2	no	—
185	#907	C₂²×C₅	1	2	yes	complemented
186	D₃×M₁₆	—	2	2	no	—
187	D₃×M₁₆	C₂²×C₅	1	2	yes	—
188	#904	C₂²×C₅	1	1	yes	characteristic
189	#901	—	2	2	no	—
190	#901	C₂²×C₅	1	2	yes	complemented
191	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic
192	C₂×D₃×C₈	—	2	2	no	—
193	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
194	#872	C₂²×C₅	1	1	yes	characteristic
195	C₃×#108	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₃×#104	C₂²×C₅	1	2	yes	complemented
197	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
198	#837	C₂²×C₅	1	2	yes	complemented
199	#825	C₂²×C₅	1	2	yes	complemented
200	#822	C₂²×C₅	1	2	yes	complemented
201	#819	C₂²×C₅	1	1	yes	characteristic, complemented
202	#815	C₂²×C₅	1	1	yes	characteristic, complemented
203	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
204	#805	C₂²×C₅	1	2	yes	complemented
205	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
206	C₅×#41	—	3	2	no	—
207	C₅×#41	—	3	2	no	—
208	C₅×#41	—	3	2	no	—
209	C₅×#41	—	6	2	no	—
210	C₅×#41	—	6	2	no	—
211	C₅×#41	C₂²×D₃	1	2	yes	—
212	C₂×C₅×Q₈	—	3	2	no	—
213	C₂×C₅×D₄	—	3	2	no	—
214	C₂×C₅×D₄	—	6	2	no	—
215	C₂²×C₄×C₅	—	3	1	no	—
216	C₂²×C₄×C₅	—	6	2	no	—
217	C₅×Q₁₆	—	3	2	no	—
218	C₅×Q₁₆	—	3	1	no	—
219	C₅×Q₁₆	C₄×D₃	1	1	yes	characteristic
220	C₅×SD₁₆	—	3	2	no	—
221	C₅×SD₁₆	—	3	2	no	—
222	C₅×SD₁₆	—	3	2	no	—
223	C₅×SD₁₆	C₄×D₃	1	2	yes	—
224	C₅×D₈	—	3	2	no	—
225	C₅×D₈	—	3	1	no	—
226	C₅×D₈	C₄×D₃	1	1	yes	characteristic
227	C₅×M₁₆	—	2	2	no	—
228	C₅×M₁₆	—	3	2	no	—
229	C₅×M₁₆	—	3	2	no	—
230	C₅×M₁₆	—	3	2	no	—
231	C₅×M₁₆	—	6	2	no	—
232	C₅×M₁₆	—	6	2	no	—
233	C₅×M₁₆	—	6	2	no	—
234	C₅×M₁₆	—	6	2	no	—
235	C₅×M₁₆	C₂²×D₃	1	2	yes	—
236	C₂×C₅×C₈	—	2	2	no	—
237	C₂×C₅×C₈	—	3	1	no	—
238	C₂×C₅×C₈	—	3	1	no	—
239	C₂×C₅×C₈	—	3	2	no	—
240	C₂×C₅×C₈	—	3	2	no	—
241	C₂×C₅×C₈	—	6	2	no	—
242	C₂×C₅×C₈	—	6	2	no	—
243	C₂×C₅×C₈	—	6	2	no	—
244	C₂×C₅×C₈	—	6	2	no	—
245	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
247	C₅×C₄⋊C₄	—	6	1	no	—
248	C₅×C₂²⋊C₄	—	6	1	no	—
249	C₄²×C₅	—	3	1	no	—
250	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
251	#575	—	3	1	no	—
252	C₂×#131	—	3	2	no	—
253	#444	—	3	2	no	—
254	#444	—	3	1	no	—
255	#444	C₅×D₃	1	1	yes	characteristic, complemented
256	#443	—	3	1	no	—
257	#443	—	3	1	no	—
258	#443	—	3	2	no	—
259	#430	—	3	1	no	—
260	#421	—	3	2	no	—
261	#405	—	3	1	no	—
262	C₂²×C₃×C₅	—	2	2	no	—
263	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
264	C₂×C₅×D₃	—	2	2	no	—
265	C₂×C₅×D₃	—	4	1	no	—
266	C₂×C₅×D₃	—	4	4	no	—
267	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
268	C₃×C₄×C₅	—	2	2	no	—
269	C₃×C₄×C₅	—	4	1	no	—
270	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
271	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
272	C₅×Dic₃	—	2	2	no	—
273	C₅×Dic₃	—	4	1	no	—
274	C₅×Dic₃	C₄×D₄	1	2	yes	—
275	C₃×#41	C₂³×C₅	1	2	yes	—
276	#239	C₂×C₄×C₅	1	2	yes	—
277	D₃×Q₈	C₂×C₄×C₅	1	2	yes	—
278	#237	—	2	2	no	—
279	#237	C₂×C₄×C₅	1	2	yes	—
280	D₃×D₄	—	2	2	no	—
281	D₃×D₄	C₂×C₄×C₅	1	2	yes	—
282	#235	—	2	2	no	—
283	#235	C₂³×C₅	1	2	yes	—
284	C₂×C₄×D₃	—	2	2	no	—
285	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
286	C₃×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
287	C₃×SD₁₆	C₂×C₄×C₅	1	2	yes	—
288	C₃×D₈	C₂×C₄×C₅	1	1	yes	characteristic
289	C₃×M₁₆	—	2	2	no	—
290	C₃×M₁₆	C₂³×C₅	1	2	yes	—
291	C₂×C₃×C₈	—	2	2	no	—
292	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
294	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
295	#216	C₂×C₄×C₅	1	2	yes	—
296	#215	C₂×C₄×C₅	1	2	yes	—
297	#214	C₂×C₄×C₅	1	2	yes	—
298	#213	C₂×C₄×C₅	1	2	yes	—
299	(C₂×D₃)⋊C₄	—	2	1	no	—
300	Dic₃⋊C₄	—	2	1	no	—
301	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
302	#208	—	2	2	no	—
303	#208	C₂³×C₅	1	2	yes	—
304	C₂×C₃⋊C₈	—	2	2	no	—
305	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
307	Dic₁₂	C₂×C₄×C₅	1	1	yes	characteristic
308	D₂₄	C₂×C₄×C₅	1	1	yes	characteristic
309	#204	C₂×C₄×C₅	1	2	yes	—
310	ΓL(1,𝔽₂₅)	—	2	2	no	—
311	ΓL(1,𝔽₂₅)	—	2	2	no	—
312	ΓL(1,𝔽₂₅)	—	2	2	no	—
313	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	2	yes	—
314	ΓL(1,𝔽₂₅)	C₂×C₄×C₅	1	2	yes	—
315	D₃×C₈	—	2	2	no	—
316	D₃×C₈	—	2	2	no	—
317	D₃×C₈	—	2	2	no	—
318	D₃×C₈	C₅×D₄	1	2	yes	—
319	D₃×C₈	C₅×D₄	1	2	yes	—
320	C₂³×C₅	—	3	1	no	—
321	C₂³×C₅	—	6	2	no	—
322	C₅×Q₈	—	3	2	no	—
323	C₅×Q₈	—	6	2	no	—
324	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
325	C₅×D₄	—	2	2	no	—
326	C₅×D₄	—	3	2	no	—
327	C₅×D₄	—	6	2	no	—
328	C₅×D₄	—	6	2	no	—
329	C₅×D₄	—	6	2	no	—
330	C₅×D₄	—	6	2	no	—
331	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
332	C₂×C₄×C₅	—	2	2	no	—
333	C₂×C₄×C₅	—	2	1	no	—
334	C₂×C₄×C₅	—	3	1	no	—
335	C₂×C₄×C₅	—	3	2	no	—
336	C₂×C₄×C₅	—	3	2	no	—
337	C₂×C₄×C₅	—	6	2	no	—
338	C₂×C₄×C₅	—	6	2	no	—
339	C₂×C₄×C₅	—	6	2	no	—
340	C₂×C₄×C₅	—	6	2	no	—
341	C₂×C₄×C₅	—	6	1	no	—
342	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
343	C₅×C₈	—	2	2	no	—
344	C₅×C₈	—	3	2	no	—
345	C₅×C₈	—	3	1	no	—
346	C₅×C₈	—	3	1	no	—
347	C₅×C₈	—	6	2	no	—
348	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
349	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
350	C₅×C₈	D₃×D₄	1	2	yes	—
351	C₂×#41	—	3	2	no	—
352	#137	—	3	2	no	—
353	#137	—	3	2	no	—
354	AGL(1,ℤ/8)	—	3	2	no	—
355	AGL(1,ℤ/8)	—	3	2	no	—
356	#135	—	3	2	no	—
357	#135	—	3	1	no	—
358	#135	C₂×C₅×D₃	1	1	yes	characteristic
359	#131	—	3	2	no	—
360	#131	—	3	2	no	—
361	#131	—	3	2	no	—
362	#131	—	6	2	no	—
363	#131	—	6	2	no	—
364	#131	C₂×C₅×D₃	1	2	yes	complemented
365	C₂×M₁₆	—	3	1	no	—
366	C₂×M₁₆	—	3	2	no	—
367	C₂×M₁₆	—	6	2	no	—
368	C₂²×C₈	—	3	1	no	—
369	C₂²×C₈	—	6	2	no	—
370	#117	—	3	1	no	—
371	#108	—	3	2	no	—
372	#108	—	3	1	no	—
373	#108	C₂×C₅×D₃	1	1	yes	characteristic, complemented
374	#104	—	3	2	no	—
375	#104	—	3	2	no	—
376	#104	—	3	2	no	—
377	#104	C₂×C₅×D₃	1	2	yes	complemented
378	#97	—	3	1	no	—
379	#97	C₂×C₅×D₃	1	1	yes	characteristic, complemented
380	C₄×C₈	—	3	1	no	—
381	C₄×C₈	—	3	1	no	—
382	C₂×C₃×C₅	—	2	1	no	—
383	C₂×C₃×C₅	—	4	2	no	—
384	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
385	C₅×D₃	—	2	2	no	—
386	C₅×D₃	—	4	2	no	—
387	C₂²×D₃	—	2	2	no	—
388	C₂²×D₃	C₅×#41	1	1	yes	characteristic
389	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
390	C₃×D₄	—	2	2	no	—
391	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
395	#67	—	2	2	no	—
396	#67	—	2	2	no	—
397	#67	—	2	2	no	—
398	C₂×Dic₃	—	2	2	no	—
399	C₂×Dic₃	—	2	1	no	—
400	C₂×Dic₃	C₅×#41	1	1	yes	characteristic
401	D₁₂	—	2	2	no	—
402	D₁₂	C₂²×C₄×C₅	1	2	yes	—
403	C₄×D₃	—	2	2	no	—
404	C₄×D₃	—	2	2	no	—
405	C₄×D₃	—	2	2	no	—
406	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
407	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
408	Dic₆	—	2	2	no	—
409	Dic₆	C₂²×C₄×C₅	1	2	yes	—
410	C₃×C₈	—	2	2	no	—
411	C₃×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
412	C₃×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
413	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
414	C₃⋊C₈	—	2	2	no	—
415	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
416	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
417	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	3	2	no	—
420	C₂²×C₅	—	6	2	no	—
421	C₂²×C₅	—	12	1	no	—
422	C₂²×C₅	—	12	4	no	—
423	C₂²×C₅	D₃×#41	1	1	yes	characteristic
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	3	2	no	—
426	C₄×C₅	—	4	1	no	—
427	C₄×C₅	—	6	2	no	—
428	C₄×C₅	—	12	1	no	—
429	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
430	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
431	#41	—	3	2	no	—
432	#41	—	3	2	no	—
433	#41	—	3	2	no	—
434	#41	—	6	2	no	—
435	#41	—	6	2	no	—
436	#41	C₂²×C₅×D₃	1	2	yes	—
437	C₂×Q₈	—	3	2	no	—
438	C₂×D₄	—	3	2	no	—
439	C₂×D₄	—	6	2	no	—
440	C₂²×C₄	—	3	1	no	—
441	C₂²×C₄	—	6	2	no	—
442	Q₁₆	—	3	2	no	—
443	Q₁₆	—	3	1	no	—
444	Q₁₆	C₄×C₅×D₃	1	1	yes	characteristic
445	SD₁₆	—	3	2	no	—
446	SD₁₆	—	3	2	no	—
447	SD₁₆	—	3	2	no	—
448	SD₁₆	C₄×C₅×D₃	1	2	yes	—
449	D₈	—	3	2	no	—
450	D₈	—	3	1	no	—
451	D₈	C₄×C₅×D₃	1	1	yes	characteristic
452	M₁₆	—	2	2	no	—
453	M₁₆	—	3	2	no	—
454	M₁₆	—	3	2	no	—
455	M₁₆	—	3	2	no	—
456	M₁₆	—	6	2	no	—
457	M₁₆	—	6	2	no	—
458	M₁₆	—	6	2	no	—
459	M₁₆	—	6	2	no	—
460	M₁₆	C₂²×C₅×D₃	1	2	yes	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	3	1	no	—
463	C₂×C₈	—	3	1	no	—
464	C₂×C₈	—	3	2	no	—
465	C₂×C₈	—	3	2	no	—
466	C₂×C₈	—	6	2	no	—
467	C₂×C₈	—	6	2	no	—
468	C₂×C₈	—	6	2	no	—
469	C₂×C₈	—	6	2	no	—
470	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
471	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
472	C₄⋊C₄	—	6	1	no	—
473	C₂²⋊C₄	—	6	1	no	—
474	C₄²	—	3	1	no	—
475	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
476	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
479	C₂×D₃	—	2	2	no	—
480	C₂×D₃	—	4	1	no	—
481	C₂×D₃	—	4	4	no	—
482	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
483	C₃×C₄	—	2	2	no	—
484	C₃×C₄	—	4	1	no	—
485	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
486	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
487	Dic₃	—	2	2	no	—
488	Dic₃	—	4	1	no	—
489	Dic₃	C₄×C₅×D₄	1	2	yes	—
490	C₂×C₅	—	2	1	no	—
491	C₂×C₅	—	4	2	no	—
492	C₂×C₅	—	6	2	no	—
493	C₂×C₅	—	12	2	no	—
494	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
495	C₂³	—	3	1	no	—
496	C₂³	—	6	2	no	—
497	Q₈	—	3	2	no	—
498	Q₈	—	6	2	no	—
499	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
500	D₄	—	2	2	no	—
501	D₄	—	3	2	no	—
502	D₄	—	6	2	no	—
503	D₄	—	6	2	no	—
504	D₄	—	6	2	no	—
505	D₄	—	6	2	no	—
506	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	3	1	no	—
510	C₂×C₄	—	3	2	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	6	2	no	—
513	C₂×C₄	—	6	2	no	—
514	C₂×C₄	—	6	2	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	—	6	1	no	—
517	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
518	C₈	—	2	2	no	—
519	C₈	—	3	2	no	—
520	C₈	—	3	1	no	—
521	C₈	—	3	1	no	—
522	C₈	—	6	2	no	—
523	C₈	C₂×C₄×C₅×D₃	1	1	yes	characteristic
524	C₈	C₂×C₄×C₅×D₃	1	1	yes	characteristic
525	C₈	C₅×D₃×D₄	1	2	yes	—
526	C₂×C₃	—	2	1	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
529	D₃	—	2	2	no	—
530	D₃	—	4	2	no	—
531	C₅	#79897	1	1	yes	characteristic, direct product factor, Sylow
532	C₂²	—	2	2	no	—
533	C₂²	—	3	2	no	—
534	C₂²	—	6	2	no	—
535	C₂²	—	12	1	no	—
536	C₂²	—	12	4	no	—
537	C₂²	C₅×D₃×#41	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	3	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	6	2	no	—
542	C₄	—	12	1	no	—
543	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
544	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
545	C₃	C₅×#2955	1	1	yes	characteristic, complemented, Sylow
546	C₂	—	2	1	no	—
547	C₂	—	4	2	no	—
548	C₂	—	6	2	no	—
549	C₂	—	12	2	no	—
550	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#444	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₅×#5768	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#444	D₃
hypocenter	C₃	C₅×#2955
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×#444

Complements

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

N	H ≅ G/N	type
2. C₅×D₃×#131	C₂	semidirect
3. C₃×C₅×#444	C₂	semidirect
4. C₅×#5196	C₂	semidirect
5. C₅×#5145	C₂	semidirect
6. C₅×#4895	C₂	semidirect
7. C₅×#4893	C₂	semidirect
8. C₅×#4824	C₂	semidirect
9. C₅×#4821	C₂	semidirect
10. C₅×#4717	C₂	semidirect
11. C₅×#4708	C₂	semidirect
15. C₃×C₅×#131	C₂²	semidirect
17. C₅×#948	C₂²	semidirect
18. C₅×#918	C₄	semidirect
19. C₅×#915	C₄	semidirect
20. C₅×#914	C₄	semidirect
21. C₅×#911	C₄	semidirect
23. C₅×#907	C₂²	semidirect
28. C₅×#901	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#104	C₂²	semidirect
35. C₃×C₅×#97	C₂²	semidirect
36. C₅×#837	C₂²	semidirect
37. C₅×#825	C₂²	semidirect
38. C₅×#822	C₂²	semidirect
39. C₅×#819	C₂²	semidirect
40. C₅×#815	C₂²	semidirect
41. C₅×C₈×Dic₃	C₂²	semidirect
42. C₅×#805	C₂²	semidirect
43. C₄×C₅×C₃⋊C₈	C₂²	semidirect
44. #79897	C₅	direct (N × H)
49. C₅×#444	D₃	semidirect
102. D₃×#131	C₂×C₅	semidirect
103. C₃×#444	C₂×C₅	semidirect
104. #5196	C₂×C₅	semidirect
105. #5145	C₂×C₅	semidirect
106. #4895	C₂×C₅	semidirect
107. #4893	C₂×C₅	semidirect
108. #4824	C₂×C₅	semidirect
109. #4821	C₂×C₅	semidirect
110. #4717	C₂×C₅	semidirect
111. #4708	C₂×C₅	semidirect
125. C₅×#131	C₂×D₃	semidirect
134. C₅×#108	C₂×D₃	semidirect
138. C₅×#104	C₂×D₃	semidirect
140. C₅×#97	C₂×D₃	semidirect
177. C₃×#131	C₂²×C₅	semidirect
179. #948	C₂²×C₅	semidirect
180. #918	C₄×C₅	semidirect
181. #915	C₄×C₅	semidirect
182. #914	C₄×C₅	semidirect
183. #911	C₄×C₅	semidirect
185. #907	C₂²×C₅	semidirect
190. #901	C₂²×C₅	semidirect
195. C₃×#108	C₂²×C₅	semidirect
196. C₃×#104	C₂²×C₅	semidirect
197. C₃×#97	C₂²×C₅	semidirect
198. #837	C₂²×C₅	semidirect
199. #825	C₂²×C₅	semidirect
200. #822	C₂²×C₅	semidirect
201. #819	C₂²×C₅	semidirect
202. #815	C₂²×C₅	semidirect
203. C₈×Dic₃	C₂²×C₅	semidirect
204. #805	C₂²×C₅	semidirect
205. C₄×C₃⋊C₈	C₂²×C₅	semidirect
255. #444	C₅×D₃	semidirect
364. #131	C₂×C₅×D₃	semidirect
373. #108	C₂×C₅×D₃	semidirect
377. #104	C₂×C₅×D₃	semidirect
379. #97	C₂×C₅×D₃	semidirect
476. C₃×C₅	#2955	semidirect
531. C₅	#79897	direct (N × H)
545. C₃	C₅×#2955	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5768	2
C₅×D₃×#131	2
C₃×C₅×#444	2
C₅×#5196	2
C₅×#5145	2
C₅×#4895	2
C₅×#4893	2
C₅×#4824	2
C₅×#4821	2
C₅×#4717	2
C₅×#4708	2
C₅×#2955	3
#79897	5

Subgroups — C5×#79897 #14418011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79897 #14418011