Subgroups — C₅×#69036 #14301705

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5745	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5524	C₂	1	1	yes	maximal, characteristic
3	C₅×#5132	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5126	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5126	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1891	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#907	—	2	2	no	—
17	C₅×D₃×M₁₆	—	2	2	no	—
18	C₅×#901	—	2	2	no	—
19	C₅×#897	—	2	1	no	—
20	C₅×#895	—	2	1	no	—
21	C₅×#886	C₄	1	2	yes	—
22	C₅×#882	C₄	1	2	yes	—
23	C₄×C₅×D₁₂	—	2	2	no	—
24	C₅×#824	—	2	1	no	—
25	C₅×#823	—	2	1	no	—
26	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
27	C₅×(C₂×D₃)⋊C₈	—	2	2	no	—
28	#69036	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₅×#568	—	3	1	no	—
30	C₅×#525	—	3	1	no	—
31	C₅×#413	—	3	1	no	—
32	C₅×#407	—	3	1	no	—
33	C₅×#407	—	3	1	no	—
34	C₅×#344	—	3	1	no	—
35	C₅×#344	D₃	1	1	yes	characteristic, complemented
36	C₂³×C₅×D₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂×C₅×#67	C₂×C₄	1	2	yes	—
39	C₂²×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
40	C₅×#235	—	2	1	no	—
41	C₅×#235	—	2	1	no	—
42	C₅×#235	—	2	1	no	—
43	C₅×#235	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	2	no	—
45	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	—	2	1	no	—
47	C₂×C₄×C₅×D₃	—	2	1	no	—
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₄×C₅×D₃	—	2	1	no	—
50	C₂×C₄×C₅×D₃	—	2	1	no	—
51	C₂×C₄×C₅×D₃	—	2	1	no	—
52	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
53	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	—	2	1	no	—
56	C₃×C₅×M₁₆	—	2	1	no	—
57	C₃×C₅×M₁₆	—	2	1	no	—
58	C₂×C₃×C₅×C₈	—	2	1	no	—
59	C₂×C₃×C₅×C₈	D₄	1	2	yes	complemented
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₄²×C₅	—	2	1	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
64	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
65	C₅×C₄⋊Dic₃	—	2	2	no	—
66	C₅×#208	—	2	1	no	—
67	C₅×#208	—	2	1	no	—
68	C₅×#208	—	2	1	no	—
69	C₅×#208	—	2	1	no	—
70	C₂×C₅×C₃⋊C₈	—	2	1	no	—
71	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	complemented
72	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
73	C₅×D₃×C₈	—	2	4	no	—
74	#5745	C₂×C₅	1	1	yes	characteristic, complemented
75	#5524	C₂×C₅	1	1	yes	characteristic
76	#5132	C₂×C₅	1	1	yes	characteristic, complemented
77	#5126	C₂×C₅	1	1	yes	characteristic, complemented
78	#5126	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#344	C₂×C₅	1	1	yes	characteristic, complemented
80	#4533	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂×C₅×#41	—	3	1	no	—
82	C₂³×C₄×C₅	—	3	1	no	—
83	C₅×#131	—	6	2	no	—
84	C₅×#131	—	6	2	no	—
85	C₂×C₅×M₁₆	—	3	1	no	—
86	C₂×C₅×M₁₆	—	3	1	no	—
87	C₂×C₅×M₁₆	—	6	2	no	—
88	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
90	C₅×#123	—	3	2	no	—
91	C₅×C₂²⋊Q₈	—	6	1	no	—
92	C₅×#121	—	6	1	no	—
93	C₅×#120	—	3	2	no	—
94	C₄×C₅×D₄	—	6	2	no	—
95	C₅×#117	C₂×D₃	1	1	yes	characteristic
96	C₅×#101	—	6	1	no	—
97	C₅×#100	—	6	1	no	—
98	C₅×C₂²⋊C₈	—	6	2	no	—
99	C₅×C₂²⋊C₈	—	6	2	no	—
100	#1891	—	3	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₅×D₃	—	2	1	no	—
103	C₂²×C₅×D₃	—	2	1	no	—
104	C₂²×C₅×D₃	—	2	1	no	—
105	C₂²×C₅×D₃	—	4	2	no	—
106	C₂²×C₅×D₃	C₂²⋊C₄	1	2	yes	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
114	C₅×#67	—	2	2	no	—
115	C₅×#67	—	2	2	no	—
116	C₂×C₅×Dic₃	—	2	1	no	—
117	C₂×C₅×Dic₃	—	2	1	no	—
118	C₂×C₅×Dic₃	—	2	1	no	—
119	C₂×C₅×Dic₃	C₂²⋊C₄	1	2	yes	—
120	C₅×D₁₂	—	2	1	no	—
121	C₅×D₁₂	—	2	1	no	—
122	C₅×D₁₂	—	4	4	no	—
123	C₄×C₅×D₃	—	2	2	no	—
124	C₄×C₅×D₃	—	2	2	no	—
125	C₄×C₅×D₃	—	4	1	no	—
126	C₄×C₅×D₃	—	4	1	no	—
127	C₄×C₅×D₃	—	4	1	no	—
128	C₄×C₅×D₃	—	4	1	no	—
129	C₅×Dic₆	—	2	1	no	—
130	C₅×Dic₆	—	2	1	no	—
131	C₃×C₅×C₈	—	2	2	no	—
132	C₃×C₅×C₈	—	4	1	no	—
133	C₅×C₃⋊C₈	—	2	2	no	—
134	C₅×C₃⋊C₈	—	4	1	no	—
135	C₂×#235	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
139	C₃×#117	C₂²×C₅	1	1	yes	characteristic
140	C₂×#208	C₂²×C₅	1	1	yes	characteristic
141	C₂×#208	C₂²×C₅	1	1	yes	characteristic
142	#907	—	2	2	no	—
143	D₃×M₁₆	—	2	2	no	—
144	#901	—	2	2	no	—
145	#897	—	2	1	no	—
146	#895	—	2	1	no	—
147	#886	C₄×C₅	1	2	yes	—
148	#882	C₄×C₅	1	2	yes	—
149	C₄×D₁₂	—	2	2	no	—
150	#824	—	2	1	no	—
151	#823	—	2	1	no	—
152	(C₂×D₃)⋊C₈	—	2	2	no	—
153	(C₂×D₃)⋊C₈	—	2	2	no	—
154	C₂⁴×C₅	—	3	1	no	—
155	C₅×#41	—	6	1	no	—
156	C₅×#41	—	6	1	no	—
157	C₅×#41	—	6	1	no	—
158	C₅×#41	—	6	1	no	—
159	C₂×C₅×Q₈	—	3	1	no	—
160	C₂×C₅×D₄	—	3	2	no	—
161	C₂×C₅×D₄	—	3	1	no	—
162	C₂×C₅×D₄	—	6	2	no	—
163	C₂²×C₄×C₅	—	3	2	no	—
164	C₂²×C₄×C₅	—	3	1	no	—
165	C₂²×C₄×C₅	—	6	1	no	—
166	C₂²×C₄×C₅	—	6	1	no	—
167	C₂²×C₄×C₅	—	6	1	no	—
168	C₂²×C₄×C₅	—	6	1	no	—
169	C₂²×C₄×C₅	—	6	1	no	—
170	C₂²×C₄×C₅	—	6	1	no	—
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₅×M₁₆	—	2	1	no	—
173	C₅×M₁₆	—	2	1	no	—
174	C₅×M₁₆	—	2	1	no	—
175	C₅×M₁₆	—	2	1	no	—
176	C₅×M₁₆	—	6	4	no	—
177	C₅×M₁₆	—	6	1	no	—
178	C₅×M₁₆	—	6	1	no	—
179	C₅×M₁₆	—	6	1	no	—
180	C₅×M₁₆	—	6	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	3	2	no	—
183	C₂×C₅×C₈	—	6	4	no	—
184	C₂×C₅×C₈	—	6	1	no	—
185	C₂×C₅×C₈	D₁₂	1	2	yes	complemented
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	6	2	no	—
188	C₅×C₂²⋊C₄	—	6	2	no	—
189	C₅×C₂²⋊C₄	—	6	2	no	—
190	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
191	C₄²×C₅	—	2	1	no	—
192	#568	—	3	1	no	—
193	#525	—	3	1	no	—
194	#413	—	3	1	no	—
195	#407	—	3	1	no	—
196	#407	—	3	1	no	—
197	#344	—	3	1	no	—
198	#344	C₅×D₃	1	1	yes	characteristic, complemented
199	C₂²×C₃×C₅	—	4	1	no	—
200	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
203	C₂×C₅×D₃	—	2	2	no	—
204	C₂×C₅×D₃	—	2	2	no	—
205	C₂×C₅×D₃	—	2	2	no	—
206	C₂×C₅×D₃	—	2	2	no	—
207	C₂×C₅×D₃	—	4	1	no	—
208	C₂×C₅×D₃	—	4	1	no	—
209	C₂×C₅×D₃	—	4	1	no	—
210	C₂×C₅×D₃	—	4	1	no	—
211	C₂×C₅×D₃	—	4	2	no	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₃×C₄×C₅	#120	1	1	yes	characteristic
214	C₃×C₄×C₅	#121	1	1	yes	characteristic
215	C₃×C₄×C₅	#121	1	1	yes	characteristic
216	C₃×C₄×C₅	#123	1	1	yes	characteristic
217	C₅×Dic₃	—	2	2	no	—
218	C₅×Dic₃	—	4	1	no	—
219	C₂³×D₃	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂×#67	C₂×C₄×C₅	1	2	yes	—
222	C₂²×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
223	#235	—	2	1	no	—
224	#235	—	2	1	no	—
225	#235	—	2	1	no	—
226	#235	—	2	1	no	—
227	C₂×D₁₂	—	2	2	no	—
228	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
229	C₂×C₄×D₃	—	2	1	no	—
230	C₂×C₄×D₃	—	2	1	no	—
231	C₂×C₄×D₃	—	2	1	no	—
232	C₂×C₄×D₃	—	2	1	no	—
233	C₂×C₄×D₃	—	2	1	no	—
234	C₂×C₄×D₃	—	2	1	no	—
235	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
236	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
237	C₃×M₁₆	—	2	1	no	—
238	C₃×M₁₆	—	2	1	no	—
239	C₃×M₁₆	—	2	1	no	—
240	C₃×M₁₆	—	2	1	no	—
241	C₂×C₃×C₈	—	2	1	no	—
242	C₂×C₃×C₈	C₅×D₄	1	2	yes	complemented
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
245	C₃×C₄²	—	2	1	no	—
246	(C₂×D₃)⋊C₄	—	2	2	no	—
247	(C₂×D₃)⋊C₄	—	2	2	no	—
248	C₄⋊Dic₃	—	2	2	no	—
249	#208	—	2	1	no	—
250	#208	—	2	1	no	—
251	#208	—	2	1	no	—
252	#208	—	2	1	no	—
253	C₂×C₃⋊C₈	—	2	1	no	—
254	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	complemented
255	ΓL(1,𝔽₂₅)	—	2	4	no	—
256	D₃×C₈	—	2	4	no	—
257	C₂³×C₅	—	3	2	no	—
258	C₂³×C₅	—	6	1	no	—
259	C₂³×C₅	—	6	1	no	—
260	C₂³×C₅	—	6	1	no	—
261	C₂³×C₅	—	12	2	no	—
262	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
263	C₅×Q₈	—	6	1	no	—
264	C₅×Q₈	—	6	1	no	—
265	C₅×D₄	—	6	2	no	—
266	C₅×D₄	—	6	2	no	—
267	C₅×D₄	—	6	1	no	—
268	C₅×D₄	—	6	1	no	—
269	C₅×D₄	—	12	4	no	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	3	2	no	—
272	C₂×C₄×C₅	—	6	2	no	—
273	C₂×C₄×C₅	—	6	2	no	—
274	C₂×C₄×C₅	—	6	1	no	—
275	C₂×C₄×C₅	—	6	1	no	—
276	C₂×C₄×C₅	—	6	1	no	—
277	C₂×C₄×C₅	—	12	1	no	—
278	C₂×C₄×C₅	—	12	1	no	—
279	C₂×C₄×C₅	—	12	1	no	—
280	C₂×C₄×C₅	—	12	1	no	—
281	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
282	C₂×C₄×C₅	#235	1	1	yes	characteristic
283	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	#239	1	1	yes	characteristic
287	C₅×C₈	—	2	2	no	—
288	C₅×C₈	—	4	1	no	—
289	C₅×C₈	—	6	2	no	—
290	C₅×C₈	—	12	1	no	—
291	C₂×#41	—	3	1	no	—
292	C₂³×C₄	—	3	1	no	—
293	#131	—	6	2	no	—
294	#131	—	6	2	no	—
295	C₂×M₁₆	—	3	1	no	—
296	C₂×M₁₆	—	3	1	no	—
297	C₂×M₁₆	—	6	2	no	—
298	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
299	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
300	#123	—	3	2	no	—
301	C₂²⋊Q₈	—	6	1	no	—
302	#121	—	6	1	no	—
303	#120	—	3	2	no	—
304	C₄×D₄	—	6	2	no	—
305	#117	C₂×C₅×D₃	1	1	yes	characteristic
306	#101	—	6	1	no	—
307	#100	—	6	1	no	—
308	C₂²⋊C₈	—	6	2	no	—
309	C₂²⋊C₈	—	6	2	no	—
310	C₂×C₃×C₅	—	2	1	no	—
311	C₂×C₃×C₅	—	2	1	no	—
312	C₂×C₃×C₅	—	2	1	no	—
313	C₂×C₃×C₅	#386	1	1	yes	characteristic
314	C₅×D₃	—	4	2	no	—
315	C₅×D₃	—	4	2	no	—
316	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂²×D₃	—	2	1	no	—
318	C₂²×D₃	—	2	1	no	—
319	C₂²×D₃	—	2	1	no	—
320	C₂²×D₃	—	4	2	no	—
321	C₂²×D₃	C₅×C₂²⋊C₄	1	2	yes	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
324	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
328	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
329	#67	—	2	2	no	—
330	#67	—	2	2	no	—
331	C₂×Dic₃	—	2	1	no	—
332	C₂×Dic₃	—	2	1	no	—
333	C₂×Dic₃	—	2	1	no	—
334	C₂×Dic₃	C₅×C₂²⋊C₄	1	2	yes	—
335	D₁₂	—	2	1	no	—
336	D₁₂	—	2	1	no	—
337	D₁₂	—	4	4	no	—
338	C₄×D₃	—	2	2	no	—
339	C₄×D₃	—	2	2	no	—
340	C₄×D₃	—	4	1	no	—
341	C₄×D₃	—	4	1	no	—
342	C₄×D₃	—	4	1	no	—
343	C₄×D₃	—	4	1	no	—
344	Dic₆	—	2	1	no	—
345	Dic₆	—	2	1	no	—
346	C₃×C₈	—	2	2	no	—
347	C₃×C₈	—	4	1	no	—
348	C₃⋊C₈	—	2	2	no	—
349	C₃⋊C₈	—	4	1	no	—
350	C₂²×C₅	—	4	1	no	—
351	C₂²×C₅	—	6	2	no	—
352	C₂²×C₅	—	6	2	no	—
353	C₂²×C₅	—	6	2	no	—
354	C₂²×C₅	—	6	2	no	—
355	C₂²×C₅	—	12	2	no	—
356	C₂²×C₅	—	12	1	no	—
357	C₂²×C₅	—	12	1	no	—
358	C₂²×C₅	—	12	1	no	—
359	C₂²×C₅	—	12	1	no	—
360	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
361	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
362	C₂²×C₅	#893	1	1	yes	characteristic
363	C₄×C₅	—	4	2	no	—
364	C₄×C₅	—	6	2	no	—
365	C₄×C₅	—	12	1	no	—
366	C₄×C₅	#882	1	1	yes	characteristic
367	C₄×C₅	#884	1	1	yes	characteristic
368	C₄×C₅	#894	1	1	yes	characteristic
369	C₄×C₅	#895	1	1	yes	characteristic
370	C₂⁴	—	3	1	no	—
371	#41	—	6	1	no	—
372	#41	—	6	1	no	—
373	#41	—	6	1	no	—
374	#41	—	6	1	no	—
375	C₂×Q₈	—	3	1	no	—
376	C₂×D₄	—	3	2	no	—
377	C₂×D₄	—	3	1	no	—
378	C₂×D₄	—	6	2	no	—
379	C₂²×C₄	—	3	2	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	6	1	no	—
382	C₂²×C₄	—	6	1	no	—
383	C₂²×C₄	—	6	1	no	—
384	C₂²×C₄	—	6	1	no	—
385	C₂²×C₄	—	6	1	no	—
386	C₂²×C₄	—	6	1	no	—
387	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
388	M₁₆	—	2	1	no	—
389	M₁₆	—	2	1	no	—
390	M₁₆	—	2	1	no	—
391	M₁₆	—	2	1	no	—
392	M₁₆	—	6	4	no	—
393	M₁₆	—	6	1	no	—
394	M₁₆	—	6	1	no	—
395	M₁₆	—	6	1	no	—
396	M₁₆	—	6	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	3	2	no	—
399	C₂×C₈	—	6	4	no	—
400	C₂×C₈	—	6	1	no	—
401	C₂×C₈	C₅×D₁₂	1	2	yes	complemented
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	6	2	no	—
404	C₂²⋊C₄	—	6	2	no	—
405	C₂²⋊C₄	—	6	2	no	—
406	C₂²⋊C₄	C₄×C₅×D₃	1	2	yes	—
407	C₄²	—	2	1	no	—
408	C₃×C₅	#1891	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
411	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
412	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
413	C₂×D₃	—	2	2	no	—
414	C₂×D₃	—	2	2	no	—
415	C₂×D₃	—	2	2	no	—
416	C₂×D₃	—	2	2	no	—
417	C₂×D₃	—	4	1	no	—
418	C₂×D₃	—	4	1	no	—
419	C₂×D₃	—	4	1	no	—
420	C₂×D₃	—	4	1	no	—
421	C₂×D₃	—	4	2	no	—
422	C₃×C₄	—	4	2	no	—
423	C₃×C₄	C₅×#120	1	1	yes	characteristic
424	C₃×C₄	C₅×#121	1	1	yes	characteristic
425	C₃×C₄	C₅×#121	1	1	yes	characteristic
426	C₃×C₄	C₅×#123	1	1	yes	characteristic
427	Dic₃	—	2	2	no	—
428	Dic₃	—	4	1	no	—
429	C₂×C₅	—	2	1	no	—
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	—	12	2	no	—
433	C₂×C₅	—	12	2	no	—
434	C₂×C₅	#4665	1	1	yes	characteristic
435	C₂³	—	3	2	no	—
436	C₂³	—	6	1	no	—
437	C₂³	—	6	1	no	—
438	C₂³	—	6	1	no	—
439	C₂³	—	12	2	no	—
440	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
441	Q₈	—	6	1	no	—
442	Q₈	—	6	1	no	—
443	D₄	—	6	2	no	—
444	D₄	—	6	2	no	—
445	D₄	—	6	1	no	—
446	D₄	—	6	1	no	—
447	D₄	—	12	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	3	2	no	—
450	C₂×C₄	—	6	2	no	—
451	C₂×C₄	—	6	2	no	—
452	C₂×C₄	—	6	1	no	—
453	C₂×C₄	—	6	1	no	—
454	C₂×C₄	—	6	1	no	—
455	C₂×C₄	—	12	1	no	—
456	C₂×C₄	—	12	1	no	—
457	C₂×C₄	—	12	1	no	—
458	C₂×C₄	—	12	1	no	—
459	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
460	C₂×C₄	C₅×#235	1	1	yes	characteristic
461	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
462	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
463	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
464	C₂×C₄	C₅×#239	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	6	2	no	—
468	C₈	—	12	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	2	1	no	—
471	C₂×C₃	—	2	1	no	—
472	C₂×C₃	C₅×#386	1	1	yes	characteristic
473	D₃	—	4	2	no	—
474	D₃	—	4	2	no	—
475	C₅	#69036	1	1	yes	characteristic, direct product factor, Sylow
476	C₂²	—	4	1	no	—
477	C₂²	—	6	2	no	—
478	C₂²	—	6	2	no	—
479	C₂²	—	6	2	no	—
480	C₂²	—	6	2	no	—
481	C₂²	—	12	2	no	—
482	C₂²	—	12	1	no	—
483	C₂²	—	12	1	no	—
484	C₂²	—	12	1	no	—
485	C₂²	—	12	1	no	—
486	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
487	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
488	C₂²	C₅×#893	1	1	yes	characteristic
489	C₄	—	4	2	no	—
490	C₄	—	6	2	no	—
491	C₄	—	12	1	no	—
492	C₄	C₅×#882	1	1	yes	characteristic
493	C₄	C₅×#884	1	1	yes	characteristic
494	C₄	C₅×#894	1	1	yes	characteristic
495	C₄	C₅×#895	1	1	yes	characteristic
496	C₃	C₅×#1891	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	2	1	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	1	no	—
500	C₂	—	12	2	no	—
501	C₂	—	12	2	no	—
502	C₂	C₅×#4665	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#882
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#344	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₅×#5524	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#344	D₃
hypocenter	C₃	C₅×#1891
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#344

Complements

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

N	H ≅ G/N	type
1. C₅×#5745	C₂	semidirect
3. C₅×#5132	C₂	semidirect
4. C₅×#5126	C₂	semidirect
5. C₅×#5126	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₅×#4533	C₂	semidirect
28. #69036	C₅	direct (N × H)
35. C₅×#344	D₃	semidirect
59. C₂×C₃×C₅×C₈	D₄	semidirect
71. C₂×C₅×C₃⋊C₈	D₄	semidirect
74. #5745	C₂×C₅	semidirect
76. #5132	C₂×C₅	semidirect
77. #5126	C₂×C₅	semidirect
78. #5126	C₂×C₅	semidirect
79. C₃×#344	C₂×C₅	semidirect
80. #4533	C₂×C₅	semidirect
185. C₂×C₅×C₈	D₁₂	semidirect
198. #344	C₅×D₃	semidirect
242. C₂×C₃×C₈	C₅×D₄	semidirect
254. C₂×C₃⋊C₈	C₅×D₄	semidirect
401. C₂×C₈	C₅×D₁₂	semidirect
408. C₃×C₅	#1891	semidirect
475. C₅	#69036	direct (N × H)
496. C₃	C₅×#1891	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5745	2
C₅×#5524	2
C₅×#5132	2
C₅×#5126	2
C₃×C₅×#344	2
C₅×#4533	2
C₅×#1891	3
#69036	5

Subgroups — C5×#69036 #14301705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69036 #14301705