Subgroups — C₅×#84018 #14458221

Order 1920.

888 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5838	C₂	1	2	yes	maximal, complemented
3	C₅×#5771	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5246	C₂	1	2	yes	maximal, complemented
5	C₅×#5205	C₂	1	2	yes	maximal, complemented
6	C₅×#5204	C₂	1	2	yes	maximal, complemented
7	C₅×#5196	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5192	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5183	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5144	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5143	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3293	—	3	1	no	maximal, Hall
13	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₅×#1010	C₂²	1	2	yes	—
15	C₃×C₅×#137	—	2	2	no	—
16	C₃×C₅×#137	C₂²	1	2	yes	—
17	C₃×C₅×#135	—	2	1	no	—
18	C₃×C₅×#135	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×#131	C₂²	1	1	yes	characteristic
22	C₅×#951	—	2	2	no	—
23	C₅×#951	C₂²	1	2	yes	—
24	C₅×#951	C₂²	1	2	yes	—
25	C₅×#950	—	2	2	no	—
26	C₅×#950	C₂²	1	1	yes	characteristic
27	C₅×#948	C₂²	1	2	yes	—
28	C₅×#944	C₂²	1	2	yes	—
29	C₂×C₅×#216	—	2	2	no	—
30	C₂×C₅×#216	C₂²	1	2	yes	—
31	C₅×#942	—	2	2	no	—
32	C₅×#942	C₂²	1	2	yes	—
33	C₅×D₃×Q₁₆	—	2	1	no	—
34	C₅×#915	—	2	2	no	—
35	C₅×#912	—	2	1	no	—
36	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
37	C₅×#901	C₂²	1	1	yes	characteristic
38	C₅×#837	C₂²	1	2	yes	—
39	C₅×#837	C₂²	1	1	yes	characteristic
40	C₅×#836	C₂²	1	2	yes	—
41	C₅×#825	C₂²	1	1	yes	characteristic
42	C₅×#824	C₂²	1	2	yes	—
43	C₅×#822	C₂²	1	1	yes	characteristic
44	C₅×#819	C₂²	1	1	yes	characteristic
45	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
46	#84018	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₅×#578	—	3	2	no	—
48	C₅×#578	—	3	1	no	—
49	C₅×#578	D₃	1	1	yes	characteristic, complemented
50	C₅×#494	—	3	1	no	—
51	C₅×#473	—	3	2	no	—
52	C₅×#473	—	3	1	no	—
53	C₅×#473	—	3	1	no	—
54	C₅×#456	—	3	2	no	—
55	C₅×#456	—	3	2	no	—
56	C₅×#443	—	3	1	no	—
57	C₅×#443	—	3	1	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	—	4	2	no	—
61	C₃×C₅×#41	C₂³	1	2	yes	—
62	C₃×C₅×#41	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×Q₈	—	2	2	no	—
64	C₂×C₃×C₅×Q₈	—	2	2	no	—
65	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
66	C₅×D₃×Q₈	—	2	2	no	—
67	C₅×#237	—	2	2	no	—
68	C₅×#237	—	4	2	no	—
69	C₅×#235	—	2	2	no	—
70	C₅×#235	C₂³	1	1	yes	characteristic
71	C₂×C₅×Dic₆	—	2	2	no	—
72	C₂×C₅×Dic₆	C₂³	1	2	yes	—
73	C₃×C₅×Q₁₆	—	2	2	no	—
74	C₃×C₅×Q₁₆	—	2	1	no	—
75	C₃×C₅×Q₁₆	—	2	1	no	—
76	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic
77	C₃×C₅×SD₁₆	—	2	2	no	—
78	C₃×C₅×SD₁₆	D₄	1	2	yes	—
79	C₃×C₅×D₈	D₄	1	1	yes	characteristic
80	C₃×C₅×M₁₆	—	2	1	no	—
81	C₃×C₅×M₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×C₈	—	2	1	no	—
83	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
84	C₅×#216	—	2	2	no	—
85	C₅×#216	—	2	2	no	—
86	C₅×#216	—	2	2	no	—
87	C₅×#216	—	2	2	no	—
88	C₅×#216	—	2	2	no	—
89	C₅×#216	D₄	1	1	yes	characteristic
90	C₅×#215	—	2	2	no	—
91	C₅×#215	D₄	1	1	yes	characteristic
92	C₅×#214	—	2	2	no	—
93	C₅×#214	—	2	2	no	—
94	C₅×#214	D₄	1	1	yes	characteristic
95	C₅×#213	D₄	1	1	yes	characteristic
96	C₅×Dic₃⋊C₄	—	4	2	no	—
97	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₅×#208	—	2	2	no	—
99	C₅×#208	C₂³	1	1	yes	characteristic
100	C₅×#208	C₂³	1	2	yes	—
101	C₂×C₅×C₃⋊C₈	—	2	2	no	—
102	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
103	C₅×Dic₁₂	—	2	1	no	—
104	C₅×Dic₁₂	—	2	1	no	—
105	C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
106	C₅×D₃×C₈	—	2	1	no	—
107	C₃×#578	C₂×C₅	1	1	yes	characteristic, complemented
108	#5838	C₂×C₅	1	2	yes	complemented
109	#5771	C₂×C₅	1	1	yes	characteristic, complemented
110	#5246	C₂×C₅	1	2	yes	complemented
111	#5205	C₂×C₅	1	2	yes	complemented
112	#5204	C₂×C₅	1	2	yes	complemented
113	#5196	C₂×C₅	1	1	yes	characteristic, complemented
114	#5192	C₂×C₅	1	1	yes	characteristic, complemented
115	#5183	C₂×C₅	1	1	yes	characteristic, complemented
116	#5144	C₂×C₅	1	1	yes	characteristic, complemented
117	#5143	C₂×C₅	1	1	yes	characteristic, complemented
118	C₅×2₋¹⁺⁴	—	3	2	no	—
119	C₅×2₋¹⁺⁴	C₂×D₃	1	2	yes	—
120	C₅×#137	—	2	2	no	—
121	C₅×#137	—	3	2	no	—
122	C₅×#137	—	3	2	no	—
123	C₅×#137	—	3	2	no	—
124	C₅×#137	—	6	2	no	—
125	C₅×#137	—	6	2	no	—
126	C₅×#137	—	6	2	no	—
127	C₅×#137	C₂×D₃	1	2	yes	—
128	C₅×#135	—	2	1	no	—
129	C₅×#135	—	3	1	no	—
130	C₅×#135	—	6	2	no	—
131	C₅×#135	—	6	1	no	—
132	C₅×#135	C₂×D₃	1	1	yes	characteristic
133	C₂×C₅×Q₁₆	—	2	1	no	—
134	C₂×C₅×Q₁₆	—	3	2	no	—
135	C₂×C₅×Q₁₆	—	3	1	no	—
136	C₂×C₅×Q₁₆	—	6	2	no	—
137	C₂×C₅×Q₁₆	—	6	1	no	—
138	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
139	C₅×#131	—	3	2	no	—
140	C₅×#131	—	3	1	no	—
141	C₅×#131	C₂×D₃	1	1	yes	characteristic
142	C₅×C₄⋊Q₈	—	3	2	no	—
143	C₅×#108	—	3	1	no	—
144	C₅×#108	—	3	1	no	—
145	C₅×#104	—	3	1	no	—
146	C₅×#104	—	3	2	no	—
147	C₅×#104	—	3	1	no	—
148	C₅×#101	—	3	2	no	—
149	C₅×#101	—	3	2	no	—
150	C₄×C₅×C₈	—	3	1	no	—
151	#3293	—	3	1	no	Sylow
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×Q₈	—	2	2	no	—
154	C₃×C₅×Q₈	—	4	2	no	—
155	C₃×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
156	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
157	C₃×C₅×D₄	—	2	2	no	—
158	C₃×C₅×D₄	—	2	1	no	—
159	C₃×C₅×D₄	—	4	2	no	—
160	C₃×C₅×D₄	C₂×D₄	1	1	yes	characteristic
161	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	2	2	no	—
165	C₂×C₃×C₄×C₅	—	4	2	no	—
166	C₂×C₃×C₄×C₅	—	4	2	no	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₅×#67	—	2	1	no	—
169	C₅×#67	—	4	2	no	—
170	C₂×C₅×Dic₃	—	2	1	no	—
171	C₂×C₅×Dic₃	—	2	2	no	—
172	C₂×C₅×Dic₃	—	4	2	no	—
173	C₅×D₁₂	C₂×D₄	1	1	yes	characteristic
174	C₄×C₅×D₃	—	2	1	no	—
175	C₄×C₅×D₃	—	4	2	no	—
176	C₅×Dic₆	—	2	2	no	—
177	C₅×Dic₆	—	2	2	no	—
178	C₅×Dic₆	—	4	2	no	—
179	C₅×Dic₆	C₂×D₄	1	1	yes	characteristic
180	C₃×C₅×C₈	—	2	1	no	—
181	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
182	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
183	C₅×C₃⋊C₈	—	2	1	no	—
184	C₅×C₃⋊C₈	—	2	2	no	—
185	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
186	C₅×C₃⋊C₈	C₂×D₄	1	1	yes	characteristic
187	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	—
188	#1010	C₂²×C₅	1	2	yes	—
189	C₃×#137	—	2	2	no	—
190	C₃×#137	C₂²×C₅	1	2	yes	—
191	C₃×#135	—	2	1	no	—
192	C₃×#135	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₃×Q₁₆	—	2	1	no	—
194	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
195	C₃×#131	C₂²×C₅	1	1	yes	characteristic
196	#951	—	2	2	no	—
197	#951	C₂²×C₅	1	2	yes	—
198	#951	C₂²×C₅	1	2	yes	—
199	#950	—	2	2	no	—
200	#950	C₂²×C₅	1	1	yes	characteristic
201	#948	C₂²×C₅	1	2	yes	—
202	#944	C₂²×C₅	1	2	yes	—
203	C₂×#216	—	2	2	no	—
204	C₂×#216	C₂²×C₅	1	2	yes	—
205	#942	—	2	2	no	—
206	#942	C₂²×C₅	1	2	yes	—
207	D₃×Q₁₆	—	2	1	no	—
208	#915	—	2	2	no	—
209	#912	—	2	1	no	—
210	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
211	#901	C₂²×C₅	1	1	yes	characteristic
212	#837	C₂²×C₅	1	1	yes	characteristic
213	#837	C₂²×C₅	1	2	yes	—
214	#836	C₂²×C₅	1	2	yes	—
215	#825	C₂²×C₅	1	1	yes	characteristic
216	#824	C₂²×C₅	1	2	yes	—
217	#822	C₂²×C₅	1	1	yes	characteristic
218	#819	C₂²×C₅	1	1	yes	characteristic
219	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
220	C₅×#41	—	2	2	no	—
221	C₅×#41	—	2	2	no	—
222	C₅×#41	—	3	1	no	—
223	C₅×#41	—	4	2	no	—
224	C₅×#41	—	6	2	no	—
225	C₅×#41	—	6	2	no	—
226	C₅×#41	—	12	2	no	—
227	C₅×#41	C₂²×D₃	1	1	yes	characteristic
228	C₅×#41	C₂²×D₃	1	2	yes	—
229	C₂×C₅×Q₈	—	2	2	no	—
230	C₂×C₅×Q₈	—	2	2	no	—
231	C₂×C₅×Q₈	—	3	2	no	—
232	C₂×C₅×Q₈	—	6	2	no	—
233	C₂×C₅×Q₈	—	6	2	no	—
234	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
235	C₅×Q₁₆	—	2	2	no	—
236	C₅×Q₁₆	—	2	1	no	—
237	C₅×Q₁₆	—	2	1	no	—
238	C₅×Q₁₆	—	3	1	no	—
239	C₅×Q₁₆	—	6	2	no	—
240	C₅×Q₁₆	—	6	2	no	—
241	C₅×Q₁₆	—	6	2	no	—
242	C₅×Q₁₆	—	6	2	no	—
243	C₅×Q₁₆	—	6	2	no	—
244	C₅×Q₁₆	—	6	1	no	—
245	C₅×Q₁₆	—	6	1	no	—
246	C₅×Q₁₆	#67	1	1	yes	characteristic
247	C₅×SD₁₆	—	2	2	no	—
248	C₅×SD₁₆	—	3	1	no	—
249	C₅×SD₁₆	—	3	1	no	—
250	C₅×SD₁₆	—	6	2	no	—
251	C₅×SD₁₆	—	6	2	no	—
252	C₅×SD₁₆	—	6	2	no	—
253	C₅×SD₁₆	#67	1	2	yes	—
254	C₅×D₈	—	3	1	no	—
255	C₅×D₈	#67	1	1	yes	characteristic
256	C₅×M₁₆	—	2	1	no	—
257	C₅×M₁₆	—	3	2	no	—
258	C₅×M₁₆	—	3	1	no	—
259	C₅×M₁₆	—	6	2	no	—
260	C₅×M₁₆	—	6	1	no	—
261	C₅×M₁₆	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₅×C₈	—	2	1	no	—
263	C₂×C₅×C₈	—	3	1	no	—
264	C₂×C₅×C₈	—	6	2	no	—
265	C₂×C₅×C₈	—	6	1	no	—
266	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₅×C₄⋊C₄	—	12	2	no	—
268	C₄²×C₅	—	3	1	no	—
269	#578	—	3	2	no	—
270	#578	—	3	1	no	—
271	#578	C₅×D₃	1	1	yes	characteristic, complemented
272	#494	—	3	1	no	—
273	#473	—	3	2	no	—
274	#473	—	3	1	no	—
275	#473	—	3	1	no	—
276	#456	—	3	2	no	—
277	#456	—	3	2	no	—
278	#443	—	3	1	no	—
279	#443	—	3	1	no	—
280	C₂²×C₃×C₅	—	2	2	no	—
281	C₂²×C₃×C₅	—	2	1	no	—
282	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
283	C₂×C₅×D₃	—	2	1	no	—
284	C₃×C₄×C₅	—	2	2	no	—
285	C₃×C₄×C₅	—	2	1	no	—
286	C₃×C₄×C₅	—	4	2	no	—
287	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
288	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
289	C₅×Dic₃	—	2	2	no	—
290	C₅×Dic₃	—	2	1	no	—
291	C₅×Dic₃	—	4	2	no	—
292	C₃×#41	—	2	2	no	—
293	C₃×#41	—	2	2	no	—
294	C₃×#41	—	4	2	no	—
295	C₃×#41	C₂³×C₅	1	2	yes	—
296	C₃×#41	C₂³×C₅	1	1	yes	characteristic
297	C₂×C₃×Q₈	—	2	2	no	—
298	C₂×C₃×Q₈	—	2	2	no	—
299	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
300	D₃×Q₈	—	2	2	no	—
301	#237	—	2	2	no	—
302	#237	—	4	2	no	—
303	#235	—	2	2	no	—
304	#235	C₂³×C₅	1	1	yes	characteristic
305	C₂×Dic₆	—	2	2	no	—
306	C₂×Dic₆	C₂³×C₅	1	2	yes	—
307	C₃×Q₁₆	—	2	2	no	—
308	C₃×Q₁₆	—	2	1	no	—
309	C₃×Q₁₆	—	2	1	no	—
310	C₃×Q₁₆	C₅×D₄	1	1	yes	characteristic
311	C₃×SD₁₆	—	2	2	no	—
312	C₃×SD₁₆	C₅×D₄	1	2	yes	—
313	C₃×D₈	C₅×D₄	1	1	yes	characteristic
314	C₃×M₁₆	—	2	1	no	—
315	C₃×M₁₆	C₂³×C₅	1	1	yes	characteristic
316	C₂×C₃×C₈	—	2	1	no	—
317	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
318	#216	—	2	2	no	—
319	#216	—	2	2	no	—
320	#216	—	2	2	no	—
321	#216	—	2	2	no	—
322	#216	—	2	2	no	—
323	#216	C₅×D₄	1	1	yes	characteristic
324	#215	—	2	2	no	—
325	#215	C₅×D₄	1	1	yes	characteristic
326	#214	—	2	2	no	—
327	#214	—	2	2	no	—
328	#214	C₅×D₄	1	1	yes	characteristic
329	#213	C₅×D₄	1	1	yes	characteristic
330	Dic₃⋊C₄	—	4	2	no	—
331	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
332	#208	—	2	2	no	—
333	#208	C₂³×C₅	1	2	yes	—
334	#208	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₃⋊C₈	—	2	2	no	—
336	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
337	Dic₁₂	—	2	1	no	—
338	Dic₁₂	—	2	1	no	—
339	ΓL(1,𝔽₂₅)	—	2	1	no	—
340	D₃×C₈	—	2	1	no	—
341	C₅×Q₈	—	2	2	no	—
342	C₅×Q₈	—	2	2	no	—
343	C₅×Q₈	—	3	1	no	—
344	C₅×Q₈	—	4	2	no	—
345	C₅×Q₈	—	6	2	no	—
346	C₅×Q₈	—	6	2	no	—
347	C₅×Q₈	—	12	2	no	—
348	C₅×Q₈	D₃×D₄	1	1	yes	characteristic
349	C₅×Q₈	C₂×#67	1	2	yes	—
350	C₅×D₄	—	2	1	no	—
351	C₅×D₄	—	2	2	no	—
352	C₅×D₄	—	3	1	no	—
353	C₅×D₄	—	4	2	no	—
354	C₅×D₄	—	6	1	no	—
355	C₅×D₄	—	12	2	no	—
356	C₅×D₄	D₃×D₄	1	1	yes	characteristic
357	C₅×D₄	C₂×#67	1	2	yes	—
358	C₂×C₄×C₅	—	2	2	no	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	2	no	—
361	C₂×C₄×C₅	—	4	2	no	—
362	C₂×C₄×C₅	—	4	2	no	—
363	C₂×C₄×C₅	—	6	1	no	—
364	C₂×C₄×C₅	—	6	1	no	—
365	C₂×C₄×C₅	—	6	2	no	—
366	C₂×C₄×C₅	—	12	2	no	—
367	C₂×C₄×C₅	—	12	2	no	—
368	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
369	C₅×C₈	—	2	1	no	—
370	C₅×C₈	—	3	1	no	—
371	C₅×C₈	—	3	1	no	—
372	C₅×C₈	—	6	2	no	—
373	C₅×C₈	—	6	1	no	—
374	C₅×C₈	C₂×#67	1	1	yes	characteristic
375	C₅×C₈	C₂×#67	1	1	yes	characteristic
376	2₋¹⁺⁴	—	3	2	no	—
377	2₋¹⁺⁴	C₂×C₅×D₃	1	2	yes	—
378	#137	—	2	2	no	—
379	#137	—	3	2	no	—
380	#137	—	3	2	no	—
381	#137	—	3	2	no	—
382	#137	—	6	2	no	—
383	#137	—	6	2	no	—
384	#137	—	6	2	no	—
385	#137	C₂×C₅×D₃	1	2	yes	—
386	#135	—	2	1	no	—
387	#135	—	3	1	no	—
388	#135	—	6	2	no	—
389	#135	—	6	1	no	—
390	#135	C₂×C₅×D₃	1	1	yes	characteristic
391	C₂×Q₁₆	—	2	1	no	—
392	C₂×Q₁₆	—	3	2	no	—
393	C₂×Q₁₆	—	3	1	no	—
394	C₂×Q₁₆	—	6	2	no	—
395	C₂×Q₁₆	—	6	1	no	—
396	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
397	#131	—	3	2	no	—
398	#131	—	3	1	no	—
399	#131	C₂×C₅×D₃	1	1	yes	characteristic
400	C₄⋊Q₈	—	3	2	no	—
401	#108	—	3	1	no	—
402	#108	—	3	1	no	—
403	#104	—	3	1	no	—
404	#104	—	3	2	no	—
405	#104	—	3	1	no	—
406	#101	—	3	2	no	—
407	#101	—	3	2	no	—
408	C₄×C₈	—	3	1	no	—
409	C₂×C₃×C₅	—	2	1	no	—
410	C₂×C₃×C₅	—	4	2	no	—
411	C₂×C₃×C₅	—	4	1	no	—
412	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
413	C₅×D₃	—	4	1	no	—
414	C₃×Q₈	—	2	2	no	—
415	C₃×Q₈	—	2	2	no	—
416	C₃×Q₈	—	4	2	no	—
417	C₃×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
418	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
419	C₃×D₄	—	2	2	no	—
420	C₃×D₄	—	2	1	no	—
421	C₃×D₄	—	4	2	no	—
422	C₃×D₄	C₂×C₅×D₄	1	1	yes	characteristic
423	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
424	C₂×C₃×C₄	—	2	2	no	—
425	C₂×C₃×C₄	—	2	1	no	—
426	C₂×C₃×C₄	—	2	2	no	—
427	C₂×C₃×C₄	—	4	2	no	—
428	C₂×C₃×C₄	—	4	2	no	—
429	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
430	#67	—	2	1	no	—
431	#67	—	4	2	no	—
432	C₂×Dic₃	—	2	1	no	—
433	C₂×Dic₃	—	2	2	no	—
434	C₂×Dic₃	—	4	2	no	—
435	D₁₂	C₂×C₅×D₄	1	1	yes	characteristic
436	C₄×D₃	—	2	1	no	—
437	C₄×D₃	—	4	2	no	—
438	Dic₆	—	2	2	no	—
439	Dic₆	—	2	2	no	—
440	Dic₆	—	4	2	no	—
441	Dic₆	C₂×C₅×D₄	1	1	yes	characteristic
442	C₃×C₈	—	2	1	no	—
443	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
444	C₃×C₈	C₂×C₅×D₄	1	1	yes	characteristic
445	C₃⋊C₈	—	2	1	no	—
446	C₃⋊C₈	—	2	2	no	—
447	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
448	C₃⋊C₈	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂²×C₅	—	2	1	no	—
450	C₂²×C₅	—	2	2	no	—
451	C₂²×C₅	—	6	1	no	—
452	C₂²×C₅	#1004	1	1	yes	characteristic
453	C₄×C₅	—	2	1	no	—
454	C₄×C₅	—	2	2	no	—
455	C₄×C₅	—	4	2	no	—
456	C₄×C₅	—	6	2	no	—
457	C₄×C₅	—	6	1	no	—
458	C₄×C₅	—	12	2	no	—
459	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
460	C₄×C₅	C₂²×#67	1	1	yes	characteristic
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	3	1	no	—
464	#41	—	4	2	no	—
465	#41	—	6	2	no	—
466	#41	—	6	2	no	—
467	#41	—	12	2	no	—
468	#41	C₂²×C₅×D₃	1	1	yes	characteristic
469	#41	C₂²×C₅×D₃	1	2	yes	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	3	2	no	—
473	C₂×Q₈	—	6	2	no	—
474	C₂×Q₈	—	6	2	no	—
475	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
476	Q₁₆	—	2	2	no	—
477	Q₁₆	—	2	1	no	—
478	Q₁₆	—	2	1	no	—
479	Q₁₆	—	3	1	no	—
480	Q₁₆	—	6	2	no	—
481	Q₁₆	—	6	2	no	—
482	Q₁₆	—	6	2	no	—
483	Q₁₆	—	6	2	no	—
484	Q₁₆	—	6	2	no	—
485	Q₁₆	—	6	1	no	—
486	Q₁₆	—	6	1	no	—
487	Q₁₆	C₅×#67	1	1	yes	characteristic
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	3	1	no	—
490	SD₁₆	—	3	1	no	—
491	SD₁₆	—	6	2	no	—
492	SD₁₆	—	6	2	no	—
493	SD₁₆	—	6	2	no	—
494	SD₁₆	C₅×#67	1	2	yes	—
495	D₈	—	3	1	no	—
496	D₈	C₅×#67	1	1	yes	characteristic
497	M₁₆	—	2	1	no	—
498	M₁₆	—	3	2	no	—
499	M₁₆	—	3	1	no	—
500	M₁₆	—	6	2	no	—
501	M₁₆	—	6	1	no	—
502	M₁₆	C₂²×C₅×D₃	1	1	yes	characteristic
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	3	1	no	—
505	C₂×C₈	—	6	2	no	—
506	C₂×C₈	—	6	1	no	—
507	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
508	C₄⋊C₄	—	12	2	no	—
509	C₄²	—	3	1	no	—
510	C₃×C₅	#3293	1	1	yes	characteristic, complemented, Hall
511	C₂²×C₃	—	2	2	no	—
512	C₂²×C₃	—	2	1	no	—
513	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×D₃	—	2	1	no	—
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	4	2	no	—
518	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
519	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
520	Dic₃	—	2	2	no	—
521	Dic₃	—	2	1	no	—
522	Dic₃	—	4	2	no	—
523	C₂×C₅	—	2	1	no	—
524	C₂×C₅	—	4	1	no	—
525	C₂×C₅	—	4	2	no	—
526	C₂×C₅	—	12	1	no	—
527	C₂×C₅	D₄×#67	1	1	yes	characteristic
528	Q₈	—	2	2	no	—
529	Q₈	—	2	2	no	—
530	Q₈	—	3	1	no	—
531	Q₈	—	4	2	no	—
532	Q₈	—	6	2	no	—
533	Q₈	—	6	2	no	—
534	Q₈	—	12	2	no	—
535	Q₈	C₅×D₃×D₄	1	1	yes	characteristic
536	Q₈	C₂×C₅×#67	1	2	yes	—
537	D₄	—	2	1	no	—
538	D₄	—	2	2	no	—
539	D₄	—	3	1	no	—
540	D₄	—	4	2	no	—
541	D₄	—	6	1	no	—
542	D₄	—	12	2	no	—
543	D₄	C₅×D₃×D₄	1	1	yes	characteristic
544	D₄	C₂×C₅×#67	1	2	yes	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	6	1	no	—
551	C₂×C₄	—	6	1	no	—
552	C₂×C₄	—	6	2	no	—
553	C₂×C₄	—	12	2	no	—
554	C₂×C₄	—	12	2	no	—
555	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
556	C₈	—	2	1	no	—
557	C₈	—	3	1	no	—
558	C₈	—	3	1	no	—
559	C₈	—	6	2	no	—
560	C₈	—	6	1	no	—
561	C₈	C₂×C₅×#67	1	1	yes	characteristic
562	C₈	C₂×C₅×#67	1	1	yes	characteristic
563	C₂×C₃	—	2	1	no	—
564	C₂×C₃	—	4	2	no	—
565	C₂×C₃	—	4	1	no	—
566	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
567	D₃	—	4	1	no	—
568	C₅	#84018	1	1	yes	characteristic, direct product factor, Sylow
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	6	1	no	—
572	C₂²	C₅×#1004	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	6	2	no	—
577	C₄	—	6	1	no	—
578	C₄	—	12	2	no	—
579	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
580	C₄	C₂²×C₅×#67	1	1	yes	characteristic
581	C₃	C₅×#3293	1	1	yes	characteristic, complemented, Sylow
582	C₂	—	2	1	no	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	12	1	no	—
586	C₂	C₅×D₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	D₄×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#578	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₅×#578	D₃
hypocenter	C₃	C₅×#3293
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#578

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#578	C₂	semidirect
2. C₅×#5838	C₂	semidirect
3. C₅×#5771	C₂	semidirect
4. C₅×#5246	C₂	semidirect
5. C₅×#5205	C₂	semidirect
6. C₅×#5204	C₂	semidirect
7. C₅×#5196	C₂	semidirect
8. C₅×#5192	C₂	semidirect
9. C₅×#5183	C₂	semidirect
10. C₅×#5144	C₂	semidirect
11. C₅×#5143	C₂	semidirect
46. #84018	C₅	direct (N × H)
49. C₅×#578	D₃	semidirect
107. C₃×#578	C₂×C₅	semidirect
108. #5838	C₂×C₅	semidirect
109. #5771	C₂×C₅	semidirect
110. #5246	C₂×C₅	semidirect
111. #5205	C₂×C₅	semidirect
112. #5204	C₂×C₅	semidirect
113. #5196	C₂×C₅	semidirect
114. #5192	C₂×C₅	semidirect
115. #5183	C₂×C₅	semidirect
116. #5144	C₂×C₅	semidirect
117. #5143	C₂×C₅	semidirect
271. #578	C₅×D₃	semidirect
510. C₃×C₅	#3293	semidirect
568. C₅	#84018	direct (N × H)
581. C₃	C₅×#3293	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#578	2
C₅×#5838	2
C₅×#5771	2
C₅×#5246	2
C₅×#5205	2
C₅×#5204	2
C₅×#5196	2
C₅×#5192	2
C₅×#5183	2
C₅×#5144	2
C₅×#5143	2
C₅×#3293	3
#84018	5

Subgroups — C5×#84018 #14458221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#84018 #14458221