Subgroups — C₅×#83416 #14425527

Order 1920.

1408 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	C₅×#5964	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#942	C₂	1	2	yes	maximal, complemented
4	C₅×#5237	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5095	C₂	1	4	yes	maximal, complemented
6	C₅×#5061	C₂	1	4	yes	maximal, complemented
7	C₅×#5005	C₂	1	2	yes	maximal, complemented
8	C₅×#3022	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
11	C₅×#1010	—	2	2	no	—
12	C₅×#1009	—	2	2	no	—
13	C₅×D₃×#41	—	2	4	no	—
14	C₅×#1007	C₂²	1	2	yes	—
15	C₅×#1004	—	2	2	no	—
16	C₅×#1004	C₂²	1	2	yes	—
17	C₂×C₅×#235	—	2	2	no	—
18	C₂×C₅×#235	C₂²	1	2	yes	—
19	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
20	C₃×C₅×#124	C₂²	1	2	yes	complemented
21	C₃×C₅×#123	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×#216	—	2	2	no	—
25	C₅×#942	—	2	4	no	—
26	C₅×#942	C₂²	1	8	yes	complemented
27	C₂×C₅×#215	—	2	2	no	—
28	C₂×C₅×#208	C₂²	1	2	yes	complemented
29	C₅×#836	C₂²	1	2	yes	complemented
30	C₅×#833	C₂²	1	2	yes	complemented
31	C₅×#805	C₂²	1	8	yes	complemented
32	#83416	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₅×#585	—	3	1	no	—
34	C₂×C₅×#137	—	3	2	no	—
35	C₅×#536	D₃	1	1	yes	characteristic, complemented
36	C₅×#456	—	3	4	no	—
37	C₅×#455	—	3	4	no	—
38	C₅×#421	—	3	2	no	—
39	C₅×#413	—	3	1	no	—
40	C₃×C₅×#41	—	2	2	no	—
41	C₃×C₅×#41	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	—	2	2	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
48	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₅×#67	—	2	4	no	—
53	C₂×C₅×#67	—	2	2	no	—
54	C₅×#239	—	2	4	no	—
55	C₅×D₃×Q₈	—	2	4	no	—
56	C₅×#237	—	2	8	no	—
57	C₅×#237	—	2	4	no	—
58	C₅×D₃×D₄	—	2	8	no	—
59	C₅×D₃×D₄	—	2	4	no	—
60	C₅×#235	—	2	4	no	—
61	C₅×#235	—	2	4	no	—
62	C₅×#235	—	2	2	no	—
63	C₅×#235	—	2	4	no	—
64	C₅×#235	—	2	2	no	—
65	C₅×#235	D₄	1	4	yes	—
66	C₅×#235	C₂³	1	4	yes	—
67	C₂×C₅×D₁₂	—	2	2	no	—
68	C₂×C₅×D₁₂	D₄	1	2	yes	—
69	C₂×C₄×C₅×D₃	—	2	4	no	—
70	C₂×C₄×C₅×D₃	—	2	2	no	—
71	C₂×C₅×Dic₆	—	2	2	no	—
72	C₂×C₅×Dic₆	D₄	1	2	yes	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	4	no	—
75	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
77	C₃×C₄²×C₅	C₂³	1	2	yes	—
78	C₅×#216	—	2	8	no	—
79	C₅×#215	—	2	8	no	—
80	C₅×#208	—	2	2	no	—
81	C₅×#208	C₂³	1	4	yes	—
82	C₂×C₅×C₃⋊C₈	—	2	2	no	—
83	#5964	C₂×C₅	1	1	yes	characteristic
84	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂×#942	C₂×C₅	1	2	yes	complemented
86	#5237	C₂×C₅	1	1	yes	characteristic, complemented
87	#5095	C₂×C₅	1	4	yes	complemented
88	#5061	C₂×C₅	1	4	yes	complemented
89	#5005	C₂×C₅	1	2	yes	complemented
90	C₅×2₋¹⁺⁴	—	3	2	no	—
91	C₅×2₋¹⁺⁴	—	6	2	no	—
92	C₅×H(5,𝔽₂)	—	3	2	no	—
93	C₅×H(5,𝔽₂)	—	6	2	no	—
94	C₅×H(5,𝔽₂)	—	6	2	no	—
95	C₂×C₅×#41	—	3	2	no	—
96	C₂×C₅×#41	—	6	4	no	—
97	C₂×C₅×#41	—	6	2	no	—
98	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
100	C₅×#137	—	3	8	no	—
101	C₅×#137	—	6	4	no	—
102	C₂×C₅×Q₁₆	—	6	2	no	—
103	C₂×C₅×SD₁₆	—	6	2	no	—
104	C₂×C₅×M₁₆	—	3	2	no	—
105	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
106	C₅×#124	C₂×D₃	1	2	yes	complemented
107	C₅×#123	—	2	2	no	—
108	C₅×C₂²⋊Q₈	—	2	2	no	—
109	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
110	C₅×#104	—	3	8	no	—
111	C₅×#101	—	3	2	no	—
112	C₅×#100	—	3	2	no	—
113	#3022	—	3	1	no	Sylow
114	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₅×D₃	—	2	4	no	—
117	C₂²×C₅×D₃	—	2	2	no	—
118	C₃×C₅×Q₈	—	2	2	no	—
119	C₃×C₅×Q₈	—	2	4	no	—
120	C₃×C₅×Q₈	—	4	1	no	—
121	C₃×C₅×Q₈	—	4	1	no	—
122	C₃×C₅×D₄	—	2	4	no	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	4	2	no	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₅×#67	—	2	8	no	—
135	C₅×#67	—	2	4	no	—
136	C₅×#67	—	2	4	no	—
137	C₂×C₅×Dic₃	—	2	4	no	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₅×D₁₂	—	2	4	no	—
140	C₅×D₁₂	—	2	2	no	—
141	C₅×D₁₂	C₂×D₄	1	4	yes	—
142	C₄×C₅×D₃	—	2	8	no	—
143	C₄×C₅×D₃	—	2	4	no	—
144	C₄×C₅×D₃	—	2	4	no	—
145	C₅×Dic₆	—	2	4	no	—
146	C₅×Dic₆	—	2	2	no	—
147	C₅×Dic₆	C₂×D₄	1	4	yes	—
148	C₅×C₃⋊C₈	—	2	4	no	—
149	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
150	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
151	#1010	—	2	2	no	—
152	#1009	—	2	2	no	—
153	D₃×#41	—	2	4	no	—
154	#1007	C₂²×C₅	1	2	yes	—
155	#1004	—	2	2	no	—
156	#1004	C₂²×C₅	1	2	yes	—
157	C₂×#235	—	2	2	no	—
158	C₂×#235	C₂²×C₅	1	2	yes	—
159	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
160	C₃×#124	C₂²×C₅	1	2	yes	complemented
161	C₃×#123	—	2	2	no	—
162	C₃×C₂²⋊Q₈	—	2	2	no	—
163	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₂×#216	—	2	2	no	—
165	#942	—	2	4	no	—
166	#942	C₂²×C₅	1	8	yes	complemented
167	C₂×#215	—	2	2	no	—
168	C₂×#208	C₂²×C₅	1	2	yes	complemented
169	#836	C₂²×C₅	1	2	yes	complemented
170	#833	C₂²×C₅	1	2	yes	complemented
171	#805	C₂²×C₅	1	8	yes	complemented
172	C₅×#41	—	2	2	no	—
173	C₅×#41	—	2	2	no	—
174	C₅×#41	—	3	4	no	—
175	C₅×#41	—	3	4	no	—
176	C₅×#41	—	6	4	no	—
177	C₅×#41	—	6	4	no	—
178	C₅×#41	—	6	4	no	—
179	C₅×#41	—	6	8	no	—
180	C₅×#41	—	6	4	no	—
181	C₅×#41	—	6	2	no	—
182	C₅×#41	—	6	2	no	—
183	C₅×#41	—	6	4	no	—
184	C₂×C₅×Q₈	—	2	1	no	—
185	C₂×C₅×Q₈	—	2	2	no	—
186	C₂×C₅×Q₈	—	2	2	no	—
187	C₂×C₅×Q₈	—	3	2	no	—
188	C₂×C₅×Q₈	—	6	2	no	—
189	C₂×C₅×Q₈	—	6	4	no	—
190	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
191	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
192	C₂×C₅×D₄	—	3	2	no	—
193	C₂×C₅×D₄	—	6	2	no	—
194	C₂×C₅×D₄	—	6	4	no	—
195	C₂×C₅×D₄	—	6	8	no	—
196	C₂×C₅×D₄	—	6	2	no	—
197	C₂×C₅×D₄	—	6	4	no	—
198	C₂×C₅×D₄	#67	1	2	yes	—
199	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
200	C₂²×C₄×C₅	—	2	1	no	—
201	C₂²×C₄×C₅	—	6	4	no	—
202	C₂²×C₄×C₅	—	6	2	no	—
203	C₂²×C₄×C₅	#67	1	2	yes	—
204	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₅×Q₁₆	—	6	8	no	—
206	C₅×SD₁₆	—	6	8	no	—
207	C₅×M₁₆	—	3	4	no	—
208	C₅×M₁₆	—	6	2	no	—
209	C₂×C₅×C₈	—	6	2	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	2	1	no	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₄²×C₅	C₂²×D₃	1	2	yes	—
215	#585	—	3	1	no	—
216	C₂×#137	—	3	2	no	—
217	#536	C₅×D₃	1	1	yes	characteristic, complemented
218	#456	—	3	4	no	—
219	#455	—	3	4	no	—
220	#421	—	3	2	no	—
221	#413	—	3	1	no	—
222	C₂²×C₃×C₅	—	2	2	no	—
223	C₂²×C₃×C₅	—	4	1	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	#120	1	2	yes	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₅×D₃	—	2	4	no	—
228	C₂×C₅×D₃	—	8	2	no	—
229	C₂×C₅×D₃	—	8	4	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	4	2	no	—
232	C₃×C₄×C₅	—	4	2	no	—
233	C₃×C₄×C₅	#120	1	1	yes	characteristic
234	C₃×C₄×C₅	#120	1	1	yes	characteristic
235	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
236	C₅×Dic₃	—	2	4	no	—
237	C₃×#41	—	2	2	no	—
238	C₃×#41	—	2	2	no	—
239	C₂×C₃×Q₈	—	2	1	no	—
240	C₂×C₃×Q₈	—	2	2	no	—
241	C₂×C₃×Q₈	—	2	2	no	—
242	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
243	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
244	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
245	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂×#67	—	2	4	no	—
250	C₂×#67	—	2	2	no	—
251	#239	—	2	4	no	—
252	D₃×Q₈	—	2	4	no	—
253	#237	—	2	8	no	—
254	#237	—	2	4	no	—
255	D₃×D₄	—	2	8	no	—
256	D₃×D₄	—	2	4	no	—
257	#235	—	2	4	no	—
258	#235	—	2	4	no	—
259	#235	—	2	2	no	—
260	#235	—	2	4	no	—
261	#235	—	2	2	no	—
262	#235	C₅×D₄	1	4	yes	—
263	#235	C₂³×C₅	1	4	yes	—
264	C₂×D₁₂	—	2	2	no	—
265	C₂×D₁₂	C₅×D₄	1	2	yes	—
266	C₂×C₄×D₃	—	2	4	no	—
267	C₂×C₄×D₃	—	2	2	no	—
268	C₂×Dic₆	—	2	2	no	—
269	C₂×Dic₆	C₅×D₄	1	2	yes	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	4	no	—
272	C₃×C₂²⋊C₄	—	2	1	no	—
273	C₃×C₂²⋊C₄	—	2	4	no	—
274	C₃×C₄²	C₂³×C₅	1	2	yes	—
275	#216	—	2	8	no	—
276	#215	—	2	8	no	—
277	#208	—	2	2	no	—
278	#208	C₂³×C₅	1	4	yes	—
279	C₂×C₃⋊C₈	—	2	2	no	—
280	C₂³×C₅	—	6	4	no	—
281	C₂³×C₅	—	6	2	no	—
282	C₂³×C₅	C₂×#67	1	2	yes	—
283	C₂³×C₅	C₂×#67	1	1	yes	characteristic
284	C₅×Q₈	—	2	2	no	—
285	C₅×Q₈	—	2	4	no	—
286	C₅×Q₈	—	3	4	no	—
287	C₅×Q₈	—	4	1	no	—
288	C₅×Q₈	—	4	1	no	—
289	C₅×Q₈	—	6	4	no	—
290	C₅×Q₈	—	6	2	no	—
291	C₅×D₄	—	2	4	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	3	4	no	—
294	C₅×D₄	—	6	4	no	—
295	C₅×D₄	—	6	8	no	—
296	C₅×D₄	—	6	4	no	—
297	C₅×D₄	—	6	4	no	—
298	C₅×D₄	—	6	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	4	2	no	—
304	C₂×C₄×C₅	—	6	8	no	—
305	C₂×C₄×C₅	—	6	4	no	—
306	C₂×C₄×C₅	—	6	2	no	—
307	C₂×C₄×C₅	—	6	4	no	—
308	C₂×C₄×C₅	—	6	4	no	—
309	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
310	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
311	C₂×C₄×C₅	C₂×#67	1	2	yes	—
312	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
314	C₅×C₈	—	6	4	no	—
315	2₋¹⁺⁴	—	3	2	no	—
316	2₋¹⁺⁴	—	6	2	no	—
317	H(5,𝔽₂)	—	3	2	no	—
318	H(5,𝔽₂)	—	6	2	no	—
319	H(5,𝔽₂)	—	6	2	no	—
320	C₂×#41	—	3	2	no	—
321	C₂×#41	—	6	4	no	—
322	C₂×#41	—	6	2	no	—
323	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
324	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
325	#137	—	3	8	no	—
326	#137	—	6	4	no	—
327	C₂×Q₁₆	—	6	2	no	—
328	C₂×SD₁₆	—	6	2	no	—
329	C₂×M₁₆	—	3	2	no	—
330	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
331	#124	C₂×C₅×D₃	1	2	yes	complemented
332	#123	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
335	#104	—	3	8	no	—
336	#101	—	3	2	no	—
337	#100	—	3	2	no	—
338	C₂×C₃×C₅	—	2	1	no	—
339	C₂×C₃×C₅	—	2	2	no	—
340	C₂×C₃×C₅	—	4	2	no	—
341	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
342	C₅×D₃	—	4	4	no	—
343	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
344	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂²×D₃	—	2	4	no	—
346	C₂²×D₃	—	2	2	no	—
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	2	4	no	—
349	C₃×Q₈	—	4	1	no	—
350	C₃×Q₈	—	4	1	no	—
351	C₃×D₄	—	2	4	no	—
352	C₃×D₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	4	2	no	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
360	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
361	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
363	#67	—	2	8	no	—
364	#67	—	2	4	no	—
365	#67	—	2	4	no	—
366	C₂×Dic₃	—	2	4	no	—
367	C₂×Dic₃	—	2	2	no	—
368	D₁₂	—	2	4	no	—
369	D₁₂	—	2	2	no	—
370	D₁₂	C₂×C₅×D₄	1	4	yes	—
371	C₄×D₃	—	2	8	no	—
372	C₄×D₃	—	2	4	no	—
373	C₄×D₃	—	2	4	no	—
374	Dic₆	—	2	4	no	—
375	Dic₆	—	2	2	no	—
376	Dic₆	C₂×C₅×D₄	1	4	yes	—
377	C₃⋊C₈	—	2	4	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	2	no	—
381	C₂²×C₅	—	6	4	no	—
382	C₂²×C₅	—	24	2	no	—
383	C₂²×C₅	—	24	4	no	—
384	C₂²×C₅	#937	1	2	yes	—
385	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	—	6	4	no	—
390	C₄×C₅	#937	1	1	yes	characteristic
391	C₄×C₅	#937	1	1	yes	characteristic
392	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	3	4	no	—
396	#41	—	3	4	no	—
397	#41	—	6	4	no	—
398	#41	—	6	4	no	—
399	#41	—	6	4	no	—
400	#41	—	6	8	no	—
401	#41	—	6	4	no	—
402	#41	—	6	2	no	—
403	#41	—	6	2	no	—
404	#41	—	6	4	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	3	2	no	—
409	C₂×Q₈	—	6	2	no	—
410	C₂×Q₈	—	6	4	no	—
411	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
412	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
413	C₂×D₄	—	3	2	no	—
414	C₂×D₄	—	6	2	no	—
415	C₂×D₄	—	6	4	no	—
416	C₂×D₄	—	6	8	no	—
417	C₂×D₄	—	6	2	no	—
418	C₂×D₄	—	6	4	no	—
419	C₂×D₄	C₅×#67	1	2	yes	—
420	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	6	4	no	—
423	C₂²×C₄	—	6	2	no	—
424	C₂²×C₄	C₅×#67	1	2	yes	—
425	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
426	Q₁₆	—	6	8	no	—
427	SD₁₆	—	6	8	no	—
428	M₁₆	—	3	4	no	—
429	M₁₆	—	6	2	no	—
430	C₂×C₈	—	6	2	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₄²	C₂²×C₅×D₃	1	2	yes	—
436	C₃×C₅	#3022	1	1	yes	characteristic, complemented, Hall
437	C₂²×C₃	—	2	2	no	—
438	C₂²×C₃	—	4	1	no	—
439	C₂²×C₃	—	4	2	no	—
440	C₂²×C₃	C₅×#120	1	2	yes	—
441	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₂×D₃	—	2	4	no	—
443	C₂×D₃	—	8	2	no	—
444	C₂×D₃	—	8	4	no	—
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	4	2	no	—
447	C₃×C₄	—	4	2	no	—
448	C₃×C₄	C₅×#120	1	1	yes	characteristic
449	C₃×C₄	C₅×#120	1	1	yes	characteristic
450	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
451	Dic₃	—	2	4	no	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	2	no	—
454	C₂×C₅	—	4	2	no	—
455	C₂×C₅	—	12	4	no	—
456	C₂×C₅	C₂×#937	1	1	yes	characteristic
457	C₂³	—	6	4	no	—
458	C₂³	—	6	2	no	—
459	C₂³	C₂×C₅×#67	1	2	yes	—
460	C₂³	C₂×C₅×#67	1	1	yes	characteristic
461	Q₈	—	2	2	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	3	4	no	—
464	Q₈	—	4	1	no	—
465	Q₈	—	4	1	no	—
466	Q₈	—	6	4	no	—
467	Q₈	—	6	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	3	4	no	—
471	D₄	—	6	4	no	—
472	D₄	—	6	8	no	—
473	D₄	—	6	4	no	—
474	D₄	—	6	4	no	—
475	D₄	—	6	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	6	8	no	—
482	C₂×C₄	—	6	4	no	—
483	C₂×C₄	—	6	2	no	—
484	C₂×C₄	—	6	4	no	—
485	C₂×C₄	—	6	4	no	—
486	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
487	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
488	C₂×C₄	C₂×C₅×#67	1	2	yes	—
489	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
491	C₈	—	6	4	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	2	no	—
494	C₂×C₃	—	4	2	no	—
495	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
496	D₃	—	4	4	no	—
497	C₅	#83416	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	6	4	no	—
502	C₂²	—	24	2	no	—
503	C₂²	—	24	4	no	—
504	C₂²	C₅×#937	1	2	yes	—
505	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	6	4	no	—
510	C₄	C₅×#937	1	1	yes	characteristic
511	C₄	C₅×#937	1	1	yes	characteristic
512	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
513	C₃	C₅×#3022	1	1	yes	characteristic, complemented, Sylow
514	C₂	—	2	1	no	—
515	C₂	—	2	2	no	—
516	C₂	—	4	2	no	—
517	C₂	—	12	4	no	—
518	C₂	C₂×C₅×#937	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#937
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#536	C₂
socle	C₂×C₃×C₅	C₂×#120
prime radical	C₅×#5964	C₂
hypercenter	C₅×#536	D₃
hypocenter	C₃	C₅×#3022
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#536

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#536	C₂	semidirect
3. C₂×C₅×#942	C₂	semidirect
4. C₅×#5237	C₂	semidirect
5. C₅×#5095	C₂	semidirect
6. C₅×#5061	C₂	semidirect
7. C₅×#5005	C₂	semidirect
10. C₂²×C₃×C₅×Q₈	C₂²	semidirect
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×C₅×#124	C₂²	semidirect
23. C₃×C₅×#117	C₂²	semidirect
26. C₅×#942	C₂²	semidirect
28. C₂×C₅×#208	C₂²	semidirect
29. C₅×#836	C₂²	semidirect
30. C₅×#833	C₂²	semidirect
31. C₅×#805	C₂²	semidirect
32. #83416	C₅	direct (N × H)
35. C₅×#536	D₃	semidirect
84. C₃×#536	C₂×C₅	semidirect
85. C₂×#942	C₂×C₅	semidirect
86. #5237	C₂×C₅	semidirect
87. #5095	C₂×C₅	semidirect
88. #5061	C₂×C₅	semidirect
89. #5005	C₂×C₅	semidirect
99. C₂²×C₅×Q₈	C₂×D₃	semidirect
105. C₅×C₄⋊Q₈	C₂×D₃	semidirect
106. C₅×#124	C₂×D₃	semidirect
109. C₅×#117	C₂×D₃	semidirect
150. C₂²×C₃×Q₈	C₂²×C₅	semidirect
159. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
160. C₃×#124	C₂²×C₅	semidirect
163. C₃×#117	C₂²×C₅	semidirect
166. #942	C₂²×C₅	semidirect
168. C₂×#208	C₂²×C₅	semidirect
169. #836	C₂²×C₅	semidirect
170. #833	C₂²×C₅	semidirect
171. #805	C₂²×C₅	semidirect
217. #536	C₅×D₃	semidirect
324. C₂²×Q₈	C₂×C₅×D₃	semidirect
330. C₄⋊Q₈	C₂×C₅×D₃	semidirect
331. #124	C₂×C₅×D₃	semidirect
334. #117	C₂×C₅×D₃	semidirect
436. C₃×C₅	#3022	semidirect
497. C₅	#83416	direct (N × H)
513. C₃	C₅×#3022	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5964	2
C₃×C₅×#536	2
C₂×C₅×#942	2
C₅×#5237	2
C₅×#5095	2
C₅×#5061	2
C₅×#5005	2
C₅×#3022	3
#83416	5

Subgroups — C5×#83416 #14425527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83416 #14425527