Subgroups — C₅×#83415 #14425374

Order 1920.

1396 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1007	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5822	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#836	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5095	C₂	1	4	yes	maximal, complemented
6	C₅×#5062	C₂	1	4	yes	maximal, complemented
7	C₅×#5005	C₂	1	2	yes	maximal, complemented
8	C₅×#3020	—	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
11	C₅×#1007	—	2	2	no	—
12	C₅×#1007	—	2	4	no	—
13	C₅×#1007	C₂²	1	4	yes	—
14	C₂×C₅×#239	—	2	2	no	—
15	C₂×C₅×D₃×Q₈	—	2	2	no	—
16	C₂×C₅×#235	—	2	2	no	—
17	C₂×C₅×#235	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#124	C₂²	1	2	yes	complemented
20	C₃×C₅×#123	—	2	2	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₃×C₅×#117	C₂²	1	1	yes	characteristic
23	C₅×#951	—	2	2	no	—
24	C₅×#950	—	2	4	no	—
25	C₅×#949	—	2	2	no	—
26	C₅×#942	C₂²	1	4	yes	complemented
27	C₅×#932	C₂²	1	4	yes	complemented
28	C₂×C₅×#208	C₂²	1	2	yes	—
29	C₅×#836	C₂²	1	4	yes	complemented
30	C₅×#805	C₂²	1	8	yes	complemented
31	#83415	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
33	C₅×#575	—	3	2	no	—
34	C₅×#536	D₃	1	1	yes	characteristic, complemented
35	C₅×#456	—	3	4	no	—
36	C₅×#454	—	3	4	no	—
37	C₅×#421	—	3	2	no	—
38	C₂×C₅×#101	—	3	1	no	—
39	C₃×C₅×#41	—	2	2	no	—
40	C₃×C₅×#41	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
44	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	—	2	2	no	—
52	C₅×#239	—	2	8	no	—
53	C₅×#239	—	2	8	no	—
54	C₅×D₃×Q₈	—	2	8	no	—
55	C₅×D₃×Q₈	—	2	8	no	—
56	C₅×#235	—	2	8	no	—
57	C₅×#235	—	2	8	no	—
58	C₅×#235	—	2	2	no	—
59	C₅×#235	—	2	2	no	—
60	C₅×#235	D₄	1	4	yes	—
61	C₅×#235	C₂³	1	4	yes	—
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	D₄	1	2	yes	—
64	C₂×C₄×C₅×D₃	—	2	4	no	—
65	C₂×C₄×C₅×D₃	—	2	2	no	—
66	C₂×C₅×Dic₆	—	2	2	no	—
67	C₂×C₅×Dic₆	D₄	1	2	yes	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	—
73	C₅×#216	—	2	4	no	—
74	C₅×#215	—	2	4	no	—
75	C₅×#214	—	2	4	no	—
76	C₅×#213	—	2	4	no	—
77	C₅×#208	—	2	2	no	—
78	C₅×#208	C₂³	1	4	yes	—
79	C₂×C₅×C₃⋊C₈	—	2	2	no	—
80	C₂×#1007	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
82	#5822	C₂×C₅	1	2	yes	complemented
83	C₂×#836	C₂×C₅	1	1	yes	characteristic, complemented
84	#5095	C₂×C₅	1	4	yes	complemented
85	#5062	C₂×C₅	1	4	yes	complemented
86	#5005	C₂×C₅	1	2	yes	complemented
87	C₅×2₋¹⁺⁴	—	3	4	no	—
88	C₅×2₋¹⁺⁴	—	6	4	no	—
89	C₅×2₋¹⁺⁴	—	6	2	no	—
90	C₂×C₅×#41	—	3	2	no	—
91	C₂×C₅×#41	—	6	2	no	—
92	C₂×C₅×#41	—	6	2	no	—
93	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₅×Q₈	—	6	2	no	—
95	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
96	C₅×#137	—	3	4	no	—
97	C₅×#137	—	6	2	no	—
98	C₅×AGL(1,ℤ/8)	—	3	4	no	—
99	C₅×AGL(1,ℤ/8)	—	6	2	no	—
100	C₅×#135	—	6	4	no	—
101	C₂×C₅×M₁₆	—	3	2	no	—
102	C₅×C₄⋊Q₈	C₂×D₃	1	2	yes	complemented
103	C₅×#124	C₂×D₃	1	2	yes	complemented
104	C₅×#123	—	2	2	no	—
105	C₅×C₂²⋊Q₈	—	2	2	no	—
106	C₅×#117	C₂×D₃	1	1	yes	characteristic
107	C₅×#104	—	3	8	no	—
108	C₅×#101	—	3	4	no	—
109	#3020	—	3	1	no	Sylow
110	C₂³×C₃×C₅	—	2	1	no	—
111	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₅×D₃	—	2	2	no	—
113	C₃×C₅×Q₈	—	2	4	no	—
114	C₃×C₅×Q₈	—	2	4	no	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	4	1	no	—
118	C₃×C₅×D₄	—	4	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	C₂×D₄	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×#67	—	2	4	no	—
130	C₅×#67	—	2	4	no	—
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₅×D₁₂	—	2	8	no	—
133	C₅×D₁₂	—	2	2	no	—
134	C₅×D₁₂	C₂×D₄	1	4	yes	—
135	C₄×C₅×D₃	—	2	16	no	—
136	C₄×C₅×D₃	—	2	4	no	—
137	C₄×C₅×D₃	—	2	4	no	—
138	C₅×Dic₆	—	2	8	no	—
139	C₅×Dic₆	—	2	2	no	—
140	C₅×Dic₆	C₂×D₄	1	4	yes	—
141	C₅×C₃⋊C₈	—	2	4	no	—
142	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
143	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
144	#1007	—	2	2	no	—
145	#1007	—	2	4	no	—
146	#1007	C₂²×C₅	1	4	yes	—
147	C₂×#239	—	2	2	no	—
148	C₂×D₃×Q₈	—	2	2	no	—
149	C₂×#235	—	2	2	no	—
150	C₂×#235	C₂²×C₅	1	2	yes	—
151	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
152	C₃×#124	C₂²×C₅	1	2	yes	complemented
153	C₃×#123	—	2	2	no	—
154	C₃×C₂²⋊Q₈	—	2	2	no	—
155	C₃×#117	C₂²×C₅	1	1	yes	characteristic
156	#951	—	2	2	no	—
157	#950	—	2	4	no	—
158	#949	—	2	2	no	—
159	#942	C₂²×C₅	1	4	yes	complemented
160	#932	C₂²×C₅	1	4	yes	complemented
161	C₂×#208	C₂²×C₅	1	2	yes	—
162	#836	C₂²×C₅	1	4	yes	complemented
163	#805	C₂²×C₅	1	8	yes	complemented
164	C₅×#41	—	2	2	no	—
165	C₅×#41	—	2	2	no	—
166	C₅×#41	—	3	4	no	—
167	C₅×#41	—	3	4	no	—
168	C₅×#41	—	6	8	no	—
169	C₅×#41	—	6	8	no	—
170	C₅×#41	—	6	8	no	—
171	C₅×#41	—	6	2	no	—
172	C₅×#41	—	6	2	no	—
173	C₅×#41	—	6	8	no	—
174	C₂×C₅×Q₈	—	2	2	no	—
175	C₂×C₅×Q₈	—	2	2	no	—
176	C₂×C₅×Q₈	—	3	2	no	—
177	C₂×C₅×Q₈	—	6	2	no	—
178	C₂×C₅×Q₈	—	6	8	no	—
179	C₂×C₅×Q₈	—	6	8	no	—
180	C₂×C₅×Q₈	#67	1	2	yes	—
181	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
182	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
183	C₂×C₅×D₄	—	2	1	no	—
184	C₂×C₅×D₄	—	3	2	no	—
185	C₂×C₅×D₄	—	6	2	no	—
186	C₂×C₅×D₄	—	6	2	no	—
187	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	—	6	4	no	—
190	C₂²×C₄×C₅	—	6	2	no	—
191	C₂²×C₄×C₅	#67	1	2	yes	—
192	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
193	C₅×Q₁₆	—	6	4	no	—
194	C₅×SD₁₆	—	6	4	no	—
195	C₅×SD₁₆	—	6	4	no	—
196	C₅×D₈	—	6	4	no	—
197	C₅×M₁₆	—	3	4	no	—
198	C₅×M₁₆	—	6	2	no	—
199	C₂×C₅×C₈	—	6	2	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₅×C₂²⋊C₄	—	2	4	no	—
204	C₄²×C₅	C₂²×D₃	1	2	yes	—
205	C₂×2₋¹⁺⁴	—	3	1	no	—
206	#575	—	3	2	no	—
207	#536	C₅×D₃	1	1	yes	characteristic, complemented
208	#456	—	3	4	no	—
209	#454	—	3	4	no	—
210	#421	—	3	2	no	—
211	C₂×#101	—	3	1	no	—
212	C₂²×C₃×C₅	—	4	1	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	—	4	1	no	—
215	C₂²×C₃×C₅	#120	1	1	yes	characteristic
216	C₂²×C₃×C₅	#120	1	1	yes	characteristic
217	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₅×D₃	—	2	4	no	—
219	C₂×C₅×D₃	—	4	4	no	—
220	C₃×C₄×C₅	—	2	4	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	1	no	—
223	C₃×C₄×C₅	#120	1	2	yes	—
224	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
225	C₅×Dic₃	—	2	4	no	—
226	C₃×#41	—	2	2	no	—
227	C₃×#41	—	2	2	no	—
228	C₂×C₃×Q₈	—	2	2	no	—
229	C₂×C₃×Q₈	—	2	2	no	—
230	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
231	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
233	C₂×C₃×D₄	—	2	1	no	—
234	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₃×C₄	—	2	1	no	—
236	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
237	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
238	C₂×#67	—	2	2	no	—
239	#239	—	2	8	no	—
240	#239	—	2	8	no	—
241	D₃×Q₈	—	2	8	no	—
242	D₃×Q₈	—	2	8	no	—
243	#235	—	2	8	no	—
244	#235	—	2	8	no	—
245	#235	—	2	2	no	—
246	#235	—	2	2	no	—
247	#235	C₅×D₄	1	4	yes	—
248	#235	C₂³×C₅	1	4	yes	—
249	C₂×D₁₂	—	2	2	no	—
250	C₂×D₁₂	C₅×D₄	1	2	yes	—
251	C₂×C₄×D₃	—	2	4	no	—
252	C₂×C₄×D₃	—	2	2	no	—
253	C₂×Dic₆	—	2	2	no	—
254	C₂×Dic₆	C₅×D₄	1	2	yes	—
255	C₃×C₄⋊C₄	—	2	1	no	—
256	C₃×C₄⋊C₄	—	2	4	no	—
257	C₃×C₂²⋊C₄	—	2	1	no	—
258	C₃×C₂²⋊C₄	—	2	4	no	—
259	C₃×C₄²	C₂³×C₅	1	2	yes	—
260	#216	—	2	4	no	—
261	#215	—	2	4	no	—
262	#214	—	2	4	no	—
263	#213	—	2	4	no	—
264	#208	—	2	2	no	—
265	#208	C₂³×C₅	1	4	yes	—
266	C₂×C₃⋊C₈	—	2	2	no	—
267	C₂³×C₅	—	2	1	no	—
268	C₂³×C₅	—	6	2	no	—
269	C₂³×C₅	C₂×#67	1	1	yes	characteristic
270	C₅×Q₈	—	2	4	no	—
271	C₅×Q₈	—	2	4	no	—
272	C₅×Q₈	—	2	2	no	—
273	C₅×Q₈	—	3	4	no	—
274	C₅×Q₈	—	6	8	no	—
275	C₅×Q₈	—	6	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	—	3	4	no	—
278	C₅×D₄	—	4	1	no	—
279	C₅×D₄	—	4	1	no	—
280	C₅×D₄	—	6	8	no	—
281	C₅×D₄	—	6	4	no	—
282	C₅×D₄	—	6	4	no	—
283	C₅×D₄	—	6	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	4	2	no	—
289	C₂×C₄×C₅	—	6	16	no	—
290	C₂×C₄×C₅	—	6	2	no	—
291	C₂×C₄×C₅	—	6	4	no	—
292	C₂×C₄×C₅	—	6	4	no	—
293	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
294	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
295	C₂×C₄×C₅	C₂×#67	1	4	yes	—
296	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
298	C₅×C₈	—	6	4	no	—
299	2₋¹⁺⁴	—	3	4	no	—
300	2₋¹⁺⁴	—	6	4	no	—
301	2₋¹⁺⁴	—	6	2	no	—
302	C₂×#41	—	3	2	no	—
303	C₂×#41	—	6	2	no	—
304	C₂×#41	—	6	2	no	—
305	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
306	C₂²×Q₈	—	6	2	no	—
307	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
308	#137	—	3	4	no	—
309	#137	—	6	2	no	—
310	AGL(1,ℤ/8)	—	3	4	no	—
311	AGL(1,ℤ/8)	—	6	2	no	—
312	#135	—	6	4	no	—
313	C₂×M₁₆	—	3	2	no	—
314	C₄⋊Q₈	C₂×C₅×D₃	1	2	yes	complemented
315	#124	C₂×C₅×D₃	1	2	yes	complemented
316	#123	—	2	2	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	#117	C₂×C₅×D₃	1	1	yes	characteristic
319	#104	—	3	8	no	—
320	#101	—	3	4	no	—
321	C₂×C₃×C₅	—	2	1	no	—
322	C₂×C₃×C₅	—	2	1	no	—
323	C₂×C₃×C₅	—	2	1	no	—
324	C₂×C₃×C₅	—	8	1	no	—
325	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
326	C₅×D₃	—	4	4	no	—
327	C₂³×C₃	—	2	1	no	—
328	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂²×D₃	—	2	2	no	—
330	C₃×Q₈	—	2	4	no	—
331	C₃×Q₈	—	2	4	no	—
332	C₃×Q₈	—	2	2	no	—
333	C₃×D₄	—	2	2	no	—
334	C₃×D₄	—	4	1	no	—
335	C₃×D₄	—	4	1	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	2	2	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	4	2	no	—
341	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
342	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
346	#67	—	2	4	no	—
347	#67	—	2	4	no	—
348	C₂×Dic₃	—	2	2	no	—
349	D₁₂	—	2	8	no	—
350	D₁₂	—	2	2	no	—
351	D₁₂	C₂×C₅×D₄	1	4	yes	—
352	C₄×D₃	—	2	16	no	—
353	C₄×D₃	—	2	4	no	—
354	C₄×D₃	—	2	4	no	—
355	Dic₆	—	2	8	no	—
356	Dic₆	—	2	2	no	—
357	Dic₆	C₂×C₅×D₄	1	4	yes	—
358	C₃⋊C₈	—	2	4	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	4	1	no	—
362	C₂²×C₅	—	6	4	no	—
363	C₂²×C₅	—	12	4	no	—
364	C₂²×C₅	#937	1	1	yes	characteristic
365	C₂²×C₅	#937	1	1	yes	characteristic
366	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
367	C₄×C₅	—	2	4	no	—
368	C₄×C₅	—	4	2	no	—
369	C₄×C₅	—	4	1	no	—
370	C₄×C₅	—	6	4	no	—
371	C₄×C₅	#937	1	2	yes	—
372	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
373	#41	—	2	2	no	—
374	#41	—	2	2	no	—
375	#41	—	3	4	no	—
376	#41	—	3	4	no	—
377	#41	—	6	8	no	—
378	#41	—	6	8	no	—
379	#41	—	6	8	no	—
380	#41	—	6	2	no	—
381	#41	—	6	2	no	—
382	#41	—	6	8	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	3	2	no	—
386	C₂×Q₈	—	6	2	no	—
387	C₂×Q₈	—	6	8	no	—
388	C₂×Q₈	—	6	8	no	—
389	C₂×Q₈	C₅×#67	1	2	yes	—
390	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
391	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	3	2	no	—
394	C₂×D₄	—	6	2	no	—
395	C₂×D₄	—	6	2	no	—
396	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	6	4	no	—
399	C₂²×C₄	—	6	2	no	—
400	C₂²×C₄	C₅×#67	1	2	yes	—
401	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
402	Q₁₆	—	6	4	no	—
403	SD₁₆	—	6	4	no	—
404	SD₁₆	—	6	4	no	—
405	D₈	—	6	4	no	—
406	M₁₆	—	3	4	no	—
407	M₁₆	—	6	2	no	—
408	C₂×C₈	—	6	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	4	no	—
413	C₄²	C₂²×C₅×D₃	1	2	yes	—
414	C₃×C₅	#3020	1	1	yes	characteristic, complemented, Hall
415	C₂²×C₃	—	4	1	no	—
416	C₂²×C₃	—	4	2	no	—
417	C₂²×C₃	—	4	1	no	—
418	C₂²×C₃	C₅×#120	1	1	yes	characteristic
419	C₂²×C₃	C₅×#120	1	1	yes	characteristic
420	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₂×D₃	—	2	4	no	—
422	C₂×D₃	—	4	4	no	—
423	C₃×C₄	—	2	4	no	—
424	C₃×C₄	—	4	2	no	—
425	C₃×C₄	—	4	1	no	—
426	C₃×C₄	C₅×#120	1	2	yes	—
427	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
428	Dic₃	—	2	4	no	—
429	C₂×C₅	—	2	1	no	—
430	C₂×C₅	—	2	1	no	—
431	C₂×C₅	—	2	1	no	—
432	C₂×C₅	—	8	1	no	—
433	C₂×C₅	—	12	4	no	—
434	C₂×C₅	C₂×#937	1	1	yes	characteristic
435	C₂³	—	2	1	no	—
436	C₂³	—	6	2	no	—
437	C₂³	C₂×C₅×#67	1	1	yes	characteristic
438	Q₈	—	2	4	no	—
439	Q₈	—	2	4	no	—
440	Q₈	—	2	2	no	—
441	Q₈	—	3	4	no	—
442	Q₈	—	6	8	no	—
443	Q₈	—	6	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	3	4	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	1	no	—
448	D₄	—	6	8	no	—
449	D₄	—	6	4	no	—
450	D₄	—	6	4	no	—
451	D₄	—	6	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	6	16	no	—
458	C₂×C₄	—	6	2	no	—
459	C₂×C₄	—	6	4	no	—
460	C₂×C₄	—	6	4	no	—
461	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
462	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
463	C₂×C₄	C₂×C₅×#67	1	4	yes	—
464	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
465	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
466	C₈	—	6	4	no	—
467	C₂×C₃	—	2	1	no	—
468	C₂×C₃	—	2	1	no	—
469	C₂×C₃	—	2	1	no	—
470	C₂×C₃	—	8	1	no	—
471	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
472	D₃	—	4	4	no	—
473	C₅	#83415	1	1	yes	characteristic, direct product factor, Sylow
474	C₂²	—	4	1	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	6	4	no	—
478	C₂²	—	12	4	no	—
479	C₂²	C₅×#937	1	1	yes	characteristic
480	C₂²	C₅×#937	1	1	yes	characteristic
481	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	6	4	no	—
486	C₄	C₅×#937	1	2	yes	—
487	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
488	C₃	C₅×#3020	1	1	yes	characteristic, complemented, Sylow
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	8	1	no	—
493	C₂	—	12	4	no	—
494	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
hypercenter	C₅×#536	D₃
hypocenter	C₃	C₅×#3020
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
1. C₂×C₅×#1007	C₂	semidirect
2. C₃×C₅×#536	C₂	semidirect
3. C₅×#5822	C₂	semidirect
4. C₂×C₅×#836	C₂	semidirect
5. C₅×#5095	C₂	semidirect
6. C₅×#5062	C₂	semidirect
7. C₅×#5005	C₂	semidirect
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₃×C₅×#124	C₂²	semidirect
26. C₅×#942	C₂²	semidirect
27. C₅×#932	C₂²	semidirect
29. C₅×#836	C₂²	semidirect
30. C₅×#805	C₂²	semidirect
31. #83415	C₅	direct (N × H)
34. C₅×#536	D₃	semidirect
80. C₂×#1007	C₂×C₅	semidirect
81. C₃×#536	C₂×C₅	semidirect
82. #5822	C₂×C₅	semidirect
83. C₂×#836	C₂×C₅	semidirect
84. #5095	C₂×C₅	semidirect
85. #5062	C₂×C₅	semidirect
86. #5005	C₂×C₅	semidirect
102. C₅×C₄⋊Q₈	C₂×D₃	semidirect
103. C₅×#124	C₂×D₃	semidirect
151. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
152. C₃×#124	C₂²×C₅	semidirect
159. #942	C₂²×C₅	semidirect
160. #932	C₂²×C₅	semidirect
162. #836	C₂²×C₅	semidirect
163. #805	C₂²×C₅	semidirect
207. #536	C₅×D₃	semidirect
314. C₄⋊Q₈	C₂×C₅×D₃	semidirect
315. #124	C₂×C₅×D₃	semidirect
414. C₃×C₅	#3020	semidirect
473. C₅	#83415	direct (N × H)
488. C₃	C₅×#3020	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1007	2
C₃×C₅×#536	2
C₅×#5822	2
C₂×C₅×#836	2
C₅×#5095	2
C₅×#5062	2
C₅×#5005	2
C₅×#3020	3
#83415	5

Subgroups — C5×#83415 #14425374

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83415 #14425374