Subgroups — C₅×#79828 #14416544

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#919	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#239	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5184	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5026	C₂	1	2	yes	maximal, complemented
6	C₅×#4869	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4860	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4817	C₂	1	2	yes	maximal, complemented
9	C₅×#4804	C₂	1	2	yes	maximal, complemented
10	C₅×#4711	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2943	—	3	1	no	maximal, Hall
13	C₂×C₅×#239	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₅×Q₈×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#215	C₂²	1	2	yes	—
18	C₅×#919	C₄	1	8	yes	complemented
19	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₅×#893	—	2	2	no	—
23	C₅×#893	C₂²	1	2	yes	—
24	C₅×#892	—	2	2	no	—
25	C₅×#892	C₂²	1	2	yes	—
26	C₄×C₅×D₁₂	—	2	2	no	—
27	C₄×C₅×D₁₂	C₂²	1	2	yes	—
28	C₄²×C₅×D₃	—	2	2	no	—
29	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic
33	C₅×#835	C₂²	1	2	yes	—
34	C₅×#821	C₂²	1	2	yes	—
35	C₅×#817	C₂²	1	1	yes	characteristic
36	C₅×#815	C₂²	1	1	yes	characteristic
37	C₅×#815	C₂²	1	1	yes	characteristic
38	C₅×#809	C₂²	1	2	yes	—
39	C₅×#807	C₂²	1	2	yes	—
40	C₅×#803	C₂²	1	1	yes	characteristic
41	#79828	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
42	C₂×C₅×#135	—	3	1	no	—
43	C₄×C₅×#41	—	3	2	no	—
44	C₅×#442	—	3	1	no	—
45	C₅×#442	—	3	1	no	—
46	C₅×#441	—	3	1	no	—
47	C₅×#441	D₃	1	1	yes	characteristic, complemented
48	C₅×#440	—	3	2	no	—
49	C₅×#440	—	3	2	no	—
50	C₅×#427	—	3	1	no	—
51	C₅×#416	—	3	2	no	—
52	C₂×C₅×#97	—	3	1	no	—
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₅×#239	—	2	4	no	—
55	C₅×#239	C₂×C₄	1	8	yes	complemented
56	C₂×C₅×D₁₂	—	2	2	no	—
57	C₂×C₅×D₁₂	C₂³	1	2	yes	—
58	C₂×C₄×C₅×D₃	—	2	2	no	—
59	C₂×C₄×C₅×D₃	—	2	2	no	—
60	C₂×C₄×C₅×D₃	—	2	2	no	—
61	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
62	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#215	C₂×C₄	1	8	yes	complemented
71	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
73	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
74	C₅×C₄⋊Dic₃	—	2	2	no	—
75	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
76	C₄×C₅×Dic₃	—	2	2	no	—
77	C₄×C₅×Dic₃	—	2	2	no	—
78	C₄×C₅×Dic₃	D₄	1	2	yes	—
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
83	C₅×D₃×C₈	—	2	2	no	—
84	C₅×D₃×C₈	C₂×C₄	1	4	yes	complemented
85	C₂×#919	C₂×C₅	1	1	yes	characteristic
86	C₄×#239	C₂×C₅	1	2	yes	complemented
87	C₃×#441	C₂×C₅	1	1	yes	characteristic, complemented
88	#5184	C₂×C₅	1	1	yes	characteristic, complemented
89	#5026	C₂×C₅	1	2	yes	complemented
90	#4869	C₂×C₅	1	1	yes	characteristic, complemented
91	#4860	C₂×C₅	1	1	yes	characteristic, complemented
92	#4817	C₂×C₅	1	2	yes	complemented
93	#4804	C₂×C₅	1	2	yes	complemented
94	#4711	C₂×C₅	1	1	yes	characteristic, complemented
95	D₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×C₅×#41	—	3	2	no	—
97	C₅×#135	—	3	8	no	—
98	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
99	C₂×C₅×SD₁₆	—	3	2	no	—
100	C₂×C₅×D₈	—	3	1	no	—
101	C₂²×C₅×C₈	—	3	1	no	—
102	C₂²×C₅×C₈	—	3	1	no	—
103	C₄×C₅×Q₈	—	3	2	no	—
104	C₄×C₅×Q₈	C₂×D₃	1	2	yes	—
105	C₄×C₅×D₄	—	3	2	no	—
106	C₄×C₅×D₄	—	3	2	no	—
107	C₄×C₅×D₄	—	6	2	no	—
108	C₄×C₅×D₄	—	6	2	no	—
109	C₅×#117	—	3	2	no	—
110	C₅×#117	—	6	2	no	—
111	C₂×C₄²×C₅	—	3	1	no	—
112	C₂×C₄²×C₅	—	6	2	no	—
113	C₅×#107	—	3	2	no	—
114	C₅×#106	—	3	1	no	—
115	C₅×#106	C₂×D₃	1	1	yes	characteristic
116	C₅×#103	—	3	2	no	—
117	C₅×#103	C₂×D₃	1	2	yes	—
118	C₅×#102	—	3	2	no	—
119	C₅×#102	—	3	2	no	—
120	C₅×#97	—	3	1	no	—
121	C₅×#97	—	3	1	no	—
122	C₅×#97	—	3	1	no	—
123	C₅×#97	C₂×D₃	1	1	yes	characteristic
124	#2943	—	3	1	no	Sylow
125	C₂²×C₅×D₃	—	2	2	no	—
126	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
127	C₃×C₅×Q₈	—	2	2	no	—
128	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₅×Dic₃	—	2	2	no	—
134	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
135	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
136	C₅×D₁₂	—	2	8	no	—
137	C₅×D₁₂	—	2	2	no	—
138	C₅×D₁₂	C₂²×C₄	1	4	yes	—
139	C₄×C₅×D₃	—	2	8	no	—
140	C₄×C₅×D₃	—	4	2	no	—
141	C₄×C₅×D₃	—	4	4	no	—
142	C₄×C₅×D₃	—	4	4	no	—
143	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
144	C₄×C₅×D₃	#41	1	2	yes	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
147	C₅×C₃⋊C₈	—	2	1	no	—
148	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×#239	C₂²×C₅	1	2	yes	—
150	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
151	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
152	Q₈×Dic₃	C₂²×C₅	1	2	yes	—
153	C₂×#215	C₂²×C₅	1	2	yes	—
154	#919	C₄×C₅	1	8	yes	complemented
155	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
158	#893	—	2	2	no	—
159	#893	C₂²×C₅	1	2	yes	—
160	#892	—	2	2	no	—
161	#892	C₂²×C₅	1	2	yes	—
162	C₄×D₁₂	—	2	2	no	—
163	C₄×D₁₂	C₂²×C₅	1	2	yes	—
164	C₄²×D₃	—	2	2	no	—
165	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
166	C₃×#106	C₂²×C₅	1	1	yes	characteristic
167	C₃×#103	C₂²×C₅	1	2	yes	—
168	C₃×#97	C₂²×C₅	1	1	yes	characteristic
169	#835	C₂²×C₅	1	2	yes	—
170	#821	C₂²×C₅	1	2	yes	—
171	#817	C₂²×C₅	1	1	yes	characteristic
172	#815	C₂²×C₅	1	1	yes	characteristic
173	#815	C₂²×C₅	1	1	yes	characteristic
174	#809	C₂²×C₅	1	2	yes	—
175	#807	C₂²×C₅	1	2	yes	—
176	#803	C₂²×C₅	1	1	yes	characteristic
177	C₅×#41	—	3	8	no	—
178	C₅×#41	—	6	4	no	—
179	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
180	C₂×C₅×D₄	—	3	2	no	—
181	C₂×C₅×D₄	—	6	2	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	2	no	—
184	C₂²×C₄×C₅	—	6	2	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂²×C₄×C₅	—	6	2	no	—
187	C₅×Q₁₆	C₄×D₃	1	4	yes	complemented
188	C₅×SD₁₆	—	3	8	no	—
189	C₅×D₈	—	3	4	no	—
190	C₂×C₅×C₈	—	3	1	no	—
191	C₂×C₅×C₈	—	3	4	no	—
192	C₂×C₅×C₈	—	3	1	no	—
193	C₂×C₅×C₈	—	6	2	no	—
194	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
195	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	3	2	no	—
198	C₅×C₄⋊C₄	—	6	2	no	—
199	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
200	C₅×C₂²⋊C₄	—	6	2	no	—
201	C₅×C₂²⋊C₄	—	6	2	no	—
202	C₅×C₂²⋊C₄	—	6	2	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	3	2	no	—
205	C₄²×C₅	—	3	1	no	—
206	C₄²×C₅	—	6	2	no	—
207	C₄²×C₅	—	6	2	no	—
208	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
209	C₂×#135	—	3	1	no	—
210	C₄×#41	—	3	2	no	—
211	#442	—	3	1	no	—
212	#442	—	3	1	no	—
213	#441	—	3	1	no	—
214	#441	C₅×D₃	1	1	yes	characteristic, complemented
215	#440	—	3	2	no	—
216	#440	—	3	2	no	—
217	#427	—	3	1	no	—
218	#416	—	3	2	no	—
219	C₂×#97	—	3	1	no	—
220	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₅×D₃	—	2	2	no	—
222	C₂×C₅×D₃	—	2	4	no	—
223	C₂×C₅×D₃	—	4	2	no	—
224	C₂×C₅×D₃	—	4	2	no	—
225	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
226	C₃×C₄×C₅	—	2	4	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	4	2	no	—
229	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
230	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₅×Dic₃	—	2	2	no	—
232	C₅×Dic₃	—	4	2	no	—
233	C₅×Dic₃	C₄×D₄	1	2	yes	—
234	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
235	#239	—	2	4	no	—
236	#239	C₂×C₄×C₅	1	8	yes	complemented
237	C₂×D₁₂	—	2	2	no	—
238	C₂×D₁₂	C₂³×C₅	1	2	yes	—
239	C₂×C₄×D₃	—	2	2	no	—
240	C₂×C₄×D₃	—	2	2	no	—
241	C₂×C₄×D₃	—	2	2	no	—
242	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
243	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
244	C₃×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
245	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
247	C₃×C₄⋊C₄	—	2	2	no	—
248	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
249	C₃×C₄²	—	2	2	no	—
250	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
251	#215	C₂×C₄×C₅	1	8	yes	complemented
252	(C₂×D₃)⋊C₄	—	2	2	no	—
253	(C₂×D₃)⋊C₄	—	2	2	no	—
254	(C₂×D₃)⋊C₄	—	2	2	no	—
255	C₄⋊Dic₃	—	2	2	no	—
256	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
257	C₄×Dic₃	—	2	2	no	—
258	C₄×Dic₃	—	2	2	no	—
259	C₄×Dic₃	C₅×D₄	1	2	yes	—
260	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
261	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
263	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
264	D₃×C₈	—	2	2	no	—
265	D₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
266	C₂³×C₅	—	3	1	no	—
267	C₂³×C₅	—	6	2	no	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	C₂×C₄×D₃	1	4	yes	—
270	C₅×D₄	—	3	4	no	—
271	C₅×D₄	—	6	8	no	—
272	C₅×D₄	—	6	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	3	1	no	—
276	C₂×C₄×C₅	—	3	2	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	3	2	no	—
279	C₂×C₄×C₅	—	6	8	no	—
280	C₂×C₄×C₅	—	6	2	no	—
281	C₂×C₄×C₅	—	12	2	no	—
282	C₂×C₄×C₅	—	12	4	no	—
283	C₂×C₄×C₅	—	12	4	no	—
284	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
285	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₅×C₈	—	2	1	no	—
287	C₅×C₈	—	3	2	no	—
288	C₅×C₈	—	6	1	no	—
289	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
290	C₂×#41	—	3	2	no	—
291	#135	—	3	8	no	—
292	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
293	C₂×SD₁₆	—	3	2	no	—
294	C₂×D₈	—	3	1	no	—
295	C₂²×C₈	—	3	1	no	—
296	C₂²×C₈	—	3	1	no	—
297	C₄×Q₈	—	3	2	no	—
298	C₄×Q₈	C₂×C₅×D₃	1	2	yes	—
299	C₄×D₄	—	3	2	no	—
300	C₄×D₄	—	3	2	no	—
301	C₄×D₄	—	6	2	no	—
302	C₄×D₄	—	6	2	no	—
303	#117	—	3	2	no	—
304	#117	—	6	2	no	—
305	C₂×C₄²	—	3	1	no	—
306	C₂×C₄²	—	6	2	no	—
307	#107	—	3	2	no	—
308	#106	—	3	1	no	—
309	#106	C₂×C₅×D₃	1	1	yes	characteristic
310	#103	—	3	2	no	—
311	#103	C₂×C₅×D₃	1	2	yes	—
312	#102	—	3	2	no	—
313	#102	—	3	2	no	—
314	#97	—	3	1	no	—
315	#97	—	3	1	no	—
316	#97	—	3	1	no	—
317	#97	C₂×C₅×D₃	1	1	yes	characteristic
318	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
319	C₂×C₃×C₅	#575	1	2	yes	—
320	C₅×D₃	—	2	2	no	—
321	C₅×D₃	—	4	4	no	—
322	C₂²×D₃	—	2	2	no	—
323	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
329	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
330	C₂×Dic₃	—	2	2	no	—
331	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
332	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
333	D₁₂	—	2	8	no	—
334	D₁₂	—	2	2	no	—
335	D₁₂	C₂²×C₄×C₅	1	4	yes	—
336	C₄×D₃	—	2	8	no	—
337	C₄×D₃	—	4	2	no	—
338	C₄×D₃	—	4	4	no	—
339	C₄×D₃	—	4	4	no	—
340	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
341	C₄×D₃	C₅×#41	1	2	yes	—
342	C₃×C₈	—	2	1	no	—
343	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
344	C₃⋊C₈	—	2	1	no	—
345	C₃⋊C₈	C₂²×C₄×C₅	1	2	yes	—
346	C₂²×C₅	—	3	2	no	—
347	C₂²×C₅	—	6	2	no	—
348	C₂²×C₅	—	6	4	no	—
349	C₂²×C₅	—	12	2	no	—
350	C₂²×C₅	—	12	2	no	—
351	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	4	no	—
354	C₄×C₅	—	3	2	no	—
355	C₄×C₅	—	4	2	no	—
356	C₄×C₅	—	6	2	no	—
357	C₄×C₅	—	12	2	no	—
358	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
359	C₄×C₅	D₃×#41	1	1	yes	characteristic
360	#41	—	3	8	no	—
361	#41	—	6	4	no	—
362	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
363	C₂×D₄	—	3	2	no	—
364	C₂×D₄	—	6	2	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	6	2	no	—
368	C₂²×C₄	—	6	2	no	—
369	C₂²×C₄	—	6	2	no	—
370	Q₁₆	C₄×C₅×D₃	1	4	yes	complemented
371	SD₁₆	—	3	8	no	—
372	D₈	—	3	4	no	—
373	C₂×C₈	—	3	1	no	—
374	C₂×C₈	—	3	4	no	—
375	C₂×C₈	—	3	1	no	—
376	C₂×C₈	—	6	2	no	—
377	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
378	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	3	2	no	—
381	C₄⋊C₄	—	6	2	no	—
382	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
383	C₂²⋊C₄	—	6	2	no	—
384	C₂²⋊C₄	—	6	2	no	—
385	C₂²⋊C₄	—	6	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	3	2	no	—
388	C₄²	—	3	1	no	—
389	C₄²	—	6	2	no	—
390	C₄²	—	6	2	no	—
391	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
392	C₃×C₅	#2943	1	1	yes	characteristic, complemented, Hall
393	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₂×D₃	—	2	2	no	—
395	C₂×D₃	—	2	4	no	—
396	C₂×D₃	—	4	2	no	—
397	C₂×D₃	—	4	2	no	—
398	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
399	C₃×C₄	—	2	4	no	—
400	C₃×C₄	—	2	2	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
403	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
404	Dic₃	—	2	2	no	—
405	Dic₃	—	4	2	no	—
406	Dic₃	C₄×C₅×D₄	1	2	yes	—
407	C₂×C₅	—	6	2	no	—
408	C₂×C₅	—	12	4	no	—
409	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
410	C₂×C₅	#5777	1	2	yes	—
411	C₂³	—	3	1	no	—
412	C₂³	—	6	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	C₂×C₄×C₅×D₃	1	4	yes	—
415	D₄	—	3	4	no	—
416	D₄	—	6	8	no	—
417	D₄	—	6	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	3	2	no	—
424	C₂×C₄	—	6	8	no	—
425	C₂×C₄	—	6	2	no	—
426	C₂×C₄	—	12	2	no	—
427	C₂×C₄	—	12	4	no	—
428	C₂×C₄	—	12	4	no	—
429	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
430	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	3	2	no	—
433	C₈	—	6	1	no	—
434	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
435	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
436	C₂×C₃	C₅×#575	1	2	yes	—
437	D₃	—	2	2	no	—
438	D₃	—	4	4	no	—
439	C₅	#79828	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	3	2	no	—
441	C₂²	—	6	2	no	—
442	C₂²	—	6	4	no	—
443	C₂²	—	12	2	no	—
444	C₂²	—	12	2	no	—
445	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	3	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	6	2	no	—
451	C₄	—	12	2	no	—
452	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
453	C₄	C₅×D₃×#41	1	1	yes	characteristic
454	C₃	C₅×#2943	1	1	yes	characteristic, complemented, Sylow
455	C₂	—	6	2	no	—
456	C₂	—	12	4	no	—
457	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
458	C₂	C₅×#5777	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#441	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#919	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#441	D₃
hypocenter	C₃	C₅×#2943
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#441

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×#239	C₂	semidirect
3. C₃×C₅×#441	C₂	semidirect
4. C₅×#5184	C₂	semidirect
5. C₅×#5026	C₂	semidirect
6. C₅×#4869	C₂	semidirect
7. C₅×#4860	C₂	semidirect
8. C₅×#4817	C₂	semidirect
9. C₅×#4804	C₂	semidirect
10. C₅×#4711	C₂	semidirect
11. C₅×D₃×#97	C₂	semidirect
18. C₅×#919	C₄	semidirect
41. #79828	C₅	direct (N × H)
47. C₅×#441	D₃	semidirect
55. C₅×#239	C₂×C₄	semidirect
63. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₅×#215	C₂×C₄	semidirect
82. C₅×D₂₄	C₂×C₄	semidirect
84. C₅×D₃×C₈	C₂×C₄	semidirect
86. C₄×#239	C₂×C₅	semidirect
87. C₃×#441	C₂×C₅	semidirect
88. #5184	C₂×C₅	semidirect
89. #5026	C₂×C₅	semidirect
90. #4869	C₂×C₅	semidirect
91. #4860	C₂×C₅	semidirect
92. #4817	C₂×C₅	semidirect
93. #4804	C₂×C₅	semidirect
94. #4711	C₂×C₅	semidirect
95. D₃×#97	C₂×C₅	semidirect
154. #919	C₄×C₅	semidirect
187. C₅×Q₁₆	C₄×D₃	semidirect
214. #441	C₅×D₃	semidirect
236. #239	C₂×C₄×C₅	semidirect
244. C₃×Q₁₆	C₂×C₄×C₅	semidirect
251. #215	C₂×C₄×C₅	semidirect
263. D₂₄	C₂×C₄×C₅	semidirect
265. D₃×C₈	C₂×C₄×C₅	semidirect
370. Q₁₆	C₄×C₅×D₃	semidirect
392. C₃×C₅	#2943	semidirect
439. C₅	#79828	direct (N × H)
454. C₃	C₅×#2943	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#919	2
C₄×C₅×#239	2
C₃×C₅×#441	2
C₅×#5184	2
C₅×#5026	2
C₅×#4869	2
C₅×#4860	2
C₅×#4817	2
C₅×#4804	2
C₅×#4711	2
C₅×D₃×#97	2
C₅×#2943	3
#79828	5

Subgroups — C5×#79828 #14416544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79828 #14416544