Subgroups — C₅×#79864 #14416538

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×#912	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×#237	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5152	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5018	C₂	1	2	yes	maximal, complemented
6	C₅×#4860	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4853	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4772	C₂	1	2	yes	maximal, complemented
9	C₅×#4757	C₂	1	2	yes	maximal, complemented
10	C₅×#4716	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×#237	C₂²	1	2	yes	—
14	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₅×D₄×Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×#214	C₂²	1	2	yes	—
18	C₄×C₅×#67	—	2	2	no	—
19	C₂×C₄×C₅×Dic₃	—	2	2	no	—
20	C₅×#912	C₄	1	8	yes	complemented
21	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
24	C₅×#892	C₂²	1	2	yes	—
25	C₅×#887	C₂²	1	2	yes	—
26	C₅×#67⋊C₄	—	2	2	no	—
27	C₅×#877	—	2	2	no	—
28	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	2	yes	—
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic
33	C₅×#832	C₂²	1	2	yes	—
34	C₅×#817	C₂²	1	1	yes	characteristic
35	C₅×#816	C₂²	1	2	yes	—
36	C₅×#815	C₂²	1	1	yes	characteristic
37	C₅×#815	C₂²	1	1	yes	characteristic
38	C₅×#810	C₂²	1	2	yes	—
39	C₅×#807	C₂²	1	2	yes	—
40	C₅×#803	C₂²	1	1	yes	characteristic
41	#79864	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	D₃	1	1	yes	characteristic, complemented
46	C₅×#441	—	3	1	no	—
47	C₅×#441	—	3	1	no	—
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×D₄	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂×C₅×#67	—	2	2	no	—
56	C₂²×C₅×Dic₃	—	2	2	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₅×#237	—	2	4	no	—
59	C₅×#237	C₂×C₄	1	8	yes	complemented
60	C₂×C₄×C₅×D₃	D₄	1	2	yes	—
61	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
62	C₂×C₅×Dic₆	C₂³	1	2	yes	—
63	C₃×C₅×D₈	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	C₂³	1	2	yes	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₅×#217	—	2	2	no	—
70	C₅×#214	C₂×C₄	1	8	yes	complemented
71	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
72	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
73	C₅×Dic₃⋊C₄	—	2	2	no	—
74	C₅×Dic₃⋊C₄	—	2	2	no	—
75	C₄×C₅×Dic₃	—	2	2	no	—
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×Dic₁₂	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×#912	C₂×C₅	1	1	yes	characteristic
86	C₄×#237	C₂×C₅	1	2	yes	complemented
87	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
88	#5152	C₂×C₅	1	1	yes	characteristic, complemented
89	#5018	C₂×C₅	1	2	yes	complemented
90	#4860	C₂×C₅	1	1	yes	characteristic, complemented
91	#4853	C₂×C₅	1	1	yes	characteristic, complemented
92	#4772	C₂×C₅	1	2	yes	complemented
93	#4757	C₂×C₅	1	2	yes	complemented
94	#4716	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	—	3	1	no	—
99	C₂×C₅×SD₁₆	—	3	2	no	—
100	C₂×C₅×D₈	C₂×D₃	1	1	yes	characteristic
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	—	3	2	no	—
105	C₄×C₅×D₄	—	3	2	no	—
106	C₄×C₅×D₄	—	6	2	no	—
107	C₄×C₅×D₄	—	6	2	no	—
108	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
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	—	3	2	no	—
118	C₅×#102	—	3	2	no	—
119	C₅×#102	C₂×D₃	1	2	yes	—
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	C₂³×C₃×C₅	—	2	2	no	—
126	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	C₂²×C₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	4	4	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₅×#67	—	2	8	no	—
134	C₂×C₅×Dic₃	—	2	2	no	—
135	C₂×C₅×Dic₃	—	2	8	no	—
136	C₂×C₅×Dic₃	—	2	2	no	—
137	C₂×C₅×Dic₃	—	4	4	no	—
138	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
139	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
140	C₄×C₅×D₃	—	4	2	no	—
141	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₄×C₅×D₃	#41	1	2	yes	—
143	C₅×Dic₆	—	2	2	no	—
144	C₅×Dic₆	C₂²×C₄	1	4	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×#237	C₂²×C₅	1	2	yes	—
150	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
151	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
152	D₄×Dic₃	C₂²×C₅	1	2	yes	—
153	C₂×#214	C₂²×C₅	1	2	yes	—
154	C₄×#67	—	2	2	no	—
155	C₂×C₄×Dic₃	—	2	2	no	—
156	#912	C₄×C₅	1	8	yes	complemented
157	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
158	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
159	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
160	#892	C₂²×C₅	1	2	yes	—
161	#887	C₂²×C₅	1	2	yes	—
162	#67⋊C₄	—	2	2	no	—
163	#877	—	2	2	no	—
164	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
165	C₄×Dic₆	C₂²×C₅	1	2	yes	—
166	C₃×#106	C₂²×C₅	1	1	yes	characteristic
167	C₃×#102	C₂²×C₅	1	2	yes	—
168	C₃×#97	C₂²×C₅	1	1	yes	characteristic
169	#832	C₂²×C₅	1	2	yes	—
170	#817	C₂²×C₅	1	1	yes	characteristic
171	#816	C₂²×C₅	1	2	yes	—
172	#815	C₂²×C₅	1	1	yes	characteristic
173	#815	C₂²×C₅	1	1	yes	characteristic
174	#810	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	—	3	2	no	—
180	C₂×C₅×D₄	—	6	2	no	—
181	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
182	C₂²×C₄×C₅	—	2	2	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	2	no	—
185	C₂²×C₄×C₅	—	6	2	no	—
186	C₂²×C₄×C₅	—	6	2	no	—
187	C₅×Q₁₆	—	3	4	no	—
188	C₅×SD₁₆	—	3	8	no	—
189	C₅×D₈	C₄×D₃	1	4	yes	complemented
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	—	3	2	no	—
197	C₅×C₄⋊C₄	—	6	2	no	—
198	C₅×C₄⋊C₄	—	6	2	no	—
199	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	6	2	no	—
202	C₅×C₂²⋊C₄	—	6	2	no	—
203	C₄²×C₅	—	3	2	no	—
204	C₄²×C₅	—	3	1	no	—
205	C₄²×C₅	—	6	2	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	C₅×D₃	1	1	yes	characteristic, complemented
213	#441	—	3	1	no	—
214	#441	—	3	1	no	—
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	—	2	4	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₅×D₃	—	2	2	no	—
225	C₂×C₅×D₃	C₄×D₄	1	2	yes	—
226	C₃×C₄×C₅	—	2	2	no	—
227	C₃×C₄×C₅	—	4	2	no	—
228	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₅×Dic₃	—	2	4	no	—
231	C₅×Dic₃	—	2	2	no	—
232	C₅×Dic₃	—	4	2	no	—
233	C₅×Dic₃	C₄×D₄	1	2	yes	—
234	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
235	C₂²×C₃×C₄	—	2	2	no	—
236	C₂×#67	—	2	2	no	—
237	C₂²×Dic₃	—	2	2	no	—
238	C₂²×Dic₃	—	2	2	no	—
239	#237	—	2	4	no	—
240	#237	C₂×C₄×C₅	1	8	yes	complemented
241	C₂×C₄×D₃	C₅×D₄	1	2	yes	—
242	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
243	C₂×Dic₆	C₂³×C₅	1	2	yes	—
244	C₃×D₈	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	C₂³×C₅	1	2	yes	—
248	C₃×C₂²⋊C₄	—	2	2	no	—
249	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
250	#217	—	2	2	no	—
251	#214	C₂×C₄×C₅	1	8	yes	complemented
252	(C₂×D₃)⋊C₄	—	2	2	no	—
253	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
254	Dic₃⋊C₄	—	2	2	no	—
255	Dic₃⋊C₄	—	2	2	no	—
256	C₄×Dic₃	—	2	2	no	—
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	Dic₁₂	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	—	2	2	no	—
267	C₂³×C₅	—	3	1	no	—
268	C₅×Q₈	—	3	4	no	—
269	C₅×Q₈	—	6	2	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	6	8	no	—
272	C₅×D₄	C₂×C₄×D₃	1	4	yes	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	3	1	no	—
275	C₂×C₄×C₅	—	3	2	no	—
276	C₂×C₄×C₅	—	3	2	no	—
277	C₂×C₄×C₅	—	3	2	no	—
278	C₂×C₄×C₅	—	4	4	no	—
279	C₂×C₄×C₅	—	6	8	no	—
280	C₂×C₄×C₅	—	6	2	no	—
281	C₂×C₄×C₅	—	6	2	no	—
282	C₂×C₄×C₅	—	12	2	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	—	3	1	no	—
293	C₂×SD₁₆	—	3	2	no	—
294	C₂×D₈	C₂×C₅×D₃	1	1	yes	characteristic
295	C₂²×C₈	—	3	1	no	—
296	C₂²×C₈	—	3	1	no	—
297	C₄×Q₈	—	3	2	no	—
298	C₄×Q₈	—	3	2	no	—
299	C₄×D₄	—	3	2	no	—
300	C₄×D₄	—	6	2	no	—
301	C₄×D₄	—	6	2	no	—
302	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
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	—	3	2	no	—
312	#102	—	3	2	no	—
313	#102	C₂×C₅×D₃	1	2	yes	—
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	—	4	4	no	—
319	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂×C₃×C₅	#575	1	2	yes	—
321	C₅×D₃	—	2	2	no	—
322	C₂³×C₃	—	2	2	no	—
323	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
324	C₃×D₄	—	2	2	no	—
325	C₃×D₄	C₂²×C₄×C₅	1	4	yes	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	4	4	no	—
328	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
329	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
330	#67	—	2	8	no	—
331	C₂×Dic₃	—	2	2	no	—
332	C₂×Dic₃	—	2	8	no	—
333	C₂×Dic₃	—	2	2	no	—
334	C₂×Dic₃	—	4	4	no	—
335	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
336	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
337	C₄×D₃	—	4	2	no	—
338	C₄×D₃	C₂²×C₄×C₅	1	2	yes	—
339	C₄×D₃	C₅×#41	1	2	yes	—
340	Dic₆	—	2	2	no	—
341	Dic₆	C₂²×C₄×C₅	1	4	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	—	2	4	no	—
347	C₂²×C₅	—	3	2	no	—
348	C₂²×C₅	—	4	2	no	—
349	C₂²×C₅	—	4	2	no	—
350	C₂²×C₅	—	6	2	no	—
351	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	3	2	no	—
354	C₄×C₅	—	4	2	no	—
355	C₄×C₅	—	6	2	no	—
356	C₄×C₅	—	6	4	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	—	3	2	no	—
363	C₂×D₄	—	6	2	no	—
364	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	3	1	no	—
367	C₂²×C₄	—	3	2	no	—
368	C₂²×C₄	—	6	2	no	—
369	C₂²×C₄	—	6	2	no	—
370	Q₁₆	—	3	4	no	—
371	SD₁₆	—	3	8	no	—
372	D₈	C₄×C₅×D₃	1	4	yes	complemented
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	—	3	2	no	—
380	C₄⋊C₄	—	6	2	no	—
381	C₄⋊C₄	—	6	2	no	—
382	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	6	2	no	—
385	C₂²⋊C₄	—	6	2	no	—
386	C₄²	—	3	2	no	—
387	C₄²	—	3	1	no	—
388	C₄²	—	6	2	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	—	2	4	no	—
394	C₂²×C₃	—	4	2	no	—
395	C₂²×C₃	—	4	2	no	—
396	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
397	C₂×D₃	—	2	2	no	—
398	C₂×D₃	C₄×C₅×D₄	1	2	yes	—
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
402	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
403	Dic₃	—	2	4	no	—
404	Dic₃	—	2	2	no	—
405	Dic₃	—	4	2	no	—
406	Dic₃	C₄×C₅×D₄	1	2	yes	—
407	C₂×C₅	—	4	4	no	—
408	C₂×C₅	—	6	2	no	—
409	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
410	C₂×C₅	#5773	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	3	1	no	—
413	Q₈	—	3	4	no	—
414	Q₈	—	6	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	6	8	no	—
417	D₄	C₂×C₄×C₅×D₃	1	4	yes	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	3	1	no	—
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	2	no	—
422	C₂×C₄	—	3	2	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	6	8	no	—
425	C₂×C₄	—	6	2	no	—
426	C₂×C₄	—	6	2	no	—
427	C₂×C₄	—	12	2	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	—	4	4	no	—
436	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
437	C₂×C₃	C₅×#575	1	2	yes	—
438	D₃	—	2	2	no	—
439	C₅	#79864	1	1	yes	characteristic, direct product factor, Sylow
440	C₂²	—	2	4	no	—
441	C₂²	—	3	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	6	2	no	—
445	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	3	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	6	2	no	—
450	C₄	—	6	4	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	—	4	4	no	—
456	C₂	—	6	2	no	—
457	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
458	C₂	C₅×#5773	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×#442	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#912	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#442	D₃
hypocenter	C₃	C₅×#2943
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#442

Complements

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

N	H ≅ G/N	type
2. C₄×C₅×#237	C₂	semidirect
3. C₃×C₅×#442	C₂	semidirect
4. C₅×#5152	C₂	semidirect
5. C₅×#5018	C₂	semidirect
6. C₅×#4860	C₂	semidirect
7. C₅×#4853	C₂	semidirect
8. C₅×#4772	C₂	semidirect
9. C₅×#4757	C₂	semidirect
10. C₅×#4716	C₂	semidirect
11. C₅×D₃×#97	C₂	semidirect
20. C₅×#912	C₄	semidirect
41. #79864	C₅	direct (N × H)
45. C₅×#442	D₃	semidirect
59. C₅×#237	C₂×C₄	semidirect
63. C₃×C₅×D₈	C₂×C₄	semidirect
70. C₅×#214	C₂×C₄	semidirect
82. C₅×Dic₁₂	C₂×C₄	semidirect
84. C₅×D₃×C₈	C₂×C₄	semidirect
86. C₄×#237	C₂×C₅	semidirect
87. C₃×#442	C₂×C₅	semidirect
88. #5152	C₂×C₅	semidirect
89. #5018	C₂×C₅	semidirect
90. #4860	C₂×C₅	semidirect
91. #4853	C₂×C₅	semidirect
92. #4772	C₂×C₅	semidirect
93. #4757	C₂×C₅	semidirect
94. #4716	C₂×C₅	semidirect
95. D₃×#97	C₂×C₅	semidirect
156. #912	C₄×C₅	semidirect
189. C₅×D₈	C₄×D₃	semidirect
212. #442	C₅×D₃	semidirect
240. #237	C₂×C₄×C₅	semidirect
244. C₃×D₈	C₂×C₄×C₅	semidirect
251. #214	C₂×C₄×C₅	semidirect
263. Dic₁₂	C₂×C₄×C₅	semidirect
265. D₃×C₈	C₂×C₄×C₅	semidirect
372. D₈	C₄×C₅×D₃	semidirect
392. C₃×C₅	#2943	semidirect
439. C₅	#79864	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×#912	2
C₄×C₅×#237	2
C₃×C₅×#442	2
C₅×#5152	2
C₅×#5018	2
C₅×#4860	2
C₅×#4853	2
C₅×#4772	2
C₅×#4757	2
C₅×#4716	2
C₅×D₃×#97	2
C₅×#2943	3
#79864	5

Subgroups — C5×#79864 #14416538

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79864 #14416538