Subgroups — C₅×#70545 #14300218

Order 1920.

540 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#901	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#825	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#822	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5002	C₂	1	1	yes	maximal, characteristic
6	C₅×#4550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1866	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₅×#901	—	2	2	no	—
17	C₅×#901	—	2	2	no	—
18	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
19	C₂×C₅×D₃×C₈	—	2	1	no	—
20	C₃×C₅×C₄⋊C₈	—	2	1	no	—
21	C₃×C₅×C₄⋊C₈	—	2	1	no	—
22	C₅×#825	—	2	2	no	—
23	C₅×#822	—	2	2	no	—
24	C₅×#810	C₄	1	1	yes	characteristic, complemented
25	C₅×#810	C₄	1	1	yes	characteristic, complemented
26	C₅×#809	C₄	1	1	yes	characteristic, complemented
27	C₅×#809	C₄	1	1	yes	characteristic, complemented
28	#70545	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×#131	—	3	1	no	—
30	C₂×C₅×#108	—	3	1	no	—
31	C₅×#424	D₃	1	1	yes	characteristic, complemented
32	C₂×C₅×#104	—	3	1	no	—
33	C₅×#416	—	3	1	no	—
34	C₅×#339	—	3	1	no	—
35	C₅×#336	—	3	1	no	—
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂×C₅×#67	—	2	1	no	—
38	C₂²×C₅×Dic₃	—	2	1	no	—
39	C₅×#235	—	2	1	no	—
40	C₅×#235	—	2	1	no	—
41	C₅×#235	D₄	1	2	yes	—
42	C₅×#235	Q₈	1	2	yes	—
43	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×C₅×D₃	—	2	1	no	—
45	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
46	C₃×C₅×M₁₆	—	2	1	no	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₂×C₃×C₅×C₈	—	2	1	no	—
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
52	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
56	C₃×C₄²×C₅	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₅×#208	—	2	1	no	—
60	C₅×#208	D₄	1	2	yes	—
61	C₂×C₅×C₃⋊C₈	—	2	1	no	—
62	C₂×C₅×C₃⋊C₈	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
67	C₅×D₃×C₈	—	2	4	no	—
68	C₂×#901	C₂×C₅	1	1	yes	characteristic
69	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#825	C₂×C₅	1	1	yes	characteristic
71	C₂×#822	C₂×C₅	1	1	yes	characteristic, complemented
72	#5002	C₂×C₅	1	1	yes	characteristic
73	#4550	C₂×C₅	1	1	yes	characteristic, complemented
74	#4532	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂×C₅×#41	—	3	1	no	—
76	C₅×#131	—	6	2	no	—
77	C₅×#131	—	6	2	no	—
78	C₂×C₅×M₁₆	—	3	1	no	—
79	C₂×C₅×M₁₆	—	6	1	no	—
80	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₅×C₈	—	3	1	no	—
82	C₂²×C₅×C₈	—	6	1	no	—
83	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
84	C₅×#117	C₂×D₃	1	1	yes	characteristic
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₅×#108	—	6	2	no	—
87	C₅×C₄⋊C₈	—	2	1	no	—
88	C₅×C₄⋊C₈	—	2	1	no	—
89	C₅×#104	—	6	2	no	—
90	C₅×#103	—	3	1	no	—
91	C₅×#103	—	3	1	no	—
92	C₅×#102	—	3	1	no	—
93	C₅×#102	—	3	1	no	—
94	#1866	—	3	1	no	Sylow
95	C₂³×C₃×C₅	#41	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	1	no	—
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
105	C₅×#67	—	2	2	no	—
106	C₅×#67	—	2	2	no	—
107	C₂×C₅×Dic₃	—	2	1	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	4	1	no	—
110	C₂×C₅×Dic₃	—	4	1	no	—
111	C₅×D₁₂	—	2	1	no	—
112	C₅×D₁₂	C₄⋊C₄	1	2	yes	—
113	C₄×C₅×D₃	—	2	2	no	—
114	C₄×C₅×D₃	—	2	2	no	—
115	C₅×Dic₆	—	2	1	no	—
116	C₅×Dic₆	C₄⋊C₄	1	2	yes	—
117	C₃×C₅×C₈	—	2	1	no	—
118	C₃×C₅×C₈	—	2	1	no	—
119	C₃×C₅×C₈	—	4	1	no	—
120	C₅×C₃⋊C₈	—	2	1	no	—
121	C₅×C₃⋊C₈	—	2	1	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₂×#235	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
125	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
126	C₃×#117	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
128	C₂×#208	C₂²×C₅	1	1	yes	characteristic
129	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
130	#901	—	2	2	no	—
131	#901	—	2	2	no	—
132	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
133	C₂×D₃×C₈	—	2	1	no	—
134	C₃×C₄⋊C₈	—	2	1	no	—
135	C₃×C₄⋊C₈	—	2	1	no	—
136	#825	—	2	2	no	—
137	#822	—	2	2	no	—
138	#810	C₄×C₅	1	1	yes	characteristic, complemented
139	#810	C₄×C₅	1	1	yes	characteristic, complemented
140	#809	C₄×C₅	1	1	yes	characteristic, complemented
141	#809	C₄×C₅	1	1	yes	characteristic, complemented
142	C₅×#41	—	3	2	no	—
143	C₅×#41	—	3	2	no	—
144	C₅×#41	—	6	1	no	—
145	C₅×#41	—	6	1	no	—
146	C₂×C₅×Q₈	—	3	1	no	—
147	C₂×C₅×D₄	—	3	1	no	—
148	C₂×C₅×D₄	—	6	1	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₅×M₁₆	—	2	1	no	—
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	—	3	2	no	—
155	C₅×M₁₆	—	6	4	no	—
156	C₅×M₁₆	—	6	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	2	1	no	—
159	C₂×C₅×C₈	—	2	1	no	—
160	C₂×C₅×C₈	—	3	1	no	—
161	C₂×C₅×C₈	—	3	1	no	—
162	C₂×C₅×C₈	—	6	4	no	—
163	C₂×C₅×C₈	—	6	1	no	—
164	C₂×C₅×C₈	—	6	1	no	—
165	C₂×C₅×C₈	—	6	1	no	—
166	C₂×C₅×C₈	#67	1	1	yes	characteristic
167	C₂×C₅×C₈	#67	1	1	yes	characteristic
168	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
169	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	6	1	no	—
173	C₄²×C₅	—	6	1	no	—
174	C₂×#131	—	3	1	no	—
175	C₂×#108	—	3	1	no	—
176	#424	C₅×D₃	1	1	yes	characteristic, complemented
177	C₂×#104	—	3	1	no	—
178	#416	—	3	1	no	—
179	#339	—	3	1	no	—
180	#336	—	3	1	no	—
181	C₂²×C₃×C₅	—	2	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₃×C₅	#123	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	2	no	—
187	C₂×C₅×D₃	—	4	1	no	—
188	C₂×C₅×D₃	—	4	1	no	—
189	C₃×C₄×C₅	—	4	1	no	—
190	C₃×C₄×C₅	—	4	1	no	—
191	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
193	C₃×C₄×C₅	#120	1	1	yes	characteristic
194	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
195	C₅×Dic₃	—	2	2	no	—
196	C₅×Dic₃	—	4	2	no	—
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂×#67	—	2	1	no	—
199	C₂²×Dic₃	—	2	1	no	—
200	#235	—	2	1	no	—
201	#235	—	2	1	no	—
202	#235	C₅×D₄	1	2	yes	—
203	#235	C₅×Q₈	1	2	yes	—
204	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₄×D₃	—	2	1	no	—
206	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
207	C₃×M₁₆	—	2	1	no	—
208	C₃×M₁₆	—	2	1	no	—
209	C₂×C₃×C₈	—	2	1	no	—
210	C₂×C₃×C₈	—	2	1	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
213	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
214	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₃×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₃×C₂²⋊C₄	—	2	1	no	—
217	C₃×C₄²	—	2	1	no	—
218	C₄×Dic₃	—	2	1	no	—
219	C₄×Dic₃	—	2	1	no	—
220	#208	—	2	1	no	—
221	#208	C₅×D₄	1	2	yes	—
222	C₂×C₃⋊C₈	—	2	1	no	—
223	C₂×C₃⋊C₈	—	2	1	no	—
224	C₂×C₃⋊C₈	—	2	1	no	—
225	C₂×C₃⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
226	C₂×C₃⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
227	ΓL(1,𝔽₂₅)	—	2	4	no	—
228	D₃×C₈	—	2	4	no	—
229	C₂³×C₅	—	6	1	no	—
230	C₂³×C₅	#235	1	1	yes	characteristic
231	C₅×Q₈	—	3	2	no	—
232	C₅×Q₈	—	6	1	no	—
233	C₅×D₄	—	3	2	no	—
234	C₅×D₄	—	6	2	no	—
235	C₅×D₄	—	6	2	no	—
236	C₅×D₄	—	6	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	6	1	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	6	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	12	1	no	—
244	C₂×C₄×C₅	—	12	1	no	—
245	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
249	C₂×C₄×C₅	#239	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
251	C₅×C₈	—	2	1	no	—
252	C₅×C₈	—	2	1	no	—
253	C₅×C₈	—	4	1	no	—
254	C₅×C₈	—	6	1	no	—
255	C₅×C₈	—	6	1	no	—
256	C₅×C₈	—	6	2	no	—
257	C₂×#41	—	3	1	no	—
258	#131	—	6	2	no	—
259	#131	—	6	2	no	—
260	C₂×M₁₆	—	3	1	no	—
261	C₂×M₁₆	—	6	1	no	—
262	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂²×C₈	—	3	1	no	—
264	C₂²×C₈	—	6	1	no	—
265	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
266	#117	C₂×C₅×D₃	1	1	yes	characteristic
267	C₂×C₄²	—	3	1	no	—
268	#108	—	6	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	#104	—	6	2	no	—
272	#103	—	3	1	no	—
273	#103	—	3	1	no	—
274	#102	—	3	1	no	—
275	#102	—	3	1	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	#385	1	1	yes	characteristic
279	C₂×C₃×C₅	#443	1	1	yes	characteristic
280	C₂×C₃×C₅	#444	1	1	yes	characteristic
281	C₅×D₃	—	4	2	no	—
282	C₂³×C₃	C₅×#41	1	1	yes	characteristic
283	C₂²×D₃	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
291	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
292	#67	—	2	2	no	—
293	#67	—	2	2	no	—
294	C₂×Dic₃	—	2	1	no	—
295	C₂×Dic₃	—	2	2	no	—
296	C₂×Dic₃	—	4	1	no	—
297	C₂×Dic₃	—	4	1	no	—
298	D₁₂	—	2	1	no	—
299	D₁₂	C₅×C₄⋊C₄	1	2	yes	—
300	C₄×D₃	—	2	2	no	—
301	C₄×D₃	—	2	2	no	—
302	Dic₆	—	2	1	no	—
303	Dic₆	C₅×C₄⋊C₄	1	2	yes	—
304	C₃×C₈	—	2	1	no	—
305	C₃×C₈	—	2	1	no	—
306	C₃×C₈	—	4	1	no	—
307	C₃⋊C₈	—	2	1	no	—
308	C₃⋊C₈	—	2	1	no	—
309	C₃⋊C₈	—	2	2	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	6	2	no	—
313	C₂²×C₅	—	12	1	no	—
314	C₂²×C₅	—	12	1	no	—
315	C₂²×C₅	#894	1	1	yes	characteristic
316	C₂²×C₅	#896	1	1	yes	characteristic
317	C₂²×C₅	C₄×#67	1	1	yes	characteristic
318	C₄×C₅	—	4	1	no	—
319	C₄×C₅	—	4	1	no	—
320	C₄×C₅	—	6	2	no	—
321	C₄×C₅	—	12	2	no	—
322	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
323	C₄×C₅	#893	1	1	yes	characteristic
324	C₄×C₅	#937	1	1	yes	characteristic
325	C₄×C₅	#946	1	1	yes	characteristic
326	#41	—	3	2	no	—
327	#41	—	3	2	no	—
328	#41	—	6	1	no	—
329	#41	—	6	1	no	—
330	C₂×Q₈	—	3	1	no	—
331	C₂×D₄	—	3	1	no	—
332	C₂×D₄	—	6	1	no	—
333	C₂²×C₄	—	6	1	no	—
334	C₂²×C₄	—	6	1	no	—
335	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
336	M₁₆	—	2	1	no	—
337	M₁₆	—	2	1	no	—
338	M₁₆	—	3	2	no	—
339	M₁₆	—	6	4	no	—
340	M₁₆	—	6	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	3	1	no	—
345	C₂×C₈	—	3	1	no	—
346	C₂×C₈	—	6	4	no	—
347	C₂×C₈	—	6	1	no	—
348	C₂×C₈	—	6	1	no	—
349	C₂×C₈	—	6	1	no	—
350	C₂×C₈	C₅×#67	1	1	yes	characteristic
351	C₂×C₈	C₅×#67	1	1	yes	characteristic
352	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
353	C₄⋊C₄	C₄×C₅×D₃	1	1	yes	characteristic
354	C₂²⋊C₄	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	6	1	no	—
357	C₄²	—	6	1	no	—
358	C₃×C₅	#1866	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
363	C₂²×C₃	C₅×#123	1	1	yes	characteristic
364	C₂×D₃	—	2	2	no	—
365	C₂×D₃	—	4	1	no	—
366	C₂×D₃	—	4	1	no	—
367	C₃×C₄	—	4	1	no	—
368	C₃×C₄	—	4	1	no	—
369	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
370	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
371	C₃×C₄	C₅×#120	1	1	yes	characteristic
372	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
373	Dic₃	—	2	2	no	—
374	Dic₃	—	4	2	no	—
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	12	2	no	—
378	C₂×C₅	#4989	1	1	yes	characteristic
379	C₂×C₅	#5144	1	1	yes	characteristic
380	C₂×C₅	#5145	1	1	yes	characteristic
381	C₂³	—	6	1	no	—
382	C₂³	C₅×#235	1	1	yes	characteristic
383	Q₈	—	3	2	no	—
384	Q₈	—	6	1	no	—
385	D₄	—	3	2	no	—
386	D₄	—	6	2	no	—
387	D₄	—	6	2	no	—
388	D₄	—	6	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	6	1	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	6	2	no	—
394	C₂×C₄	—	6	2	no	—
395	C₂×C₄	—	12	1	no	—
396	C₂×C₄	—	12	1	no	—
397	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
398	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
399	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
400	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
401	C₂×C₄	C₅×#239	1	1	yes	characteristic
402	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	6	1	no	—
407	C₈	—	6	1	no	—
408	C₈	—	6	2	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	C₅×#385	1	1	yes	characteristic
412	C₂×C₃	C₅×#443	1	1	yes	characteristic
413	C₂×C₃	C₅×#444	1	1	yes	characteristic
414	D₃	—	4	2	no	—
415	C₅	#70545	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	12	1	no	—
420	C₂²	—	12	1	no	—
421	C₂²	C₅×#894	1	1	yes	characteristic
422	C₂²	C₅×#896	1	1	yes	characteristic
423	C₂²	C₄×C₅×#67	1	1	yes	characteristic
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	6	2	no	—
427	C₄	—	12	2	no	—
428	C₄	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
429	C₄	C₅×#893	1	1	yes	characteristic
430	C₄	C₅×#937	1	1	yes	characteristic
431	C₄	C₅×#946	1	1	yes	characteristic
432	C₃	C₅×#1866	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	12	2	no	—
436	C₂	C₅×#4989	1	1	yes	characteristic
437	C₂	C₅×#5144	1	1	yes	characteristic
438	C₂	C₅×#5145	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₅×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#424	D₃
hypocenter	C₃	C₅×#1866
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×C₈ ◁ C₅×#424

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#424	C₂	semidirect
4. C₂×C₅×#822	C₂	semidirect
6. C₅×#4550	C₂	semidirect
7. C₅×#4532	C₂	semidirect
24. C₅×#810	C₄	semidirect
25. C₅×#810	C₄	semidirect
26. C₅×#809	C₄	semidirect
27. C₅×#809	C₄	semidirect
28. #70545	C₅	direct (N × H)
31. C₅×#424	D₃	semidirect
69. C₃×#424	C₂×C₅	semidirect
71. C₂×#822	C₂×C₅	semidirect
73. #4550	C₂×C₅	semidirect
74. #4532	C₂×C₅	semidirect
138. #810	C₄×C₅	semidirect
139. #810	C₄×C₅	semidirect
140. #809	C₄×C₅	semidirect
141. #809	C₄×C₅	semidirect
176. #424	C₅×D₃	semidirect
358. C₃×C₅	#1866	semidirect
415. C₅	#70545	direct (N × H)
432. C₃	C₅×#1866	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#901	2
C₃×C₅×#424	2
C₂×C₅×#825	2
C₂×C₅×#822	2
C₅×#5002	2
C₅×#4550	2
C₅×#4532	2
C₅×#1866	3
#70545	5

Subgroups — C5×#70545 #14300218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70545 #14300218