Subgroups — C₅×#70298 #14299781

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5827	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#837	C₂	1	1	yes	maximal, characteristic
4	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4964	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4555	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4554	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1860	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₅×Q₈×Dic₃	—	2	1	no	—
13	C₅×D₄×Dic₃	—	2	1	no	—
14	C₅×D₄×Dic₃	—	2	2	no	—
15	C₅×#926	—	2	1	no	—
16	C₅×#926	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	1	yes	characteristic
21	C₃×C₅×#103	—	2	1	no	—
22	C₃×C₅×#102	—	2	1	no	—
23	C₅×#837	C₄	1	4	yes	complemented
24	C₅×C₃⋊#95	—	2	2	no	—
25	C₅×#808	—	2	1	no	—
26	C₅×#807	—	2	1	no	—
27	#70298	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₅×#520	—	3	1	no	—
29	C₅×#428	—	3	1	no	—
30	C₂×C₅×#104	—	3	1	no	—
31	C₅×#417	D₃	1	1	yes	characteristic
32	C₅×#382	—	3	1	no	—
33	C₅×#343	—	3	1	no	—
34	C₅×#339	—	3	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	C₂×C₄	1	2	yes	—
38	C₃×C₅×#41	Q₈	1	2	yes	—
39	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	—	2	1	no	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₂²×C₅×Dic₃	—	2	2	no	—
47	C₂²×C₅×Dic₃	D₄	1	2	yes	—
48	C₃×C₅×M₁₆	—	2	1	no	—
49	C₃×C₅×M₁₆	—	2	1	no	—
50	C₂×C₃×C₅×C₈	—	2	1	no	—
51	C₃×C₅×C₄⋊C₄	—	2	1	no	—
52	C₃×C₅×C₄⋊C₄	—	2	1	no	—
53	C₅×#217	—	2	2	no	—
54	C₅×#217	—	2	1	no	—
55	C₅×C₄⋊Dic₃	—	2	2	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	—	2	1	no	—
58	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	—	2	2	no	—
61	C₄×C₅×Dic₃	—	2	1	no	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
64	C₅×#208	—	2	1	no	—
65	C₅×#208	C₂×C₄	1	2	yes	complemented
66	C₂×C₅×C₃⋊C₈	—	2	1	no	—
67	#5827	C₂×C₅	1	1	yes	characteristic
68	C₃×#417	C₂×C₅	1	1	yes	characteristic
69	C₂×#837	C₂×C₅	1	1	yes	characteristic
70	#4977	C₂×C₅	1	1	yes	characteristic, complemented
71	#4964	C₂×C₅	1	1	yes	characteristic, complemented
72	#4555	C₂×C₅	1	1	yes	characteristic, complemented
73	#4554	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
75	C₂×C₅×M₁₆	—	3	1	no	—
76	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
77	C₄×C₅×Q₈	—	6	1	no	—
78	C₄×C₅×D₄	—	6	2	no	—
79	C₄×C₅×D₄	—	6	1	no	—
80	C₅×#117	—	3	1	no	—
81	C₅×#117	—	6	1	no	—
82	C₂×C₅×C₄⋊C₄	—	3	1	no	—
83	C₂×C₅×C₄⋊C₄	—	6	1	no	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₅×#107	—	6	1	no	—
87	C₅×#106	—	6	1	no	—
88	C₅×#104	—	3	4	no	—
89	C₅×#103	—	2	1	no	—
90	C₅×#102	—	2	1	no	—
91	C₅×#95	—	6	2	no	—
92	#1860	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	1	no	—
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	—
97	C₃×C₅×D₄	—	2	2	no	—
98	C₃×C₅×D₄	—	2	2	no	—
99	C₃×C₅×D₄	—	2	1	no	—
100	C₃×C₅×D₄	C₄⋊C₄	1	2	yes	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	4	2	no	—
105	C₂×C₃×C₄×C₅	—	4	1	no	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
112	C₂×C₅×Dic₃	—	2	2	no	—
113	C₂×C₅×Dic₃	—	2	1	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	1	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₂×C₅×Dic₃	—	4	2	no	—
119	C₂×C₅×Dic₃	—	8	2	no	—
120	C₃×C₅×C₈	—	4	1	no	—
121	C₅×C₃⋊C₈	—	2	2	no	—
122	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
125	Q₈×Dic₃	—	2	1	no	—
126	D₄×Dic₃	—	2	1	no	—
127	D₄×Dic₃	—	2	2	no	—
128	#926	—	2	1	no	—
129	#926	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₄⋊Dic₃	—	2	1	no	—
131	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
132	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
133	C₂×#208	C₂²×C₅	1	1	yes	characteristic
134	C₃×#103	—	2	1	no	—
135	C₃×#102	—	2	1	no	—
136	#837	C₄×C₅	1	4	yes	complemented
137	C₃⋊#95	—	2	2	no	—
138	#808	—	2	1	no	—
139	#807	—	2	1	no	—
140	C₅×#41	—	2	1	no	—
141	C₅×#41	—	2	1	no	—
142	C₅×#41	Dic₆	1	2	yes	—
143	C₅×#41	C₄×D₃	1	2	yes	—
144	C₂×C₅×Q₈	#67	1	1	yes	characteristic
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	#67	1	1	yes	characteristic
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	3	2	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	—	6	2	no	—
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	—	2	1	no	—
155	C₅×M₁₆	—	3	2	no	—
156	C₅×M₁₆	—	6	1	no	—
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	3	1	no	—
162	C₅×C₄⋊C₄	—	3	1	no	—
163	C₅×C₄⋊C₄	—	6	2	no	—
164	C₅×C₄⋊C₄	—	6	1	no	—
165	C₅×C₄⋊C₄	—	6	1	no	—
166	C₅×C₂²⋊C₄	—	6	2	no	—
167	C₅×C₂²⋊C₄	—	6	1	no	—
168	C₄²×C₅	—	3	2	no	—
169	C₄²×C₅	—	6	2	no	—
170	C₄²×C₅	—	6	1	no	—
171	C₄²×C₅	—	6	1	no	—
172	#520	—	3	1	no	—
173	#428	—	3	1	no	—
174	C₂×#104	—	3	1	no	—
175	#417	C₅×D₃	1	1	yes	characteristic
176	#382	—	3	1	no	—
177	#343	—	3	1	no	—
178	#339	—	3	1	no	—
179	C₂²×C₃×C₅	—	2	1	no	—
180	C₂²×C₃×C₅	—	2	1	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	1	no	—
183	C₂²×C₃×C₅	—	4	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	#120	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
187	C₃×C₄×C₅	—	2	2	no	—
188	C₃×C₄×C₅	—	8	1	no	—
189	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
192	C₃×C₄×C₅	#123	1	1	yes	characteristic
193	C₅×Dic₃	—	4	2	no	—
194	C₅×Dic₃	—	4	1	no	—
195	C₅×Dic₃	—	4	2	no	—
196	C₅×Dic₃	—	4	1	no	—
197	C₃×#41	—	2	1	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	C₂×C₄×C₅	1	2	yes	—
200	C₃×#41	C₅×Q₈	1	2	yes	—
201	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
202	C₂×C₃×D₄	—	2	1	no	—
203	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	2	1	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₂²×Dic₃	—	2	1	no	—
208	C₂²×Dic₃	—	2	2	no	—
209	C₂²×Dic₃	C₅×D₄	1	2	yes	—
210	C₃×M₁₆	—	2	1	no	—
211	C₃×M₁₆	—	2	1	no	—
212	C₂×C₃×C₈	—	2	1	no	—
213	C₃×C₄⋊C₄	—	2	1	no	—
214	C₃×C₄⋊C₄	—	2	1	no	—
215	#217	—	2	2	no	—
216	#217	—	2	1	no	—
217	C₄⋊Dic₃	—	2	2	no	—
218	C₄⋊Dic₃	—	2	1	no	—
219	C₄⋊Dic₃	—	2	1	no	—
220	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
221	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
222	C₄×Dic₃	—	2	2	no	—
223	C₄×Dic₃	—	2	1	no	—
224	C₄×Dic₃	—	2	1	no	—
225	C₄×Dic₃	C₂×C₄×C₅	1	2	yes	complemented
226	#208	—	2	1	no	—
227	#208	C₂×C₄×C₅	1	2	yes	complemented
228	C₂×C₃⋊C₈	—	2	1	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	Dic₃⋊C₄	1	2	yes	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	Dic₃⋊C₄	1	2	yes	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	—	6	1	no	—
245	C₂×C₄×C₅	—	6	2	no	—
246	C₂×C₄×C₅	—	12	1	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	—	12	2	no	—
249	C₂×C₄×C₅	—	24	2	no	—
250	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
252	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	#237	1	1	yes	characteristic
254	C₂×C₄×C₅	#237	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
256	C₅×C₈	—	4	1	no	—
257	C₅×C₈	—	6	2	no	—
258	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
259	C₂×M₁₆	—	3	1	no	—
260	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
261	C₄×Q₈	—	6	1	no	—
262	C₄×D₄	—	6	2	no	—
263	C₄×D₄	—	6	1	no	—
264	#117	—	3	1	no	—
265	#117	—	6	1	no	—
266	C₂×C₄⋊C₄	—	3	1	no	—
267	C₂×C₄⋊C₄	—	6	1	no	—
268	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
269	C₂×C₄²	—	3	1	no	—
270	#107	—	6	1	no	—
271	#106	—	6	1	no	—
272	#104	—	3	4	no	—
273	#103	—	2	1	no	—
274	#102	—	2	1	no	—
275	#95	—	6	2	no	—
276	C₂×C₃×C₅	—	2	1	no	—
277	C₂×C₃×C₅	—	2	1	no	—
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	#385	1	1	yes	characteristic
280	C₂×C₃×C₅	#454	1	1	yes	characteristic
281	C₂×C₃×C₅	#455	1	1	yes	characteristic
282	C₂³×C₃	—	2	1	no	—
283	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₅×C₄⋊C₄	1	2	yes	—
286	C₃×D₄	—	2	2	no	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	1	no	—
289	C₃×D₄	C₅×C₄⋊C₄	1	2	yes	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	4	2	no	—
294	C₂×C₃×C₄	—	4	1	no	—
295	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
299	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
300	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	2	1	no	—
303	C₂×Dic₃	—	2	2	no	—
304	C₂×Dic₃	—	2	1	no	—
305	C₂×Dic₃	—	4	1	no	—
306	C₂×Dic₃	—	4	1	no	—
307	C₂×Dic₃	—	4	2	no	—
308	C₂×Dic₃	—	8	2	no	—
309	C₃×C₈	—	4	1	no	—
310	C₃⋊C₈	—	2	2	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	4	1	no	—
315	C₂²×C₅	—	4	1	no	—
316	C₂²×C₅	#878	1	1	yes	characteristic
317	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
318	C₂²×C₅	#937	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	8	1	no	—
321	C₄×C₅	—	12	2	no	—
322	C₄×C₅	—	12	1	no	—
323	C₄×C₅	—	12	2	no	—
324	C₄×C₅	—	12	1	no	—
325	C₄×C₅	#878	1	1	yes	characteristic
326	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
327	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
328	C₄×C₅	#935	1	1	yes	characteristic
329	#41	—	2	1	no	—
330	#41	—	2	1	no	—
331	#41	C₅×Dic₆	1	2	yes	—
332	#41	C₄×C₅×D₃	1	2	yes	—
333	C₂×Q₈	C₅×#67	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₅×#67	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	3	2	no	—
339	C₂²×C₄	—	6	1	no	—
340	C₂²×C₄	—	6	2	no	—
341	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	3	2	no	—
345	M₁₆	—	6	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	6	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	3	1	no	—
351	C₄⋊C₄	—	3	1	no	—
352	C₄⋊C₄	—	6	2	no	—
353	C₄⋊C₄	—	6	1	no	—
354	C₄⋊C₄	—	6	1	no	—
355	C₂²⋊C₄	—	6	2	no	—
356	C₂²⋊C₄	—	6	1	no	—
357	C₄²	—	3	2	no	—
358	C₄²	—	6	2	no	—
359	C₄²	—	6	1	no	—
360	C₄²	—	6	1	no	—
361	C₃×C₅	#1860	1	1	yes	characteristic, complemented, Hall
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	4	1	no	—
366	C₂²×C₃	—	4	1	no	—
367	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
368	C₂²×C₃	C₅×#120	1	1	yes	characteristic
369	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	8	1	no	—
372	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
373	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
374	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
375	C₃×C₄	C₅×#123	1	1	yes	characteristic
376	Dic₃	—	4	2	no	—
377	Dic₃	—	4	1	no	—
378	Dic₃	—	4	2	no	—
379	Dic₃	—	4	1	no	—
380	C₂×C₅	—	2	1	no	—
381	C₂×C₅	—	2	1	no	—
382	C₂×C₅	—	4	2	no	—
383	C₂×C₅	#4946	1	1	yes	characteristic
384	C₂×C₅	#5201	1	1	yes	characteristic
385	C₂×C₅	#5202	1	1	yes	characteristic
386	C₂³	—	2	1	no	—
387	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
388	Q₈	—	2	1	no	—
389	Q₈	C₅×Dic₃⋊C₄	1	2	yes	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	1	no	—
393	D₄	C₅×Dic₃⋊C₄	1	2	yes	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	6	2	no	—
400	C₂×C₄	—	6	1	no	—
401	C₂×C₄	—	6	1	no	—
402	C₂×C₄	—	6	2	no	—
403	C₂×C₄	—	12	1	no	—
404	C₂×C₄	—	12	1	no	—
405	C₂×C₄	—	12	2	no	—
406	C₂×C₄	—	24	2	no	—
407	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
409	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
410	C₂×C₄	C₅×#237	1	1	yes	characteristic
411	C₂×C₄	C₅×#237	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
413	C₈	—	4	1	no	—
414	C₈	—	6	2	no	—
415	C₂×C₃	—	2	1	no	—
416	C₂×C₃	—	2	1	no	—
417	C₂×C₃	—	4	2	no	—
418	C₂×C₃	C₅×#385	1	1	yes	characteristic
419	C₂×C₃	C₅×#454	1	1	yes	characteristic
420	C₂×C₃	C₅×#455	1	1	yes	characteristic
421	C₅	#70298	1	1	yes	characteristic, direct product factor, Sylow
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	C₅×#878	1	1	yes	characteristic
428	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
429	C₂²	C₅×#937	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	12	2	no	—
433	C₄	—	12	1	no	—
434	C₄	—	12	2	no	—
435	C₄	—	12	1	no	—
436	C₄	C₅×#878	1	1	yes	characteristic
437	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
438	C₄	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
439	C₄	C₅×#935	1	1	yes	characteristic
440	C₃	C₅×#1860	1	1	yes	characteristic, complemented, Sylow
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	4	2	no	—
444	C₂	C₅×#4946	1	1	yes	characteristic
445	C₂	C₅×#5201	1	1	yes	characteristic
446	C₂	C₅×#5202	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#417	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₃×C₅×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#417	D₃
hypocenter	C₃	C₅×#1860
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#417

Complements

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

N	H ≅ G/N	type
4. C₅×#4977	C₂	semidirect
5. C₅×#4964	C₂	semidirect
6. C₅×#4555	C₂	semidirect
7. C₅×#4554	C₂	semidirect
23. C₅×#837	C₄	semidirect
27. #70298	C₅	direct (N × H)
63. C₄×C₅×Dic₃	C₂×C₄	semidirect
65. C₅×#208	C₂×C₄	semidirect
70. #4977	C₂×C₅	semidirect
71. #4964	C₂×C₅	semidirect
72. #4555	C₂×C₅	semidirect
73. #4554	C₂×C₅	semidirect
136. #837	C₄×C₅	semidirect
225. C₄×Dic₃	C₂×C₄×C₅	semidirect
227. #208	C₂×C₄×C₅	semidirect
361. C₃×C₅	#1860	semidirect
421. C₅	#70298	direct (N × H)
440. C₃	C₅×#1860	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5827	2
C₃×C₅×#417	2
C₂×C₅×#837	2
C₅×#4977	2
C₅×#4964	2
C₅×#4555	2
C₅×#4554	2
C₅×#1860	3
#70298	5

Subgroups — C5×#70298 #14299781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#70298 #14299781