Subgroups — C₅×#68758 #14299575

Order 1920.

648 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	C₅×#5521	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic
3	C₅×#5121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4939	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4523	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1856	—	3	1	no	maximal, Hall
9	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₃×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
14	C₅×#926	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
16	C₂×C₅×#208	C₂²	1	1	yes	characteristic
17	C₅×#893	—	2	1	no	—
18	C₅×#893	—	2	1	no	—
19	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
20	C₄×C₅×D₁₂	—	2	1	no	—
21	C₄×C₅×D₁₂	—	2	1	no	—
22	C₅×#823	C₄	1	4	yes	complemented
23	C₅×#818	—	2	1	no	—
24	C₅×#817	—	2	1	no	—
25	C₅×#808	—	2	1	no	—
26	C₅×#807	—	2	1	no	—
27	#68758	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₅×#518	—	3	1	no	—
29	C₅×#428	—	3	1	no	—
30	C₅×#428	—	3	1	no	—
31	C₂×C₅×#100	—	3	1	no	—
32	C₅×#390	—	3	1	no	—
33	C₅×#339	—	3	1	no	—
34	C₅×#339	D₃	1	1	yes	characteristic, complemented
35	C₂³×C₅×D₃	D₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	—	2	1	no	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₅×Dic₃	—	2	1	no	—
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	—	2	1	no	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
44	C₂×C₅×D₁₂	Q₈	1	2	yes	—
45	C₂×C₄×C₅×D₃	—	2	2	no	—
46	C₂×C₄×C₅×D₃	—	2	2	no	—
47	C₃×C₅×M₁₆	—	2	1	no	—
48	C₃×C₅×M₁₆	C₂×C₄	1	2	yes	complemented
49	C₂×C₃×C₅×C₈	—	2	1	no	—
50	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
53	C₃×C₄²×C₅	—	2	1	no	—
54	C₃×C₄²×C₅	—	2	1	no	—
55	C₃×C₄²×C₅	—	2	1	no	—
56	C₅×#217	—	2	1	no	—
57	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
58	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
59	C₅×(C₂×D₃)⋊C₄	—	4	4	no	—
60	C₅×C₄⋊Dic₃	—	2	1	no	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
63	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
64	C₄×C₅×Dic₃	—	2	1	no	—
65	C₅×#208	—	2	1	no	—
66	C₅×#208	C₂×C₄	1	2	yes	complemented
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	#5521	C₂×C₅	1	1	yes	characteristic
69	C₂×#823	C₂×C₅	1	1	yes	characteristic
70	#5121	C₂×C₅	1	1	yes	characteristic, complemented
71	#4995	C₂×C₅	1	1	yes	characteristic, complemented
72	#4939	C₂×C₅	1	1	yes	characteristic
73	C₃×#339	C₂×C₅	1	1	yes	characteristic, complemented
74	#4523	C₂×C₅	1	1	yes	characteristic, complemented
75	C₂²×C₅×D₄	—	3	1	no	—
76	C₂×C₅×M₁₆	—	3	1	no	—
77	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
78	C₄×C₅×D₄	—	6	1	no	—
79	C₄×C₅×D₄	—	6	1	no	—
80	C₄×C₅×D₄	—	6	1	no	—
81	C₄×C₅×D₄	—	6	1	no	—
82	C₅×#117	—	3	1	no	—
83	C₅×#117	C₂×D₃	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
86	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
87	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
88	C₅×#107	—	6	1	no	—
89	C₅×#107	—	6	1	no	—
90	C₅×#106	—	6	1	no	—
91	C₅×#106	—	6	1	no	—
92	C₅×#100	—	3	4	no	—
93	#1856	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	2	2	no	—
96	C₂²×C₅×D₃	—	2	2	no	—
97	C₂²×C₅×D₃	—	4	2	no	—
98	C₂²×C₅×D₃	—	4	2	no	—
99	C₂²×C₅×D₃	C₄⋊C₄	1	4	yes	—
100	C₂×C₃×C₄×C₅	—	2	2	no	—
101	C₂×C₃×C₄×C₅	—	2	1	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	4	1	no	—
104	C₂×C₃×C₄×C₅	—	4	1	no	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
111	C₂×C₅×Dic₃	—	2	1	no	—
112	C₂×C₅×Dic₃	—	2	1	no	—
113	C₂×C₅×Dic₃	—	4	2	no	—
114	C₂×C₅×Dic₃	—	4	1	no	—
115	C₅×D₁₂	—	2	2	no	—
116	C₅×D₁₂	—	2	2	no	—
117	C₅×D₁₂	—	2	2	no	—
118	C₅×D₁₂	—	2	2	no	—
119	C₄×C₅×D₃	—	8	2	no	—
120	C₄×C₅×D₃	—	8	2	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
125	C₃×#117	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
127	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
128	#926	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
130	C₂×#208	C₂²×C₅	1	1	yes	characteristic
131	#893	—	2	1	no	—
132	#893	—	2	1	no	—
133	D₃×C₂²⋊C₄	—	2	2	no	—
134	C₄×D₁₂	—	2	1	no	—
135	C₄×D₁₂	—	2	1	no	—
136	#823	C₄×C₅	1	4	yes	complemented
137	#818	—	2	1	no	—
138	#817	—	2	1	no	—
139	#808	—	2	1	no	—
140	#807	—	2	1	no	—
141	C₂⁴×C₅	—	3	2	no	—
142	C₂×C₅×D₄	—	3	2	no	—
143	C₂×C₅×D₄	—	3	2	no	—
144	C₂×C₅×D₄	—	6	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂×C₅×D₄	—	6	1	no	—
147	C₂×C₅×D₄	—	6	1	no	—
148	C₂²×C₄×C₅	—	2	1	no	—
149	C₂²×C₄×C₅	—	6	2	no	—
150	C₂²×C₄×C₅	—	6	2	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₅×M₁₆	—	2	1	no	—
154	C₅×M₁₆	—	3	2	no	—
155	C₅×M₁₆	—	6	1	no	—
156	C₅×M₁₆	C₄×D₃	1	2	yes	complemented
157	C₂×C₅×C₈	—	2	1	no	—
158	C₂×C₅×C₈	—	6	1	no	—
159	C₅×C₄⋊C₄	—	3	1	no	—
160	C₅×C₄⋊C₄	—	3	1	no	—
161	C₅×C₄⋊C₄	—	6	1	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
164	C₅×C₄⋊C₄	D₁₂	1	1	yes	characteristic
165	C₅×C₂²⋊C₄	—	2	1	no	—
166	C₅×C₂²⋊C₄	—	6	2	no	—
167	C₅×C₂²⋊C₄	—	6	2	no	—
168	C₅×C₂²⋊C₄	—	6	1	no	—
169	C₅×C₂²⋊C₄	—	12	4	no	—
170	C₄²×C₅	—	2	1	no	—
171	C₄²×C₅	—	2	1	no	—
172	C₄²×C₅	—	2	1	no	—
173	C₄²×C₅	—	6	1	no	—
174	#518	—	3	1	no	—
175	#428	—	3	1	no	—
176	#428	—	3	1	no	—
177	C₂×#100	—	3	1	no	—
178	#390	—	3	1	no	—
179	#339	—	3	1	no	—
180	#339	C₅×D₃	1	1	yes	characteristic, complemented
181	C₂²×C₃×C₅	—	2	1	no	—
182	C₂²×C₃×C₅	—	2	1	no	—
183	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	#120	1	1	yes	characteristic
185	C₂²×C₃×C₅	#123	1	1	yes	characteristic
186	C₂×C₅×D₃	—	2	4	no	—
187	C₂×C₅×D₃	—	4	2	no	—
188	C₂×C₅×D₃	—	4	2	no	—
189	C₂×C₅×D₃	—	4	4	no	—
190	C₂×C₅×D₃	—	8	2	no	—
191	C₃×C₄×C₅	—	4	2	no	—
192	C₃×C₄×C₅	—	4	1	no	—
193	C₃×C₄×C₅	—	4	1	no	—
194	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
197	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
198	C₅×Dic₃	—	4	1	no	—
199	C₅×Dic₃	—	4	1	no	—
200	C₅×Dic₃	—	8	1	no	—
201	C₂³×D₃	C₅×D₄	1	2	yes	—
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×Dic₃	—	2	1	no	—
205	C₂×D₁₂	—	2	1	no	—
206	C₂×D₁₂	—	2	1	no	—
207	C₂×D₁₂	—	2	1	no	—
208	C₂×D₁₂	—	2	1	no	—
209	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
210	C₂×D₁₂	C₅×Q₈	1	2	yes	—
211	C₂×C₄×D₃	—	2	2	no	—
212	C₂×C₄×D₃	—	2	2	no	—
213	C₃×M₁₆	—	2	1	no	—
214	C₃×M₁₆	C₂×C₄×C₅	1	2	yes	complemented
215	C₂×C₃×C₈	—	2	1	no	—
216	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
217	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
218	C₃×C₂²⋊C₄	—	2	1	no	—
219	C₃×C₄²	—	2	1	no	—
220	C₃×C₄²	—	2	1	no	—
221	C₃×C₄²	—	2	1	no	—
222	#217	—	2	1	no	—
223	(C₂×D₃)⋊C₄	—	2	2	no	—
224	(C₂×D₃)⋊C₄	—	2	2	no	—
225	(C₂×D₃)⋊C₄	—	4	4	no	—
226	C₄⋊Dic₃	—	2	1	no	—
227	C₄⋊Dic₃	—	2	1	no	—
228	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
229	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
230	C₄×Dic₃	—	2	1	no	—
231	#208	—	2	1	no	—
232	#208	C₂×C₄×C₅	1	2	yes	complemented
233	C₂×C₃⋊C₈	—	2	1	no	—
234	C₂³×C₅	—	3	4	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	12	2	no	—
238	C₂³×C₅	—	12	2	no	—
239	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
240	C₅×D₄	—	6	2	no	—
241	C₅×D₄	—	6	2	no	—
242	C₅×D₄	—	6	2	no	—
243	C₅×D₄	—	6	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	1	no	—
246	C₂×C₄×C₅	—	2	1	no	—
247	C₂×C₄×C₅	—	4	1	no	—
248	C₂×C₄×C₅	—	4	1	no	—
249	C₂×C₄×C₅	—	6	1	no	—
250	C₂×C₄×C₅	—	6	1	no	—
251	C₂×C₄×C₅	—	12	2	no	—
252	C₂×C₄×C₅	—	12	1	no	—
253	C₂×C₄×C₅	—	24	2	no	—
254	C₂×C₄×C₅	—	24	2	no	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
257	C₂×C₄×C₅	#235	1	1	yes	characteristic
258	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	#237	1	1	yes	characteristic
260	C₂×C₄×C₅	D₃×Q₈	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	6	2	no	—
263	C₂²×D₄	—	3	1	no	—
264	C₂×M₁₆	—	3	1	no	—
265	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
266	C₄×D₄	—	6	1	no	—
267	C₄×D₄	—	6	1	no	—
268	C₄×D₄	—	6	1	no	—
269	C₄×D₄	—	6	1	no	—
270	#117	—	3	1	no	—
271	#117	C₂×C₅×D₃	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	3	1	no	—
273	C₂×C₂²⋊C₄	—	6	2	no	—
274	C₂×C₂²⋊C₄	—	6	2	no	—
275	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
276	#107	—	6	1	no	—
277	#107	—	6	1	no	—
278	#106	—	6	1	no	—
279	#106	—	6	1	no	—
280	#100	—	3	4	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	—	2	1	no	—
283	C₂×C₃×C₅	#385	1	1	yes	characteristic
284	C₂×C₃×C₅	#453	1	1	yes	characteristic
285	C₂×C₃×C₅	#455	1	1	yes	characteristic
286	C₅×D₃	—	4	4	no	—
287	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
288	C₂²×D₃	—	2	2	no	—
289	C₂²×D₃	—	2	2	no	—
290	C₂²×D₃	—	4	2	no	—
291	C₂²×D₃	—	4	2	no	—
292	C₂²×D₃	C₅×C₄⋊C₄	1	4	yes	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	4	1	no	—
297	C₂×C₃×C₄	—	4	1	no	—
298	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
303	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
304	C₂×Dic₃	—	2	1	no	—
305	C₂×Dic₃	—	2	1	no	—
306	C₂×Dic₃	—	4	2	no	—
307	C₂×Dic₃	—	4	1	no	—
308	D₁₂	—	2	2	no	—
309	D₁₂	—	2	2	no	—
310	D₁₂	—	2	2	no	—
311	D₁₂	—	2	2	no	—
312	C₄×D₃	—	8	2	no	—
313	C₄×D₃	—	8	2	no	—
314	C₃×C₈	—	2	2	no	—
315	C₃⋊C₈	—	2	2	no	—
316	C₂²×C₅	—	2	1	no	—
317	C₂²×C₅	—	2	1	no	—
318	C₂²×C₅	—	6	4	no	—
319	C₂²×C₅	—	12	4	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	12	2	no	—
322	C₂²×C₅	—	24	2	no	—
323	C₂²×C₅	#882	1	1	yes	characteristic
324	C₂²×C₅	#883	1	1	yes	characteristic
325	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	—	4	1	no	—
328	C₄×C₅	—	4	1	no	—
329	C₄×C₅	—	12	1	no	—
330	C₄×C₅	—	12	1	no	—
331	C₄×C₅	—	24	1	no	—
332	C₄×C₅	C₄×D₁₂	1	1	yes	characteristic
333	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
334	C₄×C₅	#896	1	1	yes	characteristic
335	C₄×C₅	#897	1	1	yes	characteristic
336	C₂⁴	—	3	2	no	—
337	C₂×D₄	—	3	2	no	—
338	C₂×D₄	—	3	2	no	—
339	C₂×D₄	—	6	1	no	—
340	C₂×D₄	—	6	1	no	—
341	C₂×D₄	—	6	1	no	—
342	C₂×D₄	—	6	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	6	2	no	—
345	C₂²×C₄	—	6	2	no	—
346	C₂²×C₄	—	6	1	no	—
347	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
348	M₁₆	—	2	1	no	—
349	M₁₆	—	3	2	no	—
350	M₁₆	—	6	1	no	—
351	M₁₆	C₄×C₅×D₃	1	2	yes	complemented
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	6	1	no	—
354	C₄⋊C₄	—	3	1	no	—
355	C₄⋊C₄	—	3	1	no	—
356	C₄⋊C₄	—	6	1	no	—
357	C₄⋊C₄	—	6	1	no	—
358	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
359	C₄⋊C₄	C₅×D₁₂	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	6	2	no	—
362	C₂²⋊C₄	—	6	2	no	—
363	C₂²⋊C₄	—	6	1	no	—
364	C₂²⋊C₄	—	12	4	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	6	1	no	—
369	C₃×C₅	#1856	1	1	yes	characteristic, complemented, Hall
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	2	1	no	—
372	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
373	C₂²×C₃	C₅×#120	1	1	yes	characteristic
374	C₂²×C₃	C₅×#123	1	1	yes	characteristic
375	C₂×D₃	—	2	4	no	—
376	C₂×D₃	—	4	2	no	—
377	C₂×D₃	—	4	2	no	—
378	C₂×D₃	—	4	4	no	—
379	C₂×D₃	—	8	2	no	—
380	C₃×C₄	—	4	2	no	—
381	C₃×C₄	—	4	1	no	—
382	C₃×C₄	—	4	1	no	—
383	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
384	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
385	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
386	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
387	Dic₃	—	4	1	no	—
388	Dic₃	—	4	1	no	—
389	Dic₃	—	8	1	no	—
390	C₂×C₅	—	2	1	no	—
391	C₂×C₅	—	2	1	no	—
392	C₂×C₅	—	12	4	no	—
393	C₂×C₅	#4668	1	1	yes	characteristic
394	C₂×C₅	#4822	1	1	yes	characteristic
395	C₂×C₅	#4825	1	1	yes	characteristic
396	C₂³	—	3	4	no	—
397	C₂³	—	6	2	no	—
398	C₂³	—	6	2	no	—
399	C₂³	—	12	2	no	—
400	C₂³	—	12	2	no	—
401	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
402	D₄	—	6	2	no	—
403	D₄	—	6	2	no	—
404	D₄	—	6	2	no	—
405	D₄	—	6	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	6	1	no	—
412	C₂×C₄	—	6	1	no	—
413	C₂×C₄	—	12	2	no	—
414	C₂×C₄	—	12	1	no	—
415	C₂×C₄	—	24	2	no	—
416	C₂×C₄	—	24	2	no	—
417	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
418	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
419	C₂×C₄	C₅×#235	1	1	yes	characteristic
420	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
421	C₂×C₄	C₅×#237	1	1	yes	characteristic
422	C₂×C₄	C₅×D₃×Q₈	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	6	2	no	—
425	C₂×C₃	—	2	1	no	—
426	C₂×C₃	—	2	1	no	—
427	C₂×C₃	C₅×#385	1	1	yes	characteristic
428	C₂×C₃	C₅×#453	1	1	yes	characteristic
429	C₂×C₃	C₅×#455	1	1	yes	characteristic
430	D₃	—	4	4	no	—
431	C₅	#68758	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	6	4	no	—
435	C₂²	—	12	4	no	—
436	C₂²	—	12	2	no	—
437	C₂²	—	12	2	no	—
438	C₂²	—	24	2	no	—
439	C₂²	C₅×#882	1	1	yes	characteristic
440	C₂²	C₅×#883	1	1	yes	characteristic
441	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
442	C₄	—	4	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	12	1	no	—
446	C₄	—	12	1	no	—
447	C₄	—	24	1	no	—
448	C₄	C₄×C₅×D₁₂	1	1	yes	characteristic
449	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
450	C₄	C₅×#896	1	1	yes	characteristic
451	C₄	C₅×#897	1	1	yes	characteristic
452	C₃	C₅×#1856	1	1	yes	characteristic, complemented, Sylow
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	12	4	no	—
456	C₂	C₅×#4668	1	1	yes	characteristic
457	C₂	C₅×#4822	1	1	yes	characteristic
458	C₂	C₅×#4825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#882
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#339	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#339	D₃
hypocenter	C₃	C₅×#1856
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#339

Complements

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

N	H ≅ G/N	type
3. C₅×#5121	C₂	semidirect
4. C₅×#4995	C₂	semidirect
6. C₃×C₅×#339	C₂	semidirect
7. C₅×#4523	C₂	semidirect
22. C₅×#823	C₄	semidirect
27. #68758	C₅	direct (N × H)
34. C₅×#339	D₃	semidirect
48. C₃×C₅×M₁₆	C₂×C₄	semidirect
66. C₅×#208	C₂×C₄	semidirect
70. #5121	C₂×C₅	semidirect
71. #4995	C₂×C₅	semidirect
73. C₃×#339	C₂×C₅	semidirect
74. #4523	C₂×C₅	semidirect
136. #823	C₄×C₅	semidirect
156. C₅×M₁₆	C₄×D₃	semidirect
180. #339	C₅×D₃	semidirect
214. C₃×M₁₆	C₂×C₄×C₅	semidirect
232. #208	C₂×C₄×C₅	semidirect
351. M₁₆	C₄×C₅×D₃	semidirect
369. C₃×C₅	#1856	semidirect
431. C₅	#68758	direct (N × H)
452. C₃	C₅×#1856	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5521	2
C₂×C₅×#823	2
C₅×#5121	2
C₅×#4995	2
C₅×#4939	2
C₃×C₅×#339	2
C₅×#4523	2
C₅×#1856	3
#68758	5

Subgroups — C5×#68758 #14299575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68758 #14299575