Subgroups — C₅×#92027 #72260173

Order 2400.

772 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₄×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅²×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#6790	C₂	1	2	yes	maximal, complemented
5	C₅×D₃×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#1203	C₂	1	2	yes	maximal, complemented
7	C₅×#6782	C₂	1	2	yes	maximal, complemented
8	C₅×D₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#6771	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#6769	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#6768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4144	—	3	1	no	maximal, Hall
13	C₂²×C₅×D₁₅	C₂²	1	2	yes	complemented
14	C₂²×C₅²×D₃	C₂²	1	2	yes	complemented
15	C₂×C₅×D₃×D₅	C₂²	1	2	yes	complemented
16	C₃×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₅×#1220	C₂²	1	2	yes	complemented
18	C₅×D₆₀	C₂²	1	1	yes	characteristic, complemented
19	C₄×C₅×D₁₅	C₂²	1	1	yes	characteristic, complemented
20	C₅²×#67	C₂²	1	2	yes	complemented
21	C₅²×D₁₂	C₂²	1	1	yes	characteristic, complemented
22	C₄×C₅²×D₃	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×Dic₅	C₂²	1	2	yes	complemented
25	C₃×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
27	C₅×#1204	C₂²	1	1	yes	characteristic, complemented
28	C₅×#1203	C₂²	1	2	yes	complemented
29	C₅×#1203	C₂²	1	2	yes	complemented
30	C₅×#1203	C₂²	1	1	yes	characteristic, complemented
31	C₅×#1203	C₂²	1	2	yes	complemented
32	C₅×#1202	C₂²	1	1	yes	characteristic, complemented
33	C₅×#1201	C₂²	1	1	yes	characteristic, complemented
34	C₅×#1200	C₂²	1	2	yes	complemented
35	C₅×D₃×Dic₅	C₂²	1	2	yes	complemented
36	C₅×#1009	—	5	1	no	maximal
37	#92027	C₅	1	1	yes	maximal, characteristic, direct product factor
38	C₂×C₅²×D₄	—	3	1	no	—
39	C₂×C₅×C₂²⋊D₅	—	3	2	no	—
40	C₂×C₅×C₂²⋊D₅	—	3	2	no	—
41	C₅×#711	—	3	2	no	—
42	C₅×#711	—	3	1	no	—
43	C₅×#711	D₃	1	1	yes	characteristic, complemented
44	C₅×D₄×D₅	—	3	1	no	—
45	C₅×D₄×D₅	—	3	2	no	—
46	C₅×D₄×D₅	—	3	1	no	—
47	C₅×#709	—	3	1	no	—
48	C₅×#709	—	3	1	no	—
49	C₂²×C₃×C₅²	C₂³	1	2	yes	—
50	C₂×C₅×D₁₅	—	4	2	no	—
51	C₂×C₅×D₁₅	C₂³	1	1	yes	characteristic
52	C₂×C₅×D₁₅	C₂³	1	2	yes	—
53	C₂×C₅²×D₃	—	4	2	no	—
54	C₂×C₅²×D₃	C₂³	1	1	yes	characteristic
55	C₂×C₅²×D₃	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₅	C₂³	1	1	yes	characteristic
57	C₅×D₃×D₅	—	4	2	no	—
58	C₃×C₄×C₅²	C₂³	1	1	yes	characteristic
59	C₅×Dic₁₅	C₂³	1	1	yes	characteristic
60	C₅²×Dic₃	C₂³	1	1	yes	characteristic
61	C₃×C₅×Dic₅	C₂³	1	2	yes	—
62	C₃×C₅×Dic₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×#41	—	5	1	no	—
64	D₄×D₁₅	C₂×C₅	1	1	yes	characteristic, complemented
65	C₅×#239	—	5	1	no	—
66	C₅×#239	—	5	1	no	—
67	C₅×D₃×D₄	—	2	2	no	—
68	C₅×D₃×D₄	—	5	2	no	—
69	C₅×D₃×D₄	—	5	1	no	—
70	C₅×D₃×D₄	—	5	2	no	—
71	C₅×D₃×D₄	D₅	1	1	yes	characteristic, complemented
72	C₅×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
73	C₅×#235	—	5	2	no	—
74	C₅×#235	—	5	1	no	—
75	C₂×C₅×D₁₂	—	5	2	no	—
76	C₂×C₅×D₁₂	—	5	1	no	—
77	C₃×#711	C₂×C₅	1	1	yes	characteristic, complemented
78	#6790	C₂×C₅	1	2	yes	complemented
79	D₃×C₂²⋊D₅	C₂×C₅	1	2	yes	complemented
80	C₂×#1203	C₂×C₅	1	2	yes	complemented
81	#6782	C₂×C₅	1	2	yes	complemented
82	D₅×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
83	#6771	C₂×C₅	1	1	yes	characteristic, complemented
84	#6769	C₂×C₅	1	1	yes	characteristic, complemented
85	#6768	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂³×C₅²	—	3	2	no	—
87	C₂²×C₅×D₅	—	3	2	no	—
88	C₂²×C₅×D₅	—	3	2	no	—
89	C₅²×D₄	—	3	2	no	—
90	C₅²×D₄	—	3	1	no	—
91	C₅²×D₄	C₂×D₃	1	1	yes	characteristic, complemented
92	C₂×C₄×C₅²	—	3	1	no	—
93	C₅×C₂²⋊D₅	—	3	2	no	—
94	C₅×C₂²⋊D₅	—	3	1	no	—
95	C₅×C₂²⋊D₅	—	3	1	no	—
96	C₅×C₂²⋊D₅	—	3	2	no	—
97	C₅×C₂²⋊D₅	—	3	2	no	—
98	C₅×C₂²⋊D₅	—	3	2	no	—
99	C₅×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
100	C₂×C₅×Dic₅	—	3	2	no	—
101	C₂×C₅×Dic₅	C₂×D₃	1	2	yes	complemented
102	C₅×D₂₀	—	3	1	no	—
103	C₅×D₂₀	—	3	1	no	—
104	C₄×C₅×D₅	—	3	1	no	—
105	C₄×C₅×D₅	—	3	2	no	—
106	C₄×C₅×D₅	C₂×D₃	1	1	yes	characteristic, complemented
107	C₅×Dic₁₀	—	3	1	no	—
108	C₅×Dic₁₀	C₂×D₃	1	1	yes	characteristic, complemented
109	C₅×H(5,𝔽₂)	—	15	1	no	—
110	#4144	—	3	1	no	—
111	C₂×C₃×C₅²	—	2	2	no	—
112	C₂×C₃×C₅²	C₂⁴	1	1	yes	characteristic
113	C₅×D₁₅	—	2	2	no	—
114	C₅×D₁₅	—	2	1	no	—
115	C₅²×D₃	—	2	1	no	—
116	C₅²×D₃	—	2	2	no	—
117	C₃×C₅×D₅	—	2	1	no	—
118	C₂²×D₁₅	C₂²×C₅	1	2	yes	complemented
119	C₂²×C₅×D₃	—	2	4	no	—
120	C₂²×C₅×D₃	—	5	2	no	—
121	C₂²×C₅×D₃	—	5	2	no	—
122	C₂²×C₅×D₃	C₂×D₅	1	2	yes	complemented
123	C₂²×C₅×D₃	C₂²×C₅	1	2	yes	complemented
124	C₂×D₃×D₅	C₂²×C₅	1	2	yes	complemented
125	C₃×C₅×Q₈	—	5	1	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	5	2	no	—
128	C₃×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
129	C₃×C₅×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
130	C₂×C₃×C₄×C₅	—	5	2	no	—
131	C₂×C₃×C₄×C₅	—	5	1	no	—
132	#1220	C₂²×C₅	1	2	yes	complemented
133	D₆₀	C₂²×C₅	1	1	yes	characteristic, complemented
134	C₄×D₁₅	C₂²×C₅	1	1	yes	characteristic, complemented
135	C₅×#67	—	2	4	no	—
136	C₅×#67	—	5	2	no	—
137	C₅×#67	—	5	1	no	—
138	C₅×#67	—	5	1	no	—
139	C₅×#67	C₂×D₅	1	2	yes	complemented
140	C₅×#67	C₂²×C₅	1	2	yes	complemented
141	C₅×D₁₂	—	2	2	no	—
142	C₅×D₁₂	—	5	2	no	—
143	C₅×D₁₂	—	5	1	no	—
144	C₅×D₁₂	—	5	2	no	—
145	C₅×D₁₂	—	5	2	no	—
146	C₅×D₁₂	—	5	1	no	—
147	C₅×D₁₂	C₂×D₅	1	1	yes	characteristic, complemented
148	C₅×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
149	C₄×C₅×D₃	—	2	2	no	—
150	C₄×C₅×D₃	—	5	2	no	—
151	C₄×C₅×D₃	—	5	1	no	—
152	C₄×C₅×D₃	—	5	2	no	—
153	C₄×C₅×D₃	C₂×D₅	1	1	yes	characteristic, complemented
154	C₄×C₅×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
155	C₅×Dic₆	—	5	1	no	—
156	C₃×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
157	C₂×C₃×Dic₅	C₂²×C₅	1	2	yes	complemented
158	C₃×C₄×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
159	C₃×Dic₁₀	C₂²×C₅	1	1	yes	characteristic, complemented
160	#1204	C₂²×C₅	1	1	yes	characteristic, complemented
161	#1203	C₂²×C₅	1	2	yes	complemented
162	#1203	C₂²×C₅	1	2	yes	complemented
163	#1203	C₂²×C₅	1	1	yes	characteristic, complemented
164	#1203	C₂²×C₅	1	2	yes	complemented
165	#1202	C₂²×C₅	1	1	yes	characteristic, complemented
166	#1201	C₂²×C₅	1	1	yes	characteristic, complemented
167	#1200	C₂²×C₅	1	2	yes	complemented
168	D₃×Dic₅	C₂²×C₅	1	2	yes	complemented
169	C₂²×C₅²	—	3	2	no	—
170	C₂²×C₅²	—	3	1	no	—
171	C₂²×C₅²	—	12	2	no	—
172	C₂²×C₅²	C₂²×D₃	1	2	yes	—
173	C₂×C₅×D₅	—	3	1	no	—
174	C₂×C₅×D₅	—	3	2	no	—
175	C₂×C₅×D₅	—	12	2	no	—
176	C₂×C₅×D₅	—	12	2	no	—
177	C₂×C₅×D₅	C₂²×D₃	1	1	yes	characteristic
178	C₄×C₅²	—	3	1	no	—
179	C₄×C₅²	C₂²×D₃	1	1	yes	characteristic
180	C₅×Dic₅	—	3	1	no	—
181	C₅×Dic₅	C₂²×D₃	1	1	yes	characteristic
182	C₅×Dic₅	C₂²×D₃	1	2	yes	—
183	#1009	—	5	1	no	Hall
184	C₅×#41	—	5	1	no	—
185	C₅×#41	—	15	1	no	—
186	C₅×#41	—	15	1	no	—
187	C₅×#41	—	15	2	no	—
188	C₅×#41	—	15	1	no	—
189	C₂×C₅×D₄	—	3	1	no	—
190	C₂×C₅×D₄	—	3	1	no	—
191	C₂×C₅×D₄	—	6	2	no	—
192	C₂×C₅×D₄	—	15	1	no	—
193	C₂×C₅×D₄	—	15	2	no	—
194	C₂×C₅×D₄	—	15	2	no	—
195	C₂×C₅×D₄	—	15	2	no	—
196	C₂×C₅×D₄	—	15	1	no	—
197	C₂×C₂²⋊D₅	—	3	2	no	—
198	C₂×C₂²⋊D₅	—	3	2	no	—
199	#711	—	3	2	no	—
200	#711	—	3	1	no	—
201	#711	C₅×D₃	1	1	yes	characteristic, complemented
202	D₄×D₅	—	3	1	no	—
203	D₄×D₅	—	3	2	no	—
204	D₄×D₅	—	3	1	no	—
205	#709	—	3	1	no	—
206	#709	—	3	1	no	—
207	C₃×C₅²	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
208	C₂²×C₃×C₅	—	2	4	no	—
209	C₂²×C₃×C₅	—	5	1	no	—
210	C₂²×C₃×C₅	C₂²×D₅	1	2	yes	—
211	C₂²×C₃×C₅	C₂³×C₅	1	2	yes	—
212	C₂×D₁₅	—	4	2	no	—
213	C₂×D₁₅	C₂³×C₅	1	2	yes	—
214	C₂×D₁₅	C₂³×C₅	1	1	yes	characteristic
215	C₂×C₅×D₃	—	2	2	no	—
216	C₂×C₅×D₃	—	2	4	no	—
217	C₂×C₅×D₃	—	4	2	no	—
218	C₂×C₅×D₃	—	4	2	no	—
219	C₂×C₅×D₃	—	4	8	no	—
220	C₂×C₅×D₃	—	5	1	no	—
221	C₂×C₅×D₃	—	5	2	no	—
222	C₂×C₅×D₃	—	20	2	no	—
223	C₂×C₅×D₃	—	20	2	no	—
224	C₂×C₅×D₃	C₂²×D₅	1	2	yes	—
225	C₂×C₅×D₃	C₂²×D₅	1	1	yes	characteristic
226	C₂×C₅×D₃	C₂³×C₅	1	2	yes	—
227	C₂×C₅×D₃	C₂³×C₅	1	1	yes	characteristic
228	C₂×C₃×D₅	C₂³×C₅	1	1	yes	characteristic
229	D₃×D₅	—	4	2	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	5	1	no	—
232	C₃×C₄×C₅	—	5	2	no	—
233	C₃×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
234	C₃×C₄×C₅	C₂³×C₅	1	1	yes	characteristic
235	Dic₁₅	C₂³×C₅	1	1	yes	characteristic
236	C₃×Dic₅	C₂³×C₅	1	2	yes	—
237	C₃×Dic₅	C₂³×C₅	1	1	yes	characteristic
238	C₅×Dic₃	—	2	2	no	—
239	C₅×Dic₃	—	5	1	no	—
240	C₅×Dic₃	C₂²×D₅	1	1	yes	characteristic
241	C₅×Dic₃	C₂³×C₅	1	1	yes	characteristic
242	C₂×C₅²	—	2	2	no	—
243	C₂×C₅²	—	6	1	no	—
244	C₂×C₅²	—	6	2	no	—
245	C₂×C₅²	C₂³×D₃	1	1	yes	characteristic
246	C₅×D₅	—	2	1	no	—
247	C₅×D₅	—	6	1	no	—
248	C₅×D₅	—	6	2	no	—
249	C₃×#41	—	5	1	no	—
250	#239	—	5	1	no	—
251	#239	—	5	1	no	—
252	D₃×D₄	—	5	2	no	—
253	D₃×D₄	—	5	1	no	—
254	D₃×D₄	—	5	2	no	—
255	D₃×D₄	C₅×D₅	1	1	yes	characteristic, complemented
256	#235	—	5	2	no	—
257	#235	—	5	1	no	—
258	C₂×D₁₂	—	5	2	no	—
259	C₂×D₁₂	—	5	1	no	—
260	C₂³×C₅	—	3	2	no	—
261	C₂³×C₅	—	3	2	no	—
262	C₂³×C₅	—	6	4	no	—
263	C₂³×C₅	—	15	2	no	—
264	C₂³×C₅	—	15	2	no	—
265	C₂²×D₅	—	3	2	no	—
266	C₂²×D₅	—	3	2	no	—
267	C₅×Q₈	—	5	1	no	—
268	C₅×Q₈	—	15	1	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	3	2	no	—
271	C₅×D₄	—	3	2	no	—
272	C₅×D₄	—	3	1	no	—
273	C₅×D₄	—	3	1	no	—
274	C₅×D₄	—	5	2	no	—
275	C₅×D₄	—	6	2	no	—
276	C₅×D₄	—	6	4	no	—
277	C₅×D₄	—	15	1	no	—
278	C₅×D₄	—	15	1	no	—
279	C₅×D₄	—	15	2	no	—
280	C₅×D₄	—	15	2	no	—
281	C₅×D₄	—	15	2	no	—
282	C₅×D₄	—	15	1	no	—
283	C₅×D₄	—	15	2	no	—
284	C₅×D₄	—	15	1	no	—
285	C₅×D₄	D₃×D₅	1	1	yes	characteristic, complemented
286	C₅×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	3	1	no	—
289	C₂×C₄×C₅	—	5	2	no	—
290	C₂×C₄×C₅	—	5	1	no	—
291	C₂×C₄×C₅	—	6	2	no	—
292	C₂×C₄×C₅	—	15	2	no	—
293	C₂×C₄×C₅	—	15	2	no	—
294	C₂×C₄×C₅	—	15	1	no	—
295	C₂²⋊D₅	—	3	2	no	—
296	C₂²⋊D₅	—	3	1	no	—
297	C₂²⋊D₅	—	3	1	no	—
298	C₂²⋊D₅	—	3	2	no	—
299	C₂²⋊D₅	—	3	2	no	—
300	C₂²⋊D₅	—	3	2	no	—
301	C₂²⋊D₅	C₂×C₅×D₃	1	2	yes	complemented
302	C₂×Dic₅	—	3	2	no	—
303	C₂×Dic₅	C₂×C₅×D₃	1	2	yes	complemented
304	D₂₀	—	3	1	no	—
305	D₂₀	—	3	1	no	—
306	C₄×D₅	—	3	1	no	—
307	C₄×D₅	—	3	2	no	—
308	C₄×D₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
309	Dic₁₀	—	3	1	no	—
310	Dic₁₀	C₂×C₅×D₃	1	1	yes	characteristic, complemented
311	H(5,𝔽₂)	—	15	1	no	Sylow
312	C₂×C₃×C₅	—	2	2	no	—
313	C₂×C₃×C₅	—	2	2	no	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	—	4	4	no	—
316	C₂×C₃×C₅	—	10	1	no	—
317	C₂×C₃×C₅	C₂³×D₅	1	1	yes	characteristic
318	C₂×C₃×C₅	C₂⁴×C₅	1	1	yes	characteristic
319	D₁₅	—	2	2	no	—
320	D₁₅	—	2	1	no	—
321	C₃×D₅	—	2	1	no	—
322	C₅×D₃	—	2	4	no	—
323	C₅×D₃	—	2	1	no	—
324	C₅×D₃	—	2	2	no	—
325	C₅×D₃	—	2	2	no	—
326	C₅×D₃	—	2	1	no	—
327	C₅×D₃	—	4	4	no	—
328	C₅×D₃	—	10	2	no	—
329	C₅×D₃	—	10	1	no	—
330	C₅²	#1009	1	1	yes	characteristic, complemented, Sylow
331	C₂²×D₃	—	5	2	no	—
332	C₂²×D₃	—	5	2	no	—
333	C₂²×D₃	C₂×C₅×D₅	1	2	yes	complemented
334	C₃×Q₈	—	5	1	no	—
335	C₃×D₄	—	5	2	no	—
336	C₃×D₄	C₂×C₅×D₅	1	1	yes	characteristic, complemented
337	C₂×C₃×C₄	—	5	2	no	—
338	C₂×C₃×C₄	—	5	1	no	—
339	#67	—	5	2	no	—
340	#67	—	5	1	no	—
341	#67	—	5	1	no	—
342	#67	C₂×C₅×D₅	1	2	yes	complemented
343	D₁₂	—	5	2	no	—
344	D₁₂	—	5	1	no	—
345	D₁₂	—	5	2	no	—
346	D₁₂	—	5	2	no	—
347	D₁₂	—	5	1	no	—
348	D₁₂	C₂×C₅×D₅	1	1	yes	characteristic, complemented
349	C₄×D₃	—	5	2	no	—
350	C₄×D₃	—	5	1	no	—
351	C₄×D₃	—	5	2	no	—
352	C₄×D₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented
353	Dic₆	—	5	1	no	—
354	C₂²×C₅	—	2	4	no	—
355	C₂²×C₅	—	3	1	no	—
356	C₂²×C₅	—	3	2	no	—
357	C₂²×C₅	—	3	2	no	—
358	C₂²×C₅	—	3	1	no	—
359	C₂²×C₅	—	5	1	no	—
360	C₂²×C₅	—	6	2	no	—
361	C₂²×C₅	—	6	4	no	—
362	C₂²×C₅	—	12	2	no	—
363	C₂²×C₅	—	12	2	no	—
364	C₂²×C₅	—	12	8	no	—
365	C₂²×C₅	—	15	2	no	—
366	C₂²×C₅	—	15	1	no	—
367	C₂²×C₅	—	60	2	no	—
368	C₂²×C₅	—	60	2	no	—
369	C₂²×C₅	C₂×D₃×D₅	1	2	yes	—
370	C₂²×C₅	C₂²×C₅×D₃	1	2	yes	—
371	C₂×D₅	—	3	2	no	—
372	C₂×D₅	—	3	1	no	—
373	C₂×D₅	—	12	2	no	—
374	C₂×D₅	—	12	2	no	—
375	C₂×D₅	C₂²×C₅×D₃	1	1	yes	characteristic
376	C₄×C₅	—	2	2	no	—
377	C₄×C₅	—	3	1	no	—
378	C₄×C₅	—	3	1	no	—
379	C₄×C₅	—	5	1	no	—
380	C₄×C₅	—	5	2	no	—
381	C₄×C₅	—	6	2	no	—
382	C₄×C₅	—	15	1	no	—
383	C₄×C₅	C₂×D₃×D₅	1	1	yes	characteristic
384	C₄×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
385	Dic₅	—	3	1	no	—
386	Dic₅	C₂²×C₅×D₃	1	1	yes	characteristic
387	Dic₅	C₂²×C₅×D₃	1	2	yes	—
388	#41	—	5	1	no	—
389	#41	—	15	1	no	—
390	#41	—	15	1	no	—
391	#41	—	15	2	no	—
392	#41	—	15	1	no	—
393	C₂×D₄	—	3	1	no	—
394	C₂×D₄	—	15	1	no	—
395	C₂×D₄	—	15	2	no	—
396	C₂×D₄	—	15	2	no	—
397	C₂×D₄	—	15	2	no	—
398	C₂×D₄	—	15	1	no	—
399	C₃×C₅	—	2	2	no	—
400	C₃×C₅	#4144	1	1	yes	characteristic, complemented
401	C₃×C₅	C₅×H(5,𝔽₂)	1	1	yes	characteristic, complemented
402	C₂²×C₃	—	5	1	no	—
403	C₂²×C₃	C₂²×C₅×D₅	1	2	yes	—
404	C₂×D₃	—	4	2	no	—
405	C₂×D₃	—	5	2	no	—
406	C₂×D₃	—	5	1	no	—
407	C₂×D₃	—	20	2	no	—
408	C₂×D₃	—	20	2	no	—
409	C₂×D₃	C₂²×C₅×D₅	1	2	yes	—
410	C₂×D₃	C₂²×C₅×D₅	1	1	yes	characteristic
411	C₃×C₄	—	5	1	no	—
412	C₃×C₄	—	5	2	no	—
413	C₃×C₄	C₂²×C₅×D₅	1	1	yes	characteristic
414	Dic₃	—	5	1	no	—
415	Dic₃	C₂²×C₅×D₅	1	1	yes	characteristic
416	C₂×C₅	—	2	2	no	—
417	C₂×C₅	—	2	2	no	—
418	C₂×C₅	—	2	2	no	—
419	C₂×C₅	—	4	4	no	—
420	C₂×C₅	—	6	4	no	—
421	C₂×C₅	—	6	1	no	—
422	C₂×C₅	—	6	2	no	—
423	C₂×C₅	—	6	2	no	—
424	C₂×C₅	—	6	1	no	—
425	C₂×C₅	—	10	1	no	—
426	C₂×C₅	—	12	4	no	—
427	C₂×C₅	—	30	1	no	—
428	C₂×C₅	—	30	2	no	—
429	C₂×C₅	C₂²×D₃×D₅	1	1	yes	characteristic
430	C₂×C₅	C₂³×C₅×D₃	1	1	yes	characteristic
431	D₅	—	2	1	no	—
432	D₅	—	6	2	no	—
433	D₅	—	6	1	no	—
434	C₂³	—	3	2	no	—
435	C₂³	—	15	2	no	—
436	C₂³	—	15	2	no	—
437	Q₈	—	5	1	no	—
438	Q₈	—	15	1	no	—
439	D₄	—	3	2	no	—
440	D₄	—	3	1	no	—
441	D₄	—	5	2	no	—
442	D₄	—	15	1	no	—
443	D₄	—	15	1	no	—
444	D₄	—	15	2	no	—
445	D₄	—	15	2	no	—
446	D₄	—	15	2	no	—
447	D₄	—	15	1	no	—
448	D₄	—	15	2	no	—
449	D₄	—	15	1	no	—
450	D₄	C₅×D₃×D₅	1	1	yes	characteristic, complemented
451	C₂×C₄	—	3	1	no	—
452	C₂×C₄	—	5	2	no	—
453	C₂×C₄	—	5	1	no	—
454	C₂×C₄	—	15	2	no	—
455	C₂×C₄	—	15	2	no	—
456	C₂×C₄	—	15	1	no	—
457	C₂×C₃	—	2	2	no	—
458	C₂×C₃	—	10	1	no	—
459	C₂×C₃	C₂³×C₅×D₅	1	1	yes	characteristic
460	D₃	—	2	1	no	—
461	D₃	—	2	2	no	—
462	D₃	—	10	2	no	—
463	D₃	—	10	1	no	—
464	C₅	—	2	2	no	—
465	C₅	#92027	1	1	yes	characteristic, direct product factor
466	C₅	C₅×#1009	1	1	yes	characteristic, complemented
467	C₂²	—	3	1	no	—
468	C₂²	—	3	2	no	—
469	C₂²	—	5	1	no	—
470	C₂²	—	12	2	no	—
471	C₂²	—	15	2	no	—
472	C₂²	—	15	1	no	—
473	C₂²	—	60	2	no	—
474	C₂²	—	60	2	no	—
475	C₂²	C₂×C₅×D₃×D₅	1	2	yes	—
476	C₄	—	3	1	no	—
477	C₄	—	5	1	no	—
478	C₄	—	5	2	no	—
479	C₄	—	15	1	no	—
480	C₄	C₂×C₅×D₃×D₅	1	1	yes	characteristic
481	C₃	C₅×#4144	1	1	yes	characteristic, complemented, Sylow
482	C₂	—	2	2	no	—
483	C₂	—	6	1	no	—
484	C₂	—	6	2	no	—
485	C₂	—	10	1	no	—
486	C₂	—	30	1	no	—
487	C₂	—	30	2	no	—
488	C₂	C₂²×C₅×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃×D₅
Fitting	C₃×C₅²×D₄	C₂²
socle	C₂×C₃×C₅²	C₂⁴
hypercenter	C₅×D₄	D₃×D₅
hypocenter	C₃×C₅	C₅×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₅×D₄×D₁₅	C₂	semidirect
2. C₅²×D₃×D₄	C₂	semidirect
3. C₃×C₅×#711	C₂	semidirect
4. C₅×#6790	C₂	semidirect
5. C₅×D₃×C₂²⋊D₅	C₂	semidirect
6. C₂×C₅×#1203	C₂	semidirect
7. C₅×#6782	C₂	semidirect
8. C₅×D₅×D₁₂	C₂	semidirect
9. C₅×#6771	C₂	semidirect
10. C₅×#6769	C₂	semidirect
11. C₅×#6768	C₂	semidirect
13. C₂²×C₅×D₁₅	C₂²	semidirect
14. C₂²×C₅²×D₃	C₂²	semidirect
15. C₂×C₅×D₃×D₅	C₂²	semidirect
16. C₃×C₅²×D₄	C₂²	semidirect
17. C₅×#1220	C₂²	semidirect
18. C₅×D₆₀	C₂²	semidirect
19. C₄×C₅×D₁₅	C₂²	semidirect
20. C₅²×#67	C₂²	semidirect
21. C₅²×D₁₂	C₂²	semidirect
22. C₄×C₅²×D₃	C₂²	semidirect
23. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
24. C₂×C₃×C₅×Dic₅	C₂²	semidirect
25. C₃×C₄×C₅×D₅	C₂²	semidirect
26. C₃×C₅×Dic₁₀	C₂²	semidirect
27. C₅×#1204	C₂²	semidirect
28. C₅×#1203	C₂²	semidirect
29. C₅×#1203	C₂²	semidirect
30. C₅×#1203	C₂²	semidirect
31. C₅×#1203	C₂²	semidirect
32. C₅×#1202	C₂²	semidirect
33. C₅×#1201	C₂²	semidirect
34. C₅×#1200	C₂²	semidirect
35. C₅×D₃×Dic₅	C₂²	semidirect
37. #92027	C₅	direct (N × H)
43. C₅×#711	D₃	semidirect
64. D₄×D₁₅	C₂×C₅	semidirect
71. C₅×D₃×D₄	D₅	semidirect
72. C₅×D₃×D₄	C₂×C₅	semidirect
77. C₃×#711	C₂×C₅	semidirect
78. #6790	C₂×C₅	semidirect
79. D₃×C₂²⋊D₅	C₂×C₅	semidirect
80. C₂×#1203	C₂×C₅	semidirect
81. #6782	C₂×C₅	semidirect
82. D₅×D₁₂	C₂×C₅	semidirect
83. #6771	C₂×C₅	semidirect
84. #6769	C₂×C₅	semidirect
85. #6768	C₂×C₅	semidirect
91. C₅²×D₄	C₂×D₃	semidirect
99. C₅×C₂²⋊D₅	C₂×D₃	semidirect
101. C₂×C₅×Dic₅	C₂×D₃	semidirect
106. C₄×C₅×D₅	C₂×D₃	semidirect
108. C₅×Dic₁₀	C₂×D₃	semidirect
118. C₂²×D₁₅	C₂²×C₅	semidirect
122. C₂²×C₅×D₃	C₂×D₅	semidirect
123. C₂²×C₅×D₃	C₂²×C₅	semidirect
124. C₂×D₃×D₅	C₂²×C₅	semidirect
128. C₃×C₅×D₄	C₂×D₅	semidirect
129. C₃×C₅×D₄	C₂²×C₅	semidirect
132. #1220	C₂²×C₅	semidirect
133. D₆₀	C₂²×C₅	semidirect
134. C₄×D₁₅	C₂²×C₅	semidirect
139. C₅×#67	C₂×D₅	semidirect
140. C₅×#67	C₂²×C₅	semidirect
147. C₅×D₁₂	C₂×D₅	semidirect
148. C₅×D₁₂	C₂²×C₅	semidirect
153. C₄×C₅×D₃	C₂×D₅	semidirect
154. C₄×C₅×D₃	C₂²×C₅	semidirect
156. C₃×C₂²⋊D₅	C₂²×C₅	semidirect
157. C₂×C₃×Dic₅	C₂²×C₅	semidirect
158. C₃×C₄×D₅	C₂²×C₅	semidirect
159. C₃×Dic₁₀	C₂²×C₅	semidirect
160. #1204	C₂²×C₅	semidirect
161. #1203	C₂²×C₅	semidirect
162. #1203	C₂²×C₅	semidirect
163. #1203	C₂²×C₅	semidirect
164. #1203	C₂²×C₅	semidirect
165. #1202	C₂²×C₅	semidirect
166. #1201	C₂²×C₅	semidirect
167. #1200	C₂²×C₅	semidirect
168. D₃×Dic₅	C₂²×C₅	semidirect
201. #711	C₅×D₃	semidirect
207. C₃×C₅²	H(5,𝔽₂)	semidirect
255. D₃×D₄	C₅×D₅	semidirect
285. C₅×D₄	D₃×D₅	semidirect
286. C₅×D₄	C₂×C₅×D₃	semidirect
301. C₂²⋊D₅	C₂×C₅×D₃	semidirect
303. C₂×Dic₅	C₂×C₅×D₃	semidirect
308. C₄×D₅	C₂×C₅×D₃	semidirect
310. Dic₁₀	C₂×C₅×D₃	semidirect
330. C₅²	#1009	semidirect
333. C₂²×D₃	C₂×C₅×D₅	semidirect
336. C₃×D₄	C₂×C₅×D₅	semidirect
342. #67	C₂×C₅×D₅	semidirect
348. D₁₂	C₂×C₅×D₅	semidirect
352. C₄×D₃	C₂×C₅×D₅	semidirect
400. C₃×C₅	#4144	semidirect
401. C₃×C₅	C₅×H(5,𝔽₂)	semidirect
450. D₄	C₅×D₃×D₅	semidirect
465. C₅	#92027	direct (N × H)
466. C₅	C₅×#1009	semidirect
481. C₃	C₅×#4144	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₄×D₁₅	2
C₅²×D₃×D₄	2
C₃×C₅×#711	2
C₅×#6790	2
C₅×D₃×C₂²⋊D₅	2
C₂×C₅×#1203	2
C₅×#6782	2
C₅×D₅×D₁₂	2
C₅×#6771	2
C₅×#6769	2
C₅×#6768	2
C₅×#4144	3
C₅×#1009	5
#92027	5

Subgroups — C5×#92027 #72260173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#92027 #72260173