Subgroups — C₅×#92049 #72231634

Order 2400.

772 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1220	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅²×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×C₂²⋊D₅	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	C₅×D₅×#67	C₂	1	2	yes	maximal, complemented
7	C₅×#6782	C₂	1	2	yes	maximal, complemented
8	C₅×#6780	C₂	1	2	yes	maximal, complemented
9	C₅×#6779	C₂	1	2	yes	maximal, complemented
10	C₅×#4144	—	3	1	no	maximal, Hall
11	C₂³×C₃×C₅²	C₂²	1	1	yes	characteristic, complemented
12	C₂²×C₅×D₁₅	C₂²	1	1	yes	characteristic, complemented
13	C₂²×C₅²×D₃	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₅×D₃×D₅	C₂²	1	2	yes	complemented
16	C₅×#1220	C₂²	1	2	yes	complemented
17	C₅×#1220	C₂²	1	2	yes	complemented
18	C₂×C₅×Dic₁₅	C₂²	1	1	yes	characteristic, complemented
19	C₅²×#67	C₂²	1	2	yes	complemented
20	C₅²×#67	C₂²	1	2	yes	complemented
21	C₂×C₅²×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
23	C₃×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
24	C₂×C₃×C₅×Dic₅	C₂²	1	1	yes	characteristic, complemented
25	C₅×#1204	C₂²	1	2	yes	complemented
26	C₅×#1203	C₂²	1	2	yes	complemented
27	C₅×#1202	C₂²	1	2	yes	complemented
28	C₅×#1201	C₂²	1	2	yes	complemented
29	C₅×#1200	C₂²	1	2	yes	complemented
30	C₅×D₃×Dic₅	C₂²	1	2	yes	complemented
31	C₅×D₅×Dic₃	C₂²	1	2	yes	complemented
32	C₅×#1004	—	5	1	no	maximal
33	#92049	C₅	1	1	yes	maximal, characteristic, direct product factor
34	C₂×C₅²×D₄	—	3	1	no	—
35	C₂×C₅×C₂²⋊D₅	—	3	1	no	—
36	C₂×C₅×C₂²⋊D₅	—	3	2	no	—
37	C₂×C₅×C₂²⋊D₅	D₃	1	1	yes	characteristic, complemented
38	C₅×#711	—	3	2	no	—
39	C₅×#711	—	3	2	no	—
40	C₅×D₄×D₅	—	3	2	no	—
41	C₅×D₄×D₅	—	3	2	no	—
42	C₅×#709	—	3	2	no	—
43	C₂²×C₃×C₅²	—	4	1	no	—
44	C₂²×C₃×C₅²	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₅²	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₅²	C₂³	1	1	yes	characteristic
47	C₂×C₅×D₁₅	—	4	1	no	—
48	C₂×C₅×D₁₅	C₂³	1	2	yes	—
49	C₂×C₅²×D₃	—	4	1	no	—
50	C₂×C₅²×D₃	C₂³	1	2	yes	—
51	C₂×C₃×C₅×D₅	—	4	1	no	—
52	C₂×C₃×C₅×D₅	C₂³	1	2	yes	—
53	C₅×D₃×D₅	—	4	2	no	—
54	C₅×Dic₁₅	C₂³	1	2	yes	—
55	C₅²×Dic₃	C₂³	1	2	yes	—
56	C₃×C₅×Dic₅	C₂³	1	2	yes	—
57	C₂×C₃×C₅×D₄	—	5	1	no	—
58	C₂×#1220	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×C₅×#67	—	2	2	no	—
60	C₂×C₅×#67	—	5	1	no	—
61	C₂×C₅×#67	—	5	2	no	—
62	C₂×C₅×#67	D₅	1	1	yes	characteristic, complemented
63	C₂×C₅×#67	C₂×C₅	1	1	yes	characteristic, complemented
64	C₅×#237	—	5	2	no	—
65	C₅×#237	—	5	2	no	—
66	C₅×D₃×D₄	—	5	2	no	—
67	C₅×D₃×D₄	—	5	2	no	—
68	C₅×#235	—	5	2	no	—
69	C₂×C₃×C₂²⋊D₅	C₂×C₅	1	1	yes	characteristic, complemented
70	#6790	C₂×C₅	1	2	yes	complemented
71	D₃×C₂²⋊D₅	C₂×C₅	1	2	yes	complemented
72	D₅×#67	C₂×C₅	1	2	yes	complemented
73	#6782	C₂×C₅	1	2	yes	complemented
74	#6780	C₂×C₅	1	2	yes	complemented
75	#6779	C₂×C₅	1	2	yes	complemented
76	C₂³×C₅²	—	3	1	no	—
77	C₂³×C₅²	C₂×D₃	1	1	yes	characteristic, complemented
78	C₂²×C₅×D₅	—	3	1	no	—
79	C₂²×C₅×D₅	—	3	2	no	—
80	C₂²×C₅×D₅	C₂×D₃	1	1	yes	characteristic, complemented
81	C₅²×D₄	—	3	2	no	—
82	C₅²×D₄	—	3	2	no	—
83	C₂×C₄×C₅²	—	3	1	no	—
84	C₅×C₂²⋊D₅	—	3	2	no	—
85	C₅×C₂²⋊D₅	—	3	2	no	—
86	C₅×C₂²⋊D₅	—	3	2	no	—
87	C₅×C₂²⋊D₅	—	3	2	no	—
88	C₅×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
89	C₅×C₂²⋊D₅	C₂×D₃	1	2	yes	complemented
90	C₂×C₅×Dic₅	—	3	1	no	—
91	C₂×C₅×Dic₅	—	3	2	no	—
92	C₂×C₅×Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
93	C₅×D₂₀	—	3	2	no	—
94	C₄×C₅×D₅	—	3	2	no	—
95	C₄×C₅×D₅	—	3	2	no	—
96	C₅×Dic₁₀	—	3	2	no	—
97	C₅×H(5,𝔽₂)	—	15	1	no	—
98	#4144	—	3	1	no	—
99	C₂×C₃×C₅²	—	2	1	no	—
100	C₂×C₃×C₅²	—	2	1	no	—
101	C₂×C₃×C₅²	—	2	1	no	—
102	C₂×C₃×C₅²	C₂⁴	1	1	yes	characteristic
103	C₅×D₁₅	—	2	2	no	—
104	C₅²×D₃	—	2	2	no	—
105	C₃×C₅×D₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	5	1	no	—
108	C₂³×C₃×C₅	C₂×D₅	1	1	yes	characteristic, complemented
109	C₂³×C₃×C₅	C₂²×C₅	1	1	yes	characteristic, complemented
110	C₂²×D₁₅	C₂²×C₅	1	1	yes	characteristic, complemented
111	C₂²×C₅×D₃	—	2	2	no	—
112	C₂²×C₅×D₃	—	5	1	no	—
113	C₂²×C₅×D₃	—	5	2	no	—
114	C₂²×C₅×D₃	C₂×D₅	1	1	yes	characteristic, complemented
115	C₂²×C₅×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
116	C₂²×C₃×D₅	C₂²×C₅	1	1	yes	characteristic, complemented
117	C₂×D₃×D₅	C₂²×C₅	1	2	yes	complemented
118	C₃×C₅×D₄	—	5	2	no	—
119	C₃×C₅×D₄	—	5	2	no	—
120	C₂×C₃×C₄×C₅	—	5	1	no	—
121	#1220	C₂²×C₅	1	2	yes	complemented
122	#1220	C₂²×C₅	1	2	yes	complemented
123	C₂×Dic₁₅	C₂²×C₅	1	1	yes	characteristic, complemented
124	C₅×#67	—	2	4	no	—
125	C₅×#67	—	2	4	no	—
126	C₅×#67	—	5	2	no	—
127	C₅×#67	—	5	2	no	—
128	C₅×#67	—	5	2	no	—
129	C₅×#67	—	5	2	no	—
130	C₅×#67	C₂×D₅	1	2	yes	complemented
131	C₅×#67	C₂×D₅	1	2	yes	complemented
132	C₅×#67	C₂²×C₅	1	2	yes	complemented
133	C₅×#67	C₂²×C₅	1	2	yes	complemented
134	C₂×C₅×Dic₃	—	2	2	no	—
135	C₂×C₅×Dic₃	—	5	1	no	—
136	C₂×C₅×Dic₃	—	5	2	no	—
137	C₂×C₅×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
138	C₂×C₅×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
139	C₅×D₁₂	—	5	2	no	—
140	C₄×C₅×D₃	—	5	2	no	—
141	C₄×C₅×D₃	—	5	2	no	—
142	C₅×Dic₆	—	5	2	no	—
143	C₃×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
144	C₃×C₂²⋊D₅	C₂²×C₅	1	2	yes	complemented
145	C₂×C₃×Dic₅	C₂²×C₅	1	1	yes	characteristic, complemented
146	#1204	C₂²×C₅	1	2	yes	complemented
147	#1203	C₂²×C₅	1	2	yes	complemented
148	#1202	C₂²×C₅	1	2	yes	complemented
149	#1201	C₂²×C₅	1	2	yes	complemented
150	#1200	C₂²×C₅	1	2	yes	complemented
151	D₃×Dic₅	C₂²×C₅	1	2	yes	complemented
152	D₅×Dic₃	C₂²×C₅	1	2	yes	complemented
153	C₂²×C₅²	—	3	2	no	—
154	C₂²×C₅²	—	4	1	no	—
155	C₂²×C₅²	—	12	1	no	—
156	C₂²×C₅²	C₂²×D₃	1	1	yes	characteristic
157	C₂²×C₅²	C₂²×D₃	1	1	yes	characteristic
158	C₂²×C₅²	C₂²×D₃	1	1	yes	characteristic
159	C₂×C₅×D₅	—	3	2	no	—
160	C₂×C₅×D₅	—	4	1	no	—
161	C₂×C₅×D₅	—	12	1	no	—
162	C₂×C₅×D₅	—	12	2	no	—
163	C₂×C₅×D₅	C₂²×D₃	1	2	yes	—
164	C₄×C₅²	—	3	2	no	—
165	C₅×Dic₅	—	3	2	no	—
166	C₅×Dic₅	C₂²×D₃	1	2	yes	—
167	#1004	—	5	1	no	Hall
168	C₅×#41	—	15	2	no	—
169	C₅×#41	—	15	2	no	—
170	C₅×#41	—	15	2	no	—
171	C₂×C₅×D₄	—	3	1	no	—
172	C₂×C₅×D₄	—	3	1	no	—
173	C₂×C₅×D₄	—	5	1	no	—
174	C₂×C₅×D₄	—	6	2	no	—
175	C₂×C₅×D₄	—	15	2	no	—
176	C₂×C₅×D₄	—	15	2	no	—
177	C₂×C₅×D₄	—	15	2	no	—
178	C₂×C₅×D₄	—	15	1	no	—
179	C₂×C₂²⋊D₅	—	3	1	no	—
180	C₂×C₂²⋊D₅	—	3	2	no	—
181	C₂×C₂²⋊D₅	C₅×D₃	1	1	yes	characteristic, complemented
182	#711	—	3	2	no	—
183	#711	—	3	2	no	—
184	D₄×D₅	—	3	2	no	—
185	D₄×D₅	—	3	2	no	—
186	#709	—	3	2	no	—
187	C₃×C₅²	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	—	2	2	no	—
191	C₂²×C₃×C₅	—	4	1	no	—
192	C₂²×C₃×C₅	—	4	1	no	—
193	C₂²×C₃×C₅	—	4	2	no	—
194	C₂²×C₃×C₅	—	4	2	no	—
195	C₂²×C₃×C₅	—	5	2	no	—
196	C₂²×C₃×C₅	—	20	1	no	—
197	C₂²×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
198	C₂²×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
199	C₂²×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
200	C₂²×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
202	C₂²×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
203	C₂×D₁₅	—	4	1	no	—
204	C₂×D₁₅	C₂³×C₅	1	2	yes	—
205	C₂×C₅×D₃	—	2	4	no	—
206	C₂×C₅×D₃	—	4	1	no	—
207	C₂×C₅×D₃	—	4	1	no	—
208	C₂×C₅×D₃	—	4	2	no	—
209	C₂×C₅×D₃	—	4	2	no	—
210	C₂×C₅×D₃	—	5	2	no	—
211	C₂×C₅×D₃	—	20	2	no	—
212	C₂×C₅×D₃	—	20	1	no	—
213	C₂×C₅×D₃	C₂²×D₅	1	2	yes	—
214	C₂×C₅×D₃	C₂³×C₅	1	2	yes	—
215	C₂×C₃×D₅	—	4	1	no	—
216	C₂×C₃×D₅	C₂³×C₅	1	2	yes	—
217	D₃×D₅	—	4	2	no	—
218	C₃×C₄×C₅	—	5	2	no	—
219	Dic₁₅	C₂³×C₅	1	2	yes	—
220	C₃×Dic₅	C₂³×C₅	1	2	yes	—
221	C₅×Dic₃	—	2	4	no	—
222	C₅×Dic₃	—	5	2	no	—
223	C₅×Dic₃	C₂²×D₅	1	2	yes	—
224	C₅×Dic₃	C₂³×C₅	1	2	yes	—
225	C₂×C₅²	—	2	1	no	—
226	C₂×C₅²	—	2	1	no	—
227	C₂×C₅²	—	2	1	no	—
228	C₂×C₅²	—	6	2	no	—
229	C₂×C₅²	C₂³×D₃	1	1	yes	characteristic
230	C₅×D₅	—	2	2	no	—
231	C₅×D₅	—	6	2	no	—
232	C₂×C₃×D₄	—	5	1	no	—
233	C₂×#67	—	5	1	no	—
234	C₂×#67	—	5	2	no	—
235	C₂×#67	C₅×D₅	1	1	yes	characteristic, complemented
236	#237	—	5	2	no	—
237	#237	—	5	2	no	—
238	D₃×D₄	—	5	2	no	—
239	D₃×D₄	—	5	2	no	—
240	#235	—	5	2	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	3	1	no	—
243	C₂³×C₅	—	3	1	no	—
244	C₂³×C₅	—	5	1	no	—
245	C₂³×C₅	—	6	2	no	—
246	C₂³×C₅	—	15	2	no	—
247	C₂³×C₅	—	15	1	no	—
248	C₂³×C₅	D₃×D₅	1	1	yes	characteristic, complemented
249	C₂³×C₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
250	C₂²×D₅	—	3	1	no	—
251	C₂²×D₅	—	3	2	no	—
252	C₂²×D₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
253	C₅×Q₈	—	15	2	no	—
254	C₅×D₄	—	3	2	no	—
255	C₅×D₄	—	3	2	no	—
256	C₅×D₄	—	3	2	no	—
257	C₅×D₄	—	3	2	no	—
258	C₅×D₄	—	5	2	no	—
259	C₅×D₄	—	5	2	no	—
260	C₅×D₄	—	6	4	no	—
261	C₅×D₄	—	6	4	no	—
262	C₅×D₄	—	15	2	no	—
263	C₅×D₄	—	15	2	no	—
264	C₅×D₄	—	15	2	no	—
265	C₅×D₄	—	15	2	no	—
266	C₅×D₄	—	15	2	no	—
267	C₂×C₄×C₅	—	3	1	no	—
268	C₂×C₄×C₅	—	3	1	no	—
269	C₂×C₄×C₅	—	5	1	no	—
270	C₂×C₄×C₅	—	6	2	no	—
271	C₂×C₄×C₅	—	15	2	no	—
272	C₂×C₄×C₅	—	15	2	no	—
273	C₂×C₄×C₅	—	15	2	no	—
274	C₂×C₄×C₅	—	15	1	no	—
275	C₂²⋊D₅	—	3	2	no	—
276	C₂²⋊D₅	—	3	2	no	—
277	C₂²⋊D₅	—	3	2	no	—
278	C₂²⋊D₅	—	3	2	no	—
279	C₂²⋊D₅	C₂×C₅×D₃	1	2	yes	complemented
280	C₂²⋊D₅	C₂×C₅×D₃	1	2	yes	complemented
281	C₂×Dic₅	—	3	1	no	—
282	C₂×Dic₅	—	3	2	no	—
283	C₂×Dic₅	C₂×C₅×D₃	1	1	yes	characteristic, complemented
284	D₂₀	—	3	2	no	—
285	C₄×D₅	—	3	2	no	—
286	C₄×D₅	—	3	2	no	—
287	Dic₁₀	—	3	2	no	—
288	H(5,𝔽₂)	—	15	1	no	Sylow
289	C₂×C₃×C₅	—	2	2	no	—
290	C₂×C₃×C₅	—	2	2	no	—
291	C₂×C₃×C₅	—	2	1	no	—
292	C₂×C₃×C₅	—	2	1	no	—
293	C₂×C₃×C₅	—	2	1	no	—
294	C₂×C₃×C₅	—	2	1	no	—
295	C₂×C₃×C₅	—	2	1	no	—
296	C₂×C₃×C₅	—	2	1	no	—
297	C₂×C₃×C₅	—	2	2	no	—
298	C₂×C₃×C₅	—	4	2	no	—
299	C₂×C₃×C₅	—	4	2	no	—
300	C₂×C₃×C₅	—	10	2	no	—
301	C₂×C₃×C₅	C₂³×D₅	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂⁴×C₅	1	1	yes	characteristic
303	D₁₅	—	2	2	no	—
304	C₃×D₅	—	2	2	no	—
305	C₅×D₃	—	2	2	no	—
306	C₅×D₃	—	2	2	no	—
307	C₅×D₃	—	4	4	no	—
308	C₅×D₃	—	10	2	no	—
309	C₅²	#1004	1	1	yes	characteristic, complemented, Sylow
310	C₂³×C₃	—	5	1	no	—
311	C₂³×C₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented
312	C₂²×D₃	—	5	1	no	—
313	C₂²×D₃	—	5	2	no	—
314	C₂²×D₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented
315	C₃×D₄	—	5	2	no	—
316	C₃×D₄	—	5	2	no	—
317	C₂×C₃×C₄	—	5	1	no	—
318	#67	—	5	2	no	—
319	#67	—	5	2	no	—
320	#67	—	5	2	no	—
321	#67	—	5	2	no	—
322	#67	C₂×C₅×D₅	1	2	yes	complemented
323	#67	C₂×C₅×D₅	1	2	yes	complemented
324	C₂×Dic₃	—	5	1	no	—
325	C₂×Dic₃	—	5	2	no	—
326	C₂×Dic₃	C₂×C₅×D₅	1	1	yes	characteristic, complemented
327	D₁₂	—	5	2	no	—
328	C₄×D₃	—	5	2	no	—
329	C₄×D₃	—	5	2	no	—
330	Dic₆	—	5	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	3	2	no	—
335	C₂²×C₅	—	3	2	no	—
336	C₂²×C₅	—	4	1	no	—
337	C₂²×C₅	—	4	1	no	—
338	C₂²×C₅	—	4	2	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	5	2	no	—
341	C₂²×C₅	—	6	4	no	—
342	C₂²×C₅	—	12	1	no	—
343	C₂²×C₅	—	12	1	no	—
344	C₂²×C₅	—	12	2	no	—
345	C₂²×C₅	—	12	2	no	—
346	C₂²×C₅	—	15	2	no	—
347	C₂²×C₅	—	20	1	no	—
348	C₂²×C₅	—	60	1	no	—
349	C₂²×C₅	—	60	2	no	—
350	C₂²×C₅	C₂×D₃×D₅	1	1	yes	characteristic
351	C₂²×C₅	C₂×D₃×D₅	1	1	yes	characteristic
352	C₂²×C₅	C₂×D₃×D₅	1	1	yes	characteristic
353	C₂²×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₂²×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
355	C₂²×C₅	C₂²×C₅×D₃	1	1	yes	characteristic
356	C₂×D₅	—	3	2	no	—
357	C₂×D₅	—	4	1	no	—
358	C₂×D₅	—	12	2	no	—
359	C₂×D₅	—	12	1	no	—
360	C₂×D₅	C₂²×C₅×D₃	1	2	yes	—
361	C₄×C₅	—	3	2	no	—
362	C₄×C₅	—	3	2	no	—
363	C₄×C₅	—	5	2	no	—
364	C₄×C₅	—	6	4	no	—
365	C₄×C₅	—	15	2	no	—
366	Dic₅	—	3	2	no	—
367	Dic₅	C₂²×C₅×D₃	1	2	yes	—
368	#41	—	15	2	no	—
369	#41	—	15	2	no	—
370	#41	—	15	2	no	—
371	C₂×D₄	—	3	1	no	—
372	C₂×D₄	—	5	1	no	—
373	C₂×D₄	—	15	2	no	—
374	C₂×D₄	—	15	2	no	—
375	C₂×D₄	—	15	2	no	—
376	C₂×D₄	—	15	1	no	—
377	C₃×C₅	—	2	2	no	—
378	C₃×C₅	#4144	1	1	yes	characteristic, complemented
379	C₃×C₅	C₅×H(5,𝔽₂)	1	1	yes	characteristic, complemented
380	C₂²×C₃	—	4	1	no	—
381	C₂²×C₃	—	5	2	no	—
382	C₂²×C₃	—	20	1	no	—
383	C₂²×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
384	C₂²×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
385	C₂²×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
386	C₂×D₃	—	4	1	no	—
387	C₂×D₃	—	5	2	no	—
388	C₂×D₃	—	20	2	no	—
389	C₂×D₃	—	20	1	no	—
390	C₂×D₃	C₂²×C₅×D₅	1	2	yes	—
391	C₃×C₄	—	5	2	no	—
392	Dic₃	—	5	2	no	—
393	Dic₃	C₂²×C₅×D₅	1	2	yes	—
394	C₂×C₅	—	2	2	no	—
395	C₂×C₅	—	2	2	no	—
396	C₂×C₅	—	2	1	no	—
397	C₂×C₅	—	2	1	no	—
398	C₂×C₅	—	2	1	no	—
399	C₂×C₅	—	2	1	no	—
400	C₂×C₅	—	2	1	no	—
401	C₂×C₅	—	2	1	no	—
402	C₂×C₅	—	2	2	no	—
403	C₂×C₅	—	4	2	no	—
404	C₂×C₅	—	4	2	no	—
405	C₂×C₅	—	6	2	no	—
406	C₂×C₅	—	6	2	no	—
407	C₂×C₅	—	10	2	no	—
408	C₂×C₅	—	12	4	no	—
409	C₂×C₅	—	30	2	no	—
410	C₂×C₅	C₂²×D₃×D₅	1	1	yes	characteristic
411	C₂×C₅	C₂³×C₅×D₃	1	1	yes	characteristic
412	D₅	—	2	2	no	—
413	D₅	—	6	2	no	—
414	C₂³	—	3	1	no	—
415	C₂³	—	5	1	no	—
416	C₂³	—	15	2	no	—
417	C₂³	—	15	1	no	—
418	C₂³	C₅×D₃×D₅	1	1	yes	characteristic, complemented
419	Q₈	—	15	2	no	—
420	D₄	—	3	2	no	—
421	D₄	—	3	2	no	—
422	D₄	—	5	2	no	—
423	D₄	—	5	2	no	—
424	D₄	—	15	2	no	—
425	D₄	—	15	2	no	—
426	D₄	—	15	2	no	—
427	D₄	—	15	2	no	—
428	D₄	—	15	2	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	15	2	no	—
432	C₂×C₄	—	15	2	no	—
433	C₂×C₄	—	15	2	no	—
434	C₂×C₄	—	15	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	10	2	no	—
439	C₂×C₃	C₂³×C₅×D₅	1	1	yes	characteristic
440	D₃	—	2	2	no	—
441	D₃	—	10	2	no	—
442	C₅	—	2	2	no	—
443	C₅	#92049	1	1	yes	characteristic, direct product factor
444	C₅	C₅×#1004	1	1	yes	characteristic, complemented
445	C₂²	—	3	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	5	2	no	—
448	C₂²	—	12	1	no	—
449	C₂²	—	15	2	no	—
450	C₂²	—	20	1	no	—
451	C₂²	—	60	1	no	—
452	C₂²	—	60	2	no	—
453	C₂²	C₂×C₅×D₃×D₅	1	1	yes	characteristic
454	C₂²	C₂×C₅×D₃×D₅	1	1	yes	characteristic
455	C₂²	C₂×C₅×D₃×D₅	1	1	yes	characteristic
456	C₄	—	3	2	no	—
457	C₄	—	5	2	no	—
458	C₄	—	15	2	no	—
459	C₃	C₅×#4144	1	1	yes	characteristic, complemented, Sylow
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	6	2	no	—
464	C₂	—	10	2	no	—
465	C₂	—	30	2	no	—
466	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	C₂³×C₃×C₅²	C₂²
socle	C₂×C₃×C₅²	C₂⁴
hypercenter	C₂³×C₅	D₃×D₅
hypocenter	C₃×C₅	C₅×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₂³×C₅

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1220	C₂	semidirect
2. C₂×C₅²×#67	C₂	semidirect
3. C₂×C₃×C₅×C₂²⋊D₅	C₂	semidirect
4. C₅×#6790	C₂	semidirect
5. C₅×D₃×C₂²⋊D₅	C₂	semidirect
6. C₅×D₅×#67	C₂	semidirect
7. C₅×#6782	C₂	semidirect
8. C₅×#6780	C₂	semidirect
9. C₅×#6779	C₂	semidirect
11. C₂³×C₃×C₅²	C₂²	semidirect
12. C₂²×C₅×D₁₅	C₂²	semidirect
13. C₂²×C₅²×D₃	C₂²	semidirect
14. C₂²×C₃×C₅×D₅	C₂²	semidirect
15. C₂×C₅×D₃×D₅	C₂²	semidirect
16. C₅×#1220	C₂²	semidirect
17. C₅×#1220	C₂²	semidirect
18. C₂×C₅×Dic₁₅	C₂²	semidirect
19. C₅²×#67	C₂²	semidirect
20. C₅²×#67	C₂²	semidirect
21. C₂×C₅²×Dic₃	C₂²	semidirect
22. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
23. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
24. C₂×C₃×C₅×Dic₅	C₂²	semidirect
25. C₅×#1204	C₂²	semidirect
26. C₅×#1203	C₂²	semidirect
27. C₅×#1202	C₂²	semidirect
28. C₅×#1201	C₂²	semidirect
29. C₅×#1200	C₂²	semidirect
30. C₅×D₃×Dic₅	C₂²	semidirect
31. C₅×D₅×Dic₃	C₂²	semidirect
33. #92049	C₅	direct (N × H)
37. C₂×C₅×C₂²⋊D₅	D₃	semidirect
58. C₂×#1220	C₂×C₅	semidirect
62. C₂×C₅×#67	D₅	semidirect
63. C₂×C₅×#67	C₂×C₅	semidirect
69. C₂×C₃×C₂²⋊D₅	C₂×C₅	semidirect
70. #6790	C₂×C₅	semidirect
71. D₃×C₂²⋊D₅	C₂×C₅	semidirect
72. D₅×#67	C₂×C₅	semidirect
73. #6782	C₂×C₅	semidirect
74. #6780	C₂×C₅	semidirect
75. #6779	C₂×C₅	semidirect
77. C₂³×C₅²	C₂×D₃	semidirect
80. C₂²×C₅×D₅	C₂×D₃	semidirect
88. C₅×C₂²⋊D₅	C₂×D₃	semidirect
89. C₅×C₂²⋊D₅	C₂×D₃	semidirect
92. C₂×C₅×Dic₅	C₂×D₃	semidirect
108. C₂³×C₃×C₅	C₂×D₅	semidirect
109. C₂³×C₃×C₅	C₂²×C₅	semidirect
110. C₂²×D₁₅	C₂²×C₅	semidirect
114. C₂²×C₅×D₃	C₂×D₅	semidirect
115. C₂²×C₅×D₃	C₂²×C₅	semidirect
116. C₂²×C₃×D₅	C₂²×C₅	semidirect
117. C₂×D₃×D₅	C₂²×C₅	semidirect
121. #1220	C₂²×C₅	semidirect
122. #1220	C₂²×C₅	semidirect
123. C₂×Dic₁₅	C₂²×C₅	semidirect
130. C₅×#67	C₂×D₅	semidirect
131. C₅×#67	C₂×D₅	semidirect
132. C₅×#67	C₂²×C₅	semidirect
133. C₅×#67	C₂²×C₅	semidirect
137. C₂×C₅×Dic₃	C₂×D₅	semidirect
138. C₂×C₅×Dic₃	C₂²×C₅	semidirect
143. C₃×C₂²⋊D₅	C₂²×C₅	semidirect
144. C₃×C₂²⋊D₅	C₂²×C₅	semidirect
145. C₂×C₃×Dic₅	C₂²×C₅	semidirect
146. #1204	C₂²×C₅	semidirect
147. #1203	C₂²×C₅	semidirect
148. #1202	C₂²×C₅	semidirect
149. #1201	C₂²×C₅	semidirect
150. #1200	C₂²×C₅	semidirect
151. D₃×Dic₅	C₂²×C₅	semidirect
152. D₅×Dic₃	C₂²×C₅	semidirect
181. C₂×C₂²⋊D₅	C₅×D₃	semidirect
187. C₃×C₅²	H(5,𝔽₂)	semidirect
235. C₂×#67	C₅×D₅	semidirect
248. C₂³×C₅	D₃×D₅	semidirect
249. C₂³×C₅	C₂×C₅×D₃	semidirect
252. C₂²×D₅	C₂×C₅×D₃	semidirect
279. C₂²⋊D₅	C₂×C₅×D₃	semidirect
280. C₂²⋊D₅	C₂×C₅×D₃	semidirect
283. C₂×Dic₅	C₂×C₅×D₃	semidirect
309. C₅²	#1004	semidirect
311. C₂³×C₃	C₂×C₅×D₅	semidirect
314. C₂²×D₃	C₂×C₅×D₅	semidirect
322. #67	C₂×C₅×D₅	semidirect
323. #67	C₂×C₅×D₅	semidirect
326. C₂×Dic₃	C₂×C₅×D₅	semidirect
378. C₃×C₅	#4144	semidirect
379. C₃×C₅	C₅×H(5,𝔽₂)	semidirect
418. C₂³	C₅×D₃×D₅	semidirect
443. C₅	#92049	direct (N × H)
444. C₅	C₅×#1004	semidirect
459. 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
C₂×C₅×#1220	2
C₂×C₅²×#67	2
C₂×C₃×C₅×C₂²⋊D₅	2
C₅×#6790	2
C₅×D₃×C₂²⋊D₅	2
C₅×D₅×#67	2
C₅×#6782	2
C₅×#6780	2
C₅×#6779	2
C₅×#4144	3
C₅×#1004	5
#92049	5

Subgroups — C5×#92049 #72231634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#92049 #72231634