Subgroups — C₃×#13100574 #72259807

Order 4800.

896 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#11716609	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#3937	C₂	1	2	yes	maximal, complemented
3	C₃×#11716936	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#11717471	C₂	1	1	yes	maximal, characteristic
5	C₃×C₄²×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
6	#13100574	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₅⋊D₅	—	2	1	no	—
8	C₂×C₃×C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×#709	C₂²	1	2	yes	—
10	C₃×#87886	—	2	1	no	—
11	C₃×#87880	—	2	1	no	—
12	C₃×#87877	C₄	1	1	yes	characteristic, complemented
13	C₃×C₄×D₅²	—	2	1	no	—
14	C₃×#87873	—	2	1	no	—
15	C₃×#87872	C₄	1	1	yes	characteristic, complemented
16	C₃×#87871	C₄	1	2	yes	complemented
17	C₃×C₄²×C₅²	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₄×#1039	—	2	1	no	—
19	C₃×C₄×#1039	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#681	C₂²	1	2	yes	complemented
21	C₃×#87769	—	2	1	no	—
22	C₃×#87767	—	2	1	no	—
23	C₃×D₅×#104	—	5	2	no	maximal
24	#11717471	C₂×C₃	1	1	yes	characteristic
25	C₄²×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
26	#11716936	C₂×C₃	1	1	yes	characteristic, complemented
27	C₅×#3937	C₂×C₃	1	2	yes	complemented
28	#11716609	C₂×C₃	1	2	yes	complemented
29	C₂²×C₃×C₅⋊D₅	D₄	1	1	yes	characteristic
30	C₂×C₃×D₅²	—	2	1	no	—
31	C₂×C₃×C₄×C₅²	—	2	1	no	—
32	C₂×C₃×C₄×C₅²	C₂³	1	1	yes	characteristic
33	C₂×C₃×#1039	—	2	1	no	—
34	C₂×C₃×#1039	D₄	1	1	yes	characteristic
35	C₃×C₄×C₅⋊D₅	—	2	4	no	—
36	C₃×C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
37	C₃×C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
38	C₃×C₄×C₅⋊D₅	D₄	1	1	yes	characteristic
39	C₃×C₄×C₅⋊D₅	D₄	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊D₅	—	2	2	no	—
41	C₃×C₅×D₂₀	C₂×C₄	1	2	yes	complemented
42	C₃×C₄×C₅×D₅	—	2	2	no	—
43	C₃×C₅×Dic₁₀	C₂×C₄	1	2	yes	complemented
44	C₃×#6039	—	2	1	no	—
45	C₃×#6038	—	2	2	no	—
46	C₃×#6037	—	2	1	no	—
47	C₃×#6036	—	2	1	no	—
48	C₃×D₅×Dic₅	—	2	2	no	—
49	C₃×C₅×#168	—	2	2	no	—
50	C₃×D₅×#41	—	5	2	no	—
51	C₃×D₅×M₁₆	—	5	2	no	—
52	C₃×C₄²×D₅	—	5	2	no	—
53	C₃×C₄²×D₅	—	10	2	no	—
54	C₃×C₅×#104	—	5	2	no	—
55	C₃×#3969	—	5	2	no	—
56	C₃×#3957	—	5	2	no	—
57	C₃×#3937	D₅	1	2	yes	complemented
58	C₂×C₄×C₅⋊D₅	—	2	1	no	—
59	C₂×C₄×C₅⋊D₅	C₂²×C₃	1	1	yes	characteristic
60	C₅×#709	C₂²×C₃	1	2	yes	—
61	#87886	—	2	1	no	—
62	#87880	—	2	1	no	—
63	#87877	C₃×C₄	1	1	yes	characteristic, complemented
64	C₄×D₅²	—	2	1	no	—
65	#87873	—	2	1	no	—
66	#87872	C₃×C₄	1	1	yes	characteristic, complemented
67	#87871	C₃×C₄	1	2	yes	complemented
68	C₄²×C₅²	C₂²×C₃	1	1	yes	characteristic, complemented
69	C₄×#1039	—	2	1	no	—
70	C₄×#1039	C₂²×C₃	1	1	yes	characteristic, complemented
71	C₅×#681	C₂²×C₃	1	2	yes	complemented
72	#87769	—	2	1	no	—
73	#87767	—	2	1	no	—
74	D₅×#104	—	5	2	no	—
75	C₂²×C₃×C₅²	C₂×D₄	1	1	yes	characteristic
76	C₂×C₃×C₅⋊D₅	—	2	2	no	—
77	C₂×C₃×C₅⋊D₅	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₃×C₅⋊D₅	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₃×C₅×D₅	—	2	2	no	—
80	C₃×D₅²	—	4	2	no	—
81	C₃×C₄×C₅²	—	2	2	no	—
82	C₃×C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
83	C₃×C₄×C₅²	C₂×D₄	1	1	yes	characteristic
84	C₃×#1039	—	2	2	no	—
85	C₃×#1039	C₂²⋊C₄	1	1	yes	characteristic
86	C₃×#1039	C₂²⋊C₄	1	1	yes	characteristic
87	C₃×C₅×Dic₅	—	2	2	no	—
88	C₃×C₅×#41	—	5	2	no	—
89	C₃×#713	—	5	2	no	—
90	C₃×Q₈×D₅	—	5	2	no	—
91	C₃×#711	—	5	2	no	—
92	C₃×#711	—	10	2	no	—
93	C₃×D₄×D₅	—	5	2	no	—
94	C₃×D₄×D₅	—	10	2	no	—
95	C₃×#709	—	10	2	no	—
96	C₃×#709	C₂×D₅	1	2	yes	—
97	C₂×C₃×C₄×D₅	—	5	2	no	—
98	C₂×C₃×C₄×D₅	—	10	2	no	—
99	C₂×C₃×C₄×D₅	—	10	2	no	—
100	C₂×C₃×C₄×D₅	—	10	2	no	—
101	C₂×C₃×C₄×D₅	—	10	4	no	—
102	C₃×C₅×M₁₆	—	5	2	no	—
103	C₃×C₄²×C₅	—	2	2	no	—
104	C₃×C₄²×C₅	C₂×D₅	1	2	yes	complemented
105	C₃×C₄×Dic₅	—	5	2	no	—
106	C₃×C₄×Dic₅	—	10	2	no	—
107	C₃×C₄×Dic₅	—	10	2	no	—
108	C₃×C₄×Dic₅	—	10	4	no	—
109	C₃×#681	C₂×D₅	1	2	yes	complemented
110	C₃×#676	—	10	2	no	—
111	C₃×C₈×D₅	—	10	2	no	—
112	C₂²×C₅⋊D₅	C₃×D₄	1	1	yes	characteristic
113	C₂×D₅²	—	2	1	no	—
114	C₂×C₄×C₅²	—	2	1	no	—
115	C₂×C₄×C₅²	C₂³×C₃	1	1	yes	characteristic
116	C₂×#1039	—	2	1	no	—
117	C₂×#1039	C₃×D₄	1	1	yes	characteristic
118	C₄×C₅⋊D₅	—	2	4	no	—
119	C₄×C₅⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
120	C₄×C₅⋊D₅	C₂×C₃×C₄	1	1	yes	characteristic
121	C₄×C₅⋊D₅	C₃×D₄	1	1	yes	characteristic
122	C₄×C₅⋊D₅	C₃×D₄	1	1	yes	characteristic
123	C₅×C₂²⋊D₅	—	2	2	no	—
124	C₅×D₂₀	C₂×C₃×C₄	1	2	yes	complemented
125	C₄×C₅×D₅	—	2	2	no	—
126	C₅×Dic₁₀	C₂×C₃×C₄	1	2	yes	complemented
127	#6039	—	2	1	no	—
128	#6038	—	2	2	no	—
129	#6037	—	2	1	no	—
130	#6036	—	2	1	no	—
131	D₅×Dic₅	—	2	2	no	—
132	C₅×#168	—	2	2	no	—
133	C₂×C₃×#104	—	25	1	no	Hall
134	D₅×#41	—	5	2	no	—
135	D₅×M₁₆	—	5	2	no	—
136	C₄²×D₅	—	5	2	no	—
137	C₄²×D₅	—	10	2	no	—
138	C₅×#104	—	5	2	no	—
139	#3969	—	5	2	no	—
140	#3957	—	5	2	no	—
141	#3937	C₃×D₅	1	2	yes	complemented
142	C₂×C₃×C₅²	—	2	1	no	—
143	C₂×C₃×C₅²	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₃×C₅⋊D₅	—	2	1	no	—
145	C₃×C₅⋊D₅	#104	1	2	yes	complemented
146	C₃×C₅×D₅	—	4	2	no	—
147	C₂²×C₃×D₅	—	5	2	no	—
148	C₂²×C₃×D₅	—	10	2	no	—
149	C₂²×C₃×D₅	—	10	2	no	—
150	C₃×C₅×Q₈	—	5	2	no	—
151	C₃×C₅×D₄	—	5	2	no	—
152	C₃×C₅×D₄	—	10	2	no	—
153	C₂×C₃×C₄×C₅	—	2	4	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	10	2	no	—
157	C₂×C₃×C₄×C₅	C₂²×D₅	1	2	yes	—
158	C₃×C₂²⋊D₅	—	2	2	no	—
159	C₃×C₂²⋊D₅	—	10	2	no	—
160	C₃×C₂²⋊D₅	—	10	2	no	—
161	C₂×C₃×Dic₅	—	5	2	no	—
162	C₂×C₃×Dic₅	—	10	2	no	—
163	C₂×C₃×Dic₅	—	10	2	no	—
164	C₂×C₃×Dic₅	—	10	4	no	—
165	C₂×C₃×Dic₅	—	10	2	no	—
166	C₃×D₂₀	—	10	2	no	—
167	C₃×D₂₀	C₄×D₅	1	2	yes	complemented
168	C₃×C₄×D₅	—	2	2	no	—
169	C₃×C₄×D₅	—	5	2	no	—
170	C₃×C₄×D₅	—	5	2	no	—
171	C₃×C₄×D₅	—	5	2	no	—
172	C₃×C₄×D₅	—	5	2	no	—
173	C₃×C₄×D₅	—	10	2	no	—
174	C₃×C₄×D₅	—	10	2	no	—
175	C₃×C₄×D₅	—	10	2	no	—
176	C₃×C₄×D₅	—	10	2	no	—
177	C₃×C₄×D₅	—	10	2	no	—
178	C₃×C₄×D₅	—	10	2	no	—
179	C₃×C₄×D₅	—	10	8	no	—
180	C₃×C₄×D₅	—	10	16	no	—
181	C₃×Dic₁₀	—	10	2	no	—
182	C₃×Dic₁₀	C₄×D₅	1	2	yes	complemented
183	C₃×C₅×C₈	—	10	2	no	—
184	C₃×#168	—	2	2	no	—
185	C₂²×C₅²	C₂×C₃×D₄	1	1	yes	characteristic
186	C₂×C₅⋊D₅	—	2	2	no	—
187	C₂×C₅⋊D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₅⋊D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₅×D₅	—	2	2	no	—
190	D₅²	—	4	2	no	—
191	C₄×C₅²	—	2	2	no	—
192	C₄×C₅²	C₂²×C₃×C₄	1	1	yes	characteristic
193	C₄×C₅²	C₂×C₃×D₄	1	1	yes	characteristic
194	#1039	—	2	2	no	—
195	#1039	C₃×C₂²⋊C₄	1	1	yes	characteristic
196	#1039	C₃×C₂²⋊C₄	1	1	yes	characteristic
197	C₅×Dic₅	—	2	2	no	—
198	C₂×C₃×#41	—	25	1	no	—
199	C₂×C₃×M₁₆	—	25	1	no	—
200	C₂×C₃×C₄²	—	25	1	no	—
201	C₃×#104	—	5	2	no	—
202	C₃×#104	—	25	2	no	—
203	C₅×#41	—	5	2	no	—
204	#713	—	5	2	no	—
205	Q₈×D₅	—	5	2	no	—
206	#711	—	5	2	no	—
207	#711	—	10	2	no	—
208	D₄×D₅	—	5	2	no	—
209	D₄×D₅	—	10	2	no	—
210	#709	—	10	2	no	—
211	#709	C₂×C₃×D₅	1	2	yes	—
212	C₂×C₄×D₅	—	5	2	no	—
213	C₂×C₄×D₅	—	10	2	no	—
214	C₂×C₄×D₅	—	10	2	no	—
215	C₂×C₄×D₅	—	10	2	no	—
216	C₂×C₄×D₅	—	10	4	no	—
217	C₅×M₁₆	—	5	2	no	—
218	C₄²×C₅	—	2	2	no	—
219	C₄²×C₅	C₂×C₃×D₅	1	2	yes	complemented
220	C₄×Dic₅	—	5	2	no	—
221	C₄×Dic₅	—	10	2	no	—
222	C₄×Dic₅	—	10	2	no	—
223	C₄×Dic₅	—	10	4	no	—
224	#681	C₂×C₃×D₅	1	2	yes	complemented
225	#676	—	10	2	no	—
226	C₈×D₅	—	10	2	no	—
227	C₃×C₅²	C₂×#104	1	1	yes	characteristic, complemented, Hall
228	C₂×#104	—	25	1	no	Sylow
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	—	10	2	no	—
231	C₂²×C₃×C₅	D₄×D₅	1	2	yes	—
232	C₂×C₃×D₅	—	2	2	no	—
233	C₂×C₃×D₅	—	5	2	no	—
234	C₂×C₃×D₅	—	5	2	no	—
235	C₂×C₃×D₅	—	10	2	no	—
236	C₂×C₃×D₅	—	10	2	no	—
237	C₂×C₃×D₅	—	10	4	no	—
238	C₂×C₃×D₅	—	10	8	no	—
239	C₂×C₃×D₅	—	20	4	no	—
240	C₃×C₄×C₅	—	2	8	no	—
241	C₃×C₄×C₅	—	2	4	no	—
242	C₃×C₄×C₅	—	2	2	no	—
243	C₃×C₄×C₅	—	2	2	no	—
244	C₃×C₄×C₅	—	10	2	no	—
245	C₃×C₄×C₅	C₂×C₄×D₅	1	2	yes	—
246	C₃×C₄×C₅	D₄×D₅	1	2	yes	—
247	C₃×Dic₅	—	2	2	no	—
248	C₃×Dic₅	—	5	2	no	—
249	C₃×Dic₅	—	5	2	no	—
250	C₃×Dic₅	—	10	2	no	—
251	C₃×Dic₅	—	10	2	no	—
252	C₃×Dic₅	—	10	8	no	—
253	C₃×Dic₅	—	10	4	no	—
254	C₂×C₅²	—	2	1	no	—
255	C₂×C₅²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₅⋊D₅	—	2	1	no	—
257	C₅⋊D₅	C₃×#104	1	2	yes	complemented
258	C₅×D₅	—	4	2	no	—
259	C₃×#41	—	5	2	no	—
260	C₃×#41	—	25	2	no	—
261	C₃×#41	—	50	1	no	—
262	C₃×#41	—	50	1	no	—
263	C₂×C₃×Q₈	—	25	1	no	—
264	C₂×C₃×D₄	—	25	1	no	—
265	C₂×C₃×D₄	—	50	1	no	—
266	C₂²×C₃×C₄	—	25	1	no	—
267	C₂²×C₃×C₄	—	50	1	no	—
268	C₂²×C₃×C₄	—	50	1	no	—
269	C₃×M₁₆	—	5	2	no	—
270	C₃×M₁₆	—	50	1	no	—
271	C₂×C₃×C₈	—	50	1	no	—
272	C₃×C₄²	—	25	1	no	—
273	C₃×C₄²	—	50	1	no	—
274	C₃×C₄²	D₅²	1	1	yes	characteristic, complemented
275	C₂²×D₅	—	5	2	no	—
276	C₂²×D₅	—	10	2	no	—
277	C₂²×D₅	—	10	2	no	—
278	C₅×Q₈	—	5	2	no	—
279	C₅×D₄	—	5	2	no	—
280	C₅×D₄	—	10	2	no	—
281	C₂×C₄×C₅	—	2	4	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	10	2	no	—
285	C₂×C₄×C₅	C₂²×C₃×D₅	1	2	yes	—
286	C₂²⋊D₅	—	2	2	no	—
287	C₂²⋊D₅	—	10	2	no	—
288	C₂²⋊D₅	—	10	2	no	—
289	C₂×Dic₅	—	5	2	no	—
290	C₂×Dic₅	—	10	2	no	—
291	C₂×Dic₅	—	10	2	no	—
292	C₂×Dic₅	—	10	4	no	—
293	C₂×Dic₅	—	10	2	no	—
294	D₂₀	—	10	2	no	—
295	D₂₀	C₃×C₄×D₅	1	2	yes	complemented
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	5	2	no	—
298	C₄×D₅	—	5	2	no	—
299	C₄×D₅	—	5	2	no	—
300	C₄×D₅	—	5	2	no	—
301	C₄×D₅	—	10	2	no	—
302	C₄×D₅	—	10	2	no	—
303	C₄×D₅	—	10	2	no	—
304	C₄×D₅	—	10	2	no	—
305	C₄×D₅	—	10	2	no	—
306	C₄×D₅	—	10	2	no	—
307	C₄×D₅	—	10	8	no	—
308	C₄×D₅	—	10	16	no	—
309	Dic₁₀	—	10	2	no	—
310	Dic₁₀	C₃×C₄×D₅	1	2	yes	complemented
311	C₅×C₈	—	10	2	no	—
312	#168	—	2	2	no	—
313	C₂×#41	—	25	1	no	—
314	C₂×M₁₆	—	25	1	no	—
315	C₂×C₄²	—	25	1	no	—
316	#104	—	5	2	no	—
317	#104	—	25	2	no	—
318	C₂×C₃×C₅	—	2	4	no	—
319	C₂×C₃×C₅	—	2	2	no	—
320	C₂×C₃×C₅	—	2	2	no	—
321	C₂×C₃×C₅	—	20	2	no	—
322	C₂×C₃×C₅	D₅×C₂²⋊C₄	1	2	yes	—
323	C₃×D₅	—	4	2	no	—
324	C₃×D₅	—	5	4	no	—
325	C₃×D₅	—	10	4	no	—
326	C₃×D₅	—	10	4	no	—
327	C₃×D₅	—	10	2	no	—
328	C₅²	C₂×C₃×#104	1	1	yes	characteristic, complemented, Sylow
329	C₂³×C₃	—	25	1	no	—
330	C₂³×C₃	—	50	1	no	—
331	C₃×Q₈	—	5	2	no	—
332	C₃×Q₈	—	50	1	no	—
333	C₃×D₄	—	5	2	no	—
334	C₃×D₄	—	10	2	no	—
335	C₃×D₄	—	50	2	no	—
336	C₃×D₄	—	50	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	10	2	no	—
339	C₂×C₃×C₄	—	25	1	no	—
340	C₂×C₃×C₄	—	25	1	no	—
341	C₂×C₃×C₄	—	25	1	no	—
342	C₂×C₃×C₄	—	25	1	no	—
343	C₂×C₃×C₄	—	25	1	no	—
344	C₂×C₃×C₄	—	50	4	no	—
345	C₂×C₃×C₄	—	50	1	no	—
346	C₂×C₃×C₄	—	50	2	no	—
347	C₂×C₃×C₄	—	50	1	no	—
348	C₂×C₃×C₄	C₂×D₅²	1	1	yes	characteristic
349	C₃×C₈	—	10	2	no	—
350	C₂²×C₅	—	2	2	no	—
351	C₂²×C₅	—	10	2	no	—
352	C₂²×C₅	C₃×D₄×D₅	1	2	yes	—
353	C₂×D₅	—	2	2	no	—
354	C₂×D₅	—	5	2	no	—
355	C₂×D₅	—	5	2	no	—
356	C₂×D₅	—	10	2	no	—
357	C₂×D₅	—	10	2	no	—
358	C₂×D₅	—	10	4	no	—
359	C₂×D₅	—	10	8	no	—
360	C₂×D₅	—	20	4	no	—
361	C₄×C₅	—	2	8	no	—
362	C₄×C₅	—	2	4	no	—
363	C₄×C₅	—	2	2	no	—
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	10	2	no	—
366	C₄×C₅	C₂×C₃×C₄×D₅	1	2	yes	—
367	C₄×C₅	C₃×D₄×D₅	1	2	yes	—
368	Dic₅	—	2	2	no	—
369	Dic₅	—	5	2	no	—
370	Dic₅	—	5	2	no	—
371	Dic₅	—	10	2	no	—
372	Dic₅	—	10	2	no	—
373	Dic₅	—	10	8	no	—
374	Dic₅	—	10	4	no	—
375	#41	—	5	2	no	—
376	#41	—	25	2	no	—
377	#41	—	50	1	no	—
378	#41	—	50	1	no	—
379	C₂×Q₈	—	25	1	no	—
380	C₂×D₄	—	25	1	no	—
381	C₂×D₄	—	50	1	no	—
382	C₂²×C₄	—	25	1	no	—
383	C₂²×C₄	—	50	1	no	—
384	C₂²×C₄	—	50	1	no	—
385	M₁₆	—	5	2	no	—
386	M₁₆	—	50	1	no	—
387	C₂×C₈	—	50	1	no	—
388	C₄²	—	25	1	no	—
389	C₄²	—	50	1	no	—
390	C₄²	C₃×D₅²	1	1	yes	characteristic, complemented
391	C₃×C₅	—	2	2	no	—
392	C₃×C₅	D₅×#104	1	2	yes	complemented
393	C₂²×C₃	—	10	2	no	—
394	C₂²×C₃	—	25	1	no	—
395	C₂²×C₃	—	25	1	no	—
396	C₂²×C₃	—	50	2	no	—
397	C₂²×C₃	—	100	2	no	—
398	C₂²×C₃	#87886	1	1	yes	characteristic
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	10	2	no	—
401	C₃×C₄	—	25	1	no	—
402	C₃×C₄	—	25	1	no	—
403	C₃×C₄	—	50	2	no	—
404	C₃×C₄	C₄×D₅²	1	1	yes	characteristic
405	C₃×C₄	#87877	1	1	yes	characteristic
406	C₂×C₅	—	2	4	no	—
407	C₂×C₅	—	2	2	no	—
408	C₂×C₅	—	2	2	no	—
409	C₂×C₅	—	20	2	no	—
410	C₂×C₅	C₃×D₅×C₂²⋊C₄	1	2	yes	—
411	D₅	—	4	2	no	—
412	D₅	—	5	4	no	—
413	D₅	—	10	4	no	—
414	D₅	—	10	4	no	—
415	D₅	—	10	2	no	—
416	C₂³	—	25	1	no	—
417	C₂³	—	50	1	no	—
418	Q₈	—	5	2	no	—
419	Q₈	—	50	1	no	—
420	D₄	—	5	2	no	—
421	D₄	—	10	2	no	—
422	D₄	—	50	2	no	—
423	D₄	—	50	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	25	1	no	—
427	C₂×C₄	—	25	1	no	—
428	C₂×C₄	—	25	1	no	—
429	C₂×C₄	—	25	1	no	—
430	C₂×C₄	—	25	1	no	—
431	C₂×C₄	—	50	4	no	—
432	C₂×C₄	—	50	1	no	—
433	C₂×C₄	—	50	2	no	—
434	C₂×C₄	—	50	1	no	—
435	C₂×C₄	C₂×C₃×D₅²	1	1	yes	characteristic
436	C₈	—	10	2	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	20	2	no	—
439	C₂×C₃	—	25	2	no	—
440	C₂×C₃	—	50	1	no	—
441	C₂×C₃	#11717039	1	1	yes	characteristic
442	C₅	—	2	2	no	—
443	C₅	C₃×D₅×#104	1	2	yes	complemented
444	C₂²	—	10	2	no	—
445	C₂²	—	25	1	no	—
446	C₂²	—	25	1	no	—
447	C₂²	—	50	2	no	—
448	C₂²	—	100	2	no	—
449	C₂²	C₃×#87886	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	10	2	no	—
452	C₄	—	25	1	no	—
453	C₄	—	25	1	no	—
454	C₄	—	50	2	no	—
455	C₄	C₃×C₄×D₅²	1	1	yes	characteristic
456	C₄	C₃×#87877	1	1	yes	characteristic
457	C₃	#13100574	1	1	yes	characteristic, direct product factor, Sylow
458	C₂	—	2	1	no	—
459	C₂	—	20	2	no	—
460	C₂	—	25	2	no	—
461	C₂	—	50	1	no	—
462	C₂	C₃×#11717039	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#87877
commutator	C₄×C₅²	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₅²
Fitting	C₃×C₄²×C₅²	C₂²
socle	C₂×C₃×C₅²	C₂×C₂²⋊C₄
prime radical	C₃×#11717471	C₂
cosocle	C₂×C₄×C₅²	C₂³×C₃
hypercenter	C₃×C₄²	D₅²
hypocenter	C₅²	C₂×C₃×#104
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₃×#11716609	C₂	semidirect
2. C₃×C₅×#3937	C₂	semidirect
3. C₃×#11716936	C₂	semidirect
5. C₃×C₄²×C₅⋊D₅	C₂	semidirect
6. #13100574	C₃	direct (N × H)
12. C₃×#87877	C₄	semidirect
15. C₃×#87872	C₄	semidirect
16. C₃×#87871	C₄	semidirect
17. C₃×C₄²×C₅²	C₂²	semidirect
19. C₃×C₄×#1039	C₂²	semidirect
20. C₃×C₅×#681	C₂²	semidirect
25. C₄²×C₅⋊D₅	C₂×C₃	semidirect
26. #11716936	C₂×C₃	semidirect
27. C₅×#3937	C₂×C₃	semidirect
28. #11716609	C₂×C₃	semidirect
41. C₃×C₅×D₂₀	C₂×C₄	semidirect
43. C₃×C₅×Dic₁₀	C₂×C₄	semidirect
57. C₃×#3937	D₅	semidirect
63. #87877	C₃×C₄	semidirect
66. #87872	C₃×C₄	semidirect
67. #87871	C₃×C₄	semidirect
68. C₄²×C₅²	C₂²×C₃	semidirect
70. C₄×#1039	C₂²×C₃	semidirect
71. C₅×#681	C₂²×C₃	semidirect
104. C₃×C₄²×C₅	C₂×D₅	semidirect
109. C₃×#681	C₂×D₅	semidirect
124. C₅×D₂₀	C₂×C₃×C₄	semidirect
126. C₅×Dic₁₀	C₂×C₃×C₄	semidirect
141. #3937	C₃×D₅	semidirect
145. C₃×C₅⋊D₅	#104	semidirect
167. C₃×D₂₀	C₄×D₅	semidirect
182. C₃×Dic₁₀	C₄×D₅	semidirect
219. C₄²×C₅	C₂×C₃×D₅	semidirect
224. #681	C₂×C₃×D₅	semidirect
227. C₃×C₅²	C₂×#104	semidirect
257. C₅⋊D₅	C₃×#104	semidirect
274. C₃×C₄²	D₅²	semidirect
295. D₂₀	C₃×C₄×D₅	semidirect
310. Dic₁₀	C₃×C₄×D₅	semidirect
328. C₅²	C₂×C₃×#104	semidirect
390. C₄²	C₃×D₅²	semidirect
392. C₃×C₅	D₅×#104	semidirect
443. C₅	C₃×D₅×#104	semidirect
457. C₃	#13100574	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#11716609	2
C₃×C₅×#3937	2
C₃×#11716936	2
C₃×#11717471	2
C₃×C₄²×C₅⋊D₅	2
#13100574	3
C₃×D₅×#104	5

Subgroups — C3×#13100574 #72259807

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#13100574 #72259807