Subgroups — C₅×D₃×#237 #13089324

Order 1440.

696 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3830	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#67	C₂	1	2	yes	maximal, complemented
5	C₅×#3805	C₂	1	2	yes	maximal, complemented
6	C₅×#3804	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×D₃×Dic₃	C₂	1	2	yes	maximal, complemented
8	C₄×C₅×D₃²	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3796	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3795	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×D₃×#41	—	3	1	no	maximal
13	C₂×C₅×#237	—	3	1	no	maximal
14	C₂²×C₃×C₅×D₃	C₂²	1	2	yes	—
15	C₂×C₅×D₃²	C₂²	1	1	yes	characteristic
16	C₃²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₅×#638	C₂²	1	2	yes	complemented
18	C₂×C₅×C₃⋊Dic₃	C₂²	1	2	yes	complemented
19	C₄×C₅×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
20	C₅×#634	C₂²	1	1	yes	characteristic, complemented
21	C₃×C₅×#67	C₂²	1	2	yes	complemented
22	C₃×C₅×#67	C₂²	1	2	yes	complemented
23	C₂×C₃×C₅×Dic₃	C₂²	1	2	yes	complemented
24	C₃×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₅×#627	C₂²	1	2	yes	complemented
29	C₅×#626	C₂²	1	2	yes	complemented
30	C₅×#625	C₂²	1	2	yes	complemented
31	C₅×#624	C₂²	1	1	yes	characteristic, complemented
32	C₅×D₃×Dic₃	C₂²	1	2	yes	—
33	C₅×D₃×Dic₃	C₂²	1	1	yes	characteristic
34	C₅×D₃×Dic₃	C₂²	1	2	yes	complemented
35	C₅×D₃×Dic₃	C₂²	1	2	yes	complemented
36	C₅×D₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
37	D₃×#237	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₃×C₅×#41	—	3	1	no	—
39	C₂×C₃×C₅×D₄	—	3	1	no	—
40	C₂×C₅×#67	—	3	2	no	—
41	C₂²×C₅×Dic₃	—	3	2	no	—
42	C₅×#239	—	3	1	no	—
43	C₅×D₃×Q₈	—	3	1	no	—
44	C₅×#237	—	3	1	no	—
45	C₅×#237	—	3	1	no	—
46	C₅×#237	—	3	2	no	—
47	C₅×#237	—	3	2	no	—
48	C₅×#237	—	3	2	no	—
49	C₅×#237	—	3	1	no	—
50	C₅×#237	—	3	1	no	—
51	C₅×#237	—	6	1	no	—
52	C₅×#237	D₃	1	1	yes	characteristic, direct product factor
53	C₅×D₃×D₄	—	3	2	no	—
54	C₅×D₃×D₄	D₃	1	1	yes	characteristic, complemented
55	C₅×#235	—	3	2	no	—
56	C₅×#235	—	3	1	no	—
57	C₂×C₄×C₅×D₃	—	3	2	no	—
58	C₂×C₄×C₅×D₃	—	3	1	no	—
59	C₂×C₄×C₅×D₃	—	3	1	no	—
60	C₂×C₅×Dic₆	—	3	1	no	—
61	C₂²×C₃²×C₅	C₂³	1	2	yes	—
62	C₂×C₅×C₃⋊D₃	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₃	—	2	4	no	—
64	C₂×C₃×C₅×D₃	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
67	C₅×D₃²	—	2	2	no	—
68	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₅×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
70	C₅×C₃⋊Dic₃	C₂³	1	2	yes	—
71	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₅×Dic₃	C₂³	1	2	yes	—
73	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×C₅×#41	—	9	1	no	Hall
75	#3830	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#237	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×D₃×D₄	C₂×C₅	1	1	yes	characteristic, complemented
78	D₃×#67	C₂×C₅	1	2	yes	complemented
79	#3805	C₂×C₅	1	2	yes	complemented
80	#3804	C₂×C₅	1	2	yes	complemented
81	C₂×D₃×Dic₃	C₂×C₅	1	2	yes	complemented
82	C₄×D₃²	C₂×C₅	1	1	yes	characteristic, complemented
83	#3796	C₂×C₅	1	1	yes	characteristic, complemented
84	#3795	C₂×C₅	1	1	yes	characteristic, complemented
85	D₃×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂³×C₃×C₅	—	3	2	no	—
87	C₂²×C₅×D₃	—	3	1	no	—
88	C₂²×C₅×D₃	—	3	1	no	—
89	C₂²×C₅×D₃	C₂×D₃	1	2	yes	—
90	C₃×C₅×Q₈	—	3	1	no	—
91	C₃×C₅×D₄	—	2	1	no	—
92	C₃×C₅×D₄	—	3	2	no	—
93	C₃×C₅×D₄	—	3	2	no	—
94	C₃×C₅×D₄	—	3	1	no	—
95	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
96	C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
97	C₂×C₃×C₄×C₅	—	3	2	no	—
98	C₂×C₃×C₄×C₅	—	3	1	no	—
99	C₂×C₃×C₄×C₅	—	3	1	no	—
100	C₅×#67	—	3	2	no	—
101	C₅×#67	—	3	2	no	—
102	C₅×#67	—	3	2	no	—
103	C₅×#67	—	3	2	no	—
104	C₅×#67	—	3	2	no	—
105	C₅×#67	—	6	2	no	—
106	C₅×#67	C₂×D₃	1	2	yes	complemented
107	C₅×#67	C₂×D₃	1	2	yes	complemented
108	C₂×C₅×Dic₃	—	3	2	no	—
109	C₂×C₅×Dic₃	—	3	2	no	—
110	C₂×C₅×Dic₃	—	3	2	no	—
111	C₂×C₅×Dic₃	—	3	1	no	—
112	C₂×C₅×Dic₃	—	3	1	no	—
113	C₂×C₅×Dic₃	—	3	2	no	—
114	C₂×C₅×Dic₃	—	3	2	no	—
115	C₂×C₅×Dic₃	—	6	2	no	—
116	C₂×C₅×Dic₃	C₂×D₃	1	2	yes	complemented
117	C₅×D₁₂	—	3	2	no	—
118	C₅×D₁₂	C₂×D₃	1	1	yes	characteristic, complemented
119	C₄×C₅×D₃	—	3	1	no	—
120	C₄×C₅×D₃	—	3	2	no	—
121	C₄×C₅×D₃	—	3	2	no	—
122	C₄×C₅×D₃	—	3	1	no	—
123	C₄×C₅×D₃	—	3	2	no	—
124	C₄×C₅×D₃	—	3	1	no	—
125	C₄×C₅×D₃	—	3	1	no	—
126	C₄×C₅×D₃	—	3	1	no	—
127	C₄×C₅×D₃	—	3	1	no	—
128	C₄×C₅×D₃	—	6	1	no	—
129	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic
130	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
131	C₅×Dic₆	—	3	1	no	—
132	C₅×Dic₆	—	3	1	no	—
133	C₅×Dic₆	—	3	2	no	—
134	C₅×Dic₆	—	3	2	no	—
135	C₅×Dic₆	—	6	1	no	—
136	C₅×Dic₆	C₂×D₃	1	1	yes	characteristic, complemented
137	D₃×#41	—	3	1	no	—
138	C₂×#237	—	3	1	no	—
139	C₂×C₃²×C₅	—	2	2	no	—
140	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
141	C₅×C₃⋊D₃	—	2	1	no	—
142	C₃×C₅×D₃	—	2	1	no	—
143	C₃×C₅×D₃	—	2	2	no	—
144	C₃×C₅×D₃	#41	1	2	yes	complemented
145	C₅×#41	—	3	1	no	—
146	C₅×#41	—	9	2	no	—
147	C₅×#41	—	9	1	no	—
148	C₅×#41	—	9	2	no	—
149	C₅×#41	—	9	1	no	—
150	C₅×#41	—	9	1	no	—
151	C₂×C₅×Q₈	—	9	1	no	—
152	C₂×C₅×D₄	—	3	1	no	—
153	C₂×C₅×D₄	—	9	2	no	—
154	C₂²×C₄×C₅	—	9	1	no	—
155	C₂²×C₄×C₅	—	9	2	no	—
156	C₂²×C₃×D₃	C₂²×C₅	1	2	yes	—
157	C₂×D₃²	C₂²×C₅	1	1	yes	characteristic
158	C₃²×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
159	#638	C₂²×C₅	1	2	yes	complemented
160	C₂×C₃⋊Dic₃	C₂²×C₅	1	2	yes	complemented
161	C₄×C₃⋊D₃	C₂²×C₅	1	1	yes	characteristic, complemented
162	#634	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₃×#67	C₂²×C₅	1	2	yes	complemented
164	C₃×#67	C₂²×C₅	1	2	yes	complemented
165	C₂×C₃×Dic₃	C₂²×C₅	1	2	yes	complemented
166	C₃×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
167	C₃×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₃×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
170	#627	C₂²×C₅	1	2	yes	complemented
171	#626	C₂²×C₅	1	2	yes	complemented
172	#625	C₂²×C₅	1	2	yes	complemented
173	#624	C₂²×C₅	1	1	yes	characteristic, complemented
174	D₃×Dic₃	C₂²×C₅	1	2	yes	—
175	D₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
176	D₃×Dic₃	C₂²×C₅	1	2	yes	complemented
177	D₃×Dic₃	C₂²×C₅	1	2	yes	complemented
178	D₃×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	3	1	no	—
181	C₂²×C₃×C₅	—	3	2	no	—
182	C₂²×C₃×C₅	—	3	1	no	—
183	C₂²×C₃×C₅	—	6	4	no	—
184	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
185	C₂²×C₃×C₅	C₂²×D₃	1	2	yes	—
186	C₂×C₅×D₃	—	2	4	no	—
187	C₂×C₅×D₃	—	3	1	no	—
188	C₂×C₅×D₃	—	3	1	no	—
189	C₂×C₅×D₃	—	6	1	no	—
190	C₂×C₅×D₃	—	6	2	no	—
191	C₂×C₅×D₃	—	6	2	no	—
192	C₂×C₅×D₃	C₂²×D₃	1	2	yes	—
193	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
194	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
195	C₃×C₄×C₅	—	2	1	no	—
196	C₃×C₄×C₅	—	3	1	no	—
197	C₃×C₄×C₅	—	3	2	no	—
198	C₃×C₄×C₅	—	3	1	no	—
199	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
201	C₅×Dic₃	—	3	2	no	—
202	C₅×Dic₃	—	3	2	no	—
203	C₅×Dic₃	—	3	1	no	—
204	C₅×Dic₃	—	3	1	no	—
205	C₅×Dic₃	—	6	2	no	—
206	C₅×Dic₃	—	6	1	no	—
207	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
208	C₅×Dic₃	C₂²×D₃	1	2	yes	—
209	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
210	C₃×#41	—	3	1	no	—
211	C₂×C₃×D₄	—	3	1	no	—
212	C₂×#67	—	3	2	no	—
213	C₂²×Dic₃	—	3	2	no	—
214	#239	—	3	1	no	—
215	D₃×Q₈	—	3	1	no	—
216	#237	—	3	1	no	—
217	#237	—	3	1	no	—
218	#237	—	3	2	no	—
219	#237	—	3	2	no	—
220	#237	—	3	2	no	—
221	#237	—	3	1	no	—
222	#237	—	3	1	no	—
223	#237	—	6	1	no	—
224	#237	C₅×D₃	1	1	yes	characteristic, direct product factor
225	D₃×D₄	—	3	2	no	—
226	D₃×D₄	C₅×D₃	1	1	yes	characteristic, complemented
227	#235	—	3	2	no	—
228	#235	—	3	1	no	—
229	C₂×C₄×D₃	—	3	2	no	—
230	C₂×C₄×D₃	—	3	1	no	—
231	C₂×C₄×D₃	—	3	1	no	—
232	C₂×Dic₆	—	3	1	no	—
233	C₃²×C₅	C₂×#41	1	1	yes	characteristic, complemented, Hall
234	C₂³×C₅	—	3	2	no	—
235	C₂³×C₅	—	9	1	no	—
236	C₅×Q₈	—	3	1	no	—
237	C₅×Q₈	—	9	2	no	—
238	C₅×Q₈	—	9	1	no	—
239	C₅×D₄	—	3	2	no	—
240	C₅×D₄	—	3	2	no	—
241	C₅×D₄	—	3	1	no	—
242	C₅×D₄	—	9	2	no	—
243	C₅×D₄	—	9	2	no	—
244	C₅×D₄	—	9	2	no	—
245	C₅×D₄	D₃²	1	1	yes	characteristic, complemented
246	C₂×C₄×C₅	—	3	2	no	—
247	C₂×C₄×C₅	—	3	1	no	—
248	C₂×C₄×C₅	—	3	1	no	—
249	C₂×C₄×C₅	—	9	1	no	—
250	C₂×C₄×C₅	—	9	1	no	—
251	C₂×C₄×C₅	—	9	2	no	—
252	C₂×C₄×C₅	—	9	2	no	—
253	C₂×C₄×C₅	—	9	1	no	—
254	C₂×C₄×C₅	—	9	2	no	—
255	C₂×C₄×C₅	—	9	2	no	—
256	C₂×C₄×C₅	—	9	1	no	—
257	C₂²×C₃²	C₂³×C₅	1	2	yes	—
258	C₂×C₃⋊D₃	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₃×D₃	—	2	4	no	—
260	C₂×C₃×D₃	C₂³×C₅	1	2	yes	—
261	C₂×C₃×D₃	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×D₃	C₂³×C₅	1	1	yes	characteristic
263	D₃²	—	2	2	no	—
264	C₃²×C₄	C₂³×C₅	1	1	yes	characteristic
265	C₃⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
266	C₃⋊Dic₃	C₂³×C₅	1	2	yes	—
267	C₃×Dic₃	C₂³×C₅	1	1	yes	characteristic
268	C₃×Dic₃	C₂³×C₅	1	2	yes	—
269	C₃×Dic₃	C₂³×C₅	1	1	yes	characteristic
270	C₂×#41	—	9	1	no	Sylow
271	C₂×C₃×C₅	—	2	2	no	—
272	C₂×C₃×C₅	—	2	2	no	—
273	C₂×C₃×C₅	—	2	1	no	—
274	C₂×C₃×C₅	—	3	2	no	—
275	C₂×C₃×C₅	—	4	2	no	—
276	C₂×C₃×C₅	—	6	1	no	—
277	C₂×C₃×C₅	—	6	2	no	—
278	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
279	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
280	C₅×D₃	—	2	2	no	—
281	C₅×D₃	—	2	1	no	—
282	C₅×D₃	—	6	1	no	—
283	C₅×D₃	—	6	1	no	—
284	C₅×D₃	—	12	1	no	—
285	C₅×D₃	#237	1	2	yes	direct product factor
286	C₂³×C₃	—	3	2	no	—
287	C₂²×D₃	—	3	1	no	—
288	C₂²×D₃	—	3	1	no	—
289	C₂²×D₃	C₂×C₅×D₃	1	2	yes	—
290	C₃×Q₈	—	3	1	no	—
291	C₃×D₄	—	2	1	no	—
292	C₃×D₄	—	3	2	no	—
293	C₃×D₄	—	3	2	no	—
294	C₃×D₄	—	3	1	no	—
295	C₃×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
296	C₃×D₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
297	C₂×C₃×C₄	—	3	2	no	—
298	C₂×C₃×C₄	—	3	1	no	—
299	C₂×C₃×C₄	—	3	1	no	—
300	#67	—	3	2	no	—
301	#67	—	3	2	no	—
302	#67	—	3	2	no	—
303	#67	—	3	2	no	—
304	#67	—	3	2	no	—
305	#67	—	6	2	no	—
306	#67	C₂×C₅×D₃	1	2	yes	complemented
307	#67	C₂×C₅×D₃	1	2	yes	complemented
308	C₂×Dic₃	—	3	2	no	—
309	C₂×Dic₃	—	3	2	no	—
310	C₂×Dic₃	—	3	2	no	—
311	C₂×Dic₃	—	3	1	no	—
312	C₂×Dic₃	—	3	1	no	—
313	C₂×Dic₃	—	3	2	no	—
314	C₂×Dic₃	—	3	2	no	—
315	C₂×Dic₃	—	6	2	no	—
316	C₂×Dic₃	C₂×C₅×D₃	1	2	yes	complemented
317	D₁₂	—	3	2	no	—
318	D₁₂	C₂×C₅×D₃	1	1	yes	characteristic, complemented
319	C₄×D₃	—	3	1	no	—
320	C₄×D₃	—	3	2	no	—
321	C₄×D₃	—	3	2	no	—
322	C₄×D₃	—	3	1	no	—
323	C₄×D₃	—	3	2	no	—
324	C₄×D₃	—	3	1	no	—
325	C₄×D₃	—	3	1	no	—
326	C₄×D₃	—	3	1	no	—
327	C₄×D₃	—	3	1	no	—
328	C₄×D₃	—	6	1	no	—
329	C₄×D₃	C₂×C₅×D₃	1	1	yes	characteristic
330	C₄×D₃	C₂×C₅×D₃	1	1	yes	characteristic, complemented
331	Dic₆	—	3	1	no	—
332	Dic₆	—	3	1	no	—
333	Dic₆	—	3	2	no	—
334	Dic₆	—	3	2	no	—
335	Dic₆	—	6	1	no	—
336	Dic₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
337	C₂²×C₅	—	3	1	no	—
338	C₂²×C₅	—	3	1	no	—
339	C₂²×C₅	—	3	2	no	—
340	C₂²×C₅	—	6	4	no	—
341	C₂²×C₅	—	9	1	no	—
342	C₂²×C₅	—	18	2	no	—
343	C₂²×C₅	C₂×D₃²	1	2	yes	—
344	C₄×C₅	—	3	1	no	—
345	C₄×C₅	—	3	1	no	—
346	C₄×C₅	—	3	2	no	—
347	C₄×C₅	—	9	1	no	—
348	C₄×C₅	—	9	2	no	—
349	C₄×C₅	C₂×D₃²	1	1	yes	characteristic
350	C₂×C₃²	—	2	2	no	—
351	C₂×C₃²	C₂⁴×C₅	1	1	yes	characteristic
352	C₃⋊D₃	—	2	1	no	—
353	C₃×D₃	—	2	1	no	—
354	C₃×D₃	—	2	2	no	—
355	C₃×D₃	C₅×#41	1	2	yes	complemented
356	#41	—	3	1	no	—
357	#41	—	9	2	no	—
358	#41	—	9	1	no	—
359	#41	—	9	2	no	—
360	#41	—	9	1	no	—
361	#41	—	9	1	no	—
362	C₂×Q₈	—	9	1	no	—
363	C₂×D₄	—	3	1	no	—
364	C₂×D₄	—	9	2	no	—
365	C₂²×C₄	—	9	1	no	—
366	C₂²×C₄	—	9	2	no	—
367	C₃×C₅	—	2	1	no	—
368	C₃×C₅	C₂×#237	1	1	yes	characteristic, complemented
369	C₃×C₅	D₃×#41	1	1	yes	characteristic, complemented
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	3	1	no	—
372	C₂²×C₃	—	3	2	no	—
373	C₂²×C₃	—	3	1	no	—
374	C₂²×C₃	—	6	4	no	—
375	C₂²×C₃	C₂²×C₅×D₃	1	2	yes	—
376	C₂²×C₃	C₂²×C₅×D₃	1	2	yes	—
377	C₂×D₃	—	2	4	no	—
378	C₂×D₃	—	3	1	no	—
379	C₂×D₃	—	3	1	no	—
380	C₂×D₃	—	6	1	no	—
381	C₂×D₃	—	6	2	no	—
382	C₂×D₃	—	6	2	no	—
383	C₂×D₃	C₂²×C₅×D₃	1	2	yes	—
384	C₂×D₃	C₂²×C₅×D₃	1	1	yes	characteristic
385	C₂×D₃	C₂²×C₅×D₃	1	1	yes	characteristic
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	3	1	no	—
388	C₃×C₄	—	3	2	no	—
389	C₃×C₄	—	3	1	no	—
390	C₃×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
391	C₃×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
392	Dic₃	—	3	2	no	—
393	Dic₃	—	3	2	no	—
394	Dic₃	—	3	1	no	—
395	Dic₃	—	3	1	no	—
396	Dic₃	—	6	2	no	—
397	Dic₃	—	6	1	no	—
398	Dic₃	C₂²×C₅×D₃	1	1	yes	characteristic
399	Dic₃	C₂²×C₅×D₃	1	2	yes	—
400	Dic₃	C₂²×C₅×D₃	1	1	yes	characteristic
401	C₂×C₅	—	2	2	no	—
402	C₂×C₅	—	3	2	no	—
403	C₂×C₅	—	6	2	no	—
404	C₂×C₅	—	6	1	no	—
405	C₂×C₅	—	18	1	no	—
406	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
407	C₃²	C₂×C₅×#41	1	1	yes	characteristic, complemented, Sylow
408	C₂³	—	3	2	no	—
409	C₂³	—	9	1	no	—
410	Q₈	—	3	1	no	—
411	Q₈	—	9	2	no	—
412	Q₈	—	9	1	no	—
413	D₄	—	3	2	no	—
414	D₄	—	3	2	no	—
415	D₄	—	3	1	no	—
416	D₄	—	9	2	no	—
417	D₄	—	9	2	no	—
418	D₄	—	9	2	no	—
419	D₄	C₅×D₃²	1	1	yes	characteristic, complemented
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	9	1	no	—
424	C₂×C₄	—	9	1	no	—
425	C₂×C₄	—	9	2	no	—
426	C₂×C₄	—	9	2	no	—
427	C₂×C₄	—	9	1	no	—
428	C₂×C₄	—	9	2	no	—
429	C₂×C₄	—	9	2	no	—
430	C₂×C₄	—	9	1	no	—
431	C₂×C₃	—	2	2	no	—
432	C₂×C₃	—	2	2	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	3	2	no	—
435	C₂×C₃	—	4	2	no	—
436	C₂×C₃	—	6	1	no	—
437	C₂×C₃	—	6	2	no	—
438	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
439	C₂×C₃	C₂³×C₅×D₃	1	1	yes	characteristic
440	D₃	—	2	2	no	—
441	D₃	—	2	1	no	—
442	D₃	—	6	1	no	—
443	D₃	—	6	1	no	—
444	D₃	—	12	1	no	—
445	D₃	C₅×#237	1	2	yes	direct product factor
446	C₅	D₃×#237	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	3	1	no	—
448	C₂²	—	3	1	no	—
449	C₂²	—	3	2	no	—
450	C₂²	—	6	4	no	—
451	C₂²	—	9	1	no	—
452	C₂²	—	18	2	no	—
453	C₂²	C₂×C₅×D₃²	1	2	yes	—
454	C₄	—	3	1	no	—
455	C₄	—	3	1	no	—
456	C₄	—	3	2	no	—
457	C₄	—	9	1	no	—
458	C₄	—	9	2	no	—
459	C₄	C₂×C₅×D₃²	1	1	yes	characteristic
460	C₃	—	2	1	no	—
461	C₃	C₂×C₅×#237	1	1	yes	characteristic, complemented
462	C₃	C₅×D₃×#41	1	1	yes	characteristic, complemented
463	C₂	—	2	2	no	—
464	C₂	—	3	2	no	—
465	C₂	—	6	2	no	—
466	C₂	—	6	1	no	—
467	C₂	—	18	1	no	—
468	C₂	C₂²×C₅×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂²×D₃²
commutator, cosocle	C₂×C₃²	C₂⁴×C₅
Frattini	C₂	C₂²×C₅×D₃²
Fitting	C₃²×C₅×D₄	C₂²
socle	C₂×C₃²×C₅	C₂⁴
hypercenter	C₅×D₄	D₃²
hypocenter	C₃²	C₂×C₅×#41
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₅ ◁ C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₅×#3830	C₂	semidirect
2. C₃×C₅×#237	C₂	semidirect
3. C₃×C₅×D₃×D₄	C₂	semidirect
4. C₅×D₃×#67	C₂	semidirect
5. C₅×#3805	C₂	semidirect
6. C₅×#3804	C₂	semidirect
7. C₂×C₅×D₃×Dic₃	C₂	semidirect
8. C₄×C₅×D₃²	C₂	semidirect
9. C₅×#3796	C₂	semidirect
10. C₅×#3795	C₂	semidirect
11. C₅×D₃×Dic₆	C₂	semidirect
16. C₃²×C₅×D₄	C₂²	semidirect
17. C₅×#638	C₂²	semidirect
18. C₂×C₅×C₃⋊Dic₃	C₂²	semidirect
19. C₄×C₅×C₃⋊D₃	C₂²	semidirect
20. C₅×#634	C₂²	semidirect
21. C₃×C₅×#67	C₂²	semidirect
22. C₃×C₅×#67	C₂²	semidirect
23. C₂×C₃×C₅×Dic₃	C₂²	semidirect
24. C₃×C₅×D₁₂	C₂²	semidirect
26. C₃×C₄×C₅×D₃	C₂²	semidirect
27. C₃×C₅×Dic₆	C₂²	semidirect
28. C₅×#627	C₂²	semidirect
29. C₅×#626	C₂²	semidirect
30. C₅×#625	C₂²	semidirect
31. C₅×#624	C₂²	semidirect
34. C₅×D₃×Dic₃	C₂²	semidirect
35. C₅×D₃×Dic₃	C₂²	semidirect
36. C₅×D₃×Dic₃	C₂²	semidirect
37. D₃×#237	C₅	direct (N × H)
52. C₅×#237	D₃	direct (N × H)
54. C₅×D₃×D₄	D₃	semidirect
75. #3830	C₂×C₅	semidirect
76. C₃×#237	C₂×C₅	semidirect
77. C₃×D₃×D₄	C₂×C₅	semidirect
78. D₃×#67	C₂×C₅	semidirect
79. #3805	C₂×C₅	semidirect
80. #3804	C₂×C₅	semidirect
81. C₂×D₃×Dic₃	C₂×C₅	semidirect
82. C₄×D₃²	C₂×C₅	semidirect
83. #3796	C₂×C₅	semidirect
84. #3795	C₂×C₅	semidirect
85. D₃×Dic₆	C₂×C₅	semidirect
95. C₃×C₅×D₄	C₂×D₃	semidirect
96. C₃×C₅×D₄	C₂×D₃	semidirect
106. C₅×#67	C₂×D₃	semidirect
107. C₅×#67	C₂×D₃	semidirect
116. C₂×C₅×Dic₃	C₂×D₃	semidirect
118. C₅×D₁₂	C₂×D₃	semidirect
130. C₄×C₅×D₃	C₂×D₃	semidirect
136. C₅×Dic₆	C₂×D₃	semidirect
144. C₃×C₅×D₃	#41	semidirect
158. C₃²×D₄	C₂²×C₅	semidirect
159. #638	C₂²×C₅	semidirect
160. C₂×C₃⋊Dic₃	C₂²×C₅	semidirect
161. C₄×C₃⋊D₃	C₂²×C₅	semidirect
162. #634	C₂²×C₅	semidirect
163. C₃×#67	C₂²×C₅	semidirect
164. C₃×#67	C₂²×C₅	semidirect
165. C₂×C₃×Dic₃	C₂²×C₅	semidirect
166. C₃×D₁₂	C₂²×C₅	semidirect
168. C₃×C₄×D₃	C₂²×C₅	semidirect
169. C₃×Dic₆	C₂²×C₅	semidirect
170. #627	C₂²×C₅	semidirect
171. #626	C₂²×C₅	semidirect
172. #625	C₂²×C₅	semidirect
173. #624	C₂²×C₅	semidirect
176. D₃×Dic₃	C₂²×C₅	semidirect
177. D₃×Dic₃	C₂²×C₅	semidirect
178. D₃×Dic₃	C₂²×C₅	semidirect
224. #237	C₅×D₃	direct (N × H)
226. D₃×D₄	C₅×D₃	semidirect
233. C₃²×C₅	C₂×#41	semidirect
245. C₅×D₄	D₃²	semidirect
285. C₅×D₃	#237	direct (N × H)
295. C₃×D₄	C₂×C₅×D₃	semidirect
296. C₃×D₄	C₂×C₅×D₃	semidirect
306. #67	C₂×C₅×D₃	semidirect
307. #67	C₂×C₅×D₃	semidirect
316. C₂×Dic₃	C₂×C₅×D₃	semidirect
318. D₁₂	C₂×C₅×D₃	semidirect
330. C₄×D₃	C₂×C₅×D₃	semidirect
336. Dic₆	C₂×C₅×D₃	semidirect
355. C₃×D₃	C₅×#41	semidirect
368. C₃×C₅	C₂×#237	semidirect
369. C₃×C₅	D₃×#41	semidirect
407. C₃²	C₂×C₅×#41	semidirect
419. D₄	C₅×D₃²	semidirect
445. D₃	C₅×#237	direct (N × H)
446. C₅	D₃×#237	direct (N × H)
461. C₃	C₂×C₅×#237	semidirect
462. C₃	C₅×D₃×#41	semidirect

Maximal subgroups

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

subgroup	index
C₅×#3830	2
C₃×C₅×#237	2
C₃×C₅×D₃×D₄	2
C₅×D₃×#67	2
C₅×#3805	2
C₅×#3804	2
C₂×C₅×D₃×Dic₃	2
C₄×C₅×D₃²	2
C₅×#3796	2
C₅×#3795	2
C₅×D₃×Dic₆	2
C₅×D₃×#41	3
C₂×C₅×#237	3
D₃×#237	5

Subgroups — C5×D3×#237 #13089324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#237 #13089324