Subgroups — C₅×#72023 #14302324

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#949	C₂	1	1	yes	maximal, characteristic
3	C₅×#5236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×C₃⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4559	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1903	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₃×C₅×#131	—	2	2	no	—
12	C₃×C₅×#131	—	2	2	no	—
13	C₂×C₃×C₅×M₁₆	—	2	2	no	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₅×#949	—	2	2	no	—
17	C₅×#949	—	2	2	no	—
18	C₂×C₅×#215	C₄	1	2	yes	complemented
19	C₂×C₅×#213	C₄	1	2	yes	complemented
20	C₅×#926	C₂²	1	1	yes	characteristic
21	C₂×C₅×#208	C₂²	1	1	yes	characteristic
22	C₂×C₅×#208	C₂²	1	1	yes	characteristic
23	C₅×#837	—	2	2	no	—
24	C₅×#823	—	2	2	no	—
25	C₅×#821	—	2	2	no	—
26	#72023	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
28	C₅×#568	D₃	1	1	yes	characteristic, complemented
29	C₅×#421	—	3	1	no	—
30	C₅×#418	—	3	1	no	—
31	C₂×C₅×#100	—	3	1	no	—
32	C₅×#344	—	3	1	no	—
33	C₅×#338	—	3	1	no	—
34	C₂³×C₅×D₃	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	D₄	1	2	yes	—
38	C₃×C₅×#41	D₄	1	2	yes	—
39	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	1	no	—
47	C₂×C₅×D₁₂	—	2	1	no	—
48	C₂×C₅×D₁₂	—	2	1	no	—
49	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
50	C₃×C₅×M₁₆	—	2	4	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₃×C₅×M₁₆	D₄	1	2	yes	—
55	C₂×C₃×C₅×C₈	—	2	4	no	—
56	C₂×C₃×C₅×C₈	—	2	1	no	—
57	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
58	C₅×#217	—	2	1	no	—
59	C₅×#215	—	2	4	no	—
60	C₅×#213	—	2	4	no	—
61	C₅×C₄⋊Dic₃	—	2	1	no	—
62	C₄×C₅×Dic₃	—	2	1	no	—
63	C₅×#208	—	2	1	no	—
64	C₅×#208	—	2	1	no	—
65	C₅×#208	—	2	1	no	—
66	C₅×#208	—	2	1	no	—
67	C₂×C₅×C₃⋊C₈	—	2	1	no	—
68	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
69	C₃×#568	C₂×C₅	1	1	yes	characteristic, complemented
70	C₂×#949	C₂×C₅	1	1	yes	characteristic
71	#5236	C₂×C₅	1	1	yes	characteristic, complemented
72	#5131	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃⋊#338	C₂×C₅	1	1	yes	characteristic, complemented
75	#4559	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₅×AGL(1,ℤ/8)	—	6	2	no	—
79	C₅×AGL(1,ℤ/8)	—	6	2	no	—
80	C₂×C₅×SD₁₆	—	3	2	no	—
81	C₂×C₅×D₈	—	3	2	no	—
82	C₅×#131	—	2	2	no	—
83	C₅×#131	—	2	2	no	—
84	C₂×C₅×M₁₆	—	2	2	no	—
85	C₂×C₅×M₁₆	—	3	1	no	—
86	C₂×C₅×M₁₆	—	3	1	no	—
87	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
89	C₅×#117	—	3	1	no	—
90	C₅×#104	—	6	2	no	—
91	C₅×#102	—	6	2	no	—
92	C₅×#100	—	6	2	no	—
93	#1903	—	3	1	no	Sylow
94	C₂³×C₃×C₅	—	2	1	no	—
95	C₂³×C₃×C₅	#41	1	1	yes	characteristic
96	C₂²×C₅×D₃	—	2	2	no	—
97	C₂²×C₅×D₃	—	4	1	no	—
98	C₂²×C₅×D₃	—	4	1	no	—
99	C₂²×C₅×D₃	—	8	2	no	—
100	C₃×C₅×Q₈	—	2	1	no	—
101	C₃×C₅×Q₈	C₂²⋊C₄	1	2	yes	—
102	C₃×C₅×D₄	—	2	2	no	—
103	C₃×C₅×D₄	—	2	2	no	—
104	C₃×C₅×D₄	—	2	1	no	—
105	C₃×C₅×D₄	C₂²⋊C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	—	2	1	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
115	C₂×C₅×Dic₃	—	4	1	no	—
116	C₅×D₁₂	—	2	2	no	—
117	C₅×D₁₂	—	2	2	no	—
118	C₅×D₁₂	—	4	1	no	—
119	C₅×D₁₂	—	4	1	no	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₅×C₃⋊C₈	—	2	2	no	—
123	C₅×C₃⋊C₈	—	4	1	no	—
124	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
125	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
126	C₃×#131	—	2	2	no	—
127	C₃×#131	—	2	2	no	—
128	C₂×C₃×M₁₆	—	2	2	no	—
129	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
131	#949	—	2	2	no	—
132	#949	—	2	2	no	—
133	C₂×#215	C₄×C₅	1	2	yes	complemented
134	C₂×#213	C₄×C₅	1	2	yes	complemented
135	#926	C₂²×C₅	1	1	yes	characteristic
136	C₂×#208	C₂²×C₅	1	1	yes	characteristic
137	C₂×#208	C₂²×C₅	1	1	yes	characteristic
138	#837	—	2	2	no	—
139	#823	—	2	2	no	—
140	#821	—	2	2	no	—
141	C₂⁴×C₅	—	6	1	no	—
142	C₅×#41	—	2	1	no	—
143	C₅×#41	—	2	1	no	—
144	C₅×#41	D₁₂	1	2	yes	—
145	C₅×#41	#67	1	2	yes	—
146	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	3	2	no	—
149	C₂×C₅×D₄	—	6	1	no	—
150	C₂×C₅×D₄	—	6	1	no	—
151	C₂×C₅×D₄	—	6	1	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	—	2	1	no	—
156	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
157	C₅×SD₁₆	—	6	4	no	—
158	C₅×D₈	—	6	4	no	—
159	C₅×M₁₆	—	2	4	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	6	1	no	—
164	C₅×M₁₆	—	6	1	no	—
165	C₅×M₁₆	—	6	1	no	—
166	C₅×M₁₆	—	6	1	no	—
167	C₅×M₁₆	#67	1	2	yes	—
168	C₂×C₅×C₈	—	2	4	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₂×C₅×C₈	—	3	2	no	—
171	C₂×C₅×C₈	—	6	1	no	—
172	C₂×C₅×C₈	#67	1	2	yes	—
173	C₅×C₄⋊C₄	—	6	1	no	—
174	C₅×C₂²⋊C₄	—	6	1	no	—
175	C₄²×C₅	—	6	1	no	—
176	C₂×AGL(1,ℤ/8)	—	3	1	no	—
177	#568	C₅×D₃	1	1	yes	characteristic, complemented
178	#421	—	3	1	no	—
179	#418	—	3	1	no	—
180	C₂×#100	—	3	1	no	—
181	#344	—	3	1	no	—
182	#338	—	3	1	no	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	—	8	1	no	—
186	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₅	#121	1	1	yes	characteristic
188	C₂²×C₃×C₅	#123	1	1	yes	characteristic
189	C₂×C₅×D₃	—	4	2	no	—
190	C₂×C₅×D₃	—	8	2	no	—
191	C₂×C₅×D₃	—	8	2	no	—
192	C₂×C₅×D₃	—	8	2	no	—
193	C₃×C₄×C₅	—	2	2	no	—
194	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
196	C₃×C₄×C₅	#120	1	1	yes	characteristic
197	C₃×C₄×C₅	#121	1	1	yes	characteristic
198	C₅×Dic₃	—	8	1	no	—
199	C₂³×D₃	—	2	1	no	—
200	C₃×#41	—	2	1	no	—
201	C₃×#41	—	2	1	no	—
202	C₃×#41	C₅×D₄	1	2	yes	—
203	C₃×#41	C₅×D₄	1	2	yes	—
204	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
205	C₂×C₃×D₄	—	2	1	no	—
206	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	—	2	1	no	—
213	C₂×D₁₂	—	2	1	no	—
214	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
215	C₃×M₁₆	—	2	4	no	—
216	C₃×M₁₆	—	2	1	no	—
217	C₃×M₁₆	—	2	1	no	—
218	C₃×M₁₆	—	2	1	no	—
219	C₃×M₁₆	C₅×D₄	1	2	yes	—
220	C₂×C₃×C₈	—	2	4	no	—
221	C₂×C₃×C₈	—	2	1	no	—
222	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
223	#217	—	2	1	no	—
224	#215	—	2	4	no	—
225	#213	—	2	4	no	—
226	C₄⋊Dic₃	—	2	1	no	—
227	C₄×Dic₃	—	2	1	no	—
228	#208	—	2	1	no	—
229	#208	—	2	1	no	—
230	#208	—	2	1	no	—
231	#208	—	2	1	no	—
232	C₂×C₃⋊C₈	—	2	1	no	—
233	C₂×C₃⋊C₈	C₂×C₄×C₅	1	2	yes	—
234	C₂³×C₅	—	2	1	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	—	12	1	no	—
237	C₂³×C₅	—	12	1	no	—
238	C₂³×C₅	—	24	2	no	—
239	C₂³×C₅	#235	1	1	yes	characteristic
240	C₅×Q₈	—	2	1	no	—
241	C₅×Q₈	(C₂×D₃)⋊C₄	1	2	yes	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	—	2	1	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	6	2	no	—
247	C₅×D₄	—	12	1	no	—
248	C₅×D₄	—	12	1	no	—
249	C₅×D₄	(C₂×D₃)⋊C₄	1	2	yes	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	12	1	no	—
254	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
256	C₂×C₄×C₅	#235	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
260	C₅×C₈	—	2	2	no	—
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	6	2	no	—
263	C₅×C₈	—	12	1	no	—
264	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
265	C₂²×D₄	—	3	1	no	—
266	AGL(1,ℤ/8)	—	6	2	no	—
267	AGL(1,ℤ/8)	—	6	2	no	—
268	C₂×SD₁₆	—	3	2	no	—
269	C₂×D₈	—	3	2	no	—
270	#131	—	2	2	no	—
271	#131	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	3	1	no	—
274	C₂×M₁₆	—	3	1	no	—
275	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
277	#117	—	3	1	no	—
278	#104	—	6	2	no	—
279	#102	—	6	2	no	—
280	#100	—	6	2	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	—	2	1	no	—
283	C₂×C₃×C₅	—	2	1	no	—
284	C₂×C₃×C₅	—	4	2	no	—
285	C₂×C₃×C₅	#386	1	1	yes	characteristic
286	C₅×D₃	—	8	2	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	C₅×#41	1	1	yes	characteristic
289	C₂²×D₃	—	2	2	no	—
290	C₂²×D₃	—	4	1	no	—
291	C₂²×D₃	—	4	1	no	—
292	C₂²×D₃	—	8	2	no	—
293	C₃×Q₈	—	2	1	no	—
294	C₃×Q₈	C₅×C₂²⋊C₄	1	2	yes	—
295	C₃×D₄	—	2	2	no	—
296	C₃×D₄	—	2	2	no	—
297	C₃×D₄	—	2	1	no	—
298	C₃×D₄	C₅×C₂²⋊C₄	1	2	yes	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
308	C₂×Dic₃	—	4	1	no	—
309	D₁₂	—	2	2	no	—
310	D₁₂	—	2	2	no	—
311	D₁₂	—	4	1	no	—
312	D₁₂	—	4	1	no	—
313	C₃×C₈	—	2	2	no	—
314	C₃×C₈	—	2	2	no	—
315	C₃⋊C₈	—	2	2	no	—
316	C₃⋊C₈	—	4	1	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	4	1	no	—
319	C₂²×C₅	—	8	1	no	—
320	C₂²×C₅	—	12	2	no	—
321	C₂²×C₅	—	24	2	no	—
322	C₂²×C₅	—	24	2	no	—
323	C₂²×C₅	—	24	2	no	—
324	C₂²×C₅	C₄×#67	1	1	yes	characteristic
325	C₂²×C₅	#929	1	1	yes	characteristic
326	C₂²×C₅	#930	1	1	yes	characteristic
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	24	1	no	—
329	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
330	C₄×C₅	C₄×#67	1	1	yes	characteristic
331	C₄×C₅	#930	1	1	yes	characteristic
332	C₄×C₅	#953	1	1	yes	characteristic
333	C₂⁴	—	6	1	no	—
334	#41	—	2	1	no	—
335	#41	—	2	1	no	—
336	#41	C₅×D₁₂	1	2	yes	—
337	#41	C₅×#67	1	2	yes	—
338	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	3	2	no	—
341	C₂×D₄	—	6	1	no	—
342	C₂×D₄	—	6	1	no	—
343	C₂×D₄	—	6	1	no	—
344	C₂×D₄	—	6	1	no	—
345	C₂×D₄	—	6	1	no	—
346	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
349	SD₁₆	—	6	4	no	—
350	D₈	—	6	4	no	—
351	M₁₆	—	2	4	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	6	1	no	—
356	M₁₆	—	6	1	no	—
357	M₁₆	—	6	1	no	—
358	M₁₆	—	6	1	no	—
359	M₁₆	C₅×#67	1	2	yes	—
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	3	2	no	—
363	C₂×C₈	—	6	1	no	—
364	C₂×C₈	C₅×#67	1	2	yes	—
365	C₄⋊C₄	—	6	1	no	—
366	C₂²⋊C₄	—	6	1	no	—
367	C₄²	—	6	1	no	—
368	C₃×C₅	#1903	1	1	yes	characteristic, complemented, Hall
369	C₂²×C₃	—	2	2	no	—
370	C₂²×C₃	—	4	1	no	—
371	C₂²×C₃	—	8	1	no	—
372	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₃	C₅×#121	1	1	yes	characteristic
374	C₂²×C₃	C₅×#123	1	1	yes	characteristic
375	C₂×D₃	—	4	2	no	—
376	C₂×D₃	—	8	2	no	—
377	C₂×D₃	—	8	2	no	—
378	C₂×D₃	—	8	2	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
381	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
382	C₃×C₄	C₅×#120	1	1	yes	characteristic
383	C₃×C₄	C₅×#121	1	1	yes	characteristic
384	Dic₃	—	8	1	no	—
385	C₂×C₅	—	2	1	no	—
386	C₂×C₅	—	2	1	no	—
387	C₂×C₅	—	2	1	no	—
388	C₂×C₅	—	4	2	no	—
389	C₂×C₅	—	24	2	no	—
390	C₂×C₅	#5213	1	1	yes	characteristic
391	C₂³	—	2	1	no	—
392	C₂³	—	6	2	no	—
393	C₂³	—	12	1	no	—
394	C₂³	—	12	1	no	—
395	C₂³	—	24	2	no	—
396	C₂³	C₅×#235	1	1	yes	characteristic
397	Q₈	—	2	1	no	—
398	Q₈	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	1	no	—
402	D₄	—	6	2	no	—
403	D₄	—	6	2	no	—
404	D₄	—	12	1	no	—
405	D₄	—	12	1	no	—
406	D₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	12	1	no	—
411	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
413	C₂×C₄	C₅×#235	1	1	yes	characteristic
414	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
415	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
416	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	6	2	no	—
420	C₈	—	12	1	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	4	2	no	—
425	C₂×C₃	C₅×#386	1	1	yes	characteristic
426	D₃	—	8	2	no	—
427	C₅	#72023	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	12	2	no	—
432	C₂²	—	24	2	no	—
433	C₂²	—	24	2	no	—
434	C₂²	—	24	2	no	—
435	C₂²	C₄×C₅×#67	1	1	yes	characteristic
436	C₂²	C₅×#929	1	1	yes	characteristic
437	C₂²	C₅×#930	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	24	1	no	—
440	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
441	C₄	C₄×C₅×#67	1	1	yes	characteristic
442	C₄	C₅×#930	1	1	yes	characteristic
443	C₄	C₅×#953	1	1	yes	characteristic
444	C₃	C₅×#1903	1	1	yes	characteristic, complemented, Sylow
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	24	2	no	—
450	C₂	C₅×#5213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#5213
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#568	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₅×#949	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#568	D₃
hypocenter	C₃	C₅×#1903
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#568

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#568	C₂	semidirect
3. C₅×#5236	C₂	semidirect
4. C₅×#5131	C₂	semidirect
5. C₂×C₅×#823	C₂	semidirect
6. C₅×C₃⋊#338	C₂	semidirect
7. C₅×#4559	C₂	semidirect
18. C₂×C₅×#215	C₄	semidirect
19. C₂×C₅×#213	C₄	semidirect
26. #72023	C₅	direct (N × H)
28. C₅×#568	D₃	semidirect
69. C₃×#568	C₂×C₅	semidirect
71. #5236	C₂×C₅	semidirect
72. #5131	C₂×C₅	semidirect
73. C₂×#823	C₂×C₅	semidirect
74. C₃⋊#338	C₂×C₅	semidirect
75. #4559	C₂×C₅	semidirect
133. C₂×#215	C₄×C₅	semidirect
134. C₂×#213	C₄×C₅	semidirect
177. #568	C₅×D₃	semidirect
368. C₃×C₅	#1903	semidirect
427. C₅	#72023	direct (N × H)
444. C₃	C₅×#1903	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#568	2
C₂×C₅×#949	2
C₅×#5236	2
C₅×#5131	2
C₂×C₅×#823	2
C₅×C₃⋊#338	2
C₅×#4559	2
C₅×#1903	3
#72023	5

Subgroups — C5×#72023 #14302324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#72023 #14302324