Subgroups — C₅×#69038 #14302321

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	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic
2	C₅×#5745	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#823	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5005	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5001	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×C₃⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1903	—	3	1	no	maximal, Hall
9	C₂×C₅×#235	C₂²	1	1	yes	characteristic
10	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₃×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#208	C₂²	1	1	yes	characteristic
15	C₂×C₅×#208	C₂²	1	1	yes	characteristic
16	C₅×#908	—	2	2	no	—
17	C₅×#908	—	2	2	no	—
18	C₅×#907	—	2	2	no	—
19	C₅×D₃×M₁₆	—	2	2	no	—
20	C₂×C₅×D₂₄	C₄	1	2	yes	complemented
21	C₂×C₅×#204	C₄	1	2	yes	complemented
22	C₅×#901	—	2	2	no	—
23	C₅×#823	—	2	2	no	—
24	C₅×#809	—	2	2	no	—
25	C₅×#805	—	2	2	no	—
26	#69038	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
28	C₅×#568	—	3	1	no	—
29	C₅×#421	—	3	1	no	—
30	C₅×#418	—	3	1	no	—
31	C₂×C₅×#100	—	3	1	no	—
32	C₅×#344	D₃	1	1	yes	characteristic, complemented
33	C₅×#338	—	3	1	no	—
34	C₂³×C₅×D₃	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₅×#67	—	2	1	no	—
37	C₅×#235	—	2	1	no	—
38	C₅×#235	—	2	1	no	—
39	C₅×#235	D₄	1	2	yes	—
40	C₅×#235	D₄	1	2	yes	—
41	C₂×C₅×D₁₂	—	2	1	no	—
42	C₂×C₅×D₁₂	—	2	1	no	—
43	C₂×C₅×D₁₂	—	2	1	no	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	C₂×C₄	1	2	yes	—
47	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	D₄	1	2	yes	—
54	C₂×C₃×C₅×C₈	—	2	1	no	—
55	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	1	no	—
57	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
58	C₃×C₄²×C₅	—	2	1	no	—
59	C₅×#208	—	2	1	no	—
60	C₅×#208	—	2	1	no	—
61	C₅×#208	—	2	1	no	—
62	C₅×#208	—	2	1	no	—
63	C₂×C₅×C₃⋊C₈	—	2	1	no	—
64	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
65	C₅×D₂₄	—	2	4	no	—
66	C₅×#204	—	2	4	no	—
67	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
68	C₅×D₃×C₈	—	2	4	no	—
69	C₂×#908	C₂×C₅	1	1	yes	characteristic
70	#5745	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×#823	C₂×C₅	1	1	yes	characteristic, complemented
72	#5005	C₂×C₅	1	1	yes	characteristic, complemented
73	#5001	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#344	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃⋊#338	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×C₅×#41	—	3	1	no	—
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	—	6	2	no	—
83	C₅×#131	—	6	2	no	—
84	C₂×C₅×M₁₆	—	3	1	no	—
85	C₂×C₅×M₁₆	—	3	1	no	—
86	C₂×C₅×M₁₆	—	6	2	no	—
87	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
88	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
89	C₅×#117	C₂×D₃	1	1	yes	characteristic
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	#41	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	2	1	no	—
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	C₂×C₃×C₄×C₅	—	4	1	no	—
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₅×#67	—	2	2	no	—
108	C₅×#67	—	2	2	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₅×D₁₂	—	2	2	no	—
111	C₅×D₁₂	—	2	1	no	—
112	C₅×D₁₂	—	2	2	no	—
113	C₅×D₁₂	—	4	1	no	—
114	C₅×D₁₂	—	4	1	no	—
115	C₅×D₁₂	C₂²⋊C₄	1	2	yes	—
116	C₄×C₅×D₃	—	2	2	no	—
117	C₄×C₅×D₃	—	2	2	no	—
118	C₅×Dic₆	—	2	1	no	—
119	C₅×Dic₆	C₂²⋊C₄	1	2	yes	—
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×#235	C₂²×C₅	1	1	yes	characteristic
125	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
126	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₃×#117	C₂²×C₅	1	1	yes	characteristic
129	C₂×#208	C₂²×C₅	1	1	yes	characteristic
130	C₂×#208	C₂²×C₅	1	1	yes	characteristic
131	#908	—	2	2	no	—
132	#908	—	2	2	no	—
133	#907	—	2	2	no	—
134	D₃×M₁₆	—	2	2	no	—
135	C₂×D₂₄	C₄×C₅	1	2	yes	complemented
136	C₂×#204	C₄×C₅	1	2	yes	complemented
137	#901	—	2	2	no	—
138	#823	—	2	2	no	—
139	#809	—	2	2	no	—
140	#805	—	2	2	no	—
141	C₂⁴×C₅	—	6	1	no	—
142	C₅×#41	—	3	2	no	—
143	C₅×#41	—	3	2	no	—
144	C₅×#41	—	6	1	no	—
145	C₅×#41	—	6	1	no	—
146	C₂×C₅×Q₈	—	3	1	no	—
147	C₂×C₅×D₄	—	3	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	—	6	1	no	—
155	C₂²×C₄×C₅	—	6	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	1	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	6	4	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	D₁₂	1	2	yes	—
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	3	2	no	—
170	C₂×C₅×C₈	—	6	4	no	—
171	C₂×C₅×C₈	—	6	1	no	—
172	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₂²⋊C₄	—	2	1	no	—
175	C₄²×C₅	—	2	1	no	—
176	C₂×AGL(1,ℤ/8)	—	3	1	no	—
177	#568	—	3	1	no	—
178	#421	—	3	1	no	—
179	#418	—	3	1	no	—
180	C₂×#100	—	3	1	no	—
181	#344	C₅×D₃	1	1	yes	characteristic, complemented
182	#338	—	3	1	no	—
183	C₂²×C₃×C₅	—	4	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	#121	1	1	yes	characteristic
186	C₂²×C₃×C₅	#123	1	1	yes	characteristic
187	C₂×C₅×D₃	—	2	2	no	—
188	C₂×C₅×D₃	—	4	2	no	—
189	C₂×C₅×D₃	—	8	1	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	—	8	1	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	—	2	2	no	—
199	C₂³×D₃	—	2	1	no	—
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂×#67	—	2	1	no	—
202	#235	—	2	1	no	—
203	#235	—	2	1	no	—
204	#235	C₅×D₄	1	2	yes	—
205	#235	C₅×D₄	1	2	yes	—
206	C₂×D₁₂	—	2	1	no	—
207	C₂×D₁₂	—	2	1	no	—
208	C₂×D₁₂	—	2	1	no	—
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
212	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂×C₄×D₃	—	2	1	no	—
214	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
215	C₃×M₁₆	—	2	1	no	—
216	C₃×M₁₆	—	2	1	no	—
217	C₃×M₁₆	—	2	1	no	—
218	C₃×M₁₆	C₅×D₄	1	2	yes	—
219	C₂×C₃×C₈	—	2	1	no	—
220	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
221	C₃×C₄⋊C₄	—	2	1	no	—
222	C₃×C₂²⋊C₄	—	2	1	no	—
223	C₃×C₄²	—	2	1	no	—
224	#208	—	2	1	no	—
225	#208	—	2	1	no	—
226	#208	—	2	1	no	—
227	#208	—	2	1	no	—
228	C₂×C₃⋊C₈	—	2	1	no	—
229	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
230	D₂₄	—	2	4	no	—
231	#204	—	2	4	no	—
232	ΓL(1,𝔽₂₅)	—	2	4	no	—
233	D₃×C₈	—	2	4	no	—
234	C₂³×C₅	—	6	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	—	3	2	no	—
241	C₅×Q₈	—	6	1	no	—
242	C₅×D₄	—	3	2	no	—
243	C₅×D₄	—	6	2	no	—
244	C₅×D₄	—	6	2	no	—
245	C₅×D₄	—	6	2	no	—
246	C₅×D₄	—	6	1	no	—
247	C₅×D₄	—	6	2	no	—
248	C₅×D₄	—	12	1	no	—
249	C₅×D₄	—	12	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	6	1	no	—
252	C₂×C₄×C₅	—	6	2	no	—
253	C₂×C₄×C₅	—	6	2	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	D₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
259	C₂×C₄×C₅	#239	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	—	3	1	no	—
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	—	6	2	no	—
271	#131	—	6	2	no	—
272	C₂×M₁₆	—	3	1	no	—
273	C₂×M₁₆	—	3	1	no	—
274	C₂×M₁₆	—	6	2	no	—
275	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
277	#117	C₂×C₅×D₃	1	1	yes	characteristic
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	#386	1	1	yes	characteristic
285	C₅×D₃	—	4	2	no	—
286	C₅×D₃	—	8	2	no	—
287	C₂³×C₃	C₅×#41	1	1	yes	characteristic
288	C₂²×D₃	—	2	1	no	—
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	C₂×C₃×C₄	—	4	1	no	—
294	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
300	#67	—	2	2	no	—
301	#67	—	2	2	no	—
302	C₂×Dic₃	—	2	1	no	—
303	D₁₂	—	2	2	no	—
304	D₁₂	—	2	1	no	—
305	D₁₂	—	2	2	no	—
306	D₁₂	—	4	1	no	—
307	D₁₂	—	4	1	no	—
308	D₁₂	C₅×C₂²⋊C₄	1	2	yes	—
309	C₄×D₃	—	2	2	no	—
310	C₄×D₃	—	2	2	no	—
311	Dic₆	—	2	1	no	—
312	Dic₆	C₅×C₂²⋊C₄	1	2	yes	—
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	—	4	1	no	—
318	C₂²×C₅	—	6	2	no	—
319	C₂²×C₅	—	12	2	no	—
320	C₂²×C₅	—	24	1	no	—
321	C₂²×C₅	—	24	2	no	—
322	C₂²×C₅	—	24	2	no	—
323	C₂²×C₅	—	24	2	no	—
324	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
325	C₂²×C₅	#884	1	1	yes	characteristic
326	C₂²×C₅	#894	1	1	yes	characteristic
327	C₄×C₅	—	6	2	no	—
328	C₄×C₅	—	8	1	no	—
329	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
330	C₄×C₅	#882	1	1	yes	characteristic
331	C₄×C₅	#893	1	1	yes	characteristic
332	C₄×C₅	#895	1	1	yes	characteristic
333	C₂⁴	—	6	1	no	—
334	#41	—	3	2	no	—
335	#41	—	3	2	no	—
336	#41	—	6	1	no	—
337	#41	—	6	1	no	—
338	C₂×Q₈	—	3	1	no	—
339	C₂×D₄	—	3	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	—	6	1	no	—
347	C₂²×C₄	—	6	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	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	6	4	no	—
355	M₁₆	—	6	1	no	—
356	M₁₆	—	6	1	no	—
357	M₁₆	—	6	1	no	—
358	M₁₆	—	6	1	no	—
359	M₁₆	C₅×D₁₂	1	2	yes	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	3	2	no	—
362	C₂×C₈	—	6	4	no	—
363	C₂×C₈	—	6	1	no	—
364	C₂×C₈	C₄×C₅×D₃	1	2	yes	—
365	C₄⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₃×C₅	#1903	1	1	yes	characteristic, complemented, Hall
369	C₂²×C₃	—	4	1	no	—
370	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
371	C₂²×C₃	C₅×#121	1	1	yes	characteristic
372	C₂²×C₃	C₅×#123	1	1	yes	characteristic
373	C₂×D₃	—	2	2	no	—
374	C₂×D₃	—	4	2	no	—
375	C₂×D₃	—	8	1	no	—
376	C₂×D₃	—	8	2	no	—
377	C₂×D₃	—	8	2	no	—
378	C₂×D₃	—	8	2	no	—
379	C₃×C₄	—	8	1	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	—	2	2	no	—
385	C₂×C₅	—	2	1	no	—
386	C₂×C₅	—	2	1	no	—
387	C₂×C₅	—	2	1	no	—
388	C₂×C₅	—	12	2	no	—
389	C₂×C₅	—	24	2	no	—
390	C₂×C₅	#4665	1	1	yes	characteristic
391	C₂³	—	6	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	—	3	2	no	—
398	Q₈	—	6	1	no	—
399	D₄	—	3	2	no	—
400	D₄	—	6	2	no	—
401	D₄	—	6	2	no	—
402	D₄	—	6	2	no	—
403	D₄	—	6	1	no	—
404	D₄	—	6	2	no	—
405	D₄	—	12	1	no	—
406	D₄	—	12	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	6	1	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	6	2	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×D₃×D₄	1	1	yes	characteristic
414	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
415	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
416	C₂×C₄	C₅×#239	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	C₅×#386	1	1	yes	characteristic
425	D₃	—	4	2	no	—
426	D₃	—	8	2	no	—
427	C₅	#69038	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	4	1	no	—
429	C₂²	—	6	2	no	—
430	C₂²	—	12	2	no	—
431	C₂²	—	24	1	no	—
432	C₂²	—	24	2	no	—
433	C₂²	—	24	2	no	—
434	C₂²	—	24	2	no	—
435	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
436	C₂²	C₅×#884	1	1	yes	characteristic
437	C₂²	C₅×#894	1	1	yes	characteristic
438	C₄	—	6	2	no	—
439	C₄	—	8	1	no	—
440	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
441	C₄	C₅×#882	1	1	yes	characteristic
442	C₄	C₅×#893	1	1	yes	characteristic
443	C₄	C₅×#895	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	—	12	2	no	—
449	C₂	—	24	2	no	—
450	C₂	C₅×#4665	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#4665
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#344	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₅×#908	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₅×#344	D₃
hypocenter	C₃	C₅×#1903
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#344

Complements

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

N	H ≅ G/N	type
2. C₅×#5745	C₂	semidirect
3. C₂×C₅×#823	C₂	semidirect
4. C₅×#5005	C₂	semidirect
5. C₅×#5001	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₅×C₃⋊#338	C₂	semidirect
20. C₂×C₅×D₂₄	C₄	semidirect
21. C₂×C₅×#204	C₄	semidirect
26. #69038	C₅	direct (N × H)
32. C₅×#344	D₃	semidirect
70. #5745	C₂×C₅	semidirect
71. C₂×#823	C₂×C₅	semidirect
72. #5005	C₂×C₅	semidirect
73. #5001	C₂×C₅	semidirect
74. C₃×#344	C₂×C₅	semidirect
75. C₃⋊#338	C₂×C₅	semidirect
135. C₂×D₂₄	C₄×C₅	semidirect
136. C₂×#204	C₄×C₅	semidirect
181. #344	C₅×D₃	semidirect
368. C₃×C₅	#1903	semidirect
427. C₅	#69038	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
C₂×C₅×#908	2
C₅×#5745	2
C₂×C₅×#823	2
C₅×#5005	2
C₅×#5001	2
C₃×C₅×#344	2
C₅×C₃⋊#338	2
C₅×#1903	3
#69038	5

Subgroups — C5×#69038 #14302321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69038 #14302321