Subgroups — C₅×#69027 #14302400

Order 1920.

692 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	C₂×C₅×#908	C₂	1	1	yes	maximal, characteristic
2	C₅×#5521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5139	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5131	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5006	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4557	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1904	—	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	C₅×#926	C₂²	1	1	yes	characteristic
15	C₅×#926	C₂²	1	1	yes	characteristic
16	C₅×#908	—	2	2	no	—
17	C₅×#908	—	2	2	no	—
18	C₂×C₅×D₂₄	C₄	1	2	yes	complemented
19	C₂×C₅×#204	C₄	1	2	yes	complemented
20	C₅×#893	—	2	2	no	—
21	C₅×D₃×C₂²⋊C₄	—	2	2	no	—
22	C₄×C₅×D₁₂	—	2	2	no	—
23	C₅×#825	—	2	2	no	—
24	C₅×#821	—	2	2	no	—
25	C₅×#806	—	2	2	no	—
26	#69027	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
28	C₅×#518	—	3	1	no	—
29	C₅×#421	—	3	1	no	—
30	C₅×#418	—	3	1	no	—
31	C₅×#410	—	3	1	no	—
32	C₅×#344	D₃	1	1	yes	characteristic, complemented
33	C₅×H(3,ℤ/4)	—	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	—	2	1	no	—
40	C₅×#235	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
45	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic, complemented
46	C₂×C₅×D₁₂	D₄	1	2	yes	—
47	C₂×C₅×D₁₂	D₄	1	2	yes	—
48	C₂×C₄×C₅×D₃	—	2	1	no	—
49	C₂×C₄×C₅×D₃	—	2	4	no	—
50	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic, complemented
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	—	2	1	no	—
55	C₂×C₃×C₅×C₈	—	2	1	no	—
56	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	complemented
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
59	C₃×C₄²×C₅	—	2	1	no	—
60	C₅×#217	—	2	1	no	—
61	C₅×#217	—	2	1	no	—
62	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
63	C₅×C₄⋊Dic₃	—	2	1	no	—
64	C₅×C₄⋊Dic₃	—	2	1	no	—
65	C₄×C₅×Dic₃	—	2	1	no	—
66	C₄×C₅×Dic₃	D₄	1	2	yes	—
67	C₅×D₂₄	—	2	4	no	—
68	C₅×#204	—	2	4	no	—
69	C₂×#908	C₂×C₅	1	1	yes	characteristic
70	#5521	C₂×C₅	1	1	yes	characteristic, complemented
71	#5139	C₂×C₅	1	1	yes	characteristic, complemented
72	#5131	C₂×C₅	1	1	yes	characteristic, complemented
73	#5006	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#344	C₂×C₅	1	1	yes	characteristic, complemented
75	#4557	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	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
83	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
84	C₄×C₅×D₄	—	6	2	no	—
85	C₄×C₅×D₄	—	6	2	no	—
86	C₅×#117	—	3	1	no	—
87	C₅×#117	—	3	1	no	—
88	C₅×#117	C₂×D₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
90	C₅×#104	—	6	2	no	—
91	C₅×#102	—	6	2	no	—
92	C₅×#99	—	6	2	no	—
93	#1904	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	2	2	no	—
96	C₂²×C₅×D₃	—	2	2	no	—
97	C₂²×C₅×D₃	—	2	2	no	—
98	C₂²×C₅×D₃	—	2	1	no	—
99	C₂²×C₅×D₃	—	8	2	no	—
100	C₂×C₃×C₄×C₅	—	2	2	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	#41	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
107	C₅×#67	—	4	1	no	—
108	C₅×#67	—	4	1	no	—
109	C₂×C₅×Dic₃	—	2	1	no	—
110	C₂×C₅×Dic₃	—	2	2	no	—
111	C₂×C₅×Dic₃	—	4	1	no	—
112	C₅×D₁₂	—	2	1	no	—
113	C₅×D₁₂	—	2	2	no	—
114	C₅×D₁₂	—	2	1	no	—
115	C₅×D₁₂	—	2	2	no	—
116	C₅×D₁₂	—	2	2	no	—
117	C₅×D₁₂	C₂²⋊C₄	1	4	yes	—
118	C₄×C₅×D₃	—	4	1	no	—
119	C₄×C₅×D₃	—	4	1	no	—
120	C₄×C₅×D₃	—	8	4	no	—
121	C₅×Dic₆	—	2	1	no	—
122	C₅×Dic₆	—	2	1	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃×C₅×C₈	—	4	1	no	—
125	C₂×#235	C₂²×C₅	1	1	yes	characteristic
126	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
127	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
128	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
129	C₃×#117	C₂²×C₅	1	1	yes	characteristic
130	#926	C₂²×C₅	1	1	yes	characteristic
131	#926	C₂²×C₅	1	1	yes	characteristic
132	#908	—	2	2	no	—
133	#908	—	2	2	no	—
134	C₂×D₂₄	C₄×C₅	1	2	yes	complemented
135	C₂×#204	C₄×C₅	1	2	yes	complemented
136	#893	—	2	2	no	—
137	D₃×C₂²⋊C₄	—	2	2	no	—
138	C₄×D₁₂	—	2	2	no	—
139	#825	—	2	2	no	—
140	#821	—	2	2	no	—
141	#806	—	2	2	no	—
142	C₂⁴×C₅	—	6	1	no	—
143	C₅×#41	—	6	1	no	—
144	C₅×#41	—	6	1	no	—
145	C₅×#41	—	6	1	no	—
146	C₅×#41	—	6	1	no	—
147	C₂×C₅×Q₈	—	3	1	no	—
148	C₂×C₅×D₄	—	3	2	no	—
149	C₂×C₅×D₄	—	3	1	no	—
150	C₂×C₅×D₄	—	3	2	no	—
151	C₂×C₅×D₄	—	3	2	no	—
152	C₂×C₅×D₄	—	6	1	no	—
153	C₂×C₅×D₄	—	6	1	no	—
154	C₂×C₅×D₄	—	6	1	no	—
155	C₂×C₅×D₄	—	6	1	no	—
156	C₂²×C₄×C₅	—	6	4	no	—
157	C₂²×C₄×C₅	—	6	1	no	—
158	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
159	C₅×SD₁₆	—	6	4	no	—
160	C₅×D₈	—	6	4	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	2	1	no	—
163	C₅×M₁₆	—	2	1	no	—
164	C₅×M₁₆	—	2	1	no	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	C₄×D₃	1	2	yes	complemented
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	6	1	no	—
169	C₅×C₄⋊C₄	—	6	1	no	—
170	C₅×C₂²⋊C₄	—	6	4	no	—
171	C₅×C₂²⋊C₄	—	6	1	no	—
172	C₅×C₂²⋊C₄	—	6	1	no	—
173	C₅×C₂²⋊C₄	D₁₂	1	2	yes	—
174	C₄²×C₅	—	2	1	no	—
175	C₄²×C₅	—	3	2	no	—
176	C₄²×C₅	—	6	1	no	—
177	C₂×AGL(1,ℤ/8)	—	3	1	no	—
178	#518	—	3	1	no	—
179	#421	—	3	1	no	—
180	#418	—	3	1	no	—
181	#410	—	3	1	no	—
182	#344	C₅×D₃	1	1	yes	characteristic, complemented
183	H(3,ℤ/4)	—	3	1	no	—
184	C₂²×C₃×C₅	—	4	1	no	—
185	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	#120	1	1	yes	characteristic
187	C₂²×C₃×C₅	#121	1	1	yes	characteristic
188	C₂×C₅×D₃	—	2	4	no	—
189	C₂×C₅×D₃	—	4	4	no	—
190	C₂×C₅×D₃	—	4	1	no	—
191	C₂×C₅×D₃	—	8	2	no	—
192	C₂×C₅×D₃	—	8	2	no	—
193	C₂×C₅×D₃	—	8	1	no	—
194	C₃×C₄×C₅	—	4	2	no	—
195	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	#121	1	1	yes	characteristic
198	C₃×C₄×C₅	#123	1	1	yes	characteristic
199	C₅×Dic₃	—	4	2	no	—
200	C₅×Dic₃	—	4	1	no	—
201	C₅×Dic₃	—	8	1	no	—
202	C₂³×D₃	—	2	1	no	—
203	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂×#67	—	2	1	no	—
205	#235	—	2	1	no	—
206	#235	—	2	1	no	—
207	#235	—	2	1	no	—
208	#235	—	2	1	no	—
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	—	2	1	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	C₂×C₄×C₅	1	2	yes	—
213	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic, complemented
214	C₂×D₁₂	C₅×D₄	1	2	yes	—
215	C₂×D₁₂	C₅×D₄	1	2	yes	—
216	C₂×C₄×D₃	—	2	1	no	—
217	C₂×C₄×D₃	—	2	4	no	—
218	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
219	C₃×M₁₆	—	2	1	no	—
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	2	1	no	—
222	C₃×M₁₆	—	2	1	no	—
223	C₂×C₃×C₈	—	2	1	no	—
224	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	complemented
225	C₃×C₄⋊C₄	—	2	1	no	—
226	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
227	C₃×C₄²	—	2	1	no	—
228	#217	—	2	1	no	—
229	#217	—	2	1	no	—
230	(C₂×D₃)⋊C₄	—	2	4	no	—
231	C₄⋊Dic₃	—	2	1	no	—
232	C₄⋊Dic₃	—	2	1	no	—
233	C₄×Dic₃	—	2	1	no	—
234	C₄×Dic₃	C₅×D₄	1	2	yes	—
235	D₂₄	—	2	4	no	—
236	#204	—	2	4	no	—
237	C₂³×C₅	—	6	2	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	—	6	2	no	—
240	C₂³×C₅	—	6	1	no	—
241	C₂³×C₅	—	24	2	no	—
242	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
243	C₅×Q₈	—	6	1	no	—
244	C₅×Q₈	—	6	1	no	—
245	C₅×D₄	—	3	4	no	—
246	C₅×D₄	—	6	1	no	—
247	C₅×D₄	—	6	2	no	—
248	C₅×D₄	—	6	2	no	—
249	C₅×D₄	—	6	1	no	—
250	C₅×D₄	—	6	2	no	—
251	C₅×D₄	—	12	1	no	—
252	C₅×D₄	—	12	1	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	6	1	no	—
255	C₂×C₄×C₅	—	6	2	no	—
256	C₂×C₄×C₅	—	12	1	no	—
257	C₂×C₄×C₅	—	12	1	no	—
258	C₂×C₄×C₅	—	12	1	no	—
259	C₂×C₄×C₅	—	24	4	no	—
260	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂×C₄×C₅	#235	1	1	yes	characteristic
262	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
265	C₂×C₄×C₅	#239	1	1	yes	characteristic
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	4	1	no	—
268	C₂×#41	—	3	1	no	—
269	C₂²×D₄	—	3	1	no	—
270	AGL(1,ℤ/8)	—	6	2	no	—
271	AGL(1,ℤ/8)	—	6	2	no	—
272	C₂×SD₁₆	—	3	2	no	—
273	C₂×D₈	—	3	2	no	—
274	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
275	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
276	C₄×D₄	—	6	2	no	—
277	C₄×D₄	—	6	2	no	—
278	#117	—	3	1	no	—
279	#117	—	3	1	no	—
280	#117	C₂×C₅×D₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	6	2	no	—
282	#104	—	6	2	no	—
283	#102	—	6	2	no	—
284	#99	—	6	2	no	—
285	C₂×C₃×C₅	—	2	1	no	—
286	C₂×C₃×C₅	—	2	1	no	—
287	C₂×C₃×C₅	—	2	1	no	—
288	C₂×C₃×C₅	#386	1	1	yes	characteristic
289	C₅×D₃	—	4	4	no	—
290	C₅×D₃	—	8	1	no	—
291	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	—	2	2	no	—
295	C₂²×D₃	—	2	1	no	—
296	C₂²×D₃	—	8	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
303	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
304	#67	—	4	1	no	—
305	#67	—	4	1	no	—
306	C₂×Dic₃	—	2	1	no	—
307	C₂×Dic₃	—	2	2	no	—
308	C₂×Dic₃	—	4	1	no	—
309	D₁₂	—	2	1	no	—
310	D₁₂	—	2	2	no	—
311	D₁₂	—	2	1	no	—
312	D₁₂	—	2	2	no	—
313	D₁₂	—	2	2	no	—
314	D₁₂	C₅×C₂²⋊C₄	1	4	yes	—
315	C₄×D₃	—	4	1	no	—
316	C₄×D₃	—	4	1	no	—
317	C₄×D₃	—	8	4	no	—
318	Dic₆	—	2	1	no	—
319	Dic₆	—	2	1	no	—
320	C₃×C₈	—	2	2	no	—
321	C₃×C₈	—	4	1	no	—
322	C₂²×C₅	—	4	1	no	—
323	C₂²×C₅	—	6	4	no	—
324	C₂²×C₅	—	12	4	no	—
325	C₂²×C₅	—	12	1	no	—
326	C₂²×C₅	—	24	2	no	—
327	C₂²×C₅	—	24	2	no	—
328	C₂²×C₅	—	24	1	no	—
329	C₂²×C₅	C₄×D₁₂	1	1	yes	characteristic
330	C₂²×C₅	#882	1	1	yes	characteristic
331	C₂²×C₅	#895	1	1	yes	characteristic
332	C₄×C₅	—	4	2	no	—
333	C₄×C₅	—	12	2	no	—
334	C₄×C₅	—	12	1	no	—
335	C₄×C₅	—	24	1	no	—
336	C₄×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
337	C₄×C₅	#884	1	1	yes	characteristic
338	C₄×C₅	#893	1	1	yes	characteristic
339	C₄×C₅	#894	1	1	yes	characteristic
340	C₂⁴	—	6	1	no	—
341	#41	—	6	1	no	—
342	#41	—	6	1	no	—
343	#41	—	6	1	no	—
344	#41	—	6	1	no	—
345	C₂×Q₈	—	3	1	no	—
346	C₂×D₄	—	3	2	no	—
347	C₂×D₄	—	3	1	no	—
348	C₂×D₄	—	3	2	no	—
349	C₂×D₄	—	3	2	no	—
350	C₂×D₄	—	6	1	no	—
351	C₂×D₄	—	6	1	no	—
352	C₂×D₄	—	6	1	no	—
353	C₂×D₄	—	6	1	no	—
354	C₂²×C₄	—	6	4	no	—
355	C₂²×C₄	—	6	1	no	—
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	SD₁₆	—	6	4	no	—
358	D₈	—	6	4	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	1	no	—
362	M₁₆	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	C₄×C₅×D₃	1	2	yes	complemented
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	6	1	no	—
367	C₄⋊C₄	—	6	1	no	—
368	C₂²⋊C₄	—	6	4	no	—
369	C₂²⋊C₄	—	6	1	no	—
370	C₂²⋊C₄	—	6	1	no	—
371	C₂²⋊C₄	C₅×D₁₂	1	2	yes	—
372	C₄²	—	2	1	no	—
373	C₄²	—	3	2	no	—
374	C₄²	—	6	1	no	—
375	C₃×C₅	#1904	1	1	yes	characteristic, complemented, Hall
376	C₂²×C₃	—	4	1	no	—
377	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
378	C₂²×C₃	C₅×#120	1	1	yes	characteristic
379	C₂²×C₃	C₅×#121	1	1	yes	characteristic
380	C₂×D₃	—	2	4	no	—
381	C₂×D₃	—	4	4	no	—
382	C₂×D₃	—	4	1	no	—
383	C₂×D₃	—	8	2	no	—
384	C₂×D₃	—	8	2	no	—
385	C₂×D₃	—	8	1	no	—
386	C₃×C₄	—	4	2	no	—
387	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
388	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
389	C₃×C₄	C₅×#121	1	1	yes	characteristic
390	C₃×C₄	C₅×#123	1	1	yes	characteristic
391	Dic₃	—	4	2	no	—
392	Dic₃	—	4	1	no	—
393	Dic₃	—	8	1	no	—
394	C₂×C₅	—	2	1	no	—
395	C₂×C₅	—	2	1	no	—
396	C₂×C₅	—	2	1	no	—
397	C₂×C₅	—	12	4	no	—
398	C₂×C₅	—	24	1	no	—
399	C₂×C₅	#4665	1	1	yes	characteristic
400	C₂³	—	6	2	no	—
401	C₂³	—	6	2	no	—
402	C₂³	—	6	2	no	—
403	C₂³	—	6	1	no	—
404	C₂³	—	24	2	no	—
405	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
406	Q₈	—	6	1	no	—
407	Q₈	—	6	1	no	—
408	D₄	—	3	4	no	—
409	D₄	—	6	1	no	—
410	D₄	—	6	2	no	—
411	D₄	—	6	2	no	—
412	D₄	—	6	1	no	—
413	D₄	—	6	2	no	—
414	D₄	—	12	1	no	—
415	D₄	—	12	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	6	1	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	12	1	no	—
420	C₂×C₄	—	12	1	no	—
421	C₂×C₄	—	12	1	no	—
422	C₂×C₄	—	24	4	no	—
423	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
424	C₂×C₄	C₅×#235	1	1	yes	characteristic
425	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
426	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
427	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
428	C₂×C₄	C₅×#239	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	4	1	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	C₅×#386	1	1	yes	characteristic
435	D₃	—	4	4	no	—
436	D₃	—	8	1	no	—
437	C₅	#69027	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	4	1	no	—
439	C₂²	—	6	4	no	—
440	C₂²	—	12	4	no	—
441	C₂²	—	12	1	no	—
442	C₂²	—	24	2	no	—
443	C₂²	—	24	2	no	—
444	C₂²	—	24	1	no	—
445	C₂²	C₄×C₅×D₁₂	1	1	yes	characteristic
446	C₂²	C₅×#882	1	1	yes	characteristic
447	C₂²	C₅×#895	1	1	yes	characteristic
448	C₄	—	4	2	no	—
449	C₄	—	12	2	no	—
450	C₄	—	12	1	no	—
451	C₄	—	24	1	no	—
452	C₄	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
453	C₄	C₅×#884	1	1	yes	characteristic
454	C₄	C₅×#893	1	1	yes	characteristic
455	C₄	C₅×#894	1	1	yes	characteristic
456	C₃	C₅×#1904	1	1	yes	characteristic, complemented, Sylow
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	12	4	no	—
461	C₂	—	24	1	no	—
462	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×#1904
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×#5521	C₂	semidirect
3. C₅×#5139	C₂	semidirect
4. C₅×#5131	C₂	semidirect
5. C₅×#5006	C₂	semidirect
6. C₃×C₅×#344	C₂	semidirect
7. C₅×#4557	C₂	semidirect
18. C₂×C₅×D₂₄	C₄	semidirect
19. C₂×C₅×#204	C₄	semidirect
26. #69027	C₅	direct (N × H)
32. C₅×#344	D₃	semidirect
45. C₂×C₅×D₁₂	C₂×C₄	semidirect
50. C₂×C₅×Dic₆	C₂×C₄	semidirect
56. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
70. #5521	C₂×C₅	semidirect
71. #5139	C₂×C₅	semidirect
72. #5131	C₂×C₅	semidirect
73. #5006	C₂×C₅	semidirect
74. C₃×#344	C₂×C₅	semidirect
75. #4557	C₂×C₅	semidirect
134. C₂×D₂₄	C₄×C₅	semidirect
135. C₂×#204	C₄×C₅	semidirect
166. C₂×C₅×C₈	C₄×D₃	semidirect
182. #344	C₅×D₃	semidirect
213. C₂×D₁₂	C₂×C₄×C₅	semidirect
218. C₂×Dic₆	C₂×C₄×C₅	semidirect
224. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
364. C₂×C₈	C₄×C₅×D₃	semidirect
375. C₃×C₅	#1904	semidirect
437. C₅	#69027	direct (N × H)
456. C₃	C₅×#1904	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×#5521	2
C₅×#5139	2
C₅×#5131	2
C₅×#5006	2
C₃×C₅×#344	2
C₅×#4557	2
C₅×#1904	3
#69027	5

Subgroups — C5×#69027 #14302400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69027 #14302400