Subgroups — C₂×C₅×#4752 #14425140

Order 1920.

1416 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×#1007	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#944	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#909	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#101	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#825	C₂	1	2	yes	maximal, complemented
6	C₅×#4752	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#456	—	3	1	no	maximal, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₅×#1007	—	2	2	no	—
10	C₅×#1007	—	2	4	no	—
11	C₅×#1007	C₂²	1	4	yes	—
12	C₂×C₅×#239	—	2	2	no	—
13	C₂×C₅×D₃×Q₈	—	2	2	no	—
14	C₂×C₅×#235	—	2	2	no	—
15	C₂×C₅×#235	C₂²	1	2	yes	—
16	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
18	C₅×#944	—	2	2	no	—
19	C₅×#944	C₂²	1	4	yes	complemented
20	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
21	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
22	C₅×#909	—	2	4	no	—
23	C₅×#909	C₂²	1	8	yes	complemented
24	C₂×C₅×Dic₁₂	—	2	2	no	—
25	C₂×C₅×#204	—	2	2	no	—
26	C₃×C₅×#101	C₂²	1	4	yes	complemented
27	C₅×#825	C₂²	1	8	yes	complemented
28	C₂×#4752	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
29	C₂×C₅×2₋¹⁺⁴	—	3	1	no	—
30	C₂×C₅×#137	—	3	2	no	—
31	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
32	C₅×#456	—	3	8	no	—
33	C₂×C₅×#104	—	3	2	no	—
34	C₂×C₅×#101	D₃	1	1	yes	characteristic, complemented
35	C₂×C₃×C₅×Q₈	—	2	2	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
38	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
39	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂×C₅×#67	—	2	2	no	—
42	C₂²×C₅×Dic₃	—	2	1	no	—
43	C₂²×C₅×Dic₃	—	2	1	no	—
44	C₅×#239	—	2	8	no	—
45	C₅×#239	—	2	8	no	—
46	C₅×D₃×Q₈	—	2	8	no	—
47	C₅×D₃×Q₈	—	2	8	no	—
48	C₅×#235	—	2	8	no	—
49	C₅×#235	—	2	8	no	—
50	C₅×#235	—	2	2	no	—
51	C₅×#235	—	2	2	no	—
52	C₅×#235	D₄	1	4	yes	—
53	C₅×#235	C₂³	1	4	yes	—
54	C₂×C₅×D₁₂	—	2	2	no	—
55	C₂×C₅×D₁₂	D₄	1	2	yes	—
56	C₂×C₄×C₅×D₃	—	2	4	no	—
57	C₂×C₄×C₅×D₃	—	2	2	no	—
58	C₂×C₅×Dic₆	—	2	2	no	—
59	C₂×C₅×Dic₆	—	2	2	no	—
60	C₂×C₅×Dic₆	—	2	2	no	—
61	C₂×C₅×Dic₆	—	2	1	no	—
62	C₂×C₅×Dic₆	D₄	1	2	yes	—
63	C₂×C₅×Dic₆	C₂³	1	2	yes	—
64	C₃×C₅×M₁₆	—	2	2	no	—
65	C₃×C₅×M₁₆	C₂³	1	4	yes	—
66	C₂×C₃×C₅×C₈	—	2	2	no	—
67	C₅×Dic₃⋊C₄	—	2	8	no	—
68	C₄×C₅×Dic₃	—	2	1	no	—
69	C₄×C₅×Dic₃	C₂³	1	2	yes	—
70	C₅×Dic₁₂	—	2	8	no	—
71	C₅×#204	—	2	8	no	—
72	C₂×#1007	C₂×C₅	1	1	yes	characteristic
73	C₂×#944	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#909	C₂×C₅	1	2	yes	complemented
75	C₂×C₃×#101	C₂×C₅	1	1	yes	characteristic, complemented
76	C₂×#825	C₂×C₅	1	2	yes	complemented
77	#4752	C₂×C₅	1	8	yes	direct product factor
78	C₅×2₋¹⁺⁴	—	3	4	no	—
79	C₅×2₋¹⁺⁴	—	6	4	no	—
80	C₅×2₋¹⁺⁴	—	6	2	no	—
81	C₂×C₅×#41	—	3	2	no	—
82	C₂×C₅×#41	—	6	2	no	—
83	C₂×C₅×#41	—	6	2	no	—
84	C₂²×C₅×Q₈	—	3	1	no	—
85	C₂²×C₅×Q₈	—	6	2	no	—
86	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
87	C₅×#137	—	3	8	no	—
88	C₅×#137	—	6	4	no	—
89	C₂×C₅×Q₁₆	—	6	2	no	—
90	C₂×C₅×SD₁₆	—	6	2	no	—
91	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
92	C₅×C₄⋊Q₈	—	3	4	no	—
93	C₅×C₄⋊Q₈	—	6	2	no	—
94	C₂×C₅×C₄⋊C₄	—	6	2	no	—
95	C₂×C₄²×C₅	—	3	1	no	—
96	C₅×#104	—	3	8	no	—
97	C₅×#101	C₂×D₃	1	4	yes	complemented
98	C₂×#456	—	3	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₃×C₅×Q₈	—	2	4	no	—
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₅×#67	—	2	4	no	—
111	C₅×#67	—	2	4	no	—
112	C₂×C₅×Dic₃	—	2	4	no	—
113	C₂×C₅×Dic₃	—	2	2	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	4	1	no	—
117	C₂×C₅×Dic₃	—	4	1	no	—
118	C₅×D₁₂	—	2	8	no	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	C₂×D₄	1	4	yes	—
121	C₄×C₅×D₃	—	2	16	no	—
122	C₄×C₅×D₃	—	2	4	no	—
123	C₄×C₅×D₃	—	2	4	no	—
124	C₅×Dic₆	—	2	8	no	—
125	C₅×Dic₆	—	2	2	no	—
126	C₅×Dic₆	—	2	4	no	—
127	C₅×Dic₆	—	4	2	no	—
128	C₅×Dic₆	C₂×D₄	1	4	yes	—
129	C₃×C₅×C₈	—	2	4	no	—
130	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
131	#1007	—	2	2	no	—
132	#1007	—	2	4	no	—
133	#1007	C₂²×C₅	1	4	yes	—
134	C₂×#239	—	2	2	no	—
135	C₂×D₃×Q₈	—	2	2	no	—
136	C₂×#235	—	2	2	no	—
137	C₂×#235	C₂²×C₅	1	2	yes	—
138	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
139	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
140	#944	—	2	2	no	—
141	#944	C₂²×C₅	1	4	yes	complemented
142	C₂×Dic₃⋊C₄	—	2	2	no	—
143	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
144	#909	—	2	4	no	—
145	#909	C₂²×C₅	1	8	yes	complemented
146	C₂×Dic₁₂	—	2	2	no	—
147	C₂×#204	—	2	2	no	—
148	C₃×#101	C₂²×C₅	1	4	yes	complemented
149	#825	C₂²×C₅	1	8	yes	complemented
150	C₅×#41	—	3	4	no	—
151	C₅×#41	—	3	4	no	—
152	C₅×#41	—	6	8	no	—
153	C₅×#41	—	6	8	no	—
154	C₅×#41	—	6	8	no	—
155	C₅×#41	—	6	2	no	—
156	C₅×#41	—	6	8	no	—
157	C₅×#41	—	6	2	no	—
158	C₂×C₅×Q₈	—	2	2	no	—
159	C₂×C₅×Q₈	—	2	2	no	—
160	C₂×C₅×Q₈	—	3	2	no	—
161	C₂×C₅×Q₈	—	3	2	no	—
162	C₂×C₅×Q₈	—	6	2	no	—
163	C₂×C₅×Q₈	—	6	8	no	—
164	C₂×C₅×Q₈	—	6	8	no	—
165	C₂×C₅×Q₈	—	6	1	no	—
166	C₂×C₅×Q₈	—	6	2	no	—
167	C₂×C₅×Q₈	—	6	2	no	—
168	C₂×C₅×Q₈	D₁₂	1	2	yes	—
169	C₂×C₅×Q₈	C₂²×D₃	1	2	yes	—
170	C₂×C₅×D₄	—	3	2	no	—
171	C₂×C₅×D₄	—	6	2	no	—
172	C₂×C₅×D₄	—	6	2	no	—
173	C₂²×C₄×C₅	—	6	4	no	—
174	C₂²×C₄×C₅	—	6	1	no	—
175	C₂²×C₄×C₅	—	6	2	no	—
176	C₂²×C₄×C₅	—	6	1	no	—
177	C₂²×C₄×C₅	D₁₂	1	2	yes	—
178	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₅×Q₁₆	—	6	8	no	—
180	C₅×SD₁₆	—	6	8	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₅×M₁₆	C₂²×D₃	1	4	yes	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₅×C₄⋊C₄	—	6	8	no	—
185	C₄²×C₅	—	3	2	no	—
186	C₄²×C₅	—	6	1	no	—
187	C₂×2₋¹⁺⁴	—	3	1	no	—
188	C₂×#137	—	3	2	no	—
189	C₂×C₄⋊Q₈	—	3	1	no	—
190	#456	—	3	8	no	—
191	C₂×#104	—	3	2	no	—
192	C₂×#101	C₅×D₃	1	1	yes	characteristic, complemented
193	C₂²×C₃×C₅	—	2	2	no	—
194	C₂²×C₃×C₅	#120	1	1	yes	characteristic
195	C₂²×C₃×C₅	#120	1	1	yes	characteristic
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₅×D₃	—	2	4	no	—
198	C₂×C₅×D₃	—	4	4	no	—
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	#120	1	2	yes	—
201	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
202	C₅×Dic₃	—	2	4	no	—
203	C₅×Dic₃	—	2	4	no	—
204	C₅×Dic₃	—	4	2	no	—
205	C₂×C₃×Q₈	—	2	2	no	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
208	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
211	C₂×#67	—	2	2	no	—
212	C₂²×Dic₃	—	2	1	no	—
213	C₂²×Dic₃	—	2	1	no	—
214	#239	—	2	8	no	—
215	#239	—	2	8	no	—
216	D₃×Q₈	—	2	8	no	—
217	D₃×Q₈	—	2	8	no	—
218	#235	—	2	8	no	—
219	#235	—	2	8	no	—
220	#235	—	2	2	no	—
221	#235	—	2	2	no	—
222	#235	C₅×D₄	1	4	yes	—
223	#235	C₂³×C₅	1	4	yes	—
224	C₂×D₁₂	—	2	2	no	—
225	C₂×D₁₂	C₅×D₄	1	2	yes	—
226	C₂×C₄×D₃	—	2	4	no	—
227	C₂×C₄×D₃	—	2	2	no	—
228	C₂×Dic₆	—	2	2	no	—
229	C₂×Dic₆	—	2	2	no	—
230	C₂×Dic₆	—	2	2	no	—
231	C₂×Dic₆	—	2	1	no	—
232	C₂×Dic₆	C₅×D₄	1	2	yes	—
233	C₂×Dic₆	C₂³×C₅	1	2	yes	—
234	C₃×M₁₆	—	2	2	no	—
235	C₃×M₁₆	C₂³×C₅	1	4	yes	—
236	C₂×C₃×C₈	—	2	2	no	—
237	Dic₃⋊C₄	—	2	8	no	—
238	C₄×Dic₃	—	2	1	no	—
239	C₄×Dic₃	C₂³×C₅	1	2	yes	—
240	Dic₁₂	—	2	8	no	—
241	#204	—	2	8	no	—
242	C₂³×C₅	—	6	2	no	—
243	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
244	C₅×Q₈	—	2	4	no	—
245	C₅×Q₈	—	2	4	no	—
246	C₅×Q₈	—	3	4	no	—
247	C₅×Q₈	—	6	8	no	—
248	C₅×Q₈	—	6	2	no	—
249	C₅×Q₈	—	6	4	no	—
250	C₅×Q₈	—	12	2	no	—
251	C₅×D₄	—	3	4	no	—
252	C₅×D₄	—	6	8	no	—
253	C₅×D₄	—	6	4	no	—
254	C₅×D₄	—	6	4	no	—
255	C₅×D₄	—	6	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	6	16	no	—
259	C₂×C₄×C₅	—	6	4	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	6	2	no	—
262	C₂×C₄×C₅	—	6	4	no	—
263	C₂×C₄×C₅	—	6	4	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	12	1	no	—
266	C₂×C₄×C₅	—	12	1	no	—
267	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
268	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
269	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₅×C₈	—	2	4	no	—
273	2₋¹⁺⁴	—	3	4	no	—
274	2₋¹⁺⁴	—	6	4	no	—
275	2₋¹⁺⁴	—	6	2	no	—
276	C₂×#41	—	3	2	no	—
277	C₂×#41	—	6	2	no	—
278	C₂×#41	—	6	2	no	—
279	C₂²×Q₈	—	3	1	no	—
280	C₂²×Q₈	—	6	2	no	—
281	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
282	#137	—	3	8	no	—
283	#137	—	6	4	no	—
284	C₂×Q₁₆	—	6	2	no	—
285	C₂×SD₁₆	—	6	2	no	—
286	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
287	C₄⋊Q₈	—	3	4	no	—
288	C₄⋊Q₈	—	6	2	no	—
289	C₂×C₄⋊C₄	—	6	2	no	—
290	C₂×C₄²	—	3	1	no	—
291	#104	—	3	8	no	—
292	#101	C₂×C₅×D₃	1	4	yes	complemented
293	C₂×C₃×C₅	—	2	1	no	—
294	C₂×C₃×C₅	—	2	1	no	—
295	C₂×C₃×C₅	#456	1	2	yes	complemented
296	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
297	C₅×D₃	—	4	4	no	—
298	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂²×D₃	—	2	2	no	—
300	C₃×Q₈	—	2	4	no	—
301	C₃×Q₈	—	2	4	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
308	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
309	#67	—	2	4	no	—
310	#67	—	2	4	no	—
311	C₂×Dic₃	—	2	4	no	—
312	C₂×Dic₃	—	2	2	no	—
313	C₂×Dic₃	—	2	2	no	—
314	C₂×Dic₃	—	2	2	no	—
315	C₂×Dic₃	—	4	1	no	—
316	C₂×Dic₃	—	4	1	no	—
317	D₁₂	—	2	8	no	—
318	D₁₂	—	2	2	no	—
319	D₁₂	C₂×C₅×D₄	1	4	yes	—
320	C₄×D₃	—	2	16	no	—
321	C₄×D₃	—	2	4	no	—
322	C₄×D₃	—	2	4	no	—
323	Dic₆	—	2	8	no	—
324	Dic₆	—	2	2	no	—
325	Dic₆	—	2	4	no	—
326	Dic₆	—	4	2	no	—
327	Dic₆	C₂×C₅×D₄	1	4	yes	—
328	C₃×C₈	—	2	4	no	—
329	C₂²×C₅	—	2	2	no	—
330	C₂²×C₅	—	6	4	no	—
331	C₂²×C₅	—	12	4	no	—
332	C₂²×C₅	#882	1	1	yes	characteristic
333	C₂²×C₅	#882	1	1	yes	characteristic
334	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
335	C₄×C₅	—	2	4	no	—
336	C₄×C₅	—	6	4	no	—
337	C₄×C₅	—	6	4	no	—
338	C₄×C₅	—	12	2	no	—
339	C₄×C₅	#882	1	2	yes	—
340	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
341	#41	—	3	4	no	—
342	#41	—	3	4	no	—
343	#41	—	6	8	no	—
344	#41	—	6	8	no	—
345	#41	—	6	8	no	—
346	#41	—	6	2	no	—
347	#41	—	6	8	no	—
348	#41	—	6	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	3	2	no	—
352	C₂×Q₈	—	3	2	no	—
353	C₂×Q₈	—	6	2	no	—
354	C₂×Q₈	—	6	8	no	—
355	C₂×Q₈	—	6	8	no	—
356	C₂×Q₈	—	6	1	no	—
357	C₂×Q₈	—	6	2	no	—
358	C₂×Q₈	—	6	2	no	—
359	C₂×Q₈	C₅×D₁₂	1	2	yes	—
360	C₂×Q₈	C₂²×C₅×D₃	1	2	yes	—
361	C₂×D₄	—	3	2	no	—
362	C₂×D₄	—	6	2	no	—
363	C₂×D₄	—	6	2	no	—
364	C₂²×C₄	—	6	4	no	—
365	C₂²×C₄	—	6	1	no	—
366	C₂²×C₄	—	6	2	no	—
367	C₂²×C₄	—	6	1	no	—
368	C₂²×C₄	C₅×D₁₂	1	2	yes	—
369	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
370	Q₁₆	—	6	8	no	—
371	SD₁₆	—	6	8	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	C₂²×C₅×D₃	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₄⋊C₄	—	6	8	no	—
376	C₄²	—	3	2	no	—
377	C₄²	—	6	1	no	—
378	C₃×C₅	C₂×#456	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	C₅×#120	1	1	yes	characteristic
381	C₂²×C₃	C₅×#120	1	1	yes	characteristic
382	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
383	C₂×D₃	—	2	4	no	—
384	C₂×D₃	—	4	4	no	—
385	C₃×C₄	—	2	4	no	—
386	C₃×C₄	C₅×#120	1	2	yes	—
387	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
388	Dic₃	—	2	4	no	—
389	Dic₃	—	2	4	no	—
390	Dic₃	—	4	2	no	—
391	C₂×C₅	—	2	1	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	12	4	no	—
394	C₂×C₅	#4752	1	2	yes	direct product factor
395	C₂×C₅	C₂×#882	1	1	yes	characteristic
396	C₂³	—	6	2	no	—
397	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	4	no	—
400	Q₈	—	3	4	no	—
401	Q₈	—	6	8	no	—
402	Q₈	—	6	2	no	—
403	Q₈	—	6	4	no	—
404	Q₈	—	12	2	no	—
405	D₄	—	3	4	no	—
406	D₄	—	6	8	no	—
407	D₄	—	6	4	no	—
408	D₄	—	6	4	no	—
409	D₄	—	6	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	6	16	no	—
413	C₂×C₄	—	6	4	no	—
414	C₂×C₄	—	6	2	no	—
415	C₂×C₄	—	6	2	no	—
416	C₂×C₄	—	6	4	no	—
417	C₂×C₄	—	6	4	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	12	1	no	—
420	C₂×C₄	—	12	1	no	—
421	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
422	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
423	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
424	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
425	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₂×C₃	—	2	1	no	—
428	C₂×C₃	—	2	1	no	—
429	C₂×C₃	C₅×#456	1	2	yes	complemented
430	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
431	D₃	—	4	4	no	—
432	C₅	C₂×#4752	1	1	yes	characteristic, direct product factor, Sylow
433	C₂²	—	2	2	no	—
434	C₂²	—	6	4	no	—
435	C₂²	—	12	4	no	—
436	C₂²	C₅×#882	1	1	yes	characteristic
437	C₂²	C₅×#882	1	1	yes	characteristic
438	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	6	4	no	—
441	C₄	—	6	4	no	—
442	C₄	—	12	2	no	—
443	C₄	C₅×#882	1	2	yes	—
444	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
445	C₃	C₂×C₅×#456	1	1	yes	characteristic, complemented, Sylow
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	12	4	no	—
449	C₂	C₅×#4752	1	2	yes	direct product factor
450	C₂	C₂×C₅×#882	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#882
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#101	C₂
socle	C₂²×C₃×C₅	#120
prime radical	C₂×C₅×#1007	C₂
hypercenter	C₂×C₅×#101	D₃
hypocenter	C₃	C₂×C₅×#456
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#101

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#944	C₂	semidirect
3. C₂×C₅×#909	C₂	semidirect
4. C₂×C₃×C₅×#101	C₂	semidirect
5. C₂×C₅×#825	C₂	semidirect
6. C₅×#4752	C₂	direct (N × H)
19. C₅×#944	C₂²	semidirect
23. C₅×#909	C₂²	semidirect
26. C₃×C₅×#101	C₂²	semidirect
27. C₅×#825	C₂²	semidirect
28. C₂×#4752	C₅	direct (N × H)
34. C₂×C₅×#101	D₃	semidirect
73. C₂×#944	C₂×C₅	semidirect
74. C₂×#909	C₂×C₅	semidirect
75. C₂×C₃×#101	C₂×C₅	semidirect
76. C₂×#825	C₂×C₅	semidirect
77. #4752	C₂×C₅	direct (N × H)
97. C₅×#101	C₂×D₃	semidirect
141. #944	C₂²×C₅	semidirect
145. #909	C₂²×C₅	semidirect
148. C₃×#101	C₂²×C₅	semidirect
149. #825	C₂²×C₅	semidirect
192. C₂×#101	C₅×D₃	semidirect
292. #101	C₂×C₅×D₃	semidirect
295. C₂×C₃×C₅	#456	semidirect
378. C₃×C₅	C₂×#456	semidirect
394. C₂×C₅	#4752	direct (N × H)
429. C₂×C₃	C₅×#456	semidirect
432. C₅	C₂×#4752	direct (N × H)
445. C₃	C₂×C₅×#456	semidirect
449. C₂	C₅×#4752	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#1007	2
C₂×C₅×#944	2
C₂×C₅×#909	2
C₂×C₃×C₅×#101	2
C₂×C₅×#825	2
C₅×#4752	2
C₂×C₅×#456	3
C₂×#4752	5

Subgroups — C2×C5×#4752 #14425140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4752 #14425140