Subgroups — C₂×C₅×#4748 #14429289

Order 1920.

936 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#214	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#932	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#909	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#907	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#824	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#822	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4748	C₂	1	8	yes	maximal, direct product factor
9	C₂×C₅×#471	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂×C₅×#235	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₅×#214	—	2	1	no	—
16	C₂×C₅×#214	—	2	1	no	—
17	C₂×C₅×#214	—	2	1	no	—
18	C₂×C₅×#214	—	2	2	no	—
19	C₂×C₅×#214	C₂²	1	4	yes	complemented
20	C₅×#932	—	2	2	no	—
21	C₅×#932	C₂²	1	4	yes	—
22	C₂×C₅×#213	—	2	1	no	—
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₅×#909	—	2	2	no	—
26	C₅×#909	C₂²	1	4	yes	complemented
27	C₅×#907	—	2	2	no	—
28	C₅×#907	C₂²	1	4	yes	complemented
29	C₂×C₅×Dic₁₂	—	2	1	no	—
30	C₂×C₅×#204	—	2	1	no	—
31	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
32	C₂×C₅×D₃×C₈	—	2	1	no	—
33	C₃×C₅×#100	C₂²	1	4	yes	complemented
34	C₅×#824	C₂²	1	4	yes	complemented
35	C₅×#822	C₂²	1	4	yes	complemented
36	C₂×#4748	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₂×C₅×#137	—	3	1	no	—
38	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
39	C₂²×C₅×SD₁₆	—	3	1	no	—
40	C₂×C₅×#131	—	3	1	no	—
41	C₅×#471	—	3	8	no	—
42	C₂×C₅×#108	—	3	1	no	—
43	C₂×C₅×#101	—	3	1	no	—
44	C₂×C₅×#100	D₃	1	1	yes	characteristic, complemented
45	C₂⁴×C₃×C₅	—	2	1	no	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	1	no	—
48	C₂×C₃×C₅×D₄	—	2	1	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	2	1	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	2	1	no	—
54	C₂²×C₅×Dic₃	—	2	1	no	—
55	C₅×#235	—	2	1	no	—
56	C₅×#235	—	2	1	no	—
57	C₅×#235	D₄	1	2	yes	—
58	C₅×#235	C₂³	1	2	yes	—
59	C₂×C₅×D₁₂	D₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	1	no	—
61	C₂×C₅×Dic₆	—	2	1	no	—
62	C₂×C₅×Dic₆	—	2	1	no	—
63	C₂×C₅×Dic₆	—	2	1	no	—
64	C₂×C₅×Dic₆	—	2	1	no	—
65	C₂×C₅×Dic₆	—	2	1	no	—
66	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
67	C₂×C₅×Dic₆	C₂³	1	2	yes	—
68	C₃×C₅×M₁₆	—	2	1	no	—
69	C₃×C₅×M₁₆	—	2	1	no	—
70	C₃×C₅×M₁₆	C₂³	1	2	yes	—
71	C₃×C₅×M₁₆	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	—	2	1	no	—
73	C₂×C₃×C₅×C₈	—	2	1	no	—
74	C₅×#214	—	2	4	no	—
75	C₅×#214	—	2	4	no	—
76	C₅×#214	—	2	4	no	—
77	C₅×#213	—	2	4	no	—
78	C₅×#208	—	2	1	no	—
79	C₅×#208	C₂³	1	2	yes	—
80	C₂×C₅×C₃⋊C₈	—	2	1	no	—
81	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	D₄	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	D₄	1	2	yes	—
84	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
85	C₅×Dic₁₂	—	2	4	no	—
86	C₅×#204	—	2	4	no	—
87	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
88	C₅×D₃×C₈	—	2	4	no	—
89	C₂²×#214	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×#932	C₂×C₅	1	1	yes	characteristic
91	C₂×#909	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#907	C₂×C₅	1	1	yes	characteristic, complemented
93	C₂×C₃×#100	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#824	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#822	C₂×C₅	1	1	yes	characteristic, complemented
96	#4748	C₂×C₅	1	8	yes	direct product factor
97	C₂×C₅×#41	—	3	1	no	—
98	C₂²×C₅×Q₈	—	3	1	no	—
99	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
100	C₅×#137	—	3	4	no	—
101	C₅×#137	—	6	2	no	—
102	C₅×AGL(1,ℤ/8)	—	3	4	no	—
103	C₅×AGL(1,ℤ/8)	—	6	2	no	—
104	C₂×C₅×Q₁₆	—	6	1	no	—
105	C₂×C₅×SD₁₆	—	3	4	no	—
106	C₂×C₅×SD₁₆	—	6	1	no	—
107	C₂×C₅×SD₁₆	—	6	1	no	—
108	C₂×C₅×SD₁₆	—	6	1	no	—
109	C₂×C₅×SD₁₆	—	6	2	no	—
110	C₂×C₅×SD₁₆	—	6	1	no	—
111	C₂×C₅×D₈	—	6	1	no	—
112	C₅×#131	—	3	4	no	—
113	C₅×#131	—	6	2	no	—
114	C₂×C₅×M₁₆	—	3	1	no	—
115	C₂×C₅×M₁₆	—	6	1	no	—
116	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
117	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
118	C₂²×C₅×C₈	—	3	1	no	—
119	C₂²×C₅×C₈	—	6	1	no	—
120	C₅×#108	—	3	4	no	—
121	C₅×#101	—	3	4	no	—
122	C₅×#100	C₂×D₃	1	4	yes	complemented
123	C₂×#471	—	3	1	no	Sylow
124	C₂³×C₃×C₅	—	2	2	no	—
125	C₂³×C₃×C₅	—	4	1	no	—
126	C₂³×C₃×C₅	—	4	1	no	—
127	C₂³×C₃×C₅	—	8	2	no	—
128	C₂³×C₃×C₅	#41	1	1	yes	characteristic
129	C₂²×C₅×D₃	—	2	1	no	—
130	C₃×C₅×D₄	—	2	2	no	—
131	C₃×C₅×D₄	—	2	2	no	—
132	C₃×C₅×D₄	—	4	1	no	—
133	C₃×C₅×D₄	—	4	1	no	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×#67	—	2	2	no	—
141	C₅×#67	—	2	2	no	—
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	—	4	1	no	—
145	C₂×C₅×Dic₃	—	4	1	no	—
146	C₅×D₁₂	—	2	1	no	—
147	C₅×D₁₂	C₂×D₄	1	2	yes	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	—	2	2	no	—
150	C₅×Dic₆	—	2	1	no	—
151	C₅×Dic₆	—	2	2	no	—
152	C₅×Dic₆	—	2	2	no	—
153	C₅×Dic₆	—	4	1	no	—
154	C₅×Dic₆	—	4	1	no	—
155	C₅×Dic₆	C₂×D₄	1	2	yes	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₅×C₃⋊C₈	—	2	2	no	—
159	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
160	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	—
161	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
162	C₂×#235	C₂²×C₅	1	1	yes	characteristic
163	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₂×#214	—	2	1	no	—
167	C₂×#214	—	2	1	no	—
168	C₂×#214	—	2	1	no	—
169	C₂×#214	—	2	2	no	—
170	C₂×#214	C₂²×C₅	1	4	yes	complemented
171	#932	—	2	2	no	—
172	#932	C₂²×C₅	1	4	yes	—
173	C₂×#213	—	2	1	no	—
174	C₂×#208	C₂²×C₅	1	1	yes	characteristic
175	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
176	#909	—	2	2	no	—
177	#909	C₂²×C₅	1	4	yes	complemented
178	#907	—	2	2	no	—
179	#907	C₂²×C₅	1	4	yes	complemented
180	C₂×Dic₁₂	—	2	1	no	—
181	C₂×#204	—	2	1	no	—
182	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
183	C₂×D₃×C₈	—	2	1	no	—
184	C₃×#100	C₂²×C₅	1	4	yes	complemented
185	#824	C₂²×C₅	1	4	yes	complemented
186	#822	C₂²×C₅	1	4	yes	complemented
187	C₂⁴×C₅	—	2	1	no	—
188	C₅×#41	—	3	2	no	—
189	C₅×#41	—	3	2	no	—
190	C₅×#41	—	6	1	no	—
191	C₅×#41	—	6	1	no	—
192	C₂×C₅×Q₈	—	3	1	no	—
193	C₂×C₅×Q₈	—	3	2	no	—
194	C₂×C₅×Q₈	—	6	1	no	—
195	C₂×C₅×Q₈	—	6	1	no	—
196	C₂×C₅×Q₈	—	6	1	no	—
197	C₂×C₅×Q₈	—	6	1	no	—
198	C₂×C₅×Q₈	—	6	1	no	—
199	C₂×C₅×D₄	—	2	1	no	—
200	C₂×C₅×D₄	—	2	1	no	—
201	C₂×C₅×D₄	—	2	1	no	—
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	—	2	1	no	—
204	C₂×C₅×D₄	—	3	1	no	—
205	C₂×C₅×D₄	—	6	1	no	—
206	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
207	C₂²×C₄×C₅	—	6	1	no	—
208	C₂²×C₄×C₅	—	6	1	no	—
209	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
210	C₅×Q₁₆	—	6	4	no	—
211	C₅×SD₁₆	—	6	4	no	—
212	C₅×SD₁₆	—	6	4	no	—
213	C₅×SD₁₆	—	6	4	no	—
214	C₅×SD₁₆	—	6	4	no	—
215	C₅×D₈	—	6	4	no	—
216	C₅×M₁₆	—	2	1	no	—
217	C₅×M₁₆	—	2	1	no	—
218	C₅×M₁₆	—	3	2	no	—
219	C₅×M₁₆	—	6	4	no	—
220	C₅×M₁₆	—	6	1	no	—
221	C₅×M₁₆	C₂²×D₃	1	2	yes	—
222	C₅×M₁₆	C₂²×D₃	1	2	yes	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	2	1	no	—
225	C₂×C₅×C₈	—	3	1	no	—
226	C₂×C₅×C₈	—	3	1	no	—
227	C₂×C₅×C₈	—	3	2	no	—
228	C₂×C₅×C₈	—	3	2	no	—
229	C₂×C₅×C₈	—	6	4	no	—
230	C₂×C₅×C₈	—	6	1	no	—
231	C₂×#137	—	3	1	no	—
232	C₂×AGL(1,ℤ/8)	—	3	1	no	—
233	C₂²×SD₁₆	—	3	1	no	—
234	C₂×#131	—	3	1	no	—
235	#471	—	3	8	no	—
236	C₂×#108	—	3	1	no	—
237	C₂×#101	—	3	1	no	—
238	C₂×#100	C₅×D₃	1	1	yes	characteristic, complemented
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	4	2	no	—
241	C₂²×C₃×C₅	—	8	2	no	—
242	C₂²×C₃×C₅	—	8	2	no	—
243	C₂²×C₃×C₅	—	8	2	no	—
244	C₂²×C₃×C₅	#121	1	1	yes	characteristic
245	C₂²×C₃×C₅	#121	1	1	yes	characteristic
246	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
247	C₂×C₅×D₃	—	2	2	no	—
248	C₂×C₅×D₃	—	4	2	no	—
249	C₃×C₄×C₅	#121	1	1	yes	characteristic
250	C₃×C₄×C₅	#121	1	1	yes	characteristic
251	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₅×Dic₃	—	2	2	no	—
254	C₅×Dic₃	—	4	2	no	—
255	C₂⁴×C₃	—	2	1	no	—
256	C₂×C₃×D₄	—	2	1	no	—
257	C₂×C₃×D₄	—	2	1	no	—
258	C₂×C₃×D₄	—	2	1	no	—
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	—	2	1	no	—
261	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂×#67	—	2	1	no	—
264	C₂²×Dic₃	—	2	1	no	—
265	#235	—	2	1	no	—
266	#235	—	2	1	no	—
267	#235	C₅×D₄	1	2	yes	—
268	#235	C₂³×C₅	1	2	yes	—
269	C₂×D₁₂	C₅×D₄	1	1	yes	characteristic
270	C₂×C₄×D₃	—	2	1	no	—
271	C₂×Dic₆	—	2	1	no	—
272	C₂×Dic₆	—	2	1	no	—
273	C₂×Dic₆	—	2	1	no	—
274	C₂×Dic₆	—	2	1	no	—
275	C₂×Dic₆	—	2	1	no	—
276	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
277	C₂×Dic₆	C₂³×C₅	1	2	yes	—
278	C₃×M₁₆	—	2	1	no	—
279	C₃×M₁₆	—	2	1	no	—
280	C₃×M₁₆	C₂³×C₅	1	2	yes	—
281	C₃×M₁₆	C₂³×C₅	1	2	yes	—
282	C₂×C₃×C₈	—	2	1	no	—
283	C₂×C₃×C₈	—	2	1	no	—
284	#214	—	2	4	no	—
285	#214	—	2	4	no	—
286	#214	—	2	4	no	—
287	#213	—	2	4	no	—
288	#208	—	2	1	no	—
289	#208	C₂³×C₅	1	2	yes	—
290	C₂×C₃⋊C₈	—	2	1	no	—
291	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
292	C₂×C₃⋊C₈	C₅×D₄	1	1	yes	characteristic
293	C₂×C₃⋊C₈	C₅×D₄	1	2	yes	—
294	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
295	Dic₁₂	—	2	4	no	—
296	#204	—	2	4	no	—
297	ΓL(1,𝔽₂₅)	—	2	4	no	—
298	D₃×C₈	—	2	4	no	—
299	C₂³×C₅	—	2	2	no	—
300	C₂³×C₅	—	4	1	no	—
301	C₂³×C₅	—	4	1	no	—
302	C₂³×C₅	—	6	1	no	—
303	C₂³×C₅	—	8	2	no	—
304	C₂³×C₅	#235	1	1	yes	characteristic
305	C₅×Q₈	—	3	2	no	—
306	C₅×Q₈	—	6	1	no	—
307	C₅×Q₈	—	6	2	no	—
308	C₅×Q₈	—	6	2	no	—
309	C₅×Q₈	—	12	1	no	—
310	C₅×Q₈	—	12	1	no	—
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	2	2	no	—
313	C₅×D₄	—	3	2	no	—
314	C₅×D₄	—	4	1	no	—
315	C₅×D₄	—	4	1	no	—
316	C₅×D₄	—	6	2	no	—
317	C₅×D₄	—	6	2	no	—
318	C₅×D₄	—	6	1	no	—
319	C₂×C₄×C₅	—	6	1	no	—
320	C₂×C₄×C₅	—	6	2	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	12	1	no	—
324	C₂×C₄×C₅	—	12	1	no	—
325	C₂×C₄×C₅	#235	1	1	yes	characteristic
326	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
331	C₅×C₈	—	2	2	no	—
332	C₅×C₈	—	2	2	no	—
333	C₅×C₈	—	3	2	no	—
334	C₅×C₈	—	3	2	no	—
335	C₅×C₈	—	6	2	no	—
336	C₂×#41	—	3	1	no	—
337	C₂²×Q₈	—	3	1	no	—
338	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
339	#137	—	3	4	no	—
340	#137	—	6	2	no	—
341	AGL(1,ℤ/8)	—	3	4	no	—
342	AGL(1,ℤ/8)	—	6	2	no	—
343	C₂×Q₁₆	—	6	1	no	—
344	C₂×SD₁₆	—	3	4	no	—
345	C₂×SD₁₆	—	6	1	no	—
346	C₂×SD₁₆	—	6	1	no	—
347	C₂×SD₁₆	—	6	1	no	—
348	C₂×SD₁₆	—	6	2	no	—
349	C₂×SD₁₆	—	6	1	no	—
350	C₂×D₈	—	6	1	no	—
351	#131	—	3	4	no	—
352	#131	—	6	2	no	—
353	C₂×M₁₆	—	3	1	no	—
354	C₂×M₁₆	—	6	1	no	—
355	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
356	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
357	C₂²×C₈	—	3	1	no	—
358	C₂²×C₈	—	6	1	no	—
359	#108	—	3	4	no	—
360	#101	—	3	4	no	—
361	#100	C₂×C₅×D₃	1	4	yes	complemented
362	C₂×C₃×C₅	—	2	1	no	—
363	C₂×C₃×C₅	—	2	1	no	—
364	C₂×C₃×C₅	—	8	2	no	—
365	C₂×C₃×C₅	#471	1	2	yes	complemented
366	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
367	C₅×D₃	—	4	2	no	—
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	—	4	1	no	—
370	C₂³×C₃	—	4	1	no	—
371	C₂³×C₃	—	8	2	no	—
372	C₂³×C₃	C₅×#41	1	1	yes	characteristic
373	C₂²×D₃	—	2	1	no	—
374	C₃×D₄	—	2	2	no	—
375	C₃×D₄	—	2	2	no	—
376	C₃×D₄	—	4	1	no	—
377	C₃×D₄	—	4	1	no	—
378	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
384	#67	—	2	2	no	—
385	#67	—	2	2	no	—
386	C₂×Dic₃	—	2	1	no	—
387	C₂×Dic₃	—	2	2	no	—
388	C₂×Dic₃	—	4	1	no	—
389	C₂×Dic₃	—	4	1	no	—
390	D₁₂	—	2	1	no	—
391	D₁₂	C₂×C₅×D₄	1	2	yes	—
392	C₄×D₃	—	2	2	no	—
393	C₄×D₃	—	2	2	no	—
394	Dic₆	—	2	1	no	—
395	Dic₆	—	2	2	no	—
396	Dic₆	—	2	2	no	—
397	Dic₆	—	4	1	no	—
398	Dic₆	—	4	1	no	—
399	Dic₆	C₂×C₅×D₄	1	2	yes	—
400	C₃×C₈	—	2	2	no	—
401	C₃×C₈	—	2	2	no	—
402	C₃⋊C₈	—	2	2	no	—
403	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
404	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	—
405	C₂²×C₅	—	2	2	no	—
406	C₂²×C₅	—	4	2	no	—
407	C₂²×C₅	—	6	2	no	—
408	C₂²×C₅	—	8	2	no	—
409	C₂²×C₅	—	8	2	no	—
410	C₂²×C₅	—	8	2	no	—
411	C₂²×C₅	—	12	2	no	—
412	C₂²×C₅	#884	1	1	yes	characteristic
413	C₂²×C₅	#884	1	1	yes	characteristic
414	C₂²×C₅	C₂×#235	1	1	yes	characteristic
415	C₄×C₅	—	6	2	no	—
416	C₄×C₅	—	12	2	no	—
417	C₄×C₅	#884	1	1	yes	characteristic
418	C₄×C₅	#884	1	1	yes	characteristic
419	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
420	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
421	C₂⁴	—	2	1	no	—
422	#41	—	3	2	no	—
423	#41	—	3	2	no	—
424	#41	—	6	1	no	—
425	#41	—	6	1	no	—
426	C₂×Q₈	—	3	1	no	—
427	C₂×Q₈	—	3	2	no	—
428	C₂×Q₈	—	6	1	no	—
429	C₂×Q₈	—	6	1	no	—
430	C₂×Q₈	—	6	1	no	—
431	C₂×Q₈	—	6	1	no	—
432	C₂×Q₈	—	6	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	3	1	no	—
439	C₂×D₄	—	6	1	no	—
440	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
441	C₂²×C₄	—	6	1	no	—
442	C₂²×C₄	—	6	1	no	—
443	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
444	Q₁₆	—	6	4	no	—
445	SD₁₆	—	6	4	no	—
446	SD₁₆	—	6	4	no	—
447	SD₁₆	—	6	4	no	—
448	SD₁₆	—	6	4	no	—
449	D₈	—	6	4	no	—
450	M₁₆	—	2	1	no	—
451	M₁₆	—	2	1	no	—
452	M₁₆	—	3	2	no	—
453	M₁₆	—	6	4	no	—
454	M₁₆	—	6	1	no	—
455	M₁₆	C₂²×C₅×D₃	1	2	yes	—
456	M₁₆	C₂²×C₅×D₃	1	2	yes	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	3	1	no	—
460	C₂×C₈	—	3	1	no	—
461	C₂×C₈	—	3	2	no	—
462	C₂×C₈	—	3	2	no	—
463	C₂×C₈	—	6	4	no	—
464	C₂×C₈	—	6	1	no	—
465	C₃×C₅	C₂×#471	1	1	yes	characteristic, complemented, Hall
466	C₂²×C₃	—	2	2	no	—
467	C₂²×C₃	—	4	2	no	—
468	C₂²×C₃	—	8	2	no	—
469	C₂²×C₃	—	8	2	no	—
470	C₂²×C₃	—	8	2	no	—
471	C₂²×C₃	C₅×#121	1	1	yes	characteristic
472	C₂²×C₃	C₅×#121	1	1	yes	characteristic
473	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
474	C₂×D₃	—	2	2	no	—
475	C₂×D₃	—	4	2	no	—
476	C₃×C₄	C₅×#121	1	1	yes	characteristic
477	C₃×C₄	C₅×#121	1	1	yes	characteristic
478	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
479	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
480	Dic₃	—	2	2	no	—
481	Dic₃	—	4	2	no	—
482	C₂×C₅	—	2	1	no	—
483	C₂×C₅	—	2	1	no	—
484	C₂×C₅	—	8	2	no	—
485	C₂×C₅	—	12	2	no	—
486	C₂×C₅	#4748	1	2	yes	direct product factor
487	C₂×C₅	C₂×#884	1	1	yes	characteristic
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	6	1	no	—
492	C₂³	—	8	2	no	—
493	C₂³	C₅×#235	1	1	yes	characteristic
494	Q₈	—	3	2	no	—
495	Q₈	—	6	1	no	—
496	Q₈	—	6	2	no	—
497	Q₈	—	6	2	no	—
498	Q₈	—	12	1	no	—
499	Q₈	—	12	1	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	3	2	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	6	2	no	—
506	D₄	—	6	2	no	—
507	D₄	—	6	1	no	—
508	C₂×C₄	—	6	1	no	—
509	C₂×C₄	—	6	2	no	—
510	C₂×C₄	—	6	2	no	—
511	C₂×C₄	—	6	2	no	—
512	C₂×C₄	—	12	1	no	—
513	C₂×C₄	—	12	1	no	—
514	C₂×C₄	C₅×#235	1	1	yes	characteristic
515	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
516	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
517	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
518	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	3	2	no	—
523	C₈	—	3	2	no	—
524	C₈	—	6	2	no	—
525	C₂×C₃	—	2	1	no	—
526	C₂×C₃	—	2	1	no	—
527	C₂×C₃	—	8	2	no	—
528	C₂×C₃	C₅×#471	1	2	yes	complemented
529	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
530	D₃	—	4	2	no	—
531	C₅	C₂×#4748	1	1	yes	characteristic, direct product factor, Sylow
532	C₂²	—	2	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	6	2	no	—
535	C₂²	—	8	2	no	—
536	C₂²	—	8	2	no	—
537	C₂²	—	8	2	no	—
538	C₂²	—	12	2	no	—
539	C₂²	C₅×#884	1	1	yes	characteristic
540	C₂²	C₅×#884	1	1	yes	characteristic
541	C₂²	C₂×C₅×#235	1	1	yes	characteristic
542	C₄	—	6	2	no	—
543	C₄	—	12	2	no	—
544	C₄	C₅×#884	1	1	yes	characteristic
545	C₄	C₅×#884	1	1	yes	characteristic
546	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
547	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
548	C₃	C₂×C₅×#471	1	1	yes	characteristic, complemented, Sylow
549	C₂	—	2	1	no	—
550	C₂	—	2	1	no	—
551	C₂	—	8	2	no	—
552	C₂	—	12	2	no	—
553	C₂	C₅×#4748	1	2	yes	direct product factor
554	C₂	C₂×C₅×#884	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#884
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#100	C₂
socle	C₂²×C₃×C₅	#121
prime radical	C₂×C₅×#932	C₂
hypercenter	C₂×C₅×#100	D₃
hypocenter	C₃	C₂×C₅×#471
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#100

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#214	C₂	semidirect
3. C₂×C₅×#909	C₂	semidirect
4. C₂×C₅×#907	C₂	semidirect
5. C₂×C₃×C₅×#100	C₂	semidirect
6. C₂×C₅×#824	C₂	semidirect
7. C₂×C₅×#822	C₂	semidirect
8. C₅×#4748	C₂	direct (N × H)
19. C₂×C₅×#214	C₂²	semidirect
26. C₅×#909	C₂²	semidirect
28. C₅×#907	C₂²	semidirect
33. C₃×C₅×#100	C₂²	semidirect
34. C₅×#824	C₂²	semidirect
35. C₅×#822	C₂²	semidirect
36. C₂×#4748	C₅	direct (N × H)
44. C₂×C₅×#100	D₃	semidirect
89. C₂²×#214	C₂×C₅	semidirect
91. C₂×#909	C₂×C₅	semidirect
92. C₂×#907	C₂×C₅	semidirect
93. C₂×C₃×#100	C₂×C₅	semidirect
94. C₂×#824	C₂×C₅	semidirect
95. C₂×#822	C₂×C₅	semidirect
96. #4748	C₂×C₅	direct (N × H)
122. C₅×#100	C₂×D₃	semidirect
170. C₂×#214	C₂²×C₅	semidirect
177. #909	C₂²×C₅	semidirect
179. #907	C₂²×C₅	semidirect
184. C₃×#100	C₂²×C₅	semidirect
185. #824	C₂²×C₅	semidirect
186. #822	C₂²×C₅	semidirect
238. C₂×#100	C₅×D₃	semidirect
361. #100	C₂×C₅×D₃	semidirect
365. C₂×C₃×C₅	#471	semidirect
465. C₃×C₅	C₂×#471	semidirect
486. C₂×C₅	#4748	direct (N × H)
528. C₂×C₃	C₅×#471	semidirect
531. C₅	C₂×#4748	direct (N × H)
548. C₃	C₂×C₅×#471	semidirect
553. C₂	C₅×#4748	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#214	2
C₂×C₅×#932	2
C₂×C₅×#909	2
C₂×C₅×#907	2
C₂×C₃×C₅×#100	2
C₂×C₅×#824	2
C₂×C₅×#822	2
C₅×#4748	2
C₂×C₅×#471	3
C₂×#4748	5

Subgroups — C2×C5×#4748 #14429289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4748 #14429289