Subgroups — D₅×#1833 #12099469

Order 1280.

786 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×#108	C₂	1	1	yes	maximal, characteristic
2	D₅×#427	C₂	1	1	yes	maximal, characteristic
3	D₅×#405	C₂	1	1	yes	maximal, characteristic
4	C₅×#1833	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601491	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601450	C₂	1	1	yes	maximal, characteristic, complemented
7	#10600689	C₂	1	1	yes	maximal, characteristic, complemented
8	D₅×#344	C₂	1	2	yes	maximal
9	#10599806	C₂	1	2	yes	maximal, complemented
10	D₅×H(3,ℤ/4)	C₂	1	2	yes	maximal
11	#10599492	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₂²	1	2	yes	—
13	C₂×D₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
15	D₅×#117	C₂²	1	2	yes	—
16	D₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₅×#108	C₂²	1	1	yes	characteristic
18	C₅×#427	C₂²	1	1	yes	characteristic
19	C₅×#405	C₂²	1	1	yes	characteristic
20	C₂×#3954	C₂²	1	2	yes	—
21	#65411	C₂²	1	1	yes	characteristic
22	C₂×#3951	C₂²	1	1	yes	characteristic
23	#65395	C₂²	1	1	yes	characteristic
24	#65390	C₂²	1	1	yes	characteristic
25	#65287	C₂²	1	2	yes	—
26	#65286	C₂²	1	1	yes	characteristic
27	D₅×#108	—	2	1	no	—
28	D₅×#108	—	2	1	no	—
29	D₅×#108	—	2	1	no	—
30	D₅×#108	—	2	1	no	—
31	#65169	—	2	1	no	—
32	D₅×#107	—	2	1	no	—
33	#65149	—	2	1	no	—
34	D₅×#106	—	2	1	no	—
35	#64997	C₄	1	2	yes	complemented
36	D₅×#97	C₄	1	2	yes	complemented
37	#64978	C₄	1	2	yes	complemented
38	C₄×C₈×D₅	C₄	1	2	yes	complemented
39	C₅×#344	C₂²	1	2	yes	—
40	C₅×H(3,ℤ/4)	C₂²	1	2	yes	—
41	#64779	C₂²	1	2	yes	—
42	#64777	C₂²	1	2	yes	—
43	#64776	C₂²	1	2	yes	—
44	#64753	C₂²	1	2	yes	—
45	#64751	C₂²	1	2	yes	—
46	#64751	C₂²	1	2	yes	—
47	C₂×#1833	—	5	1	no	maximal, Sylow
48	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×M₁₆	C₂³	1	2	yes	—
50	C₂×C₅×M₁₆	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₅×#117	C₂³	1	2	yes	—
53	C₅×#117	C₂³	1	1	yes	characteristic
54	#4072	C₂³	1	2	yes	—
55	#4072	C₂³	1	1	yes	characteristic
56	C₂×#681	C₂³	1	2	yes	—
57	C₂×#681	C₂³	1	1	yes	characteristic
58	C₂²×#168	C₂³	1	1	yes	characteristic
59	D₅×M₁₆	—	2	1	no	—
60	D₅×M₁₆	—	2	1	no	—
61	D₅×M₁₆	—	2	1	no	—
62	D₅×M₁₆	—	2	1	no	—
63	D₅×M₁₆	—	2	2	no	—
64	D₅×M₁₆	—	2	2	no	—
65	D₅×M₁₆	—	2	2	no	—
66	D₅×M₁₆	—	2	2	no	—
67	C₂×#676	—	2	2	no	—
68	C₂×#676	C₂×C₄	1	2	yes	—
69	C₂×C₈×D₅	—	2	2	no	—
70	C₂×C₈×D₅	C₂×C₄	1	2	yes	—
71	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₅	D₄	1	1	yes	characteristic
76	C₂×C₈×D₅	D₄	1	1	yes	characteristic
77	C₂×C₈×D₅	D₄	1	1	yes	characteristic
78	C₂×C₈×D₅	D₄	1	1	yes	characteristic
79	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
80	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
81	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
82	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
83	#4038	—	2	1	no	—
84	#4038	—	2	2	no	—
85	D₅×C₄⋊C₄	—	2	1	no	—
86	D₅×C₄⋊C₄	—	2	2	no	—
87	D₅×C₂²⋊C₄	—	2	1	no	—
88	D₅×C₂²⋊C₄	—	2	2	no	—
89	#4023	—	2	1	no	—
90	#4023	—	2	2	no	—
91	#4018	—	2	2	no	—
92	#4018	C₂×C₄	1	2	yes	—
93	C₄²×D₅	—	2	2	no	—
94	C₄²×D₅	C₂×C₄	1	2	yes	—
95	C₅×#108	—	2	1	no	—
96	C₅×#108	—	2	1	no	—
97	C₅×#107	—	2	1	no	—
98	C₅×#106	—	2	1	no	—
99	C₅×#97	C₂×C₄	1	2	yes	complemented
100	C₄×C₅×C₈	C₂×C₄	1	2	yes	complemented
101	#3954	—	2	2	no	—
102	#3954	—	2	2	no	—
103	#3951	—	2	1	no	—
104	#3951	—	2	1	no	—
105	#3950	—	2	1	no	—
106	#3949	—	2	1	no	—
107	#3947	C₂×C₄	1	2	yes	complemented
108	#3947	C₂×C₄	1	2	yes	complemented
109	C₈×Dic₅	C₂×C₄	1	2	yes	complemented
110	C₈×Dic₅	C₂×C₄	1	2	yes	complemented
111	#3940	—	2	2	no	—
112	#3939	—	2	2	no	—
113	#3935	C₂×C₄	1	2	yes	complemented
114	C₄×#168	C₂×C₄	1	2	yes	complemented
115	C₂²×#108	—	5	1	no	—
116	C₂×#427	—	5	1	no	—
117	C₂×#405	—	5	1	no	—
118	#1833	—	5	1	no	—
119	#1833	—	5	1	no	—
120	#1833	—	5	1	no	—
121	#1833	—	5	2	no	—
122	#1833	—	5	2	no	—
123	#1833	D₅	1	1	yes	characteristic, direct product factor
124	C₂×#344	—	5	2	no	—
125	C₂×H(3,ℤ/4)	—	5	2	no	—
126	C₂³×D₅	#41	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
128	C₂²×Dic₅	#41	1	1	yes	characteristic
129	C₂×C₄×D₅	—	2	2	no	—
130	C₂×C₄×D₅	—	4	2	no	—
131	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
136	C₂×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
137	C₂×C₄×D₅	#41	1	1	yes	characteristic
138	C₂×C₄×D₅	#41	1	1	yes	characteristic
139	C₂×C₄×D₅	#41	1	1	yes	characteristic
140	C₂×C₄×D₅	#41	1	1	yes	characteristic
141	C₂×C₄×D₅	#41	1	1	yes	characteristic
142	C₂×C₄×D₅	#41	1	1	yes	characteristic
143	C₅×M₁₆	—	2	1	no	—
144	C₅×M₁₆	—	2	1	no	—
145	C₅×M₁₆	—	2	2	no	—
146	C₅×M₁₆	—	2	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	C₂²×C₄	1	2	yes	—
161	C₂²⋊Dic₅	—	2	1	no	—
162	C₂²⋊Dic₅	—	2	2	no	—
163	#685	—	2	2	no	—
164	#685	—	4	2	no	—
165	C₄⋊Dic₅	—	2	1	no	—
166	C₄⋊Dic₅	—	2	2	no	—
167	#683	—	2	2	no	—
168	#683	—	4	2	no	—
169	C₄×Dic₅	—	2	2	no	—
170	C₄×Dic₅	—	2	2	no	—
171	C₄×Dic₅	—	4	2	no	—
172	C₄×Dic₅	C₂²×C₄	1	2	yes	—
173	#681	—	2	1	no	—
174	#681	—	2	1	no	—
175	#681	—	2	2	no	—
176	#681	—	2	2	no	—
177	C₂×#168	—	2	2	no	—
178	C₂×#168	C₂²×C₄	1	2	yes	—
179	C₂×#168	C₂²×C₄	1	1	yes	characteristic
180	C₂×#168	C₂²×C₄	1	1	yes	characteristic
181	C₂×#168	C₂×D₄	1	1	yes	characteristic
182	C₂×#168	C₂×D₄	1	1	yes	characteristic
183	C₂×#168	C₂×Q₈	1	1	yes	characteristic
184	C₂×#168	C₂×Q₈	1	1	yes	characteristic
185	#676	—	2	2	no	—
186	#676	—	2	2	no	—
187	#676	—	4	2	no	—
188	#676	—	4	2	no	—
189	C₈×D₅	—	2	2	no	—
190	C₈×D₅	—	2	2	no	—
191	C₈×D₅	—	4	2	no	—
192	C₈×D₅	—	4	2	no	—
193	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
194	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
195	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
196	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
197	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
198	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
199	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
200	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
201	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
202	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
203	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
204	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
205	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
206	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
207	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
208	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
209	C₂²×M₁₆	—	5	1	no	—
210	C₂²×M₁₆	—	5	2	no	—
211	C₂³×C₈	—	5	1	no	—
212	C₂×#117	—	5	1	no	—
213	C₂×#117	—	5	2	no	—
214	C₂×#108	—	5	2	no	—
215	C₂×#108	—	5	1	no	—
216	C₂×#108	—	10	1	no	—
217	C₂×#108	—	10	1	no	—
218	C₂×#108	—	10	1	no	—
219	C₂×#108	—	10	1	no	—
220	C₂×#108	C₂×D₅	1	1	yes	characteristic
221	#427	—	5	1	no	—
222	#427	—	5	2	no	—
223	#427	—	10	1	no	—
224	#427	—	10	1	no	—
225	#427	C₂×D₅	1	1	yes	characteristic
226	C₂×#107	—	10	1	no	—
227	C₂×#106	—	10	1	no	—
228	#405	—	5	1	no	—
229	#405	—	5	1	no	—
230	#405	—	5	1	no	—
231	#405	—	5	2	no	—
232	#405	—	5	2	no	—
233	#405	C₂×D₅	1	1	yes	characteristic
234	C₂×#97	—	5	2	no	—
235	C₂×C₄×C₈	—	5	2	no	—
236	#344	—	5	2	no	—
237	#344	—	5	2	no	—
238	#344	—	5	2	no	—
239	#344	C₂×D₅	1	2	yes	—
240	H(3,ℤ/4)	—	5	2	no	—
241	H(3,ℤ/4)	—	5	2	no	—
242	H(3,ℤ/4)	—	5	2	no	—
243	H(3,ℤ/4)	C₂×D₅	1	2	yes	—
244	C₂³×C₅	C₂×#41	1	1	yes	characteristic
245	C₂²×D₅	—	4	2	no	—
246	C₂²×D₅	#117	1	1	yes	characteristic
247	C₂²×D₅	#117	1	1	yes	characteristic
248	C₂²×D₅	#124	1	1	yes	characteristic
249	C₂²×D₅	#124	1	1	yes	characteristic
250	C₂²×D₅	#125	1	1	yes	characteristic
251	C₂²×D₅	#125	1	1	yes	characteristic
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
260	C₂×Dic₅	—	2	2	no	—
261	C₂×Dic₅	—	4	2	no	—
262	C₂×Dic₅	#117	1	1	yes	characteristic
263	C₂×Dic₅	#117	1	1	yes	characteristic
264	C₂×Dic₅	#124	1	1	yes	characteristic
265	C₂×Dic₅	#124	1	1	yes	characteristic
266	C₂×Dic₅	#125	1	1	yes	characteristic
267	C₂×Dic₅	#125	1	1	yes	characteristic
268	C₄×D₅	—	4	4	no	—
269	C₄×D₅	—	8	4	no	—
270	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
271	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
272	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
273	C₄×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₄×D₅	#117	1	1	yes	characteristic
275	C₄×D₅	#117	1	1	yes	characteristic
276	C₄×D₅	#117	1	1	yes	characteristic
277	C₄×D₅	#117	1	1	yes	characteristic
278	C₄×D₅	#124	1	1	yes	characteristic
279	C₄×D₅	#124	1	1	yes	characteristic
280	C₄×D₅	#124	1	1	yes	characteristic
281	C₄×D₅	#124	1	1	yes	characteristic
282	C₄×D₅	#125	1	1	yes	characteristic
283	C₄×D₅	#125	1	1	yes	characteristic
284	C₄×D₅	#125	1	1	yes	characteristic
285	C₄×D₅	#125	1	1	yes	characteristic
286	C₅×C₈	—	2	2	no	—
287	C₅×C₈	—	4	2	no	—
288	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
289	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
290	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
291	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
292	#168	—	2	2	no	—
293	#168	—	4	2	no	—
294	#168	C₂×C₄⋊C₄	1	1	yes	characteristic
295	#168	C₂×C₄⋊C₄	1	1	yes	characteristic
296	#168	C₂×C₄⋊C₄	1	1	yes	characteristic
297	#168	C₂×C₄⋊C₄	1	1	yes	characteristic
298	C₂³×C₄	—	5	1	no	—
299	C₂×M₁₆	—	5	1	no	—
300	C₂×M₁₆	—	5	2	no	—
301	C₂×M₁₆	—	5	2	no	—
302	C₂×M₁₆	—	10	2	no	—
303	C₂×M₁₆	—	10	1	no	—
304	C₂×M₁₆	—	10	1	no	—
305	C₂×M₁₆	—	10	1	no	—
306	C₂×M₁₆	—	10	1	no	—
307	C₂×M₁₆	—	10	2	no	—
308	C₂×M₁₆	—	10	2	no	—
309	C₂×M₁₆	—	10	2	no	—
310	C₂×M₁₆	—	10	2	no	—
311	C₂×M₁₆	C₂²×D₅	1	2	yes	—
312	C₂×M₁₆	C₂²×D₅	1	1	yes	characteristic
313	C₂²×C₈	—	5	1	no	—
314	C₂²×C₈	—	5	1	no	—
315	C₂²×C₈	—	5	1	no	—
316	C₂²×C₈	—	5	1	no	—
317	C₂²×C₈	—	5	1	no	—
318	C₂²×C₈	—	5	1	no	—
319	C₂²×C₈	—	5	1	no	—
320	C₂²×C₈	—	5	1	no	—
321	C₂²×C₈	—	5	1	no	—
322	C₂²×C₈	—	5	1	no	—
323	C₂²×C₈	—	5	1	no	—
324	C₂²×C₈	—	5	1	no	—
325	C₂²×C₈	—	5	1	no	—
326	C₂²×C₈	—	5	2	no	—
327	C₂²×C₈	—	10	2	no	—
328	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
329	#117	—	5	1	no	—
330	#117	—	5	2	no	—
331	#117	—	5	2	no	—
332	#117	—	10	2	no	—
333	#117	—	10	1	no	—
334	#117	—	10	1	no	—
335	#117	—	10	2	no	—
336	#117	—	10	2	no	—
337	#117	C₂²×D₅	1	2	yes	—
338	#117	C₂²×D₅	1	1	yes	characteristic
339	C₂×C₄⋊C₄	—	10	1	no	—
340	C₂×C₄⋊C₄	—	10	2	no	—
341	C₂×C₂²⋊C₄	—	10	1	no	—
342	C₂×C₂²⋊C₄	—	10	2	no	—
343	C₂×C₄²	—	5	2	no	—
344	C₂×C₄²	—	10	2	no	—
345	#108	—	2	1	no	—
346	#108	—	2	1	no	—
347	#108	—	10	2	no	—
348	#108	—	10	2	no	—
349	#108	—	10	1	no	—
350	#108	—	10	1	no	—
351	#107	—	2	1	no	—
352	#107	—	10	2	no	—
353	#107	—	10	1	no	—
354	#106	—	2	1	no	—
355	#106	—	10	2	no	—
356	#106	—	10	1	no	—
357	#97	—	5	2	no	—
358	#97	—	5	2	no	—
359	#97	—	5	2	no	—
360	#97	C₄×D₅	1	2	yes	complemented
361	C₄×C₈	—	5	2	no	—
362	C₄×C₈	—	5	2	no	—
363	C₄×C₈	—	5	2	no	—
364	C₄×C₈	C₄×D₅	1	2	yes	complemented
365	C₂²×C₅	—	4	1	no	—
366	C₂²×C₅	C₂×#117	1	1	yes	characteristic
367	C₂²×C₅	C₂×#124	1	1	yes	characteristic
368	C₂²×C₅	C₂×#125	1	1	yes	characteristic
369	C₂×D₅	—	2	2	no	—
370	C₂×D₅	—	2	2	no	—
371	C₂×D₅	—	2	2	no	—
372	C₂×D₅	—	4	1	no	—
373	C₂×D₅	—	4	1	no	—
374	C₂×D₅	—	4	1	no	—
375	C₂×D₅	#382	1	1	yes	characteristic
376	C₂×D₅	#382	1	1	yes	characteristic
377	C₂×D₅	#382	1	1	yes	characteristic
378	C₂×D₅	#382	1	1	yes	characteristic
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	8	2	no	—
381	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
382	C₄×C₅	C₂×#117	1	1	yes	characteristic
383	C₄×C₅	C₂×#124	1	1	yes	characteristic
384	C₄×C₅	C₂×#125	1	1	yes	characteristic
385	Dic₅	—	4	2	no	—
386	Dic₅	—	8	2	no	—
387	Dic₅	#382	1	1	yes	characteristic
388	Dic₅	#382	1	1	yes	characteristic
389	Dic₅	#382	1	1	yes	characteristic
390	Dic₅	#382	1	1	yes	characteristic
391	C₂⁴	—	5	1	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	5	1	no	—
394	C₂²×C₄	—	5	1	no	—
395	C₂²×C₄	—	5	1	no	—
396	C₂²×C₄	—	5	1	no	—
397	C₂²×C₄	—	5	1	no	—
398	C₂²×C₄	—	5	1	no	—
399	C₂²×C₄	—	5	1	no	—
400	C₂²×C₄	—	5	1	no	—
401	C₂²×C₄	—	5	1	no	—
402	C₂²×C₄	—	5	1	no	—
403	C₂²×C₄	—	5	1	no	—
404	C₂²×C₄	—	5	1	no	—
405	C₂²×C₄	—	10	2	no	—
406	C₂²×C₄	—	20	2	no	—
407	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	10	2	no	—
413	M₁₆	—	10	2	no	—
414	M₁₆	—	10	1	no	—
415	M₁₆	—	10	1	no	—
416	M₁₆	—	10	2	no	—
417	M₁₆	—	10	2	no	—
418	M₁₆	—	20	2	no	—
419	M₁₆	—	20	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	5	1	no	—
422	C₂×C₈	—	5	1	no	—
423	C₂×C₈	—	5	1	no	—
424	C₂×C₈	—	5	1	no	—
425	C₂×C₈	—	5	1	no	—
426	C₂×C₈	—	5	1	no	—
427	C₂×C₈	—	5	1	no	—
428	C₂×C₈	—	5	1	no	—
429	C₂×C₈	—	5	1	no	—
430	C₂×C₈	—	5	1	no	—
431	C₂×C₈	—	5	1	no	—
432	C₂×C₈	—	5	1	no	—
433	C₂×C₈	—	5	1	no	—
434	C₂×C₈	—	5	1	no	—
435	C₂×C₈	—	5	1	no	—
436	C₂×C₈	—	5	1	no	—
437	C₂×C₈	—	5	1	no	—
438	C₂×C₈	—	5	1	no	—
439	C₂×C₈	—	5	1	no	—
440	C₂×C₈	—	5	1	no	—
441	C₂×C₈	—	5	1	no	—
442	C₂×C₈	—	5	1	no	—
443	C₂×C₈	—	5	2	no	—
444	C₂×C₈	—	10	2	no	—
445	C₂×C₈	—	10	2	no	—
446	C₂×C₈	—	10	2	no	—
447	C₂×C₈	—	20	2	no	—
448	C₂×C₈	—	20	2	no	—
449	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
450	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
451	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
452	C₂×C₈	D₄×D₅	1	1	yes	characteristic
453	C₂×C₈	D₄×D₅	1	1	yes	characteristic
454	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
455	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	10	2	no	—
459	C₄⋊C₄	—	10	1	no	—
460	C₄⋊C₄	—	10	2	no	—
461	C₄⋊C₄	—	20	2	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	10	2	no	—
465	C₂²⋊C₄	—	10	1	no	—
466	C₂²⋊C₄	—	10	2	no	—
467	C₂²⋊C₄	—	20	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	5	2	no	—
470	C₄²	—	10	2	no	—
471	C₄²	—	10	2	no	—
472	C₄²	—	20	2	no	—
473	C₄²	C₂×C₄×D₅	1	2	yes	—
474	C₂×C₅	—	2	1	no	—
475	C₂×C₅	—	2	1	no	—
476	C₂×C₅	—	2	1	no	—
477	C₂×C₅	C₂×#382	1	1	yes	characteristic
478	D₅	—	2	1	no	—
479	D₅	—	2	1	no	—
480	D₅	—	2	1	no	—
481	D₅	#1833	1	2	yes	direct product factor
482	C₂³	—	5	1	no	—
483	C₂³	—	5	1	no	—
484	C₂³	—	5	1	no	—
485	C₂³	—	5	1	no	—
486	C₂³	—	5	1	no	—
487	C₂³	—	5	1	no	—
488	C₂³	—	20	2	no	—
489	C₂³	D₅×#41	1	1	yes	characteristic
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	5	1	no	—
493	C₂×C₄	—	5	1	no	—
494	C₂×C₄	—	5	1	no	—
495	C₂×C₄	—	5	1	no	—
496	C₂×C₄	—	5	1	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	5	1	no	—
499	C₂×C₄	—	5	1	no	—
500	C₂×C₄	—	5	1	no	—
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	5	1	no	—
507	C₂×C₄	—	5	1	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	5	1	no	—
512	C₂×C₄	—	5	1	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	10	2	no	—
515	C₂×C₄	—	20	4	no	—
516	C₂×C₄	—	20	2	no	—
517	C₂×C₄	—	40	4	no	—
518	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
519	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
520	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
521	C₂×C₄	D₅×#41	1	1	yes	characteristic
522	C₂×C₄	D₅×#41	1	1	yes	characteristic
523	C₂×C₄	D₅×#41	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	4	2	no	—
526	C₈	—	5	1	no	—
527	C₈	—	5	1	no	—
528	C₈	—	5	1	no	—
529	C₈	—	5	1	no	—
530	C₈	—	10	2	no	—
531	C₈	—	20	2	no	—
532	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
533	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
534	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
535	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
536	C₅	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
537	C₂²	—	4	1	no	—
538	C₂²	—	5	1	no	—
539	C₂²	—	5	1	no	—
540	C₂²	—	5	1	no	—
541	C₂²	—	5	1	no	—
542	C₂²	—	10	2	no	—
543	C₂²	—	10	2	no	—
544	C₂²	—	10	2	no	—
545	C₂²	—	20	1	no	—
546	C₂²	—	20	1	no	—
547	C₂²	—	20	1	no	—
548	C₂²	D₅×#117	1	1	yes	characteristic
549	C₂²	D₅×#124	1	1	yes	characteristic
550	C₂²	D₅×#125	1	1	yes	characteristic
551	C₄	—	4	2	no	—
552	C₄	—	5	1	no	—
553	C₄	—	5	1	no	—
554	C₄	—	5	1	no	—
555	C₄	—	5	1	no	—
556	C₄	—	8	2	no	—
557	C₄	—	20	2	no	—
558	C₄	—	40	2	no	—
559	C₄	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
560	C₄	D₅×#117	1	1	yes	characteristic
561	C₄	D₅×#124	1	1	yes	characteristic
562	C₄	D₅×#125	1	1	yes	characteristic
563	C₂	—	2	1	no	—
564	C₂	—	2	1	no	—
565	C₂	—	2	1	no	—
566	C₂	—	5	2	no	—
567	C₂	—	10	1	no	—
568	C₂	—	10	1	no	—
569	C₂	—	10	1	no	—
570	C₂	D₅×#382	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅×#117
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1833	C₂
socle	C₂×C₅	C₂×#382
prime radical	C₂³×D₅	#41
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1833	D₅
hypocenter	C₅	C₂×#1833
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. C₅×#1833	C₂	semidirect
5. #10601491	C₂	semidirect
6. #10601450	C₂	semidirect
7. #10600689	C₂	semidirect
9. #10599806	C₂	semidirect
11. #10599492	C₂	semidirect
35. #64997	C₄	semidirect
36. D₅×#97	C₄	semidirect
37. #64978	C₄	semidirect
38. C₄×C₈×D₅	C₄	semidirect
99. C₅×#97	C₂×C₄	semidirect
100. C₄×C₅×C₈	C₂×C₄	semidirect
107. #3947	C₂×C₄	semidirect
108. #3947	C₂×C₄	semidirect
109. C₈×Dic₅	C₂×C₄	semidirect
110. C₈×Dic₅	C₂×C₄	semidirect
113. #3935	C₂×C₄	semidirect
114. C₄×#168	C₂×C₄	semidirect
123. #1833	D₅	direct (N × H)
360. #97	C₄×D₅	semidirect
364. C₄×C₈	C₄×D₅	semidirect
481. D₅	#1833	direct (N × H)
536. C₅	C₂×#1833	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×#108	2
D₅×#427	2
D₅×#405	2
C₅×#1833	2
#10601491	2
#10601450	2
#10600689	2
D₅×#344	2
#10599806	2
D₅×H(3,ℤ/4)	2
#10599492	2
C₂×#1833	5

Subgroups — D5×#1833 #12099469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#1833 #12099469