Subgroups — D₅×#1772 #12097304

Order 1280.

1102 conjugacy classes of subgroups.

The subgroup lattice has 468 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	2	yes	maximal
4	C₂×C₄×C₈×D₅	C₂	1	1	yes	maximal, characteristic
5	C₅×#1772	C₂	1	1	yes	maximal, characteristic, complemented
6	#10601495	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601452	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600682	C₂	1	2	yes	maximal, complemented
9	#10600572	C₂	1	1	yes	maximal, characteristic, complemented
10	D₅×#339	C₂	1	2	yes	maximal
11	#10599534	C₂	1	2	yes	maximal, complemented
12	C₂×D₅×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
15	D₅×#117	C₂²	1	2	yes	—
16	C₂×C₄²×D₅	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	2	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×#3954	C₂²	1	2	yes	—
22	#65411	C₂²	1	2	yes	—
23	C₂×#3951	C₂²	1	1	yes	characteristic
24	#65395	C₂²	1	1	yes	characteristic
25	#65390	C₂²	1	2	yes	—
26	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₅	C₂²	1	1	yes	characteristic
28	#65287	C₂²	1	2	yes	—
29	#65286	C₂²	1	2	yes	—
30	C₂×C₄×#168	C₂²	1	1	yes	characteristic
31	D₅×#108	C₄	1	8	yes	complemented
32	#65169	C₄	1	2	yes	complemented
33	D₅×#107	C₄	1	2	yes	complemented
34	#65149	C₄	1	2	yes	complemented
35	D₅×#106	C₄	1	2	yes	complemented
36	#64997	—	2	2	no	—
37	D₅×#97	—	2	2	no	—
38	#64978	—	2	2	no	—
39	C₄×C₈×D₅	—	2	2	no	—
40	C₄×C₈×D₅	C₄	1	8	yes	complemented
41	C₅×#339	C₂²	1	2	yes	—
42	#64775	C₂²	1	2	yes	—
43	#64752	C₂²	1	2	yes	—
44	#64743	C₂²	1	2	yes	—
45	C₂×#1772	—	5	1	no	maximal, Sylow
46	C₂²×C₄×D₅	—	2	1	no	—
47	C₂²×C₄×D₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×M₁₆	C₂³	1	2	yes	—
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₅×#117	C₂³	1	2	yes	—
52	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
53	#4072	C₂³	1	2	yes	—
54	C₂×C₄×Dic₅	—	2	1	no	—
55	C₂×C₄×Dic₅	C₂³	1	1	yes	characteristic
56	C₂×#681	C₂³	1	2	yes	—
57	C₂²×#168	C₂³	1	1	yes	characteristic
58	C₂²×#168	C₂³	1	1	yes	characteristic
59	D₅×M₁₆	—	2	4	no	—
60	D₅×M₁₆	C₂×C₄	1	8	yes	—
61	C₂×#676	—	2	2	no	—
62	C₂×C₈×D₅	—	2	2	no	—
63	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
68	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
69	C₂×C₈×D₅	C₂×C₄	1	4	yes	—
70	C₂×C₈×D₅	D₄	1	1	yes	characteristic
71	C₂×C₈×D₅	D₄	1	1	yes	characteristic
72	C₂×C₈×D₅	D₄	1	1	yes	characteristic
73	C₂×C₈×D₅	D₄	1	1	yes	characteristic
74	C₂×C₈×D₅	Q₈	1	4	yes	—
75	#4038	C₂×C₄	1	4	yes	—
76	D₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
77	D₅×C₂²⋊C₄	—	2	2	no	—
78	#4023	—	2	2	no	—
79	#4018	—	2	2	no	—
80	C₄²×D₅	—	2	2	no	—
81	C₄²×D₅	—	2	2	no	—
82	C₄²×D₅	C₂×C₄	1	4	yes	—
83	C₅×#108	C₂×C₄	1	4	yes	complemented
84	C₅×#107	C₂×C₄	1	2	yes	complemented
85	C₅×#106	C₂×C₄	1	2	yes	complemented
86	C₅×#97	—	2	2	no	—
87	C₄×C₅×C₈	—	2	2	no	—
88	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
89	#3954	C₂×C₄	1	8	yes	complemented
90	#3951	C₂×C₄	1	4	yes	complemented
91	#3950	C₂×C₄	1	2	yes	complemented
92	#3949	C₂×C₄	1	2	yes	complemented
93	#3947	—	2	2	no	—
94	#3947	—	2	2	no	—
95	C₈×Dic₅	—	2	2	no	—
96	C₈×Dic₅	—	2	2	no	—
97	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
98	C₈×Dic₅	C₂×C₄	1	4	yes	complemented
99	#3940	C₂×C₄	1	4	yes	complemented
100	#3939	C₂×C₄	1	4	yes	complemented
101	#3935	—	2	2	no	—
102	C₄×#168	—	2	2	no	—
103	C₄×#168	C₂×C₄	1	4	yes	complemented
104	C₂²×#108	—	5	1	no	—
105	C₂×#427	—	5	1	no	—
106	C₂×#405	—	5	2	no	—
107	C₂²×C₄×C₈	—	5	1	no	—
108	#1772	—	5	1	no	—
109	#1772	—	5	1	no	—
110	#1772	—	5	2	no	—
111	#1772	—	5	1	no	—
112	#1772	—	5	2	no	—
113	#1772	D₅	1	1	yes	characteristic, direct product factor
114	C₂×#339	—	5	2	no	—
115	C₂³×D₅	#41	1	1	yes	characteristic
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₅	—	2	1	no	—
119	C₂²×Dic₅	#41	1	1	yes	characteristic
120	C₂×C₄×D₅	—	2	8	no	—
121	C₂×C₄×D₅	—	2	4	no	—
122	C₂×C₄×D₅	—	2	4	no	—
123	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
124	C₂×C₄×D₅	C₂²×C₄	1	2	yes	—
125	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂×Q₈	1	2	yes	—
130	C₂×C₄×D₅	#41	1	2	yes	—
131	C₅×M₁₆	—	2	2	no	—
132	C₅×M₁₆	C₂²×C₄	1	4	yes	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
142	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
143	C₅×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	1	no	—
146	C₄²×C₅	C₂²×C₄	1	2	yes	—
147	C₂²⋊Dic₅	—	2	2	no	—
148	#685	—	2	4	no	—
149	C₄⋊Dic₅	C₂²×C₄	1	4	yes	—
150	#683	—	2	4	no	—
151	C₄×Dic₅	—	2	2	no	—
152	C₄×Dic₅	—	2	1	no	—
153	C₄×Dic₅	—	2	4	no	—
154	C₄×Dic₅	—	2	4	no	—
155	C₄×Dic₅	C₂²×C₄	1	2	yes	—
156	#681	—	2	2	no	—
157	#681	C₂²×C₄	1	4	yes	—
158	C₂×#168	—	2	2	no	—
159	C₂×#168	C₂²×C₄	1	2	yes	—
160	C₂×#168	C₂²×C₄	1	1	yes	characteristic
161	C₂×#168	C₂²×C₄	1	1	yes	characteristic
162	C₂×#168	C₂²×C₄	1	2	yes	—
163	C₂×#168	C₂²×C₄	1	2	yes	—
164	C₂×#168	C₂×D₄	1	1	yes	characteristic
165	C₂×#168	C₂×D₄	1	1	yes	characteristic
166	C₂×#168	C₂×Q₈	1	2	yes	—
167	#676	—	2	8	no	—
168	C₈×D₅	—	2	8	no	—
169	C₈×D₅	C₄²	1	4	yes	—
170	C₈×D₅	C₄²	1	4	yes	—
171	C₈×D₅	C₄²	1	4	yes	—
172	C₈×D₅	C₄²	1	4	yes	—
173	C₈×D₅	C₄⋊C₄	1	4	yes	—
174	C₈×D₅	C₄⋊C₄	1	4	yes	—
175	C₈×D₅	C₄⋊C₄	1	4	yes	—
176	C₈×D₅	C₄⋊C₄	1	4	yes	—
177	C₂²×M₁₆	—	5	2	no	—
178	C₂³×C₈	—	5	1	no	—
179	C₂³×C₈	—	5	1	no	—
180	C₂×#117	—	5	2	no	—
181	C₂²×C₄²	—	5	1	no	—
182	C₂×#108	—	5	2	no	—
183	C₂×#108	—	5	1	no	—
184	C₂×#108	—	5	8	no	—
185	C₂×#108	C₂×D₅	1	1	yes	characteristic
186	#427	—	5	1	no	—
187	#427	—	5	2	no	—
188	#427	—	5	2	no	—
189	#427	—	5	2	no	—
190	#427	C₂×D₅	1	1	yes	characteristic
191	C₂×#107	—	5	2	no	—
192	C₂×#106	—	5	2	no	—
193	#405	—	5	2	no	—
194	#405	—	5	2	no	—
195	#405	—	5	2	no	—
196	#405	—	10	2	no	—
197	#405	—	10	2	no	—
198	#405	C₂×D₅	1	2	yes	—
199	C₂×#97	—	10	2	no	—
200	C₂×C₄×C₈	—	5	1	no	—
201	C₂×C₄×C₈	—	5	1	no	—
202	C₂×C₄×C₈	—	5	1	no	—
203	C₂×C₄×C₈	—	5	8	no	—
204	C₂×C₄×C₈	—	10	2	no	—
205	C₂×C₄×C₈	C₂×D₅	1	1	yes	characteristic
206	#339	—	5	2	no	—
207	#339	—	5	2	no	—
208	#339	—	5	2	no	—
209	#339	C₂×D₅	1	2	yes	—
210	C₂³×C₅	C₂×#41	1	1	yes	characteristic
211	C₂²×D₅	—	2	4	no	—
212	C₂²×D₅	#117	1	2	yes	—
213	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
214	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
215	C₂²×D₅	C₄×Q₈	1	2	yes	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	4	no	—
219	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
225	C₂×Dic₅	—	2	4	no	—
226	C₂×Dic₅	—	2	2	no	—
227	C₂×Dic₅	—	2	4	no	—
228	C₂×Dic₅	#117	1	2	yes	—
229	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
231	C₂×Dic₅	C₄×Q₈	1	2	yes	—
232	C₄×D₅	—	2	16	no	—
233	C₄×D₅	—	4	8	no	—
234	C₄×D₅	C₂×C₄²	1	2	yes	—
235	C₄×D₅	C₂×C₄²	1	2	yes	—
236	C₄×D₅	C₂×C₄⋊C₄	1	2	yes	—
237	C₄×D₅	C₂×C₄⋊C₄	1	2	yes	—
238	C₄×D₅	C₄×D₄	1	2	yes	—
239	C₄×D₅	C₄×D₄	1	2	yes	—
240	C₄×D₅	C₄×Q₈	1	2	yes	—
241	C₄×D₅	C₄×Q₈	1	2	yes	—
242	C₅×C₈	—	2	4	no	—
243	C₅×C₈	C₂×C₄²	1	2	yes	—
244	C₅×C₈	C₂×C₄²	1	2	yes	—
245	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
246	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
247	#168	—	2	4	no	—
248	#168	C₂×C₄²	1	2	yes	—
249	#168	C₂×C₄²	1	2	yes	—
250	#168	C₂×C₄⋊C₄	1	2	yes	—
251	#168	C₂×C₄⋊C₄	1	2	yes	—
252	C₂³×C₄	—	5	1	no	—
253	C₂³×C₄	—	10	1	no	—
254	C₂×M₁₆	—	5	2	no	—
255	C₂×M₁₆	—	5	8	no	—
256	C₂×M₁₆	—	10	2	no	—
257	C₂×M₁₆	—	10	4	no	—
258	C₂×M₁₆	C₂²×D₅	1	2	yes	—
259	C₂²×C₈	—	5	1	no	—
260	C₂²×C₈	—	5	1	no	—
261	C₂²×C₈	—	5	4	no	—
262	C₂²×C₈	—	5	4	no	—
263	C₂²×C₈	—	5	1	no	—
264	C₂²×C₈	—	5	1	no	—
265	C₂²×C₈	—	5	1	no	—
266	C₂²×C₈	—	5	1	no	—
267	C₂²×C₈	—	5	4	no	—
268	C₂²×C₈	—	5	1	no	—
269	C₂²×C₈	—	5	1	no	—
270	C₂²×C₈	—	5	1	no	—
271	C₂²×C₈	—	5	1	no	—
272	C₂²×C₈	—	5	4	no	—
273	C₂²×C₈	—	10	2	no	—
274	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
276	#117	—	5	2	no	—
277	#117	—	5	4	no	—
278	#117	—	10	2	no	—
279	#117	—	10	2	no	—
280	#117	C₂²×D₅	1	2	yes	—
281	C₂×C₄⋊C₄	—	5	4	no	—
282	C₂×C₂²⋊C₄	—	10	2	no	—
283	C₂×C₄²	—	5	1	no	—
284	C₂×C₄²	—	5	4	no	—
285	C₂×C₄²	—	10	2	no	—
286	C₂×C₄²	—	10	2	no	—
287	C₂×C₄²	—	10	1	no	—
288	C₂×C₄²	C₂²×D₅	1	1	yes	characteristic
289	#108	—	5	8	no	—
290	#108	—	5	4	no	—
291	#108	C₄×D₅	1	4	yes	complemented
292	#107	—	5	2	no	—
293	#107	—	5	4	no	—
294	#107	C₄×D₅	1	2	yes	complemented
295	#106	—	5	2	no	—
296	#106	—	5	4	no	—
297	#106	C₄×D₅	1	2	yes	complemented
298	#97	—	2	2	no	—
299	#97	—	10	2	no	—
300	#97	—	10	2	no	—
301	#97	—	10	2	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	5	4	no	—
304	C₄×C₈	—	5	4	no	—
305	C₄×C₈	—	5	4	no	—
306	C₄×C₈	—	10	2	no	—
307	C₄×C₈	—	10	2	no	—
308	C₄×C₈	—	10	2	no	—
309	C₄×C₈	C₄×D₅	1	4	yes	complemented
310	C₂²×C₅	—	2	2	no	—
311	C₂²×C₅	C₂×#117	1	1	yes	characteristic
312	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
314	C₂×D₅	—	2	2	no	—
315	C₂×D₅	—	2	4	no	—
316	C₂×D₅	—	2	4	no	—
317	C₂×D₅	C₄×C₄⋊C₄	1	2	yes	—
318	C₂×D₅	C₄×C₄⋊C₄	1	2	yes	—
319	C₂×D₅	#443	1	4	yes	—
320	C₄×C₅	—	2	4	no	—
321	C₄×C₅	—	4	4	no	—
322	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
323	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
324	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
325	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
326	Dic₅	—	2	4	no	—
327	Dic₅	—	4	4	no	—
328	Dic₅	C₄×C₄⋊C₄	1	2	yes	—
329	Dic₅	C₄×C₄⋊C₄	1	2	yes	—
330	C₂⁴	—	5	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	5	1	no	—
333	C₂²×C₄	—	5	2	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	5	2	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	1	no	—
339	C₂²×C₄	—	5	2	no	—
340	C₂²×C₄	—	5	2	no	—
341	C₂²×C₄	—	10	4	no	—
342	C₂²×C₄	—	10	8	no	—
343	C₂²×C₄	—	10	4	no	—
344	C₂²×C₄	—	10	1	no	—
345	C₂²×C₄	C₂³×D₅	1	1	yes	characteristic
346	M₁₆	—	2	2	no	—
347	M₁₆	—	5	4	no	—
348	M₁₆	—	10	8	no	—
349	M₁₆	—	10	2	no	—
350	M₁₆	C₂×C₄×D₅	1	4	yes	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	5	1	no	—
355	C₂×C₈	—	5	1	no	—
356	C₂×C₈	—	5	2	no	—
357	C₂×C₈	—	5	1	no	—
358	C₂×C₈	—	5	1	no	—
359	C₂×C₈	—	5	2	no	—
360	C₂×C₈	—	5	4	no	—
361	C₂×C₈	—	5	4	no	—
362	C₂×C₈	—	5	4	no	—
363	C₂×C₈	—	5	4	no	—
364	C₂×C₈	—	5	4	no	—
365	C₂×C₈	—	5	4	no	—
366	C₂×C₈	—	5	4	no	—
367	C₂×C₈	—	5	4	no	—
368	C₂×C₈	—	10	8	no	—
369	C₂×C₈	—	10	2	no	—
370	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
371	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
372	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
374	C₂×C₈	C₂×C₄×D₅	1	2	yes	—
375	C₂×C₈	D₄×D₅	1	1	yes	characteristic
376	C₂×C₈	D₄×D₅	1	1	yes	characteristic
377	C₂×C₈	Q₈×D₅	1	2	yes	—
378	C₄⋊C₄	—	5	4	no	—
379	C₄⋊C₄	—	10	4	no	—
380	C₄⋊C₄	C₂×C₄×D₅	1	4	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	10	4	no	—
383	C₂²⋊C₄	—	10	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	5	2	no	—
387	C₄²	—	10	4	no	—
388	C₄²	—	10	4	no	—
389	C₄²	—	10	2	no	—
390	C₄²	—	10	1	no	—
391	C₄²	C₂×C₄×D₅	1	2	yes	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	1	no	—
394	C₂×C₅	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
395	C₂×C₅	C₂×#443	1	2	yes	—
396	D₅	—	2	2	no	—
397	D₅	#1772	1	4	yes	direct product factor
398	C₂³	—	5	1	no	—
399	C₂³	—	5	2	no	—
400	C₂³	—	5	1	no	—
401	C₂³	—	5	2	no	—
402	C₂³	—	10	4	no	—
403	C₂³	D₅×#41	1	1	yes	characteristic
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	5	2	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	2	no	—
411	C₂×C₄	—	5	2	no	—
412	C₂×C₄	—	5	2	no	—
413	C₂×C₄	—	5	2	no	—
414	C₂×C₄	—	5	2	no	—
415	C₂×C₄	—	5	2	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	—	5	2	no	—
418	C₂×C₄	—	5	2	no	—
419	C₂×C₄	—	10	16	no	—
420	C₂×C₄	—	10	4	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	4	no	—
423	C₂×C₄	—	20	8	no	—
424	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
428	C₂×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
429	C₂×C₄	D₅×#41	1	1	yes	characteristic
430	C₈	—	2	4	no	—
431	C₈	—	5	2	no	—
432	C₈	—	5	2	no	—
433	C₈	—	5	2	no	—
434	C₈	—	5	2	no	—
435	C₈	—	10	4	no	—
436	C₈	C₄²×D₅	1	2	yes	—
437	C₈	C₄²×D₅	1	2	yes	—
438	C₈	D₅×C₄⋊C₄	1	2	yes	—
439	C₈	D₅×C₄⋊C₄	1	2	yes	—
440	C₅	C₂×#1772	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	2	2	no	—
442	C₂²	—	5	4	no	—
443	C₂²	—	5	2	no	—
444	C₂²	—	5	2	no	—
445	C₂²	—	10	4	no	—
446	C₂²	—	10	4	no	—
447	C₂²	—	10	2	no	—
448	C₂²	D₅×#117	1	1	yes	characteristic
449	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
450	C₂²	C₄×Q₈×D₅	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	4	4	no	—
453	C₄	—	5	2	no	—
454	C₄	—	5	2	no	—
455	C₄	—	10	4	no	—
456	C₄	—	20	4	no	—
457	C₄	C₂×C₄²×D₅	1	1	yes	characteristic
458	C₄	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
459	C₄	C₄×D₄×D₅	1	1	yes	characteristic
460	C₄	C₄×Q₈×D₅	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	5	4	no	—
464	C₂	—	10	2	no	—
465	C₂	C₄×D₅×C₄⋊C₄	1	1	yes	characteristic
466	C₂	D₅×#443	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₅
commutator	C₄×C₅	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅
Fitting	C₅×#1772	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂³×D₅	#41
cosocle	C₂²×C₄×C₅	C₂⁴
hypercenter	#1772	D₅
hypocenter	C₅	C₂×#1772
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. C₅×#1772	C₂	semidirect
6. #10601495	C₂	semidirect
7. #10601452	C₂	semidirect
8. #10600682	C₂	semidirect
9. #10600572	C₂	semidirect
11. #10599534	C₂	semidirect
31. D₅×#108	C₄	semidirect
32. #65169	C₄	semidirect
33. D₅×#107	C₄	semidirect
34. #65149	C₄	semidirect
35. D₅×#106	C₄	semidirect
40. C₄×C₈×D₅	C₄	semidirect
83. C₅×#108	C₂×C₄	semidirect
84. C₅×#107	C₂×C₄	semidirect
85. C₅×#106	C₂×C₄	semidirect
88. C₄×C₅×C₈	C₂×C₄	semidirect
89. #3954	C₂×C₄	semidirect
90. #3951	C₂×C₄	semidirect
91. #3950	C₂×C₄	semidirect
92. #3949	C₂×C₄	semidirect
97. C₈×Dic₅	C₂×C₄	semidirect
98. C₈×Dic₅	C₂×C₄	semidirect
99. #3940	C₂×C₄	semidirect
100. #3939	C₂×C₄	semidirect
103. C₄×#168	C₂×C₄	semidirect
113. #1772	D₅	direct (N × H)
291. #108	C₄×D₅	semidirect
294. #107	C₄×D₅	semidirect
297. #106	C₄×D₅	semidirect
309. C₄×C₈	C₄×D₅	semidirect
397. D₅	#1772	direct (N × H)
440. C₅	C₂×#1772	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
C₂×C₄×C₈×D₅	2
C₅×#1772	2
#10601495	2
#10601452	2
#10600682	2
#10600572	2
D₅×#339	2
#10599534	2
C₂×#1772	5

Subgroups — D5×#1772 #12097304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#1772 #12097304