Subgroups — D₅×#1389 #12014233

Order 1280.

570 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₅×#108	C₂	1	1	yes	maximal, characteristic
3	D₅×#427	C₂	1	1	yes	maximal, characteristic
4	C₅×#1389	C₂	1	1	yes	maximal, characteristic, complemented
5	#10598313	C₂	1	1	yes	maximal, characteristic, complemented
6	#10598226	C₂	1	1	yes	maximal, characteristic, complemented
7	#10598218	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅×M₁₆	—	2	1	no	—
9	C₂²×C₈×D₅	C₂²	1	1	yes	characteristic
10	D₅×#117	—	2	1	no	—
11	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
12	C₂×C₅×#108	C₂²	1	1	yes	characteristic
13	C₅×#427	C₂²	1	1	yes	characteristic
14	C₂×#3954	—	2	1	no	—
15	C₂×#3951	C₂²	1	1	yes	characteristic
16	#65395	C₂²	1	1	yes	characteristic
17	C₂×#3944	C₂²	1	1	yes	characteristic
18	#65287	—	2	1	no	—
19	D₅×M₃₂	—	2	1	no	—
20	D₅×M₃₂	—	2	1	no	—
21	D₅×M₃₂	C₄	1	2	yes	complemented
22	D₅×M₃₂	C₄	1	2	yes	complemented
23	C₂×#3930	—	2	1	no	—
24	C₂×D₅×C₁₆	—	2	1	no	—
25	D₅×#108	—	2	1	no	—
26	D₅×#108	—	2	1	no	—
27	D₅×#108	C₄	1	2	yes	complemented
28	D₅×#108	C₄	1	2	yes	complemented
29	#65169	—	2	1	no	—
30	D₅×#107	—	2	1	no	—
31	#65149	C₄	1	2	yes	—
32	D₅×#106	C₄	1	2	yes	—
33	C₂×#1389	—	5	1	no	maximal, Sylow
34	C₂²×C₄×D₅	D₄	1	1	yes	characteristic
35	C₂×C₅×M₁₆	—	2	1	no	—
36	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
37	C₅×#117	—	2	1	no	—
38	#4072	—	2	1	no	—
39	C₂×#681	—	2	1	no	—
40	C₂²×#168	D₄	1	1	yes	characteristic
41	D₅×M₁₆	—	2	2	no	—
42	D₅×M₁₆	—	2	2	no	—
43	D₅×M₁₆	—	4	1	no	—
44	D₅×M₁₆	—	4	1	no	—
45	C₂×#676	—	4	1	no	—
46	C₂×C₈×D₅	—	4	1	no	—
47	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅	D₄	1	1	yes	characteristic
54	C₂×C₈×D₅	D₄	1	1	yes	characteristic
55	C₂×C₈×D₅	D₄	1	1	yes	characteristic
56	C₂×C₈×D₅	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
58	C₂×C₈×D₅	Q₈	1	1	yes	characteristic
59	#4038	—	2	2	no	—
60	D₅×C₄⋊C₄	—	2	2	no	—
61	D₅×C₂²⋊C₄	—	4	1	no	—
62	#4023	—	4	1	no	—
63	#4018	—	4	1	no	—
64	C₄²×D₅	—	4	1	no	—
65	C₅×M₃₂	—	2	1	no	—
66	C₅×M₃₂	C₂×C₄	1	2	yes	complemented
67	C₂×C₅×C₁₆	—	2	1	no	—
68	C₅×#108	—	2	1	no	—
69	C₅×#108	C₂×C₄	1	2	yes	complemented
70	C₅×#107	—	2	1	no	—
71	C₅×#106	C₂×C₄	1	2	yes	—
72	#3954	—	2	2	no	—
73	#3954	—	2	2	no	—
74	#3951	—	2	1	no	—
75	#3951	C₂×C₄	1	2	yes	complemented
76	#3950	—	2	1	no	—
77	#3949	C₂×C₄	1	2	yes	—
78	#3944	—	2	1	no	—
79	#3944	C₂×C₄	1	2	yes	complemented
80	C₂×#672	—	2	1	no	—
81	#3940	—	2	2	no	—
82	#3939	—	2	2	no	—
83	#3930	—	2	2	no	—
84	#3930	—	2	2	no	—
85	D₅×C₁₆	—	2	2	no	—
86	D₅×C₁₆	—	2	2	no	—
87	C₂²×M₃₂	—	5	1	no	—
88	C₂²×#108	—	5	1	no	—
89	C₂×#427	—	5	1	no	—
90	#1389	—	5	1	no	—
91	#1389	—	5	1	no	—
92	#1389	—	5	1	no	—
93	#1389	D₅	1	1	yes	characteristic, direct product factor
94	C₂³×D₅	SD₁₆	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×Dic₅	SD₁₆	1	1	yes	characteristic
97	C₂×C₄×D₅	—	4	2	no	—
98	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₅	D₈	1	1	yes	characteristic
105	C₂×C₄×D₅	D₈	1	1	yes	characteristic
106	C₂×C₄×D₅	SD₁₆	1	1	yes	characteristic
107	C₂×C₄×D₅	SD₁₆	1	1	yes	characteristic
108	C₂×C₄×D₅	Q₁₆	1	1	yes	characteristic
109	C₂×C₄×D₅	Q₁₆	1	1	yes	characteristic
110	C₅×M₁₆	—	2	2	no	—
111	C₅×M₁₆	—	4	1	no	—
112	C₂×C₅×C₈	—	4	1	no	—
113	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
119	C₅×C₄⋊C₄	—	2	2	no	—
120	C₅×C₂²⋊C₄	—	4	1	no	—
121	C₄²×C₅	—	4	1	no	—
122	C₂²⋊Dic₅	—	4	1	no	—
123	#685	—	4	2	no	—
124	C₄⋊Dic₅	—	2	2	no	—
125	#683	—	4	2	no	—
126	C₄×Dic₅	—	4	1	no	—
127	C₄×Dic₅	—	4	2	no	—
128	#681	—	2	2	no	—
129	#681	—	4	1	no	—
130	C₂×#168	—	4	1	no	—
131	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
133	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×#168	C₂²⋊C₄	1	1	yes	characteristic
135	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
136	C₂×#168	C₄⋊C₄	1	1	yes	characteristic
137	#676	—	4	2	no	—
138	#676	—	4	2	no	—
139	C₈×D₅	—	4	2	no	—
140	C₈×D₅	—	4	2	no	—
141	C₈×D₅	C₄²	1	1	yes	characteristic
142	C₈×D₅	C₄²	1	1	yes	characteristic
143	C₈×D₅	C₄²	1	1	yes	characteristic
144	C₈×D₅	C₄²	1	1	yes	characteristic
145	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
146	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
147	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
148	C₈×D₅	C₂²⋊C₄	1	1	yes	characteristic
149	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
150	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
151	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
152	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
153	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
154	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
155	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
156	C₈×D₅	C₄⋊C₄	1	1	yes	characteristic
157	C₅×C₁₆	—	2	2	no	—
158	#672	—	2	2	no	—
159	C₂²×M₁₆	—	10	1	no	—
160	C₂³×C₈	—	5	1	no	—
161	C₂×#117	—	10	1	no	—
162	C₂×M₃₂	—	5	1	no	—
163	C₂×M₃₂	—	5	2	no	—
164	C₂×M₃₂	—	5	2	no	—
165	C₂×M₃₂	—	10	1	no	—
166	C₂×M₃₂	—	10	1	no	—
167	C₂×M₃₂	—	10	1	no	—
168	C₂×M₃₂	C₂×D₅	1	1	yes	characteristic
169	C₂²×C₁₆	—	10	1	no	—
170	C₂×#108	—	5	1	no	—
171	C₂×#108	—	5	2	no	—
172	C₂×#108	—	5	2	no	—
173	C₂×#108	—	10	1	no	—
174	C₂×#108	—	10	1	no	—
175	C₂×#108	—	10	1	no	—
176	C₂×#108	C₂×D₅	1	1	yes	characteristic
177	#427	—	5	1	no	—
178	#427	—	5	2	no	—
179	#427	—	10	1	no	—
180	#427	—	10	1	no	—
181	#427	C₂×D₅	1	1	yes	characteristic
182	C₂×#107	—	10	1	no	—
183	C₂×#106	—	5	2	no	—
184	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
185	C₂²×D₅	—	4	2	no	—
186	C₂²×D₅	#102	1	1	yes	characteristic
187	C₂²×D₅	#102	1	1	yes	characteristic
188	C₂²×D₅	#103	1	1	yes	characteristic
189	C₂²×D₅	#103	1	1	yes	characteristic
190	C₂²×D₅	#106	1	1	yes	characteristic
191	C₂²×D₅	#106	1	1	yes	characteristic
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×Q₁₆	1	1	yes	characteristic
199	C₂×Dic₅	—	4	2	no	—
200	C₂×Dic₅	#102	1	1	yes	characteristic
201	C₂×Dic₅	#102	1	1	yes	characteristic
202	C₂×Dic₅	#103	1	1	yes	characteristic
203	C₂×Dic₅	#103	1	1	yes	characteristic
204	C₂×Dic₅	#106	1	1	yes	characteristic
205	C₂×Dic₅	#106	1	1	yes	characteristic
206	C₄×D₅	—	8	4	no	—
207	C₄×D₅	#95	1	1	yes	characteristic
208	C₄×D₅	#95	1	1	yes	characteristic
209	C₄×D₅	#95	1	1	yes	characteristic
210	C₄×D₅	#95	1	1	yes	characteristic
211	C₄×D₅	#102	1	1	yes	characteristic
212	C₄×D₅	#102	1	1	yes	characteristic
213	C₄×D₅	#102	1	1	yes	characteristic
214	C₄×D₅	#102	1	1	yes	characteristic
215	C₄×D₅	#103	1	1	yes	characteristic
216	C₄×D₅	#103	1	1	yes	characteristic
217	C₄×D₅	#103	1	1	yes	characteristic
218	C₄×D₅	#103	1	1	yes	characteristic
219	C₄×D₅	#107	1	1	yes	characteristic
220	C₄×D₅	#107	1	1	yes	characteristic
221	C₄×D₅	#107	1	1	yes	characteristic
222	C₄×D₅	#107	1	1	yes	characteristic
223	C₅×C₈	—	4	2	no	—
224	C₅×C₈	C₂×C₄²	1	1	yes	characteristic
225	C₅×C₈	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
228	#168	—	4	2	no	—
229	#168	#95	1	1	yes	characteristic
230	#168	#95	1	1	yes	characteristic
231	#168	#95	1	1	yes	characteristic
232	#168	#95	1	1	yes	characteristic
233	C₂³×C₄	—	5	1	no	—
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	10	2	no	—
236	C₂×M₁₆	—	10	2	no	—
237	C₂×M₁₆	—	10	1	no	—
238	C₂×M₁₆	—	20	1	no	—
239	C₂×M₁₆	—	20	1	no	—
240	C₂×M₁₆	—	20	1	no	—
241	C₂²×C₈	—	5	1	no	—
242	C₂²×C₈	—	5	1	no	—
243	C₂²×C₈	—	5	1	no	—
244	C₂²×C₈	—	5	1	no	—
245	C₂²×C₈	—	5	1	no	—
246	C₂²×C₈	—	5	1	no	—
247	C₂²×C₈	—	5	1	no	—
248	C₂²×C₈	—	5	1	no	—
249	C₂²×C₈	—	5	1	no	—
250	C₂²×C₈	—	5	1	no	—
251	C₂²×C₈	—	5	1	no	—
252	C₂²×C₈	—	5	1	no	—
253	C₂²×C₈	—	5	1	no	—
254	C₂²×C₈	—	20	1	no	—
255	C₂²×C₈	C₂²×D₅	1	1	yes	characteristic
256	#117	—	2	1	no	—
257	#117	—	10	2	no	—
258	#117	—	10	1	no	—
259	#117	—	20	1	no	—
260	#117	—	20	1	no	—
261	C₂×C₄⋊C₄	—	10	2	no	—
262	C₂×C₂²⋊C₄	—	20	1	no	—
263	C₂×C₄²	—	20	1	no	—
264	M₃₂	—	2	1	no	—
265	M₃₂	—	5	2	no	—
266	M₃₂	—	10	2	no	—
267	M₃₂	—	10	2	no	—
268	M₃₂	—	10	1	no	—
269	M₃₂	C₄×D₅	1	2	yes	complemented
270	C₂×C₁₆	—	2	1	no	—
271	C₂×C₁₆	—	10	2	no	—
272	C₂×C₁₆	—	10	2	no	—
273	C₂×C₁₆	—	10	1	no	—
274	#108	—	2	1	no	—
275	#108	—	5	2	no	—
276	#108	—	10	2	no	—
277	#108	—	10	2	no	—
278	#108	—	10	1	no	—
279	#108	C₄×D₅	1	2	yes	complemented
280	#107	—	2	1	no	—
281	#107	—	10	2	no	—
282	#107	—	10	1	no	—
283	#106	—	5	2	no	—
284	#106	—	10	2	no	—
285	#106	C₄×D₅	1	2	yes	—
286	C₂²×C₅	—	4	1	no	—
287	C₂²×C₅	C₂×#102	1	1	yes	characteristic
288	C₂²×C₅	C₂×#103	1	1	yes	characteristic
289	C₂²×C₅	C₂×#106	1	1	yes	characteristic
290	C₂×D₅	—	2	2	no	—
291	C₂×D₅	—	2	2	no	—
292	C₂×D₅	—	2	2	no	—
293	C₂×D₅	—	4	1	no	—
294	C₂×D₅	—	4	1	no	—
295	C₂×D₅	—	4	1	no	—
296	C₂×D₅	#340	1	1	yes	characteristic
297	C₂×D₅	#340	1	1	yes	characteristic
298	C₂×D₅	#340	1	1	yes	characteristic
299	C₂×D₅	#340	1	1	yes	characteristic
300	C₄×C₅	—	8	2	no	—
301	C₄×C₅	C₂×#95	1	1	yes	characteristic
302	C₄×C₅	C₂×#102	1	1	yes	characteristic
303	C₄×C₅	C₂×#103	1	1	yes	characteristic
304	C₄×C₅	C₂×#107	1	1	yes	characteristic
305	Dic₅	—	8	2	no	—
306	Dic₅	#340	1	1	yes	characteristic
307	Dic₅	#340	1	1	yes	characteristic
308	Dic₅	#340	1	1	yes	characteristic
309	Dic₅	#340	1	1	yes	characteristic
310	C₂⁴	—	5	1	no	—
311	C₂²×C₄	—	5	1	no	—
312	C₂²×C₄	—	5	1	no	—
313	C₂²×C₄	—	5	1	no	—
314	C₂²×C₄	—	5	1	no	—
315	C₂²×C₄	—	5	1	no	—
316	C₂²×C₄	—	5	1	no	—
317	C₂²×C₄	—	5	1	no	—
318	C₂²×C₄	—	5	1	no	—
319	C₂²×C₄	—	5	1	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	5	1	no	—
322	C₂²×C₄	—	5	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	20	2	no	—
325	C₂²×C₄	D₄×D₅	1	1	yes	characteristic
326	M₁₆	—	2	2	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	10	2	no	—
329	M₁₆	—	20	2	no	—
330	M₁₆	—	20	2	no	—
331	M₁₆	—	20	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	5	1	no	—
334	C₂×C₈	—	5	1	no	—
335	C₂×C₈	—	5	1	no	—
336	C₂×C₈	—	5	1	no	—
337	C₂×C₈	—	5	1	no	—
338	C₂×C₈	—	5	1	no	—
339	C₂×C₈	—	5	1	no	—
340	C₂×C₈	—	5	1	no	—
341	C₂×C₈	—	5	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	1	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	5	1	no	—
348	C₂×C₈	—	5	1	no	—
349	C₂×C₈	—	5	1	no	—
350	C₂×C₈	—	5	1	no	—
351	C₂×C₈	—	5	1	no	—
352	C₂×C₈	—	5	1	no	—
353	C₂×C₈	—	5	1	no	—
354	C₂×C₈	—	5	1	no	—
355	C₂×C₈	—	20	2	no	—
356	C₂×C₈	—	20	2	no	—
357	C₂×C₈	—	20	1	no	—
358	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
359	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
360	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
361	C₂×C₈	D₄×D₅	1	1	yes	characteristic
362	C₂×C₈	D₄×D₅	1	1	yes	characteristic
363	C₂×C₈	Q₈×D₅	1	1	yes	characteristic
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	10	2	no	—
366	C₄⋊C₄	—	20	2	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	20	2	no	—
369	C₂²⋊C₄	—	20	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	20	2	no	—
372	C₄²	—	20	1	no	—
373	C₁₆	—	2	2	no	—
374	C₁₆	—	10	2	no	—
375	C₂×C₅	—	2	1	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	2	1	no	—
378	C₂×C₅	C₂×#340	1	1	yes	characteristic
379	D₅	—	2	1	no	—
380	D₅	—	2	1	no	—
381	D₅	—	2	1	no	—
382	D₅	#1389	1	2	yes	direct product factor
383	C₂³	—	5	1	no	—
384	C₂³	—	5	1	no	—
385	C₂³	—	5	1	no	—
386	C₂³	—	5	1	no	—
387	C₂³	—	5	1	no	—
388	C₂³	—	5	1	no	—
389	C₂³	—	20	2	no	—
390	C₂³	D₅×SD₁₆	1	1	yes	characteristic
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	5	1	no	—
402	C₂×C₄	—	5	1	no	—
403	C₂×C₄	—	5	1	no	—
404	C₂×C₄	—	5	1	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	5	1	no	—
412	C₂×C₄	—	5	1	no	—
413	C₂×C₄	—	5	1	no	—
414	C₂×C₄	—	20	2	no	—
415	C₂×C₄	—	40	4	no	—
416	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
417	C₂×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
418	C₂×C₄	D₅×C₄⋊C₄	1	1	yes	characteristic
419	C₂×C₄	D₅×D₈	1	1	yes	characteristic
420	C₂×C₄	D₅×SD₁₆	1	1	yes	characteristic
421	C₂×C₄	D₅×Q₁₆	1	1	yes	characteristic
422	C₈	—	4	2	no	—
423	C₈	—	5	1	no	—
424	C₈	—	5	1	no	—
425	C₈	—	5	1	no	—
426	C₈	—	5	1	no	—
427	C₈	—	20	2	no	—
428	C₈	C₄²×D₅	1	1	yes	characteristic
429	C₈	D₅×C₂²⋊C₄	1	1	yes	characteristic
430	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
431	C₈	D₅×C₄⋊C₄	1	1	yes	characteristic
432	C₅	C₂×#1389	1	1	yes	characteristic, complemented, Sylow
433	C₂²	—	4	1	no	—
434	C₂²	—	5	1	no	—
435	C₂²	—	5	1	no	—
436	C₂²	—	5	1	no	—
437	C₂²	—	5	1	no	—
438	C₂²	—	10	2	no	—
439	C₂²	—	10	2	no	—
440	C₂²	—	10	2	no	—
441	C₂²	—	20	1	no	—
442	C₂²	—	20	1	no	—
443	C₂²	—	20	1	no	—
444	C₂²	D₅×#102	1	1	yes	characteristic
445	C₂²	D₅×#103	1	1	yes	characteristic
446	C₂²	D₅×#106	1	1	yes	characteristic
447	C₄	—	5	1	no	—
448	C₄	—	5	1	no	—
449	C₄	—	5	1	no	—
450	C₄	—	5	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	40	2	no	—
453	C₄	D₅×#95	1	1	yes	characteristic
454	C₄	D₅×#102	1	1	yes	characteristic
455	C₄	D₅×#103	1	1	yes	characteristic
456	C₄	D₅×#107	1	1	yes	characteristic
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	5	2	no	—
461	C₂	—	10	1	no	—
462	C₂	—	10	1	no	—
463	C₂	—	10	1	no	—
464	C₂	D₅×#340	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₅×#102
commutator	C₅×C₈	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₅
Fitting	C₅×#1389	C₂
socle	C₂×C₅	C₂×#340
prime radical	C₂³×D₅	SD₁₆
cosocle	C₂²×C₅×C₈	C₂³
hypercenter	#1389	D₅
hypocenter	C₅	C₂×#1389
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1389

Complements

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

N	H ≅ G/N	type
4. C₅×#1389	C₂	semidirect
5. #10598313	C₂	semidirect
6. #10598226	C₂	semidirect
7. #10598218	C₂	semidirect
21. D₅×M₃₂	C₄	semidirect
22. D₅×M₃₂	C₄	semidirect
27. D₅×#108	C₄	semidirect
28. D₅×#108	C₄	semidirect
66. C₅×M₃₂	C₂×C₄	semidirect
69. C₅×#108	C₂×C₄	semidirect
75. #3951	C₂×C₄	semidirect
79. #3944	C₂×C₄	semidirect
93. #1389	D₅	direct (N × H)
269. M₃₂	C₄×D₅	semidirect
279. #108	C₄×D₅	semidirect
382. D₅	#1389	direct (N × H)
432. C₅	C₂×#1389	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅×M₃₂	2
C₂×D₅×#108	2
D₅×#427	2
C₅×#1389	2
#10598313	2
#10598226	2
#10598218	2
C₂×#1389	5

Subgroups — D5×#1389 #12014233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×#1389 #12014233