Subgroups — #13040343

Order 1280.

846 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617440	C₂	1	2	yes	maximal
2	#10617416	C₂	1	2	yes	maximal, complemented
3	D₅×#443	C₂	1	1	yes	maximal, characteristic
4	#10604781	C₂	1	2	yes	maximal, complemented
5	#10604088	C₂	1	2	yes	maximal, complemented
6	#10604004	C₂	1	4	yes	maximal, complemented
7	#10603851	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603849	C₂	1	1	yes	maximal, characteristic, complemented
9	#66266	C₂²	1	4	yes	—
10	D₅×#135	C₂²	1	1	yes	characteristic
11	D₅×#131	C₂²	1	2	yes	—
12	#65793	C₂²	1	4	yes	—
13	Q₁₆×AGL(1,𝔽₅)	—	2	2	no	—
14	#65735	—	2	4	no	—
15	D₈×AGL(1,𝔽₅)	—	2	2	no	—
16	#65727	—	2	4	no	—
17	#65727	C₂²	1	4	yes	—
18	D₅⋊#108	C₂²	1	1	yes	characteristic
19	#65721	—	2	2	no	—
20	#65721	C₂²	1	1	yes	characteristic
21	C₂×#3994	C₂²	1	2	yes	—
22	C₂×#3993	—	2	2	no	—
23	C₂×#3993	C₂²	1	2	yes	—
24	#65718	C₂²	1	2	yes	—
25	#65689	C₂²	1	2	yes	—
26	C₅×#443	C₄	1	1	yes	characteristic, complemented
27	#65485	C₄	1	1	yes	characteristic, complemented
28	#65433	C₄	1	2	yes	complemented
29	#65184	C₄	1	1	yes	characteristic, complemented
30	D₅×#108	C₂²	1	1	yes	characteristic
31	#65113	C₄	1	2	yes	complemented
32	D₅×#104	C₂²	1	2	yes	—
33	#64989	C₄	1	1	yes	characteristic, complemented
34	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
35	#64899	C₂²	1	4	yes	—
36	#64862	C₂²	1	2	yes	—
37	#22690	—	5	1	no	maximal, Sylow
38	D₅×#41	C₂³	1	2	yes	—
39	Q₈×AGL(1,𝔽₅)	—	2	4	no	—
40	D₄×AGL(1,𝔽₅)	—	2	4	no	—
41	D₄×AGL(1,𝔽₅)	—	4	4	no	—
42	#4130	—	2	4	no	—
43	#4130	C₂³	1	2	yes	—
44	C₂×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
45	C₂×C₄⋊AGL(1,𝔽₅)	C₂³	1	4	yes	—
46	D₅⋊M₁₆	C₂³	1	2	yes	—
47	C₅×#135	C₂×C₄	1	1	yes	characteristic
48	C₅×#131	C₂×C₄	1	2	yes	complemented
49	#4096	C₂×C₄	1	2	yes	—
50	#4094	C₂×C₄	1	2	yes	complemented
51	#4065	Q₈	1	1	yes	characteristic
52	D₅×Q₁₆	D₄	1	1	yes	characteristic
53	#4062	Q₈	1	2	yes	—
54	D₅×SD₁₆	D₄	1	2	yes	—
55	#4058	Q₈	1	1	yes	characteristic
56	D₅×D₈	D₄	1	1	yes	characteristic
57	#4053	—	2	2	no	—
58	#4053	C₂×C₄	1	2	yes	complemented
59	D₅×M₁₆	—	2	2	no	—
60	D₅×M₁₆	C₂³	1	2	yes	—
61	#4050	C₂×C₄	1	1	yes	characteristic
62	#4047	—	2	2	no	—
63	#4047	C₂×C₄	1	2	yes	complemented
64	C₂×C₈×D₅	—	2	2	no	—
65	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₅	C₂³	1	1	yes	characteristic
67	C₄²×D₅	C₂³	1	1	yes	characteristic
68	#4009	—	2	4	no	—
69	#4007	—	2	4	no	—
70	(C₂×AGL(1,𝔽₅))⋊C₄	—	4	2	no	—
71	#3996	—	2	1	no	—
72	#3995	—	2	1	no	—
73	#3994	—	2	4	no	—
74	#3994	—	2	2	no	—
75	#3994	—	2	2	no	—
76	#3994	D₄	1	2	yes	—
77	#3993	—	2	4	no	—
78	#3993	—	2	2	no	—
79	#3993	—	2	2	no	—
80	#3993	D₄	1	1	yes	characteristic
81	#3993	D₄	1	1	yes	characteristic
82	#3992	—	2	2	no	—
83	C₈×AGL(1,𝔽₅)	—	2	2	no	—
84	C₅×#108	C₂×C₄	1	1	yes	characteristic, complemented
85	C₅×#104	C₂×C₄	1	2	yes	complemented
86	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
87	#3969	C₂×C₄	1	2	yes	complemented
88	#3957	C₂×C₄	1	2	yes	complemented
89	#3954	C₂×C₄	1	2	yes	complemented
90	#3951	C₂×C₄	1	1	yes	characteristic, complemented
91	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
92	C₈×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
93	#3937	C₂×C₄	1	2	yes	complemented
94	C₄×#168	C₂×C₄	1	1	yes	characteristic, complemented
95	C₂×#443	—	5	1	no	—
96	#2951	—	5	2	no	—
97	#2912	—	5	2	no	—
98	#1952	—	5	2	no	—
99	#1860	—	5	4	no	—
100	#1846	—	5	1	no	—
101	#1815	—	5	2	no	—
102	#1772	—	5	1	no	—
103	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
104	C₂²×AGL(1,𝔽₅)	—	4	4	no	—
105	C₅×#41	C₂²×C₄	1	2	yes	—
106	#713	C₂×Q₈	1	2	yes	—
107	Q₈×D₅	C₂×D₄	1	2	yes	—
108	#711	—	2	2	no	—
109	#711	C₂×Q₈	1	2	yes	—
110	D₄×D₅	—	2	2	no	—
111	D₄×D₅	C₂×D₄	1	2	yes	—
112	#709	—	2	2	no	—
113	#709	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₅	—	2	2	no	—
115	C₂×C₄×D₅	—	2	1	no	—
116	C₂×C₄×D₅	C₂⁴	1	1	yes	characteristic
117	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
118	C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
119	#704	—	2	2	no	—
120	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
121	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
122	C₄⋊AGL(1,𝔽₅)	—	4	4	no	—
123	C₄⋊AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
124	C₄⋊AGL(1,𝔽₅)	C₂×D₄	1	2	yes	—
125	C₄×AGL(1,𝔽₅)	—	2	2	no	—
126	C₄×AGL(1,𝔽₅)	—	4	4	no	—
127	#700	—	2	2	no	—
128	D₅⋊C₈	—	2	2	no	—
129	C₅×Q₁₆	C₄⋊C₄	1	1	yes	characteristic
130	C₅×SD₁₆	C₄⋊C₄	1	2	yes	—
131	C₅×D₈	C₄⋊C₄	1	1	yes	characteristic
132	C₅×M₁₆	—	2	2	no	—
133	C₅×M₁₆	C₂²×C₄	1	2	yes	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
138	#689	C₄⋊C₄	1	2	yes	—
139	#688	C₄⋊C₄	1	2	yes	—
140	#687	C₄⋊C₄	1	2	yes	—
141	#686	C₄⋊C₄	1	2	yes	—
142	C₄×Dic₅	—	2	1	no	—
143	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	#681	—	2	2	no	—
145	#681	C₂²×C₄	1	2	yes	—
146	C₂×#168	—	2	2	no	—
147	C₂×#168	C₂²×C₄	1	1	yes	characteristic
148	C₂×#168	C₂²×C₄	1	1	yes	characteristic
149	Dic₂₀	C₄⋊C₄	1	1	yes	characteristic
150	D₄₀	C₄⋊C₄	1	1	yes	characteristic
151	#677	C₄⋊C₄	1	2	yes	—
152	#676	—	2	2	no	—
153	#676	—	2	2	no	—
154	#676	—	2	2	no	—
155	C₈×D₅	—	2	2	no	—
156	C₈×D₅	—	2	2	no	—
157	C₈×D₅	—	2	2	no	—
158	C₈×D₅	C₂×D₄	1	1	yes	characteristic
159	C₈×D₅	C₂×D₄	1	1	yes	characteristic
160	C₈×D₅	C₂×D₄	1	1	yes	characteristic
161	C₈×D₅	C₂×D₄	1	1	yes	characteristic
162	C₈×D₅	C₂×Q₈	1	1	yes	characteristic
163	C₈×D₅	C₂×Q₈	1	1	yes	characteristic
164	C₈×D₅	#41	1	1	yes	characteristic
165	C₈×D₅	#41	1	1	yes	characteristic
166	C₂×#135	—	5	1	no	—
167	C₂×#131	—	5	2	no	—
168	#520	—	5	4	no	—
169	#443	—	5	1	no	—
170	#443	—	5	2	no	—
171	#443	—	5	1	no	—
172	#443	—	5	2	no	—
173	#443	—	5	1	no	—
174	#443	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
175	#440	—	10	4	no	—
176	C₄×Q₁₆	—	10	2	no	—
177	C₄×D₈	—	10	2	no	—
178	C₂×#108	—	5	1	no	—
179	C₂×#108	—	5	1	no	—
180	#428	—	5	4	no	—
181	#428	—	10	4	no	—
182	#427	—	5	1	no	—
183	#427	—	10	2	no	—
184	C₂×#107	—	5	2	no	—
185	C₂×#106	—	5	2	no	—
186	C₂×#106	—	10	2	no	—
187	C₂×#104	—	5	2	no	—
188	#417	—	5	4	no	—
189	#405	—	5	2	no	—
190	C₂×C₄×C₈	—	5	1	no	—
191	#382	—	5	2	no	—
192	#343	—	5	4	no	—
193	#339	—	5	2	no	—
194	C₂²×D₅	—	2	2	no	—
195	C₂²×D₅	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×AGL(1,𝔽₅)	—	2	2	no	—
197	C₂×AGL(1,𝔽₅)	—	2	2	no	—
198	C₂×AGL(1,𝔽₅)	—	4	4	no	—
199	C₂×AGL(1,𝔽₅)	—	8	4	no	—
200	C₂×AGL(1,𝔽₅)	—	16	4	no	—
201	C₅×Q₈	C₂×C₄⋊C₄	1	2	yes	—
202	C₅×D₄	—	2	2	no	—
203	C₅×D₄	C₂×C₄⋊C₄	1	2	yes	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
207	C₂²⋊D₅	—	2	2	no	—
208	C₂²⋊D₅	—	2	2	no	—
209	C₂²⋊D₅	—	2	2	no	—
210	C₂×Dic₅	—	2	2	no	—
211	C₂×Dic₅	—	2	1	no	—
212	C₂×Dic₅	2₋¹⁺⁴	1	1	yes	characteristic
213	D₂₀	—	2	2	no	—
214	D₂₀	C₂×C₄⋊C₄	1	2	yes	—
215	C₄×D₅	—	2	2	no	—
216	C₄×D₅	—	2	2	no	—
217	C₄×D₅	—	2	2	no	—
218	C₄×D₅	—	4	2	no	—
219	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
220	C₄×D₅	C₂²×D₄	1	1	yes	characteristic
221	C₄×D₅	C₂²×Q₈	1	1	yes	characteristic
222	C₄×D₅	C₂×#41	1	1	yes	characteristic
223	Dic₁₀	—	2	2	no	—
224	Dic₁₀	C₂×C₄⋊C₄	1	2	yes	—
225	#170	—	4	2	no	—
226	C₅×C₈	—	2	2	no	—
227	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₅×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₅×C₈	C₄×D₄	1	1	yes	characteristic
230	C₅×C₈	C₄×D₄	1	1	yes	characteristic
231	#168	—	2	2	no	—
232	#168	C₂×C₄⋊C₄	1	1	yes	characteristic
233	#168	C₂×C₄⋊C₄	1	1	yes	characteristic
234	#168	C₄×D₄	1	1	yes	characteristic
235	#168	C₄×D₄	1	1	yes	characteristic
236	C₂×#41	—	5	2	no	—
237	#135	—	5	2	no	—
238	#135	—	5	1	no	—
239	#135	—	5	2	no	—
240	#135	—	5	1	no	—
241	#135	—	5	1	no	—
242	#135	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
243	C₂×Q₁₆	—	5	1	no	—
244	C₂×SD₁₆	—	5	2	no	—
245	C₂×D₈	—	5	1	no	—
246	#131	—	5	2	no	—
247	#131	—	5	2	no	—
248	#131	—	5	2	no	—
249	#131	—	10	2	no	—
250	#131	—	10	2	no	—
251	#131	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
252	C₂×M₁₆	—	5	2	no	—
253	C₂×M₁₆	—	5	2	no	—
254	C₂×M₁₆	—	10	2	no	—
255	C₂²×C₈	—	5	1	no	—
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	10	2	no	—
258	C₄×Q₈	—	10	4	no	—
259	C₄×D₄	—	10	4	no	—
260	C₄×D₄	—	20	4	no	—
261	#117	—	5	2	no	—
262	#117	—	10	4	no	—
263	C₂×C₄⋊C₄	—	5	4	no	—
264	C₂×C₄⋊C₄	—	10	4	no	—
265	C₂×C₄²	—	5	1	no	—
266	#108	—	5	2	no	—
267	#108	—	5	1	no	—
268	#108	—	10	1	no	—
269	#108	—	10	1	no	—
270	#108	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
271	#107	—	5	2	no	—
272	#107	—	10	4	no	—
273	#107	—	10	2	no	—
274	#107	—	10	2	no	—
275	#106	—	5	1	no	—
276	#106	—	5	1	no	—
277	#106	—	10	4	no	—
278	#106	—	10	2	no	—
279	#106	—	10	2	no	—
280	#104	—	5	2	no	—
281	#104	—	5	2	no	—
282	#104	—	5	2	no	—
283	#104	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
284	#103	—	10	4	no	—
285	#102	—	10	4	no	—
286	#97	—	10	2	no	—
287	C₄×C₈	—	5	1	no	—
288	C₄×C₈	—	5	1	no	—
289	C₄×C₈	—	5	1	no	—
290	C₄×C₈	—	10	2	no	—
291	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
292	#95	—	20	2	no	—
293	C₂²×C₅	—	2	2	no	—
294	C₂²×C₅	#520	1	1	yes	characteristic
295	C₂×D₅	—	2	2	no	—
296	C₂×D₅	—	2	2	no	—
297	C₂×D₅	—	4	4	no	—
298	C₂×D₅	D₄²	1	1	yes	characteristic
299	C₂×D₅	#554	1	1	yes	characteristic
300	AGL(1,𝔽₅)	—	4	2	no	—
301	AGL(1,𝔽₅)	—	4	2	no	—
302	AGL(1,𝔽₅)	—	8	4	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	4	1	no	—
305	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
306	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
307	Dic₅	—	2	2	no	—
308	Dic₅	—	4	1	no	—
309	Dic₅	#547	1	1	yes	characteristic
310	Dic₅	D₄×Q₈	1	1	yes	characteristic
311	#41	—	5	2	no	—
312	#41	—	5	2	no	—
313	#41	—	5	2	no	—
314	#41	—	10	2	no	—
315	#41	—	10	2	no	—
316	#41	C₂²×AGL(1,𝔽₅)	1	2	yes	—
317	C₂×Q₈	—	5	2	no	—
318	C₂×D₄	—	5	2	no	—
319	C₂×D₄	—	10	2	no	—
320	C₂²×C₄	—	5	1	no	—
321	C₂²×C₄	—	10	2	no	—
322	C₂²×C₄	—	10	1	no	—
323	C₂²×C₄	—	10	4	no	—
324	C₂²×C₄	—	20	4	no	—
325	Q₁₆	—	5	2	no	—
326	Q₁₆	—	5	1	no	—
327	Q₁₆	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
328	SD₁₆	—	5	2	no	—
329	SD₁₆	—	5	2	no	—
330	SD₁₆	—	5	2	no	—
331	SD₁₆	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
332	D₈	—	5	2	no	—
333	D₈	—	5	1	no	—
334	D₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
335	M₁₆	—	2	2	no	—
336	M₁₆	—	5	2	no	—
337	M₁₆	—	10	2	no	—
338	M₁₆	—	10	2	no	—
339	M₁₆	—	10	2	no	—
340	M₁₆	—	10	2	no	—
341	M₁₆	—	10	2	no	—
342	M₁₆	—	10	2	no	—
343	M₁₆	C₂²×AGL(1,𝔽₅)	1	2	yes	—
344	C₂×C₈	—	2	2	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	—	10	2	no	—
356	C₂×C₈	—	10	2	no	—
357	C₂×C₈	—	10	2	no	—
358	C₂×C₈	—	10	2	no	—
359	C₂×C₈	—	10	2	no	—
360	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
362	C₄⋊C₄	—	5	2	no	—
363	C₄⋊C₄	—	5	2	no	—
364	C₄⋊C₄	—	10	4	no	—
365	C₄⋊C₄	—	10	4	no	—
366	C₄⋊C₄	—	20	4	no	—
367	C₂²⋊C₄	—	10	2	no	—
368	C₂²⋊C₄	—	20	4	no	—
369	C₄²	—	5	1	no	—
370	C₄²	—	10	1	no	—
371	C₄²	—	10	2	no	—
372	C₄²	—	20	4	no	—
373	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₂×C₅	—	2	1	no	—
375	C₂×C₅	—	4	2	no	—
376	C₂×C₅	D₄×C₄⋊C₄	1	1	yes	characteristic
377	D₅	—	2	1	no	—
378	D₅	—	4	2	no	—
379	D₅	#3290	1	2	yes	—
380	C₂³	—	5	1	no	—
381	C₂³	—	10	2	no	—
382	Q₈	—	5	2	no	—
383	Q₈	—	10	2	no	—
384	Q₈	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
385	D₄	—	2	2	no	—
386	D₄	—	5	2	no	—
387	D₄	—	10	2	no	—
388	D₄	—	10	2	no	—
389	D₄	—	10	2	no	—
390	D₄	—	10	2	no	—
391	D₄	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	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	—	10	2	no	—
400	C₂×C₄	—	10	2	no	—
401	C₂×C₄	—	10	2	no	—
402	C₂×C₄	—	10	2	no	—
403	C₂×C₄	—	10	2	no	—
404	C₂×C₄	—	10	2	no	—
405	C₂×C₄	—	10	1	no	—
406	C₂×C₄	—	20	2	no	—
407	C₂×C₄	—	20	4	no	—
408	C₂×C₄	—	40	4	no	—
409	C₂×C₄	—	80	4	no	—
410	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	5	1	no	—
413	C₈	—	5	1	no	—
414	C₈	—	5	1	no	—
415	C₈	—	5	1	no	—
416	C₈	—	10	2	no	—
417	C₈	—	20	2	no	—
418	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₈	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
420	C₈	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
421	C₈	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
422	C₅	#22690	1	1	yes	characteristic, complemented, Sylow
423	C₂²	—	2	2	no	—
424	C₂²	—	5	1	no	—
425	C₂²	—	5	1	no	—
426	C₂²	—	10	2	no	—
427	C₂²	—	10	2	no	—
428	C₂²	—	20	4	no	—
429	C₂²	#66266	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	5	1	no	—
433	C₄	—	5	1	no	—
434	C₄	—	10	2	no	—
435	C₄	—	20	1	no	—
436	C₄	—	20	2	no	—
437	C₄	—	20	2	no	—
438	C₄	—	40	4	no	—
439	C₄	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₄	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	4	2	no	—
443	C₂	—	5	2	no	—
444	C₂	—	10	1	no	—
445	C₂	—	20	2	no	—
446	C₂	D₄×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×C₄⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
Fitting	C₅×#443	C₄
socle	C₂×C₅	D₄×C₄⋊C₄
prime radical	D₅×#135	C₂²
cosocle	C₂×C₄×D₅	C₂⁴
hypercenter	#443	AGL(1,𝔽₅)
hypocenter	C₅	#22690
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #443

Complements

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

N	H ≅ G/N	type
2. #10617416	C₂	semidirect
4. #10604781	C₂	semidirect
5. #10604088	C₂	semidirect
6. #10604004	C₂	semidirect
7. #10603851	C₂	semidirect
8. #10603849	C₂	semidirect
26. C₅×#443	C₄	semidirect
27. #65485	C₄	semidirect
28. #65433	C₄	semidirect
29. #65184	C₄	semidirect
31. #65113	C₄	semidirect
33. #64989	C₄	semidirect
48. C₅×#131	C₂×C₄	semidirect
50. #4094	C₂×C₄	semidirect
58. #4053	C₂×C₄	semidirect
63. #4047	C₂×C₄	semidirect
84. C₅×#108	C₂×C₄	semidirect
85. C₅×#104	C₂×C₄	semidirect
86. C₄×C₅×C₈	C₂×C₄	semidirect
87. #3969	C₂×C₄	semidirect
88. #3957	C₂×C₄	semidirect
89. #3954	C₂×C₄	semidirect
90. #3951	C₂×C₄	semidirect
91. C₈×Dic₅	C₂×C₄	semidirect
92. C₈×Dic₅	C₂×C₄	semidirect
93. #3937	C₂×C₄	semidirect
94. C₄×#168	C₂×C₄	semidirect
174. #443	AGL(1,𝔽₅)	semidirect
251. #131	C₂×AGL(1,𝔽₅)	semidirect
270. #108	C₂×AGL(1,𝔽₅)	semidirect
283. #104	C₂×AGL(1,𝔽₅)	semidirect
291. C₄×C₈	C₂×AGL(1,𝔽₅)	semidirect
422. C₅	#22690	semidirect

Maximal subgroups

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

subgroup	index
#10617440	2
#10617416	2
D₅×#443	2
#10604781	2
#10604088	2
#10604004	2
#10603851	2
#10603849	2
#22690	5