Subgroups — D₅⋊#5196 #14417852

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊#948	C₂	1	2	yes	maximal, complemented
2	C₃×D₅×#135	C₂	1	1	yes	maximal, characteristic
3	D₅⋊#837	C₂	1	2	yes	maximal, complemented
4	#11752399	C₂	1	2	yes	maximal, complemented
5	#11752395	C₂	1	4	yes	maximal, complemented
6	#11752391	C₂	1	2	yes	maximal, complemented
7	D₅⋊#819	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅⋊#443	—	3	1	no	maximal, Hall
10	C₃×D₅×#41	C₂²	1	2	yes	—
11	#91992	C₂²	1	4	yes	complemented
12	#91990	—	2	4	no	—
13	#91990	C₂²	1	4	yes	complemented
14	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
15	D₅⋊#208	—	2	2	no	—
16	D₅⋊#208	C₂²	1	2	yes	—
17	C₂×D₅⋊(C₃⋊C₈)	—	2	2	no	—
18	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₃×C₅×#135	C₄	1	1	yes	characteristic, complemented
20	C₃×#4096	C₄	1	2	yes	complemented
21	C₃×#4065	C₂²	1	1	yes	characteristic
22	C₃×D₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
23	C₃×#4062	C₂²	1	2	yes	—
24	C₃×D₅×SD₁₆	C₄	1	2	yes	complemented
25	C₃×#4058	C₂²	1	1	yes	characteristic
26	C₃×D₅×D₈	C₄	1	1	yes	characteristic, complemented
27	C₃×#4050	C₄	1	1	yes	characteristic, complemented
28	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
29	#91239	C₂²	1	4	yes	complemented
30	#91237	C₂²	1	4	yes	complemented
31	#91225	C₂²	1	2	yes	complemented
32	#91224	C₂²	1	2	yes	complemented
33	C₈×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
34	C₈×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	complemented
35	C₂×#5196	—	5	1	no	maximal, Hall
36	D₅⋊#131	—	3	2	no	—
37	D₅×#135	D₃	1	1	yes	characteristic
38	D₅⋊#104	—	3	2	no	—
39	#65740	—	3	2	no	—
40	#65736	—	3	4	no	—
41	#65732	—	3	2	no	—
42	D₅⋊#108	—	3	1	no	—
43	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
44	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
45	C₃×C₅×#41	C₂×C₄	1	2	yes	—
46	C₃×#713	C₂³	1	2	yes	—
47	C₃×Q₈×D₅	C₂×C₄	1	2	yes	—
48	C₃×#711	—	2	2	no	—
49	C₃×#711	C₂³	1	2	yes	—
50	C₃×D₄×D₅	—	2	2	no	—
51	C₃×D₄×D₅	C₂×C₄	1	2	yes	—
52	C₃×#709	—	2	2	no	—
53	C₃×#709	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₄×D₅	—	2	2	no	—
55	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
56	#6762	—	2	2	no	—
57	#6762	—	2	4	no	—
58	C₂×C₃⋊#170	—	2	4	no	—
59	C₂×C₃⋊#170	D₄	1	2	yes	—
60	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
61	C₄×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
62	#6758	—	2	4	no	—
63	#6758	C₂³	1	4	yes	—
64	D₅⋊(C₃⋊C₈)	—	2	2	no	—
65	D₅⋊(C₃⋊C₈)	—	2	4	no	—
66	D₅⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
67	D₅⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
68	D₅⋊(C₃⋊C₈)	C₂³	1	2	yes	—
69	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
70	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
71	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
72	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
73	C₃×#689	C₂×C₄	1	2	yes	complemented
74	C₃×#688	C₂×C₄	1	2	yes	complemented
75	C₃×#687	C₂×C₄	1	2	yes	complemented
76	C₃×#686	C₂×C₄	1	2	yes	complemented
77	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
78	C₃×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
79	C₃×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
80	C₃×#677	C₂×C₄	1	2	yes	complemented
81	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
84	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×#135	—	5	1	no	—
86	C₂×#948	—	5	2	no	—
87	C₂×#837	—	5	2	no	—
88	#5196	—	5	2	no	—
89	#5196	—	5	4	no	—
90	#5196	—	5	2	no	—
91	C₂×#819	—	5	1	no	—
92	C₂×C₈×Dic₃	—	5	1	no	—
93	D₅×#41	C₂×D₃	1	2	yes	—
94	#4133	—	3	4	no	—
95	#4131	—	3	4	no	—
96	#4131	—	6	4	no	—
97	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
98	D₅⋊M₁₆	—	3	2	no	—
99	D₅⋊M₁₆	—	6	2	no	—
100	C₂×D₅⋊C₈	—	3	1	no	—
101	C₂×D₅⋊C₈	—	6	2	no	—
102	C₅×#135	Dic₃	1	1	yes	characteristic, complemented
103	#4096	Dic₃	1	2	yes	complemented
104	#4065	C₂×D₃	1	1	yes	characteristic
105	D₅×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
106	#4062	C₂×D₃	1	2	yes	—
107	D₅×SD₁₆	Dic₃	1	2	yes	complemented
108	#4058	C₂×D₃	1	1	yes	characteristic
109	D₅×D₈	Dic₃	1	1	yes	characteristic, complemented
110	#4050	Dic₃	1	1	yes	characteristic, complemented
111	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
112	#4010	—	3	4	no	—
113	#4008	—	3	4	no	—
114	#3996	—	3	2	no	—
115	#3995	—	3	2	no	—
116	C₈×AGL(1,𝔽₅)	—	3	2	no	—
117	C₈×AGL(1,𝔽₅)	—	3	2	no	—
118	C₂×#443	—	15	1	no	Sylow
119	C₂²×C₃×D₅	—	2	2	no	—
120	C₂²×C₃×D₅	#41	1	1	yes	characteristic
121	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
122	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
123	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
124	C₃×C₅×D₄	—	2	2	no	—
125	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₃×C₂²⋊D₅	—	2	2	no	—
129	C₃×C₂²⋊D₅	—	2	2	no	—
130	C₃×C₂²⋊D₅	—	2	2	no	—
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
133	C₃×D₂₀	—	2	2	no	—
134	C₃×D₂₀	C₂²×C₄	1	2	yes	—
135	C₃×C₄×D₅	—	2	2	no	—
136	C₃×C₄×D₅	—	2	2	no	—
137	C₃×C₄×D₅	—	2	2	no	—
138	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
140	C₃×C₄×D₅	#41	1	1	yes	characteristic
141	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
142	C₃×Dic₁₀	—	2	2	no	—
143	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
144	C₃⋊#170	—	2	4	no	—
145	C₃⋊#170	C₂×D₄	1	2	yes	—
146	C₃⋊#170	C₂×D₄	1	2	yes	—
147	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₃×#168	C₂²×C₄	1	1	yes	characteristic
150	C₃×#168	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×#41	—	5	2	no	—
152	C₃×#135	—	5	2	no	—
153	C₃×#135	—	5	1	no	—
154	C₃×#135	—	5	2	no	—
155	C₃×#135	—	5	1	no	—
156	C₃×#135	—	5	1	no	—
157	C₃×#135	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
158	C₂×C₃×Q₁₆	—	5	1	no	—
159	C₂×C₃×SD₁₆	—	5	2	no	—
160	C₂×C₃×D₈	—	5	1	no	—
161	C₂²×C₃×C₈	—	5	1	no	—
162	#948	—	5	4	no	—
163	#948	—	5	4	no	—
164	#948	—	10	4	no	—
165	C₂×C₄×Dic₃	—	5	1	no	—
166	C₂×#208	—	5	2	no	—
167	C₂×#208	—	10	2	no	—
168	C₂²×C₃⋊C₈	—	5	1	no	—
169	C₂²×C₃⋊C₈	—	10	2	no	—
170	#837	—	5	4	no	—
171	#837	—	5	4	no	—
172	#819	—	5	2	no	—
173	#819	—	5	2	no	—
174	C₈×Dic₃	—	5	2	no	—
175	C₈×Dic₃	—	5	2	no	—
176	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
177	C₅×#41	C₂×Dic₃	1	2	yes	—
178	#713	C₂²×D₃	1	2	yes	—
179	Q₈×D₅	C₂×Dic₃	1	2	yes	—
180	#711	—	2	2	no	—
181	#711	C₂²×D₃	1	2	yes	—
182	D₄×D₅	—	2	2	no	—
183	D₄×D₅	C₂×Dic₃	1	2	yes	—
184	#709	—	2	2	no	—
185	#709	C₂×Dic₃	1	2	yes	—
186	C₂×C₄×D₅	—	2	2	no	—
187	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
188	#704	—	6	4	no	—
189	#704	—	6	2	no	—
190	C₂×#170	—	3	2	no	—
191	C₂×#170	—	6	4	no	—
192	C₄×AGL(1,𝔽₅)	—	3	2	no	—
193	C₄×AGL(1,𝔽₅)	—	6	1	no	—
194	#700	—	3	4	no	—
195	#700	—	6	4	no	—
196	D₅⋊C₈	—	3	1	no	—
197	D₅⋊C₈	—	3	1	no	—
198	D₅⋊C₈	—	3	2	no	—
199	D₅⋊C₈	—	6	4	no	—
200	D₅⋊C₈	—	6	2	no	—
201	C₅×Q₁₆	C₂×Dic₃	1	1	yes	characteristic, complemented
202	C₅×SD₁₆	C₂×Dic₃	1	2	yes	complemented
203	C₅×D₈	C₂×Dic₃	1	1	yes	characteristic, complemented
204	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
205	#689	C₂×Dic₃	1	2	yes	complemented
206	#688	C₂×Dic₃	1	2	yes	complemented
207	#687	C₂×Dic₃	1	2	yes	complemented
208	#686	C₂×Dic₃	1	2	yes	complemented
209	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
210	Dic₂₀	C₂×Dic₃	1	1	yes	characteristic, complemented
211	D₄₀	C₂×Dic₃	1	1	yes	characteristic, complemented
212	#677	C₂×Dic₃	1	2	yes	complemented
213	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
214	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
215	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
216	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
217	C₂×#135	—	5	1	no	—
218	C₂×#131	—	15	2	no	—
219	#443	—	15	2	no	—
220	#443	—	15	4	no	—
221	#443	—	15	2	no	—
222	C₂×#108	—	15	1	no	—
223	C₂×#104	—	15	2	no	—
224	C₂×C₄×C₈	—	15	1	no	—
225	C₂²×C₃×C₅	—	2	2	no	—
226	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
227	C₂×C₃×D₅	—	2	2	no	—
228	C₂×C₃×D₅	—	2	2	no	—
229	C₂×C₃×D₅	—	4	4	no	—
230	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
231	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
232	ΓL(1,𝔽₁₆)	—	2	4	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
235	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₃×Dic₅	—	2	2	no	—
237	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
238	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
239	C₃×#41	—	5	2	no	—
240	C₃×#41	—	5	2	no	—
241	C₃×#41	—	5	2	no	—
242	C₃×#41	—	10	2	no	—
243	C₃×#41	—	10	2	no	—
244	C₃×#41	C₂×AGL(1,𝔽₅)	1	2	yes	—
245	C₂×C₃×Q₈	—	5	2	no	—
246	C₂×C₃×D₄	—	5	2	no	—
247	C₂×C₃×D₄	—	10	2	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	10	2	no	—
250	C₂²×Dic₃	—	10	1	no	—
251	C₃×Q₁₆	—	5	2	no	—
252	C₃×Q₁₆	—	5	1	no	—
253	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
254	C₃×SD₁₆	—	5	2	no	—
255	C₃×SD₁₆	—	5	2	no	—
256	C₃×SD₁₆	—	5	2	no	—
257	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
258	C₃×D₈	—	5	2	no	—
259	C₃×D₈	—	5	1	no	—
260	C₃×D₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
261	C₂×C₃×C₈	—	5	1	no	—
262	C₂×C₃×C₈	—	5	1	no	—
263	C₂×C₃×C₈	—	5	1	no	—
264	C₂×C₃×C₈	—	5	1	no	—
265	C₂×C₃×C₈	—	5	1	no	—
266	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
267	C₄×Dic₃	—	5	2	no	—
268	C₄×Dic₃	—	10	1	no	—
269	#208	—	5	4	no	—
270	#208	—	10	4	no	—
271	#208	—	10	4	no	—
272	#208	—	10	2	no	—
273	C₂×C₃⋊C₈	—	5	2	no	—
274	C₂×C₃⋊C₈	—	5	1	no	—
275	C₂×C₃⋊C₈	—	5	1	no	—
276	C₂×C₃⋊C₈	—	5	2	no	—
277	C₂×C₃⋊C₈	—	10	4	no	—
278	C₂×C₃⋊C₈	—	10	4	no	—
279	C₂×C₃⋊C₈	—	10	2	no	—
280	C₂²×D₅	—	2	2	no	—
281	C₂²×D₅	#237	1	1	yes	characteristic
282	C₂×AGL(1,𝔽₅)	—	6	4	no	—
283	C₂×AGL(1,𝔽₅)	—	6	2	no	—
284	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	C₂²×Dic₃	1	2	yes	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
289	C₂²⋊D₅	—	2	2	no	—
290	C₂²⋊D₅	—	2	2	no	—
291	C₂²⋊D₅	—	2	2	no	—
292	C₂×Dic₅	—	2	2	no	—
293	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
294	D₂₀	—	2	2	no	—
295	D₂₀	C₂²×Dic₃	1	2	yes	—
296	C₄×D₅	—	2	2	no	—
297	C₄×D₅	—	2	2	no	—
298	C₄×D₅	—	2	2	no	—
299	C₄×D₅	D₃×D₄	1	1	yes	characteristic
300	C₄×D₅	#237	1	1	yes	characteristic
301	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
302	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
303	Dic₁₀	—	2	2	no	—
304	Dic₁₀	C₂²×Dic₃	1	2	yes	—
305	#170	—	3	2	no	—
306	#170	—	3	2	no	—
307	#170	—	6	4	no	—
308	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
309	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
310	#168	C₂²×Dic₃	1	1	yes	characteristic
311	#168	C₂²×Dic₃	1	1	yes	characteristic
312	C₂×#41	—	5	2	no	—
313	#135	—	5	2	no	—
314	#135	—	5	1	no	—
315	#135	—	5	2	no	—
316	#135	—	5	1	no	—
317	#135	—	5	1	no	—
318	#135	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
319	C₂×Q₁₆	—	5	1	no	—
320	C₂×SD₁₆	—	5	2	no	—
321	C₂×D₈	—	5	1	no	—
322	#131	—	15	4	no	—
323	#131	—	15	4	no	—
324	#131	—	30	4	no	—
325	C₂×M₁₆	—	15	2	no	—
326	C₂×M₁₆	—	30	2	no	—
327	C₂²×C₈	—	5	1	no	—
328	C₂²×C₈	—	15	1	no	—
329	C₂²×C₈	—	30	2	no	—
330	C₂×C₄²	—	15	1	no	—
331	#108	—	15	2	no	—
332	#108	—	15	2	no	—
333	#104	—	15	4	no	—
334	#104	—	15	4	no	—
335	C₄×C₈	—	15	2	no	—
336	C₄×C₈	—	15	2	no	—
337	C₂×C₃×C₅	—	2	1	no	—
338	C₂×C₃×C₅	—	4	2	no	—
339	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
340	C₃×D₅	—	2	1	no	—
341	C₃×D₅	—	4	2	no	—
342	C₃×D₅	#443	1	2	yes	complemented
343	C₂³×C₃	—	5	1	no	—
344	C₂³×C₃	—	10	2	no	—
345	C₃×Q₈	—	5	2	no	—
346	C₃×Q₈	—	10	2	no	—
347	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
348	C₃×D₄	—	2	2	no	—
349	C₃×D₄	—	5	2	no	—
350	C₃×D₄	—	10	2	no	—
351	C₃×D₄	—	10	2	no	—
352	C₃×D₄	—	10	2	no	—
353	C₃×D₄	—	10	2	no	—
354	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	5	1	no	—
357	C₂×C₃×C₄	—	5	1	no	—
358	C₂×C₃×C₄	—	5	1	no	—
359	C₂×C₃×C₄	—	5	1	no	—
360	C₂×C₃×C₄	—	5	1	no	—
361	C₂×C₃×C₄	—	10	2	no	—
362	C₂×C₃×C₄	—	10	2	no	—
363	C₂×C₃×C₄	—	10	2	no	—
364	C₂×C₃×C₄	—	10	2	no	—
365	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₂×Dic₃	—	10	2	no	—
367	C₂×Dic₃	—	10	4	no	—
368	C₃×C₈	—	5	1	no	—
369	C₃×C₈	—	5	1	no	—
370	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
372	C₃⋊C₈	—	5	2	no	—
373	C₃⋊C₈	—	5	2	no	—
374	C₃⋊C₈	—	10	4	no	—
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
377	C₂×D₅	—	2	2	no	—
378	C₂×D₅	—	2	2	no	—
379	C₂×D₅	—	4	4	no	—
380	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
381	C₂×D₅	C₂×#237	1	1	yes	characteristic
382	AGL(1,𝔽₅)	—	6	4	no	—
383	C₄×C₅	—	2	2	no	—
384	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
385	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
386	Dic₅	—	2	2	no	—
387	Dic₅	D₄×Dic₃	1	1	yes	characteristic
388	Dic₅	C₂×D₃×D₄	1	1	yes	characteristic
389	#41	—	5	2	no	—
390	#41	—	5	2	no	—
391	#41	—	5	2	no	—
392	#41	—	10	2	no	—
393	#41	—	10	2	no	—
394	#41	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
395	C₂×Q₈	—	5	2	no	—
396	C₂×D₄	—	5	2	no	—
397	C₂×D₄	—	10	2	no	—
398	C₂²×C₄	—	5	1	no	—
399	C₂²×C₄	—	10	2	no	—
400	C₂²×C₄	—	30	1	no	—
401	Q₁₆	—	5	2	no	—
402	Q₁₆	—	5	1	no	—
403	Q₁₆	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
404	SD₁₆	—	5	2	no	—
405	SD₁₆	—	5	2	no	—
406	SD₁₆	—	5	2	no	—
407	SD₁₆	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
408	D₈	—	5	2	no	—
409	D₈	—	5	1	no	—
410	D₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
411	M₁₆	—	15	4	no	—
412	M₁₆	—	30	4	no	—
413	M₁₆	—	30	4	no	—
414	M₁₆	—	30	2	no	—
415	C₂×C₈	—	5	1	no	—
416	C₂×C₈	—	5	1	no	—
417	C₂×C₈	—	5	1	no	—
418	C₂×C₈	—	5	1	no	—
419	C₂×C₈	—	5	1	no	—
420	C₂×C₈	—	15	2	no	—
421	C₂×C₈	—	15	1	no	—
422	C₂×C₈	—	15	1	no	—
423	C₂×C₈	—	15	2	no	—
424	C₂×C₈	—	30	4	no	—
425	C₂×C₈	—	30	4	no	—
426	C₂×C₈	—	30	2	no	—
427	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
428	C₄²	—	15	2	no	—
429	C₄²	—	30	1	no	—
430	C₃×C₅	C₂×#443	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	5	1	no	—
433	C₂²×C₃	—	5	1	no	—
434	C₂²×C₃	—	10	2	no	—
435	C₂²×C₃	—	10	2	no	—
436	C₂²×C₃	—	20	4	no	—
437	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	5	1	no	—
440	C₃×C₄	—	5	1	no	—
441	C₃×C₄	—	10	2	no	—
442	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
443	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
444	Dic₃	—	10	4	no	—
445	C₂×C₅	—	2	1	no	—
446	C₂×C₅	—	4	2	no	—
447	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
448	D₅	—	2	1	no	—
449	D₅	—	4	2	no	—
450	D₅	#5196	1	2	yes	complemented
451	C₂³	—	5	1	no	—
452	C₂³	—	10	2	no	—
453	Q₈	—	5	2	no	—
454	Q₈	—	10	2	no	—
455	Q₈	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
456	D₄	—	2	2	no	—
457	D₄	—	5	2	no	—
458	D₄	—	10	2	no	—
459	D₄	—	10	2	no	—
460	D₄	—	10	2	no	—
461	D₄	—	10	2	no	—
462	D₄	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	5	1	no	—
465	C₂×C₄	—	5	1	no	—
466	C₂×C₄	—	5	1	no	—
467	C₂×C₄	—	5	1	no	—
468	C₂×C₄	—	5	1	no	—
469	C₂×C₄	—	10	2	no	—
470	C₂×C₄	—	10	2	no	—
471	C₂×C₄	—	10	2	no	—
472	C₂×C₄	—	10	2	no	—
473	C₂×C₄	—	30	2	no	—
474	C₂×C₄	—	30	4	no	—
475	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
476	C₈	—	5	1	no	—
477	C₈	—	5	1	no	—
478	C₈	—	15	2	no	—
479	C₈	—	15	2	no	—
480	C₈	—	30	4	no	—
481	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
482	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
483	C₂×C₃	—	2	1	no	—
484	C₂×C₃	—	4	2	no	—
485	C₂×C₃	—	5	2	no	—
486	C₂×C₃	—	10	1	no	—
487	C₂×C₃	—	20	2	no	—
488	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
489	C₅	C₂×#5196	1	1	yes	characteristic, complemented, Sylow
490	C₂²	—	2	2	no	—
491	C₂²	—	5	1	no	—
492	C₂²	—	5	1	no	—
493	C₂²	—	10	2	no	—
494	C₂²	—	10	2	no	—
495	C₂²	—	20	4	no	—
496	C₂²	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
497	C₄	—	2	2	no	—
498	C₄	—	5	1	no	—
499	C₄	—	5	1	no	—
500	C₄	—	10	2	no	—
501	C₄	—	30	4	no	—
502	C₄	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
503	C₄	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
504	C₃	D₅⋊#443	1	1	yes	characteristic, complemented, Sylow
505	C₂	—	2	1	no	—
506	C₂	—	4	2	no	—
507	C₂	—	5	2	no	—
508	C₂	—	10	1	no	—
509	C₂	—	20	2	no	—
510	C₂	C₂×D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×ΓL(1,𝔽₁₆)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂³×ΓL(1,𝔽₁₆)
Fitting	C₃×C₅×#135	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×D₅×#135	C₂
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	#135	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₂×#443
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. D₅⋊#948	C₂	semidirect
3. D₅⋊#837	C₂	semidirect
4. #11752399	C₂	semidirect
5. #11752395	C₂	semidirect
6. #11752391	C₂	semidirect
7. D₅⋊#819	C₂	semidirect
8. C₂×C₈×ΓL(1,𝔽₁₆)	C₂	semidirect
11. #91992	C₂²	semidirect
13. #91990	C₂²	semidirect
19. C₃×C₅×#135	C₄	semidirect
20. C₃×#4096	C₄	semidirect
22. C₃×D₅×Q₁₆	C₄	semidirect
24. C₃×D₅×SD₁₆	C₄	semidirect
26. C₃×D₅×D₈	C₄	semidirect
27. C₃×#4050	C₄	semidirect
29. #91239	C₂²	semidirect
30. #91237	C₂²	semidirect
31. #91225	C₂²	semidirect
32. #91224	C₂²	semidirect
33. C₈×ΓL(1,𝔽₁₆)	C₂²	semidirect
34. C₈×ΓL(1,𝔽₁₆)	C₂²	semidirect
69. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₃×C₅×SD₁₆	C₂×C₄	semidirect
71. C₃×C₅×D₈	C₂×C₄	semidirect
73. C₃×#689	C₂×C₄	semidirect
74. C₃×#688	C₂×C₄	semidirect
75. C₃×#687	C₂×C₄	semidirect
76. C₃×#686	C₂×C₄	semidirect
78. C₃×Dic₂₀	C₂×C₄	semidirect
79. C₃×D₄₀	C₂×C₄	semidirect
80. C₃×#677	C₂×C₄	semidirect
102. C₅×#135	Dic₃	semidirect
103. #4096	Dic₃	semidirect
105. D₅×Q₁₆	Dic₃	semidirect
107. D₅×SD₁₆	Dic₃	semidirect
109. D₅×D₈	Dic₃	semidirect
110. #4050	Dic₃	semidirect
157. C₃×#135	AGL(1,𝔽₅)	semidirect
201. C₅×Q₁₆	C₂×Dic₃	semidirect
202. C₅×SD₁₆	C₂×Dic₃	semidirect
203. C₅×D₈	C₂×Dic₃	semidirect
205. #689	C₂×Dic₃	semidirect
206. #688	C₂×Dic₃	semidirect
207. #687	C₂×Dic₃	semidirect
208. #686	C₂×Dic₃	semidirect
210. Dic₂₀	C₂×Dic₃	semidirect
211. D₄₀	C₂×Dic₃	semidirect
212. #677	C₂×Dic₃	semidirect
253. C₃×Q₁₆	C₂×AGL(1,𝔽₅)	semidirect
257. C₃×SD₁₆	C₂×AGL(1,𝔽₅)	semidirect
260. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
318. #135	ΓL(1,𝔽₁₆)	semidirect
342. C₃×D₅	#443	semidirect
403. Q₁₆	C₂×ΓL(1,𝔽₁₆)	semidirect
407. SD₁₆	C₂×ΓL(1,𝔽₁₆)	semidirect
410. D₈	C₂×ΓL(1,𝔽₁₆)	semidirect
430. C₃×C₅	C₂×#443	semidirect
450. D₅	#5196	semidirect
489. C₅	C₂×#5196	semidirect
504. C₃	D₅⋊#443	semidirect

Maximal subgroups

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

subgroup	index
D₅⋊#948	2
C₃×D₅×#135	2
D₅⋊#837	2
#11752399	2
#11752395	2
#11752391	2
D₅⋊#819	2
C₂×C₈×ΓL(1,𝔽₁₆)	2
D₅⋊#443	3
C₂×#5196	5

Subgroups — D5⋊#5196 #14417852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#5196 #14417852