Subgroups — D₅⋊#5197 #14417941

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 504 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	#11752400	C₂	1	2	yes	maximal, complemented
5	#11752396	C₂	1	4	yes	maximal, complemented
6	#11752392	C₂	1	2	yes	maximal, complemented
7	D₅⋊#819	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#91221	C₂	1	1	yes	maximal, characteristic, complemented
9	D₅⋊#444	—	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	#91221	C₂²	1	2	yes	complemented
34	#91221	C₂²	1	2	yes	complemented
35	C₂×#5197	—	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	#65741	—	3	2	no	—
40	#65737	—	3	4	no	—
41	#65733	—	3	2	no	—
42	D₅⋊#108	—	3	1	no	—
43	C₂×#3992	—	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	2	yes	—
67	D₅⋊(C₃⋊C₈)	C₂³	1	2	yes	—
68	C₃×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
69	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
70	C₃×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
72	C₃×#689	C₂×C₄	1	2	yes	complemented
73	C₃×#688	C₂×C₄	1	2	yes	complemented
74	C₃×#687	C₂×C₄	1	2	yes	complemented
75	C₃×#686	C₂×C₄	1	2	yes	complemented
76	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
77	C₃×Dic₂₀	C₂×C₄	1	1	yes	characteristic, complemented
78	C₃×D₄₀	C₂×C₄	1	1	yes	characteristic, complemented
79	C₃×#677	C₂×C₄	1	2	yes	complemented
80	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
83	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×#135	—	5	1	no	—
85	C₂×#948	—	5	2	no	—
86	C₂×#837	—	5	2	no	—
87	#5197	—	5	2	no	—
88	#5197	—	5	4	no	—
89	#5197	—	5	2	no	—
90	C₂×#819	—	5	1	no	—
91	C₂×#815	—	5	1	no	—
92	D₅×#41	C₂×D₃	1	2	yes	—
93	#4133	—	3	4	no	—
94	#4131	—	3	4	no	—
95	#4131	—	6	4	no	—
96	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
97	D₅⋊M₁₆	—	3	2	no	—
98	D₅⋊M₁₆	—	6	2	no	—
99	C₂×D₅⋊C₈	—	3	1	no	—
100	C₂×D₅⋊C₈	—	6	2	no	—
101	C₅×#135	Dic₃	1	1	yes	characteristic, complemented
102	#4096	Dic₃	1	2	yes	complemented
103	#4065	C₂×D₃	1	1	yes	characteristic
104	D₅×Q₁₆	Dic₃	1	1	yes	characteristic, complemented
105	#4062	C₂×D₃	1	2	yes	—
106	D₅×SD₁₆	Dic₃	1	2	yes	complemented
107	#4058	C₂×D₃	1	1	yes	characteristic
108	D₅×D₈	Dic₃	1	1	yes	characteristic, complemented
109	#4050	Dic₃	1	1	yes	characteristic, complemented
110	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
111	#4010	—	3	4	no	—
112	#4008	—	3	4	no	—
113	#3996	—	3	2	no	—
114	#3995	—	3	2	no	—
115	#3992	—	3	2	no	—
116	#3992	—	3	2	no	—
117	C₂×#444	—	15	1	no	Sylow
118	C₂²×C₃×D₅	—	2	2	no	—
119	C₂²×C₃×D₅	#41	1	1	yes	characteristic
120	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
121	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
122	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
123	C₃×C₅×D₄	—	2	2	no	—
124	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₃×C₂²⋊D₅	—	2	2	no	—
128	C₃×C₂²⋊D₅	—	2	2	no	—
129	C₃×C₂²⋊D₅	—	2	2	no	—
130	C₂×C₃×Dic₅	—	2	2	no	—
131	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
132	C₃×D₂₀	—	2	2	no	—
133	C₃×D₂₀	C₂²×C₄	1	2	yes	—
134	C₃×C₄×D₅	—	2	2	no	—
135	C₃×C₄×D₅	—	2	2	no	—
136	C₃×C₄×D₅	—	2	2	no	—
137	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
138	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₄×D₅	#41	1	1	yes	characteristic
140	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
141	C₃×Dic₁₀	—	2	2	no	—
142	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
143	C₃⋊#170	—	2	4	no	—
144	C₃⋊#170	C₂×D₄	1	4	yes	—
145	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₃×#168	C₂²×C₄	1	1	yes	characteristic
148	C₃×#168	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×#41	—	5	2	no	—
150	C₃×#135	—	5	2	no	—
151	C₃×#135	—	5	1	no	—
152	C₃×#135	—	5	2	no	—
153	C₃×#135	—	5	1	no	—
154	C₃×#135	—	5	1	no	—
155	C₃×#135	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
156	C₂×C₃×Q₁₆	—	5	1	no	—
157	C₂×C₃×SD₁₆	—	5	2	no	—
158	C₂×C₃×D₈	—	5	1	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	#948	—	5	4	no	—
161	#948	—	5	4	no	—
162	#948	—	10	4	no	—
163	C₂×C₄×Dic₃	—	5	1	no	—
164	C₂×#208	—	5	2	no	—
165	C₂×#208	—	10	2	no	—
166	C₂²×C₃⋊C₈	—	5	1	no	—
167	C₂²×C₃⋊C₈	—	10	2	no	—
168	#837	—	5	4	no	—
169	#837	—	5	4	no	—
170	#819	—	5	2	no	—
171	#819	—	5	2	no	—
172	#815	—	5	2	no	—
173	#815	—	5	2	no	—
174	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
175	C₅×#41	C₂×Dic₃	1	2	yes	—
176	#713	C₂²×D₃	1	2	yes	—
177	Q₈×D₅	C₂×Dic₃	1	2	yes	—
178	#711	—	2	2	no	—
179	#711	C₂²×D₃	1	2	yes	—
180	D₄×D₅	—	2	2	no	—
181	D₄×D₅	C₂×Dic₃	1	2	yes	—
182	#709	—	2	2	no	—
183	#709	C₂×Dic₃	1	2	yes	—
184	C₂×C₄×D₅	—	2	2	no	—
185	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
186	#704	—	6	4	no	—
187	#704	—	6	2	no	—
188	C₂×#170	—	3	2	no	—
189	C₂×#170	—	6	4	no	—
190	C₄×AGL(1,𝔽₅)	—	3	2	no	—
191	C₄×AGL(1,𝔽₅)	—	6	1	no	—
192	#700	—	3	4	no	—
193	#700	—	6	4	no	—
194	D₅⋊C₈	—	3	2	no	—
195	D₅⋊C₈	—	3	2	no	—
196	D₅⋊C₈	—	6	4	no	—
197	D₅⋊C₈	—	6	2	no	—
198	C₅×Q₁₆	C₂×Dic₃	1	1	yes	characteristic, complemented
199	C₅×SD₁₆	C₂×Dic₃	1	2	yes	complemented
200	C₅×D₈	C₂×Dic₃	1	1	yes	characteristic, complemented
201	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
202	#689	C₂×Dic₃	1	2	yes	complemented
203	#688	C₂×Dic₃	1	2	yes	complemented
204	#687	C₂×Dic₃	1	2	yes	complemented
205	#686	C₂×Dic₃	1	2	yes	complemented
206	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
207	Dic₂₀	C₂×Dic₃	1	1	yes	characteristic, complemented
208	D₄₀	C₂×Dic₃	1	1	yes	characteristic, complemented
209	#677	C₂×Dic₃	1	2	yes	complemented
210	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
211	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic
212	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
213	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
214	C₂×#135	—	5	1	no	—
215	C₂×#131	—	15	2	no	—
216	#444	—	15	2	no	—
217	#444	—	15	4	no	—
218	#444	—	15	2	no	—
219	C₂×#108	—	15	1	no	—
220	C₂×#104	—	15	2	no	—
221	C₂×#97	—	15	1	no	—
222	C₂²×C₃×C₅	—	2	2	no	—
223	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
224	C₂×C₃×D₅	—	2	2	no	—
225	C₂×C₃×D₅	—	2	2	no	—
226	C₂×C₃×D₅	—	4	4	no	—
227	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
229	ΓL(1,𝔽₁₆)	—	4	2	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
232	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
233	C₃×Dic₅	—	2	2	no	—
234	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
235	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
236	C₃×#41	—	5	2	no	—
237	C₃×#41	—	5	2	no	—
238	C₃×#41	—	5	2	no	—
239	C₃×#41	—	10	2	no	—
240	C₃×#41	—	10	2	no	—
241	C₃×#41	C₂×AGL(1,𝔽₅)	1	2	yes	—
242	C₂×C₃×Q₈	—	5	2	no	—
243	C₂×C₃×D₄	—	5	2	no	—
244	C₂×C₃×D₄	—	10	2	no	—
245	C₂²×C₃×C₄	—	5	1	no	—
246	C₂²×C₃×C₄	—	10	2	no	—
247	C₂²×Dic₃	—	10	1	no	—
248	C₃×Q₁₆	—	5	2	no	—
249	C₃×Q₁₆	—	5	1	no	—
250	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
251	C₃×SD₁₆	—	5	2	no	—
252	C₃×SD₁₆	—	5	2	no	—
253	C₃×SD₁₆	—	5	2	no	—
254	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
255	C₃×D₈	—	5	2	no	—
256	C₃×D₈	—	5	1	no	—
257	C₃×D₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	—	5	1	no	—
261	C₂×C₃×C₈	—	5	1	no	—
262	C₂×C₃×C₈	—	5	1	no	—
263	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
264	C₄×Dic₃	—	5	2	no	—
265	C₄×Dic₃	—	10	1	no	—
266	#208	—	5	4	no	—
267	#208	—	10	4	no	—
268	#208	—	10	4	no	—
269	#208	—	10	2	no	—
270	C₂×C₃⋊C₈	—	5	2	no	—
271	C₂×C₃⋊C₈	—	5	2	no	—
272	C₂×C₃⋊C₈	—	5	2	no	—
273	C₂×C₃⋊C₈	—	10	4	no	—
274	C₂×C₃⋊C₈	—	10	4	no	—
275	C₂×C₃⋊C₈	—	10	2	no	—
276	C₂²×D₅	—	2	2	no	—
277	C₂²×D₅	#237	1	1	yes	characteristic
278	C₂×AGL(1,𝔽₅)	—	6	2	no	—
279	C₂×AGL(1,𝔽₅)	—	12	2	no	—
280	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	C₂²×Dic₃	1	2	yes	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
285	C₂²⋊D₅	—	2	2	no	—
286	C₂²⋊D₅	—	2	2	no	—
287	C₂²⋊D₅	—	2	2	no	—
288	C₂×Dic₅	—	2	2	no	—
289	C₂×Dic₅	D₃×D₄	1	1	yes	characteristic
290	D₂₀	—	2	2	no	—
291	D₂₀	C₂²×Dic₃	1	2	yes	—
292	C₄×D₅	—	2	2	no	—
293	C₄×D₅	—	2	2	no	—
294	C₄×D₅	—	2	2	no	—
295	C₄×D₅	D₃×D₄	1	1	yes	characteristic
296	C₄×D₅	#237	1	1	yes	characteristic
297	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
298	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
299	Dic₁₀	—	2	2	no	—
300	Dic₁₀	C₂²×Dic₃	1	2	yes	—
301	#170	—	3	4	no	—
302	#170	—	6	4	no	—
303	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
304	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
305	#168	C₂²×Dic₃	1	1	yes	characteristic
306	#168	C₂²×Dic₃	1	1	yes	characteristic
307	C₂×#41	—	5	2	no	—
308	#135	—	5	2	no	—
309	#135	—	5	1	no	—
310	#135	—	5	2	no	—
311	#135	—	5	1	no	—
312	#135	—	5	1	no	—
313	#135	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
314	C₂×Q₁₆	—	5	1	no	—
315	C₂×SD₁₆	—	5	2	no	—
316	C₂×D₈	—	5	1	no	—
317	#131	—	15	4	no	—
318	#131	—	15	4	no	—
319	#131	—	30	4	no	—
320	C₂×M₁₆	—	15	2	no	—
321	C₂×M₁₆	—	30	2	no	—
322	C₂²×C₈	—	5	1	no	—
323	C₂²×C₈	—	15	1	no	—
324	C₂²×C₈	—	30	2	no	—
325	C₂×C₄²	—	15	1	no	—
326	#108	—	15	2	no	—
327	#108	—	15	2	no	—
328	#104	—	15	4	no	—
329	#104	—	15	4	no	—
330	#97	—	15	2	no	—
331	#97	—	15	2	no	—
332	C₂×C₃×C₅	—	2	1	no	—
333	C₂×C₃×C₅	—	4	2	no	—
334	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
335	C₃×D₅	—	2	1	no	—
336	C₃×D₅	—	4	2	no	—
337	C₃×D₅	#444	1	2	yes	complemented
338	C₂³×C₃	—	5	1	no	—
339	C₂³×C₃	—	10	2	no	—
340	C₃×Q₈	—	5	2	no	—
341	C₃×Q₈	—	10	2	no	—
342	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
343	C₃×D₄	—	2	2	no	—
344	C₃×D₄	—	5	2	no	—
345	C₃×D₄	—	10	2	no	—
346	C₃×D₄	—	10	2	no	—
347	C₃×D₄	—	10	2	no	—
348	C₃×D₄	—	10	2	no	—
349	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	5	1	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	5	1	no	—
354	C₂×C₃×C₄	—	5	1	no	—
355	C₂×C₃×C₄	—	5	1	no	—
356	C₂×C₃×C₄	—	10	2	no	—
357	C₂×C₃×C₄	—	10	2	no	—
358	C₂×C₃×C₄	—	10	2	no	—
359	C₂×C₃×C₄	—	10	2	no	—
360	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₂×Dic₃	—	10	2	no	—
362	C₂×Dic₃	—	20	2	no	—
363	C₃×C₈	—	5	1	no	—
364	C₃×C₈	—	5	1	no	—
365	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₃⋊C₈	—	5	4	no	—
368	C₃⋊C₈	—	10	4	no	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
371	C₂×D₅	—	2	2	no	—
372	C₂×D₅	—	2	2	no	—
373	C₂×D₅	—	4	4	no	—
374	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
375	C₂×D₅	C₂×#237	1	1	yes	characteristic
376	AGL(1,𝔽₅)	—	12	2	no	—
377	C₄×C₅	—	2	2	no	—
378	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
379	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
380	Dic₅	—	2	2	no	—
381	Dic₅	D₄×Dic₃	1	1	yes	characteristic
382	Dic₅	C₂×D₃×D₄	1	1	yes	characteristic
383	#41	—	5	2	no	—
384	#41	—	5	2	no	—
385	#41	—	5	2	no	—
386	#41	—	10	2	no	—
387	#41	—	10	2	no	—
388	#41	C₂×ΓL(1,𝔽₁₆)	1	2	yes	—
389	C₂×Q₈	—	5	2	no	—
390	C₂×D₄	—	5	2	no	—
391	C₂×D₄	—	10	2	no	—
392	C₂²×C₄	—	5	1	no	—
393	C₂²×C₄	—	10	2	no	—
394	C₂²×C₄	—	30	1	no	—
395	Q₁₆	—	5	2	no	—
396	Q₁₆	—	5	1	no	—
397	Q₁₆	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
398	SD₁₆	—	5	2	no	—
399	SD₁₆	—	5	2	no	—
400	SD₁₆	—	5	2	no	—
401	SD₁₆	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
402	D₈	—	5	2	no	—
403	D₈	—	5	1	no	—
404	D₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
405	M₁₆	—	15	4	no	—
406	M₁₆	—	30	4	no	—
407	M₁₆	—	30	4	no	—
408	M₁₆	—	30	2	no	—
409	C₂×C₈	—	5	1	no	—
410	C₂×C₈	—	5	1	no	—
411	C₂×C₈	—	5	1	no	—
412	C₂×C₈	—	5	1	no	—
413	C₂×C₈	—	5	1	no	—
414	C₂×C₈	—	15	2	no	—
415	C₂×C₈	—	15	2	no	—
416	C₂×C₈	—	15	2	no	—
417	C₂×C₈	—	30	4	no	—
418	C₂×C₈	—	30	4	no	—
419	C₂×C₈	—	30	2	no	—
420	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
421	C₄²	—	15	2	no	—
422	C₄²	—	30	1	no	—
423	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	5	1	no	—
426	C₂²×C₃	—	5	1	no	—
427	C₂²×C₃	—	10	2	no	—
428	C₂²×C₃	—	10	2	no	—
429	C₂²×C₃	—	20	4	no	—
430	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	5	1	no	—
433	C₃×C₄	—	5	1	no	—
434	C₃×C₄	—	10	2	no	—
435	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
436	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
437	Dic₃	—	20	2	no	—
438	C₂×C₅	—	2	1	no	—
439	C₂×C₅	—	4	2	no	—
440	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
441	D₅	—	2	1	no	—
442	D₅	—	4	2	no	—
443	D₅	#5197	1	2	yes	complemented
444	C₂³	—	5	1	no	—
445	C₂³	—	10	2	no	—
446	Q₈	—	5	2	no	—
447	Q₈	—	10	2	no	—
448	Q₈	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
449	D₄	—	2	2	no	—
450	D₄	—	5	2	no	—
451	D₄	—	10	2	no	—
452	D₄	—	10	2	no	—
453	D₄	—	10	2	no	—
454	D₄	—	10	2	no	—
455	D₄	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	5	1	no	—
459	C₂×C₄	—	5	1	no	—
460	C₂×C₄	—	5	1	no	—
461	C₂×C₄	—	5	1	no	—
462	C₂×C₄	—	10	2	no	—
463	C₂×C₄	—	10	2	no	—
464	C₂×C₄	—	10	2	no	—
465	C₂×C₄	—	10	2	no	—
466	C₂×C₄	—	30	2	no	—
467	C₂×C₄	—	60	2	no	—
468	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
469	C₈	—	5	1	no	—
470	C₈	—	5	1	no	—
471	C₈	—	15	4	no	—
472	C₈	—	30	4	no	—
473	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
474	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
475	C₂×C₃	—	2	1	no	—
476	C₂×C₃	—	4	2	no	—
477	C₂×C₃	—	5	2	no	—
478	C₂×C₃	—	10	1	no	—
479	C₂×C₃	—	20	2	no	—
480	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
481	C₅	C₂×#5197	1	1	yes	characteristic, complemented, Sylow
482	C₂²	—	2	2	no	—
483	C₂²	—	5	1	no	—
484	C₂²	—	5	1	no	—
485	C₂²	—	10	2	no	—
486	C₂²	—	10	2	no	—
487	C₂²	—	20	4	no	—
488	C₂²	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
489	C₄	—	2	2	no	—
490	C₄	—	5	1	no	—
491	C₄	—	5	1	no	—
492	C₄	—	10	2	no	—
493	C₄	—	60	2	no	—
494	C₄	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
495	C₄	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
496	C₃	D₅⋊#444	1	1	yes	characteristic, complemented, Sylow
497	C₂	—	2	1	no	—
498	C₂	—	4	2	no	—
499	C₂	—	5	2	no	—
500	C₂	—	10	1	no	—
501	C₂	—	20	2	no	—
502	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×#444
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. #11752400	C₂	semidirect
5. #11752396	C₂	semidirect
6. #11752392	C₂	semidirect
7. D₅⋊#819	C₂	semidirect
8. C₂×#91221	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. #91221	C₂²	semidirect
34. #91221	C₂²	semidirect
68. C₃×C₅×Q₁₆	C₂×C₄	semidirect
69. C₃×C₅×SD₁₆	C₂×C₄	semidirect
70. C₃×C₅×D₈	C₂×C₄	semidirect
72. C₃×#689	C₂×C₄	semidirect
73. C₃×#688	C₂×C₄	semidirect
74. C₃×#687	C₂×C₄	semidirect
75. C₃×#686	C₂×C₄	semidirect
77. C₃×Dic₂₀	C₂×C₄	semidirect
78. C₃×D₄₀	C₂×C₄	semidirect
79. C₃×#677	C₂×C₄	semidirect
101. C₅×#135	Dic₃	semidirect
102. #4096	Dic₃	semidirect
104. D₅×Q₁₆	Dic₃	semidirect
106. D₅×SD₁₆	Dic₃	semidirect
108. D₅×D₈	Dic₃	semidirect
109. #4050	Dic₃	semidirect
155. C₃×#135	AGL(1,𝔽₅)	semidirect
198. C₅×Q₁₆	C₂×Dic₃	semidirect
199. C₅×SD₁₆	C₂×Dic₃	semidirect
200. C₅×D₈	C₂×Dic₃	semidirect
202. #689	C₂×Dic₃	semidirect
203. #688	C₂×Dic₃	semidirect
204. #687	C₂×Dic₃	semidirect
205. #686	C₂×Dic₃	semidirect
207. Dic₂₀	C₂×Dic₃	semidirect
208. D₄₀	C₂×Dic₃	semidirect
209. #677	C₂×Dic₃	semidirect
250. C₃×Q₁₆	C₂×AGL(1,𝔽₅)	semidirect
254. C₃×SD₁₆	C₂×AGL(1,𝔽₅)	semidirect
257. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
313. #135	ΓL(1,𝔽₁₆)	semidirect
337. C₃×D₅	#444	semidirect
397. Q₁₆	C₂×ΓL(1,𝔽₁₆)	semidirect
401. SD₁₆	C₂×ΓL(1,𝔽₁₆)	semidirect
404. D₈	C₂×ΓL(1,𝔽₁₆)	semidirect
423. C₃×C₅	C₂×#444	semidirect
443. D₅	#5197	semidirect
481. C₅	C₂×#5197	semidirect
496. C₃	D₅⋊#444	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
#11752400	2
#11752396	2
#11752392	2
D₅⋊#819	2
C₂×#91221	2
D₅⋊#444	3
C₂×#5197	5

Subgroups — D5⋊#5197 #14417941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊#5197 #14417941