Subgroups — #14417636

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756995	C₂	1	2	yes	maximal, complemented
2	C₃×D₅×#135	C₂	1	1	yes	maximal, characteristic
3	#11752452	C₂	1	2	yes	maximal, complemented
4	Q₁₆×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
5	#11752394	C₂	1	4	yes	maximal, complemented
6	D₈×ΓL(1,𝔽₁₆)	C₂	1	2	yes	maximal, complemented
7	C₂×#91223	C₂	1	1	yes	maximal, characteristic, complemented
8	#11752377	C₂	1	1	yes	maximal, characteristic, complemented
9	#10617440	—	3	1	no	maximal, Hall
10	C₃×D₅×#41	C₂²	1	2	yes	—
11	Q₈×ΓL(1,𝔽₁₆)	C₂²	1	4	yes	—
12	D₄×ΓL(1,𝔽₁₆)	—	2	4	no	—
13	D₄×ΓL(1,𝔽₁₆)	C₂²	1	4	yes	—
14	#91989	—	2	2	no	—
15	#91989	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
17	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
18	D₅⋊#208	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	C₄	1	1	yes	characteristic, complemented
22	C₃×D₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₃×#4062	C₄	1	2	yes	complemented
24	C₃×D₅×SD₁₆	C₂²	1	2	yes	—
25	C₃×#4058	C₄	1	1	yes	characteristic, complemented
26	C₃×D₅×D₈	C₂²	1	1	yes	characteristic
27	C₃×#4050	C₄	1	1	yes	characteristic, complemented
28	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
29	#91238	C₂²	1	4	yes	—
30	#91236	C₂²	1	4	yes	—
31	#91223	C₂²	1	2	yes	—
32	#91223	C₂²	1	2	yes	—
33	#91221	C₂²	1	2	yes	—
34	C₈×ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
35	#83898	—	5	1	no	maximal, Hall
36	#66266	—	3	2	no	—
37	D₅×#135	D₃	1	1	yes	characteristic
38	#65793	—	3	2	no	—
39	Q₁₆×AGL(1,𝔽₅)	—	3	2	no	—
40	#65735	—	3	4	no	—
41	D₈×AGL(1,𝔽₅)	—	3	2	no	—
42	C₂×#3994	—	3	1	no	—
43	#65718	—	3	1	no	—
44	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
45	C₂²×ΓL(1,𝔽₁₆)	—	2	4	no	—
46	C₃×C₅×#41	C₂×C₄	1	2	yes	complemented
47	C₃×#713	C₂×C₄	1	2	yes	complemented
48	C₃×Q₈×D₅	C₂³	1	2	yes	—
49	C₃×#711	—	2	2	no	—
50	C₃×#711	C₂×C₄	1	2	yes	complemented
51	C₃×D₄×D₅	—	2	2	no	—
52	C₃×D₄×D₅	C₂³	1	2	yes	—
53	C₃×#709	—	2	2	no	—
54	C₃×#709	C₂×C₄	1	2	yes	complemented
55	C₂×C₃×C₄×D₅	—	2	2	no	—
56	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
57	#6763	—	2	4	no	—
58	#6763	D₄	1	2	yes	—
59	#6762	—	2	1	no	—
60	C₄⋊ΓL(1,𝔽₁₆)	—	2	4	no	—
61	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
62	C₄⋊ΓL(1,𝔽₁₆)	D₄	1	1	yes	characteristic
63	C₄⋊ΓL(1,𝔽₁₆)	D₄	1	1	yes	characteristic
64	C₄⋊ΓL(1,𝔽₁₆)	C₂³	1	4	yes	—
65	C₄×ΓL(1,𝔽₁₆)	—	2	4	no	—
66	C₄×ΓL(1,𝔽₁₆)	C₂³	1	2	yes	—
67	#6758	—	2	1	no	—
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, complemented
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, complemented
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, complemented
82	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
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	#5827	—	5	2	no	—
87	#5232	—	5	2	no	—
88	Dic₃×Q₁₆	—	5	2	no	—
89	#5164	—	5	4	no	—
90	Dic₃×D₈	—	5	2	no	—
91	C₂×#818	—	5	1	no	—
92	#5101	—	5	1	no	—
93	D₅×#41	C₂×D₃	1	2	yes	—
94	Q₈×AGL(1,𝔽₅)	—	3	4	no	—
95	D₄×AGL(1,𝔽₅)	—	3	4	no	—
96	D₄×AGL(1,𝔽₅)	—	6	4	no	—
97	#4130	—	3	1	no	—
98	#4130	—	6	2	no	—
99	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
100	C₂×C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
101	D₅⋊M₁₆	—	3	1	no	—
102	C₅×#135	Dic₃	1	1	yes	characteristic, complemented
103	#4096	Dic₃	1	2	yes	complemented
104	#4065	Dic₃	1	1	yes	characteristic, complemented
105	D₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
106	#4062	Dic₃	1	2	yes	complemented
107	D₅×SD₁₆	C₂×D₃	1	2	yes	—
108	#4058	Dic₃	1	1	yes	characteristic, complemented
109	D₅×D₈	C₂×D₃	1	1	yes	characteristic
110	#4050	Dic₃	1	1	yes	characteristic, complemented
111	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
112	#4009	—	3	4	no	—
113	#4007	—	3	4	no	—
114	#3994	—	3	2	no	—
115	#3994	—	3	2	no	—
116	#3992	—	3	2	no	—
117	C₈×AGL(1,𝔽₅)	—	3	2	no	—
118	#2951	—	15	1	no	Sylow
119	C₂²×C₃×D₅	—	2	2	no	—
120	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
121	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
122	C₂×ΓL(1,𝔽₁₆)	—	8	4	no	—
123	C₂×ΓL(1,𝔽₁₆)	—	8	2	no	—
124	C₂×ΓL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
125	C₂×ΓL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
126	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₃×C₂²⋊D₅	—	2	2	no	—
132	C₃×C₂²⋊D₅	—	2	2	no	—
133	C₃×C₂²⋊D₅	—	2	2	no	—
134	C₂×C₃×Dic₅	—	2	2	no	—
135	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
136	C₃×D₂₀	—	2	2	no	—
137	C₃×D₂₀	C₂²×C₄	1	2	yes	—
138	C₃×C₄×D₅	—	2	2	no	—
139	C₃×C₄×D₅	—	2	2	no	—
140	C₃×C₄×D₅	—	2	2	no	—
141	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
142	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
143	C₃×C₄×D₅	#41	1	1	yes	characteristic
144	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
145	C₃×Dic₁₀	—	2	2	no	—
146	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
147	C₃⋊#170	—	2	2	no	—
148	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₃×#168	C₂²×C₄	1	1	yes	characteristic
151	C₃×#168	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×#41	—	5	2	no	—
153	C₃×#135	—	5	2	no	—
154	C₃×#135	—	5	1	no	—
155	C₃×#135	—	5	2	no	—
156	C₃×#135	—	5	1	no	—
157	C₃×#135	—	5	1	no	—
158	C₃×#135	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
159	C₂×C₃×Q₁₆	—	5	1	no	—
160	C₂×C₃×SD₁₆	—	5	2	no	—
161	C₂×C₃×D₈	—	5	1	no	—
162	C₂²×C₃×C₈	—	5	1	no	—
163	Q₈×Dic₃	—	5	4	no	—
164	D₄×Dic₃	—	5	4	no	—
165	D₄×Dic₃	—	10	4	no	—
166	#926	—	5	1	no	—
167	#926	—	10	2	no	—
168	C₂×C₄⋊Dic₃	—	5	2	no	—
169	C₂×C₄⋊Dic₃	—	10	2	no	—
170	C₂×#208	—	5	1	no	—
171	#835	—	5	4	no	—
172	#832	—	5	4	no	—
173	#818	—	5	2	no	—
174	#818	—	5	2	no	—
175	#815	—	5	2	no	—
176	C₈×Dic₃	—	5	2	no	—
177	C₂²×AGL(1,𝔽₅)	—	6	4	no	—
178	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
179	C₅×#41	C₂×Dic₃	1	2	yes	complemented
180	#713	C₂×Dic₃	1	2	yes	complemented
181	Q₈×D₅	C₂²×D₃	1	2	yes	—
182	#711	—	2	2	no	—
183	#711	C₂×Dic₃	1	2	yes	complemented
184	D₄×D₅	—	2	2	no	—
185	D₄×D₅	C₂²×D₃	1	2	yes	—
186	#709	—	2	2	no	—
187	#709	C₂×Dic₃	1	2	yes	complemented
188	C₂×C₄×D₅	—	2	2	no	—
189	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
190	C₂²⋊AGL(1,𝔽₅)	—	3	2	no	—
191	C₂²⋊AGL(1,𝔽₅)	—	6	4	no	—
192	#704	—	6	1	no	—
193	C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
194	C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
195	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
196	C₄⋊AGL(1,𝔽₅)	—	6	4	no	—
197	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
198	C₄×AGL(1,𝔽₅)	—	3	2	no	—
199	C₄×AGL(1,𝔽₅)	—	6	4	no	—
200	#700	—	6	1	no	—
201	D₅⋊C₈	—	3	2	no	—
202	C₅×Q₁₆	C₂×Dic₃	1	1	yes	characteristic, complemented
203	C₅×SD₁₆	C₂×Dic₃	1	2	yes	complemented
204	C₅×D₈	C₂×Dic₃	1	1	yes	characteristic, complemented
205	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic, complemented
206	#689	C₂×Dic₃	1	2	yes	complemented
207	#688	C₂×Dic₃	1	2	yes	complemented
208	#687	C₂×Dic₃	1	2	yes	complemented
209	#686	C₂×Dic₃	1	2	yes	complemented
210	C₂×#168	C₂×Dic₃	1	1	yes	characteristic, complemented
211	Dic₂₀	C₂×Dic₃	1	1	yes	characteristic, complemented
212	D₄₀	C₂×Dic₃	1	1	yes	characteristic, complemented
213	#677	C₂×Dic₃	1	2	yes	complemented
214	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic, complemented
215	C₈×D₅	C₂×Dic₃	1	1	yes	characteristic, complemented
216	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
217	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
218	C₂×#135	—	5	1	no	—
219	#520	—	15	2	no	—
220	#440	—	15	4	no	—
221	C₄×Q₁₆	—	15	2	no	—
222	C₄×D₈	—	15	2	no	—
223	C₂×#107	—	15	1	no	—
224	#417	—	15	2	no	—
225	#405	—	15	1	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂×C₃×D₅	—	2	1	no	—
229	C₂×C₃×D₅	—	2	1	no	—
230	C₂×C₃×D₅	—	2	2	no	—
231	C₂×C₃×D₅	—	4	2	no	—
232	C₂×C₃×D₅	—	4	2	no	—
233	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
234	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
235	ΓL(1,𝔽₁₆)	—	2	2	no	—
236	ΓL(1,𝔽₁₆)	—	2	2	no	—
237	ΓL(1,𝔽₁₆)	—	4	4	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
243	C₃×Dic₅	C₂×#41	1	1	yes	characteristic
244	C₃×#41	—	5	2	no	—
245	C₃×#41	—	5	2	no	—
246	C₃×#41	—	5	2	no	—
247	C₃×#41	—	10	2	no	—
248	C₃×#41	—	10	2	no	—
249	C₃×#41	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
250	C₂×C₃×Q₈	—	5	2	no	—
251	C₂×C₃×D₄	—	5	2	no	—
252	C₂×C₃×D₄	—	10	2	no	—
253	C₂²×C₃×C₄	—	5	1	no	—
254	C₂²×C₃×C₄	—	10	2	no	—
255	C₂²×Dic₃	—	10	4	no	—
256	C₂²×Dic₃	—	10	2	no	—
257	C₃×Q₁₆	—	5	2	no	—
258	C₃×Q₁₆	—	5	1	no	—
259	C₃×Q₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
260	C₃×SD₁₆	—	5	2	no	—
261	C₃×SD₁₆	—	5	2	no	—
262	C₃×SD₁₆	—	5	2	no	—
263	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
264	C₃×D₈	—	5	2	no	—
265	C₃×D₈	—	5	1	no	—
266	C₃×D₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
267	C₂×C₃×C₈	—	5	1	no	—
268	C₂×C₃×C₈	—	5	1	no	—
269	C₂×C₃×C₈	—	5	1	no	—
270	C₂×C₃×C₈	—	5	1	no	—
271	C₂×C₃×C₈	—	5	1	no	—
272	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
273	#217	—	5	2	no	—
274	#217	—	10	4	no	—
275	C₄⋊Dic₃	—	5	1	no	—
276	C₄⋊Dic₃	—	5	1	no	—
277	C₄⋊Dic₃	—	5	4	no	—
278	C₄⋊Dic₃	—	10	4	no	—
279	C₄⋊Dic₃	—	10	2	no	—
280	C₄×Dic₃	—	5	2	no	—
281	C₄×Dic₃	—	10	4	no	—
282	#208	—	10	1	no	—
283	#208	—	10	1	no	—
284	C₂×C₃⋊C₈	—	5	2	no	—
285	C₂²×D₅	—	2	2	no	—
286	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
287	C₂×AGL(1,𝔽₅)	—	3	2	no	—
288	C₂×AGL(1,𝔽₅)	—	3	2	no	—
289	C₂×AGL(1,𝔽₅)	—	6	4	no	—
290	C₂×AGL(1,𝔽₅)	—	24	4	no	—
291	C₂×AGL(1,𝔽₅)	—	24	2	no	—
292	C₅×Q₈	C₂²×Dic₃	1	2	yes	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	C₂²×Dic₃	1	2	yes	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
297	C₂²⋊D₅	—	2	2	no	—
298	C₂²⋊D₅	—	2	2	no	—
299	C₂²⋊D₅	—	2	2	no	—
300	C₂×Dic₅	—	2	2	no	—
301	C₂×Dic₅	#237	1	1	yes	characteristic
302	D₂₀	—	2	2	no	—
303	D₂₀	C₂²×Dic₃	1	2	yes	—
304	C₄×D₅	—	2	2	no	—
305	C₄×D₅	—	2	2	no	—
306	C₄×D₅	—	2	2	no	—
307	C₄×D₅	D₃×D₄	1	1	yes	characteristic
308	C₄×D₅	#237	1	1	yes	characteristic
309	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
310	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
311	Dic₁₀	—	2	2	no	—
312	Dic₁₀	C₂²×Dic₃	1	2	yes	—
313	#170	—	6	2	no	—
314	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
315	C₅×C₈	C₂²×Dic₃	1	1	yes	characteristic
316	#168	C₂²×Dic₃	1	1	yes	characteristic
317	#168	C₂²×Dic₃	1	1	yes	characteristic
318	C₂×#41	—	5	2	no	—
319	#135	—	5	2	no	—
320	#135	—	5	1	no	—
321	#135	—	5	2	no	—
322	#135	—	5	1	no	—
323	#135	—	5	1	no	—
324	#135	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
325	C₂×Q₁₆	—	5	1	no	—
326	C₂×SD₁₆	—	5	2	no	—
327	C₂×D₈	—	5	1	no	—
328	C₂×M₁₆	—	15	1	no	—
329	C₂²×C₈	—	5	1	no	—
330	C₄×Q₈	—	15	4	no	—
331	C₄×D₄	—	15	4	no	—
332	C₄×D₄	—	30	4	no	—
333	#117	—	15	1	no	—
334	#117	—	30	2	no	—
335	C₂×C₄⋊C₄	—	15	2	no	—
336	C₂×C₄⋊C₄	—	30	2	no	—
337	#107	—	15	2	no	—
338	#107	—	15	2	no	—
339	#103	—	15	4	no	—
340	#102	—	15	4	no	—
341	#97	—	15	2	no	—
342	C₄×C₈	—	15	2	no	—
343	C₂×C₃×C₅	—	2	1	no	—
344	C₂×C₃×C₅	—	4	2	no	—
345	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
346	C₃×D₅	—	2	1	no	—
347	C₃×D₅	—	4	2	no	—
348	C₃×D₅	#576	1	1	yes	characteristic
349	C₃×D₅	#578	1	1	yes	characteristic
350	C₂³×C₃	—	5	1	no	—
351	C₂³×C₃	—	10	2	no	—
352	C₃×Q₈	—	5	2	no	—
353	C₃×Q₈	—	10	2	no	—
354	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
355	C₃×D₄	—	2	2	no	—
356	C₃×D₄	—	5	2	no	—
357	C₃×D₄	—	10	2	no	—
358	C₃×D₄	—	10	2	no	—
359	C₃×D₄	—	10	2	no	—
360	C₃×D₄	—	10	2	no	—
361	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
362	C₂×C₃×C₄	—	2	2	no	—
363	C₂×C₃×C₄	—	5	1	no	—
364	C₂×C₃×C₄	—	5	1	no	—
365	C₂×C₃×C₄	—	5	1	no	—
366	C₂×C₃×C₄	—	5	1	no	—
367	C₂×C₃×C₄	—	5	1	no	—
368	C₂×C₃×C₄	—	10	2	no	—
369	C₂×C₃×C₄	—	10	2	no	—
370	C₂×C₃×C₄	—	10	2	no	—
371	C₂×C₃×C₄	—	10	2	no	—
372	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₂×Dic₃	—	5	2	no	—
374	C₂×Dic₃	—	5	2	no	—
375	C₂×Dic₃	—	10	4	no	—
376	C₂×Dic₃	—	40	4	no	—
377	C₂×Dic₃	—	40	2	no	—
378	C₃×C₈	—	5	1	no	—
379	C₃×C₈	—	5	1	no	—
380	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
381	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₃⋊C₈	—	10	2	no	—
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
385	C₂×D₅	—	2	1	no	—
386	C₂×D₅	—	2	1	no	—
387	C₂×D₅	—	2	2	no	—
388	C₂×D₅	—	4	2	no	—
389	C₂×D₅	—	4	2	no	—
390	C₂×D₅	D₄×Dic₃	1	1	yes	characteristic
391	C₂×D₅	C₂×D₃×D₄	1	1	yes	characteristic
392	AGL(1,𝔽₅)	—	6	2	no	—
393	AGL(1,𝔽₅)	—	6	2	no	—
394	AGL(1,𝔽₅)	—	12	4	no	—
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
397	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
398	Dic₅	—	2	2	no	—
399	Dic₅	D₄×Dic₃	1	1	yes	characteristic
400	Dic₅	C₂×#237	1	1	yes	characteristic
401	#41	—	5	2	no	—
402	#41	—	5	2	no	—
403	#41	—	5	2	no	—
404	#41	—	10	2	no	—
405	#41	—	10	2	no	—
406	#41	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
407	C₂×Q₈	—	5	2	no	—
408	C₂×D₄	—	5	2	no	—
409	C₂×D₄	—	10	2	no	—
410	C₂²×C₄	—	5	1	no	—
411	C₂²×C₄	—	10	2	no	—
412	C₂²×C₄	—	30	4	no	—
413	C₂²×C₄	—	30	2	no	—
414	Q₁₆	—	5	2	no	—
415	Q₁₆	—	5	1	no	—
416	Q₁₆	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
417	SD₁₆	—	5	2	no	—
418	SD₁₆	—	5	2	no	—
419	SD₁₆	—	5	2	no	—
420	SD₁₆	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
421	D₈	—	5	2	no	—
422	D₈	—	5	1	no	—
423	D₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
424	M₁₆	—	30	1	no	—
425	M₁₆	—	30	1	no	—
426	C₂×C₈	—	5	1	no	—
427	C₂×C₈	—	5	1	no	—
428	C₂×C₈	—	5	1	no	—
429	C₂×C₈	—	5	1	no	—
430	C₂×C₈	—	5	1	no	—
431	C₂×C₈	—	15	2	no	—
432	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
433	C₄⋊C₄	—	15	1	no	—
434	C₄⋊C₄	—	15	1	no	—
435	C₄⋊C₄	—	15	4	no	—
436	C₄⋊C₄	—	30	2	no	—
437	C₄⋊C₄	—	30	4	no	—
438	C₂²⋊C₄	—	15	2	no	—
439	C₂²⋊C₄	—	30	4	no	—
440	C₄²	—	15	2	no	—
441	C₄²	—	30	4	no	—
442	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
443	C₂²×C₃	—	2	2	no	—
444	C₂²×C₃	—	5	1	no	—
445	C₂²×C₃	—	5	1	no	—
446	C₂²×C₃	—	10	1	no	—
447	C₂²×C₃	—	10	1	no	—
448	C₂²×C₃	—	10	2	no	—
449	C₂²×C₃	—	20	2	no	—
450	C₂²×C₃	—	20	2	no	—
451	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	5	1	no	—
454	C₃×C₄	—	5	1	no	—
455	C₃×C₄	—	10	2	no	—
456	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
457	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
458	Dic₃	—	10	2	no	—
459	Dic₃	—	10	2	no	—
460	Dic₃	—	20	4	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	4	2	no	—
463	C₂×C₅	C₂×D₄×Dic₃	1	1	yes	characteristic
464	D₅	—	2	1	no	—
465	D₅	—	4	2	no	—
466	D₅	#5769	1	1	yes	characteristic
467	D₅	#5771	1	1	yes	characteristic
468	C₂³	—	5	1	no	—
469	C₂³	—	10	2	no	—
470	Q₈	—	5	2	no	—
471	Q₈	—	10	2	no	—
472	Q₈	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
473	D₄	—	2	2	no	—
474	D₄	—	5	2	no	—
475	D₄	—	10	2	no	—
476	D₄	—	10	2	no	—
477	D₄	—	10	2	no	—
478	D₄	—	10	2	no	—
479	D₄	C₂²×ΓL(1,𝔽₁₆)	1	2	yes	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	5	1	no	—
482	C₂×C₄	—	5	1	no	—
483	C₂×C₄	—	5	1	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	5	1	no	—
486	C₂×C₄	—	10	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	10	2	no	—
490	C₂×C₄	—	15	2	no	—
491	C₂×C₄	—	15	2	no	—
492	C₂×C₄	—	30	4	no	—
493	C₂×C₄	—	120	4	no	—
494	C₂×C₄	—	120	2	no	—
495	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
496	C₈	—	5	1	no	—
497	C₈	—	5	1	no	—
498	C₈	—	30	2	no	—
499	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
500	C₈	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
501	C₂×C₃	—	2	1	no	—
502	C₂×C₃	—	4	2	no	—
503	C₂×C₃	—	5	1	no	—
504	C₂×C₃	—	5	1	no	—
505	C₂×C₃	—	10	1	no	—
506	C₂×C₃	—	20	2	no	—
507	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
508	C₅	#83898	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	5	1	no	—
511	C₂²	—	5	1	no	—
512	C₂²	—	10	1	no	—
513	C₂²	—	10	1	no	—
514	C₂²	—	10	2	no	—
515	C₂²	—	20	2	no	—
516	C₂²	—	20	2	no	—
517	C₂²	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	5	1	no	—
520	C₄	—	5	1	no	—
521	C₄	—	10	2	no	—
522	C₄	—	30	2	no	—
523	C₄	—	30	2	no	—
524	C₄	—	60	4	no	—
525	C₄	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
526	C₄	C₂³×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
527	C₃	#10617440	1	1	yes	characteristic, complemented, Sylow
528	C₂	—	2	1	no	—
529	C₂	—	4	2	no	—
530	C₂	—	5	1	no	—
531	C₂	—	5	1	no	—
532	C₂	—	10	1	no	—
533	C₂	—	20	2	no	—
534	C₂	C₂×D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×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	#2951
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #11756995	C₂	semidirect
3. #11752452	C₂	semidirect
4. Q₁₆×ΓL(1,𝔽₁₆)	C₂	semidirect
5. #11752394	C₂	semidirect
6. D₈×ΓL(1,𝔽₁₆)	C₂	semidirect
7. C₂×#91223	C₂	semidirect
8. #11752377	C₂	semidirect
19. C₃×C₅×#135	C₄	semidirect
20. C₃×#4096	C₄	semidirect
21. C₃×#4065	C₄	semidirect
23. C₃×#4062	C₄	semidirect
25. C₃×#4058	C₄	semidirect
27. C₃×#4050	C₄	semidirect
46. C₃×C₅×#41	C₂×C₄	semidirect
47. C₃×#713	C₂×C₄	semidirect
50. C₃×#711	C₂×C₄	semidirect
54. C₃×#709	C₂×C₄	semidirect
69. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₃×C₅×SD₁₆	C₂×C₄	semidirect
71. C₃×C₅×D₈	C₂×C₄	semidirect
72. C₂×C₃×C₅×C₈	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
77. C₂×C₃×#168	C₂×C₄	semidirect
78. C₃×Dic₂₀	C₂×C₄	semidirect
79. C₃×D₄₀	C₂×C₄	semidirect
80. C₃×#677	C₂×C₄	semidirect
81. C₃×C₈×D₅	C₂×C₄	semidirect
82. C₃×C₈×D₅	C₂×C₄	semidirect
102. C₅×#135	Dic₃	semidirect
103. #4096	Dic₃	semidirect
104. #4065	Dic₃	semidirect
106. #4062	Dic₃	semidirect
108. #4058	Dic₃	semidirect
110. #4050	Dic₃	semidirect
158. C₃×#135	AGL(1,𝔽₅)	semidirect
179. C₅×#41	C₂×Dic₃	semidirect
180. #713	C₂×Dic₃	semidirect
183. #711	C₂×Dic₃	semidirect
187. #709	C₂×Dic₃	semidirect
202. C₅×Q₁₆	C₂×Dic₃	semidirect
203. C₅×SD₁₆	C₂×Dic₃	semidirect
204. C₅×D₈	C₂×Dic₃	semidirect
205. C₂×C₅×C₈	C₂×Dic₃	semidirect
206. #689	C₂×Dic₃	semidirect
207. #688	C₂×Dic₃	semidirect
208. #687	C₂×Dic₃	semidirect
209. #686	C₂×Dic₃	semidirect
210. C₂×#168	C₂×Dic₃	semidirect
211. Dic₂₀	C₂×Dic₃	semidirect
212. D₄₀	C₂×Dic₃	semidirect
213. #677	C₂×Dic₃	semidirect
214. C₈×D₅	C₂×Dic₃	semidirect
215. C₈×D₅	C₂×Dic₃	semidirect
249. C₃×#41	C₂×AGL(1,𝔽₅)	semidirect
259. C₃×Q₁₆	C₂×AGL(1,𝔽₅)	semidirect
263. C₃×SD₁₆	C₂×AGL(1,𝔽₅)	semidirect
266. C₃×D₈	C₂×AGL(1,𝔽₅)	semidirect
272. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
324. #135	ΓL(1,𝔽₁₆)	semidirect
406. #41	C₂×ΓL(1,𝔽₁₆)	semidirect
416. Q₁₆	C₂×ΓL(1,𝔽₁₆)	semidirect
420. SD₁₆	C₂×ΓL(1,𝔽₁₆)	semidirect
423. D₈	C₂×ΓL(1,𝔽₁₆)	semidirect
432. C₂×C₈	C₂×ΓL(1,𝔽₁₆)	semidirect
442. C₃×C₅	#2951	semidirect
508. C₅	#83898	semidirect
527. C₃	#10617440	semidirect

Maximal subgroups

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

subgroup	index
#11756995	2
C₃×D₅×#135	2
#11752452	2
Q₁₆×ΓL(1,𝔽₁₆)	2
#11752394	2
D₈×ΓL(1,𝔽₁₆)	2
C₂×#91223	2
#11752377	2
#10617440	3
#83898	5