Subgroups — #14300163

Order 1920.

596 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×ΓL(1,𝔽₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₂×#91238	C₂	1	1	yes	maximal, characteristic
3	C₂×#91222	C₂	1	1	yes	maximal, characteristic
4	#11752371	C₂	1	1	yes	maximal, characteristic
5	C₃×D₅×#103	C₂	1	1	yes	maximal, characteristic
6	#11746763	C₂	1	1	yes	maximal, characteristic
7	#11746745	C₂	1	1	yes	maximal, characteristic
8	#10603990	—	3	1	no	maximal, Hall
9	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
10	Q₈×ΓL(1,𝔽₁₆)	—	2	2	no	—
11	Q₈×ΓL(1,𝔽₁₆)	—	2	2	no	—
12	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
13	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
14	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
16	C₂×C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
17	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
18	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
20	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	#91238	—	2	2	no	—
22	#91235	—	2	1	no	—
23	#91222	—	2	2	no	—
24	C₃×C₅×#103	C₄	1	1	yes	characteristic, complemented
25	C₃×#3967	C₄	1	1	yes	characteristic, complemented
26	C₃×#3948	C₄	1	1	yes	characteristic, complemented
27	C₃×#3942	C₄	1	1	yes	characteristic, complemented
28	#70238	—	5	1	no	maximal, Hall
29	C₂×Q₈×AGL(1,𝔽₅)	—	3	1	no	—
30	C₂×#4009	—	3	1	no	—
31	C₂×#3993	—	3	1	no	—
32	#65712	—	3	1	no	—
33	D₅×#103	D₃	1	1	yes	characteristic
34	(C₂×AGL(1,𝔽₅))⋊C₈	—	3	1	no	—
35	#64874	—	3	1	no	—
36	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
37	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
38	C₂²×ΓL(1,𝔽₁₆)	D₄	1	1	yes	characteristic
39	C₂²×ΓL(1,𝔽₁₆)	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
41	C₃×Q₈×D₅	—	2	1	no	—
42	C₃×Q₈×D₅	—	2	1	no	—
43	C₃×Q₈×D₅	D₄	1	2	yes	—
44	C₃×Q₈×D₅	Q₈	1	2	yes	—
45	C₂×C₃×C₄×D₅	—	2	1	no	—
46	C₂×C₃×C₄×D₅	—	2	1	no	—
47	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×Dic₁₀	—	2	1	no	—
49	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃⋊#170	—	2	1	no	—
51	C₄⋊ΓL(1,𝔽₁₆)	—	2	4	no	—
52	C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
53	C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
54	C₄⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
55	C₄⋊ΓL(1,𝔽₁₆)	—	4	2	no	—
56	C₄⋊ΓL(1,𝔽₁₆)	D₄	1	2	yes	—
57	C₄×ΓL(1,𝔽₁₆)	—	2	4	no	—
58	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
59	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
60	D₅⋊(C₃⋊C₈)	—	2	1	no	—
61	D₅⋊(C₃⋊C₈)	—	2	1	no	—
62	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
65	C₃×#683	—	2	1	no	—
66	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
67	C₃×C₈×D₅	—	2	1	no	—
68	C₃×C₈×D₅	—	2	1	no	—
69	C₂×Q₈×Dic₃	—	5	1	no	—
70	C₂×C₃×#103	—	5	1	no	—
71	C₂×#835	—	5	1	no	—
72	C₂×#817	—	5	1	no	—
73	#4984	—	5	1	no	—
74	#4550	—	5	1	no	—
75	#4529	—	5	1	no	—
76	C₂×Q₈×D₅	C₂×D₃	1	1	yes	characteristic
77	Q₈×AGL(1,𝔽₅)	—	6	2	no	—
78	Q₈×AGL(1,𝔽₅)	—	6	2	no	—
79	C₂×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
80	C₂×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
81	C₂×C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
82	C₂×C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
83	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
84	C₂×C₄×AGL(1,𝔽₅)	—	6	1	no	—
85	C₂×D₅⋊C₈	—	3	1	no	—
86	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
87	D₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
88	#4009	—	6	2	no	—
89	(C₂×AGL(1,𝔽₅))⋊C₄	—	6	1	no	—
90	#3993	—	6	2	no	—
91	C₅×#103	Dic₃	1	1	yes	characteristic, complemented
92	#3967	Dic₃	1	1	yes	characteristic, complemented
93	#3948	Dic₃	1	1	yes	characteristic, complemented
94	#3942	Dic₃	1	1	yes	characteristic, complemented
95	#1865	—	15	1	no	Sylow
96	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
97	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
98	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
99	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
100	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
101	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
102	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
103	C₂×ΓL(1,𝔽₁₆)	—	4	1	no	—
104	C₂×ΓL(1,𝔽₁₆)	—	4	1	no	—
105	C₂×ΓL(1,𝔽₁₆)	—	4	1	no	—
106	C₂×ΓL(1,𝔽₁₆)	—	4	1	no	—
107	C₂×ΓL(1,𝔽₁₆)	—	4	1	no	—
108	C₂×ΓL(1,𝔽₁₆)	SD₁₆	1	2	yes	—
109	C₃×C₅×Q₈	—	2	1	no	—
110	C₃×C₅×Q₈	C₄⋊C₄	1	2	yes	complemented
111	C₂×C₃×C₄×C₅	—	2	1	no	—
112	C₂×C₃×C₄×C₅	—	2	1	no	—
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₃×Dic₅	—	2	1	no	—
115	C₂×C₃×Dic₅	—	2	1	no	—
116	C₂×C₃×Dic₅	#41	1	1	yes	characteristic
117	C₃×C₄×D₅	—	2	2	no	—
118	C₃×C₄×D₅	—	2	2	no	—
119	C₃×C₄×D₅	—	4	1	no	—
120	C₃×C₄×D₅	—	4	1	no	—
121	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
122	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
123	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
124	C₃×C₄×D₅	#41	1	1	yes	characteristic
125	C₃×Dic₁₀	—	2	1	no	—
126	C₃×Dic₁₀	—	2	2	no	—
127	C₃×Dic₁₀	—	2	2	no	—
128	C₃×Dic₁₀	C₄⋊C₄	1	2	yes	complemented
129	C₃⋊#170	—	4	1	no	—
130	C₃×C₅×C₈	—	2	1	no	—
131	C₃×#168	—	2	1	no	—
132	C₂²×C₃×Q₈	—	5	1	no	—
133	C₂²×C₃×C₈	—	5	1	no	—
134	C₂×C₃×C₄⋊C₄	—	5	1	no	—
135	Q₈×Dic₃	—	10	2	no	—
136	Q₈×Dic₃	—	10	2	no	—
137	C₂×C₄⋊Dic₃	—	5	1	no	—
138	C₂×C₄⋊Dic₃	—	5	1	no	—
139	C₂×C₄⋊Dic₃	—	10	1	no	—
140	C₂×C₄⋊Dic₃	—	10	1	no	—
141	C₂×C₄×Dic₃	—	5	1	no	—
142	C₂×C₄×Dic₃	—	10	1	no	—
143	C₂²×C₃⋊C₈	—	5	1	no	—
144	C₃×#103	—	5	1	no	—
145	C₃×#103	—	5	1	no	—
146	C₃×#103	—	5	1	no	—
147	C₃×#103	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
148	#835	—	10	2	no	—
149	C₃⋊#95	—	10	1	no	—
150	#817	—	10	2	no	—
151	C₂²×AGL(1,𝔽₅)	—	3	1	no	—
152	C₂²×AGL(1,𝔽₅)	—	3	1	no	—
153	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
154	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
155	C₂×C₅×Q₈	C₂×Dic₃	1	1	yes	characteristic
156	Q₈×D₅	—	2	1	no	—
157	Q₈×D₅	—	2	1	no	—
158	Q₈×D₅	Dic₆	1	2	yes	—
159	Q₈×D₅	D₁₂	1	2	yes	—
160	C₂×C₄×D₅	—	2	1	no	—
161	C₂×C₄×D₅	—	2	1	no	—
162	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
163	C₂×Dic₁₀	—	2	1	no	—
164	C₂×Dic₁₀	C₂×Dic₃	1	1	yes	characteristic
165	C₂×#170	—	6	1	no	—
166	C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
167	C₄⋊AGL(1,𝔽₅)	—	6	4	no	—
168	C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
169	C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
170	C₄⋊AGL(1,𝔽₅)	—	6	1	no	—
171	C₄⋊AGL(1,𝔽₅)	—	12	2	no	—
172	C₄×AGL(1,𝔽₅)	—	6	4	no	—
173	C₄×AGL(1,𝔽₅)	—	6	1	no	—
174	C₄×AGL(1,𝔽₅)	—	6	1	no	—
175	D₅⋊C₈	—	6	1	no	—
176	D₅⋊C₈	—	6	1	no	—
177	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
178	C₅×C₄⋊C₄	C₂×Dic₃	1	1	yes	characteristic
179	C₄⋊Dic₅	C₂×Dic₃	1	1	yes	characteristic
180	#683	—	2	1	no	—
181	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
182	C₈×D₅	—	2	1	no	—
183	C₈×D₅	—	2	1	no	—
184	C₂×C₄×Q₈	—	15	1	no	—
185	C₂×#106	—	15	1	no	—
186	C₂×#103	—	5	1	no	—
187	C₂×#103	—	15	1	no	—
188	#389	—	15	1	no	—
189	#340	—	15	1	no	—
190	#336	—	15	1	no	—
191	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
192	C₂×C₃×D₅	#120	1	1	yes	characteristic
193	C₂×C₃×D₅	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×C₃×D₅	C₂×SD₁₆	1	1	yes	characteristic
195	C₂×C₃×D₅	#135	1	1	yes	characteristic
196	C₂×C₃×D₅	#137	1	1	yes	characteristic
197	C₂×C₃×D₅	#137	1	1	yes	characteristic
198	ΓL(1,𝔽₁₆)	—	2	2	no	—
199	ΓL(1,𝔽₁₆)	—	4	1	no	—
200	ΓL(1,𝔽₁₆)	—	4	2	no	—
201	ΓL(1,𝔽₁₆)	—	8	1	no	—
202	C₃×C₄×C₅	—	2	2	no	—
203	C₃×C₄×C₅	—	4	1	no	—
204	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
205	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
206	C₃×Dic₅	—	2	2	no	—
207	C₃×Dic₅	—	4	1	no	—
208	C₃×Dic₅	C₂²⋊Q₈	1	1	yes	characteristic
209	C₃×Dic₅	#123	1	1	yes	characteristic
210	C₂×C₃×Q₈	—	5	2	no	—
211	C₂×C₃×Q₈	—	5	2	no	—
212	C₂×C₃×Q₈	—	5	1	no	—
213	C₂×C₃×Q₈	—	10	1	no	—
214	C₂×C₃×Q₈	—	10	1	no	—
215	C₂×C₃×Q₈	—	10	1	no	—
216	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
217	C₂²×C₃×C₄	—	5	1	no	—
218	C₂²×C₃×C₄	—	10	1	no	—
219	C₂²×C₃×C₄	—	10	1	no	—
220	C₂²×Dic₃	—	5	1	no	—
221	C₂²×Dic₃	—	5	1	no	—
222	C₂²×Dic₃	—	10	1	no	—
223	C₂²×Dic₃	—	10	1	no	—
224	C₂×C₃×C₈	—	5	1	no	—
225	C₂×C₃×C₈	—	10	1	no	—
226	C₂×C₃×C₈	—	10	1	no	—
227	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
228	C₃×C₄⋊C₄	—	5	1	no	—
229	C₃×C₄⋊C₄	—	10	1	no	—
230	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
231	C₄⋊Dic₃	—	5	2	no	—
232	C₄⋊Dic₃	—	10	1	no	—
233	C₄⋊Dic₃	—	10	4	no	—
234	C₄⋊Dic₃	—	10	1	no	—
235	C₄⋊Dic₃	—	10	1	no	—
236	C₄⋊Dic₃	—	20	2	no	—
237	C₄×Dic₃	—	10	1	no	—
238	C₄×Dic₃	—	10	1	no	—
239	C₄×Dic₃	—	10	4	no	—
240	C₂×C₃⋊C₈	—	10	1	no	—
241	C₂×C₃⋊C₈	—	10	1	no	—
242	C₂×C₃⋊C₈	—	10	1	no	—
243	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
244	C₂×AGL(1,𝔽₅)	—	3	2	no	—
245	C₂×AGL(1,𝔽₅)	—	6	1	no	—
246	C₂×AGL(1,𝔽₅)	—	6	1	no	—
247	C₂×AGL(1,𝔽₅)	—	6	2	no	—
248	C₂×AGL(1,𝔽₅)	—	6	1	no	—
249	C₂×AGL(1,𝔽₅)	—	6	1	no	—
250	C₂×AGL(1,𝔽₅)	—	6	1	no	—
251	C₂×AGL(1,𝔽₅)	—	12	1	no	—
252	C₂×AGL(1,𝔽₅)	—	12	1	no	—
253	C₂×AGL(1,𝔽₅)	—	12	1	no	—
254	C₂×AGL(1,𝔽₅)	—	12	1	no	—
255	C₂×AGL(1,𝔽₅)	—	12	1	no	—
256	C₅×Q₈	—	2	1	no	—
257	C₅×Q₈	C₄⋊Dic₃	1	2	yes	complemented
258	C₂×C₄×C₅	—	2	1	no	—
259	C₂×C₄×C₅	—	2	1	no	—
260	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
261	C₂×Dic₅	—	2	1	no	—
262	C₂×Dic₅	—	2	1	no	—
263	C₂×Dic₅	#237	1	1	yes	characteristic
264	C₄×D₅	—	2	2	no	—
265	C₄×D₅	—	2	2	no	—
266	C₄×D₅	—	4	1	no	—
267	C₄×D₅	—	4	1	no	—
268	C₄×D₅	C₂×Dic₆	1	1	yes	characteristic
269	C₄×D₅	C₂×D₁₂	1	1	yes	characteristic
270	C₄×D₅	D₃×D₄	1	1	yes	characteristic
271	C₄×D₅	#237	1	1	yes	characteristic
272	Dic₁₀	—	2	1	no	—
273	Dic₁₀	—	2	2	no	—
274	Dic₁₀	—	2	2	no	—
275	Dic₁₀	C₄⋊Dic₃	1	2	yes	complemented
276	#170	—	12	1	no	—
277	C₅×C₈	—	2	1	no	—
278	#168	—	2	1	no	—
279	C₂²×Q₈	—	5	1	no	—
280	C₂²×C₈	—	5	1	no	—
281	C₂²×C₈	—	15	1	no	—
282	C₄×Q₈	—	30	2	no	—
283	C₄×Q₈	—	30	2	no	—
284	C₂×C₄⋊C₄	—	5	1	no	—
285	C₂×C₄⋊C₄	—	15	1	no	—
286	C₂×C₄⋊C₄	—	15	1	no	—
287	C₂×C₄⋊C₄	—	30	1	no	—
288	C₂×C₄⋊C₄	—	30	1	no	—
289	C₂×C₄²	—	15	1	no	—
290	C₂×C₄²	—	30	1	no	—
291	#106	—	30	2	no	—
292	#103	—	5	1	no	—
293	#103	—	5	1	no	—
294	#103	—	5	1	no	—
295	#103	—	30	2	no	—
296	#103	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
297	#95	—	30	1	no	—
298	C₂×C₃×C₅	#385	1	1	yes	characteristic
299	C₂×C₃×C₅	C₄×SD₁₆	1	1	yes	characteristic
300	C₂×C₃×C₅	#441	1	1	yes	characteristic
301	C₃×D₅	#448	1	1	yes	characteristic
302	C₃×D₅	#452	1	1	yes	characteristic
303	C₃×D₅	#475	1	1	yes	characteristic
304	C₃×D₅	#479	1	1	yes	characteristic
305	C₂³×C₃	—	5	1	no	—
306	C₃×Q₈	—	2	1	no	—
307	C₃×Q₈	—	5	2	no	—
308	C₃×Q₈	—	10	2	no	—
309	C₃×Q₈	—	10	2	no	—
310	C₃×Q₈	—	10	1	no	—
311	C₃×Q₈	C₄⋊AGL(1,𝔽₅)	1	2	yes	complemented
312	C₂×C₃×C₄	—	2	1	no	—
313	C₂×C₃×C₄	—	2	1	no	—
314	C₂×C₃×C₄	—	5	1	no	—
315	C₂×C₃×C₄	—	5	1	no	—
316	C₂×C₃×C₄	—	5	1	no	—
317	C₂×C₃×C₄	—	5	1	no	—
318	C₂×C₃×C₄	—	5	1	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	10	1	no	—
322	C₂×C₃×C₄	—	10	1	no	—
323	C₂×C₃×C₄	—	20	1	no	—
324	C₂×C₃×C₄	—	20	1	no	—
325	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
326	C₂×Dic₃	—	5	2	no	—
327	C₂×Dic₃	—	10	1	no	—
328	C₂×Dic₃	—	10	1	no	—
329	C₂×Dic₃	—	10	2	no	—
330	C₂×Dic₃	—	10	1	no	—
331	C₂×Dic₃	—	10	1	no	—
332	C₂×Dic₃	—	10	1	no	—
333	C₂×Dic₃	—	20	1	no	—
334	C₂×Dic₃	—	20	1	no	—
335	C₂×Dic₃	—	20	1	no	—
336	C₂×Dic₃	—	20	1	no	—
337	C₂×Dic₃	—	20	1	no	—
338	C₃×C₈	—	2	1	no	—
339	C₃×C₈	—	10	1	no	—
340	C₃⋊C₈	—	20	1	no	—
341	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
342	C₂×D₅	#878	1	1	yes	characteristic
343	C₂×D₅	#882	1	1	yes	characteristic
344	C₂×D₅	D₃×SD₁₆	1	1	yes	characteristic
345	C₂×D₅	#916	1	1	yes	characteristic
346	C₂×D₅	#918	1	1	yes	characteristic
347	C₂×D₅	#918	1	1	yes	characteristic
348	AGL(1,𝔽₅)	—	6	2	no	—
349	AGL(1,𝔽₅)	—	12	1	no	—
350	AGL(1,𝔽₅)	—	12	2	no	—
351	AGL(1,𝔽₅)	—	24	1	no	—
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	4	1	no	—
354	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
355	C₄×C₅	D₄×Dic₃	1	1	yes	characteristic
356	Dic₅	—	2	2	no	—
357	Dic₅	—	4	1	no	—
358	Dic₅	#878	1	1	yes	characteristic
359	Dic₅	#886	1	1	yes	characteristic
360	C₂×Q₈	—	5	2	no	—
361	C₂×Q₈	—	5	2	no	—
362	C₂×Q₈	—	5	1	no	—
363	C₂×Q₈	—	10	1	no	—
364	C₂×Q₈	—	10	1	no	—
365	C₂×Q₈	—	10	1	no	—
366	C₂×Q₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
367	C₂²×C₄	—	5	1	no	—
368	C₂²×C₄	—	10	1	no	—
369	C₂²×C₄	—	10	1	no	—
370	C₂²×C₄	—	15	1	no	—
371	C₂²×C₄	—	15	1	no	—
372	C₂²×C₄	—	30	1	no	—
373	C₂²×C₄	—	30	1	no	—
374	C₂×C₈	—	5	1	no	—
375	C₂×C₈	—	10	1	no	—
376	C₂×C₈	—	10	1	no	—
377	C₂×C₈	—	30	1	no	—
378	C₂×C₈	—	30	1	no	—
379	C₂×C₈	—	30	1	no	—
380	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
381	C₄⋊C₄	—	5	1	no	—
382	C₄⋊C₄	—	10	1	no	—
383	C₄⋊C₄	—	15	2	no	—
384	C₄⋊C₄	—	30	1	no	—
385	C₄⋊C₄	—	30	1	no	—
386	C₄⋊C₄	—	30	1	no	—
387	C₄⋊C₄	—	30	4	no	—
388	C₄⋊C₄	—	60	2	no	—
389	C₄⋊C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
390	C₄²	—	30	1	no	—
391	C₄²	—	30	1	no	—
392	C₄²	—	30	4	no	—
393	C₃×C₅	#1865	1	1	yes	characteristic, complemented, Hall
394	C₂²×C₃	—	5	1	no	—
395	C₂²×C₃	—	5	1	no	—
396	C₂²×C₃	—	5	1	no	—
397	C₂²×C₃	—	5	1	no	—
398	C₂²×C₃	—	5	1	no	—
399	C₂²×C₃	—	5	1	no	—
400	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	4	1	no	—
403	C₃×C₄	—	5	1	no	—
404	C₃×C₄	—	5	1	no	—
405	C₃×C₄	—	10	2	no	—
406	C₃×C₄	—	20	1	no	—
407	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
408	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
409	Dic₃	—	10	2	no	—
410	Dic₃	—	20	1	no	—
411	Dic₃	—	20	2	no	—
412	Dic₃	—	40	1	no	—
413	C₂×C₅	#4950	1	1	yes	characteristic
414	C₂×C₅	Dic₃×SD₁₆	1	1	yes	characteristic
415	C₂×C₅	#5184	1	1	yes	characteristic
416	D₅	#4791	1	1	yes	characteristic
417	D₅	#4799	1	1	yes	characteristic
418	D₅	#4806	1	1	yes	characteristic
419	D₅	#4808	1	1	yes	characteristic
420	C₂³	—	5	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	5	2	no	—
423	Q₈	—	10	2	no	—
424	Q₈	—	10	2	no	—
425	Q₈	—	10	1	no	—
426	Q₈	C₄⋊ΓL(1,𝔽₁₆)	1	2	yes	complemented
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	5	1	no	—
430	C₂×C₄	—	5	1	no	—
431	C₂×C₄	—	5	1	no	—
432	C₂×C₄	—	5	1	no	—
433	C₂×C₄	—	5	1	no	—
434	C₂×C₄	—	10	2	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	10	1	no	—
437	C₂×C₄	—	10	1	no	—
438	C₂×C₄	—	15	2	no	—
439	C₂×C₄	—	20	1	no	—
440	C₂×C₄	—	20	1	no	—
441	C₂×C₄	—	30	1	no	—
442	C₂×C₄	—	30	1	no	—
443	C₂×C₄	—	30	2	no	—
444	C₂×C₄	—	30	1	no	—
445	C₂×C₄	—	30	1	no	—
446	C₂×C₄	—	30	1	no	—
447	C₂×C₄	—	60	1	no	—
448	C₂×C₄	—	60	1	no	—
449	C₂×C₄	—	60	1	no	—
450	C₂×C₄	—	60	1	no	—
451	C₂×C₄	—	60	1	no	—
452	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
453	C₈	—	2	1	no	—
454	C₈	—	10	1	no	—
455	C₈	—	60	1	no	—
456	C₂×C₃	—	5	1	no	—
457	C₂×C₃	—	5	1	no	—
458	C₂×C₃	—	5	1	no	—
459	C₂×C₃	—	5	1	no	—
460	C₂×C₃	#65699	1	1	yes	characteristic
461	C₂×C₃	SD₁₆×AGL(1,𝔽₅)	1	1	yes	characteristic
462	C₂×C₃	#65739	1	1	yes	characteristic
463	C₅	#70238	1	1	yes	characteristic, complemented, Sylow
464	C₂²	—	5	1	no	—
465	C₂²	—	5	1	no	—
466	C₂²	—	5	1	no	—
467	C₂²	—	5	1	no	—
468	C₂²	—	5	1	no	—
469	C₂²	—	5	1	no	—
470	C₂²	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
471	C₄	—	2	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	5	1	no	—
474	C₄	—	5	1	no	—
475	C₄	—	10	2	no	—
476	C₄	—	20	1	no	—
477	C₄	—	30	2	no	—
478	C₄	—	60	1	no	—
479	C₄	—	60	2	no	—
480	C₄	—	120	1	no	—
481	C₄	C₂×C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
482	C₄	D₄×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
483	C₃	#10603990	1	1	yes	characteristic, complemented, Sylow
484	C₂	—	5	1	no	—
485	C₂	—	5	1	no	—
486	C₂	—	5	1	no	—
487	C₂	—	5	1	no	—
488	C₂	#11752358	1	1	yes	characteristic
489	C₂	SD₁₆×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
490	C₂	#11752398	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₃×C₅×#103	C₄
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	#103	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1865
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
24. C₃×C₅×#103	C₄	semidirect
25. C₃×#3967	C₄	semidirect
26. C₃×#3948	C₄	semidirect
27. C₃×#3942	C₄	semidirect
91. C₅×#103	Dic₃	semidirect
92. #3967	Dic₃	semidirect
93. #3948	Dic₃	semidirect
94. #3942	Dic₃	semidirect
110. C₃×C₅×Q₈	C₄⋊C₄	semidirect
128. C₃×Dic₁₀	C₄⋊C₄	semidirect
147. C₃×#103	AGL(1,𝔽₅)	semidirect
257. C₅×Q₈	C₄⋊Dic₃	semidirect
275. Dic₁₀	C₄⋊Dic₃	semidirect
296. #103	ΓL(1,𝔽₁₆)	semidirect
311. C₃×Q₈	C₄⋊AGL(1,𝔽₅)	semidirect
393. C₃×C₅	#1865	semidirect
426. Q₈	C₄⋊ΓL(1,𝔽₁₆)	semidirect
463. C₅	#70238	semidirect
483. C₃	#10603990	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×ΓL(1,𝔽₁₆)	2
C₂×#91238	2
C₂×#91222	2
#11752371	2
C₃×D₅×#103	2
#11746763	2
#11746745	2
#10603990	3
#70238	5