Subgroups — #72230438

Order 2880.

564 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₃⋊ΓL(1,𝔽₁₆))	C₂	1	1	yes	maximal, characteristic
2	C₃×#91989	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#208	C₂	1	1	yes	maximal, characteristic
4	#13085455	C₂	1	2	yes	maximal, complemented
5	#13085454	C₂	1	2	yes	maximal, complemented
6	#11752386	—	3	1	no	maximal
7	#11751728	—	3	1	no	maximal
8	C₂²×C₃⋊ΓL(1,𝔽₁₆)	—	2	1	no	—
9	C₂×C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
10	C₄⋊(C₃⋊ΓL(1,𝔽₁₆))	—	2	1	no	—
11	C₄⋊(C₃⋊ΓL(1,𝔽₁₆))	C₂²	1	2	yes	—
12	C₃×#6763	—	2	1	no	—
13	C₃×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
14	C₃×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
15	C₃×C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
16	C₃×#6710	C₄	1	1	yes	characteristic, complemented
17	C₃×C₅×#208	C₄	1	1	yes	characteristic, complemented
18	C₃×#6649	C₄	1	2	yes	complemented
19	C₃×D₅×C₃⋊C₈	C₂²	1	2	yes	—
20	#10591131	—	5	1	no	maximal, Hall
21	#91989	D₃	1	1	yes	characteristic
22	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	3	1	no	—
23	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	3	1	no	—
24	C₂×C₄⋊ΓL(1,𝔽₁₆)	—	6	1	no	—
25	C₃×#4130	—	3	1	no	—
26	C₃×D₅×M₁₆	—	3	1	no	—
27	D₅×#208	D₃	1	1	yes	characteristic
28	#91223	—	3	2	no	—
29	#91222	—	3	2	no	—
30	#91160	—	3	2	no	—
31	#91159	—	3	2	no	—
32	C₂²×C₃²×D₅	D₄	1	1	yes	characteristic
33	C₂×C₃⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
34	C₂×C₃⋊ΓL(1,𝔽₁₆)	—	4	2	no	—
35	C₂×C₃×ΓL(1,𝔽₁₆)	—	2	1	no	—
36	C₂×C₃×ΓL(1,𝔽₁₆)	—	2	1	no	—
37	C₂×C₃²×C₄×C₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃²×Dic₅	Q₈	1	1	yes	characteristic
39	C₃²×C₄×D₅	C₂×C₄	1	1	yes	characteristic
40	C₃²×C₄×D₅	D₄	1	1	yes	characteristic
41	C₃²×C₄×D₅	Q₈	1	1	yes	characteristic
42	C₃²×C₄×D₅	C₂³	1	1	yes	characteristic
43	C₃×C₃⋊#168	C₂×C₄	1	2	yes	complemented
44	C₃×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
45	#65727	—	9	1	no	Hall
46	C₂×C₄⋊(C₃⋊Dic₃)	—	5	1	no	—
47	C₃×#926	—	5	1	no	—
48	C₂×C₃×#208	—	5	1	no	—
49	#63575	—	5	2	no	—
50	#63573	—	5	2	no	—
51	C₂²×ΓL(1,𝔽₁₆)	—	6	1	no	—
52	C₂²×ΓL(1,𝔽₁₆)	—	6	1	no	—
53	C₂²×ΓL(1,𝔽₁₆)	—	6	1	no	—
54	C₂²×ΓL(1,𝔽₁₆)	—	6	1	no	—
55	C₂×C₃×C₄×D₅	—	2	1	no	—
56	C₂×C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic
58	#6763	—	2	1	no	—
59	C₄⋊ΓL(1,𝔽₁₆)	—	3	2	no	—
60	C₄⋊ΓL(1,𝔽₁₆)	—	3	2	no	—
61	C₄⋊ΓL(1,𝔽₁₆)	—	6	2	no	—
62	C₄⋊ΓL(1,𝔽₁₆)	—	6	1	no	—
63	C₄⋊ΓL(1,𝔽₁₆)	—	6	1	no	—
64	C₄⋊ΓL(1,𝔽₁₆)	—	6	1	no	—
65	C₄⋊ΓL(1,𝔽₁₆)	—	6	1	no	—
66	C₄⋊ΓL(1,𝔽₁₆)	C₂×D₃	1	1	yes	characteristic
67	C₄⋊ΓL(1,𝔽₁₆)	C₂×D₃	1	1	yes	characteristic
68	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
69	C₃×C₂²⋊AGL(1,𝔽₅)	—	6	1	no	—
70	C₃×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
71	C₃×C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
72	C₃×C₄×AGL(1,𝔽₅)	—	6	1	no	—
73	C₃×C₅×M₁₆	—	3	1	no	—
74	#6710	Dic₃	1	1	yes	characteristic, complemented
75	C₅×#208	Dic₃	1	1	yes	characteristic, complemented
76	C₃×#681	—	3	1	no	—
77	C₃×#676	—	3	2	no	—
78	C₃×C₈×D₅	—	3	2	no	—
79	#6649	Dic₃	1	2	yes	complemented
80	D₅×C₃⋊C₈	C₂×D₃	1	2	yes	—
81	#5121	—	15	1	no	—
82	#4995	—	15	1	no	—
83	C₂²×C₃²×C₅	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₃²×D₅	—	2	1	no	—
85	C₂×C₃²×D₅	—	2	1	no	—
86	C₂×C₃²×D₅	C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₃²×D₅	C₂×D₄	1	1	yes	characteristic
88	C₃⋊ΓL(1,𝔽₁₆)	—	4	2	no	—
89	C₃×ΓL(1,𝔽₁₆)	—	4	1	no	—
90	C₃×ΓL(1,𝔽₁₆)	—	4	1	no	—
91	C₃²×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
92	C₃²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₃²×Dic₅	C₄⋊C₄	1	1	yes	characteristic
94	C₃²×Dic₅	C₂×Q₈	1	1	yes	characteristic
95	#4130	—	3	1	no	—
96	C₂×C₄⋊AGL(1,𝔽₅)	—	9	1	no	—
97	D₅×M₁₆	—	3	1	no	—
98	#3994	—	9	2	no	—
99	#3993	—	9	2	no	—
100	C₂²×C₃²×C₄	—	5	1	no	—
101	C₂²×C₃⋊Dic₃	—	10	1	no	—
102	C₄⋊(C₃⋊Dic₃)	—	5	2	no	—
103	C₄⋊(C₃⋊Dic₃)	—	10	1	no	—
104	C₃×#217	—	10	1	no	—
105	C₃×C₄⋊Dic₃	—	5	1	no	—
106	C₃×C₄⋊Dic₃	—	5	1	no	—
107	C₃×C₄×Dic₃	—	10	1	no	—
108	C₃×#208	—	5	1	no	—
109	C₃×#208	—	5	2	no	—
110	C₃×#208	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
111	C₂×C₃×C₃⋊C₈	—	5	2	no	—
112	C₂²×C₃×D₅	—	2	1	no	—
113	C₂²×C₃×D₅	D₁₂	1	1	yes	characteristic
114	C₂²×C₃×D₅	#67	1	1	yes	characteristic
115	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
116	C₂×ΓL(1,𝔽₁₆)	—	2	1	no	—
117	C₂×ΓL(1,𝔽₁₆)	—	6	2	no	—
118	C₂×ΓL(1,𝔽₁₆)	—	6	2	no	—
119	C₂×ΓL(1,𝔽₁₆)	—	6	2	no	—
120	C₂×ΓL(1,𝔽₁₆)	—	6	2	no	—
121	C₂×ΓL(1,𝔽₁₆)	—	12	2	no	—
122	C₂×ΓL(1,𝔽₁₆)	—	12	2	no	—
123	C₂×ΓL(1,𝔽₁₆)	—	12	2	no	—
124	C₂×ΓL(1,𝔽₁₆)	—	12	2	no	—
125	C₂×C₃×AGL(1,𝔽₅)	—	6	1	no	—
126	C₂×C₃×AGL(1,𝔽₅)	—	6	1	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	C₄×D₃	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
130	C₂×C₃×Dic₅	—	2	1	no	—
131	C₂×C₃×Dic₅	Dic₆	1	1	yes	characteristic
132	C₂×C₃×Dic₅	Dic₆	1	1	yes	characteristic
133	C₃×C₄×D₅	—	2	1	no	—
134	C₃×C₄×D₅	—	2	1	no	—
135	C₃×C₄×D₅	—	2	1	no	—
136	C₃×C₄×D₅	—	2	1	no	—
137	C₃×C₄×D₅	Dic₆	1	1	yes	characteristic
138	C₃×C₄×D₅	Dic₆	1	1	yes	characteristic
139	C₃×C₄×D₅	C₄×D₃	1	1	yes	characteristic
140	C₃×C₄×D₅	D₁₂	1	1	yes	characteristic
141	C₃×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
142	C₃×C₄×D₅	#67	1	1	yes	characteristic
143	C₃×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
144	C₃×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
145	C₃×C₅×C₈	—	3	2	no	—
146	C₃⋊#168	C₂×Dic₃	1	2	yes	complemented
147	C₃×#168	—	3	2	no	—
148	C₅×C₃⋊C₈	C₂×Dic₃	1	2	yes	complemented
149	C₂×C₃×M₁₆	—	15	1	no	—
150	C₃×#117	—	15	1	no	—
151	#926	—	5	1	no	—
152	C₂×C₄⋊Dic₃	—	15	1	no	—
153	C₂×C₄⋊Dic₃	—	15	1	no	—
154	C₂×C₄⋊Dic₃	—	30	1	no	—
155	C₂×#208	—	5	1	no	—
156	#818	—	15	2	no	—
157	#817	—	15	2	no	—
158	#808	—	15	2	no	—
159	#807	—	15	2	no	—
160	C₂×C₃²×C₅	—	2	1	no	—
161	C₂×C₃²×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₃²×D₅	—	2	1	no	—
163	C₃²×D₅	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₃²×D₅	#137	1	1	yes	characteristic
165	C₂²×AGL(1,𝔽₅)	—	18	1	no	—
166	C₂×C₄×D₅	D₃²	1	1	yes	characteristic
167	C₂²⋊AGL(1,𝔽₅)	—	6	1	no	—
168	C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
169	C₄⋊AGL(1,𝔽₅)	—	3	1	no	—
170	C₄⋊AGL(1,𝔽₅)	—	9	2	no	—
171	C₄⋊AGL(1,𝔽₅)	—	18	1	no	—
172	C₄×AGL(1,𝔽₅)	—	6	1	no	—
173	C₅×M₁₆	—	3	1	no	—
174	#681	—	3	1	no	—
175	#676	—	3	2	no	—
176	C₈×D₅	—	3	2	no	—
177	C₂³×C₃²	—	5	1	no	—
178	C₂×C₃²×C₄	—	5	1	no	—
179	C₂×C₃²×C₄	—	5	1	no	—
180	C₂×C₃²×C₄	—	5	1	no	—
181	C₂×C₃²×C₄	—	5	1	no	—
182	C₂×C₃²×C₄	—	5	1	no	—
183	C₂×C₃²×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
184	C₂×C₃⋊Dic₃	—	10	2	no	—
185	C₂×C₃⋊Dic₃	—	20	2	no	—
186	C₂×C₃×Dic₃	—	10	1	no	—
187	C₂×C₃×Dic₃	—	10	1	no	—
188	C₃×C₃⋊C₈	—	5	2	no	—
189	C₃×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
190	#428	—	45	1	no	Sylow
191	C₂²×C₃×C₅	—	2	1	no	—
192	C₂²×C₃×C₅	Dic₃⋊C₄	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₄⋊Dic₃	1	1	yes	characteristic
194	C₂×C₃×D₅	—	2	1	no	—
195	C₂×C₃×D₅	—	2	1	no	—
196	C₂×C₃×D₅	—	2	1	no	—
197	C₂×C₃×D₅	—	2	1	no	—
198	C₂×C₃×D₅	—	2	1	no	—
199	C₂×C₃×D₅	—	2	1	no	—
200	C₂×C₃×D₅	—	2	1	no	—
201	C₂×C₃×D₅	—	2	1	no	—
202	C₂×C₃×D₅	—	2	1	no	—
203	C₂×C₃×D₅	—	2	1	no	—
204	C₂×C₃×D₅	Dic₃⋊C₄	1	1	yes	characteristic
205	C₂×C₃×D₅	C₄⋊Dic₃	1	1	yes	characteristic
206	C₂×C₃×D₅	C₂×D₁₂	1	1	yes	characteristic
207	C₂×C₃×D₅	C₂×#67	1	1	yes	characteristic
208	ΓL(1,𝔽₁₆)	—	4	1	no	—
209	ΓL(1,𝔽₁₆)	—	4	1	no	—
210	ΓL(1,𝔽₁₆)	—	12	2	no	—
211	ΓL(1,𝔽₁₆)	—	12	2	no	—
212	ΓL(1,𝔽₁₆)	—	12	2	no	—
213	ΓL(1,𝔽₁₆)	—	12	2	no	—
214	C₃×AGL(1,𝔽₅)	—	12	1	no	—
215	C₃×AGL(1,𝔽₅)	—	12	1	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	Dic₃⋊C₄	1	1	yes	characteristic
219	C₃×C₄×C₅	C₄⋊Dic₃	1	1	yes	characteristic
220	C₃×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
221	C₃×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
222	C₃×Dic₅	—	2	1	no	—
223	C₃×Dic₅	—	2	1	no	—
224	C₃×Dic₅	Dic₃⋊C₄	1	1	yes	characteristic
225	C₃×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
226	C₃×Dic₅	C₂×Dic₆	1	1	yes	characteristic
227	C₃×Dic₅	C₂×Dic₆	1	1	yes	characteristic
228	C₂²×C₃×C₄	—	5	1	no	—
229	C₂²×C₃×C₄	—	5	1	no	—
230	C₂²×C₃×C₄	—	10	1	no	—
231	C₂²×Dic₃	—	30	1	no	—
232	C₂²×Dic₃	—	30	1	no	—
233	C₂²×Dic₃	—	30	1	no	—
234	C₂²×Dic₃	—	30	1	no	—
235	C₃×M₁₆	—	3	1	no	—
236	C₃×M₁₆	—	15	2	no	—
237	C₃×M₁₆	—	15	1	no	—
238	C₂×C₃×C₈	—	15	2	no	—
239	C₃×C₄⋊C₄	—	15	1	no	—
240	C₃×C₄⋊C₄	—	15	1	no	—
241	C₃×C₂²⋊C₄	—	30	1	no	—
242	C₃×C₄²	—	30	1	no	—
243	#217	—	10	1	no	—
244	C₄⋊Dic₃	—	5	1	no	—
245	C₄⋊Dic₃	—	5	1	no	—
246	C₄⋊Dic₃	—	15	2	no	—
247	C₄⋊Dic₃	—	15	2	no	—
248	C₄⋊Dic₃	—	30	2	no	—
249	C₄⋊Dic₃	—	30	1	no	—
250	C₄⋊Dic₃	—	30	1	no	—
251	C₄⋊Dic₃	—	30	1	no	—
252	C₄⋊Dic₃	—	30	1	no	—
253	C₄×Dic₃	—	10	1	no	—
254	#208	—	5	1	no	—
255	#208	—	5	2	no	—
256	#208	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
257	C₂×C₃⋊C₈	—	5	2	no	—
258	C₃²×C₅	#428	1	1	yes	characteristic, complemented, Hall
259	C₂²×D₅	#626	1	1	yes	characteristic
260	C₂×AGL(1,𝔽₅)	—	6	1	no	—
261	C₂×AGL(1,𝔽₅)	—	6	1	no	—
262	C₂×AGL(1,𝔽₅)	—	18	2	no	—
263	C₂×AGL(1,𝔽₅)	—	36	2	no	—
264	C₂×C₄×C₅	D₃×Dic₃	1	1	yes	characteristic
265	C₂×Dic₅	#627	1	1	yes	characteristic
266	C₄×D₅	D₃×Dic₃	1	1	yes	characteristic
267	C₄×D₅	#626	1	1	yes	characteristic
268	C₄×D₅	#627	1	1	yes	characteristic
269	C₄×D₅	C₂×D₃²	1	1	yes	characteristic
270	C₅×C₈	—	3	2	no	—
271	#168	—	3	2	no	—
272	C₂²×C₃²	—	5	1	no	—
273	C₂²×C₃²	—	5	1	no	—
274	C₂²×C₃²	—	10	1	no	—
275	C₂²×C₃²	—	10	1	no	—
276	C₂²×C₃²	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
277	C₃²×C₄	—	5	1	no	—
278	C₃²×C₄	—	5	1	no	—
279	C₃²×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
280	C₃²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
281	C₃⋊Dic₃	—	20	2	no	—
282	C₃×Dic₃	—	20	1	no	—
283	C₃×Dic₃	—	20	1	no	—
284	C₂×M₁₆	—	15	1	no	—
285	#117	—	15	1	no	—
286	C₂×C₄⋊C₄	—	45	1	no	—
287	#107	—	45	2	no	—
288	#106	—	45	2	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	2	1	no	—
291	C₂×C₃×C₅	—	2	1	no	—
292	C₂×C₃×C₅	—	2	1	no	—
293	C₂×C₃×C₅	—	2	1	no	—
294	C₂×C₃×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
295	C₂×C₃×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
296	C₃×D₅	—	2	1	no	—
297	C₃×D₅	—	2	1	no	—
298	C₃×D₅	—	2	1	no	—
299	C₃×D₅	—	2	1	no	—
300	C₃×D₅	—	2	1	no	—
301	C₃×D₅	—	2	1	no	—
302	C₃×D₅	#908	1	1	yes	characteristic
303	C₃×D₅	#909	1	1	yes	characteristic
304	C₃×D₅	#949	1	1	yes	characteristic
305	C₃×D₅	#951	1	1	yes	characteristic
306	C₂³×C₃	—	5	1	no	—
307	C₂³×C₃	—	5	1	no	—
308	C₂³×C₃	—	10	1	no	—
309	C₂×C₃×C₄	—	2	1	no	—
310	C₂×C₃×C₄	—	5	1	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	5	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	—	5	1	no	—
320	C₂×C₃×C₄	—	10	1	no	—
321	C₂×C₃×C₄	—	10	1	no	—
322	C₂×C₃×C₄	—	10	1	no	—
323	C₂×C₃×C₄	—	10	1	no	—
324	C₂×C₃×C₄	—	10	1	no	—
325	C₂×C₃×C₄	—	30	1	no	—
326	C₂×C₃×C₄	—	30	1	no	—
327	C₂×C₃×C₄	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
329	C₂×Dic₃	—	10	1	no	—
330	C₂×Dic₃	—	10	1	no	—
331	C₂×Dic₃	—	30	2	no	—
332	C₂×Dic₃	—	30	2	no	—
333	C₂×Dic₃	—	30	2	no	—
334	C₂×Dic₃	—	30	2	no	—
335	C₂×Dic₃	—	60	2	no	—
336	C₂×Dic₃	—	60	2	no	—
337	C₂×Dic₃	—	60	2	no	—
338	C₂×Dic₃	—	60	2	no	—
339	C₃×C₈	—	3	2	no	—
340	C₃×C₈	—	15	2	no	—
341	C₃⋊C₈	—	5	2	no	—
342	C₃⋊C₈	C₂×ΓL(1,𝔽₁₆)	1	2	yes	complemented
343	C₂²×C₅	Dic₃⋊Dic₃	1	1	yes	characteristic
344	C₂×D₅	—	2	1	no	—
345	C₂×D₅	—	2	1	no	—
346	C₂×D₅	Dic₃⋊Dic₃	1	1	yes	characteristic
347	C₂×D₅	C₂×#626	1	1	yes	characteristic
348	AGL(1,𝔽₅)	—	12	1	no	—
349	AGL(1,𝔽₅)	—	12	1	no	—
350	AGL(1,𝔽₅)	—	36	2	no	—
351	C₄×C₅	Dic₃⋊Dic₃	1	1	yes	characteristic
352	C₄×C₅	C₂×D₃×Dic₃	1	1	yes	characteristic
353	Dic₅	Dic₃⋊Dic₃	1	1	yes	characteristic
354	Dic₅	C₂×#627	1	1	yes	characteristic
355	C₂×C₃²	—	2	1	no	—
356	C₂×C₃²	—	5	1	no	—
357	C₂×C₃²	—	5	1	no	—
358	C₂×C₃²	—	10	1	no	—
359	C₂×C₃²	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
360	C₂²×C₄	—	5	1	no	—
361	C₂²×C₄	—	90	1	no	—
362	M₁₆	—	3	1	no	—
363	M₁₆	—	15	2	no	—
364	M₁₆	—	15	1	no	—
365	C₂×C₈	—	15	2	no	—
366	C₄⋊C₄	—	15	1	no	—
367	C₄⋊C₄	—	15	1	no	—
368	C₄⋊C₄	—	45	2	no	—
369	C₄⋊C₄	—	90	1	no	—
370	C₂²⋊C₄	—	30	1	no	—
371	C₄²	—	30	1	no	—
372	C₃×C₅	—	2	1	no	—
373	C₃×C₅	#4995	1	1	yes	characteristic, complemented
374	C₃×C₅	#5121	1	1	yes	characteristic, complemented
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	5	1	no	—
377	C₂²×C₃	—	5	1	no	—
378	C₂²×C₃	—	5	1	no	—
379	C₂²×C₃	—	5	1	no	—
380	C₂²×C₃	—	10	1	no	—
381	C₂²×C₃	—	10	1	no	—
382	C₂²×C₃	—	10	1	no	—
383	C₂²×C₃	—	10	1	no	—
384	C₂²×C₃	—	10	1	no	—
385	C₂²×C₃	—	10	1	no	—
386	C₂²×C₃	—	10	1	no	—
387	C₂²×C₃	—	10	1	no	—
388	C₂²×C₃	—	10	1	no	—
389	C₂²×C₃	—	10	1	no	—
390	C₂²×C₃	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
391	C₂²×C₃	C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	2	1	no	—
394	C₃×C₄	—	5	1	no	—
395	C₃×C₄	—	5	1	no	—
396	C₃×C₄	—	5	1	no	—
397	C₃×C₄	—	5	1	no	—
398	C₃×C₄	—	10	1	no	—
399	C₃×C₄	—	10	1	no	—
400	C₃×C₄	—	60	1	no	—
401	C₃×C₄	—	60	1	no	—
402	C₃×C₄	Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₃×C₄	C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
404	C₃×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
405	C₃×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
406	Dic₃	—	20	1	no	—
407	Dic₃	—	20	1	no	—
408	Dic₃	—	60	2	no	—
409	Dic₃	—	60	2	no	—
410	Dic₃	—	60	2	no	—
411	Dic₃	—	60	2	no	—
412	C₂×C₅	—	2	1	no	—
413	C₂×C₅	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
414	D₅	—	2	1	no	—
415	D₅	#63825	1	1	yes	characteristic
416	D₅	#63831	1	1	yes	characteristic
417	C₃²	#65727	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	5	1	no	—
419	C₂×C₄	—	5	1	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	5	1	no	—
422	C₂×C₄	—	5	1	no	—
423	C₂×C₄	—	5	1	no	—
424	C₂×C₄	—	30	1	no	—
425	C₂×C₄	—	30	1	no	—
426	C₂×C₄	—	90	2	no	—
427	C₂×C₄	—	180	2	no	—
428	C₂×C₄	D₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
429	C₈	—	3	2	no	—
430	C₈	—	15	2	no	—
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	2	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	5	1	no	—
437	C₂×C₃	—	5	1	no	—
438	C₂×C₃	—	5	1	no	—
439	C₂×C₃	—	5	1	no	—
440	C₂×C₃	—	10	1	no	—
441	C₂×C₃	—	10	1	no	—
442	C₂×C₃	—	10	1	no	—
443	C₂×C₃	—	10	1	no	—
444	C₂×C₃	—	10	1	no	—
445	C₂×C₃	—	10	1	no	—
446	C₂×C₃	C₂×Dic₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic
447	C₂×C₃	C₂×C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
448	C₅	#10591131	1	1	yes	characteristic, complemented, Sylow
449	C₂²	—	5	1	no	—
450	C₂²	—	5	1	no	—
451	C₂²	—	10	1	no	—
452	C₂²	—	10	1	no	—
453	C₂²	Dic₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
454	C₄	—	5	1	no	—
455	C₄	—	5	1	no	—
456	C₄	—	60	1	no	—
457	C₄	—	60	1	no	—
458	C₄	—	180	2	no	—
459	C₄	Dic₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
460	C₄	C₂×D₃×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
461	C₃	—	2	1	no	—
462	C₃	#11751728	1	1	yes	characteristic, complemented
463	C₃	#11752386	1	1	yes	characteristic, complemented
464	C₂	—	2	1	no	—
465	C₂	—	5	1	no	—
466	C₂	—	5	1	no	—
467	C₂	—	10	1	no	—
468	C₂	C₂×Dic₃⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×Dic₃⋊ΓL(1,𝔽₁₆)
commutator	C₃²×C₄×C₅	C₂²×C₄
Frattini	C₄	C₂×D₃×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃²×C₄×C₅	C₂×C₄
socle	C₂×C₃²×C₅	C₂×C₄⋊C₄
prime radical	C₂²×C₃²×D₅	D₄
cosocle	C₃²×C₄×D₅	C₂³
hypercenter	C₂×C₄	D₃×ΓL(1,𝔽₁₆)
hypocenter	C₃²×C₅	#428
LCS	G ▷ C₃²×C₄×C₅ ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
4. #13085455	C₂	semidirect
5. #13085454	C₂	semidirect
16. C₃×#6710	C₄	semidirect
17. C₃×C₅×#208	C₄	semidirect
18. C₃×#6649	C₄	semidirect
43. C₃×C₃⋊#168	C₂×C₄	semidirect
44. C₃×C₅×C₃⋊C₈	C₂×C₄	semidirect
74. #6710	Dic₃	semidirect
75. C₅×#208	Dic₃	semidirect
79. #6649	Dic₃	semidirect
110. C₃×#208	AGL(1,𝔽₅)	semidirect
146. C₃⋊#168	C₂×Dic₃	semidirect
148. C₅×C₃⋊C₈	C₂×Dic₃	semidirect
189. C₃×C₃⋊C₈	C₂×AGL(1,𝔽₅)	semidirect
256. #208	ΓL(1,𝔽₁₆)	semidirect
258. C₃²×C₅	#428	semidirect
342. C₃⋊C₈	C₂×ΓL(1,𝔽₁₆)	semidirect
373. C₃×C₅	#4995	semidirect
374. C₃×C₅	#5121	semidirect
417. C₃²	#65727	semidirect
448. C₅	#10591131	semidirect
462. C₃	#11751728	semidirect
463. C₃	#11752386	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₃⋊ΓL(1,𝔽₁₆))	2
C₃×#91989	2
C₃×D₅×#208	2
#13085455	2
#13085454	2
#11752386	3
#11751728	3
#10591131	5