Subgroups — #14297947

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#11752424	C₂	1	2	yes	maximal
3	C₂×#91223	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#91222	C₂	1	1	yes	maximal, characteristic, complemented
5	#11746764	C₂	1	2	yes	maximal, complemented
6	#10604761	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
8	C₂×#6763	—	2	2	no	—
9	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
10	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
11	C₂×C₃×C₅×M₁₆	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃×#681	C₄	1	1	yes	characteristic, complemented
13	C₃×D₅×M₁₆	—	2	2	no	—
14	C₃×D₅×M₁₆	—	2	2	no	—
15	C₂×C₃×#676	C₄	1	1	yes	characteristic, complemented
16	C₂×C₃×#676	C₄	1	1	yes	characteristic, complemented
17	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
19	#91235	—	2	2	no	—
20	#91223	—	2	2	no	—
21	#91222	—	2	2	no	—
22	#71988	—	5	1	no	maximal, Hall
23	C₂×D₅×M₁₆	D₃	1	1	yes	characteristic
24	#65765	—	3	2	no	—
25	C₂×#3994	—	3	1	no	—
26	C₂×#3993	—	3	1	no	—
27	#64893	—	3	2	no	—
28	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
29	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
30	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×Dic₅	Q₈	1	1	yes	characteristic
33	C₂×C₃×C₄×D₅	—	2	1	no	—
34	C₂×C₃×C₄×D₅	—	2	1	no	—
35	C₂×C₃×C₄×D₅	—	2	1	no	—
36	C₂×C₃×C₄×D₅	—	2	1	no	—
37	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
39	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
41	#6763	—	4	4	no	—
42	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
43	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
44	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
45	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
46	C₃×C₅×M₁₆	—	2	2	no	—
47	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
49	C₃×#681	—	2	2	no	—
50	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
52	C₃×#676	—	2	2	no	—
53	C₃×#676	—	2	2	no	—
54	C₃×C₈×D₅	—	2	1	no	—
55	C₃×C₈×D₅	—	2	1	no	—
56	C₃×C₈×D₅	D₄	1	2	yes	—
57	C₃×C₈×D₅	D₄	1	2	yes	—
58	C₂²×C₃×M₁₆	—	5	1	no	—
59	#5212	—	5	2	no	—
60	C₂×#818	—	5	1	no	—
61	C₂×#817	—	5	1	no	—
62	#4551	—	5	2	no	—
63	C₂²×C₄×D₅	C₂×D₃	1	1	yes	characteristic
64	C₂×C₂²⋊AGL(1,𝔽₅)	—	6	2	no	—
65	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
66	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
67	C₂×C₅×M₁₆	Dic₃	1	1	yes	characteristic, complemented
68	C₂×#681	Dic₃	1	1	yes	characteristic, complemented
69	D₅×M₁₆	—	2	2	no	—
70	D₅×M₁₆	—	2	2	no	—
71	C₂×#676	Dic₃	1	1	yes	characteristic, complemented
72	C₂×#676	Dic₃	1	1	yes	characteristic, complemented
73	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
74	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
75	(C₂×AGL(1,𝔽₅))⋊C₄	—	6	2	no	—
76	#3994	—	6	2	no	—
77	#3993	—	6	2	no	—
78	#1809	—	15	1	no	Sylow
79	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₃×D₅	—	2	1	no	—
81	C₂²×C₃×D₅	—	2	1	no	—
82	C₂²×C₃×D₅	—	2	2	no	—
83	C₂²×C₃×D₅	—	2	2	no	—
84	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
86	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
87	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
88	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
89	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
90	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
91	C₂×ΓL(1,𝔽₁₆)	—	4	2	no	—
92	C₂×C₃×C₄×C₅	—	2	1	no	—
93	C₂×C₃×C₄×C₅	—	2	1	no	—
94	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₃×Dic₅	—	2	1	no	—
97	C₂×C₃×Dic₅	—	2	1	no	—
98	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
100	C₃×C₄×D₅	—	2	1	no	—
101	C₃×C₄×D₅	—	2	1	no	—
102	C₃×C₄×D₅	—	2	1	no	—
103	C₃×C₄×D₅	—	2	1	no	—
104	C₃×C₄×D₅	—	2	1	no	—
105	C₃×C₄×D₅	—	2	1	no	—
106	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
107	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₄×D₅	#41	1	1	yes	characteristic
109	C₃×C₄×D₅	#41	1	1	yes	characteristic
110	C₃×C₅×C₈	—	2	1	no	—
111	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	complemented
112	C₃×#168	—	2	1	no	—
113	C₃×#168	C₂²⋊C₄	1	2	yes	complemented
114	C₂³×C₃×C₄	—	5	1	no	—
115	C₂×C₃×M₁₆	—	5	1	no	—
116	C₂×C₃×M₁₆	—	5	1	no	—
117	C₂×C₃×M₁₆	—	5	1	no	—
118	C₂×C₃×M₁₆	—	10	2	no	—
119	C₂×C₃×M₁₆	—	10	2	no	—
120	C₂×C₃×M₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
121	C₂²×C₃×C₈	—	5	1	no	—
122	C₂²×C₃×C₈	—	5	1	no	—
123	C₂×#217	—	10	2	no	—
124	C₂×C₄⋊Dic₃	—	5	2	no	—
125	C₂×C₄⋊Dic₃	—	5	2	no	—
126	C₃⋊#95	—	10	2	no	—
127	#818	—	10	2	no	—
128	#817	—	10	2	no	—
129	C₂³×D₅	D₁₂	1	1	yes	characteristic
130	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
131	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
132	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
133	C₂²×Dic₅	Dic₆	1	1	yes	characteristic
134	C₂×C₄×D₅	—	2	1	no	—
135	C₂×C₄×D₅	—	2	1	no	—
136	C₂×C₄×D₅	—	2	1	no	—
137	C₂×C₄×D₅	—	2	1	no	—
138	C₂×C₄×D₅	Dic₆	1	1	yes	characteristic
139	C₂×C₄×D₅	D₁₂	1	1	yes	characteristic
140	C₂×C₄×D₅	C₂×Dic₃	1	1	yes	characteristic
141	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
142	C₂²⋊AGL(1,𝔽₅)	—	12	4	no	—
143	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
144	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
145	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
146	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
147	C₅×M₁₆	—	2	2	no	—
148	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂×Dic₃	1	1	yes	characteristic
150	#681	—	2	2	no	—
151	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
152	C₂×#168	C₂×Dic₃	1	1	yes	characteristic
153	#676	—	2	2	no	—
154	#676	—	2	2	no	—
155	C₈×D₅	—	2	1	no	—
156	C₈×D₅	—	2	1	no	—
157	C₈×D₅	#67	1	2	yes	—
158	C₈×D₅	#67	1	2	yes	—
159	C₂²×M₁₆	—	5	1	no	—
160	C₂×#107	—	15	1	no	—
161	C₂×#106	—	15	1	no	—
162	#380	—	15	2	no	—
163	#340	—	15	2	no	—
164	C₂²×C₃×C₅	—	2	1	no	—
165	C₂²×C₃×C₅	—	2	2	no	—
166	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₃×D₅	—	2	1	no	—
168	C₂×C₃×D₅	—	2	2	no	—
169	C₂×C₃×D₅	—	4	2	no	—
170	C₂×C₃×D₅	—	4	1	no	—
171	C₂×C₃×D₅	—	4	1	no	—
172	C₂×C₃×D₅	#121	1	1	yes	characteristic
173	C₂×C₃×D₅	#121	1	1	yes	characteristic
174	C₂×C₃×D₅	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₃×D₅	#137	1	2	yes	—
176	ΓL(1,𝔽₁₆)	—	8	2	no	—
177	ΓL(1,𝔽₁₆)	—	8	2	no	—
178	C₃×C₄×C₅	—	2	1	no	—
179	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₃×C₄×C₅	#117	1	1	yes	characteristic
181	C₃×Dic₅	—	2	1	no	—
182	C₃×Dic₅	C₂²⋊Q₈	1	1	yes	characteristic
183	C₃×Dic₅	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂⁴×C₃	—	5	1	no	—
185	C₂²×C₃×C₄	—	5	1	no	—
186	C₂²×C₃×C₄	—	5	1	no	—
187	C₂²×C₃×C₄	—	5	1	no	—
188	C₂²×C₃×C₄	—	5	1	no	—
189	C₂²×C₃×C₄	—	5	1	no	—
190	C₂²×C₃×C₄	—	10	1	no	—
191	C₂²×C₃×C₄	—	10	1	no	—
192	C₂²×C₃×C₄	—	10	1	no	—
193	C₂²×C₃×C₄	—	10	1	no	—
194	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
195	C₂²×Dic₃	—	10	2	no	—
196	C₂²×Dic₃	—	10	2	no	—
197	C₃×M₁₆	—	2	2	no	—
198	C₃×M₁₆	—	10	2	no	—
199	C₃×M₁₆	—	10	2	no	—
200	C₃×M₁₆	—	10	2	no	—
201	C₂×C₃×C₈	—	5	1	no	—
202	C₂×C₃×C₈	—	5	2	no	—
203	C₂×C₃×C₈	—	5	2	no	—
204	C₂×C₃×C₈	—	5	1	no	—
205	C₂×C₃×C₈	—	10	1	no	—
206	C₂×C₃×C₈	—	10	1	no	—
207	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
209	#217	—	20	4	no	—
210	C₄⋊Dic₃	—	10	2	no	—
211	C₄⋊Dic₃	—	10	2	no	—
212	C₄⋊Dic₃	—	10	2	no	—
213	C₄⋊Dic₃	—	10	2	no	—
214	C₂³×C₅	C₄⋊Dic₃	1	1	yes	characteristic
215	C₂²×D₅	—	2	2	no	—
216	C₂²×D₅	—	2	2	no	—
217	C₂²×D₅	—	2	1	no	—
218	C₂²×D₅	—	2	1	no	—
219	C₂²×D₅	C₄⋊Dic₃	1	1	yes	characteristic
220	C₂²×D₅	C₂×D₁₂	1	1	yes	characteristic
221	C₂×AGL(1,𝔽₅)	—	12	2	no	—
222	C₂×AGL(1,𝔽₅)	—	12	2	no	—
223	C₂×AGL(1,𝔽₅)	—	12	2	no	—
224	C₂×AGL(1,𝔽₅)	—	12	2	no	—
225	C₂×AGL(1,𝔽₅)	—	12	2	no	—
226	C₂×AGL(1,𝔽₅)	—	12	2	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	C₄⋊Dic₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
231	C₂×Dic₅	—	2	1	no	—
232	C₂×Dic₅	—	2	1	no	—
233	C₂×Dic₅	C₄⋊Dic₃	1	1	yes	characteristic
234	C₂×Dic₅	C₂×Dic₆	1	1	yes	characteristic
235	C₄×D₅	—	2	1	no	—
236	C₄×D₅	—	2	1	no	—
237	C₄×D₅	—	2	1	no	—
238	C₄×D₅	—	2	1	no	—
239	C₄×D₅	—	2	1	no	—
240	C₄×D₅	—	2	1	no	—
241	C₄×D₅	#235	1	1	yes	characteristic
242	C₄×D₅	#235	1	1	yes	characteristic
243	C₄×D₅	C₂×#67	1	1	yes	characteristic
244	C₄×D₅	C₂×#67	1	1	yes	characteristic
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	#217	1	2	yes	complemented
247	#168	—	2	1	no	—
248	#168	#217	1	2	yes	complemented
249	C₂³×C₄	—	5	1	no	—
250	C₂×M₁₆	—	5	1	no	—
251	C₂×M₁₆	—	5	1	no	—
252	C₂×M₁₆	—	5	1	no	—
253	C₂×M₁₆	—	10	2	no	—
254	C₂×M₁₆	—	10	2	no	—
255	C₂×M₁₆	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented
256	C₂²×C₈	—	5	1	no	—
257	C₂²×C₈	—	5	1	no	—
258	C₂×C₄⋊C₄	—	15	2	no	—
259	C₂×C₄⋊C₄	—	15	2	no	—
260	C₂×C₂²⋊C₄	—	30	2	no	—
261	#107	—	30	2	no	—
262	#106	—	30	2	no	—
263	#95	—	30	2	no	—
264	C₂×C₃×C₅	—	4	1	no	—
265	C₂×C₃×C₅	#380	1	1	yes	characteristic
266	C₂×C₃×C₅	#428	1	2	yes	—
267	C₃×D₅	—	4	1	no	—
268	C₃×D₅	#468	1	2	yes	—
269	C₃×D₅	#469	1	1	yes	characteristic
270	C₃×D₅	#470	1	1	yes	characteristic
271	C₂³×C₃	—	5	1	no	—
272	C₂³×C₃	—	5	1	no	—
273	C₂³×C₃	—	10	2	no	—
274	C₂³×C₃	—	10	1	no	—
275	C₂³×C₃	—	10	1	no	—
276	C₂³×C₃	—	10	2	no	—
277	C₂³×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	2	1	no	—
280	C₂×C₃×C₄	—	5	1	no	—
281	C₂×C₃×C₄	—	5	1	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	1	no	—
284	C₂×C₃×C₄	—	5	1	no	—
285	C₂×C₃×C₄	—	5	1	no	—
286	C₂×C₃×C₄	—	10	1	no	—
287	C₂×C₃×C₄	—	10	1	no	—
288	C₂×C₃×C₄	—	10	1	no	—
289	C₂×C₃×C₄	—	10	1	no	—
290	C₂×C₃×C₄	—	10	1	no	—
291	C₂×C₃×C₄	—	10	1	no	—
292	C₂×C₃×C₄	—	10	1	no	—
293	C₂×C₃×C₄	—	10	1	no	—
294	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
296	C₂×Dic₃	—	20	2	no	—
297	C₂×Dic₃	—	20	2	no	—
298	C₂×Dic₃	—	20	2	no	—
299	C₂×Dic₃	—	20	2	no	—
300	C₂×Dic₃	—	20	2	no	—
301	C₂×Dic₃	—	20	2	no	—
302	C₃×C₈	—	2	1	no	—
303	C₃×C₈	—	5	2	no	—
304	C₃×C₈	—	10	1	no	—
305	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
309	C₂×D₅	—	2	2	no	—
310	C₂×D₅	—	2	1	no	—
311	C₂×D₅	—	4	2	no	—
312	C₂×D₅	—	4	1	no	—
313	C₂×D₅	—	4	1	no	—
314	C₂×D₅	#908	1	2	yes	—
315	C₂×D₅	#909	1	2	yes	—
316	C₂×D₅	#930	1	1	yes	characteristic
317	C₂×D₅	#930	1	1	yes	characteristic
318	AGL(1,𝔽₅)	—	24	2	no	—
319	AGL(1,𝔽₅)	—	24	2	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	#926	1	1	yes	characteristic
322	C₄×C₅	C₂×#217	1	1	yes	characteristic
323	Dic₅	—	2	1	no	—
324	Dic₅	#924	1	1	yes	characteristic
325	Dic₅	#924	1	1	yes	characteristic
326	C₂⁴	—	5	1	no	—
327	C₂²×C₄	—	5	1	no	—
328	C₂²×C₄	—	5	1	no	—
329	C₂²×C₄	—	5	1	no	—
330	C₂²×C₄	—	5	1	no	—
331	C₂²×C₄	—	5	1	no	—
332	C₂²×C₄	—	10	1	no	—
333	C₂²×C₄	—	10	1	no	—
334	C₂²×C₄	—	10	1	no	—
335	C₂²×C₄	—	10	1	no	—
336	C₂²×C₄	—	30	2	no	—
337	C₂²×C₄	—	30	2	no	—
338	C₂²×C₄	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
339	M₁₆	—	2	2	no	—
340	M₁₆	—	10	2	no	—
341	M₁₆	—	10	2	no	—
342	M₁₆	—	10	2	no	—
343	C₂×C₈	—	5	1	no	—
344	C₂×C₈	—	5	2	no	—
345	C₂×C₈	—	5	2	no	—
346	C₂×C₈	—	5	1	no	—
347	C₂×C₈	—	10	1	no	—
348	C₂×C₈	—	10	1	no	—
349	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
350	C₂×C₈	C₂×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
351	C₄⋊C₄	—	30	2	no	—
352	C₄⋊C₄	—	30	2	no	—
353	C₄⋊C₄	—	30	2	no	—
354	C₄⋊C₄	—	30	2	no	—
355	C₂²⋊C₄	—	60	4	no	—
356	C₃×C₅	#1809	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	5	2	no	—
360	C₂²×C₃	—	5	2	no	—
361	C₂²×C₃	—	5	1	no	—
362	C₂²×C₃	—	5	1	no	—
363	C₂²×C₃	—	10	2	no	—
364	C₂²×C₃	—	10	1	no	—
365	C₂²×C₃	—	20	1	no	—
366	C₂²×C₃	—	20	2	no	—
367	C₂²×C₃	—	20	1	no	—
368	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
369	C₃×C₄	—	2	1	no	—
370	C₃×C₄	—	5	1	no	—
371	C₃×C₄	—	5	1	no	—
372	C₃×C₄	—	10	1	no	—
373	C₃×C₄	#4130	1	1	yes	characteristic
374	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
375	Dic₃	—	40	2	no	—
376	Dic₃	—	40	2	no	—
377	C₂×C₅	—	4	1	no	—
378	C₂×C₅	#5121	1	2	yes	—
379	C₂×C₅	#5212	1	1	yes	characteristic
380	D₅	—	4	1	no	—
381	D₅	#5134	1	2	yes	—
382	D₅	#5135	1	1	yes	characteristic
383	D₅	#5137	1	1	yes	characteristic
384	C₂³	—	5	1	no	—
385	C₂³	—	5	1	no	—
386	C₂³	—	10	2	no	—
387	C₂³	—	10	1	no	—
388	C₂³	—	10	1	no	—
389	C₂³	—	10	2	no	—
390	C₂³	C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	5	1	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	10	1	no	—
400	C₂×C₄	—	10	1	no	—
401	C₂×C₄	—	10	1	no	—
402	C₂×C₄	—	10	1	no	—
403	C₂×C₄	—	10	1	no	—
404	C₂×C₄	—	10	1	no	—
405	C₂×C₄	—	10	1	no	—
406	C₂×C₄	—	10	1	no	—
407	C₂×C₄	—	60	2	no	—
408	C₂×C₄	—	60	2	no	—
409	C₂×C₄	—	60	2	no	—
410	C₂×C₄	—	60	2	no	—
411	C₂×C₄	—	60	2	no	—
412	C₂×C₄	—	60	2	no	—
413	C₂×C₄	C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
414	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)	1	1	yes	characteristic
415	C₈	—	2	1	no	—
416	C₈	—	5	2	no	—
417	C₈	—	10	1	no	—
418	C₈	#6763	1	2	yes	complemented
419	C₂×C₃	—	4	1	no	—
420	C₂×C₃	—	5	1	no	—
421	C₂×C₃	—	5	2	no	—
422	C₂×C₃	—	5	1	no	—
423	C₂×C₃	—	20	1	no	—
424	C₂×C₃	#65727	1	2	yes	—
425	C₂×C₃	#65765	1	1	yes	characteristic
426	C₅	#71988	1	1	yes	characteristic, complemented, Sylow
427	C₂²	—	2	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	5	2	no	—
430	C₂²	—	5	2	no	—
431	C₂²	—	5	1	no	—
432	C₂²	—	5	1	no	—
433	C₂²	—	10	2	no	—
434	C₂²	—	10	1	no	—
435	C₂²	—	20	1	no	—
436	C₂²	—	20	2	no	—
437	C₂²	—	20	1	no	—
438	C₂²	C₂×C₄⋊ΓL(1,𝔽₁₆)	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	5	1	no	—
441	C₄	—	5	1	no	—
442	C₄	—	10	1	no	—
443	C₄	—	120	2	no	—
444	C₄	—	120	2	no	—
445	C₄	#91989	1	1	yes	characteristic
446	C₄	C₂×#6763	1	1	yes	characteristic
447	C₃	#10604761	1	1	yes	characteristic, complemented, Sylow
448	C₂	—	4	1	no	—
449	C₂	—	5	1	no	—
450	C₂	—	5	2	no	—
451	C₂	—	5	1	no	—
452	C₂	—	20	1	no	—
453	C₂	#11752386	1	2	yes	—
454	C₂	#11752424	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊ΓL(1,𝔽₁₆)
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₂×C₃×C₅×M₁₆	C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂×M₁₆	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	#1809
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#91223	C₂	semidirect
4. C₂×#91222	C₂	semidirect
5. #11746764	C₂	semidirect
11. C₂×C₃×C₅×M₁₆	C₄	semidirect
12. C₂×C₃×#681	C₄	semidirect
15. C₂×C₃×#676	C₄	semidirect
16. C₂×C₃×#676	C₄	semidirect
67. C₂×C₅×M₁₆	Dic₃	semidirect
68. C₂×#681	Dic₃	semidirect
71. C₂×#676	Dic₃	semidirect
72. C₂×#676	Dic₃	semidirect
111. C₃×C₅×C₈	C₂²⋊C₄	semidirect
113. C₃×#168	C₂²⋊C₄	semidirect
120. C₂×C₃×M₁₆	AGL(1,𝔽₅)	semidirect
246. C₅×C₈	#217	semidirect
248. #168	#217	semidirect
255. C₂×M₁₆	ΓL(1,𝔽₁₆)	semidirect
305. C₃×C₈	C₂²⋊AGL(1,𝔽₅)	semidirect
356. C₃×C₅	#1809	semidirect
418. C₈	#6763	semidirect
426. C₅	#71988	semidirect
447. C₃	#10604761	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₅×M₁₆	2
#11752424	2
C₂×#91223	2
C₂×#91222	2
#11746764	2
#10604761	3
#71988	5