Subgroups — #14413491

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11756838	C₂	1	2	yes	maximal
2	D₅×#901	C₂	1	1	yes	maximal, characteristic
3	C₂×#91222	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65721	C₂	1	1	yes	maximal, characteristic, complemented
5	#11751728	C₂	1	2	yes	maximal, complemented
6	#11751657	C₂	1	2	yes	maximal, complemented
7	#11751654	C₂	1	4	yes	maximal, complemented
8	D₃×#3993	C₂	1	2	yes	maximal, complemented
9	#10617416	—	3	1	no	maximal, Hall
10	D₅×#235	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊ΓL(1,𝔽₁₆)	C₂²	1	2	yes	—
12	C₃×#4130	C₂²	1	2	yes	—
13	#67⋊AGL(1,𝔽₅)	—	2	4	no	—
14	D₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
15	AGL(1,𝔽₅)×D₁₂	—	2	2	no	—
16	#91907	C₂²	1	4	yes	—
17	AGL(1,𝔽₅)×Dic₆	—	2	2	no	—
18	#91790	C₄	1	1	yes	characteristic, complemented
19	C₅×#901	C₄	1	1	yes	characteristic, complemented
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	#91290	C₄	1	1	yes	characteristic, complemented
22	#91286	C₄	1	1	yes	characteristic, complemented
23	D₅×#208	C₂²	1	1	yes	characteristic
24	#91266	C₄	1	2	yes	complemented
25	#91265	C₄	1	2	yes	complemented
26	D₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
27	D₃×C₈×D₅	C₂²	1	2	yes	—
28	#91222	C₂²	1	2	yes	—
29	#91222	C₂²	1	2	yes	—
30	C₃×#3994	C₂²	1	2	yes	—
31	C₃×#3993	C₂²	1	1	yes	characteristic
32	C₃×#3993	C₂²	1	1	yes	characteristic
33	#91160	C₂²	1	4	yes	—
34	#91159	C₂²	1	4	yes	—
35	#79178	—	5	1	no	maximal, Hall
36	#66266	—	3	2	no	—
37	D₅×#131	—	3	1	no	—
38	#65727	—	3	4	no	—
39	#65727	—	3	2	no	—
40	#65721	—	3	2	no	—
41	#65721	D₃	1	1	yes	characteristic, complemented
42	C₂×#3993	—	3	1	no	—
43	C₂×#3993	—	3	2	no	—
44	C₂²×ΓL(1,𝔽₁₆)	—	2	2	no	—
45	C₂×D₃×AGL(1,𝔽₅)	—	2	4	no	—
46	#6817	C₂×C₄	1	1	yes	characteristic
47	C₅×#235	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
49	D₅×#67	D₄	1	2	yes	—
50	#6782	Q₈	1	2	yes	—
51	D₅×D₁₂	D₄	1	1	yes	characteristic
52	C₄×D₃×D₅	C₂³	1	2	yes	—
53	#6773	Q₈	1	1	yes	characteristic
54	#6772	Q₈	1	1	yes	characteristic
55	#6771	C₂×C₄	1	2	yes	—
56	D₅×Dic₆	D₄	1	1	yes	characteristic
57	C₄⋊ΓL(1,𝔽₁₆)	—	2	2	no	—
58	C₄⋊ΓL(1,𝔽₁₆)	C₂³	1	4	yes	—
59	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
60	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
61	C₃×C₄⋊AGL(1,𝔽₅)	C₂³	1	2	yes	—
62	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
63	Dic₃⋊AGL(1,𝔽₅)	—	2	4	no	—
64	(C₂×D₃)⋊AGL(1,𝔽₅)	—	2	4	no	—
65	Dic₃×AGL(1,𝔽₅)	—	2	4	no	—
66	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic, complemented
67	#6710	C₂×C₄	1	1	yes	characteristic, complemented
68	#6705	C₂×C₄	1	2	yes	complemented
69	C₈×D₁₅	C₂×C₄	1	2	yes	complemented
70	C₅×#208	C₂×C₄	1	1	yes	characteristic, complemented
71	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	complemented
72	C₅×D₃×C₈	C₂×C₄	1	2	yes	complemented
73	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic, complemented
74	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
75	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic, complemented
76	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
77	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
78	#6651	C₂×C₄	1	2	yes	complemented
79	#6650	C₂×C₄	1	2	yes	complemented
80	#6649	C₂×C₄	1	2	yes	complemented
81	#6648	C₂×C₄	1	2	yes	complemented
82	D₃×#168	C₂×C₄	1	2	yes	complemented
83	D₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂×#901	—	5	1	no	—
85	#5523	—	5	2	no	—
86	C₃×#427	—	5	1	no	—
87	C₂×#817	—	5	1	no	—
88	#4995	—	5	2	no	—
89	#4881	—	5	4	no	—
90	#4860	—	5	2	no	—
91	D₃×#106	—	5	2	no	—
92	D₅×#41	—	3	1	no	—
93	Q₈×AGL(1,𝔽₅)	—	6	2	no	—
94	D₄×AGL(1,𝔽₅)	—	6	2	no	—
95	D₄×AGL(1,𝔽₅)	—	6	4	no	—
96	#4130	—	3	4	no	—
97	#4130	C₂×D₃	1	2	yes	—
98	C₂×C₄⋊AGL(1,𝔽₅)	—	3	2	no	—
99	C₂×C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
100	C₅×#131	—	3	1	no	—
101	#4094	—	3	1	no	—
102	#4053	—	3	1	no	—
103	#4053	—	3	2	no	—
104	D₅×M₁₆	—	3	1	no	—
105	D₅×M₁₆	—	3	2	no	—
106	#4047	—	3	1	no	—
107	#4047	—	3	2	no	—
108	C₂×C₈×D₅	—	3	2	no	—
109	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
110	#3994	—	3	4	no	—
111	#3994	C₂×D₃	1	2	yes	—
112	#3993	—	3	4	no	—
113	#3993	—	3	2	no	—
114	#3993	—	3	2	no	—
115	#3993	C₂×D₃	1	1	yes	characteristic
116	#3993	C₂×D₃	1	1	yes	characteristic
117	#2912	—	15	1	no	Sylow
118	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
119	C₂×D₃×D₅	C₂×D₄	1	2	yes	—
120	C₂×ΓL(1,𝔽₁₆)	—	2	4	no	—
121	C₂×ΓL(1,𝔽₁₆)	—	8	2	no	—
122	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
123	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
124	D₃×AGL(1,𝔽₅)	—	8	4	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	#1220	C₄⋊C₄	1	2	yes	—
127	D₆₀	C₄⋊C₄	1	1	yes	characteristic
128	C₄×D₁₅	C₂²×C₄	1	2	yes	—
129	Dic₃₀	C₄⋊C₄	1	1	yes	characteristic
130	C₅×#67	C₄⋊C₄	1	2	yes	—
131	C₅×D₁₂	C₄⋊C₄	1	1	yes	characteristic
132	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
133	C₅×Dic₆	C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
135	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
136	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
138	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
139	#1204	C₄⋊C₄	1	2	yes	—
140	#1203	C₄⋊C₄	1	2	yes	—
141	#1202	C₄⋊C₄	1	2	yes	—
142	#1201	C₄⋊C₄	1	2	yes	—
143	#1200	C₂×Q₈	1	2	yes	—
144	D₃×Dic₅	C₂×Q₈	1	2	yes	—
145	D₅×Dic₃	C₂×D₄	1	2	yes	—
146	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₃⋊#168	C₂²×C₄	1	2	yes	—
149	C₃×#168	C₂²×C₄	1	1	yes	characteristic
150	C₃×#168	C₂²×C₄	1	1	yes	characteristic
151	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×#235	—	5	1	no	—
153	C₂²×C₃×C₈	—	5	1	no	—
154	C₃×#117	—	5	2	no	—
155	C₂×C₄⋊Dic₃	—	5	2	no	—
156	C₂×#208	—	5	1	no	—
157	#901	—	5	1	no	—
158	#901	—	5	1	no	—
159	#901	—	5	1	no	—
160	#901	—	5	2	no	—
161	#901	—	5	2	no	—
162	#901	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
163	C₂×ΓL(1,𝔽₂₅)	—	5	2	no	—
164	C₂×D₃×C₈	—	5	2	no	—
165	#892	—	5	4	no	—
166	D₃×C₄⋊C₄	—	5	4	no	—
167	#67⋊C₄	—	10	4	no	—
168	C₄×D₁₂	—	10	2	no	—
169	C₄×Dic₆	—	10	2	no	—
170	C₃×#107	—	5	2	no	—
171	C₃×#106	—	5	1	no	—
172	C₃×#106	—	5	1	no	—
173	#817	—	5	2	no	—
174	#817	—	5	2	no	—
175	#808	—	5	4	no	—
176	#807	—	5	4	no	—
177	C₂²×AGL(1,𝔽₅)	—	6	4	no	—
178	C₂²×AGL(1,𝔽₅)	—	6	2	no	—
179	C₅×#41	—	3	1	no	—
180	#713	—	3	1	no	—
181	Q₈×D₅	—	3	1	no	—
182	#711	—	3	2	no	—
183	#711	—	3	1	no	—
184	D₄×D₅	—	3	2	no	—
185	D₄×D₅	—	3	1	no	—
186	#709	—	3	1	no	—
187	#709	—	3	2	no	—
188	C₂×C₄×D₅	—	3	2	no	—
189	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
190	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
191	C₂²⋊AGL(1,𝔽₅)	—	6	4	no	—
192	C₄⋊AGL(1,𝔽₅)	—	3	4	no	—
193	C₄⋊AGL(1,𝔽₅)	—	6	4	no	—
194	C₄⋊AGL(1,𝔽₅)	—	6	2	no	—
195	C₄⋊AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
196	C₄⋊AGL(1,𝔽₅)	C₂²×D₃	1	2	yes	—
197	C₄×AGL(1,𝔽₅)	—	2	2	no	—
198	C₄×AGL(1,𝔽₅)	—	6	4	no	—
199	C₅×M₁₆	—	3	1	no	—
200	C₅×M₁₆	—	3	2	no	—
201	C₂×C₅×C₈	—	3	2	no	—
202	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic, complemented
203	#681	—	3	1	no	—
204	#681	—	3	2	no	—
205	C₂×#168	—	3	2	no	—
206	C₂×#168	C₄×D₃	1	1	yes	characteristic, complemented
207	#676	—	3	2	no	—
208	#676	—	3	2	no	—
209	#676	—	3	2	no	—
210	C₈×D₅	—	3	2	no	—
211	C₈×D₅	—	3	2	no	—
212	C₈×D₅	—	3	2	no	—
213	C₈×D₅	C₄×D₃	1	1	yes	characteristic, complemented
214	C₈×D₅	C₄×D₃	1	1	yes	characteristic, complemented
215	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
216	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
217	C₂×#131	—	15	1	no	—
218	#520	—	15	2	no	—
219	#428	—	15	4	no	—
220	#428	—	15	2	no	—
221	#427	—	5	1	no	—
222	#427	—	15	2	no	—
223	C₂×#106	—	15	2	no	—
224	C₂×#106	—	15	1	no	—
225	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₂×D₁₅	C₂×C₄⋊C₄	1	2	yes	—
227	C₂×C₅×D₃	C₂×C₄⋊C₄	1	2	yes	—
228	C₂×C₃×D₅	—	2	2	no	—
229	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₃×D₅	C₂²×D₄	1	1	yes	characteristic
231	D₃×D₅	—	2	4	no	—
232	ΓL(1,𝔽₁₆)	—	4	4	no	—
233	C₃×AGL(1,𝔽₅)	—	4	2	no	—
234	C₃×AGL(1,𝔽₅)	—	4	2	no	—
235	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
237	Dic₁₅	C₂×C₄⋊C₄	1	2	yes	—
238	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
239	C₃×Dic₅	C₂²×Q₈	1	1	yes	characteristic
240	C₅×Dic₃	C₂×C₄⋊C₄	1	2	yes	—
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂×#67	—	5	2	no	—
243	C₂²×Dic₃	—	10	2	no	—
244	#235	—	5	1	no	—
245	#235	—	5	2	no	—
246	#235	—	5	1	no	—
247	#235	—	5	2	no	—
248	#235	—	5	1	no	—
249	#235	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
250	C₂×D₁₂	—	5	1	no	—
251	C₂×C₄×D₃	—	5	2	no	—
252	C₂×C₄×D₃	—	10	4	no	—
253	C₂×Dic₆	—	5	1	no	—
254	C₂×C₃×C₈	—	5	1	no	—
255	C₂×C₃×C₈	—	5	1	no	—
256	C₂×C₃×C₈	—	5	1	no	—
257	C₂×C₃×C₈	—	5	1	no	—
258	C₂×C₃×C₈	—	5	1	no	—
259	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
260	C₃×C₄⋊C₄	—	5	2	no	—
261	C₃×C₄⋊C₄	—	5	2	no	—
262	C₃×C₂²⋊C₄	—	10	2	no	—
263	C₃×C₄²	—	10	2	no	—
264	(C₂×D₃)⋊C₄	—	10	4	no	—
265	C₄⋊Dic₃	—	5	4	no	—
266	C₄⋊Dic₃	—	10	2	no	—
267	Dic₃⋊C₄	—	10	4	no	—
268	C₄×Dic₃	—	10	4	no	—
269	#208	—	5	1	no	—
270	#208	—	5	2	no	—
271	#208	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
272	C₂×C₃⋊C₈	—	5	2	no	—
273	ΓL(1,𝔽₂₅)	—	5	2	no	—
274	ΓL(1,𝔽₂₅)	—	5	2	no	—
275	ΓL(1,𝔽₂₅)	—	5	2	no	—
276	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
277	D₃×C₈	—	5	2	no	—
278	D₃×C₈	—	5	2	no	—
279	D₃×C₈	—	5	2	no	—
280	D₃×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
281	C₂²×D₅	—	3	2	no	—
282	C₂²×D₅	D₃×D₄	1	1	yes	characteristic
283	C₂×AGL(1,𝔽₅)	—	2	2	no	—
284	C₂×AGL(1,𝔽₅)	—	2	2	no	—
285	C₂×AGL(1,𝔽₅)	—	6	4	no	—
286	C₂×AGL(1,𝔽₅)	—	24	4	no	—
287	C₂×AGL(1,𝔽₅)	—	24	2	no	—
288	C₅×Q₈	—	3	1	no	—
289	C₅×D₄	—	3	2	no	—
290	C₅×D₄	—	3	1	no	—
291	C₂×C₄×C₅	—	3	2	no	—
292	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂²⋊D₅	—	3	2	no	—
294	C₂²⋊D₅	—	3	2	no	—
295	C₂²⋊D₅	—	3	2	no	—
296	C₂×Dic₅	—	3	2	no	—
297	C₂×Dic₅	D₃×Q₈	1	1	yes	characteristic
298	D₂₀	—	3	2	no	—
299	D₂₀	—	3	1	no	—
300	C₄×D₅	—	3	2	no	—
301	C₄×D₅	—	3	2	no	—
302	C₄×D₅	—	3	2	no	—
303	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
304	C₄×D₅	D₃×D₄	1	1	yes	characteristic
305	C₄×D₅	D₃×Q₈	1	1	yes	characteristic
306	C₄×D₅	C₂³×D₃	1	1	yes	characteristic
307	Dic₁₀	—	3	1	no	—
308	Dic₁₀	—	3	2	no	—
309	C₅×C₈	—	3	2	no	—
310	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
311	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
312	#168	—	3	2	no	—
313	#168	C₂×C₄×D₃	1	1	yes	characteristic
314	#168	C₂×C₄×D₃	1	1	yes	characteristic
315	C₂×#41	—	15	1	no	—
316	#131	—	3	1	no	—
317	#131	—	15	2	no	—
318	#131	—	15	1	no	—
319	#131	—	15	2	no	—
320	#131	—	15	1	no	—
321	#131	—	15	1	no	—
322	C₂×M₁₆	—	15	2	no	—
323	C₂×M₁₆	—	15	1	no	—
324	C₂²×C₈	—	5	1	no	—
325	C₂²×C₈	—	15	2	no	—
326	C₄×Q₈	—	30	2	no	—
327	C₄×D₄	—	30	2	no	—
328	C₄×D₄	—	30	4	no	—
329	#117	—	5	2	no	—
330	#117	—	15	4	no	—
331	C₂×C₄⋊C₄	—	15	4	no	—
332	C₂×C₄⋊C₄	—	15	2	no	—
333	#107	—	5	2	no	—
334	#107	—	15	4	no	—
335	#106	—	5	1	no	—
336	#106	—	5	1	no	—
337	#106	—	15	4	no	—
338	#106	—	15	2	no	—
339	#106	—	15	2	no	—
340	C₂×C₃×C₅	—	2	1	no	—
341	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
342	D₁₅	—	2	2	no	—
343	C₃×D₅	—	2	1	no	—
344	C₃×D₅	#577	1	2	yes	—
345	C₅×D₃	—	2	2	no	—
346	C₂³×C₃	—	5	1	no	—
347	C₂²×D₃	—	5	2	no	—
348	C₂×C₃×C₄	—	5	1	no	—
349	C₂×C₃×C₄	—	5	1	no	—
350	C₂×C₃×C₄	—	5	1	no	—
351	C₂×C₃×C₄	—	5	1	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	10	2	no	—
354	C₂×C₃×C₄	—	10	2	no	—
355	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
356	#67	—	5	2	no	—
357	#67	—	5	2	no	—
358	#67	—	5	2	no	—
359	#67	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
360	C₂×Dic₃	—	5	2	no	—
361	C₂×Dic₃	—	10	4	no	—
362	C₂×Dic₃	—	40	2	no	—
363	D₁₂	—	5	2	no	—
364	D₁₂	—	5	1	no	—
365	D₁₂	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
366	C₄×D₃	—	5	2	no	—
367	C₄×D₃	—	5	2	no	—
368	C₄×D₃	—	5	2	no	—
369	C₄×D₃	—	40	4	no	—
370	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
371	Dic₆	—	5	1	no	—
372	Dic₆	—	5	2	no	—
373	Dic₆	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
374	C₃×C₈	—	5	1	no	—
375	C₃×C₈	—	5	1	no	—
376	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
377	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₃⋊C₈	—	5	2	no	—
379	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
380	C₂²×C₅	—	3	2	no	—
381	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
382	C₂×D₅	—	2	2	no	—
383	C₂×D₅	—	3	2	no	—
384	C₂×D₅	—	6	4	no	—
385	C₂×D₅	D₃×C₄⋊C₄	1	1	yes	characteristic
386	C₂×D₅	C₂×D₃×D₄	1	1	yes	characteristic
387	AGL(1,𝔽₅)	—	4	2	no	—
388	AGL(1,𝔽₅)	—	4	2	no	—
389	AGL(1,𝔽₅)	—	12	4	no	—
390	C₄×C₅	—	3	2	no	—
391	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
392	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
393	Dic₅	—	3	2	no	—
394	Dic₅	D₃×C₄⋊C₄	1	1	yes	characteristic
395	Dic₅	C₂×D₃×Q₈	1	1	yes	characteristic
396	#41	—	3	1	no	—
397	#41	—	15	2	no	—
398	#41	—	15	2	no	—
399	#41	—	15	1	no	—
400	#41	—	15	1	no	—
401	#41	—	15	1	no	—
402	C₂×Q₈	—	15	1	no	—
403	C₂×D₄	—	15	1	no	—
404	C₂×D₄	—	15	2	no	—
405	C₂²×C₄	—	5	1	no	—
406	C₂²×C₄	—	15	2	no	—
407	C₂²×C₄	—	30	4	no	—
408	C₂²×C₄	—	30	2	no	—
409	M₁₆	—	3	1	no	—
410	M₁₆	—	3	2	no	—
411	M₁₆	—	15	2	no	—
412	M₁₆	—	15	2	no	—
413	M₁₆	—	15	2	no	—
414	M₁₆	—	15	1	no	—
415	M₁₆	—	15	2	no	—
416	C₂×C₈	—	3	2	no	—
417	C₂×C₈	—	5	1	no	—
418	C₂×C₈	—	5	1	no	—
419	C₂×C₈	—	5	1	no	—
420	C₂×C₈	—	5	1	no	—
421	C₂×C₈	—	5	1	no	—
422	C₂×C₈	—	15	2	no	—
423	C₂×C₈	—	15	2	no	—
424	C₂×C₈	—	15	2	no	—
425	C₂×C₈	—	15	2	no	—
426	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
427	C₄⋊C₄	—	5	2	no	—
428	C₄⋊C₄	—	5	2	no	—
429	C₄⋊C₄	—	15	4	no	—
430	C₄⋊C₄	—	30	2	no	—
431	C₄⋊C₄	—	30	4	no	—
432	C₂²⋊C₄	—	10	2	no	—
433	C₂²⋊C₄	—	30	4	no	—
434	C₄²	—	10	2	no	—
435	C₄²	—	30	4	no	—
436	C₃×C₅	#2912	1	1	yes	characteristic, complemented, Hall
437	C₂²×C₃	—	5	1	no	—
438	C₂²×C₃	—	5	1	no	—
439	C₂²×C₃	—	10	2	no	—
440	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
441	C₂×D₃	—	5	2	no	—
442	C₂×D₃	—	10	4	no	—
443	C₂×D₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
444	C₃×C₄	—	5	1	no	—
445	C₃×C₄	—	5	1	no	—
446	C₃×C₄	—	20	2	no	—
447	C₃×C₄	—	20	2	no	—
448	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
449	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
450	Dic₃	—	5	2	no	—
451	Dic₃	—	20	4	no	—
452	Dic₃	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	—
453	C₂×C₅	—	2	1	no	—
454	C₂×C₅	—	6	2	no	—
455	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
456	D₅	—	2	1	no	—
457	D₅	—	6	2	no	—
458	D₅	#5770	1	2	yes	—
459	C₂³	—	5	1	no	—
460	C₂³	—	15	2	no	—
461	Q₈	—	3	1	no	—
462	Q₈	—	15	2	no	—
463	Q₈	—	15	1	no	—
464	D₄	—	3	2	no	—
465	D₄	—	3	1	no	—
466	D₄	—	15	2	no	—
467	D₄	—	15	2	no	—
468	D₄	—	15	2	no	—
469	D₄	—	15	2	no	—
470	D₄	—	15	1	no	—
471	C₂×C₄	—	3	2	no	—
472	C₂×C₄	—	5	1	no	—
473	C₂×C₄	—	5	1	no	—
474	C₂×C₄	—	5	1	no	—
475	C₂×C₄	—	5	1	no	—
476	C₂×C₄	—	5	1	no	—
477	C₂×C₄	—	10	2	no	—
478	C₂×C₄	—	10	2	no	—
479	C₂×C₄	—	15	2	no	—
480	C₂×C₄	—	15	2	no	—
481	C₂×C₄	—	15	2	no	—
482	C₂×C₄	—	15	2	no	—
483	C₂×C₄	—	30	4	no	—
484	C₂×C₄	—	120	4	no	—
485	C₂×C₄	—	120	2	no	—
486	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
487	C₈	—	3	2	no	—
488	C₈	—	5	1	no	—
489	C₈	—	5	1	no	—
490	C₈	—	15	2	no	—
491	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
492	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	5	2	no	—
495	C₂×C₃	—	10	1	no	—
496	C₂×C₃	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
497	D₃	—	2	2	no	—
498	D₃	—	10	2	no	—
499	C₅	#79178	1	1	yes	characteristic, complemented, Sylow
500	C₂²	—	3	2	no	—
501	C₂²	—	5	1	no	—
502	C₂²	—	5	1	no	—
503	C₂²	—	10	2	no	—
504	C₂²	—	15	2	no	—
505	C₂²	—	30	4	no	—
506	C₂²	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
507	C₄	—	3	2	no	—
508	C₄	—	5	1	no	—
509	C₄	—	5	1	no	—
510	C₄	—	15	2	no	—
511	C₄	—	20	2	no	—
512	C₄	—	20	2	no	—
513	C₄	—	60	4	no	—
514	C₄	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
515	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
516	C₃	#10617416	1	1	yes	characteristic, complemented, Sylow
517	C₂	—	2	1	no	—
518	C₂	—	5	2	no	—
519	C₂	—	6	2	no	—
520	C₂	—	10	1	no	—
521	C₂	—	30	2	no	—
522	C₂	C₂×D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃×C₄⋊AGL(1,𝔽₅)
commutator	C₃×C₄×C₅	C₂³×C₄
Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
socle	C₂×C₃×C₅	C₂²×C₄⋊C₄
prime radical	D₅×#235	C₂²
cosocle	C₃×C₄×D₅	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#2912
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#91222	C₂	semidirect
4. C₃×#65721	C₂	semidirect
5. #11751728	C₂	semidirect
6. #11751657	C₂	semidirect
7. #11751654	C₂	semidirect
8. D₃×#3993	C₂	semidirect
18. #91790	C₄	semidirect
19. C₅×#901	C₄	semidirect
21. #91290	C₄	semidirect
22. #91286	C₄	semidirect
24. #91266	C₄	semidirect
25. #91265	C₄	semidirect
41. #65721	D₃	semidirect
66. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
67. #6710	C₂×C₄	semidirect
68. #6705	C₂×C₄	semidirect
69. C₈×D₁₅	C₂×C₄	semidirect
70. C₅×#208	C₂×C₄	semidirect
71. C₅×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
72. C₅×D₃×C₈	C₂×C₄	semidirect
73. C₂×C₃×#168	C₂×C₄	semidirect
74. C₃×C₈×D₅	C₂×C₄	semidirect
75. C₃×C₈×D₅	C₂×C₄	semidirect
78. #6651	C₂×C₄	semidirect
79. #6650	C₂×C₄	semidirect
80. #6649	C₂×C₄	semidirect
81. #6648	C₂×C₄	semidirect
82. D₃×#168	C₂×C₄	semidirect
162. #901	AGL(1,𝔽₅)	semidirect
202. C₂×C₅×C₈	C₄×D₃	semidirect
206. C₂×#168	C₄×D₃	semidirect
213. C₈×D₅	C₄×D₃	semidirect
214. C₈×D₅	C₄×D₃	semidirect
259. C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
271. #208	C₂×AGL(1,𝔽₅)	semidirect
276. ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	semidirect
280. D₃×C₈	C₂×AGL(1,𝔽₅)	semidirect
426. C₂×C₈	D₃×AGL(1,𝔽₅)	semidirect
436. C₃×C₅	#2912	semidirect
499. C₅	#79178	semidirect
516. C₃	#10617416	semidirect

Maximal subgroups

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

subgroup	index
#11756838	2
D₅×#901	2
C₂×#91222	2
C₃×#65721	2
#11751728	2
#11751657	2
#11751654	2
D₃×#3993	2
#10617416	3
#79178	5