Subgroups — #14297710

Order 1920.

616 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	D₅⋊(C₄⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic
3	C₃×#65688	C₂	1	1	yes	maximal, characteristic
4	C₂×#91153	C₂	1	2	yes	maximal
5	#11746528	C₂	1	2	yes	maximal
6	#10604451	—	3	1	no	maximal, Hall
7	C₂×D₅×Dic₆	C₂²	1	1	yes	characteristic
8	C₂×D₅⋊(C₃⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
10	C₂×C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
11	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
12	C₄×Dic₃₀	C₄	1	1	yes	characteristic, complemented
13	C₄×C₅×Dic₆	C₄	1	1	yes	characteristic, complemented
14	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
15	C₄×#1204	—	2	1	no	—
16	D₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
17	D₅×Dic₃⋊C₄	—	2	1	no	—
18	C₄×D₅×Dic₃	—	2	1	no	—
19	#91333	C₄	1	1	yes	characteristic, complemented
20	Dic₅×Dic₆	C₄	1	1	yes	characteristic, complemented
21	#91323	—	2	1	no	—
22	#91233	—	2	1	no	—
23	C₄⋊(C₃⋊#170)	—	2	1	no	—
24	#91153	—	2	4	no	—
25	#69588	—	5	1	no	maximal, Hall
26	C₄×Q₈×D₅	—	3	1	no	—
27	C₂×#4009	—	3	2	no	—
28	#65688	D₃	1	1	yes	characteristic
29	D₅⋊(C₄⋊C₈)	—	3	1	no	—
30	#64874	—	3	2	no	—
31	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
32	C₂×Dic₃₀	C₂×C₄	1	1	yes	characteristic
33	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
34	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
35	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
36	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
37	C₂×#1204	—	2	1	no	—
38	C₂×D₅×Dic₃	—	2	1	no	—
39	C₂×D₅×Dic₃	—	2	1	no	—
40	D₅×Dic₆	—	2	1	no	—
41	D₅×Dic₆	—	2	1	no	—
42	D₅×Dic₆	D₄	1	2	yes	—
43	D₅×Dic₆	Q₈	1	2	yes	—
44	C₂×C₃⋊#170	—	2	2	no	—
45	D₅⋊(C₃⋊C₈)	—	2	2	no	—
46	D₅⋊(C₃⋊C₈)	—	2	2	no	—
47	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
48	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
49	C₃×C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
50	C₃×C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
51	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
52	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
53	#6712	—	2	1	no	—
54	C₄×Dic₁₅	—	2	1	no	—
55	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
60	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
61	Dic₃⋊Dic₅	—	2	1	no	—
62	#6669	—	2	1	no	—
63	#6668	—	2	1	no	—
64	Dic₃×Dic₅	—	2	1	no	—
65	Dic₃×Dic₅	—	2	1	no	—
66	C₂×C₄×Dic₆	—	5	1	no	—
67	C₃×#384	—	5	1	no	—
68	C₂×#810	—	5	2	no	—
69	C₂×C₄⋊(C₃⋊C₈)	—	5	1	no	—
70	#4529	—	5	2	no	—
71	C₂×Q₈×D₅	—	3	1	no	—
72	C₂×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
73	C₂×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
74	C₂×C₄⋊AGL(1,𝔽₅)	C₂×D₃	1	2	yes	—
75	C₂×D₅⋊C₈	—	3	2	no	—
76	C₄×C₅×Q₈	—	3	1	no	—
77	Q₈×Dic₅	—	3	1	no	—
78	D₅×C₄⋊C₄	—	3	1	no	—
79	D₅×C₄⋊C₄	—	6	1	no	—
80	#4033	—	3	1	no	—
81	#4033	—	6	1	no	—
82	C₄²×D₅	—	6	1	no	—
83	C₄²×D₅	C₂×D₃	1	1	yes	characteristic
84	C₄×Dic₁₀	—	3	1	no	—
85	C₄×Dic₁₀	—	6	1	no	—
86	#4009	—	6	4	no	—
87	#4004	—	6	1	no	—
88	C₄⋊#170	—	6	1	no	—
89	#1803	—	15	1	no	Sylow
90	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
91	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
92	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
93	C₂×C₃×AGL(1,𝔽₅)	—	4	2	no	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂×Dic₁₅	—	2	1	no	—
98	C₂×Dic₁₅	—	2	1	no	—
99	Dic₃₀	—	2	1	no	—
100	Dic₃₀	C₄⋊C₄	1	2	yes	complemented
101	C₂×C₅×Dic₃	—	2	1	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₅×Dic₆	—	2	1	no	—
104	C₅×Dic₆	C₄⋊C₄	1	2	yes	complemented
105	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₄×D₅	—	2	1	no	—
109	C₃×C₄×D₅	—	2	1	no	—
110	C₃×C₄×D₅	SD₁₆	1	2	yes	—
111	C₃×C₄×D₅	Q₁₆	1	2	yes	—
112	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
113	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
114	C₃×C₄×D₅	#41	1	1	yes	characteristic
115	C₃×C₄×D₅	#41	1	1	yes	characteristic
116	#1204	—	2	2	no	—
117	#1204	—	2	2	no	—
118	D₅×Dic₃	—	2	2	no	—
119	D₅×Dic₃	—	2	2	no	—
120	D₅×Dic₃	—	4	1	no	—
121	D₅×Dic₃	—	4	1	no	—
122	C₃⋊#170	—	4	2	no	—
123	C₂²×Dic₆	—	5	1	no	—
124	C₂×C₃×C₄⋊C₄	—	5	2	no	—
125	C₂×C₃×C₄⋊C₄	—	10	1	no	—
126	C₂×C₃×C₄⋊C₄	—	10	1	no	—
127	C₂×C₃×C₄²	—	5	1	no	—
128	C₂×C₄⋊Dic₃	—	5	1	no	—
129	C₂×Dic₃⋊C₄	—	10	1	no	—
130	C₂×C₄×Dic₃	—	10	1	no	—
131	C₂²×C₃⋊C₈	—	5	2	no	—
132	C₄×Dic₆	—	5	1	no	—
133	C₄×Dic₆	—	5	1	no	—
134	C₄×Dic₆	—	5	1	no	—
135	C₄×Dic₆	—	10	1	no	—
136	C₄×Dic₆	—	10	1	no	—
137	C₄×Dic₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
138	#810	—	10	4	no	—
139	C₄⋊(C₃⋊C₈)	—	10	1	no	—
140	C₄⋊(C₃⋊C₈)	—	10	1	no	—
141	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
142	C₂×C₅×Q₈	—	3	1	no	—
143	Q₈×D₅	—	3	2	no	—
144	Q₈×D₅	—	3	2	no	—
145	Q₈×D₅	—	6	1	no	—
146	Q₈×D₅	—	6	1	no	—
147	C₂×C₄×D₅	—	6	1	no	—
148	C₂×C₄×D₅	—	6	1	no	—
149	C₂×C₄×D₅	#67	1	1	yes	characteristic
150	C₂×C₄×D₅	#67	1	1	yes	characteristic
151	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
152	C₂×Dic₁₀	—	3	1	no	—
153	C₂×Dic₁₀	—	6	1	no	—
154	C₂×#170	—	6	2	no	—
155	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
156	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
157	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
158	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
159	D₅⋊C₈	—	6	2	no	—
160	D₅⋊C₈	—	6	2	no	—
161	C₅×C₄⋊C₄	—	3	1	no	—
162	C₅×C₄⋊C₄	—	6	1	no	—
163	C₄²×C₅	—	6	1	no	—
164	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
165	C₄⋊Dic₅	—	3	1	no	—
166	C₄⋊Dic₅	—	6	1	no	—
167	#683	—	6	1	no	—
168	#683	—	6	1	no	—
169	#683	—	6	1	no	—
170	C₄×Dic₅	—	6	1	no	—
171	C₄×Dic₅	—	6	1	no	—
172	C₄×Dic₅	—	6	1	no	—
173	C₄×Dic₅	C₄×D₃	1	1	yes	characteristic
174	C₄×Dic₅	D₁₂	1	1	yes	characteristic
175	C₄×Dic₅	D₁₂	1	1	yes	characteristic
176	C₂×C₄×Q₈	—	15	1	no	—
177	C₂×C₄⋊C₈	—	15	1	no	—
178	C₂×#103	—	15	2	no	—
179	#384	—	5	1	no	—
180	#340	—	15	2	no	—
181	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₃×D₅	#121	1	1	yes	characteristic
183	C₂×C₃×D₅	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×C₃×D₅	C₂×SD₁₆	1	1	yes	characteristic
185	C₂×C₃×D₅	C₂×Q₁₆	1	1	yes	characteristic
186	C₂×C₃×D₅	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₃×D₅	#137	1	1	yes	characteristic
188	C₃×AGL(1,𝔽₅)	—	8	2	no	—
189	C₃×C₄×C₅	—	2	1	no	—
190	C₃×C₄×C₅	#103	1	2	yes	complemented
191	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₃×C₄×C₅	#117	1	1	yes	characteristic
193	Dic₁₅	—	2	2	no	—
194	Dic₁₅	—	4	1	no	—
195	C₃×Dic₅	—	2	1	no	—
196	C₃×Dic₅	#103	1	2	yes	complemented
197	C₃×Dic₅	#121	1	1	yes	characteristic
198	C₃×Dic₅	C₂²⋊Q₈	1	1	yes	characteristic
199	C₅×Dic₃	—	2	2	no	—
200	C₅×Dic₃	—	4	1	no	—
201	C₂²×C₃×C₄	—	5	1	no	—
202	C₂²×C₃×C₄	—	5	1	no	—
203	C₂²×C₃×C₄	—	5	1	no	—
204	C₂²×C₃×C₄	—	10	2	no	—
205	C₂²×Dic₃	—	10	1	no	—
206	C₂²×Dic₃	—	10	1	no	—
207	C₂×Dic₆	—	5	1	no	—
208	C₂×Dic₆	—	5	2	no	—
209	C₂×Dic₆	—	5	2	no	—
210	C₂×Dic₆	—	10	1	no	—
211	C₂×Dic₆	—	10	1	no	—
212	C₂×Dic₆	—	10	1	no	—
213	C₂×Dic₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
214	C₃×C₄⋊C₄	—	10	2	no	—
215	C₃×C₄⋊C₄	—	10	2	no	—
216	C₃×C₄⋊C₄	—	20	2	no	—
217	C₃×C₄⋊C₄	—	20	2	no	—
218	C₃×C₄²	—	5	1	no	—
219	C₃×C₄²	—	5	1	no	—
220	C₃×C₄²	—	5	1	no	—
221	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
222	C₄⋊Dic₃	—	5	1	no	—
223	C₄⋊Dic₃	—	10	1	no	—
224	C₄⋊Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
225	Dic₃⋊C₄	—	2	1	no	—
226	Dic₃⋊C₄	—	10	1	no	—
227	Dic₃⋊C₄	—	10	1	no	—
228	Dic₃⋊C₄	—	10	1	no	—
229	C₄×Dic₃	—	2	1	no	—
230	C₄×Dic₃	—	10	1	no	—
231	C₄×Dic₃	—	10	1	no	—
232	C₄×Dic₃	—	10	1	no	—
233	C₂×C₃⋊C₈	—	10	2	no	—
234	C₂×C₃⋊C₈	—	10	2	no	—
235	C₂×C₃⋊C₈	—	10	2	no	—
236	C₂²×D₅	C₂×#67	1	1	yes	characteristic
237	C₂×AGL(1,𝔽₅)	—	4	2	no	—
238	C₂×AGL(1,𝔽₅)	—	4	2	no	—
239	C₂×AGL(1,𝔽₅)	—	4	2	no	—
240	C₅×Q₈	—	3	2	no	—
241	C₅×Q₈	—	6	1	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
247	C₂×Dic₅	—	6	1	no	—
248	C₂×Dic₅	—	6	1	no	—
249	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
250	C₂×Dic₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
251	C₂×Dic₅	C₂×D₁₂	1	1	yes	characteristic
252	C₄×D₅	—	2	1	no	—
253	C₄×D₅	—	2	1	no	—
254	C₄×D₅	—	6	2	no	—
255	C₄×D₅	—	6	2	no	—
256	C₄×D₅	—	12	1	no	—
257	C₄×D₅	—	12	1	no	—
258	C₄×D₅	#214	1	2	yes	—
259	C₄×D₅	#216	1	2	yes	—
260	C₄×D₅	D₃×D₄	1	1	yes	characteristic
261	C₄×D₅	#237	1	1	yes	characteristic
262	C₄×D₅	D₃×Q₈	1	1	yes	characteristic
263	C₄×D₅	#239	1	1	yes	characteristic
264	Dic₁₀	—	3	2	no	—
265	Dic₁₀	—	6	1	no	—
266	Dic₁₀	—	6	2	no	—
267	Dic₁₀	—	6	2	no	—
268	#170	—	12	2	no	—
269	C₂²×Q₈	—	15	1	no	—
270	C₂²×C₈	—	15	2	no	—
271	C₄×Q₈	—	3	1	no	—
272	C₄×Q₈	—	15	1	no	—
273	C₄×Q₈	—	15	1	no	—
274	C₄×Q₈	—	15	1	no	—
275	C₄×Q₈	—	30	1	no	—
276	C₄×Q₈	—	30	1	no	—
277	C₂×C₄⋊C₄	—	5	2	no	—
278	C₂×C₄⋊C₄	—	10	1	no	—
279	C₂×C₄⋊C₄	—	10	1	no	—
280	C₂×C₄⋊C₄	—	15	1	no	—
281	C₂×C₄⋊C₄	—	30	1	no	—
282	C₂×C₄²	—	5	1	no	—
283	C₂×C₄²	—	30	1	no	—
284	C₄⋊C₈	—	30	1	no	—
285	C₄⋊C₈	—	30	1	no	—
286	#103	—	30	4	no	—
287	C₂×C₃×C₅	#380	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
289	C₂×C₃×C₅	#417	1	1	yes	characteristic
290	C₃×D₅	#460	1	1	yes	characteristic
291	C₃×D₅	#462	1	1	yes	characteristic
292	C₃×D₅	#475	1	1	yes	characteristic
293	C₃×D₅	#477	1	1	yes	characteristic
294	C₂³×C₃	—	5	1	no	—
295	C₂×C₃×C₄	—	5	1	no	—
296	C₂×C₃×C₄	—	5	1	no	—
297	C₂×C₃×C₄	—	5	1	no	—
298	C₂×C₃×C₄	—	5	1	no	—
299	C₂×C₃×C₄	—	5	1	no	—
300	C₂×C₃×C₄	—	5	1	no	—
301	C₂×C₃×C₄	—	5	2	no	—
302	C₂×C₃×C₄	—	5	2	no	—
303	C₂×C₃×C₄	—	5	1	no	—
304	C₂×C₃×C₄	—	10	1	no	—
305	C₂×C₃×C₄	—	10	1	no	—
306	C₂×C₃×C₄	—	20	2	no	—
307	C₂×C₃×C₄	—	20	2	no	—
308	C₂×C₃×C₄	—	20	2	no	—
309	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
312	C₂×Dic₃	—	2	1	no	—
313	C₂×Dic₃	—	2	1	no	—
314	C₂×Dic₃	—	10	2	no	—
315	C₂×Dic₃	—	10	2	no	—
316	C₂×Dic₃	—	10	1	no	—
317	C₂×Dic₃	—	10	1	no	—
318	C₂×Dic₃	—	20	1	no	—
319	C₂×Dic₃	—	20	1	no	—
320	Dic₆	—	2	1	no	—
321	Dic₆	—	5	2	no	—
322	Dic₆	—	10	2	no	—
323	Dic₆	—	10	2	no	—
324	Dic₆	—	10	1	no	—
325	Dic₆	C₄⋊AGL(1,𝔽₅)	1	2	yes	complemented
326	C₃⋊C₈	—	20	2	no	—
327	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
328	C₂×D₅	#932	1	1	yes	characteristic
329	C₂×D₅	C₂×#214	1	1	yes	characteristic
330	C₂×D₅	#938	1	1	yes	characteristic
331	C₂×D₅	#942	1	1	yes	characteristic
332	C₂×D₅	C₂×#216	1	1	yes	characteristic
333	C₂×D₅	#946	1	1	yes	characteristic
334	AGL(1,𝔽₅)	—	8	2	no	—
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	6	2	no	—
337	C₄×C₅	—	12	1	no	—
338	C₄×C₅	#810	1	2	yes	complemented
339	C₄×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
340	C₄×C₅	#892	1	1	yes	characteristic
341	Dic₅	—	2	1	no	—
342	Dic₅	—	6	2	no	—
343	Dic₅	—	12	1	no	—
344	Dic₅	#810	1	2	yes	complemented
345	Dic₅	#895	1	1	yes	characteristic
346	Dic₅	#897	1	1	yes	characteristic
347	C₂×Q₈	—	3	1	no	—
348	C₂×Q₈	—	15	2	no	—
349	C₂×Q₈	—	15	2	no	—
350	C₂×Q₈	—	15	1	no	—
351	C₂×Q₈	—	30	1	no	—
352	C₂×Q₈	—	30	1	no	—
353	C₂×Q₈	—	30	1	no	—
354	C₂²×C₄	—	5	1	no	—
355	C₂²×C₄	—	5	1	no	—
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	10	2	no	—
358	C₂²×C₄	—	30	1	no	—
359	C₂²×C₄	—	30	1	no	—
360	C₂×C₈	—	30	2	no	—
361	C₂×C₈	—	30	2	no	—
362	C₂×C₈	—	30	2	no	—
363	C₄⋊C₄	—	3	1	no	—
364	C₄⋊C₄	—	6	1	no	—
365	C₄⋊C₄	—	10	2	no	—
366	C₄⋊C₄	—	10	2	no	—
367	C₄⋊C₄	—	15	1	no	—
368	C₄⋊C₄	—	20	2	no	—
369	C₄⋊C₄	—	20	2	no	—
370	C₄⋊C₄	—	30	1	no	—
371	C₄⋊C₄	—	30	1	no	—
372	C₄⋊C₄	—	30	1	no	—
373	C₄⋊C₄	—	30	1	no	—
374	C₄²	—	5	1	no	—
375	C₄²	—	5	1	no	—
376	C₄²	—	5	1	no	—
377	C₄²	—	6	1	no	—
378	C₄²	—	30	1	no	—
379	C₄²	—	30	1	no	—
380	C₄²	—	30	1	no	—
381	C₄²	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₃×C₅	#1803	1	1	yes	characteristic, complemented, Hall
383	C₂²×C₃	—	5	1	no	—
384	C₂²×C₃	—	5	1	no	—
385	C₂²×C₃	—	5	1	no	—
386	C₂²×C₃	—	5	1	no	—
387	C₂²×C₃	—	5	1	no	—
388	C₂²×C₃	—	5	1	no	—
389	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	5	1	no	—
392	C₃×C₄	—	5	1	no	—
393	C₃×C₄	—	5	2	no	—
394	C₃×C₄	—	10	1	no	—
395	C₃×C₄	—	40	2	no	—
396	C₃×C₄	#4009	1	2	yes	complemented
397	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
398	C₃×C₄	#4130	1	1	yes	characteristic
399	Dic₃	—	2	2	no	—
400	Dic₃	—	4	1	no	—
401	Dic₃	—	10	2	no	—
402	Dic₃	—	20	1	no	—
403	C₂×C₅	#4966	1	1	yes	characteristic
404	C₂×C₅	C₂×#810	1	1	yes	characteristic
405	C₂×C₅	#4987	1	1	yes	characteristic
406	D₅	#5075	1	1	yes	characteristic
407	D₅	#5090	1	1	yes	characteristic
408	D₅	#5091	1	1	yes	characteristic
409	D₅	#5094	1	1	yes	characteristic
410	C₂³	—	5	1	no	—
411	Q₈	—	3	2	no	—
412	Q₈	—	6	1	no	—
413	Q₈	—	15	2	no	—
414	Q₈	—	30	2	no	—
415	Q₈	—	30	2	no	—
416	Q₈	—	30	1	no	—
417	C₂×C₄	—	5	1	no	—
418	C₂×C₄	—	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	2	no	—
424	C₂×C₄	—	5	2	no	—
425	C₂×C₄	—	5	1	no	—
426	C₂×C₄	—	6	1	no	—
427	C₂×C₄	—	6	1	no	—
428	C₂×C₄	—	10	1	no	—
429	C₂×C₄	—	10	1	no	—
430	C₂×C₄	—	20	2	no	—
431	C₂×C₄	—	20	2	no	—
432	C₂×C₄	—	20	2	no	—
433	C₂×C₄	—	30	2	no	—
434	C₂×C₄	—	30	2	no	—
435	C₂×C₄	—	30	1	no	—
436	C₂×C₄	—	30	1	no	—
437	C₂×C₄	—	60	1	no	—
438	C₂×C₄	—	60	1	no	—
439	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₂×C₄	(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
441	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
442	C₈	—	60	2	no	—
443	C₂×C₃	—	5	1	no	—
444	C₂×C₃	—	5	1	no	—
445	C₂×C₃	—	5	1	no	—
446	C₂×C₃	—	5	1	no	—
447	C₂×C₃	#65765	1	1	yes	characteristic
448	C₂×C₃	C₂×#4009	1	1	yes	characteristic
449	C₂×C₃	#65793	1	1	yes	characteristic
450	C₅	#69588	1	1	yes	characteristic, complemented, Sylow
451	C₂²	—	5	1	no	—
452	C₂²	—	5	1	no	—
453	C₂²	—	5	1	no	—
454	C₂²	—	5	1	no	—
455	C₂²	—	5	1	no	—
456	C₂²	—	5	1	no	—
457	C₂²	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	5	2	no	—
460	C₄	—	5	1	no	—
461	C₄	—	5	1	no	—
462	C₄	—	6	2	no	—
463	C₄	—	10	1	no	—
464	C₄	—	12	1	no	—
465	C₄	—	30	2	no	—
466	C₄	—	40	2	no	—
467	C₄	—	60	1	no	—
468	C₄	#91153	1	2	yes	complemented
469	C₄	#91907	1	1	yes	characteristic
470	C₄	D₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
471	C₃	#10604451	1	1	yes	characteristic, complemented, Sylow
472	C₂	—	5	1	no	—
473	C₂	—	5	1	no	—
474	C₂	—	5	1	no	—
475	C₂	—	5	1	no	—
476	C₂	#11751705	1	1	yes	characteristic
477	C₂	C₂×#91153	1	1	yes	characteristic
478	C₂	#11751855	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×(C₂×D₃)⋊AGL(1,𝔽₅)
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₃×C₄²×C₅	C₂×C₄
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₃×D₅	C₂×D₄
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₄²	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1803
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
12. C₄×Dic₃₀	C₄	semidirect
13. C₄×C₅×Dic₆	C₄	semidirect
19. #91333	C₄	semidirect
20. Dic₅×Dic₆	C₄	semidirect
100. Dic₃₀	C₄⋊C₄	semidirect
104. C₅×Dic₆	C₄⋊C₄	semidirect
137. C₄×Dic₆	AGL(1,𝔽₅)	semidirect
190. C₃×C₄×C₅	#103	semidirect
196. C₃×Dic₅	#103	semidirect
325. Dic₆	C₄⋊AGL(1,𝔽₅)	semidirect
338. C₄×C₅	#810	semidirect
344. Dic₅	#810	semidirect
382. C₃×C₅	#1803	semidirect
396. C₃×C₄	#4009	semidirect
450. C₅	#69588	semidirect
468. C₄	#91153	semidirect
471. C₃	#10604451	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₅×Dic₆	2
D₅⋊(C₄⋊(C₃⋊C₈))	2
C₃×#65688	2
C₂×#91153	2
#11746528	2
#10604451	3
#69588	5