Subgroups — #14478191

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91266	C₂	1	1	yes	maximal, characteristic
2	D₅⋊#812	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	#11751741	C₂	1	2	yes	maximal, complemented
5	D₃×#3998	C₂	1	2	yes	maximal, complemented
6	#11751644	C₂	1	4	yes	maximal, complemented
7	#11751642	C₂	1	4	yes	maximal, complemented
8	#10617404	—	3	1	no	maximal, Hall
9	C₂×#6771	C₄	1	1	yes	characteristic
10	C₂×#6705	C₄	1	1	yes	characteristic
11	C₂×C₅×ΓL(1,𝔽₂₅)	C₄	1	1	yes	characteristic
12	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
13	C₂×#6649	C₄	1	1	yes	characteristic
14	C₂×#6648	C₂²	1	1	yes	characteristic
15	C₂×D₃×#168	C₂²	1	1	yes	characteristic
16	#91266	C₄	1	2	yes	—
17	#91266	C₄	1	2	yes	—
18	#91266	C₂²	1	2	yes	—
19	#91266	C₂²	1	2	yes	—
20	#91227	C₂²	1	2	yes	—
21	#91219	C₂²	1	2	yes	complemented
22	D₅⋊(C₃⋊C₁₆)	C₂²	1	2	yes	complemented
23	C₃×#3998	C₂²	1	2	yes	—
24	C₃×#3990	C₂²	1	2	yes	complemented
25	C₃×D₅⋊C₁₆	C₂²	1	2	yes	complemented
26	#91166	C₂²	1	4	yes	complemented
27	#91165	C₂²	1	4	yes	complemented
28	#91164	C₂²	1	4	yes	complemented
29	D₃×#674	C₂²	1	4	yes	complemented
30	#82007	—	5	1	no	maximal, Hall
31	C₂×#4053	—	3	1	no	—
32	C₂×#3998	—	3	2	no	—
33	#65725	—	3	4	no	—
34	#65725	—	3	4	no	—
35	D₅⋊M₃₂	—	3	1	no	—
36	D₅⋊M₃₂	—	3	2	no	—
37	D₅⋊M₃₂	D₃	1	1	yes	characteristic, complemented
38	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×#1204	C₈	1	1	yes	characteristic
42	C₂×#1203	C₈	1	1	yes	characteristic
43	C₂×#1202	C₈	1	1	yes	characteristic
44	C₂×#1201	C₈	1	1	yes	characteristic
45	#6771	C₈	1	2	yes	—
46	#6771	C₈	1	2	yes	—
47	#6771	C₂×C₄	1	2	yes	—
48	#6771	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
51	#6705	C₂×C₄	1	2	yes	—
52	#6705	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
55	C₅×ΓL(1,𝔽₂₅)	C₂×C₄	1	2	yes	—
56	C₂×C₃×#168	C₂³	1	1	yes	characteristic
57	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₈×D₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
60	C₃×C₈×D₅	C₂³	1	1	yes	characteristic
61	#6649	C₂×C₄	1	2	yes	—
62	#6649	C₂×C₄	1	2	yes	—
63	#6648	C₂×C₄	1	2	yes	—
64	#6648	C₂³	1	2	yes	—
65	D₃×#168	C₂×C₄	1	2	yes	—
66	D₃×#168	C₂³	1	2	yes	—
67	C₃⋊#674	C₂³	1	4	yes	—
68	C₃×#674	C₂³	1	4	yes	—
69	C₂×#901	—	5	1	no	—
70	C₂×C₃×M₃₂	—	5	1	no	—
71	C₂×#812	—	5	1	no	—
72	#4907	—	5	4	no	—
73	D₃×M₃₂	—	5	2	no	—
74	D₃×M₃₂	—	5	2	no	—
75	#4901	—	5	4	no	—
76	C₂×#709	—	3	1	no	—
77	C₂×C₅×M₁₆	—	3	1	no	—
78	C₂²×#168	—	3	1	no	—
79	#4053	—	3	2	no	—
80	#4053	—	3	2	no	—
81	#4053	—	3	2	no	—
82	#4053	—	3	2	no	—
83	C₂×#676	—	3	1	no	—
84	C₂×#676	—	3	1	no	—
85	C₂×C₈×D₅	—	3	1	no	—
86	C₂×C₈×D₅	C₂×D₃	1	1	yes	characteristic
87	#3998	—	3	2	no	—
88	#3998	—	3	4	no	—
89	#3998	C₂×D₃	1	2	yes	—
90	C₂×#674	—	3	4	no	—
91	#3990	—	3	2	no	—
92	#3990	—	3	4	no	—
93	#3990	C₂×D₃	1	2	yes	complemented
94	D₅⋊C₁₆	—	3	2	no	—
95	D₅⋊C₁₆	—	3	4	no	—
96	D₅⋊C₁₆	C₂×D₃	1	2	yes	complemented
97	#3407	—	15	1	no	Sylow
98	C₂²×D₁₅	C₂×C₈	1	1	yes	characteristic
99	C₂²×C₅×D₃	C₂×C₈	1	1	yes	characteristic
100	C₂²×C₃×D₅	C₂×C₈	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×Dic₁₅	C₂×C₈	1	1	yes	characteristic
103	C₄×D₁₅	C₂×C₈	1	2	yes	—
104	C₄×D₁₅	C₂²×C₄	1	2	yes	—
105	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
106	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
107	C₄×C₅×D₃	C₂²×C₄	1	2	yes	—
108	C₂×C₃×Dic₅	C₂×C₈	1	1	yes	characteristic
109	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
110	C₃×C₄×D₅	C₂×C₈	1	1	yes	characteristic
111	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
112	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
113	#1204	C₂×C₈	1	2	yes	—
114	#1204	C₂×C₈	1	2	yes	—
115	#1203	C₂×C₈	1	2	yes	—
116	#1203	C₂×C₈	1	2	yes	—
117	#1202	C₂×C₈	1	2	yes	—
118	#1202	C₂×C₈	1	2	yes	—
119	#1201	C₂×C₈	1	2	yes	—
120	#1201	C₂×C₈	1	2	yes	—
121	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
123	C₃⋊#168	C₂²×C₄	1	2	yes	—
124	C₃×#168	C₂²×C₄	1	1	yes	characteristic
125	C₃×#168	C₂⁴	1	1	yes	characteristic
126	C₅×C₃⋊C₈	C₂²×C₄	1	2	yes	—
127	C₂×#235	—	5	1	no	—
128	C₂²×C₃×C₈	—	5	1	no	—
129	C₂×#208	—	5	1	no	—
130	#901	—	5	2	no	—
131	#901	—	5	2	no	—
132	#901	—	5	2	no	—
133	#901	—	5	2	no	—
134	C₂×ΓL(1,𝔽₂₅)	—	5	1	no	—
135	C₂×ΓL(1,𝔽₂₅)	AGL(1,𝔽₅)	1	1	yes	characteristic
136	C₂×D₃×C₈	—	5	1	no	—
137	C₂×D₃×C₈	—	5	1	no	—
138	C₃×M₃₂	—	5	2	no	—
139	C₃×M₃₂	—	5	2	no	—
140	C₂×C₃×C₁₆	—	5	2	no	—
141	#812	—	5	2	no	—
142	#812	—	5	2	no	—
143	C₂×C₃⋊C₁₆	—	5	2	no	—
144	#798	—	5	4	no	—
145	#798	—	5	4	no	—
146	D₃×C₁₆	—	5	4	no	—
147	D₃×C₁₆	—	5	4	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂×C₂²⋊D₅	—	3	1	no	—
150	C₂×C₂²⋊D₅	—	3	1	no	—
151	#709	—	3	2	no	—
152	#709	—	3	2	no	—
153	#709	—	3	2	no	—
154	#709	—	3	2	no	—
155	C₂×D₂₀	—	3	1	no	—
156	C₂×C₄×D₅	—	3	1	no	—
157	C₂×C₄×D₅	C₄×D₃	1	1	yes	characteristic
158	C₂×Dic₁₀	—	3	1	no	—
159	C₅×M₁₆	—	3	2	no	—
160	C₅×M₁₆	—	3	2	no	—
161	C₂×C₅×C₈	—	3	1	no	—
162	C₂×C₅×C₈	C₄×D₃	1	1	yes	characteristic
163	C₂×#168	—	3	1	no	—
164	C₂×#168	—	3	2	no	—
165	C₂×#168	—	3	2	no	—
166	C₂×#168	C₂²×D₃	1	1	yes	characteristic
167	#676	—	3	2	no	—
168	#676	—	3	2	no	—
169	#676	—	3	2	no	—
170	#676	—	3	2	no	—
171	C₈×D₅	—	3	2	no	—
172	C₈×D₅	—	3	2	no	—
173	C₈×D₅	C₄×D₃	1	1	yes	characteristic
174	C₈×D₅	C₄×D₃	1	1	yes	characteristic
175	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
176	C₈×D₅	C₂²×D₃	1	1	yes	characteristic
177	#674	—	3	4	no	—
178	#674	C₂²×D₃	1	4	yes	—
179	C₂×#131	—	15	1	no	—
180	#504	—	15	4	no	—
181	#504	—	15	4	no	—
182	C₂×M₃₂	—	5	1	no	—
183	C₂×M₃₂	—	15	2	no	—
184	C₂×M₃₂	—	15	2	no	—
185	C₂×M₃₂	—	15	1	no	—
186	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
187	C₂×D₁₅	—	4	1	no	—
188	C₂×D₁₅	C₂²×C₈	1	2	yes	—
189	C₂×C₅×D₃	—	4	1	no	—
190	C₂×C₅×D₃	C₂²×C₈	1	2	yes	—
191	C₂×C₃×D₅	—	4	1	no	—
192	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₃×D₅	C₂²×C₈	1	1	yes	characteristic
194	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
195	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
196	Dic₁₅	C₂²×C₈	1	2	yes	—
197	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
198	C₃×Dic₅	C₂²×C₈	1	1	yes	characteristic
199	C₅×Dic₃	C₂²×C₈	1	2	yes	—
200	C₂²×C₃×C₄	—	5	1	no	—
201	C₂×#67	—	5	1	no	—
202	C₂×#67	—	5	1	no	—
203	#235	—	5	2	no	—
204	#235	—	5	2	no	—
205	#235	—	5	2	no	—
206	#235	—	5	2	no	—
207	C₂×D₁₂	—	5	1	no	—
208	C₂×C₄×D₃	—	5	1	no	—
209	C₂×C₄×D₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
210	C₂×Dic₆	—	5	1	no	—
211	C₂×C₃×C₈	—	5	1	no	—
212	C₂×C₃×C₈	—	5	1	no	—
213	C₂×C₃×C₈	—	5	1	no	—
214	C₂×C₃×C₈	—	5	1	no	—
215	C₂×C₃×C₈	—	5	1	no	—
216	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
217	#208	—	5	2	no	—
218	#208	—	5	2	no	—
219	C₂×C₃⋊C₈	—	5	1	no	—
220	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
221	ΓL(1,𝔽₂₅)	—	5	2	no	—
222	ΓL(1,𝔽₂₅)	—	5	2	no	—
223	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	2	yes	—
224	ΓL(1,𝔽₂₅)	C₂×AGL(1,𝔽₅)	1	2	yes	—
225	D₃×C₈	—	5	2	no	—
226	D₃×C₈	—	5	2	no	—
227	D₃×C₈	—	5	2	no	—
228	D₃×C₈	—	5	2	no	—
229	C₃×C₁₆	—	5	4	no	—
230	C₃⋊C₁₆	—	5	4	no	—
231	C₂³×C₅	—	3	1	no	—
232	C₂²×D₅	—	3	1	no	—
233	C₂²×D₅	D₃×C₈	1	1	yes	characteristic
234	C₂×C₄×C₅	—	3	1	no	—
235	C₂×C₄×C₅	—	3	2	no	—
236	C₂×C₄×C₅	—	3	2	no	—
237	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
238	C₂²⋊D₅	—	3	2	no	—
239	C₂²⋊D₅	—	3	2	no	—
240	C₂²⋊D₅	—	3	2	no	—
241	C₂²⋊D₅	—	3	2	no	—
242	C₂×Dic₅	—	3	1	no	—
243	C₂×Dic₅	D₃×C₈	1	1	yes	characteristic
244	D₂₀	—	3	2	no	—
245	D₂₀	—	3	2	no	—
246	C₄×D₅	—	3	2	no	—
247	C₄×D₅	—	3	2	no	—
248	C₄×D₅	D₃×C₈	1	1	yes	characteristic
249	C₄×D₅	D₃×C₈	1	1	yes	characteristic
250	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
251	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
252	Dic₁₀	—	3	2	no	—
253	Dic₁₀	—	3	2	no	—
254	C₅×C₈	—	3	2	no	—
255	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
256	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
257	#168	—	3	2	no	—
258	#168	C₂×C₄×D₃	1	1	yes	characteristic
259	#168	C₂³×D₃	1	1	yes	characteristic
260	C₂×#41	—	15	1	no	—
261	#131	—	15	2	no	—
262	#131	—	15	2	no	—
263	#131	—	15	2	no	—
264	#131	—	15	2	no	—
265	C₂×M₁₆	—	3	1	no	—
266	C₂×M₁₆	—	15	1	no	—
267	C₂×M₁₆	—	15	1	no	—
268	C₂²×C₈	—	5	1	no	—
269	C₂²×C₈	—	15	1	no	—
270	C₂²×C₈	—	15	1	no	—
271	M₃₂	—	5	2	no	—
272	M₃₂	—	5	2	no	—
273	M₃₂	—	15	4	no	—
274	M₃₂	—	15	4	no	—
275	M₃₂	—	15	2	no	—
276	M₃₂	—	15	2	no	—
277	C₂×C₁₆	—	5	2	no	—
278	C₂×C₁₆	—	15	4	no	—
279	C₂×C₁₆	—	15	4	no	—
280	C₂×C₁₆	—	15	2	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
283	D₁₅	—	2	2	no	—
284	C₃×D₅	—	2	1	no	—
285	C₃×D₅	—	2	1	no	—
286	C₅×D₃	—	2	2	no	—
287	C₂³×C₃	—	5	1	no	—
288	C₂²×D₃	—	5	1	no	—
289	C₂²×D₃	D₅⋊C₈	1	1	yes	characteristic
290	C₂×C₃×C₄	—	5	1	no	—
291	C₂×C₃×C₄	—	5	1	no	—
292	C₂×C₃×C₄	—	5	1	no	—
293	C₂×C₃×C₄	—	5	1	no	—
294	C₂×C₃×C₄	—	5	1	no	—
295	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
296	#67	—	5	2	no	—
297	#67	—	5	2	no	—
298	#67	—	5	2	no	—
299	#67	—	5	2	no	—
300	C₂×Dic₃	—	5	1	no	—
301	C₂×Dic₃	D₅⋊C₈	1	1	yes	characteristic
302	D₁₂	—	5	2	no	—
303	D₁₂	—	5	2	no	—
304	C₄×D₃	—	5	2	no	—
305	C₄×D₃	—	5	2	no	—
306	C₄×D₃	D₅⋊C₈	1	2	yes	—
307	C₄×D₃	C₂²×AGL(1,𝔽₅)	1	2	yes	—
308	Dic₆	—	5	2	no	—
309	Dic₆	—	5	2	no	—
310	C₃×C₈	—	5	1	no	—
311	C₃×C₈	—	5	1	no	—
312	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
313	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
314	C₃⋊C₈	—	5	2	no	—
315	C₃⋊C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
316	C₂²×C₅	—	3	2	no	—
317	C₂²×C₅	—	12	1	no	—
318	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
319	C₂×D₅	—	3	2	no	—
320	C₂×D₅	—	4	1	no	—
321	C₂×D₅	—	12	1	no	—
322	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
323	C₂×D₅	C₂×D₃×C₈	1	1	yes	characteristic
324	C₄×C₅	—	3	2	no	—
325	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
326	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
327	Dic₅	—	3	2	no	—
328	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
329	Dic₅	C₂×D₃×C₈	1	1	yes	characteristic
330	#41	—	15	2	no	—
331	#41	—	15	2	no	—
332	#41	—	15	2	no	—
333	#41	—	15	2	no	—
334	C₂×Q₈	—	15	1	no	—
335	C₂×D₄	—	15	1	no	—
336	C₂×D₄	—	15	1	no	—
337	C₂×D₄	—	15	1	no	—
338	C₂²×C₄	—	3	1	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	—	15	1	no	—
341	M₁₆	—	3	2	no	—
342	M₁₆	—	3	2	no	—
343	M₁₆	—	15	2	no	—
344	M₁₆	—	15	2	no	—
345	M₁₆	—	15	2	no	—
346	M₁₆	—	15	2	no	—
347	C₂×C₈	—	3	1	no	—
348	C₂×C₈	—	5	1	no	—
349	C₂×C₈	—	5	1	no	—
350	C₂×C₈	—	5	1	no	—
351	C₂×C₈	—	5	1	no	—
352	C₂×C₈	—	5	1	no	—
353	C₂×C₈	—	15	2	no	—
354	C₂×C₈	—	15	2	no	—
355	C₂×C₈	—	15	2	no	—
356	C₂×C₈	—	15	2	no	—
357	C₂×C₈	—	15	1	no	—
358	C₂×C₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
359	C₁₆	—	5	4	no	—
360	C₁₆	—	15	4	no	—
361	C₃×C₅	#3407	1	1	yes	characteristic, complemented, Hall
362	C₂²×C₃	—	5	1	no	—
363	C₂²×C₃	—	5	1	no	—
364	C₂²×C₃	—	20	1	no	—
365	C₂²×C₃	C₂×D₅⋊C₈	1	1	yes	characteristic
366	C₂×D₃	—	4	1	no	—
367	C₂×D₃	—	5	2	no	—
368	C₂×D₃	—	20	1	no	—
369	C₂×D₃	C₂×D₅⋊C₈	1	2	yes	—
370	C₃×C₄	—	5	1	no	—
371	C₃×C₄	—	5	1	no	—
372	C₃×C₄	C₂×D₅⋊C₈	1	1	yes	characteristic
373	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
374	Dic₃	—	5	2	no	—
375	Dic₃	C₂×D₅⋊C₈	1	2	yes	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	6	2	no	—
378	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
379	D₅	—	2	1	no	—
380	D₅	—	2	1	no	—
381	D₅	—	6	2	no	—
382	C₂³	—	3	1	no	—
383	C₂³	—	5	1	no	—
384	C₂³	—	15	1	no	—
385	Q₈	—	15	2	no	—
386	Q₈	—	15	2	no	—
387	D₄	—	15	2	no	—
388	D₄	—	15	2	no	—
389	D₄	—	15	2	no	—
390	D₄	—	15	2	no	—
391	D₄	—	15	2	no	—
392	D₄	—	15	2	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	3	2	no	—
395	C₂×C₄	—	3	2	no	—
396	C₂×C₄	—	5	1	no	—
397	C₂×C₄	—	5	1	no	—
398	C₂×C₄	—	5	1	no	—
399	C₂×C₄	—	5	1	no	—
400	C₂×C₄	—	5	1	no	—
401	C₂×C₄	—	15	1	no	—
402	C₂×C₄	—	15	2	no	—
403	C₂×C₄	—	15	2	no	—
404	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
405	C₈	—	3	2	no	—
406	C₈	—	5	1	no	—
407	C₈	—	5	1	no	—
408	C₈	—	15	2	no	—
409	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
410	C₈	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
411	C₂×C₃	—	2	1	no	—
412	C₂×C₃	—	10	1	no	—
413	C₂×C₃	—	10	1	no	—
414	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
415	D₃	—	2	2	no	—
416	D₃	—	10	2	no	—
417	C₅	#82007	1	1	yes	characteristic, complemented, Sylow
418	C₂²	—	3	2	no	—
419	C₂²	—	5	1	no	—
420	C₂²	—	5	1	no	—
421	C₂²	—	12	1	no	—
422	C₂²	—	15	2	no	—
423	C₂²	—	20	1	no	—
424	C₂²	—	60	1	no	—
425	C₂²	D₃×D₅⋊C₈	1	1	yes	characteristic
426	C₄	—	3	2	no	—
427	C₄	—	5	1	no	—
428	C₄	—	5	1	no	—
429	C₄	—	15	2	no	—
430	C₄	D₃×D₅⋊C₈	1	1	yes	characteristic
431	C₄	C₂²×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
432	C₃	#10617404	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	2	1	no	—
434	C₂	—	6	2	no	—
435	C₂	—	10	1	no	—
436	C₂	—	10	1	no	—
437	C₂	—	30	2	no	—
438	C₂	C₂×D₃×D₅⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Fitting	C₂×C₃×C₅×C₈	C₂×C₄
prime radical	C₂×#6771	C₄
cosocle	C₃×#168	C₂⁴
hypercenter	C₂×C₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#3407
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. D₅⋊#812	C₂	semidirect
3. C₃×D₅⋊M₃₂	C₂	semidirect
4. #11751741	C₂	semidirect
5. D₃×#3998	C₂	semidirect
6. #11751644	C₂	semidirect
7. #11751642	C₂	semidirect
21. #91219	C₂²	semidirect
22. D₅⋊(C₃⋊C₁₆)	C₂²	semidirect
24. C₃×#3990	C₂²	semidirect
25. C₃×D₅⋊C₁₆	C₂²	semidirect
26. #91166	C₂²	semidirect
27. #91165	C₂²	semidirect
28. #91164	C₂²	semidirect
29. D₃×#674	C₂²	semidirect
37. D₅⋊M₃₂	D₃	semidirect
93. #3990	C₂×D₃	semidirect
96. D₅⋊C₁₆	C₂×D₃	semidirect
361. C₃×C₅	#3407	semidirect
417. C₅	#82007	semidirect
432. C₃	#10617404	semidirect

Maximal subgroups

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

subgroup	index
C₂×#91266	2
D₅⋊#812	2
C₃×D₅⋊M₃₂	2
#11751741	2
D₃×#3998	2
#11751644	2
#11751642	2
#10617404	3
#82007	5