Subgroups — #14295986

Order 1920.

600 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×C₃×#4133	C₂	1	1	yes	maximal, characteristic
2	C₂×#91239	C₂	1	1	yes	maximal, characteristic
3	#11751767	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×ΓL(1,𝔽₁₆)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#11749207	C₂	1	1	yes	maximal, characteristic
6	#11746532	C₂	1	1	yes	maximal, characteristic, complemented
7	#11746524	C₂	1	1	yes	maximal, characteristic, complemented
8	#10603991	—	3	1	no	maximal, Hall
9	C₂×C₃×#713	C₂²	1	1	yes	characteristic
10	C₂×C₄×ΓL(1,𝔽₁₆)	C₂²	1	1	yes	characteristic
11	C₂×#6758	C₂²	1	1	yes	characteristic
12	C₃×#4133	—	2	2	no	—
13	C₃×#4133	C₄	1	4	yes	complemented
14	C₂×C₃×#700	—	2	1	no	—
15	C₂×C₃×#700	C₂²	1	1	yes	characteristic
16	C₂×C₃×D₅⋊C₈	—	2	1	no	—
17	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
18	#91358	C₂²	1	1	yes	characteristic
19	C₂×D₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	#91239	C₄	1	4	yes	complemented
21	#91169	—	2	1	no	—
22	Dic₃×#170	—	2	1	no	—
23	ΓL(1,𝔽₁₆)⋊C₈	—	2	2	no	—
24	#91119	C₄	1	1	yes	characteristic, complemented
25	C₅×#835	C₄	1	1	yes	characteristic, complemented
26	#90965	C₄	1	1	yes	characteristic, complemented
27	#90964	C₄	1	1	yes	characteristic, complemented
28	#72008	—	5	1	no	maximal, Hall
29	C₂×#4133	D₃	1	1	yes	characteristic
30	C₂×#4010	—	3	1	no	—
31	C₂×C₈×AGL(1,𝔽₅)	—	3	1	no	—
32	#65701	—	3	1	no	—
33	#65093	—	3	1	no	—
34	#64896	—	3	1	no	—
35	#64875	—	3	1	no	—
36	C₂²×ΓL(1,𝔽₁₆)	—	2	1	no	—
37	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
38	C₃×#713	—	2	1	no	—
39	C₃×#713	—	2	1	no	—
40	C₃×#713	C₂×C₄	1	2	yes	—
41	C₃×#713	C₂×C₄	1	2	yes	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	—	2	1	no	—
45	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
46	C₂×C₃⋊#170	—	2	1	no	—
47	C₄×ΓL(1,𝔽₁₆)	—	2	1	no	—
48	C₄×ΓL(1,𝔽₁₆)	C₂×C₄	1	2	yes	—
49	#6758	—	2	1	no	—
50	#6758	C₂×C₄	1	2	yes	—
51	C₂×C₃×#170	—	2	1	no	—
52	C₂×C₃×#170	D₄	1	1	yes	characteristic
53	C₂×C₃×#170	D₄	1	1	yes	characteristic
54	C₃×#700	—	2	1	no	—
55	C₃×#700	—	2	4	no	—
56	C₃×#700	C₂×C₄	1	2	yes	—
57	C₃×D₅⋊C₈	—	2	4	no	—
58	C₃×D₅⋊C₈	C₂×C₄	1	2	yes	—
59	C₃×D₅⋊C₈	D₄	1	2	yes	—
60	C₄⋊Dic₁₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃⋊#168	C₂×C₄	1	1	yes	characteristic
62	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
64	#6665	—	2	1	no	—
65	Dic₃×Dic₅	—	2	1	no	—
66	D₅×C₃⋊C₈	—	2	1	no	—
67	D₅×C₃⋊C₈	—	2	1	no	—
68	C₂×C₃×#131	—	5	1	no	—
69	C₂×#837	—	5	1	no	—
70	#5233	—	5	1	no	—
71	#5101	—	5	1	no	—
72	C₂×C₈×Dic₃	—	5	1	no	—
73	#4558	—	5	1	no	—
74	#4555	—	5	1	no	—
75	C₂×#713	C₂×D₃	1	1	yes	characteristic
76	#4133	—	2	2	no	—
77	#4133	Dic₃	1	4	yes	complemented
78	C₂×C₄×AGL(1,𝔽₅)	—	3	1	no	—
79	C₂×#700	—	2	1	no	—
80	C₂×#700	—	3	1	no	—
81	C₂×#700	C₂×D₃	1	1	yes	characteristic
82	C₂×D₅⋊C₈	—	2	1	no	—
83	C₂×D₅⋊C₈	C₂×D₃	1	1	yes	characteristic
84	C₂×C₈×D₅	—	3	1	no	—
85	#4038	—	3	1	no	—
86	#4010	—	3	4	no	—
87	#4002	—	6	1	no	—
88	C₄×#170	—	6	1	no	—
89	C₈×AGL(1,𝔽₅)	—	6	2	no	—
90	C₅×#103	—	3	1	no	—
91	#3967	—	3	1	no	—
92	#3953	—	3	1	no	—
93	#3941	—	3	1	no	—
94	#1764	—	15	1	no	Sylow
95	C₂²×C₃×D₅	—	2	1	no	—
96	C₂²×C₃×D₅	#41	1	1	yes	characteristic
97	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
98	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
99	C₂×ΓL(1,𝔽₁₆)	—	2	2	no	—
100	C₃×C₅×Q₈	—	2	1	no	—
101	C₃×C₅×Q₈	C₄²	1	2	yes	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
104	C₂×Dic₁₅	—	2	1	no	—
105	C₂×C₅×Dic₃	—	2	1	no	—
106	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
107	C₃×D₂₀	—	2	2	no	—
108	C₃×D₂₀	—	2	2	no	—
109	C₃×D₂₀	—	2	1	no	—
110	C₃×D₂₀	C₄²	1	2	yes	—
111	C₃×C₄×D₅	—	2	2	no	—
112	C₃×C₄×D₅	—	2	2	no	—
113	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
114	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
115	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
116	C₃×C₄×D₅	#41	1	1	yes	characteristic
117	C₃⋊#170	—	2	2	no	—
118	C₃×#170	—	2	2	no	—
119	C₃×#170	C₂²⋊C₄	1	2	yes	—
120	C₃×#170	C₂²⋊C₄	1	2	yes	—
121	C₃⋊#168	—	2	1	no	—
122	C₅×C₃⋊C₈	—	2	1	no	—
123	C₂×C₃×#41	—	5	1	no	—
124	C₃×#131	—	5	4	no	—
125	C₃×#131	—	10	2	no	—
126	C₂×C₃×M₁₆	—	5	1	no	—
127	C₂×C₃×M₁₆	—	10	1	no	—
128	C₂²×C₃×C₈	—	5	1	no	—
129	C₂²×C₃×C₈	—	10	1	no	—
130	#926	—	5	1	no	—
131	C₂×C₄×Dic₃	—	5	1	no	—
132	C₂×#208	—	5	1	no	—
133	C₂²×C₃⋊C₈	—	5	1	no	—
134	#837	—	5	4	no	—
135	#835	—	5	1	no	—
136	#835	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
137	#832	—	5	1	no	—
138	#832	—	5	1	no	—
139	#815	—	10	1	no	—
140	C₈×Dic₃	—	10	2	no	—
141	C₈×Dic₃	—	10	1	no	—
142	C₂²×AGL(1,𝔽₅)	—	6	1	no	—
143	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
144	#713	—	2	1	no	—
145	#713	—	2	1	no	—
146	#713	C₄×D₃	1	2	yes	—
147	#713	C₂×Dic₃	1	2	yes	—
148	C₂×D₂₀	—	2	1	no	—
149	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
150	C₂×C₄×D₅	—	2	1	no	—
151	C₂×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
152	C₂×#170	—	2	1	no	—
153	C₂×#170	—	6	1	no	—
154	C₂×#170	#67	1	1	yes	characteristic
155	C₂×#170	#67	1	1	yes	characteristic
156	C₄×AGL(1,𝔽₅)	—	3	2	no	—
157	C₄×AGL(1,𝔽₅)	—	6	1	no	—
158	#700	—	2	1	no	—
159	#700	—	2	4	no	—
160	#700	—	3	2	no	—
161	#700	—	6	1	no	—
162	#700	C₂×Dic₃	1	2	yes	—
163	D₅⋊C₈	—	2	4	no	—
164	D₅⋊C₈	C₂×Dic₃	1	2	yes	—
165	D₅⋊C₈	#67	1	2	yes	—
166	C₂×C₅×C₈	—	3	1	no	—
167	C₅×C₄⋊C₄	—	3	1	no	—
168	#685	—	6	1	no	—
169	C₄⋊Dic₅	—	3	1	no	—
170	C₄×Dic₅	—	6	1	no	—
171	C₂×#168	—	3	1	no	—
172	C₈×D₅	—	6	1	no	—
173	C₈×D₅	—	6	1	no	—
174	C₂×#131	—	5	1	no	—
175	C₂×#104	—	15	1	no	—
176	#416	—	15	1	no	—
177	#405	—	15	1	no	—
178	C₂×C₄×C₈	—	15	1	no	—
179	#341	—	15	1	no	—
180	#339	—	15	1	no	—
181	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
182	C₂×C₃×D₅	—	2	1	no	—
183	C₂×C₃×D₅	—	2	1	no	—
184	C₂×C₃×D₅	—	2	2	no	—
185	C₂×C₃×D₅	—	4	1	no	—
186	C₂×C₃×D₅	—	4	1	no	—
187	C₂×C₃×D₅	#117	1	1	yes	characteristic
188	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
189	ΓL(1,𝔽₁₆)	—	2	4	no	—
190	C₃×C₄×C₅	—	2	2	no	—
191	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
192	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
193	Dic₁₅	—	4	1	no	—
194	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
196	C₅×Dic₃	—	4	1	no	—
197	C₃×#41	—	5	2	no	—
198	C₃×#41	—	5	2	no	—
199	C₃×#41	—	10	1	no	—
200	C₃×#41	—	10	1	no	—
201	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
202	C₂×C₃×D₄	—	5	1	no	—
203	C₂×C₃×D₄	—	10	1	no	—
204	C₂²×C₃×C₄	—	5	1	no	—
205	C₂²×C₃×C₄	—	10	1	no	—
206	C₂²×Dic₃	—	10	1	no	—
207	C₃×M₁₆	—	5	2	no	—
208	C₃×M₁₆	—	10	4	no	—
209	C₃×M₁₆	—	10	1	no	—
210	C₂×C₃×C₈	—	5	2	no	—
211	C₂×C₃×C₈	—	5	1	no	—
212	C₂×C₃×C₈	—	5	1	no	—
213	C₂×C₃×C₈	—	5	2	no	—
214	C₂×C₃×C₈	—	10	4	no	—
215	C₂×C₃×C₈	—	10	1	no	—
216	#217	—	10	1	no	—
217	C₄⋊Dic₃	—	5	1	no	—
218	C₄⋊Dic₃	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
219	C₄×Dic₃	—	5	2	no	—
220	C₄×Dic₃	—	10	1	no	—
221	C₄×Dic₃	—	10	1	no	—
222	#208	—	5	2	no	—
223	#208	—	10	1	no	—
224	C₂×C₃⋊C₈	—	5	1	no	—
225	C₂×C₃⋊C₈	—	10	1	no	—
226	C₂×C₃⋊C₈	—	10	1	no	—
227	C₂×C₃⋊C₈	—	10	1	no	—
228	C₂×C₃⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
229	C₂²×D₅	—	2	1	no	—
230	C₂²×D₅	#235	1	1	yes	characteristic
231	C₂×AGL(1,𝔽₅)	—	6	2	no	—
232	C₂×AGL(1,𝔽₅)	—	6	2	no	—
233	C₂×AGL(1,𝔽₅)	—	6	2	no	—
234	C₅×Q₈	—	2	1	no	—
235	C₅×Q₈	C₄×Dic₃	1	2	yes	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂×Dic₅	—	6	1	no	—
240	C₂×Dic₅	C₂×#67	1	1	yes	characteristic
241	D₂₀	—	2	2	no	—
242	D₂₀	—	2	2	no	—
243	D₂₀	—	2	1	no	—
244	D₂₀	C₄×Dic₃	1	2	yes	—
245	C₄×D₅	—	2	2	no	—
246	C₄×D₅	—	2	2	no	—
247	C₄×D₅	C₂×C₄×D₃	1	1	yes	characteristic
248	C₄×D₅	#235	1	1	yes	characteristic
249	C₄×D₅	C₂²×Dic₃	1	1	yes	characteristic
250	C₄×D₅	C₂×#67	1	1	yes	characteristic
251	#170	—	2	2	no	—
252	#170	—	6	2	no	—
253	#170	#217	1	2	yes	—
254	#170	#217	1	2	yes	—
255	C₅×C₈	—	6	1	no	—
256	#168	—	6	1	no	—
257	C₂×#41	—	5	1	no	—
258	#131	—	5	4	no	—
259	#131	—	10	2	no	—
260	C₂×M₁₆	—	5	1	no	—
261	C₂×M₁₆	—	10	1	no	—
262	C₂×M₁₆	—	15	1	no	—
263	C₂²×C₈	—	5	1	no	—
264	C₂²×C₈	—	10	1	no	—
265	C₂²×C₈	—	15	1	no	—
266	#117	—	15	1	no	—
267	C₂×C₄²	—	15	1	no	—
268	#104	—	15	4	no	—
269	#103	—	3	1	no	—
270	#103	—	15	1	no	—
271	#102	—	15	1	no	—
272	#102	—	15	1	no	—
273	#97	—	30	1	no	—
274	C₄×C₈	—	30	2	no	—
275	C₄×C₈	—	30	1	no	—
276	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₃×C₅	#443	1	1	yes	characteristic
278	C₂×C₃×C₅	#443	1	1	yes	characteristic
279	C₃×D₅	—	2	1	no	—
280	C₃×D₅	—	2	1	no	—
281	C₃×D₅	—	4	2	no	—
282	C₂³×C₃	—	5	1	no	—
283	C₂³×C₃	—	10	1	no	—
284	C₃×Q₈	—	2	1	no	—
285	C₃×Q₈	C₄×AGL(1,𝔽₅)	1	2	yes	—
286	C₃×D₄	—	5	2	no	—
287	C₃×D₄	—	10	2	no	—
288	C₃×D₄	—	10	2	no	—
289	C₃×D₄	—	10	1	no	—
290	C₂×C₃×C₄	—	2	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	—	5	1	no	—
296	C₂×C₃×C₄	—	10	2	no	—
297	C₂×C₃×C₄	—	10	2	no	—
298	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
299	C₂×Dic₃	—	2	1	no	—
300	C₂×Dic₃	—	10	2	no	—
301	C₂×Dic₃	—	10	2	no	—
302	C₂×Dic₃	—	10	2	no	—
303	C₂×Dic₃	—	10	1	no	—
304	C₃×C₈	—	5	2	no	—
305	C₃×C₈	—	5	2	no	—
306	C₃×C₈	—	10	2	no	—
307	C₃⋊C₈	—	2	1	no	—
308	C₃⋊C₈	—	10	2	no	—
309	C₃⋊C₈	—	10	1	no	—
310	C₂²×C₅	C₄×#67	1	1	yes	characteristic
311	C₂×D₅	—	2	1	no	—
312	C₂×D₅	—	2	1	no	—
313	C₂×D₅	—	2	2	no	—
314	C₂×D₅	—	4	1	no	—
315	C₂×D₅	—	4	1	no	—
316	C₂×D₅	#926	1	1	yes	characteristic
317	C₂×D₅	C₄×#67	1	1	yes	characteristic
318	AGL(1,𝔽₅)	—	6	4	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	12	1	no	—
321	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
322	C₄×C₅	C₄×#67	1	1	yes	characteristic
323	Dic₅	—	12	1	no	—
324	Dic₅	C₄×#67	1	1	yes	characteristic
325	Dic₅	C₂×#217	1	1	yes	characteristic
326	#41	—	5	2	no	—
327	#41	—	5	2	no	—
328	#41	—	10	1	no	—
329	#41	—	10	1	no	—
330	C₂×Q₈	D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
331	C₂×D₄	—	5	1	no	—
332	C₂×D₄	—	10	1	no	—
333	C₂²×C₄	—	5	1	no	—
334	C₂²×C₄	—	10	1	no	—
335	C₂²×C₄	—	30	1	no	—
336	M₁₆	—	5	2	no	—
337	M₁₆	—	10	4	no	—
338	M₁₆	—	10	1	no	—
339	M₁₆	—	15	2	no	—
340	M₁₆	—	30	1	no	—
341	C₂×C₈	—	3	1	no	—
342	C₂×C₈	—	5	1	no	—
343	C₂×C₈	—	5	2	no	—
344	C₂×C₈	—	5	1	no	—
345	C₂×C₈	—	5	2	no	—
346	C₂×C₈	—	10	4	no	—
347	C₂×C₈	—	10	1	no	—
348	C₂×C₈	—	15	1	no	—
349	C₂×C₈	—	30	1	no	—
350	C₂×C₈	—	30	1	no	—
351	C₂×C₈	—	30	1	no	—
352	C₄⋊C₄	—	3	1	no	—
353	C₄⋊C₄	—	15	1	no	—
354	C₂²⋊C₄	—	30	1	no	—
355	C₄²	—	15	2	no	—
356	C₄²	—	30	1	no	—
357	C₄²	—	30	1	no	—
358	C₃×C₅	#1764	1	1	yes	characteristic, complemented, Hall
359	C₂²×C₃	—	5	1	no	—
360	C₂²×C₃	—	5	1	no	—
361	C₂²×C₃	—	10	1	no	—
362	C₂²×C₃	—	10	1	no	—
363	C₂²×C₃	—	10	2	no	—
364	C₂²×C₃	—	20	1	no	—
365	C₂²×C₃	—	20	1	no	—
366	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	5	1	no	—
369	C₃×C₄	—	5	1	no	—
370	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
371	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
372	Dic₃	—	4	1	no	—
373	Dic₃	—	10	4	no	—
374	Dic₃	—	20	1	no	—
375	C₂×C₅	#5144	1	1	yes	characteristic
376	C₂×C₅	#5144	1	1	yes	characteristic
377	C₂×C₅	C₄×#217	1	1	yes	characteristic
378	D₅	—	2	1	no	—
379	D₅	—	2	1	no	—
380	D₅	—	4	2	no	—
381	C₂³	—	5	1	no	—
382	C₂³	—	10	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	Dic₃×AGL(1,𝔽₅)	1	2	yes	—
385	D₄	—	5	2	no	—
386	D₄	—	10	2	no	—
387	D₄	—	10	2	no	—
388	D₄	—	10	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	5	1	no	—
391	C₂×C₄	—	5	1	no	—
392	C₂×C₄	—	5	1	no	—
393	C₂×C₄	—	5	1	no	—
394	C₂×C₄	—	5	1	no	—
395	C₂×C₄	—	6	1	no	—
396	C₂×C₄	—	10	2	no	—
397	C₂×C₄	—	10	2	no	—
398	C₂×C₄	—	30	2	no	—
399	C₂×C₄	—	30	2	no	—
400	C₂×C₄	—	30	2	no	—
401	C₂×C₄	—	30	1	no	—
402	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)	1	1	yes	characteristic
403	C₈	—	5	2	no	—
404	C₈	—	5	2	no	—
405	C₈	—	6	1	no	—
406	C₈	—	10	2	no	—
407	C₈	—	30	2	no	—
408	C₈	—	30	1	no	—
409	C₂×C₃	—	10	1	no	—
410	C₂×C₃	—	10	1	no	—
411	C₂×C₃	—	20	2	no	—
412	C₂×C₃	C₂²⋊C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
413	C₂×C₃	#65736	1	1	yes	characteristic
414	C₂×C₃	#65740	1	1	yes	characteristic
415	C₅	#72008	1	1	yes	characteristic, complemented, Sylow
416	C₂²	—	5	1	no	—
417	C₂²	—	5	1	no	—
418	C₂²	—	10	1	no	—
419	C₂²	—	10	1	no	—
420	C₂²	—	10	2	no	—
421	C₂²	—	20	1	no	—
422	C₂²	—	20	1	no	—
423	C₂²	AGL(1,𝔽₅)×#67	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	5	1	no	—
426	C₄	—	5	1	no	—
427	C₄	—	12	1	no	—
428	C₄	—	30	4	no	—
429	C₄	—	60	1	no	—
430	C₄	C₂×Dic₃×AGL(1,𝔽₅)	1	1	yes	characteristic
431	C₄	AGL(1,𝔽₅)×#67	1	1	yes	characteristic
432	C₃	#10603991	1	1	yes	characteristic, complemented, Sylow
433	C₂	—	10	1	no	—
434	C₂	—	10	1	no	—
435	C₂	—	20	2	no	—
436	C₂	#11751975	1	1	yes	characteristic
437	C₂	#11751977	1	1	yes	characteristic
438	C₂	AGL(1,𝔽₅)×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	AGL(1,𝔽₅)×#67
commutator	C₃×C₄×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₅×Q₈	C₂×C₄
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#713	C₂²
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	C₂×Q₈	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1764
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
3. #11751767	C₂	semidirect
4. C₂×ΓL(1,𝔽₁₆)⋊C₈	C₂	semidirect
6. #11746532	C₂	semidirect
7. #11746524	C₂	semidirect
13. C₃×#4133	C₄	semidirect
20. #91239	C₄	semidirect
24. #91119	C₄	semidirect
25. C₅×#835	C₄	semidirect
26. #90965	C₄	semidirect
27. #90964	C₄	semidirect
77. #4133	Dic₃	semidirect
136. #835	AGL(1,𝔽₅)	semidirect
358. C₃×C₅	#1764	semidirect
415. C₅	#72008	semidirect
432. C₃	#10603991	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#4133	2
C₂×#91239	2
#11751767	2
C₂×ΓL(1,𝔽₁₆)⋊C₈	2
#11749207	2
#11746532	2
#11746524	2
#10603991	3
#72008	5