Subgroups — D₃×#65196 #14478131

Order 1920.

736 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#4047	C₂	1	1	yes	maximal, characteristic
2	#11751008	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65196	C₂	1	1	yes	maximal, characteristic, complemented
5	#11747531	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₃×#672	C₂	1	1	yes	maximal, characteristic, complemented
7	#11747525	C₂	1	1	yes	maximal, characteristic, complemented
8	#11746813	C₂	1	2	yes	maximal, complemented
9	#11746811	C₂	1	2	yes	maximal, complemented
10	D₃×#3930	C₂	1	2	yes	maximal, complemented
11	D₃×D₅×C₁₆	C₂	1	2	yes	maximal, complemented
12	C₂×#65196	—	3	1	no	maximal, Hall
13	D₃×#709	C₄	1	1	yes	characteristic
14	#91790	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
16	C₃×#4047	C₂²	1	1	yes	characteristic
17	#91291	C₄	1	1	yes	characteristic
18	D₃×#681	C₄	1	1	yes	characteristic
19	#91283	C₄	1	1	yes	characteristic
20	#91267	C₄	1	2	yes	—
21	#91265	C₂²	1	2	yes	—
22	D₃×#676	C₄	1	2	yes	—
23	D₃×C₈×D₅	C₂²	1	2	yes	—
24	C₃×C₅×M₃₂	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃⋊#672	C₂²	1	1	yes	characteristic, complemented
26	#91082	C₂²	1	2	yes	complemented
27	C₁₆×D₁₅	C₂²	1	2	yes	complemented
28	C₅×#812	C₂²	1	1	yes	characteristic, complemented
29	C₅×#798	C₂²	1	2	yes	complemented
30	C₅×D₃×C₁₆	C₂²	1	2	yes	—
31	C₂×C₃×#672	C₂²	1	1	yes	characteristic, complemented
32	C₃×#3930	C₂²	1	2	yes	complemented
33	C₃×D₅×C₁₆	C₂²	1	2	yes	complemented
34	#90936	C₂²	1	2	yes	complemented
35	#90934	C₂²	1	2	yes	complemented
36	#90933	C₂²	1	2	yes	complemented
37	D₃×#672	C₂²	1	1	yes	characteristic
38	D₃×#672	C₂²	1	1	yes	characteristic
39	D₃×#672	C₂²	1	1	yes	characteristic, complemented
40	D₃×#672	C₂²	1	1	yes	characteristic, complemented
41	D₅×C₃⋊C₁₆	C₂²	1	2	yes	complemented
42	D₃×#504	—	5	1	no	maximal, Hall
43	C₂×#4047	—	3	1	no	—
44	C₂×C₅×M₃₂	—	3	1	no	—
45	C₂²×#672	—	3	1	no	—
46	#65196	—	3	1	no	—
47	#65196	—	3	1	no	—
48	#65196	—	3	1	no	—
49	#65196	—	3	2	no	—
50	#65196	—	3	2	no	—
51	#65196	D₃	1	1	yes	characteristic, direct product factor
52	C₂×#3930	—	3	2	no	—
53	C₂×D₅×C₁₆	—	3	2	no	—
54	#6817	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
56	C₃×#709	C₂×C₄	1	1	yes	characteristic
57	D₃×C₂²⋊D₅	C₈	1	2	yes	—
58	#6779	C₈	1	2	yes	—
59	D₃×D₂₀	C₈	1	1	yes	characteristic
60	C₄×D₃×D₅	C₂×C₄	1	2	yes	—
61	#6771	C₂×C₄	1	2	yes	—
62	#6769	C₈	1	1	yes	characteristic
63	D₃×Dic₁₀	C₈	1	1	yes	characteristic
64	#6765	C₈	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	#6710	C₂×C₄	1	1	yes	characteristic
67	#6705	C₂×C₄	1	2	yes	—
68	C₈×D₁₅	C₂³	1	2	yes	—
69	C₂×C₅×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
70	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
71	C₅×D₃×C₈	C₂×C₄	1	1	yes	characteristic
72	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
73	C₅×D₃×C₈	C₂³	1	1	yes	characteristic
74	C₃×#681	C₂×C₄	1	1	yes	characteristic
75	C₃×#676	C₂×C₄	1	2	yes	—
76	C₃×C₈×D₅	C₂³	1	2	yes	—
77	#6651	C₂×C₄	1	2	yes	—
78	#6650	C₂×C₄	1	2	yes	—
79	#6649	C₂×C₄	1	2	yes	—
80	#6648	C₂×C₄	1	2	yes	—
81	D₃×#168	C₂×C₄	1	2	yes	—
82	D₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
83	C₃×C₅×C₁₆	C₂³	1	2	yes	—
84	C₃⋊#672	C₂³	1	1	yes	characteristic
85	C₃⋊#672	C₂³	1	1	yes	characteristic
86	C₃×#672	C₂³	1	1	yes	characteristic
87	C₃×#672	C₂³	1	1	yes	characteristic
88	C₅×C₃⋊C₁₆	C₂³	1	2	yes	—
89	D₃×#131	—	5	1	no	—
90	C₃×#504	—	5	1	no	—
91	#5140	—	5	1	no	—
92	#4907	—	5	1	no	—
93	#4907	—	5	2	no	—
94	D₃×M₃₂	—	5	2	no	—
95	D₃×M₃₂	D₅	1	1	yes	characteristic, complemented
96	#4901	—	5	1	no	—
97	#4901	—	5	2	no	—
98	C₂×D₃×C₁₆	—	5	1	no	—
99	C₂×D₃×C₁₆	—	5	2	no	—
100	C₂×#709	—	3	1	no	—
101	C₂²×C₅×C₈	—	3	1	no	—
102	C₂×#681	—	3	1	no	—
103	#4047	—	3	1	no	—
104	#4047	—	3	1	no	—
105	#4047	—	3	1	no	—
106	#4047	—	3	2	no	—
107	#4047	—	3	2	no	—
108	#4047	C₂×D₃	1	1	yes	characteristic
109	C₂×#676	—	3	2	no	—
110	C₂×C₈×D₅	—	3	2	no	—
111	C₅×M₃₂	—	3	1	no	—
112	C₅×M₃₂	—	3	2	no	—
113	C₅×M₃₂	C₂×D₃	1	1	yes	characteristic, complemented
114	C₂×C₅×C₁₆	—	3	2	no	—
115	C₂×#672	—	3	1	no	—
116	C₂×#672	—	3	1	no	—
117	C₂×#672	—	3	1	no	—
118	C₂×#672	—	3	1	no	—
119	C₂×#672	—	3	1	no	—
120	C₂×#672	C₂×D₃	1	1	yes	characteristic, complemented
121	#3930	—	3	2	no	—
122	#3930	—	3	2	no	—
123	#3930	—	3	2	no	—
124	#3930	C₂×D₃	1	2	yes	complemented
125	D₅×C₁₆	—	3	2	no	—
126	D₅×C₁₆	—	3	2	no	—
127	D₅×C₁₆	—	3	2	no	—
128	D₅×C₁₆	C₂×D₃	1	2	yes	complemented
129	C₂×#504	—	15	1	no	Sylow
130	C₂²×C₅×D₃	C₂×C₈	1	1	yes	characteristic
131	C₂×D₃×D₅	C₂×C₈	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	#1220	C₂×C₈	1	2	yes	—
134	D₆₀	C₂×C₈	1	1	yes	characteristic
135	C₄×D₁₅	C₂²×C₄	1	2	yes	—
136	Dic₃₀	C₂×C₈	1	1	yes	characteristic
137	C₂×C₅×Dic₃	C₂×C₈	1	1	yes	characteristic
138	C₄×C₅×D₃	C₂×C₈	1	1	yes	characteristic
139	C₄×C₅×D₃	C₂×C₈	1	1	yes	characteristic
140	C₄×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
142	C₃×C₂²⋊D₅	C₂×C₈	1	2	yes	—
143	C₃×D₂₀	C₂×C₈	1	1	yes	characteristic
144	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
145	C₃×Dic₁₀	C₂×C₈	1	1	yes	characteristic
146	#1204	C₂×C₈	1	2	yes	—
147	#1203	C₂×C₈	1	2	yes	—
148	#1202	C₂×C₈	1	2	yes	—
149	#1201	C₂×C₈	1	2	yes	—
150	#1200	C₂×C₈	1	2	yes	—
151	D₃×Dic₅	C₂×C₈	1	2	yes	—
152	D₅×Dic₃	C₂×C₈	1	2	yes	—
153	C₃×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
154	C₃×C₅×C₈	C₂⁴	1	1	yes	characteristic
155	C₃⋊#168	C₂²×C₄	1	2	yes	—
156	C₃×#168	C₂²×C₄	1	2	yes	—
157	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
158	C₅×C₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	D₃×#41	—	5	1	no	—
160	C₃×#131	—	5	1	no	—
161	#948	—	5	1	no	—
162	#907	—	5	1	no	—
163	#907	—	5	2	no	—
164	D₃×M₁₆	—	5	1	no	—
165	D₃×M₁₆	—	5	2	no	—
166	#901	—	5	1	no	—
167	#901	—	5	2	no	—
168	C₂×D₃×C₈	—	5	2	no	—
169	C₂×D₃×C₈	C₂×D₅	1	1	yes	characteristic
170	C₃×M₃₂	—	5	2	no	—
171	C₃×M₃₂	C₂×D₅	1	1	yes	characteristic, complemented
172	C₂×C₃×C₁₆	—	5	1	no	—
173	C₂×C₃×C₁₆	—	5	2	no	—
174	#812	—	5	2	no	—
175	#812	C₂×D₅	1	1	yes	characteristic, complemented
176	C₂×C₃⋊C₁₆	—	5	1	no	—
177	C₂×C₃⋊C₁₆	—	5	2	no	—
178	#798	—	5	2	no	—
179	#798	—	5	2	no	—
180	#798	C₂×D₅	1	2	yes	complemented
181	D₃×C₁₆	—	5	1	no	—
182	D₃×C₁₆	—	5	1	no	—
183	D₃×C₁₆	—	5	1	no	—
184	D₃×C₁₆	—	5	1	no	—
185	D₃×C₁₆	—	5	2	no	—
186	D₃×C₁₆	—	5	2	no	—
187	D₃×C₁₆	C₂×D₅	1	2	yes	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂×C₂²⋊D₅	—	3	2	no	—
190	#709	—	3	1	no	—
191	#709	—	3	2	no	—
192	#709	—	3	1	no	—
193	#709	—	3	2	no	—
194	#709	—	3	1	no	—
195	#709	C₄×D₃	1	1	yes	characteristic
196	C₂×D₂₀	—	3	1	no	—
197	C₂×C₄×D₅	—	3	2	no	—
198	C₂×Dic₁₀	—	3	1	no	—
199	C₂×C₅×C₈	—	3	1	no	—
200	C₂×C₅×C₈	—	3	1	no	—
201	C₂×C₅×C₈	—	3	1	no	—
202	C₂×C₅×C₈	—	3	1	no	—
203	C₂×C₅×C₈	—	3	1	no	—
204	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
205	#681	—	3	1	no	—
206	#681	—	3	2	no	—
207	#681	C₄×D₃	1	1	yes	characteristic
208	C₂×#168	—	3	2	no	—
209	#676	—	3	2	no	—
210	#676	—	3	2	no	—
211	#676	—	3	2	no	—
212	#676	C₄×D₃	1	2	yes	—
213	C₈×D₅	—	3	2	no	—
214	C₈×D₅	—	3	2	no	—
215	C₈×D₅	—	3	2	no	—
216	C₈×D₅	C₂²×D₃	1	2	yes	—
217	C₅×C₁₆	—	3	2	no	—
218	C₅×C₁₆	C₂²×D₃	1	2	yes	—
219	#672	—	3	1	no	—
220	#672	—	3	1	no	—
221	#672	C₂²×D₃	1	1	yes	characteristic
222	#672	C₂²×D₃	1	1	yes	characteristic
223	C₂×#131	—	15	1	no	—
224	#504	—	5	1	no	—
225	#504	—	15	1	no	—
226	#504	—	15	2	no	—
227	#504	—	15	2	no	—
228	#504	—	15	1	no	—
229	#504	—	15	1	no	—
230	C₂×M₃₂	—	3	1	no	—
231	C₂×M₃₂	—	15	2	no	—
232	C₂²×C₁₆	—	15	2	no	—
233	C₂²×C₁₆	—	15	1	no	—
234	C₂²×C₃×C₅	C₂²×C₈	1	1	yes	characteristic
235	C₂×D₁₅	C₂²×C₈	1	2	yes	—
236	C₂×C₅×D₃	—	2	2	no	—
237	C₂×C₅×D₃	C₂²×C₈	1	1	yes	characteristic
238	C₂×C₅×D₃	C₂²×C₈	1	1	yes	characteristic
239	C₂×C₃×D₅	C₂²×C₈	1	2	yes	—
240	D₃×D₅	—	2	4	no	—
241	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
243	Dic₁₅	C₂²×C₈	1	2	yes	—
244	C₃×Dic₅	C₂²×C₈	1	2	yes	—
245	C₅×Dic₃	C₂²×C₈	1	1	yes	characteristic
246	C₅×Dic₃	C₂²×C₈	1	1	yes	characteristic
247	C₃×#41	—	5	1	no	—
248	#239	—	5	1	no	—
249	D₃×Q₈	—	5	1	no	—
250	#237	—	5	2	no	—
251	#237	—	5	1	no	—
252	D₃×D₄	—	5	2	no	—
253	D₃×D₄	—	5	1	no	—
254	#235	—	5	1	no	—
255	#235	—	5	2	no	—
256	C₂×C₄×D₃	—	5	2	no	—
257	C₂×C₄×D₃	C₄×D₅	1	1	yes	characteristic
258	C₃×M₁₆	—	5	1	no	—
259	C₃×M₁₆	—	5	2	no	—
260	C₂×C₃×C₈	—	5	2	no	—
261	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
262	#208	—	5	1	no	—
263	#208	—	5	2	no	—
264	C₂×C₃⋊C₈	—	5	2	no	—
265	C₂×C₃⋊C₈	C₄×D₅	1	1	yes	characteristic
266	ΓL(1,𝔽₂₅)	—	5	2	no	—
267	ΓL(1,𝔽₂₅)	—	5	2	no	—
268	ΓL(1,𝔽₂₅)	—	5	2	no	—
269	D₃×C₈	—	5	2	no	—
270	D₃×C₈	—	5	2	no	—
271	D₃×C₈	—	5	2	no	—
272	D₃×C₈	C₄×D₅	1	1	yes	characteristic
273	D₃×C₈	C₄×D₅	1	1	yes	characteristic
274	D₃×C₈	C₂²×D₅	1	1	yes	characteristic
275	D₃×C₈	C₂²×D₅	1	1	yes	characteristic
276	C₃×C₁₆	—	5	1	no	—
277	C₃×C₁₆	—	5	1	no	—
278	C₃×C₁₆	C₂²×D₅	1	2	yes	—
279	C₃⋊C₁₆	—	5	1	no	—
280	C₃⋊C₁₆	—	5	1	no	—
281	C₃⋊C₁₆	C₂²×D₅	1	2	yes	—
282	C₂³×C₅	—	3	1	no	—
283	C₂²×D₅	—	3	2	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	3	1	no	—
286	C₂×C₄×C₅	—	3	1	no	—
287	C₂×C₄×C₅	—	3	1	no	—
288	C₂×C₄×C₅	—	3	1	no	—
289	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
290	C₂²⋊D₅	—	3	2	no	—
291	C₂²⋊D₅	—	3	2	no	—
292	C₂²⋊D₅	—	3	2	no	—
293	C₂²⋊D₅	D₃×C₈	1	2	yes	—
294	C₂×Dic₅	—	3	2	no	—
295	D₂₀	—	3	2	no	—
296	D₂₀	—	3	1	no	—
297	D₂₀	D₃×C₈	1	1	yes	characteristic
298	C₄×D₅	—	3	2	no	—
299	C₄×D₅	—	3	2	no	—
300	C₄×D₅	—	3	2	no	—
301	C₄×D₅	C₂×C₄×D₃	1	2	yes	—
302	Dic₁₀	—	3	1	no	—
303	Dic₁₀	—	3	2	no	—
304	Dic₁₀	D₃×C₈	1	1	yes	characteristic
305	C₅×C₈	—	3	1	no	—
306	C₅×C₈	—	3	1	no	—
307	C₅×C₈	C₂×C₄×D₃	1	1	yes	characteristic
308	C₅×C₈	C₂³×D₃	1	1	yes	characteristic
309	#168	—	3	2	no	—
310	#168	C₂×C₄×D₃	1	2	yes	—
311	C₂×#41	—	15	1	no	—
312	#131	—	5	1	no	—
313	#131	—	15	2	no	—
314	#131	—	15	1	no	—
315	#131	—	15	2	no	—
316	#131	—	15	1	no	—
317	#131	—	15	1	no	—
318	C₂×M₁₆	—	15	2	no	—
319	C₂×M₁₆	—	15	1	no	—
320	C₂²×C₈	—	3	1	no	—
321	C₂²×C₈	—	15	2	no	—
322	M₃₂	—	3	1	no	—
323	M₃₂	—	3	2	no	—
324	M₃₂	—	5	2	no	—
325	M₃₂	—	15	2	no	—
326	M₃₂	—	15	2	no	—
327	M₃₂	—	15	2	no	—
328	M₃₂	D₃×D₅	1	1	yes	characteristic, complemented
329	C₂×C₁₆	—	3	2	no	—
330	C₂×C₁₆	—	5	1	no	—
331	C₂×C₁₆	—	5	2	no	—
332	C₂×C₁₆	—	15	2	no	—
333	C₂×C₁₆	—	15	2	no	—
334	C₂×C₁₆	—	15	1	no	—
335	C₂×C₁₆	—	15	1	no	—
336	C₂×C₁₆	—	15	1	no	—
337	C₂×C₁₆	—	15	1	no	—
338	C₂×C₁₆	—	15	1	no	—
339	C₂×C₁₆	—	15	2	no	—
340	C₂×C₃×C₅	—	2	1	no	—
341	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
342	D₁₅	—	2	2	no	—
343	C₃×D₅	—	2	2	no	—
344	C₅×D₃	—	2	1	no	—
345	C₅×D₃	#504	1	2	yes	complemented
346	C₂²×D₃	—	5	2	no	—
347	C₂²×D₃	C₈×D₅	1	1	yes	characteristic
348	C₃×Q₈	—	5	1	no	—
349	C₃×D₄	—	5	2	no	—
350	C₃×D₄	—	5	1	no	—
351	C₂×C₃×C₄	—	5	2	no	—
352	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
353	#67	—	5	2	no	—
354	#67	—	5	2	no	—
355	#67	—	5	2	no	—
356	C₂×Dic₃	—	5	2	no	—
357	C₂×Dic₃	C₈×D₅	1	1	yes	characteristic
358	D₁₂	—	5	2	no	—
359	D₁₂	—	5	1	no	—
360	C₄×D₃	—	5	2	no	—
361	C₄×D₃	—	5	2	no	—
362	C₄×D₃	—	5	2	no	—
363	C₄×D₃	C₈×D₅	1	1	yes	characteristic
364	C₄×D₃	C₈×D₅	1	1	yes	characteristic
365	C₄×D₃	C₂×C₄×D₅	1	1	yes	characteristic
366	C₄×D₃	C₂×C₄×D₅	1	1	yes	characteristic
367	Dic₆	—	5	1	no	—
368	Dic₆	—	5	2	no	—
369	C₃×C₈	—	5	2	no	—
370	C₃×C₈	C₂×C₄×D₅	1	1	yes	characteristic
371	C₃×C₈	C₂³×D₅	1	1	yes	characteristic
372	C₃⋊C₈	—	5	2	no	—
373	C₃⋊C₈	C₂×C₄×D₅	1	1	yes	characteristic
374	C₃⋊C₈	C₂×C₄×D₅	1	1	yes	characteristic
375	C₂²×C₅	—	3	1	no	—
376	C₂²×C₅	—	3	1	no	—
377	C₂²×C₅	—	6	2	no	—
378	C₂²×C₅	C₂×D₃×C₈	1	1	yes	characteristic
379	C₂×D₅	—	3	2	no	—
380	C₂×D₅	—	6	4	no	—
381	C₂×D₅	C₂×D₃×C₈	1	2	yes	—
382	C₄×C₅	—	3	1	no	—
383	C₄×C₅	—	3	1	no	—
384	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
385	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
386	Dic₅	—	3	2	no	—
387	Dic₅	C₂×D₃×C₈	1	2	yes	—
388	#41	—	5	1	no	—
389	#41	—	15	2	no	—
390	#41	—	15	2	no	—
391	#41	—	15	1	no	—
392	#41	—	15	1	no	—
393	#41	—	15	1	no	—
394	C₂×Q₈	—	15	1	no	—
395	C₂×D₄	—	15	1	no	—
396	C₂×D₄	—	15	2	no	—
397	C₂²×C₄	—	3	1	no	—
398	C₂²×C₄	—	15	2	no	—
399	M₁₆	—	5	1	no	—
400	M₁₆	—	5	2	no	—
401	M₁₆	—	15	2	no	—
402	M₁₆	—	15	2	no	—
403	M₁₆	—	15	2	no	—
404	M₁₆	—	15	1	no	—
405	M₁₆	—	15	2	no	—
406	C₂×C₈	—	3	1	no	—
407	C₂×C₈	—	3	1	no	—
408	C₂×C₈	—	3	1	no	—
409	C₂×C₈	—	3	1	no	—
410	C₂×C₈	—	3	1	no	—
411	C₂×C₈	—	5	2	no	—
412	C₂×C₈	—	15	2	no	—
413	C₂×C₈	—	15	2	no	—
414	C₂×C₈	—	15	2	no	—
415	C₂×C₈	—	15	2	no	—
416	C₂×C₈	C₂×D₃×D₅	1	1	yes	characteristic
417	C₁₆	—	3	2	no	—
418	C₁₆	—	5	1	no	—
419	C₁₆	—	5	1	no	—
420	C₁₆	—	15	1	no	—
421	C₁₆	—	15	1	no	—
422	C₁₆	C₂×D₃×D₅	1	2	yes	—
423	C₃×C₅	C₂×#504	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	5	2	no	—
425	C₂²×C₃	C₂×C₈×D₅	1	1	yes	characteristic
426	C₂×D₃	—	2	2	no	—
427	C₂×D₃	—	5	2	no	—
428	C₂×D₃	—	10	4	no	—
429	C₂×D₃	C₂×C₈×D₅	1	1	yes	characteristic
430	C₂×D₃	C₂×C₈×D₅	1	1	yes	characteristic
431	C₃×C₄	—	5	2	no	—
432	C₃×C₄	C₂×C₈×D₅	1	1	yes	characteristic
433	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
434	Dic₃	—	5	2	no	—
435	Dic₃	C₂×C₈×D₅	1	1	yes	characteristic
436	Dic₃	C₂×C₈×D₅	1	1	yes	characteristic
437	C₂×C₅	—	2	1	no	—
438	C₂×C₅	—	3	2	no	—
439	C₂×C₅	—	6	1	no	—
440	C₂×C₅	C₂²×D₃×C₈	1	1	yes	characteristic
441	D₅	—	2	2	no	—
442	D₅	—	6	2	no	—
443	C₂³	—	3	1	no	—
444	C₂³	—	15	2	no	—
445	Q₈	—	5	1	no	—
446	Q₈	—	15	2	no	—
447	Q₈	—	15	1	no	—
448	D₄	—	5	2	no	—
449	D₄	—	5	1	no	—
450	D₄	—	15	2	no	—
451	D₄	—	15	2	no	—
452	D₄	—	15	2	no	—
453	D₄	—	15	2	no	—
454	D₄	—	15	1	no	—
455	C₂×C₄	—	3	1	no	—
456	C₂×C₄	—	3	1	no	—
457	C₂×C₄	—	3	1	no	—
458	C₂×C₄	—	3	1	no	—
459	C₂×C₄	—	3	1	no	—
460	C₂×C₄	—	5	2	no	—
461	C₂×C₄	—	15	2	no	—
462	C₂×C₄	—	15	2	no	—
463	C₂×C₄	—	15	2	no	—
464	C₂×C₄	—	15	2	no	—
465	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
466	C₈	—	3	1	no	—
467	C₈	—	3	1	no	—
468	C₈	—	5	2	no	—
469	C₈	—	15	2	no	—
470	C₈	C₄×D₃×D₅	1	1	yes	characteristic
471	C₈	C₂²×D₃×D₅	1	1	yes	characteristic
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	10	2	no	—
474	C₂×C₃	C₂²×C₈×D₅	1	1	yes	characteristic
475	D₃	—	2	1	no	—
476	D₃	—	10	2	no	—
477	D₃	#65196	1	2	yes	direct product factor
478	C₅	D₃×#504	1	1	yes	characteristic, complemented, Sylow
479	C₂²	—	3	1	no	—
480	C₂²	—	3	1	no	—
481	C₂²	—	5	2	no	—
482	C₂²	—	6	2	no	—
483	C₂²	—	15	2	no	—
484	C₂²	—	30	4	no	—
485	C₂²	D₃×C₈×D₅	1	1	yes	characteristic
486	C₄	—	3	1	no	—
487	C₄	—	3	1	no	—
488	C₄	—	5	2	no	—
489	C₄	—	15	2	no	—
490	C₄	D₃×C₈×D₅	1	1	yes	characteristic
491	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
492	C₃	C₂×#65196	1	1	yes	characteristic, complemented, Sylow
493	C₂	—	2	1	no	—
494	C₂	—	3	2	no	—
495	C₂	—	6	1	no	—
496	C₂	—	10	2	no	—
497	C₂	—	30	2	no	—
498	C₂	C₂×D₃×C₈×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₃×D₅
commutator, socle	C₂×C₃×C₅	C₂³×C₈
Fitting	C₃×C₅×M₃₂	C₂²
prime radical	D₃×#709	C₄
cosocle	C₃×C₅×C₈	C₂⁴
hypercenter	M₃₂	D₃×D₅
hypocenter	C₃×C₅	C₂×#504
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #11751008	C₂	semidirect
3. C₅×D₃×M₃₂	C₂	semidirect
4. C₃×#65196	C₂	semidirect
5. #11747531	C₂	semidirect
6. C₂×D₃×#672	C₂	semidirect
7. #11747525	C₂	semidirect
8. #11746813	C₂	semidirect
9. #11746811	C₂	semidirect
10. D₃×#3930	C₂	semidirect
11. D₃×D₅×C₁₆	C₂	semidirect
24. C₃×C₅×M₃₂	C₂²	semidirect
25. C₂×C₃⋊#672	C₂²	semidirect
26. #91082	C₂²	semidirect
27. C₁₆×D₁₅	C₂²	semidirect
28. C₅×#812	C₂²	semidirect
29. C₅×#798	C₂²	semidirect
31. C₂×C₃×#672	C₂²	semidirect
32. C₃×#3930	C₂²	semidirect
33. C₃×D₅×C₁₆	C₂²	semidirect
34. #90936	C₂²	semidirect
35. #90934	C₂²	semidirect
36. #90933	C₂²	semidirect
39. D₃×#672	C₂²	semidirect
40. D₃×#672	C₂²	semidirect
41. D₅×C₃⋊C₁₆	C₂²	semidirect
51. #65196	D₃	direct (N × H)
95. D₃×M₃₂	D₅	semidirect
113. C₅×M₃₂	C₂×D₃	semidirect
120. C₂×#672	C₂×D₃	semidirect
124. #3930	C₂×D₃	semidirect
128. D₅×C₁₆	C₂×D₃	semidirect
171. C₃×M₃₂	C₂×D₅	semidirect
175. #812	C₂×D₅	semidirect
180. #798	C₂×D₅	semidirect
328. M₃₂	D₃×D₅	semidirect
345. C₅×D₃	#504	semidirect
423. C₃×C₅	C₂×#504	semidirect
477. D₃	#65196	direct (N × H)
478. C₅	D₃×#504	semidirect
492. C₃	C₂×#65196	semidirect

Maximal subgroups

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

subgroup	index
D₃×#4047	2
#11751008	2
C₅×D₃×M₃₂	2
C₃×#65196	2
#11747531	2
C₂×D₃×#672	2
#11747525	2
#11746813	2
#11746811	2
D₃×#3930	2
D₃×D₅×C₁₆	2
C₂×#65196	3
D₃×#504	5

Subgroups — D3×#65196 #14478131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65196 #14478131