Subgroups — C₃×#25448 #10644055

Order 768.

860 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3156	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#3069	C₂	1	2	yes	maximal, complemented
3	C₃×#3067	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#2957	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#2049	C₂	1	2	yes	maximal, complemented
7	C₃×#2009	C₂	1	2	yes	maximal, complemented
8	C₃×#1979	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1915	C₂	1	2	yes	maximal, complemented
11	C₃×#1757	C₂	1	1	yes	maximal, characteristic, complemented
12	#25448	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×#575	C₂²	1	2	yes	—
14	C₂×C₃×#137	C₂²	1	2	yes	—
15	C₂×C₃×#137	C₂²	1	2	yes	—
16	C₂×C₃×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₃×#568	C₂²	1	2	yes	—
19	C₂×C₃×#131	C₂²	1	1	yes	characteristic
20	C₃×#536	C₂²	1	2	yes	—
21	C₃×#497	—	2	2	no	—
22	C₃×#495	—	2	1	no	—
23	C₃×#494	—	2	1	no	—
24	C₃×#473	—	2	1	no	—
25	C₃×#473	—	2	2	no	—
26	C₃×#473	—	2	2	no	—
27	C₃×#473	—	2	4	no	—
28	C₃×#472	—	2	1	no	—
29	C₃×#471	—	2	2	no	—
30	C₃×#471	—	2	4	no	—
31	C₃×#444	—	2	2	no	—
32	C₃×#443	—	2	2	no	—
33	C₃×#430	C₂²	1	2	yes	—
34	C₂×C₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₃×#108	C₂²	1	1	yes	characteristic
36	C₃×#421	C₂²	1	2	yes	—
37	C₃×#419	C₂²	1	2	yes	—
38	C₃×#413	C₂²	1	2	yes	—
39	C₃×#413	C₂²	1	1	yes	characteristic
40	C₂×C₃×#101	C₂²	1	2	yes	—
41	C₂×C₃×#101	C₂²	1	2	yes	—
42	C₃×#410	C₂²	1	1	yes	characteristic
43	C₃×#405	C₂²	1	1	yes	characteristic
44	C₃×#405	C₂²	1	1	yes	characteristic
45	C₃×#344	C₂²	1	2	yes	—
46	C₃×#344	C₂²	1	1	yes	characteristic
47	C₃×#344	C₂²	1	1	yes	characteristic
48	#3156	C₂×C₃	1	1	yes	characteristic, complemented
49	#3069	C₂×C₃	1	2	yes	complemented
50	#3067	C₂×C₃	1	1	yes	characteristic
51	C₂×#473	C₂×C₃	1	1	yes	characteristic, complemented
52	#2957	C₂×C₃	1	1	yes	characteristic, complemented
53	#2049	C₂×C₃	1	2	yes	complemented
54	#2009	C₂×C₃	1	2	yes	complemented
55	#1979	C₂×C₃	1	1	yes	characteristic, complemented
56	#1953	C₂×C₃	1	1	yes	characteristic, complemented
57	#1915	C₂×C₃	1	2	yes	complemented
58	#1757	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×#41	C₂³	1	1	yes	characteristic
60	C₂×C₃×#41	C₂³	1	2	yes	—
61	C₂²×C₃×Q₈	C₂³	1	2	yes	—
62	C₃×#137	—	2	2	no	—
63	C₃×#137	—	2	2	no	—
64	C₃×#137	—	2	4	no	—
65	C₃×#137	—	2	4	no	—
66	C₃×#137	—	4	2	no	—
67	C₃×#137	—	4	2	no	—
68	C₃×AGL(1,ℤ/8)	—	2	2	no	—
69	C₃×AGL(1,ℤ/8)	—	2	2	no	—
70	C₃×#135	—	2	1	no	—
71	C₃×#135	—	2	1	no	—
72	C₃×#135	—	2	1	no	—
73	C₃×#135	—	2	1	no	—
74	C₃×#135	—	4	2	no	—
75	C₂×C₃×Q₁₆	—	2	2	no	—
76	C₂×C₃×Q₁₆	—	2	2	no	—
77	C₂×C₃×Q₁₆	—	2	1	no	—
78	C₂×C₃×Q₁₆	—	2	1	no	—
79	C₂×C₃×Q₁₆	—	2	1	no	—
80	C₂×C₃×Q₁₆	—	2	1	no	—
81	C₂×C₃×Q₁₆	—	2	1	no	—
82	C₂×C₃×Q₁₆	—	2	1	no	—
83	C₂×C₃×Q₁₆	D₄	1	1	yes	characteristic
84	C₂×C₃×SD₁₆	—	2	2	no	—
85	C₂×C₃×SD₁₆	—	2	2	no	—
86	C₂×C₃×SD₁₆	D₄	1	2	yes	—
87	C₂×C₃×D₈	D₄	1	1	yes	characteristic
88	C₃×#131	—	2	4	no	—
89	C₃×#131	—	2	4	no	—
90	C₃×#131	—	2	1	no	—
91	C₃×#131	—	2	1	no	—
92	C₃×#131	—	2	1	no	—
93	C₃×#131	—	2	1	no	—
94	C₂×C₃×M₁₆	—	2	1	no	—
95	C₂×C₃×M₁₆	—	4	2	no	—
96	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₃×M₁₆	C₂³	1	2	yes	—
98	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
99	C₂×C₃×M₁₆	C₂³	1	2	yes	—
100	C₂×C₃×M₁₆	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₈	—	2	1	no	—
102	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
103	C₃×C₄⋊Q₈	—	2	2	no	—
104	C₃×#124	—	2	2	no	—
105	C₃×#123	—	2	4	no	—
106	C₃×C₂²⋊Q₈	—	4	2	no	—
107	C₃×#117	C₂³	1	1	yes	characteristic
108	C₃×#117	C₂³	1	1	yes	characteristic
109	C₃×#108	—	2	4	no	—
110	C₃×#108	—	2	1	no	—
111	C₃×#108	—	2	1	no	—
112	C₃×#108	D₄	1	2	yes	—
113	C₃×#108	D₄	1	2	yes	—
114	C₃×#104	—	2	4	no	—
115	C₃×#103	—	4	2	no	—
116	C₃×#101	—	2	2	no	—
117	C₃×#101	—	2	4	no	—
118	C₃×#101	—	2	4	no	—
119	C₃×#101	D₄	1	2	yes	—
120	C₃×#100	—	2	2	no	—
121	C₃×#100	D₄	1	2	yes	—
122	C₃×#99	—	2	2	no	—
123	C₃×#97	—	2	1	no	—
124	C₃×#97	—	2	1	no	—
125	C₃×C₄×C₈	—	2	1	no	—
126	C₃×C₄×C₈	—	2	1	no	—
127	#575	C₂²×C₃	1	2	yes	—
128	C₂×#137	C₂²×C₃	1	2	yes	—
129	C₂×#137	C₂²×C₃	1	2	yes	—
130	C₂×#135	C₂²×C₃	1	1	yes	characteristic
131	C₂²×Q₁₆	C₂²×C₃	1	1	yes	characteristic
132	#568	C₂²×C₃	1	2	yes	—
133	C₂×#131	C₂²×C₃	1	1	yes	characteristic
134	#536	C₂²×C₃	1	2	yes	—
135	#497	—	2	2	no	—
136	#495	—	2	1	no	—
137	#494	—	2	1	no	—
138	#473	—	2	1	no	—
139	#473	—	2	2	no	—
140	#473	—	2	2	no	—
141	#473	—	2	4	no	—
142	#472	—	2	1	no	—
143	#471	—	2	2	no	—
144	#471	—	2	4	no	—
145	#444	—	2	2	no	—
146	#443	—	2	2	no	—
147	#430	C₂²×C₃	1	2	yes	—
148	C₂×#108	C₂²×C₃	1	1	yes	characteristic
149	C₂×#108	C₂²×C₃	1	1	yes	characteristic
150	#421	C₂²×C₃	1	2	yes	—
151	#419	C₂²×C₃	1	2	yes	—
152	#413	C₂²×C₃	1	2	yes	—
153	#413	C₂²×C₃	1	1	yes	characteristic
154	C₂×#101	C₂²×C₃	1	2	yes	—
155	C₂×#101	C₂²×C₃	1	2	yes	—
156	#410	C₂²×C₃	1	1	yes	characteristic
157	#405	C₂²×C₃	1	1	yes	characteristic
158	#405	C₂²×C₃	1	1	yes	characteristic
159	#344	C₂²×C₃	1	1	yes	characteristic
160	#344	C₂²×C₃	1	1	yes	characteristic
161	#344	C₂²×C₃	1	2	yes	—
162	C₃×#41	—	2	2	no	—
163	C₃×#41	—	2	1	no	—
164	C₃×#41	—	2	2	no	—
165	C₃×#41	—	2	1	no	—
166	C₃×#41	—	2	2	no	—
167	C₃×#41	—	2	1	no	—
168	C₃×#41	—	2	2	no	—
169	C₃×#41	—	2	1	no	—
170	C₂×C₃×Q₈	—	2	2	no	—
171	C₂×C₃×Q₈	—	2	2	no	—
172	C₂×C₃×Q₈	—	2	2	no	—
173	C₂×C₃×Q₈	—	2	2	no	—
174	C₂×C₃×Q₈	—	2	2	no	—
175	C₂×C₃×Q₈	—	2	2	no	—
176	C₂×C₃×Q₈	C₂×D₄	1	2	yes	—
177	C₂×C₃×Q₈	C₂×D₄	1	1	yes	characteristic
178	C₂×C₃×D₄	—	2	1	no	—
179	C₂×C₃×D₄	—	2	2	no	—
180	C₂×C₃×D₄	C₂×D₄	1	2	yes	—
181	C₂×C₃×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	2	no	—
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
186	C₃×Q₁₆	—	2	1	no	—
187	C₃×Q₁₆	—	2	1	no	—
188	C₃×Q₁₆	—	4	4	no	—
189	C₃×Q₁₆	—	4	4	no	—
190	C₃×Q₁₆	—	4	2	no	—
191	C₃×Q₁₆	—	4	1	no	—
192	C₃×Q₁₆	—	4	1	no	—
193	C₃×Q₁₆	—	4	1	no	—
194	C₃×Q₁₆	—	4	1	no	—
195	C₃×SD₁₆	—	2	2	no	—
196	C₃×SD₁₆	—	2	2	no	—
197	C₃×SD₁₆	—	4	4	no	—
198	C₃×SD₁₆	—	4	4	no	—
199	C₃×SD₁₆	—	4	2	no	—
200	C₃×SD₁₆	—	4	2	no	—
201	C₃×D₈	—	2	1	no	—
202	C₃×D₈	—	2	1	no	—
203	C₃×D₈	—	4	2	no	—
204	C₃×M₁₆	—	2	1	no	—
205	C₃×M₁₆	—	2	2	no	—
206	C₃×M₁₆	—	2	1	no	—
207	C₃×M₁₆	—	2	1	no	—
208	C₃×M₁₆	—	2	2	no	—
209	C₃×M₁₆	—	2	1	no	—
210	C₃×M₁₆	—	2	2	no	—
211	C₃×M₁₆	—	4	4	no	—
212	C₃×M₁₆	—	4	1	no	—
213	C₃×M₁₆	—	4	1	no	—
214	C₃×M₁₆	C₂×D₄	1	2	yes	—
215	C₃×M₁₆	C₂×D₄	1	2	yes	—
216	C₃×M₁₆	C₂×D₄	1	4	yes	—
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	2	2	no	—
220	C₂×C₃×C₈	—	2	1	no	—
221	C₂×C₃×C₈	—	2	2	no	—
222	C₂×C₃×C₈	—	4	4	no	—
223	C₂×C₃×C₈	—	4	1	no	—
224	C₂×C₃×C₈	—	4	1	no	—
225	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
226	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×C₈	#41	1	1	yes	characteristic
230	C₂×C₃×C₈	#41	1	1	yes	characteristic
231	C₃×C₄⋊C₄	—	2	1	no	—
232	C₃×C₄⋊C₄	—	2	1	no	—
233	C₃×C₄⋊C₄	—	4	4	no	—
234	C₃×C₂²⋊C₄	—	2	1	no	—
235	C₃×C₂²⋊C₄	—	4	4	no	—
236	C₃×C₂²⋊C₄	#41	1	2	yes	—
237	C₃×C₄²	—	2	1	no	—
238	C₃×C₄²	—	2	1	no	—
239	C₂×#41	C₂³×C₃	1	2	yes	—
240	C₂×#41	C₂³×C₃	1	1	yes	characteristic
241	C₂²×Q₈	C₂³×C₃	1	2	yes	—
242	#137	—	2	2	no	—
243	#137	—	2	2	no	—
244	#137	—	2	4	no	—
245	#137	—	2	4	no	—
246	#137	—	4	2	no	—
247	#137	—	4	2	no	—
248	AGL(1,ℤ/8)	—	2	2	no	—
249	AGL(1,ℤ/8)	—	2	2	no	—
250	#135	—	2	1	no	—
251	#135	—	2	1	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	4	2	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	—	2	1	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×Q₁₆	—	2	1	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×Q₁₆	C₃×D₄	1	1	yes	characteristic
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×SD₁₆	C₃×D₄	1	2	yes	—
267	C₂×D₈	C₃×D₄	1	1	yes	characteristic
268	#131	—	2	4	no	—
269	#131	—	2	4	no	—
270	#131	—	2	1	no	—
271	#131	—	2	1	no	—
272	#131	—	2	1	no	—
273	#131	—	2	1	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	4	2	no	—
276	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
277	C₂×M₁₆	C₂³×C₃	1	2	yes	—
278	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
279	C₂×M₁₆	C₂³×C₃	1	2	yes	—
280	C₂×M₁₆	C₂³×C₃	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	2	no	—
284	#124	—	2	2	no	—
285	#123	—	2	4	no	—
286	C₂²⋊Q₈	—	4	2	no	—
287	#117	C₂³×C₃	1	1	yes	characteristic
288	#117	C₂³×C₃	1	1	yes	characteristic
289	#108	—	2	4	no	—
290	#108	—	2	1	no	—
291	#108	—	2	1	no	—
292	#108	C₃×D₄	1	2	yes	—
293	#108	C₃×D₄	1	2	yes	—
294	#104	—	2	4	no	—
295	#103	—	4	2	no	—
296	#101	—	2	2	no	—
297	#101	—	2	4	no	—
298	#101	—	2	4	no	—
299	#101	C₃×D₄	1	2	yes	—
300	#100	—	2	2	no	—
301	#100	C₃×D₄	1	2	yes	—
302	#99	—	2	2	no	—
303	#97	—	2	1	no	—
304	#97	—	2	1	no	—
305	C₄×C₈	—	2	1	no	—
306	C₄×C₈	—	2	1	no	—
307	C₂³×C₃	—	2	1	no	—
308	C₂³×C₃	—	2	2	no	—
309	C₂³×C₃	C₂×#41	1	1	yes	characteristic
310	C₃×Q₈	—	2	2	no	—
311	C₃×Q₈	—	2	1	no	—
312	C₃×Q₈	—	2	2	no	—
313	C₃×Q₈	—	2	1	no	—
314	C₃×Q₈	—	4	2	no	—
315	C₃×Q₈	—	4	2	no	—
316	C₃×Q₈	—	4	2	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×D₄	—	2	2	no	—
319	C₃×D₄	—	2	1	no	—
320	C₃×D₄	—	2	2	no	—
321	C₃×D₄	—	2	1	no	—
322	C₃×D₄	—	4	2	no	—
323	C₃×D₄	—	4	1	no	—
324	C₃×D₄	—	4	1	no	—
325	C₃×D₄	—	4	2	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	4	1	no	—
330	C₂×C₃×C₄	—	4	1	no	—
331	C₂×C₃×C₄	—	4	2	no	—
332	C₂×C₃×C₄	—	4	2	no	—
333	C₂×C₃×C₄	—	4	2	no	—
334	C₂×C₃×C₄	—	4	2	no	—
335	C₂×C₃×C₄	—	4	1	no	—
336	C₂×C₃×C₄	—	4	2	no	—
337	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
341	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
343	C₃×C₈	—	2	2	no	—
344	C₃×C₈	—	2	4	no	—
345	C₃×C₈	—	2	2	no	—
346	C₃×C₈	—	4	1	no	—
347	C₃×C₈	—	4	2	no	—
348	C₃×C₈	#121	1	1	yes	characteristic
349	C₃×C₈	#121	1	1	yes	characteristic
350	C₃×C₈	#121	1	1	yes	characteristic
351	C₃×C₈	#121	1	1	yes	characteristic
352	#41	—	2	2	no	—
353	#41	—	2	1	no	—
354	#41	—	2	2	no	—
355	#41	—	2	1	no	—
356	#41	—	2	2	no	—
357	#41	—	2	1	no	—
358	#41	—	2	2	no	—
359	#41	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	—	2	2	no	—
366	C₂×Q₈	C₂×C₃×D₄	1	2	yes	—
367	C₂×Q₈	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	C₂×C₃×D₄	1	2	yes	—
371	C₂×D₄	C₂×C₃×D₄	1	1	yes	characteristic
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
376	Q₁₆	—	2	1	no	—
377	Q₁₆	—	2	1	no	—
378	Q₁₆	—	4	4	no	—
379	Q₁₆	—	4	4	no	—
380	Q₁₆	—	4	2	no	—
381	Q₁₆	—	4	1	no	—
382	Q₁₆	—	4	1	no	—
383	Q₁₆	—	4	1	no	—
384	Q₁₆	—	4	1	no	—
385	SD₁₆	—	2	2	no	—
386	SD₁₆	—	2	2	no	—
387	SD₁₆	—	4	4	no	—
388	SD₁₆	—	4	4	no	—
389	SD₁₆	—	4	2	no	—
390	SD₁₆	—	4	2	no	—
391	D₈	—	2	1	no	—
392	D₈	—	2	1	no	—
393	D₈	—	4	2	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	2	no	—
401	M₁₆	—	4	4	no	—
402	M₁₆	—	4	1	no	—
403	M₁₆	—	4	1	no	—
404	M₁₆	C₂×C₃×D₄	1	2	yes	—
405	M₁₆	C₂×C₃×D₄	1	2	yes	—
406	M₁₆	C₂×C₃×D₄	1	4	yes	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	4	4	no	—
413	C₂×C₈	—	4	1	no	—
414	C₂×C₈	—	4	1	no	—
415	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
416	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
417	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
418	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
419	C₂×C₈	C₃×#41	1	1	yes	characteristic
420	C₂×C₈	C₃×#41	1	1	yes	characteristic
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	C₃×#41	1	2	yes	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₂²×C₃	—	4	1	no	—
430	C₂²×C₃	—	4	1	no	—
431	C₂²×C₃	—	4	2	no	—
432	C₂²×C₃	—	8	2	no	—
433	C₂²×C₃	—	8	1	no	—
434	C₂²×C₃	#532	1	1	yes	characteristic
435	C₂²×C₃	#546	1	1	yes	characteristic
436	C₂²×C₃	#550	1	1	yes	characteristic
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	4	2	no	—
440	C₃×C₄	—	8	1	no	—
441	C₃×C₄	—	8	2	no	—
442	C₃×C₄	C₂×#121	1	1	yes	characteristic
443	C₃×C₄	#540	1	1	yes	characteristic
444	C₃×C₄	D₄²	1	1	yes	characteristic
445	C₃×C₄	D₄²	1	1	yes	characteristic
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	C₂×C₃×#41	1	1	yes	characteristic
449	Q₈	—	2	2	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	2	2	no	—
452	Q₈	—	2	1	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	1	no	—
459	D₄	—	2	2	no	—
460	D₄	—	2	1	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
479	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
480	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	4	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	1	no	—
486	C₈	—	4	2	no	—
487	C₈	C₃×#121	1	1	yes	characteristic
488	C₈	C₃×#121	1	1	yes	characteristic
489	C₈	C₃×#121	1	1	yes	characteristic
490	C₈	C₃×#121	1	1	yes	characteristic
491	C₂×C₃	—	2	1	no	—
492	C₂×C₃	—	2	1	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	8	1	no	—
495	C₂×C₃	—	8	2	no	—
496	C₂×C₃	#2428	1	1	yes	characteristic
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	1	no	—
502	C₂²	C₃×#532	1	1	yes	characteristic
503	C₂²	C₃×#546	1	1	yes	characteristic
504	C₂²	C₃×#550	1	1	yes	characteristic
505	C₄	—	4	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	8	1	no	—
509	C₄	—	8	2	no	—
510	C₄	C₂×C₃×#121	1	1	yes	characteristic
511	C₄	C₃×#540	1	1	yes	characteristic
512	C₄	C₃×D₄²	1	1	yes	characteristic
513	C₄	C₃×D₄²	1	1	yes	characteristic
514	C₃	#25448	1	1	yes	characteristic, direct product factor, Sylow
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	8	1	no	—
519	C₂	—	8	2	no	—
520	C₂	C₃×#2428	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	#2428
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₃×#3067	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3156	C₂	semidirect
2. C₃×#3069	C₂	semidirect
4. C₂×C₃×#473	C₂	semidirect
5. C₃×#2957	C₂	semidirect
6. C₃×#2049	C₂	semidirect
7. C₃×#2009	C₂	semidirect
8. C₃×#1979	C₂	semidirect
9. C₃×#1953	C₂	semidirect
10. C₃×#1915	C₂	semidirect
11. C₃×#1757	C₂	semidirect
12. #25448	C₃	direct (N × H)
48. #3156	C₂×C₃	semidirect
49. #3069	C₂×C₃	semidirect
51. C₂×#473	C₂×C₃	semidirect
52. #2957	C₂×C₃	semidirect
53. #2049	C₂×C₃	semidirect
54. #2009	C₂×C₃	semidirect
55. #1979	C₂×C₃	semidirect
56. #1953	C₂×C₃	semidirect
57. #1915	C₂×C₃	semidirect
58. #1757	C₂×C₃	semidirect
514. C₃	#25448	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3156	2
C₃×#3069	2
C₃×#3067	2
C₂×C₃×#473	2
C₃×#2957	2
C₃×#2049	2
C₃×#2009	2
C₃×#1979	2
C₃×#1953	2
C₃×#1915	2
C₃×#1757	2
#25448	3

Subgroups — C3×#25448 #10644055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#25448 #10644055