Subgroups — C₂×C₃×#5160 #11867909

Order 1152.

1145 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#932	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#833	C₂	1	2	yes	maximal, complemented
5	C₃×#5160	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#472	—	3	1	no	maximal
8	C₂×#5160	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃²×D₄	C₂²	1	2	yes	—
10	C₂×C₃×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃²×D₈	—	2	1	no	—
12	C₂×C₃²×D₈	—	2	1	no	—
13	C₂×C₃²×D₈	—	2	2	no	—
14	C₂×C₃²×D₈	C₂²	1	4	yes	complemented
15	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×#214	—	2	2	no	—
17	C₃×#932	—	2	4	no	—
18	C₃×#932	C₂²	1	8	yes	complemented
19	C₂×C₃×#213	—	2	2	no	—
20	C₂×C₃×#208	C₂²	1	2	yes	—
21	C₂×C₃×#208	C₂²	1	1	yes	characteristic
22	C₃×#901	—	2	2	no	—
23	C₃×#901	C₂²	1	4	yes	complemented
24	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
25	C₂×C₃×D₃×C₈	—	2	1	no	—
26	C₃×#833	C₂²	1	8	yes	complemented
27	C₃×#819	C₂²	1	4	yes	complemented
28	C₂×C₃×AGL(1,ℤ/8)	—	3	2	no	—
29	C₂²×C₃×D₈	—	2	1	no	—
30	C₂²×C₃×D₈	D₃	1	1	yes	characteristic, complemented
31	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×C₃×#131	—	3	1	no	—
33	C₂×#932	C₂×C₃	1	2	yes	complemented
34	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
35	C₃×#472	—	3	8	no	—
36	C₂×C₃×#108	—	3	1	no	—
37	C₂×C₃×#100	—	3	2	no	—
38	C₂×#833	C₂×C₃	1	2	yes	complemented
39	#5160	C₂×C₃	1	8	yes	direct product factor
40	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃²	—	2	2	no	—
42	C₂×C₃²×D₄	—	2	2	no	—
43	C₂×C₃²×D₄	—	2	2	no	—
44	C₂×C₃²×D₄	—	2	2	no	—
45	C₂×C₃²×D₄	—	2	2	no	—
46	C₂×C₃²×D₄	—	2	2	no	—
47	C₂×C₃²×D₄	C₂³	1	4	yes	—
48	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃×#67	—	2	1	no	—
50	C₃×#235	—	2	1	no	—
51	C₃×#235	—	2	1	no	—
52	C₃×#235	D₄	1	2	yes	—
53	C₃×#235	C₂³	1	2	yes	—
54	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
55	C₂×C₃×C₄×D₃	—	2	1	no	—
56	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
57	C₃²×D₈	—	2	4	no	—
58	C₃²×D₈	—	2	4	no	—
59	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
60	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
61	C₂×C₃²×C₈	D₄	1	2	yes	—
62	C₂×C₃²×C₈	C₂³	1	2	yes	—
63	C₃×#214	—	2	8	no	—
64	C₃×#213	—	2	8	no	—
65	C₃×#208	—	2	1	no	—
66	C₃×#208	—	2	2	no	—
67	C₃×#208	C₂³	1	2	yes	—
68	C₃×#208	C₂³	1	4	yes	—
69	C₂×C₃×C₃⋊C₈	—	2	1	no	—
70	C₂×C₃×C₃⋊C₈	—	2	2	no	—
71	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
72	C₃×D₃×C₈	—	2	4	no	—
73	C₂×#472	—	3	1	no	Sylow
74	C₂×C₃×#41	—	3	1	no	—
75	C₂²×C₃×D₄	—	2	2	no	—
76	C₂²×C₃×D₄	C₂×D₃	1	2	yes	—
77	C₂²×C₃×D₄	C₂²×C₃	1	2	yes	—
78	C₂×#235	C₂²×C₃	1	1	yes	characteristic
79	C₃×AGL(1,ℤ/8)	—	3	8	no	—
80	C₃×AGL(1,ℤ/8)	—	6	4	no	—
81	C₂×C₃×SD₁₆	—	6	2	no	—
82	C₂×C₃×D₈	—	2	2	no	—
83	C₂×C₃×D₈	—	2	2	no	—
84	C₂×C₃×D₈	—	2	4	no	—
85	C₂×C₃×D₈	—	2	1	no	—
86	C₂×C₃×D₈	—	2	1	no	—
87	C₂×C₃×D₈	—	2	2	no	—
88	C₂×C₃×D₈	—	2	1	no	—
89	C₂×C₃×D₈	—	2	1	no	—
90	C₂×C₃×D₈	—	2	2	no	—
91	C₂×C₃×D₈	—	2	4	no	—
92	C₂×C₃×D₈	—	6	2	no	—
93	C₂×C₃×D₈	C₂×D₃	1	4	yes	complemented
94	C₂×C₃×D₈	C₂²×C₃	1	4	yes	complemented
95	C₃×#131	—	3	4	no	—
96	C₃×#131	—	6	2	no	—
97	C₂×C₃×M₁₆	—	3	1	no	—
98	C₂×C₃×M₁₆	—	3	2	no	—
99	C₂×C₃×M₁₆	—	6	1	no	—
100	C₂²×C₃×C₈	—	2	1	no	—
101	C₂²×C₃×C₈	—	6	1	no	—
102	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
104	C₂×#214	—	2	2	no	—
105	#932	—	2	4	no	—
106	#932	C₂²×C₃	1	8	yes	complemented
107	C₂×#213	—	2	2	no	—
108	C₂×#208	C₂²×C₃	1	1	yes	characteristic
109	C₂×#208	C₂²×C₃	1	2	yes	—
110	#901	—	2	2	no	—
111	#901	C₂²×C₃	1	4	yes	complemented
112	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
113	C₂×D₃×C₈	—	2	1	no	—
114	C₃×#108	—	3	4	no	—
115	C₃×#100	—	3	8	no	—
116	#833	C₂²×C₃	1	8	yes	complemented
117	#819	C₂²×C₃	1	4	yes	complemented
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	—	4	2	no	—
120	C₂³×C₃²	—	4	2	no	—
121	C₂³×C₃²	—	8	4	no	—
122	C₂³×C₃²	#41	1	1	yes	characteristic
123	C₂²×C₃×D₃	—	2	1	no	—
124	C₃²×D₄	—	2	4	no	—
125	C₃²×D₄	—	2	4	no	—
126	C₃²×D₄	—	4	2	no	—
127	C₃²×D₄	—	4	2	no	—
128	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	#41	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
134	C₃×#67	—	2	2	no	—
135	C₃×#67	—	2	2	no	—
136	C₂×C₃×Dic₃	—	2	1	no	—
137	C₃×D₁₂	—	2	1	no	—
138	C₃×D₁₂	C₂×D₄	1	2	yes	—
139	C₃×C₄×D₃	—	2	2	no	—
140	C₃×C₄×D₃	—	2	2	no	—
141	C₃×Dic₆	—	2	1	no	—
142	C₃×Dic₆	C₂×D₄	1	2	yes	—
143	C₃²×C₈	C₂×D₄	1	2	yes	—
144	C₃²×C₈	C₂×D₄	1	2	yes	—
145	C₃×C₃⋊C₈	—	2	2	no	—
146	C₃×C₃⋊C₈	—	2	4	no	—
147	C₂×AGL(1,ℤ/8)	—	3	2	no	—
148	C₂²×D₈	C₃×D₃	1	1	yes	characteristic, complemented
149	C₂×#131	—	3	1	no	—
150	#472	—	3	8	no	—
151	C₂×#108	—	3	1	no	—
152	C₂×#100	—	3	2	no	—
153	C₂⁴×C₃	—	2	2	no	—
154	C₂⁴×C₃	—	2	2	no	—
155	C₂⁴×C₃	—	4	2	no	—
156	C₃×#41	—	3	2	no	—
157	C₃×#41	—	3	2	no	—
158	C₃×#41	—	6	1	no	—
159	C₃×#41	—	6	1	no	—
160	C₂×C₃×Q₈	—	3	1	no	—
161	C₂×C₃×D₄	—	2	4	no	—
162	C₂×C₃×D₄	—	2	4	no	—
163	C₂×C₃×D₄	—	2	2	no	—
164	C₂×C₃×D₄	—	2	2	no	—
165	C₂×C₃×D₄	—	2	2	no	—
166	C₂×C₃×D₄	—	2	2	no	—
167	C₂×C₃×D₄	—	2	2	no	—
168	C₂×C₃×D₄	—	2	2	no	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	—	2	2	no	—
171	C₂×C₃×D₄	—	2	2	no	—
172	C₂×C₃×D₄	—	2	2	no	—
173	C₂×C₃×D₄	—	2	4	no	—
174	C₂×C₃×D₄	—	3	1	no	—
175	C₂×C₃×D₄	—	4	2	no	—
176	C₂×C₃×D₄	—	4	2	no	—
177	C₂×C₃×D₄	—	4	2	no	—
178	C₂×C₃×D₄	—	6	1	no	—
179	C₂×C₃×D₄	C₂²×D₃	1	4	yes	—
180	C₂×C₃×D₄	C₂³×C₃	1	4	yes	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	6	1	no	—
183	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
185	C₂×#67	—	2	1	no	—
186	#235	—	2	1	no	—
187	#235	—	2	1	no	—
188	#235	C₃×D₄	1	2	yes	—
189	#235	C₂³×C₃	1	2	yes	—
190	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	1	no	—
192	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
193	C₃×SD₁₆	—	6	8	no	—
194	C₃×D₈	—	2	8	no	—
195	C₃×D₈	—	2	8	no	—
196	C₃×D₈	—	2	4	no	—
197	C₃×D₈	—	2	4	no	—
198	C₃×D₈	—	2	4	no	—
199	C₃×D₈	—	2	4	no	—
200	C₃×D₈	—	6	8	no	—
201	C₃×M₁₆	—	3	2	no	—
202	C₃×M₁₆	—	3	4	no	—
203	C₃×M₁₆	—	6	2	no	—
204	C₃×M₁₆	—	6	1	no	—
205	C₃×M₁₆	—	6	4	no	—
206	C₂×C₃×C₈	—	2	1	no	—
207	C₂×C₃×C₈	—	2	1	no	—
208	C₂×C₃×C₈	—	2	2	no	—
209	C₂×C₃×C₈	—	2	2	no	—
210	C₂×C₃×C₈	—	6	2	no	—
211	C₂×C₃×C₈	—	6	1	no	—
212	C₂×C₃×C₈	—	6	4	no	—
213	C₂×C₃×C₈	#67	1	1	yes	characteristic
214	C₂×C₃×C₈	#67	1	1	yes	characteristic
215	C₂×C₃×C₈	#67	1	2	yes	—
216	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
217	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
218	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
219	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
220	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
221	#214	—	2	8	no	—
222	#213	—	2	8	no	—
223	#208	—	2	1	no	—
224	#208	—	2	2	no	—
225	#208	C₂³×C₃	1	4	yes	—
226	#208	C₂³×C₃	1	2	yes	—
227	C₂×C₃⋊C₈	—	2	1	no	—
228	C₂×C₃⋊C₈	—	2	2	no	—
229	ΓL(1,𝔽₂₅)	—	2	4	no	—
230	D₃×C₈	—	2	4	no	—
231	C₂²×C₃²	—	2	2	no	—
232	C₂²×C₃²	—	4	4	no	—
233	C₂²×C₃²	—	8	4	no	—
234	C₂²×C₃²	—	8	4	no	—
235	C₂²×C₃²	—	8	4	no	—
236	C₂²×C₃²	#121	1	1	yes	characteristic
237	C₂²×C₃²	#121	1	1	yes	characteristic
238	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
239	C₂×C₃×D₃	—	2	2	no	—
240	C₂×C₃×D₃	—	4	2	no	—
241	C₃²×C₄	#121	1	1	yes	characteristic
242	C₃²×C₄	#121	1	1	yes	characteristic
243	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
244	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
245	C₃×Dic₃	—	2	2	no	—
246	C₂×#41	—	3	1	no	—
247	C₂²×D₄	C₂×C₃×D₃	1	2	yes	—
248	AGL(1,ℤ/8)	—	3	8	no	—
249	AGL(1,ℤ/8)	—	6	4	no	—
250	C₂×SD₁₆	—	6	2	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×D₈	—	6	2	no	—
255	C₂×D₈	C₂×C₃×D₃	1	4	yes	complemented
256	#131	—	3	4	no	—
257	#131	—	6	2	no	—
258	C₂×M₁₆	—	3	1	no	—
259	C₂×M₁₆	—	3	2	no	—
260	C₂×M₁₆	—	6	1	no	—
261	C₂²×C₈	—	6	1	no	—
262	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
263	#108	—	3	4	no	—
264	#100	—	3	8	no	—
265	C₂³×C₃	—	2	4	no	—
266	C₂³×C₃	—	2	4	no	—
267	C₂³×C₃	—	2	1	no	—
268	C₂³×C₃	—	4	4	no	—
269	C₂³×C₃	—	4	4	no	—
270	C₂³×C₃	—	4	4	no	—
271	C₂³×C₃	—	4	2	no	—
272	C₂³×C₃	—	4	2	no	—
273	C₂³×C₃	—	4	2	no	—
274	C₂³×C₃	—	4	2	no	—
275	C₂³×C₃	—	6	1	no	—
276	C₂³×C₃	—	8	4	no	—
277	C₂³×C₃	—	8	4	no	—
278	C₂³×C₃	—	8	8	no	—
279	C₂³×C₃	#237	1	1	yes	characteristic
280	C₂³×C₃	C₃×#41	1	1	yes	characteristic
281	C₂²×D₃	—	2	1	no	—
282	C₃×Q₈	—	3	2	no	—
283	C₃×Q₈	—	6	1	no	—
284	C₃×D₄	—	2	8	no	—
285	C₃×D₄	—	2	4	no	—
286	C₃×D₄	—	2	4	no	—
287	C₃×D₄	—	2	4	no	—
288	C₃×D₄	—	2	4	no	—
289	C₃×D₄	—	3	2	no	—
290	C₃×D₄	—	4	4	no	—
291	C₃×D₄	—	4	4	no	—
292	C₃×D₄	—	4	4	no	—
293	C₃×D₄	—	4	2	no	—
294	C₃×D₄	—	4	2	no	—
295	C₃×D₄	—	4	2	no	—
296	C₃×D₄	—	4	2	no	—
297	C₃×D₄	—	6	2	no	—
298	C₃×D₄	—	6	2	no	—
299	C₃×D₄	—	6	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	1	no	—
302	C₂×C₃×C₄	—	2	1	no	—
303	C₂×C₃×C₄	—	2	1	no	—
304	C₂×C₃×C₄	—	2	1	no	—
305	C₂×C₃×C₄	—	2	1	no	—
306	C₂×C₃×C₄	—	6	1	no	—
307	C₂×C₃×C₄	—	6	2	no	—
308	C₂×C₃×C₄	—	6	2	no	—
309	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
310	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
311	C₂×C₃×C₄	#237	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
318	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
321	#67	—	2	2	no	—
322	#67	—	2	2	no	—
323	C₂×Dic₃	—	2	1	no	—
324	D₁₂	—	2	1	no	—
325	D₁₂	C₂×C₃×D₄	1	2	yes	—
326	C₄×D₃	—	2	2	no	—
327	C₄×D₃	—	2	2	no	—
328	Dic₆	—	2	1	no	—
329	Dic₆	C₂×C₃×D₄	1	2	yes	—
330	C₃×C₈	—	2	2	no	—
331	C₃×C₈	—	2	2	no	—
332	C₃×C₈	—	6	4	no	—
333	C₃×C₈	—	6	2	no	—
334	C₃×C₈	C₂×#67	1	2	yes	—
335	C₃×C₈	C₂×#67	1	2	yes	—
336	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
337	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
338	C₃⋊C₈	—	2	2	no	—
339	C₃⋊C₈	—	2	4	no	—
340	C₂×C₃²	—	2	1	no	—
341	C₂×C₃²	—	2	1	no	—
342	C₂×C₃²	—	8	4	no	—
343	C₂×C₃²	#472	1	2	yes	complemented
344	C₂×C₃²	C₂×#121	1	1	yes	characteristic
345	C₃×D₃	—	4	2	no	—
346	C₂⁴	—	2	2	no	—
347	#41	—	3	2	no	—
348	#41	—	3	2	no	—
349	#41	—	6	1	no	—
350	#41	—	6	1	no	—
351	C₂×Q₈	—	3	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	3	1	no	—
358	C₂×D₄	—	6	1	no	—
359	C₂×D₄	C₂²×C₃×D₃	1	4	yes	—
360	C₂²×C₄	—	6	1	no	—
361	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
362	SD₁₆	—	6	8	no	—
363	D₈	—	2	4	no	—
364	D₈	—	2	4	no	—
365	D₈	—	6	8	no	—
366	M₁₆	—	3	2	no	—
367	M₁₆	—	3	4	no	—
368	M₁₆	—	6	2	no	—
369	M₁₆	—	6	1	no	—
370	M₁₆	—	6	4	no	—
371	C₂×C₈	—	6	2	no	—
372	C₂×C₈	—	6	1	no	—
373	C₂×C₈	—	6	4	no	—
374	C₂×C₈	C₃×#67	1	1	yes	characteristic
375	C₂×C₈	C₃×#67	1	1	yes	characteristic
376	C₂×C₈	C₃×#67	1	2	yes	—
377	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
378	C₂²×C₃	—	2	4	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	2	no	—
381	C₂²×C₃	—	2	1	no	—
382	C₂²×C₃	—	2	1	no	—
383	C₂²×C₃	—	2	1	no	—
384	C₂²×C₃	—	4	8	no	—
385	C₂²×C₃	—	4	4	no	—
386	C₂²×C₃	—	4	4	no	—
387	C₂²×C₃	—	6	2	no	—
388	C₂²×C₃	—	8	4	no	—
389	C₂²×C₃	—	8	4	no	—
390	C₂²×C₃	—	8	8	no	—
391	C₂²×C₃	—	8	8	no	—
392	C₂²×C₃	—	8	4	no	—
393	C₂²×C₃	—	8	4	no	—
394	C₂²×C₃	—	8	8	no	—
395	C₂²×C₃	—	8	4	no	—
396	C₂²×C₃	—	8	4	no	—
397	C₂²×C₃	—	12	2	no	—
398	C₂²×C₃	#938	1	1	yes	characteristic
399	C₂²×C₃	#938	1	1	yes	characteristic
400	C₂²×C₃	C₃×#121	1	1	yes	characteristic
401	C₂²×C₃	C₃×#121	1	1	yes	characteristic
402	C₂²×C₃	C₂×#237	1	1	yes	characteristic
403	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
404	C₂×D₃	—	2	2	no	—
405	C₂×D₃	—	4	2	no	—
406	C₃×C₄	—	2	1	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	1	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	6	2	no	—
411	C₃×C₄	#938	1	1	yes	characteristic
412	C₃×C₄	#938	1	1	yes	characteristic
413	C₃×C₄	C₃×#121	1	1	yes	characteristic
414	C₃×C₄	C₃×#121	1	1	yes	characteristic
415	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
416	C₃×C₄	C₂²×#67	1	1	yes	characteristic
417	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
418	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
419	Dic₃	—	2	2	no	—
420	C₃²	C₂×#472	1	1	yes	characteristic, complemented, Sylow
421	C₂³	—	2	4	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	6	1	no	—
425	C₂³	—	8	4	no	—
426	C₂³	C₃×#237	1	1	yes	characteristic
427	Q₈	—	3	2	no	—
428	Q₈	—	6	1	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	3	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	2	no	—
434	D₄	—	6	2	no	—
435	D₄	—	6	2	no	—
436	D₄	—	6	1	no	—
437	C₂×C₄	—	6	1	no	—
438	C₂×C₄	—	6	2	no	—
439	C₂×C₄	—	6	2	no	—
440	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
441	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
442	C₂×C₄	C₃×#237	1	1	yes	characteristic
443	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
444	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
445	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
446	C₈	—	6	4	no	—
447	C₈	—	6	2	no	—
448	C₈	C₂×C₃×#67	1	2	yes	—
449	C₈	C₂×C₃×#67	1	2	yes	—
450	C₂×C₃	—	2	2	no	—
451	C₂×C₃	—	2	2	no	—
452	C₂×C₃	—	2	1	no	—
453	C₂×C₃	—	2	1	no	—
454	C₂×C₃	—	2	1	no	—
455	C₂×C₃	—	2	1	no	—
456	C₂×C₃	—	2	2	no	—
457	C₂×C₃	—	2	1	no	—
458	C₂×C₃	—	8	8	no	—
459	C₂×C₃	—	8	4	no	—
460	C₂×C₃	—	8	4	no	—
461	C₂×C₃	—	12	2	no	—
462	C₂×C₃	#5160	1	2	yes	direct product factor
463	C₂×C₃	C₃×#472	1	2	yes	complemented
464	C₂×C₃	C₂×#938	1	1	yes	characteristic
465	C₂×C₃	C₂×C₃×#121	1	1	yes	characteristic
466	D₃	—	4	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	6	2	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	—	8	4	no	—
473	C₂²	—	12	2	no	—
474	C₂²	C₃×#938	1	1	yes	characteristic
475	C₂²	C₃×#938	1	1	yes	characteristic
476	C₂²	C₂×C₃×#237	1	1	yes	characteristic
477	C₄	—	6	2	no	—
478	C₄	C₃×#938	1	1	yes	characteristic
479	C₄	C₃×#938	1	1	yes	characteristic
480	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
481	C₄	C₂²×C₃×#67	1	1	yes	characteristic
482	C₃	—	2	1	no	—
483	C₃	C₂×#5160	1	1	yes	characteristic, direct product factor
484	C₃	C₂×C₃×#472	1	1	yes	characteristic, complemented
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	8	4	no	—
488	C₂	—	12	2	no	—
489	C₂	C₃×#5160	1	2	yes	direct product factor
490	C₂	C₂×C₃×#938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#938
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂²×C₃²×D₈	C₂
socle	C₂²×C₃²	#121
hypercenter	C₂²×C₃×D₈	D₃
hypocenter	C₃	C₂×C₃×#472
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×D₈	C₂	semidirect
2. C₂×C₃×#932	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₂×C₃×#833	C₂	semidirect
5. C₃×#5160	C₂	direct (N × H)
6. C₂×C₃×#819	C₂	semidirect
8. C₂×#5160	C₃	direct (N × H)
14. C₂×C₃²×D₈	C₂²	semidirect
18. C₃×#932	C₂²	semidirect
23. C₃×#901	C₂²	semidirect
26. C₃×#833	C₂²	semidirect
27. C₃×#819	C₂²	semidirect
30. C₂²×C₃×D₈	D₃	semidirect
31. C₂²×C₃×D₈	C₂×C₃	semidirect
33. C₂×#932	C₂×C₃	semidirect
34. C₂×#901	C₂×C₃	semidirect
38. C₂×#833	C₂×C₃	semidirect
39. #5160	C₂×C₃	direct (N × H)
40. C₂×#819	C₂×C₃	semidirect
93. C₂×C₃×D₈	C₂×D₃	semidirect
94. C₂×C₃×D₈	C₂²×C₃	semidirect
106. #932	C₂²×C₃	semidirect
111. #901	C₂²×C₃	semidirect
116. #833	C₂²×C₃	semidirect
117. #819	C₂²×C₃	semidirect
148. C₂²×D₈	C₃×D₃	semidirect
255. C₂×D₈	C₂×C₃×D₃	semidirect
343. C₂×C₃²	#472	semidirect
420. C₃²	C₂×#472	semidirect
462. C₂×C₃	#5160	direct (N × H)
463. C₂×C₃	C₃×#472	semidirect
483. C₃	C₂×#5160	direct (N × H)
484. C₃	C₂×C₃×#472	semidirect
489. C₂	C₃×#5160	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×D₈	2
C₂×C₃×#932	2
C₂×C₃×#901	2
C₂×C₃×#833	2
C₃×#5160	2
C₂×C₃×#819	2
C₂×C₃×#472	3
C₂×#5160	3

Subgroups — C2×C3×#5160 #11867909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5160 #11867909