Subgroups — C₂×C₃×#5145 #11861036

Order 1152.

1061 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#950	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#837	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5145	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#825	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#822	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#815	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#444	—	3	1	no	maximal
10	C₂×#5145	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
12	C₂×C₃×#235	C₂²	1	1	yes	characteristic
13	C₃²×#131	—	2	2	no	—
14	C₃²×#131	C₂²	1	4	yes	complemented
15	C₂×C₃²×M₁₆	—	2	1	no	—
16	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₃²×C₈	—	2	1	no	—
18	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
19	C₃×#950	C₄	1	4	yes	complemented
20	C₃×#950	C₂²	1	4	yes	—
21	C₂×C₃×#216	C₄	1	1	yes	characteristic, complemented
22	C₂×C₃×#215	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×#214	C₄	1	1	yes	characteristic, complemented
24	C₂×C₃×#213	C₄	1	1	yes	characteristic, complemented
25	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×#208	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×#901	—	2	2	no	—
29	C₃×#901	C₂²	1	4	yes	complemented
30	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
31	C₂×C₃×D₃×C₈	—	2	1	no	—
32	C₃×#837	C₂²	1	4	yes	complemented
33	C₃×#825	C₂²	1	4	yes	complemented
34	C₃×#822	C₂²	1	4	yes	complemented
35	C₃×#815	C₂²	1	4	yes	complemented
36	C₂×C₃×#135	—	3	1	no	—
37	C₂×C₃×#131	—	2	1	no	—
38	C₂×C₃×#131	—	3	1	no	—
39	C₂×C₃×#131	D₃	1	1	yes	characteristic, complemented
40	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×#950	C₂×C₃	1	1	yes	characteristic
42	C₂×#901	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×#444	—	3	8	no	—
44	C₂×C₃×#108	—	3	1	no	—
45	C₂×C₃×#104	—	3	1	no	—
46	C₂×C₃×#104	—	3	1	no	—
47	C₂×C₃×#97	—	3	1	no	—
48	C₂×#837	C₂×C₃	1	1	yes	characteristic, complemented
49	#5145	C₂×C₃	1	8	yes	direct product factor
50	C₂×#825	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×#822	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#815	C₂×C₃	1	1	yes	characteristic, complemented
53	C₃²×#41	—	2	1	no	—
54	C₃²×#41	—	2	1	no	—
55	C₃²×#41	C₂×C₄	1	2	yes	—
56	C₃²×#41	C₂³	1	2	yes	—
57	C₂×C₃²×Q₈	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃²×D₄	—	2	1	no	—
59	C₂×C₃²×D₄	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₃²×C₄	—	2	1	no	—
61	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
62	C₂×C₃×#67	—	2	1	no	—
63	C₂²×C₃×Dic₃	—	2	1	no	—
64	C₃×#235	—	2	1	no	—
65	C₃×#235	—	2	1	no	—
66	C₃×#235	C₂×C₄	1	2	yes	—
67	C₃×#235	C₂³	1	2	yes	—
68	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	—	2	1	no	—
70	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
71	C₃²×M₁₆	—	2	1	no	—
72	C₃²×M₁₆	—	2	4	no	—
73	C₃²×M₁₆	C₂³	1	2	yes	—
74	C₂×C₃²×C₈	—	2	1	no	—
75	C₂×C₃²×C₈	—	2	4	no	—
76	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
77	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
78	C₂×C₃²×C₈	D₄	1	2	yes	—
79	C₂×C₃²×C₈	C₂³	1	2	yes	—
80	C₃×#216	C₂×C₄	1	4	yes	complemented
81	C₃×#215	C₂×C₄	1	4	yes	complemented
82	C₃×#214	C₂×C₄	1	4	yes	complemented
83	C₃×#213	C₂×C₄	1	4	yes	complemented
84	C₃×C₄×Dic₃	—	2	1	no	—
85	C₃×C₄×Dic₃	C₂³	1	2	yes	—
86	C₃×#208	—	2	1	no	—
87	C₃×#208	C₂³	1	2	yes	—
88	C₂×C₃×C₃⋊C₈	—	2	1	no	—
89	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₂×C₃×C₃⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
92	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
93	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
94	C₃×D₃×C₈	—	2	4	no	—
95	C₂×#444	—	3	1	no	Sylow
96	C₂×C₃×#41	—	2	1	no	—
97	C₂×C₃×#41	—	3	1	no	—
98	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
99	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
100	C₂×#235	C₂²×C₃	1	1	yes	characteristic
101	C₃×#135	—	3	4	no	—
102	C₃×#135	—	3	4	no	—
103	C₂×C₃×Q₁₆	—	3	1	no	—
104	C₂×C₃×SD₁₆	—	3	1	no	—
105	C₂×C₃×SD₁₆	—	3	1	no	—
106	C₂×C₃×D₈	—	3	1	no	—
107	C₃×#131	—	2	4	no	—
108	C₃×#131	—	2	2	no	—
109	C₃×#131	—	2	2	no	—
110	C₃×#131	—	2	4	no	—
111	C₃×#131	—	3	4	no	—
112	C₃×#131	—	6	2	no	—
113	C₃×#131	C₂×D₃	1	4	yes	complemented
114	C₃×#131	C₂²×C₃	1	4	yes	complemented
115	C₂×C₃×M₁₆	—	2	2	no	—
116	C₂×C₃×M₁₆	—	2	1	no	—
117	C₂×C₃×M₁₆	—	2	1	no	—
118	C₂×C₃×M₁₆	—	2	1	no	—
119	C₂×C₃×M₁₆	—	3	1	no	—
120	C₂×C₃×M₁₆	—	6	1	no	—
121	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
122	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₃×C₈	—	2	2	no	—
124	C₂²×C₃×C₈	—	2	1	no	—
125	C₂²×C₃×C₈	—	2	1	no	—
126	C₂²×C₃×C₈	—	2	1	no	—
127	C₂²×C₃×C₈	—	3	1	no	—
128	C₂²×C₃×C₈	—	6	1	no	—
129	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
130	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₄²	—	3	1	no	—
132	#950	C₃×C₄	1	4	yes	complemented
133	#950	C₂²×C₃	1	4	yes	—
134	C₂×#216	C₃×C₄	1	1	yes	characteristic, complemented
135	C₂×#215	C₃×C₄	1	1	yes	characteristic, complemented
136	C₂×#214	C₃×C₄	1	1	yes	characteristic, complemented
137	C₂×#213	C₃×C₄	1	1	yes	characteristic, complemented
138	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
139	C₂×#208	C₂²×C₃	1	1	yes	characteristic
140	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
141	#901	—	2	2	no	—
142	#901	C₂²×C₃	1	4	yes	complemented
143	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
144	C₂×D₃×C₈	—	2	1	no	—
145	C₃×#108	—	3	4	no	—
146	C₃×#104	—	3	4	no	—
147	C₃×#104	—	3	4	no	—
148	C₃×#97	—	3	4	no	—
149	#837	C₂²×C₃	1	4	yes	complemented
150	#825	C₂²×C₃	1	4	yes	complemented
151	#822	C₂²×C₃	1	4	yes	complemented
152	#815	C₂²×C₃	1	4	yes	complemented
153	C₂³×C₃²	—	2	1	no	—
154	C₂³×C₃²	#41	1	1	yes	characteristic
155	C₂²×C₃×D₃	—	2	1	no	—
156	C₃²×Q₈	—	2	1	no	—
157	C₃²×Q₈	C₂²×C₄	1	2	yes	—
158	C₃²×D₄	—	2	2	no	—
159	C₃²×D₄	—	2	2	no	—
160	C₃²×D₄	—	2	1	no	—
161	C₃²×D₄	C₂²×C₄	1	2	yes	—
162	C₂×C₃²×C₄	—	2	1	no	—
163	C₂×C₃²×C₄	—	2	2	no	—
164	C₂×C₃²×C₄	—	2	2	no	—
165	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
169	C₂×C₃²×C₄	#41	1	1	yes	characteristic
170	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
171	C₃×#67	—	2	2	no	—
172	C₃×#67	—	2	2	no	—
173	C₂×C₃×Dic₃	—	2	1	no	—
174	C₂×C₃×Dic₃	—	2	2	no	—
175	C₂×C₃×Dic₃	—	4	2	no	—
176	C₃×D₁₂	—	2	1	no	—
177	C₃×D₁₂	C₂²×C₄	1	2	yes	—
178	C₃×C₄×D₃	—	2	2	no	—
179	C₃×C₄×D₃	—	2	2	no	—
180	C₃×Dic₆	—	2	1	no	—
181	C₃×Dic₆	C₂²×C₄	1	2	yes	—
182	C₃²×C₈	—	2	2	no	—
183	C₃²×C₈	C₂×D₄	1	2	yes	—
184	C₃²×C₈	C₂×D₄	1	2	yes	—
185	C₃×C₃⋊C₈	—	2	2	no	—
186	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
187	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
188	C₂×#135	—	3	1	no	—
189	C₂×#131	—	3	1	no	—
190	C₂×#131	C₃×D₃	1	1	yes	characteristic, complemented
191	#444	—	3	8	no	—
192	C₂×#108	—	3	1	no	—
193	C₂×#104	—	3	1	no	—
194	C₂×#104	—	3	1	no	—
195	C₂×#97	—	3	1	no	—
196	C₃×#41	—	2	2	no	—
197	C₃×#41	—	2	2	no	—
198	C₃×#41	—	2	1	no	—
199	C₃×#41	—	2	1	no	—
200	C₃×#41	—	2	1	no	—
201	C₃×#41	—	2	1	no	—
202	C₃×#41	—	2	2	no	—
203	C₃×#41	—	2	2	no	—
204	C₃×#41	—	3	2	no	—
205	C₃×#41	—	3	2	no	—
206	C₃×#41	—	6	1	no	—
207	C₃×#41	—	6	1	no	—
208	C₃×#41	C₄×D₃	1	2	yes	—
209	C₃×#41	C₂×C₃×C₄	1	2	yes	—
210	C₃×#41	C₂²×D₃	1	2	yes	—
211	C₃×#41	C₂³×C₃	1	2	yes	—
212	C₂×C₃×Q₈	—	2	1	no	—
213	C₂×C₃×Q₈	—	3	1	no	—
214	C₂×C₃×Q₈	C₄×D₃	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
216	C₂×C₃×D₄	—	2	2	no	—
217	C₂×C₃×D₄	—	2	1	no	—
218	C₂×C₃×D₄	—	2	1	no	—
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	—	3	1	no	—
221	C₂×C₃×D₄	—	6	1	no	—
222	C₂×C₃×D₄	C₄×D₃	1	1	yes	characteristic
223	C₂×C₃×D₄	C₂×C₃×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	—	2	2	no	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	—	2	1	no	—
227	C₂²×C₃×C₄	—	2	1	no	—
228	C₂²×C₃×C₄	—	6	1	no	—
229	C₂²×C₃×C₄	—	6	1	no	—
230	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
232	C₂×#67	—	2	1	no	—
233	C₂²×Dic₃	—	2	1	no	—
234	#235	—	2	1	no	—
235	#235	—	2	1	no	—
236	#235	C₂×C₃×C₄	1	2	yes	—
237	#235	C₂³×C₃	1	2	yes	—
238	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
239	C₂×C₄×D₃	—	2	1	no	—
240	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
241	C₃×Q₁₆	—	3	4	no	—
242	C₃×SD₁₆	—	3	4	no	—
243	C₃×SD₁₆	—	3	4	no	—
244	C₃×D₈	—	3	4	no	—
245	C₃×M₁₆	—	2	2	no	—
246	C₃×M₁₆	—	2	8	no	—
247	C₃×M₁₆	—	2	1	no	—
248	C₃×M₁₆	—	2	1	no	—
249	C₃×M₁₆	—	2	4	no	—
250	C₃×M₁₆	—	2	4	no	—
251	C₃×M₁₆	—	2	2	no	—
252	C₃×M₁₆	—	3	2	no	—
253	C₃×M₁₆	—	6	1	no	—
254	C₃×M₁₆	—	6	4	no	—
255	C₃×M₁₆	C₂²×D₃	1	2	yes	—
256	C₃×M₁₆	C₂³×C₃	1	2	yes	—
257	C₂×C₃×C₈	—	2	2	no	—
258	C₂×C₃×C₈	—	2	8	no	—
259	C₂×C₃×C₈	—	2	1	no	—
260	C₂×C₃×C₈	—	2	1	no	—
261	C₂×C₃×C₈	—	2	4	no	—
262	C₂×C₃×C₈	—	2	4	no	—
263	C₂×C₃×C₈	—	2	1	no	—
264	C₂×C₃×C₈	—	2	1	no	—
265	C₂×C₃×C₈	—	2	2	no	—
266	C₂×C₃×C₈	—	2	2	no	—
267	C₂×C₃×C₈	—	3	1	no	—
268	C₂×C₃×C₈	—	3	1	no	—
269	C₂×C₃×C₈	—	3	2	no	—
270	C₂×C₃×C₈	—	3	2	no	—
271	C₂×C₃×C₈	—	6	1	no	—
272	C₂×C₃×C₈	—	6	4	no	—
273	C₂×C₃×C₈	#67	1	2	yes	—
274	C₂×C₃×C₈	#67	1	1	yes	characteristic
275	C₂×C₃×C₈	#67	1	1	yes	characteristic
276	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
277	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
278	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
279	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
280	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
281	C₃×C₄²	—	3	2	no	—
282	C₃×C₄²	—	6	1	no	—
283	#216	C₂×C₃×C₄	1	4	yes	complemented
284	#215	C₂×C₃×C₄	1	4	yes	complemented
285	#214	C₂×C₃×C₄	1	4	yes	complemented
286	#213	C₂×C₃×C₄	1	4	yes	complemented
287	C₄×Dic₃	—	2	1	no	—
288	C₄×Dic₃	C₂³×C₃	1	2	yes	—
289	#208	—	2	1	no	—
290	#208	C₂³×C₃	1	2	yes	—
291	C₂×C₃⋊C₈	—	2	1	no	—
292	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
293	C₂×C₃⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
294	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
295	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
296	ΓL(1,𝔽₂₅)	—	2	4	no	—
297	D₃×C₈	—	2	4	no	—
298	C₂²×C₃²	—	2	2	no	—
299	C₂²×C₃²	—	2	2	no	—
300	C₂²×C₃²	—	4	2	no	—
301	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
302	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
303	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
304	C₂×C₃×D₃	—	2	2	no	—
305	C₂×C₃×D₃	—	4	2	no	—
306	C₃²×C₄	—	2	2	no	—
307	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
308	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
309	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
310	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₃×Dic₃	—	2	2	no	—
312	C₃×Dic₃	—	4	2	no	—
313	C₂×#41	—	3	1	no	—
314	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
315	#135	—	3	4	no	—
316	#135	—	3	4	no	—
317	C₂×Q₁₆	—	3	1	no	—
318	C₂×SD₁₆	—	3	1	no	—
319	C₂×SD₁₆	—	3	1	no	—
320	C₂×D₈	—	3	1	no	—
321	#131	—	2	2	no	—
322	#131	—	3	4	no	—
323	#131	—	6	2	no	—
324	#131	C₂×C₃×D₃	1	4	yes	complemented
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	3	1	no	—
327	C₂×M₁₆	—	6	1	no	—
328	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	—	3	1	no	—
331	C₂²×C₈	—	6	1	no	—
332	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
333	C₂×C₄²	—	3	1	no	—
334	#108	—	3	4	no	—
335	#104	—	3	4	no	—
336	#104	—	3	4	no	—
337	#97	—	3	4	no	—
338	C₂³×C₃	—	2	2	no	—
339	C₂³×C₃	—	2	1	no	—
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	—	2	1	no	—
342	C₂³×C₃	—	6	1	no	—
343	C₂³×C₃	#235	1	1	yes	characteristic
344	C₂³×C₃	C₃×#41	1	1	yes	characteristic
345	C₂²×D₃	—	2	1	no	—
346	C₃×Q₈	—	2	2	no	—
347	C₃×Q₈	—	2	1	no	—
348	C₃×Q₈	—	2	1	no	—
349	C₃×Q₈	—	2	2	no	—
350	C₃×Q₈	—	3	2	no	—
351	C₃×Q₈	—	6	1	no	—
352	C₃×Q₈	C₂×C₄×D₃	1	2	yes	—
353	C₃×Q₈	C₂²×C₃×C₄	1	2	yes	—
354	C₃×D₄	—	2	4	no	—
355	C₃×D₄	—	2	4	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	2	2	no	—
364	C₃×D₄	—	3	2	no	—
365	C₃×D₄	—	6	2	no	—
366	C₃×D₄	—	6	2	no	—
367	C₃×D₄	—	6	1	no	—
368	C₃×D₄	C₂×C₄×D₃	1	2	yes	—
369	C₃×D₄	C₂²×C₃×C₄	1	2	yes	—
370	C₂×C₃×C₄	—	2	4	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	4	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	6	1	no	—
386	C₂×C₃×C₄	—	6	2	no	—
387	C₂×C₃×C₄	—	6	2	no	—
388	C₂×C₃×C₄	—	6	2	no	—
389	C₂×C₃×C₄	—	12	2	no	—
390	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
392	C₂×C₃×C₄	#235	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
399	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
402	#67	—	2	2	no	—
403	#67	—	2	2	no	—
404	C₂×Dic₃	—	2	1	no	—
405	C₂×Dic₃	—	2	2	no	—
406	C₂×Dic₃	—	4	2	no	—
407	D₁₂	—	2	1	no	—
408	D₁₂	C₂²×C₃×C₄	1	2	yes	—
409	C₄×D₃	—	2	2	no	—
410	C₄×D₃	—	2	2	no	—
411	Dic₆	—	2	1	no	—
412	Dic₆	C₂²×C₃×C₄	1	2	yes	—
413	C₃×C₈	—	2	4	no	—
414	C₃×C₈	—	2	2	no	—
415	C₃×C₈	—	2	2	no	—
416	C₃×C₈	—	2	2	no	—
417	C₃×C₈	—	2	2	no	—
418	C₃×C₈	—	3	2	no	—
419	C₃×C₈	—	3	2	no	—
420	C₃×C₈	—	6	2	no	—
421	C₃×C₈	C₂×#67	1	2	yes	—
422	C₃×C₈	C₂×#67	1	2	yes	—
423	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
424	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
425	C₃⋊C₈	—	2	2	no	—
426	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
427	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
428	C₂×C₃²	—	2	1	no	—
429	C₂×C₃²	—	2	1	no	—
430	C₂×C₃²	—	4	2	no	—
431	C₂×C₃²	#444	1	2	yes	complemented
432	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
433	C₃×D₃	—	4	2	no	—
434	#41	—	2	1	no	—
435	#41	—	2	1	no	—
436	#41	—	3	2	no	—
437	#41	—	3	2	no	—
438	#41	—	6	1	no	—
439	#41	—	6	1	no	—
440	#41	C₃×C₄×D₃	1	2	yes	—
441	#41	C₂²×C₃×D₃	1	2	yes	—
442	C₂×Q₈	—	3	1	no	—
443	C₂×Q₈	C₃×C₄×D₃	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	3	1	no	—
446	C₂×D₄	—	6	1	no	—
447	C₂×D₄	C₃×C₄×D₃	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	6	1	no	—
450	C₂²×C₄	—	6	1	no	—
451	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
452	Q₁₆	—	3	4	no	—
453	SD₁₆	—	3	4	no	—
454	SD₁₆	—	3	4	no	—
455	D₈	—	3	4	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	2	4	no	—
458	M₁₆	—	3	2	no	—
459	M₁₆	—	6	1	no	—
460	M₁₆	—	6	4	no	—
461	M₁₆	C₂²×C₃×D₃	1	2	yes	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	4	no	—
464	C₂×C₈	—	3	2	no	—
465	C₂×C₈	—	3	1	no	—
466	C₂×C₈	—	3	1	no	—
467	C₂×C₈	—	3	2	no	—
468	C₂×C₈	—	6	1	no	—
469	C₂×C₈	—	6	4	no	—
470	C₂×C₈	C₃×#67	1	1	yes	characteristic
471	C₂×C₈	C₃×#67	1	1	yes	characteristic
472	C₂×C₈	C₃×#67	1	2	yes	—
473	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
474	C₄²	—	3	2	no	—
475	C₄²	—	6	1	no	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	4	no	—
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	4	4	no	—
486	C₂²×C₃	—	4	2	no	—
487	C₂²×C₃	—	4	2	no	—
488	C₂²×C₃	—	6	2	no	—
489	C₂²×C₃	—	12	2	no	—
490	C₂²×C₃	C₄×#67	1	1	yes	characteristic
491	C₂²×C₃	C₄×#67	1	1	yes	characteristic
492	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
493	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
494	C₂²×C₃	C₂×#235	1	1	yes	characteristic
495	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
496	C₂×D₃	—	2	2	no	—
497	C₂×D₃	—	4	2	no	—
498	C₃×C₄	—	2	4	no	—
499	C₃×C₄	—	2	2	no	—
500	C₃×C₄	—	2	2	no	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	6	2	no	—
506	C₃×C₄	—	12	2	no	—
507	C₃×C₄	C₄×#67	1	1	yes	characteristic
508	C₃×C₄	C₄×#67	1	1	yes	characteristic
509	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
510	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
511	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
512	C₃×C₄	C₂²×#67	1	1	yes	characteristic
513	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
514	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
515	Dic₃	—	2	2	no	—
516	Dic₃	—	4	2	no	—
517	C₃²	C₂×#444	1	1	yes	characteristic, complemented, Sylow
518	C₂³	—	2	1	no	—
519	C₂³	—	6	1	no	—
520	C₂³	C₃×#235	1	1	yes	characteristic
521	Q₈	—	2	1	no	—
522	Q₈	—	3	2	no	—
523	Q₈	—	6	1	no	—
524	Q₈	C₂×C₃×C₄×D₃	1	2	yes	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	1	no	—
528	D₄	—	3	2	no	—
529	D₄	—	6	2	no	—
530	D₄	—	6	2	no	—
531	D₄	—	6	1	no	—
532	D₄	C₂×C₃×C₄×D₃	1	2	yes	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	6	1	no	—
537	C₂×C₄	—	6	2	no	—
538	C₂×C₄	—	6	2	no	—
539	C₂×C₄	—	6	2	no	—
540	C₂×C₄	—	12	2	no	—
541	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
542	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
543	C₂×C₄	C₃×#235	1	1	yes	characteristic
544	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
545	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
546	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	3	2	no	—
549	C₈	—	3	2	no	—
550	C₈	—	6	2	no	—
551	C₈	C₂×C₃×#67	1	2	yes	—
552	C₈	C₂×C₃×#67	1	2	yes	—
553	C₂×C₃	—	2	1	no	—
554	C₂×C₃	—	2	1	no	—
555	C₂×C₃	—	2	1	no	—
556	C₂×C₃	—	2	1	no	—
557	C₂×C₃	—	2	1	no	—
558	C₂×C₃	—	2	2	no	—
559	C₂×C₃	—	4	1	no	—
560	C₂×C₃	—	4	1	no	—
561	C₂×C₃	—	4	4	no	—
562	C₂×C₃	—	4	2	no	—
563	C₂×C₃	—	4	2	no	—
564	C₂×C₃	—	12	2	no	—
565	C₂×C₃	#5145	1	2	yes	direct product factor
566	C₂×C₃	C₃×#444	1	2	yes	complemented
567	C₂×C₃	C₂×C₄×#67	1	1	yes	characteristic
568	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
569	D₃	—	4	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	4	2	no	—
573	C₂²	—	6	2	no	—
574	C₂²	—	12	2	no	—
575	C₂²	C₃×C₄×#67	1	1	yes	characteristic
576	C₂²	C₃×C₄×#67	1	1	yes	characteristic
577	C₂²	C₂×C₃×#235	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	6	2	no	—
580	C₄	—	12	2	no	—
581	C₄	C₃×C₄×#67	1	1	yes	characteristic
582	C₄	C₃×C₄×#67	1	1	yes	characteristic
583	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
584	C₄	C₂²×C₃×#67	1	1	yes	characteristic
585	C₃	—	2	1	no	—
586	C₃	C₂×#5145	1	1	yes	characteristic, direct product factor
587	C₃	C₂×C₃×#444	1	1	yes	characteristic, complemented
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	4	2	no	—
591	C₂	—	12	2	no	—
592	C₂	C₃×#5145	1	2	yes	direct product factor
593	C₂	C₂×C₃×C₄×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×#67
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×C₃×#950	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₂×C₃×#444
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#131	C₂	semidirect
3. C₂×C₃×#901	C₂	semidirect
4. C₂×C₃×#837	C₂	semidirect
5. C₃×#5145	C₂	direct (N × H)
6. C₂×C₃×#825	C₂	semidirect
7. C₂×C₃×#822	C₂	semidirect
8. C₂×C₃×#815	C₂	semidirect
10. C₂×#5145	C₃	direct (N × H)
14. C₃²×#131	C₂²	semidirect
19. C₃×#950	C₄	semidirect
21. C₂×C₃×#216	C₄	semidirect
22. C₂×C₃×#215	C₄	semidirect
23. C₂×C₃×#214	C₄	semidirect
24. C₂×C₃×#213	C₄	semidirect
29. C₃×#901	C₂²	semidirect
32. C₃×#837	C₂²	semidirect
33. C₃×#825	C₂²	semidirect
34. C₃×#822	C₂²	semidirect
35. C₃×#815	C₂²	semidirect
39. C₂×C₃×#131	D₃	semidirect
40. C₂×C₃×#131	C₂×C₃	semidirect
42. C₂×#901	C₂×C₃	semidirect
48. C₂×#837	C₂×C₃	semidirect
49. #5145	C₂×C₃	direct (N × H)
50. C₂×#825	C₂×C₃	semidirect
51. C₂×#822	C₂×C₃	semidirect
52. C₂×#815	C₂×C₃	semidirect
80. C₃×#216	C₂×C₄	semidirect
81. C₃×#215	C₂×C₄	semidirect
82. C₃×#214	C₂×C₄	semidirect
83. C₃×#213	C₂×C₄	semidirect
113. C₃×#131	C₂×D₃	semidirect
114. C₃×#131	C₂²×C₃	semidirect
132. #950	C₃×C₄	semidirect
134. C₂×#216	C₃×C₄	semidirect
135. C₂×#215	C₃×C₄	semidirect
136. C₂×#214	C₃×C₄	semidirect
137. C₂×#213	C₃×C₄	semidirect
142. #901	C₂²×C₃	semidirect
149. #837	C₂²×C₃	semidirect
150. #825	C₂²×C₃	semidirect
151. #822	C₂²×C₃	semidirect
152. #815	C₂²×C₃	semidirect
190. C₂×#131	C₃×D₃	semidirect
283. #216	C₂×C₃×C₄	semidirect
284. #215	C₂×C₃×C₄	semidirect
285. #214	C₂×C₃×C₄	semidirect
286. #213	C₂×C₃×C₄	semidirect
324. #131	C₂×C₃×D₃	semidirect
431. C₂×C₃²	#444	semidirect
517. C₃²	C₂×#444	semidirect
565. C₂×C₃	#5145	direct (N × H)
566. C₂×C₃	C₃×#444	semidirect
586. C₃	C₂×#5145	direct (N × H)
587. C₃	C₂×C₃×#444	semidirect
592. C₂	C₃×#5145	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#131	2
C₂×C₃×#950	2
C₂×C₃×#901	2
C₂×C₃×#837	2
C₃×#5145	2
C₂×C₃×#825	2
C₂×C₃×#822	2
C₂×C₃×#815	2
C₂×C₃×#444	3
C₂×#5145	3

Subgroups — C2×C3×#5145 #11861036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#5145 #11861036