Subgroups — C₃×#10589711 #13152812

Order 1728.

1378 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄×D₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63502	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63499	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#611	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63457	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#63455	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#63446	C₂	1	2	yes	maximal, complemented
11	C₃×#63444	C₂	1	2	yes	maximal, complemented
12	C₃×#5609	—	3	1	no	maximal
13	#10589711	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₃×D₉	C₂²	1	2	yes	complemented
15	C₂³×C₃×D₉	C₂²	1	2	yes	complemented
16	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
17	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₃×#611	C₂²	1	1	yes	characteristic
20	C₂×C₃×#611	C₂²	1	2	yes	complemented
21	C₂×C₃×#611	C₂²	1	2	yes	complemented
22	C₂×C₃×#611	C₂²	1	2	yes	complemented
23	C₃×D₄×D₉	—	2	8	no	—
24	C₃×D₄×D₉	—	2	4	no	—
25	C₂×C₃×D₃₆	—	2	4	no	—
26	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×D₃₆	C₂²	1	2	yes	complemented
29	C₂×C₃×D₃₆	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄×D₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄×D₉	C₂²	1	2	yes	complemented
32	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
34	C₃×#3676	C₂²	1	1	yes	characteristic, complemented
35	C₃×(C₂×D₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	complemented
37	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	complemented
38	C₃×Dic₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₃×C₄×Dic₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×D₃×D₄	—	3	1	no	—
41	C₂×C₃×D₃×D₄	—	3	2	no	—
42	C₂²×C₃×D₁₂	—	3	1	no	—
43	C₃²×#121	D₃	1	1	yes	characteristic
44	C₃×#940	—	3	1	no	—
45	C₃×#937	—	3	2	no	—
46	C₃×C₄×#67	—	3	1	no	—
47	C₃×#895	—	3	1	no	—
48	C₃×#893	—	3	1	no	—
49	C₃×#884	—	3	2	no	—
50	C₃×#882	—	3	2	no	—
51	C₂×D₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×D₄×D₉	C₂×C₃	1	2	yes	complemented
53	C₂²×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
54	C₉×#121	—	2	1	no	—
55	C₉×#121	C₂×C₃	1	1	yes	characteristic, complemented
56	#63502	C₂×C₃	1	1	yes	characteristic, complemented
57	#63499	C₂×C₃	1	2	yes	complemented
58	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
59	#63457	C₂×C₃	1	1	yes	characteristic, complemented
60	#63455	C₂×C₃	1	1	yes	characteristic, complemented
61	#63446	C₂×C₃	1	2	yes	complemented
62	#63444	C₂×C₃	1	2	yes	complemented
63	C₂³×C₃×C₉	C₂³	1	2	yes	—
64	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
65	C₂²×C₃×D₉	—	2	4	no	—
66	C₂²×C₃×D₉	—	2	4	no	—
67	C₂²×C₃×D₉	—	2	4	no	—
68	C₂²×C₃×D₉	—	2	4	no	—
69	C₂²×C₃×D₉	—	4	2	no	—
70	C₂²×C₃×D₉	—	4	2	no	—
71	C₂²×C₃×D₉	C₂³	1	2	yes	—
72	C₂²×C₃×D₉	C₂³	1	2	yes	—
73	C₂²×C₃×D₉	C₂³	1	1	yes	characteristic
74	C₃×D₄×C₉	—	2	4	no	—
75	C₃×D₄×C₉	—	2	2	no	—
76	C₂×C₃×C₄×C₉	—	2	2	no	—
77	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
78	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₃×#611	—	2	4	no	—
81	C₃×#611	—	2	4	no	—
82	C₃×#611	—	4	2	no	—
83	C₃×#611	D₄	1	4	yes	complemented
84	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
86	C₂×C₃×Dic₉	C₂³	1	1	yes	characteristic
87	C₃×D₃₆	—	2	4	no	—
88	C₃×D₃₆	—	2	4	no	—
89	C₃×D₃₆	—	2	2	no	—
90	C₃×D₃₆	D₄	1	4	yes	complemented
91	C₃×C₄×D₉	—	2	2	no	—
92	C₃×C₄×D₉	—	2	4	no	—
93	C₃×D₄²	—	9	1	no	—
94	#5609	—	3	1	no	—
95	C₂³×C₃×D₃	—	3	2	no	—
96	C₂³×C₃×D₃	—	3	2	no	—
97	C₂×C₃²×D₄	C₂×D₃	1	2	yes	—
98	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
100	C₂×C₃×#67	—	3	1	no	—
101	C₂×C₃×#67	—	3	2	no	—
102	C₂×C₃×#67	—	3	2	no	—
103	C₂×C₃×#67	—	3	2	no	—
104	C₃×D₃×D₄	—	6	4	no	—
105	C₃×D₃×D₄	—	6	8	no	—
106	C₂×C₃×D₁₂	—	3	1	no	—
107	C₂×C₃×D₁₂	—	3	2	no	—
108	C₂×C₃×D₁₂	—	3	2	no	—
109	C₂×C₃×D₁₂	—	3	1	no	—
110	C₂×C₃×D₁₂	—	6	4	no	—
111	C₂×C₃×C₄×D₃	—	3	2	no	—
112	C₂×C₃×C₄×D₃	—	3	1	no	—
113	C₂³×D₉	C₂²×C₃	1	2	yes	complemented
114	C₂³×D₉	C₂²×C₃	1	2	yes	complemented
115	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
116	C₃²×C₂²⋊C₄	C₂×D₃	1	2	yes	—
117	C₃×#217	—	3	1	no	—
118	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
119	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
120	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
121	C₃×Dic₃⋊C₄	—	3	1	no	—
122	C₃×C₄×Dic₃	—	3	1	no	—
123	C₂×D₄×C₉	—	2	1	no	—
124	C₂×D₄×C₉	—	2	2	no	—
125	C₂×D₄×C₉	C₂²×C₃	1	2	yes	complemented
126	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₂²×C₄×C₉	—	2	1	no	—
128	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×#611	C₂²×C₃	1	1	yes	characteristic
130	C₂×#611	C₂²×C₃	1	2	yes	complemented
131	C₂×#611	C₂²×C₃	1	2	yes	complemented
132	C₂×#611	C₂²×C₃	1	2	yes	complemented
133	D₄×D₉	—	2	8	no	—
134	D₄×D₉	—	2	4	no	—
135	C₂×D₃₆	—	2	4	no	—
136	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
137	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂×D₃₆	C₂²×C₃	1	2	yes	complemented
139	C₂×D₃₆	C₂²×C₃	1	2	yes	complemented
140	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
141	C₂×C₄×D₉	C₂²×C₃	1	2	yes	complemented
142	C₉×C₄⋊C₄	—	2	1	no	—
143	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
144	C₉×C₂²⋊C₄	—	2	2	no	—
145	C₉×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
146	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
147	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
148	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	complemented
149	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	complemented
150	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
151	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂²×C₃×C₉	—	2	1	no	—
153	C₂²×C₃×C₉	—	2	1	no	—
154	C₂²×C₃×C₉	—	2	2	no	—
155	C₂²×C₃×C₉	—	2	2	no	—
156	C₂²×C₃×C₉	—	2	2	no	—
157	C₂²×C₃×C₉	C₂×D₄	1	2	yes	complemented
158	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₃×D₉	—	2	1	no	—
160	C₂×C₃×D₉	—	2	2	no	—
161	C₂×C₃×D₉	—	2	2	no	—
162	C₂×C₃×D₉	—	2	1	no	—
163	C₂×C₃×D₉	—	2	2	no	—
164	C₂×C₃×D₉	—	2	2	no	—
165	C₂×C₃×D₉	—	2	2	no	—
166	C₂×C₃×D₉	—	4	8	no	—
167	C₂×C₃×D₉	—	4	8	no	—
168	C₂×C₃×D₉	C₂×D₄	1	2	yes	complemented
169	C₂×C₃×D₉	C₂×D₄	1	4	yes	complemented
170	C₃×C₄×C₉	—	2	2	no	—
171	C₃×C₄×C₉	—	2	1	no	—
172	C₃×C₄×C₉	C₂×D₄	1	2	yes	complemented
173	C₃×Dic₉	—	2	1	no	—
174	C₃×Dic₉	—	2	1	no	—
175	C₃×Dic₉	C₂×D₄	1	2	yes	complemented
176	C₂²×C₃×D₄	—	9	2	no	—
177	C₂²×C₃×D₄	—	9	1	no	—
178	C₂²×C₃×D₄	—	9	1	no	—
179	C₂×D₃×D₄	—	3	2	no	—
180	C₂×D₃×D₄	—	3	1	no	—
181	C₂²×D₁₂	—	3	1	no	—
182	C₃×#127	—	9	1	no	—
183	C₃×#121	—	2	1	no	—
184	C₃×#121	—	9	1	no	—
185	C₃×#121	—	9	2	no	—
186	C₃×#121	D₉	1	1	yes	characteristic, complemented
187	C₃×#121	C₃×D₃	1	1	yes	characteristic
188	C₃×#120	—	9	2	no	—
189	C₃×#120	—	9	2	no	—
190	C₃×C₄×D₄	—	9	1	no	—
191	C₃×C₄×D₄	—	9	1	no	—
192	#940	—	3	1	no	—
193	#937	—	3	2	no	—
194	C₄×#67	—	3	1	no	—
195	#895	—	3	1	no	—
196	#893	—	3	1	no	—
197	#884	—	3	2	no	—
198	#882	—	3	2	no	—
199	C₂³×C₃²	C₂²×D₃	1	2	yes	—
200	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
201	C₂²×C₃×D₃	—	3	2	no	—
202	C₂²×C₃×D₃	—	3	1	no	—
203	C₂²×C₃×D₃	—	3	2	no	—
204	C₂²×C₃×D₃	—	6	4	no	—
205	C₂²×C₃×D₃	—	6	4	no	—
206	C₂²×C₃×D₃	—	6	4	no	—
207	C₂²×C₃×D₃	—	6	4	no	—
208	C₂²×C₃×D₃	—	12	2	no	—
209	C₂²×C₃×D₃	—	12	2	no	—
210	C₃²×D₄	—	2	4	no	—
211	C₃²×D₄	—	2	2	no	—
212	C₂×C₃²×C₄	—	2	2	no	—
213	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
215	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
216	C₃×#67	—	3	4	no	—
217	C₃×#67	—	6	4	no	—
218	C₃×#67	—	6	4	no	—
219	C₃×#67	—	12	2	no	—
220	C₂×C₃×Dic₃	—	3	1	no	—
221	C₂×C₃×Dic₃	—	3	1	no	—
222	C₂×C₃×Dic₃	—	3	1	no	—
223	C₃×D₁₂	—	3	4	no	—
224	C₃×D₁₂	—	6	4	no	—
225	C₃×D₁₂	—	6	4	no	—
226	C₃×D₁₂	—	6	2	no	—
227	C₃×C₄×D₃	—	6	4	no	—
228	C₃×C₄×D₃	—	6	2	no	—
229	C₂³×C₉	—	2	1	no	—
230	C₂³×C₉	—	2	2	no	—
231	C₂³×C₉	C₂³×C₃	1	2	yes	—
232	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
233	C₂²×D₉	—	2	4	no	—
234	C₂²×D₉	—	2	4	no	—
235	C₂²×D₉	—	2	4	no	—
236	C₂²×D₉	—	2	4	no	—
237	C₂²×D₉	—	4	2	no	—
238	C₂²×D₉	—	4	2	no	—
239	C₂²×D₉	C₂³×C₃	1	2	yes	—
240	C₂²×D₉	C₂³×C₃	1	2	yes	—
241	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
242	D₄×C₉	—	2	4	no	—
243	D₄×C₉	—	2	2	no	—
244	D₄×C₉	—	4	2	no	—
245	D₄×C₉	—	4	4	no	—
246	C₂×C₄×C₉	—	2	2	no	—
247	C₂×C₄×C₉	—	2	1	no	—
248	C₂×C₄×C₉	—	2	1	no	—
249	C₂×C₄×C₉	—	2	2	no	—
250	C₂×C₄×C₉	—	4	2	no	—
251	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
252	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
253	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
254	#611	—	2	4	no	—
255	#611	—	2	4	no	—
256	#611	—	4	2	no	—
257	#611	C₃×D₄	1	4	yes	complemented
258	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
259	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
260	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
261	D₃₆	—	2	4	no	—
262	D₃₆	—	2	4	no	—
263	D₃₆	—	2	2	no	—
264	D₃₆	C₃×D₄	1	4	yes	complemented
265	C₄×D₉	—	2	2	no	—
266	C₄×D₉	—	2	4	no	—
267	D₄²	—	9	1	no	Sylow
268	C₂×C₃×C₉	—	2	2	no	—
269	C₂×C₃×C₉	—	4	2	no	—
270	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
273	C₃×D₉	—	2	2	no	—
274	C₃×D₉	—	2	4	no	—
275	C₃×D₉	—	4	2	no	—
276	C₂⁴×C₃	—	9	2	no	—
277	C₂⁴×C₃	—	9	2	no	—
278	C₂³×D₃	—	3	2	no	—
279	C₂³×D₃	—	3	2	no	—
280	C₂×C₃×D₄	—	2	2	no	—
281	C₂×C₃×D₄	—	2	1	no	—
282	C₂×C₃×D₄	—	9	1	no	—
283	C₂×C₃×D₄	—	9	2	no	—
284	C₂×C₃×D₄	—	9	2	no	—
285	C₂×C₃×D₄	—	9	2	no	—
286	C₂×C₃×D₄	—	9	1	no	—
287	C₂×C₃×D₄	—	9	2	no	—
288	C₂×C₃×D₄	—	9	2	no	—
289	C₂×C₃×D₄	—	9	1	no	—
290	C₂×C₃×D₄	—	18	4	no	—
291	C₂×C₃×D₄	—	18	8	no	—
292	C₂×C₃×D₄	—	18	4	no	—
293	C₂×C₃×D₄	C₂×D₉	1	2	yes	complemented
294	C₂×C₃×D₄	C₂×D₉	1	1	yes	characteristic, complemented
295	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
296	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	—	9	2	no	—
299	C₂²×C₃×C₄	—	9	1	no	—
300	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic, complemented
301	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
302	C₂×#67	—	3	1	no	—
303	C₂×#67	—	3	2	no	—
304	C₂×#67	—	3	2	no	—
305	C₂×#67	—	3	2	no	—
306	D₃×D₄	—	6	4	no	—
307	D₃×D₄	—	6	8	no	—
308	C₂×D₁₂	—	3	1	no	—
309	C₂×D₁₂	—	3	2	no	—
310	C₂×D₁₂	—	3	2	no	—
311	C₂×D₁₂	—	3	1	no	—
312	C₂×D₁₂	—	6	4	no	—
313	C₂×C₄×D₃	—	3	2	no	—
314	C₂×C₄×D₃	—	3	1	no	—
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₄⋊C₄	—	9	1	no	—
317	C₃×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic, complemented
318	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	—	2	2	no	—
320	C₃×C₂²⋊C₄	—	9	1	no	—
321	C₃×C₂²⋊C₄	—	9	2	no	—
322	C₃×C₂²⋊C₄	—	9	1	no	—
323	C₃×C₂²⋊C₄	—	9	2	no	—
324	C₃×C₂²⋊C₄	C₂×D₉	1	2	yes	complemented
325	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
326	C₃×C₄²	—	9	1	no	—
327	#217	—	3	1	no	—
328	(C₂×D₃)⋊C₄	—	3	1	no	—
329	(C₂×D₃)⋊C₄	—	3	2	no	—
330	(C₂×D₃)⋊C₄	—	3	2	no	—
331	Dic₃⋊C₄	—	3	1	no	—
332	C₄×Dic₃	—	3	1	no	—
333	C₂²×C₃²	—	2	1	no	—
334	C₂²×C₃²	—	2	1	no	—
335	C₂²×C₃²	—	2	2	no	—
336	C₂²×C₃²	—	2	2	no	—
337	C₂²×C₃²	—	2	2	no	—
338	C₂²×C₃²	D₃×D₄	1	2	yes	—
339	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
340	C₂×C₃×D₃	—	3	4	no	—
341	C₂×C₃×D₃	—	3	2	no	—
342	C₂×C₃×D₃	—	6	2	no	—
343	C₂×C₃×D₃	—	6	1	no	—
344	C₂×C₃×D₃	—	6	2	no	—
345	C₂×C₃×D₃	—	6	1	no	—
346	C₂×C₃×D₃	—	6	2	no	—
347	C₂×C₃×D₃	—	6	2	no	—
348	C₂×C₃×D₃	—	6	2	no	—
349	C₂×C₃×D₃	—	12	8	no	—
350	C₂×C₃×D₃	—	12	8	no	—
351	C₃²×C₄	—	2	2	no	—
352	C₃²×C₄	—	2	1	no	—
353	C₃²×C₄	D₃×D₄	1	2	yes	—
354	C₃×Dic₃	—	3	2	no	—
355	C₃×Dic₃	—	6	1	no	—
356	C₃×Dic₃	—	6	1	no	—
357	C₂²×C₉	—	2	1	no	—
358	C₂²×C₉	—	2	1	no	—
359	C₂²×C₉	—	2	2	no	—
360	C₂²×C₉	—	2	2	no	—
361	C₂²×C₉	—	2	2	no	—
362	C₂²×C₉	—	2	1	no	—
363	C₂²×C₉	—	2	2	no	—
364	C₂²×C₉	—	4	1	no	—
365	C₂²×C₉	—	4	1	no	—
366	C₂²×C₉	—	4	2	no	—
367	C₂²×C₉	—	4	2	no	—
368	C₂²×C₉	—	4	2	no	—
369	C₂²×C₉	C₂×C₃×D₄	1	2	yes	complemented
370	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
371	C₂×D₉	—	2	1	no	—
372	C₂×D₉	—	2	2	no	—
373	C₂×D₉	—	2	2	no	—
374	C₂×D₉	—	2	1	no	—
375	C₂×D₉	—	2	2	no	—
376	C₂×D₉	—	2	2	no	—
377	C₂×D₉	—	2	2	no	—
378	C₂×D₉	—	4	8	no	—
379	C₂×D₉	—	4	8	no	—
380	C₂×D₉	C₂×C₃×D₄	1	2	yes	complemented
381	C₂×D₉	C₂×C₃×D₄	1	4	yes	complemented
382	C₄×C₉	—	2	2	no	—
383	C₄×C₉	—	2	1	no	—
384	C₄×C₉	—	2	2	no	—
385	C₄×C₉	—	4	1	no	—
386	C₄×C₉	—	4	2	no	—
387	C₄×C₉	C₂×C₃×D₄	1	2	yes	complemented
388	Dic₉	—	2	1	no	—
389	Dic₉	—	2	1	no	—
390	Dic₉	C₂×C₃×D₄	1	2	yes	complemented
391	C₂²×D₄	—	9	2	no	—
392	C₂²×D₄	—	9	1	no	—
393	C₂²×D₄	—	9	1	no	—
394	#127	—	9	1	no	—
395	#121	—	9	1	no	—
396	#121	—	9	2	no	—
397	#121	C₃×D₉	1	1	yes	characteristic, complemented
398	#120	—	9	2	no	—
399	#120	—	9	2	no	—
400	C₄×D₄	—	9	1	no	—
401	C₄×D₄	—	9	1	no	—
402	C₃×C₉	D₄²	1	1	yes	characteristic, complemented, Sylow
403	C₂³×C₃	—	2	1	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	9	1	no	—
406	C₂³×C₃	—	9	2	no	—
407	C₂³×C₃	—	9	2	no	—
408	C₂³×C₃	—	18	4	no	—
409	C₂³×C₃	—	18	4	no	—
410	C₂³×C₃	—	18	4	no	—
411	C₂³×C₃	—	18	4	no	—
412	C₂³×C₃	—	36	2	no	—
413	C₂³×C₃	—	36	2	no	—
414	C₂³×C₃	C₂²×D₉	1	2	yes	—
415	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
416	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
417	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
418	C₂²×D₃	—	3	2	no	—
419	C₂²×D₃	—	3	1	no	—
420	C₂²×D₃	—	3	2	no	—
421	C₂²×D₃	—	6	4	no	—
422	C₂²×D₃	—	6	4	no	—
423	C₂²×D₃	—	6	4	no	—
424	C₂²×D₃	—	6	4	no	—
425	C₂²×D₃	—	12	2	no	—
426	C₂²×D₃	—	12	2	no	—
427	C₃×D₄	—	2	4	no	—
428	C₃×D₄	—	2	4	no	—
429	C₃×D₄	—	2	2	no	—
430	C₃×D₄	—	2	2	no	—
431	C₃×D₄	—	4	2	no	—
432	C₃×D₄	—	4	4	no	—
433	C₃×D₄	—	9	4	no	—
434	C₃×D₄	—	9	4	no	—
435	C₃×D₄	—	18	4	no	—
436	C₃×D₄	—	18	4	no	—
437	C₃×D₄	—	18	4	no	—
438	C₃×D₄	—	18	4	no	—
439	C₃×D₄	—	18	2	no	—
440	C₃×D₄	—	36	2	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	4	2	no	—
447	C₂×C₃×C₄	—	9	1	no	—
448	C₂×C₃×C₄	—	9	1	no	—
449	C₂×C₃×C₄	—	9	1	no	—
450	C₂×C₃×C₄	—	18	4	no	—
451	C₂×C₃×C₄	—	18	2	no	—
452	C₂×C₃×C₄	C₂²×D₉	1	2	yes	—
453	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
454	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
455	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
456	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
457	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
458	#67	—	3	4	no	—
459	#67	—	6	4	no	—
460	#67	—	6	4	no	—
461	#67	—	12	2	no	—
462	C₂×Dic₃	—	3	1	no	—
463	C₂×Dic₃	—	3	1	no	—
464	C₂×Dic₃	—	3	1	no	—
465	D₁₂	—	3	4	no	—
466	D₁₂	—	6	4	no	—
467	D₁₂	—	6	4	no	—
468	D₁₂	—	6	2	no	—
469	C₄×D₃	—	6	4	no	—
470	C₄×D₃	—	6	2	no	—
471	C₂×C₃²	—	2	2	no	—
472	C₂×C₃²	—	4	2	no	—
473	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
474	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
475	C₂×C₃²	#1009	1	1	yes	characteristic
476	C₃×D₃	—	6	4	no	—
477	C₃×D₃	—	6	2	no	—
478	C₃×D₃	—	12	2	no	—
479	C₂×C₉	—	2	2	no	—
480	C₂×C₉	—	2	1	no	—
481	C₂×C₉	—	2	1	no	—
482	C₂×C₉	—	2	1	no	—
483	C₂×C₉	—	4	2	no	—
484	C₂×C₉	—	4	2	no	—
485	C₂×C₉	—	8	2	no	—
486	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
487	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
488	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
489	D₉	—	2	2	no	—
490	D₉	—	2	4	no	—
491	D₉	—	4	2	no	—
492	C₂⁴	—	9	2	no	—
493	C₂⁴	—	9	2	no	—
494	C₂×D₄	—	9	1	no	—
495	C₂×D₄	—	9	2	no	—
496	C₂×D₄	—	9	2	no	—
497	C₂×D₄	—	9	2	no	—
498	C₂×D₄	—	9	1	no	—
499	C₂×D₄	—	9	2	no	—
500	C₂×D₄	—	9	2	no	—
501	C₂×D₄	—	9	1	no	—
502	C₂×D₄	—	18	4	no	—
503	C₂×D₄	—	18	8	no	—
504	C₂×D₄	—	18	4	no	—
505	C₂×D₄	C₂×C₃×D₉	1	2	yes	complemented
506	C₂×D₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
507	C₂²×C₄	—	9	2	no	—
508	C₂²×C₄	—	9	1	no	—
509	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
510	C₄⋊C₄	—	9	1	no	—
511	C₄⋊C₄	C₂×C₃×D₉	1	1	yes	characteristic, complemented
512	C₂²⋊C₄	—	9	1	no	—
513	C₂²⋊C₄	—	9	2	no	—
514	C₂²⋊C₄	—	9	1	no	—
515	C₂²⋊C₄	—	9	2	no	—
516	C₂²⋊C₄	C₂×C₃×D₉	1	2	yes	complemented
517	C₄²	—	9	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	4	1	no	—
531	C₂²×C₃	—	4	1	no	—
532	C₂²×C₃	—	4	2	no	—
533	C₂²×C₃	—	4	2	no	—
534	C₂²×C₃	—	4	2	no	—
535	C₂²×C₃	—	9	2	no	—
536	C₂²×C₃	—	9	4	no	—
537	C₂²×C₃	—	18	2	no	—
538	C₂²×C₃	—	18	1	no	—
539	C₂²×C₃	—	18	2	no	—
540	C₂²×C₃	—	18	1	no	—
541	C₂²×C₃	—	18	2	no	—
542	C₂²×C₃	—	18	2	no	—
543	C₂²×C₃	—	18	2	no	—
544	C₂²×C₃	—	36	8	no	—
545	C₂²×C₃	—	36	8	no	—
546	C₂²×C₃	D₄×D₉	1	2	yes	complemented
547	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
548	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
549	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
550	C₂×D₃	—	3	4	no	—
551	C₂×D₃	—	3	2	no	—
552	C₂×D₃	—	6	2	no	—
553	C₂×D₃	—	6	1	no	—
554	C₂×D₃	—	6	2	no	—
555	C₂×D₃	—	6	1	no	—
556	C₂×D₃	—	6	2	no	—
557	C₂×D₃	—	6	2	no	—
558	C₂×D₃	—	6	2	no	—
559	C₂×D₃	—	12	8	no	—
560	C₂×D₃	—	12	8	no	—
561	C₃×C₄	—	2	2	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	2	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	4	1	no	—
567	C₃×C₄	—	4	2	no	—
568	C₃×C₄	—	9	2	no	—
569	C₃×C₄	—	18	1	no	—
570	C₃×C₄	—	18	1	no	—
571	C₃×C₄	D₄×D₉	1	2	yes	complemented
572	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
573	Dic₃	—	3	2	no	—
574	Dic₃	—	6	1	no	—
575	Dic₃	—	6	1	no	—
576	C₃²	#5609	1	1	yes	characteristic
577	C₉	—	2	1	no	—
578	C₉	C₃×D₄²	1	1	yes	characteristic, complemented
579	C₂³	—	9	1	no	—
580	C₂³	—	9	2	no	—
581	C₂³	—	9	2	no	—
582	C₂³	—	18	4	no	—
583	C₂³	—	18	4	no	—
584	C₂³	—	18	4	no	—
585	C₂³	—	18	4	no	—
586	C₂³	—	36	2	no	—
587	C₂³	—	36	2	no	—
588	C₂³	C₂²×C₃×D₉	1	2	yes	—
589	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	9	4	no	—
593	D₄	—	9	4	no	—
594	D₄	—	18	4	no	—
595	D₄	—	18	4	no	—
596	D₄	—	18	4	no	—
597	D₄	—	18	4	no	—
598	D₄	—	18	2	no	—
599	D₄	—	36	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	9	1	no	—
602	C₂×C₄	—	9	1	no	—
603	C₂×C₄	—	9	1	no	—
604	C₂×C₄	—	18	4	no	—
605	C₂×C₄	—	18	2	no	—
606	C₂×C₄	C₂²×C₃×D₉	1	2	yes	—
607	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
608	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
609	C₂×C₃	—	2	2	no	—
610	C₂×C₃	—	2	2	no	—
611	C₂×C₃	—	2	1	no	—
612	C₂×C₃	—	2	1	no	—
613	C₂×C₃	—	2	1	no	—
614	C₂×C₃	—	4	2	no	—
615	C₂×C₃	—	4	2	no	—
616	C₂×C₃	—	4	2	no	—
617	C₂×C₃	—	8	2	no	—
618	C₂×C₃	—	18	4	no	—
619	C₂×C₃	—	18	2	no	—
620	C₂×C₃	—	36	2	no	—
621	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
622	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
623	C₂×C₃	#63715	1	1	yes	characteristic
624	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
625	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
626	C₂×C₃	C₃×#1009	1	1	yes	characteristic
627	D₃	—	6	4	no	—
628	D₃	—	6	2	no	—
629	D₃	—	12	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	9	2	no	—
636	C₂²	—	9	4	no	—
637	C₂²	—	18	2	no	—
638	C₂²	—	18	1	no	—
639	C₂²	—	18	2	no	—
640	C₂²	—	18	1	no	—
641	C₂²	—	18	2	no	—
642	C₂²	—	18	2	no	—
643	C₂²	—	18	2	no	—
644	C₂²	—	36	8	no	—
645	C₂²	—	36	8	no	—
646	C₂²	C₃×D₄×D₉	1	2	yes	complemented
647	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	9	2	no	—
651	C₄	—	18	1	no	—
652	C₄	—	18	1	no	—
653	C₄	C₃×D₄×D₉	1	2	yes	complemented
654	C₃	—	2	1	no	—
655	C₃	#10589711	1	1	yes	characteristic, direct product factor
656	C₃	C₃×#5609	1	1	yes	characteristic
657	C₂	—	2	2	no	—
658	C₂	—	4	2	no	—
659	C₂	—	18	4	no	—
660	C₂	—	18	2	no	—
661	C₂	—	36	2	no	—
662	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
663	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic
664	C₂	C₃×#63715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle	C₂²×C₃²	C₂³×D₃
hypercenter	C₃×#121	D₉
hypocenter	C₉	C₃×D₄²
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₉	C₂	semidirect
2. C₂×C₃×D₄×D₉	C₂	semidirect
3. C₂²×C₃×D₃₆	C₂	semidirect
4. C₃×C₉×#121	C₂	semidirect
5. C₃×#63502	C₂	semidirect
6. C₃×#63499	C₂	semidirect
7. C₃×C₄×#611	C₂	semidirect
8. C₃×#63457	C₂	semidirect
9. C₃×#63455	C₂	semidirect
10. C₃×#63446	C₂	semidirect
11. C₃×#63444	C₂	semidirect
13. #10589711	C₃	direct (N × H)
14. C₂³×C₃×D₉	C₂²	semidirect
15. C₂³×C₃×D₉	C₂²	semidirect
16. C₂×C₃×D₄×C₉	C₂²	semidirect
17. C₂×C₃×D₄×C₉	C₂²	semidirect
18. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₂×C₃×#611	C₂²	semidirect
21. C₂×C₃×#611	C₂²	semidirect
22. C₂×C₃×#611	C₂²	semidirect
27. C₂×C₃×D₃₆	C₂²	semidirect
28. C₂×C₃×D₃₆	C₂²	semidirect
29. C₂×C₃×D₃₆	C₂²	semidirect
30. C₂×C₃×C₄×D₉	C₂²	semidirect
31. C₂×C₃×C₄×D₉	C₂²	semidirect
32. C₃×C₉×C₄⋊C₄	C₂²	semidirect
33. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
34. C₃×#3676	C₂²	semidirect
35. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
36. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
37. C₃×(C₂×D₉)⋊C₄	C₂²	semidirect
38. C₃×Dic₉⋊C₄	C₂²	semidirect
39. C₃×C₄×Dic₉	C₂²	semidirect
51. C₂×D₄×D₉	C₂×C₃	semidirect
52. C₂×D₄×D₉	C₂×C₃	semidirect
53. C₂²×D₃₆	C₂×C₃	semidirect
55. C₉×#121	C₂×C₃	semidirect
56. #63502	C₂×C₃	semidirect
57. #63499	C₂×C₃	semidirect
58. C₄×#611	C₂×C₃	semidirect
59. #63457	C₂×C₃	semidirect
60. #63455	C₂×C₃	semidirect
61. #63446	C₂×C₃	semidirect
62. #63444	C₂×C₃	semidirect
83. C₃×#611	D₄	semidirect
90. C₃×D₃₆	D₄	semidirect
113. C₂³×D₉	C₂²×C₃	semidirect
114. C₂³×D₉	C₂²×C₃	semidirect
125. C₂×D₄×C₉	C₂²×C₃	semidirect
126. C₂×D₄×C₉	C₂²×C₃	semidirect
128. C₂²×C₄×C₉	C₂²×C₃	semidirect
130. C₂×#611	C₂²×C₃	semidirect
131. C₂×#611	C₂²×C₃	semidirect
132. C₂×#611	C₂²×C₃	semidirect
137. C₂×D₃₆	C₂²×C₃	semidirect
138. C₂×D₃₆	C₂²×C₃	semidirect
139. C₂×D₃₆	C₂²×C₃	semidirect
140. C₂×C₄×D₉	C₂²×C₃	semidirect
141. C₂×C₄×D₉	C₂²×C₃	semidirect
143. C₉×C₄⋊C₄	C₂²×C₃	semidirect
145. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
146. #3676	C₂²×C₃	semidirect
147. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
148. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
149. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
150. Dic₉⋊C₄	C₂²×C₃	semidirect
151. C₄×Dic₉	C₂²×C₃	semidirect
157. C₂²×C₃×C₉	C₂×D₄	semidirect
168. C₂×C₃×D₉	C₂×D₄	semidirect
169. C₂×C₃×D₉	C₂×D₄	semidirect
172. C₃×C₄×C₉	C₂×D₄	semidirect
175. C₃×Dic₉	C₂×D₄	semidirect
186. C₃×#121	D₉	semidirect
257. #611	C₃×D₄	semidirect
264. D₃₆	C₃×D₄	semidirect
293. C₂×C₃×D₄	C₂×D₉	semidirect
294. C₂×C₃×D₄	C₂×D₉	semidirect
300. C₂²×C₃×C₄	C₂×D₉	semidirect
317. C₃×C₄⋊C₄	C₂×D₉	semidirect
324. C₃×C₂²⋊C₄	C₂×D₉	semidirect
369. C₂²×C₉	C₂×C₃×D₄	semidirect
380. C₂×D₉	C₂×C₃×D₄	semidirect
381. C₂×D₉	C₂×C₃×D₄	semidirect
387. C₄×C₉	C₂×C₃×D₄	semidirect
390. Dic₉	C₂×C₃×D₄	semidirect
397. #121	C₃×D₉	semidirect
402. C₃×C₉	D₄²	semidirect
505. C₂×D₄	C₂×C₃×D₉	semidirect
506. C₂×D₄	C₂×C₃×D₉	semidirect
509. C₂²×C₄	C₂×C₃×D₉	semidirect
511. C₄⋊C₄	C₂×C₃×D₉	semidirect
516. C₂²⋊C₄	C₂×C₃×D₉	semidirect
546. C₂²×C₃	D₄×D₉	semidirect
571. C₃×C₄	D₄×D₉	semidirect
578. C₉	C₃×D₄²	semidirect
646. C₂²	C₃×D₄×D₉	semidirect
653. C₄	C₃×D₄×D₉	semidirect
655. C₃	#10589711	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×C₃×D₄×D₉	2
C₂²×C₃×D₃₆	2
C₃×C₉×#121	2
C₃×#63502	2
C₃×#63499	2
C₃×C₄×#611	2
C₃×#63457	2
C₃×#63455	2
C₃×#63446	2
C₃×#63444	2
C₃×#5609	3
#10589711	3

Subgroups — C3×#10589711 #13152812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589711 #13152812