Subgroups — C₃²×#5550 #13178930

Order 1728.

2380 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#235	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃²×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#937	C₂	1	2	yes	maximal, complemented
5	C₃²×#930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃²×#894	C₂	1	2	yes	maximal, complemented
8	C₃²×#884	C₂	1	2	yes	maximal, complemented
9	C₃²×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₃²×#875	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃²×C₄×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃²×#546	—	3	1	no	maximal
13	C₃×#5550	C₃	1	4	yes	maximal, direct product factor
14	C₂³×C₃²×D₃	C₂²	1	2	yes	—
15	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃²×#67	C₂²	1	2	yes	complemented
19	C₂×C₃²×#67	C₂²	1	2	yes	complemented
20	C₃²×#235	—	2	4	no	—
21	C₂×C₃²×D₁₂	—	2	4	no	—
22	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
23	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
24	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
25	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
26	C₂×C₃²×C₄×D₃	C₂²	1	2	yes	complemented
27	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
32	C₃²×#217	C₂²	1	2	yes	—
33	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
34	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
35	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
36	C₃²×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₃²×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
38	C₃²×Dic₃⋊C₄	C₂²	1	2	yes	complemented
39	C₂×C₃²×#41	—	3	1	no	—
40	C₂²×C₃²×D₄	—	3	1	no	—
41	C₂×C₃×#235	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃×D₁₂	C₂×C₃	1	4	yes	complemented
43	C₃²×#124	—	3	1	no	—
44	C₃²×#123	—	3	2	no	—
45	C₃²×C₂²⋊Q₈	—	3	1	no	—
46	C₃²×#121	—	3	1	no	—
47	C₃²×#121	—	3	2	no	—
48	C₃²×#120	—	3	2	no	—
49	C₃²×C₄×D₄	—	2	4	no	—
50	C₃²×C₄×D₄	—	3	1	no	—
51	C₃²×C₄×D₄	D₃	1	1	yes	characteristic, complemented
52	C₃²×C₄×D₄	C₂×C₃	1	4	yes	complemented
53	C₂×C₃²×C₂²⋊C₄	—	3	2	no	—
54	C₃×#937	C₂×C₃	1	8	yes	complemented
55	C₃×#930	C₂×C₃	1	4	yes	complemented
56	C₃×#924	C₂×C₃	1	4	yes	complemented
57	C₃×#894	C₂×C₃	1	8	yes	complemented
58	C₃×#884	C₂×C₃	1	8	yes	complemented
59	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	8	yes	complemented
60	C₃×#875	C₂×C₃	1	4	yes	complemented
61	C₃×C₄×D₁₂	C₂×C₃	1	4	yes	complemented
62	C₂³×C₃³	C₂³	1	1	yes	characteristic
63	C₂³×C₃³	C₂³	1	1	yes	characteristic
64	C₂²×C₃²×D₃	—	2	4	no	—
65	C₂²×C₃²×D₃	—	2	4	no	—
66	C₂²×C₃²×D₃	—	4	2	no	—
67	C₂²×C₃²×D₃	C₂³	1	2	yes	—
68	C₂²×C₃²×D₃	C₂³	1	2	yes	—
69	C₃³×D₄	—	2	2	no	—
70	C₂×C₃³×C₄	—	2	2	no	—
71	C₂×C₃³×C₄	—	2	2	no	—
72	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
73	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
74	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
75	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	C₃²×#67	—	2	4	no	—
78	C₃²×#67	—	4	2	no	—
79	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
80	C₂×C₃²×Dic₃	C₂³	1	2	yes	—
81	C₃²×D₁₂	—	2	4	no	—
82	C₃²×D₁₂	—	2	2	no	—
83	C₃²×D₁₂	D₄	1	4	yes	complemented
84	C₃²×C₄×D₃	—	2	4	no	—
85	C₃²×C₄×D₃	—	4	2	no	—
86	C₃²×Dic₆	—	2	2	no	—
87	C₃×#546	—	3	4	no	—
88	#5550	C₃²	1	1	yes	characteristic, direct product factor
89	C₂⁴×C₃²	—	3	2	no	—
90	C₂³×C₃×D₃	C₂²×C₃	1	8	yes	—
91	C₃²×#41	—	6	4	no	—
92	C₂×C₃²×Q₈	—	3	1	no	—
93	C₂×C₃²×D₄	—	2	4	no	—
94	C₂×C₃²×D₄	—	3	2	no	—
95	C₂×C₃²×D₄	—	3	2	no	—
96	C₂×C₃²×D₄	—	3	1	no	—
97	C₂×C₃²×D₄	—	3	2	no	—
98	C₂×C₃²×D₄	—	3	1	no	—
99	C₂×C₃²×D₄	—	6	4	no	—
100	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
101	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
102	C₂²×C₃²×C₄	—	2	4	no	—
103	C₂²×C₃²×C₄	—	2	4	no	—
104	C₂²×C₃²×C₄	—	3	2	no	—
105	C₂²×C₃²×C₄	—	3	2	no	—
106	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
107	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic, complemented
108	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
109	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	complemented
110	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
111	C₂×C₃×#67	C₂²×C₃	1	8	yes	complemented
112	C₃×#235	—	2	16	no	—
113	C₂×C₃×D₁₂	—	2	16	no	—
114	C₂×C₃×D₁₂	C₂²×C₃	1	8	yes	—
115	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
116	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
117	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
118	C₂×C₃×C₄×D₃	C₂²×C₃	1	8	yes	complemented
119	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
120	C₃²×C₄⋊C₄	—	2	4	no	—
121	C₃²×C₄⋊C₄	—	3	1	no	—
122	C₃²×C₄⋊C₄	—	3	2	no	—
123	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
124	C₃²×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
125	C₃²×C₂²⋊C₄	—	2	4	no	—
126	C₃²×C₂²⋊C₄	—	2	4	no	—
127	C₃²×C₂²⋊C₄	—	3	2	no	—
128	C₃²×C₂²⋊C₄	—	3	2	no	—
129	C₃²×C₂²⋊C₄	—	3	2	no	—
130	C₃²×C₂²⋊C₄	—	3	2	no	—
131	C₃²×C₂²⋊C₄	—	3	2	no	—
132	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
134	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
135	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
136	C₃²×C₄²	—	2	4	no	—
137	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
138	C₃²×C₄²	C₂²×C₃	1	4	yes	complemented
139	C₃×#217	C₂²×C₃	1	8	yes	—
140	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
141	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
142	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
143	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	complemented
144	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	complemented
145	C₃×Dic₃⋊C₄	C₂²×C₃	1	8	yes	complemented
146	C₂²×C₃³	—	2	1	no	—
147	C₂²×C₃³	—	2	1	no	—
148	C₂²×C₃³	—	2	1	no	—
149	C₂²×C₃³	—	2	1	no	—
150	C₂²×C₃³	—	2	1	no	—
151	C₂²×C₃³	#41	1	2	yes	complemented
152	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
153	C₂×C₃²×D₃	—	2	2	no	—
154	C₂×C₃²×D₃	—	2	2	no	—
155	C₂×C₃²×D₃	—	2	2	no	—
156	C₂×C₃²×D₃	—	2	2	no	—
157	C₂×C₃²×D₃	—	2	2	no	—
158	C₂×C₃²×D₃	—	4	8	no	—
159	C₂×C₃²×D₃	C₂×D₄	1	4	yes	—
160	C₃³×C₄	—	2	1	no	—
161	C₃³×C₄	—	2	1	no	—
162	C₃³×C₄	—	2	1	no	—
163	C₃³×C₄	—	2	1	no	—
164	C₃³×C₄	C₂×D₄	1	2	yes	—
165	C₃²×Dic₃	—	2	2	no	—
166	C₃²×Dic₃	—	2	2	no	—
167	C₂×C₃×#41	—	3	4	no	—
168	C₂²×C₃×D₄	—	3	4	no	—
169	C₂×#235	C₂×C₃²	1	1	yes	characteristic, complemented
170	C₂²×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
171	C₃×#124	—	3	4	no	—
172	C₃×#123	—	3	8	no	—
173	C₃×C₂²⋊Q₈	—	3	4	no	—
174	C₃×#121	—	3	4	no	—
175	C₃×#121	—	3	8	no	—
176	C₃×#120	—	3	8	no	—
177	C₃×C₄×D₄	—	2	4	no	—
178	C₃×C₄×D₄	—	3	4	no	—
179	C₃×C₄×D₄	C₃×D₃	1	4	yes	complemented
180	C₃×C₄×D₄	C₂×C₃²	1	1	yes	characteristic, complemented
181	C₂×C₃×C₂²⋊C₄	—	3	8	no	—
182	#937	C₂×C₃²	1	2	yes	complemented
183	#930	C₂×C₃²	1	1	yes	characteristic, complemented
184	#924	C₂×C₃²	1	1	yes	characteristic, complemented
185	#894	C₂×C₃²	1	2	yes	complemented
186	#884	C₂×C₃²	1	2	yes	complemented
187	D₃×C₂²⋊C₄	C₂×C₃²	1	2	yes	complemented
188	#875	C₂×C₃²	1	1	yes	characteristic, complemented
189	C₄×D₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
190	C₂³×C₃²	—	2	4	no	—
191	C₂³×C₃²	—	2	4	no	—
192	C₂³×C₃²	—	3	2	no	—
193	C₂³×C₃²	—	3	2	no	—
194	C₂³×C₃²	—	6	4	no	—
195	C₂³×C₃²	—	6	4	no	—
196	C₂³×C₃²	—	12	2	no	—
197	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
198	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
199	C₂³×C₃²	C₂³×C₃	1	4	yes	—
200	C₂³×C₃²	C₂³×C₃	1	4	yes	—
201	C₂²×C₃×D₃	—	2	16	no	—
202	C₂²×C₃×D₃	—	2	16	no	—
203	C₂²×C₃×D₃	—	4	8	no	—
204	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
205	C₂²×C₃×D₃	C₂³×C₃	1	8	yes	—
206	C₃²×Q₈	—	6	2	no	—
207	C₃²×D₄	—	2	16	no	—
208	C₃²×D₄	—	2	2	no	—
209	C₃²×D₄	—	2	8	no	—
210	C₃²×D₄	—	3	4	no	—
211	C₃²×D₄	—	6	4	no	—
212	C₃²×D₄	—	6	4	no	—
213	C₃²×D₄	—	6	2	no	—
214	C₃²×D₄	—	12	2	no	—
215	C₂×C₃²×C₄	—	2	2	no	—
216	C₂×C₃²×C₄	—	2	2	no	—
217	C₂×C₃²×C₄	—	2	4	no	—
218	C₂×C₃²×C₄	—	2	4	no	—
219	C₂×C₃²×C₄	—	2	4	no	—
220	C₂×C₃²×C₄	—	2	4	no	—
221	C₂×C₃²×C₄	—	2	4	no	—
222	C₂×C₃²×C₄	—	2	8	no	—
223	C₂×C₃²×C₄	—	2	8	no	—
224	C₂×C₃²×C₄	—	3	2	no	—
225	C₂×C₃²×C₄	—	3	2	no	—
226	C₂×C₃²×C₄	—	4	8	no	—
227	C₂×C₃²×C₄	—	4	8	no	—
228	C₂×C₃²×C₄	—	6	4	no	—
229	C₂×C₃²×C₄	—	12	2	no	—
230	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
236	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
237	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
238	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
239	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
240	C₃×#67	—	2	16	no	—
241	C₃×#67	—	4	8	no	—
242	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
243	C₂×C₃×Dic₃	C₂³×C₃	1	8	yes	—
244	C₃×D₁₂	—	2	16	no	—
245	C₃×D₁₂	—	2	8	no	—
246	C₃×D₁₂	C₃×D₄	1	16	yes	complemented
247	C₃×C₄×D₃	—	2	16	no	—
248	C₃×C₄×D₃	—	4	8	no	—
249	C₃×Dic₆	—	2	8	no	—
250	#546	—	3	1	no	Sylow
251	C₂×C₃³	—	2	2	no	—
252	C₂×C₃³	—	4	1	no	—
253	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₃³	C₂×#41	1	1	yes	characteristic
255	C₂×C₃³	H(5,𝔽₂)	1	1	yes	characteristic
256	C₃²×D₃	—	2	4	no	—
257	C₃²×D₃	—	4	2	no	—
258	C₂⁴×C₃	—	3	8	no	—
259	C₂³×D₃	C₂²×C₃²	1	2	yes	—
260	C₃×#41	—	6	16	no	—
261	C₂×C₃×Q₈	—	3	4	no	—
262	C₂×C₃×D₄	—	2	4	no	—
263	C₂×C₃×D₄	—	3	8	no	—
264	C₂×C₃×D₄	—	3	8	no	—
265	C₂×C₃×D₄	—	3	4	no	—
266	C₂×C₃×D₄	—	3	8	no	—
267	C₂×C₃×D₄	—	3	4	no	—
268	C₂×C₃×D₄	—	6	16	no	—
269	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
270	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
271	C₂²×C₃×C₄	—	2	4	no	—
272	C₂²×C₃×C₄	—	2	4	no	—
273	C₂²×C₃×C₄	—	3	8	no	—
274	C₂²×C₃×C₄	—	3	8	no	—
275	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
276	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	complemented
277	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
279	C₂×#67	C₂²×C₃²	1	2	yes	complemented
280	C₂×#67	C₂²×C₃²	1	2	yes	complemented
281	#235	—	2	4	no	—
282	C₂×D₁₂	—	2	4	no	—
283	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
284	C₂×D₁₂	C₂²×C₃²	1	2	yes	—
285	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
286	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
287	C₂×C₄×D₃	C₂²×C₃²	1	2	yes	complemented
288	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
289	C₃×C₄⋊C₄	—	2	4	no	—
290	C₃×C₄⋊C₄	—	3	8	no	—
291	C₃×C₄⋊C₄	—	3	4	no	—
292	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
293	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
294	C₃×C₂²⋊C₄	—	2	4	no	—
295	C₃×C₂²⋊C₄	—	2	4	no	—
296	C₃×C₂²⋊C₄	—	3	8	no	—
297	C₃×C₂²⋊C₄	—	3	8	no	—
298	C₃×C₂²⋊C₄	—	3	8	no	—
299	C₃×C₂²⋊C₄	—	3	8	no	—
300	C₃×C₂²⋊C₄	—	3	8	no	—
301	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
302	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	complemented
303	C₃×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic
304	C₃×C₂²⋊C₄	C₂²×C₃²	1	1	yes	characteristic, complemented
305	C₃×C₄²	—	2	4	no	—
306	C₃×C₄²	C₂×C₃×D₃	1	4	yes	complemented
307	C₃×C₄²	C₂²×C₃²	1	1	yes	characteristic, complemented
308	#217	C₂²×C₃²	1	2	yes	—
309	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
310	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
311	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
312	(C₂×D₃)⋊C₄	C₂²×C₃²	1	2	yes	complemented
313	C₄⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
314	Dic₃⋊C₄	C₂²×C₃²	1	2	yes	complemented
315	C₂²×C₃²	—	2	1	no	—
316	C₂²×C₃²	—	2	1	no	—
317	C₂²×C₃²	—	2	8	no	—
318	C₂²×C₃²	—	2	1	no	—
319	C₂²×C₃²	—	2	1	no	—
320	C₂²×C₃²	—	2	1	no	—
321	C₂²×C₃²	—	2	4	no	—
322	C₂²×C₃²	—	2	4	no	—
323	C₂²×C₃²	—	2	8	no	—
324	C₂²×C₃²	—	2	4	no	—
325	C₂²×C₃²	—	2	4	no	—
326	C₂²×C₃²	—	2	4	no	—
327	C₂²×C₃²	—	2	4	no	—
328	C₂²×C₃²	—	3	4	no	—
329	C₂²×C₃²	—	4	4	no	—
330	C₂²×C₃²	—	4	4	no	—
331	C₂²×C₃²	—	4	4	no	—
332	C₂²×C₃²	—	4	4	no	—
333	C₂²×C₃²	—	6	2	no	—
334	C₂²×C₃²	—	6	2	no	—
335	C₂²×C₃²	—	6	2	no	—
336	C₂²×C₃²	—	6	2	no	—
337	C₂²×C₃²	—	6	2	no	—
338	C₂²×C₃²	—	12	8	no	—
339	C₂²×C₃²	#235	1	2	yes	complemented
340	C₂²×C₃²	C₃×#41	1	8	yes	complemented
341	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
342	C₂²×C₃²	C₂⁴×C₃	1	4	yes	—
343	C₂×C₃×D₃	—	2	8	no	—
344	C₂×C₃×D₃	—	2	8	no	—
345	C₂×C₃×D₃	—	2	8	no	—
346	C₂×C₃×D₃	—	2	8	no	—
347	C₂×C₃×D₃	—	2	8	no	—
348	C₂×C₃×D₃	—	4	32	no	—
349	C₂×C₃×D₃	C₂×C₃×D₄	1	16	yes	—
350	C₃²×C₄	—	2	8	no	—
351	C₃²×C₄	—	2	1	no	—
352	C₃²×C₄	—	2	1	no	—
353	C₃²×C₄	—	2	1	no	—
354	C₃²×C₄	—	2	1	no	—
355	C₃²×C₄	—	2	4	no	—
356	C₃²×C₄	—	2	8	no	—
357	C₃²×C₄	—	2	4	no	—
358	C₃²×C₄	—	2	4	no	—
359	C₃²×C₄	—	2	4	no	—
360	C₃²×C₄	—	4	4	no	—
361	C₃²×C₄	—	4	4	no	—
362	C₃²×C₄	—	4	4	no	—
363	C₃²×C₄	—	6	2	no	—
364	C₃²×C₄	—	6	2	no	—
365	C₃²×C₄	D₃×D₄	1	2	yes	—
366	C₃²×C₄	C₂×C₃×D₄	1	8	yes	—
367	C₃×Dic₃	—	2	8	no	—
368	C₃×Dic₃	—	2	8	no	—
369	C₂×#41	—	3	1	no	—
370	C₂²×D₄	—	3	1	no	—
371	#124	—	3	1	no	—
372	#123	—	3	2	no	—
373	C₂²⋊Q₈	—	3	1	no	—
374	#121	—	3	1	no	—
375	#121	—	3	2	no	—
376	#120	—	3	2	no	—
377	C₄×D₄	—	3	1	no	—
378	C₄×D₄	C₃²×D₃	1	1	yes	characteristic, complemented
379	C₂×C₂²⋊C₄	—	3	2	no	—
380	C₃³	#546	1	1	yes	characteristic, complemented, Sylow
381	C₂³×C₃	—	2	4	no	—
382	C₂³×C₃	—	2	4	no	—
383	C₂³×C₃	—	3	8	no	—
384	C₂³×C₃	—	3	8	no	—
385	C₂³×C₃	—	6	16	no	—
386	C₂³×C₃	—	6	16	no	—
387	C₂³×C₃	—	12	8	no	—
388	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
389	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
390	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
391	C₂³×C₃	C₂³×C₃²	1	1	yes	characteristic
392	C₂²×D₃	—	2	4	no	—
393	C₂²×D₃	—	2	4	no	—
394	C₂²×D₃	—	4	2	no	—
395	C₂²×D₃	C₂³×C₃²	1	2	yes	—
396	C₂²×D₃	C₂³×C₃²	1	2	yes	—
397	C₃×Q₈	—	6	8	no	—
398	C₃×D₄	—	2	16	no	—
399	C₃×D₄	—	2	8	no	—
400	C₃×D₄	—	2	2	no	—
401	C₃×D₄	—	3	16	no	—
402	C₃×D₄	—	6	16	no	—
403	C₃×D₄	—	6	16	no	—
404	C₃×D₄	—	6	8	no	—
405	C₃×D₄	—	12	8	no	—
406	C₂×C₃×C₄	—	2	8	no	—
407	C₂×C₃×C₄	—	2	8	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	—	2	2	no	—
410	C₂×C₃×C₄	—	2	4	no	—
411	C₂×C₃×C₄	—	2	4	no	—
412	C₂×C₃×C₄	—	2	4	no	—
413	C₂×C₃×C₄	—	2	4	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	3	8	no	—
416	C₂×C₃×C₄	—	3	8	no	—
417	C₂×C₃×C₄	—	4	8	no	—
418	C₂×C₃×C₄	—	4	8	no	—
419	C₂×C₃×C₄	—	6	16	no	—
420	C₂×C₃×C₄	—	12	8	no	—
421	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
422	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
423	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
424	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
425	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
426	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
429	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
430	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
431	#67	—	2	4	no	—
432	#67	—	4	2	no	—
433	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
434	C₂×Dic₃	C₂³×C₃²	1	2	yes	—
435	D₁₂	—	2	4	no	—
436	D₁₂	—	2	2	no	—
437	D₁₂	C₃²×D₄	1	4	yes	complemented
438	C₄×D₃	—	2	4	no	—
439	C₄×D₃	—	4	2	no	—
440	Dic₆	—	2	2	no	—
441	C₂×C₃²	—	2	2	no	—
442	C₂×C₃²	—	2	4	no	—
443	C₂×C₃²	—	2	4	no	—
444	C₂×C₃²	—	2	4	no	—
445	C₂×C₃²	—	2	8	no	—
446	C₂×C₃²	—	4	8	no	—
447	C₂×C₃²	—	4	8	no	—
448	C₂×C₃²	—	4	1	no	—
449	C₂×C₃²	—	4	4	no	—
450	C₂×C₃²	—	6	4	no	—
451	C₂×C₃²	—	12	2	no	—
452	C₂×C₃²	C₂×#235	1	1	yes	characteristic
453	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
454	C₂×C₃²	#1009	1	1	yes	characteristic
455	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
456	C₂×C₃²	C₂×C₃×#41	1	4	yes	—
457	C₂×C₃²	C₃×H(5,𝔽₂)	1	4	yes	—
458	C₃×D₃	—	2	16	no	—
459	C₃×D₃	—	4	8	no	—
460	C₂⁴	—	3	2	no	—
461	#41	—	6	4	no	—
462	C₂×Q₈	—	3	1	no	—
463	C₂×D₄	—	3	2	no	—
464	C₂×D₄	—	3	2	no	—
465	C₂×D₄	—	3	1	no	—
466	C₂×D₄	—	3	2	no	—
467	C₂×D₄	—	3	1	no	—
468	C₂×D₄	—	6	4	no	—
469	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
470	C₂²×C₄	—	3	2	no	—
471	C₂²×C₄	—	3	2	no	—
472	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
474	C₄⋊C₄	—	3	1	no	—
475	C₄⋊C₄	—	3	2	no	—
476	C₄⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
477	C₂²⋊C₄	—	3	2	no	—
478	C₂²⋊C₄	—	3	2	no	—
479	C₂²⋊C₄	—	3	2	no	—
480	C₂²⋊C₄	—	3	2	no	—
481	C₂²⋊C₄	—	3	2	no	—
482	C₂²⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic
483	C₂²⋊C₄	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
484	C₄²	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
485	C₂²×C₃	—	2	4	no	—
486	C₂²×C₃	—	2	4	no	—
487	C₂²×C₃	—	2	1	no	—
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	8	no	—
490	C₂²×C₃	—	2	4	no	—
491	C₂²×C₃	—	2	4	no	—
492	C₂²×C₃	—	2	4	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	4	no	—
497	C₂²×C₃	—	2	8	no	—
498	C₂²×C₃	—	3	16	no	—
499	C₂²×C₃	—	4	4	no	—
500	C₂²×C₃	—	4	4	no	—
501	C₂²×C₃	—	4	4	no	—
502	C₂²×C₃	—	4	4	no	—
503	C₂²×C₃	—	6	8	no	—
504	C₂²×C₃	—	6	8	no	—
505	C₂²×C₃	—	6	8	no	—
506	C₂²×C₃	—	6	8	no	—
507	C₂²×C₃	—	6	8	no	—
508	C₂²×C₃	—	12	32	no	—
509	C₂²×C₃	C₃×#235	1	8	yes	complemented
510	C₂²×C₃	C₃²×#41	1	2	yes	complemented
511	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
512	C₂²×C₃	C₂⁴×C₃²	1	1	yes	characteristic
513	C₂×D₃	—	2	2	no	—
514	C₂×D₃	—	2	2	no	—
515	C₂×D₃	—	2	2	no	—
516	C₂×D₃	—	2	2	no	—
517	C₂×D₃	—	2	2	no	—
518	C₂×D₃	—	4	8	no	—
519	C₂×D₃	C₂×C₃²×D₄	1	4	yes	—
520	C₃×C₄	—	2	8	no	—
521	C₃×C₄	—	2	4	no	—
522	C₃×C₄	—	2	4	no	—
523	C₃×C₄	—	2	4	no	—
524	C₃×C₄	—	2	4	no	—
525	C₃×C₄	—	2	1	no	—
526	C₃×C₄	—	2	1	no	—
527	C₃×C₄	—	2	1	no	—
528	C₃×C₄	—	2	1	no	—
529	C₃×C₄	—	2	8	no	—
530	C₃×C₄	—	4	4	no	—
531	C₃×C₄	—	4	4	no	—
532	C₃×C₄	—	4	4	no	—
533	C₃×C₄	—	6	8	no	—
534	C₃×C₄	—	6	8	no	—
535	C₃×C₄	C₃×D₃×D₄	1	8	yes	—
536	C₃×C₄	C₂×C₃²×D₄	1	2	yes	—
537	Dic₃	—	2	2	no	—
538	Dic₃	—	2	2	no	—
539	C₃²	—	2	4	no	—
540	C₃²	#5550	1	1	yes	characteristic, direct product factor
541	C₃²	C₃×#546	1	4	yes	complemented
542	C₂³	—	3	2	no	—
543	C₂³	—	3	2	no	—
544	C₂³	—	6	4	no	—
545	C₂³	—	6	4	no	—
546	C₂³	—	12	2	no	—
547	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
548	C₂³	C₂²×C₃²×D₃	1	1	yes	characteristic
549	Q₈	—	6	2	no	—
550	D₄	—	2	2	no	—
551	D₄	—	3	4	no	—
552	D₄	—	6	4	no	—
553	D₄	—	6	4	no	—
554	D₄	—	6	2	no	—
555	D₄	—	12	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	3	2	no	—
559	C₂×C₄	—	3	2	no	—
560	C₂×C₄	—	6	4	no	—
561	C₂×C₄	—	12	2	no	—
562	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
564	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
567	C₂×C₃	—	2	8	no	—
568	C₂×C₃	—	2	2	no	—
569	C₂×C₃	—	2	4	no	—
570	C₂×C₃	—	2	4	no	—
571	C₂×C₃	—	2	4	no	—
572	C₂×C₃	—	4	8	no	—
573	C₂×C₃	—	4	8	no	—
574	C₂×C₃	—	4	4	no	—
575	C₂×C₃	—	4	1	no	—
576	C₂×C₃	—	6	16	no	—
577	C₂×C₃	—	12	8	no	—
578	C₂×C₃	C₂×C₃×#235	1	4	yes	—
579	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
580	C₂×C₃	C₃×#1009	1	4	yes	—
581	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
582	C₂×C₃	C₂×C₃²×#41	1	1	yes	characteristic
583	C₂×C₃	C₃²×H(5,𝔽₂)	1	1	yes	characteristic
584	D₃	—	2	4	no	—
585	D₃	—	4	2	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	3	4	no	—
592	C₂²	—	6	2	no	—
593	C₂²	—	6	2	no	—
594	C₂²	—	6	2	no	—
595	C₂²	—	6	2	no	—
596	C₂²	—	6	2	no	—
597	C₂²	—	12	8	no	—
598	C₂²	C₃²×#235	1	2	yes	complemented
599	C₂²	C₂³×C₃²×D₃	1	1	yes	characteristic
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	6	2	no	—
605	C₄	—	6	2	no	—
606	C₄	C₃²×D₃×D₄	1	2	yes	—
607	C₃	—	2	4	no	—
608	C₃	C₃×#5550	1	4	yes	direct product factor
609	C₃	C₃²×#546	1	1	yes	characteristic, complemented
610	C₂	—	2	2	no	—
611	C₂	—	4	1	no	—
612	C₂	—	6	4	no	—
613	C₂	—	12	2	no	—
614	C₂	C₂×C₃²×#235	1	1	yes	characteristic
615	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic
616	C₂	C₃²×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃²
Frattini	C₂²	C₂³×C₃²×D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₃²×C₄×D₄	D₃
hypocenter	C₃	C₃²×#546
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#235	C₂	semidirect
2. C₂²×C₃²×D₁₂	C₂	semidirect
3. C₃³×C₄×D₄	C₂	semidirect
4. C₃²×#937	C₂	semidirect
5. C₃²×#930	C₂	semidirect
6. C₃²×#924	C₂	semidirect
7. C₃²×#894	C₂	semidirect
8. C₃²×#884	C₂	semidirect
9. C₃²×D₃×C₂²⋊C₄	C₂	semidirect
10. C₃²×#875	C₂	semidirect
11. C₃²×C₄×D₁₂	C₂	semidirect
13. C₃×#5550	C₃	direct (N × H)
17. C₂²×C₃³×C₄	C₂²	semidirect
18. C₂×C₃²×#67	C₂²	semidirect
19. C₂×C₃²×#67	C₂²	semidirect
25. C₂×C₃²×C₄×D₃	C₂²	semidirect
26. C₂×C₃²×C₄×D₃	C₂²	semidirect
27. C₂×C₃²×Dic₆	C₂²	semidirect
28. C₃³×C₄⋊C₄	C₂²	semidirect
30. C₃³×C₂²⋊C₄	C₂²	semidirect
31. C₃³×C₄²	C₂²	semidirect
33. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
34. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
35. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₃²×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₃²×C₄⋊Dic₃	C₂²	semidirect
38. C₃²×Dic₃⋊C₄	C₂²	semidirect
41. C₂×C₃×#235	C₂×C₃	semidirect
42. C₂²×C₃×D₁₂	C₂×C₃	semidirect
51. C₃²×C₄×D₄	D₃	semidirect
52. C₃²×C₄×D₄	C₂×C₃	semidirect
54. C₃×#937	C₂×C₃	semidirect
55. C₃×#930	C₂×C₃	semidirect
56. C₃×#924	C₂×C₃	semidirect
57. C₃×#894	C₂×C₃	semidirect
58. C₃×#884	C₂×C₃	semidirect
59. C₃×D₃×C₂²⋊C₄	C₂×C₃	semidirect
60. C₃×#875	C₂×C₃	semidirect
61. C₃×C₄×D₁₂	C₂×C₃	semidirect
83. C₃²×D₁₂	D₄	semidirect
88. #5550	C₃²	direct (N × H)
107. C₂²×C₃²×C₄	C₂×D₃	semidirect
109. C₂²×C₃²×C₄	C₂²×C₃	semidirect
110. C₂×C₃×#67	C₂²×C₃	semidirect
111. C₂×C₃×#67	C₂²×C₃	semidirect
117. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
118. C₂×C₃×C₄×D₃	C₂²×C₃	semidirect
119. C₂×C₃×Dic₆	C₂²×C₃	semidirect
123. C₃²×C₄⋊C₄	C₂×D₃	semidirect
124. C₃²×C₄⋊C₄	C₂²×C₃	semidirect
133. C₃²×C₂²⋊C₄	C₂×D₃	semidirect
135. C₃²×C₂²⋊C₄	C₂²×C₃	semidirect
137. C₃²×C₄²	C₂×D₃	semidirect
138. C₃²×C₄²	C₂²×C₃	semidirect
140. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
141. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
142. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
143. C₃×(C₂×D₃)⋊C₄	C₂²×C₃	semidirect
144. C₃×C₄⋊Dic₃	C₂²×C₃	semidirect
145. C₃×Dic₃⋊C₄	C₂²×C₃	semidirect
151. C₂²×C₃³	#41	semidirect
169. C₂×#235	C₂×C₃²	semidirect
170. C₂²×D₁₂	C₂×C₃²	semidirect
179. C₃×C₄×D₄	C₃×D₃	semidirect
180. C₃×C₄×D₄	C₂×C₃²	semidirect
182. #937	C₂×C₃²	semidirect
183. #930	C₂×C₃²	semidirect
184. #924	C₂×C₃²	semidirect
185. #894	C₂×C₃²	semidirect
186. #884	C₂×C₃²	semidirect
187. D₃×C₂²⋊C₄	C₂×C₃²	semidirect
188. #875	C₂×C₃²	semidirect
189. C₄×D₁₂	C₂×C₃²	semidirect
246. C₃×D₁₂	C₃×D₄	semidirect
276. C₂²×C₃×C₄	C₂×C₃×D₃	semidirect
278. C₂²×C₃×C₄	C₂²×C₃²	semidirect
279. C₂×#67	C₂²×C₃²	semidirect
280. C₂×#67	C₂²×C₃²	semidirect
286. C₂×C₄×D₃	C₂²×C₃²	semidirect
287. C₂×C₄×D₃	C₂²×C₃²	semidirect
288. C₂×Dic₆	C₂²×C₃²	semidirect
292. C₃×C₄⋊C₄	C₂×C₃×D₃	semidirect
293. C₃×C₄⋊C₄	C₂²×C₃²	semidirect
302. C₃×C₂²⋊C₄	C₂×C₃×D₃	semidirect
304. C₃×C₂²⋊C₄	C₂²×C₃²	semidirect
306. C₃×C₄²	C₂×C₃×D₃	semidirect
307. C₃×C₄²	C₂²×C₃²	semidirect
309. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
310. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
311. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
312. (C₂×D₃)⋊C₄	C₂²×C₃²	semidirect
313. C₄⋊Dic₃	C₂²×C₃²	semidirect
314. Dic₃⋊C₄	C₂²×C₃²	semidirect
339. C₂²×C₃²	#235	semidirect
340. C₂²×C₃²	C₃×#41	semidirect
378. C₄×D₄	C₃²×D₃	semidirect
380. C₃³	#546	semidirect
437. D₁₂	C₃²×D₄	semidirect
473. C₂²×C₄	C₂×C₃²×D₃	semidirect
476. C₄⋊C₄	C₂×C₃²×D₃	semidirect
483. C₂²⋊C₄	C₂×C₃²×D₃	semidirect
484. C₄²	C₂×C₃²×D₃	semidirect
509. C₂²×C₃	C₃×#235	semidirect
510. C₂²×C₃	C₃²×#41	semidirect
540. C₃²	#5550	direct (N × H)
541. C₃²	C₃×#546	semidirect
598. C₂²	C₃²×#235	semidirect
608. C₃	C₃×#5550	direct (N × H)
609. C₃	C₃²×#546	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#235	2
C₂²×C₃²×D₁₂	2
C₃³×C₄×D₄	2
C₃²×#937	2
C₃²×#930	2
C₃²×#924	2
C₃²×#894	2
C₃²×#884	2
C₃²×D₃×C₂²⋊C₄	2
C₃²×#875	2
C₃²×C₄×D₁₂	2
C₃²×#546	3
C₃×#5550	3

Subgroups — C32×#5550 #13178930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#5550 #13178930