Subgroups — C₃×#3560 #87444

Order 384.

1056 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#563	C₂	1	2	yes	maximal, complemented
2	C₃×#560	C₂	1	2	yes	maximal, complemented
3	C₃×#553	C₂	1	2	yes	maximal, complemented
4	C₃×#553	C₂	1	2	yes	maximal, complemented
5	C₃×#551	C₂	1	2	yes	maximal, complemented
6	C₃×#547	C₂	1	2	yes	maximal, complemented
7	C₃×#546	C₂	1	2	yes	maximal, complemented
8	C₃×#546	C₂	1	2	yes	maximal, complemented
9	C₃×#542	C₂	1	2	yes	maximal, complemented
10	C₃×#539	C₂	1	2	yes	maximal, complemented
11	C₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#538	C₂	1	2	yes	maximal, complemented
14	C₃×#538	C₂	1	2	yes	maximal, complemented
15	C₃×#537	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×#126	C₂	1	1	yes	maximal, characteristic, complemented
20	#3560	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂×C₃×#41	C₂²	1	2	yes	complemented
22	C₂×C₃×#41	C₂²	1	2	yes	complemented
23	C₂²×C₃×D₄	C₂²	1	2	yes	—
24	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×#127	C₂²	1	1	yes	characteristic, complemented
27	C₃×#126	C₂²	1	2	yes	complemented
28	C₃×#126	C₂²	1	2	yes	complemented
29	C₃×#126	C₂²	1	2	yes	complemented
30	C₃×#126	C₂²	1	2	yes	complemented
31	C₃×#126	C₂²	1	2	yes	complemented
32	C₃×#126	C₂²	1	2	yes	complemented
33	C₃×#126	C₂²	1	2	yes	complemented
34	C₃×#126	C₂²	1	2	yes	complemented
35	C₃×#126	C₂²	1	2	yes	complemented
36	C₃×#125	C₂²	1	2	yes	complemented
37	C₃×#125	C₂²	1	2	yes	complemented
38	C₃×#125	C₂²	1	1	yes	characteristic, complemented
39	C₃×#124	C₂²	1	2	yes	—
40	C₃×#124	C₂²	1	2	yes	—
41	C₃×#124	C₂²	1	1	yes	characteristic, complemented
42	C₃×#124	C₂²	1	2	yes	complemented
43	C₃×#124	C₂²	1	2	yes	complemented
44	C₃×#123	C₂²	1	2	yes	—
45	C₃×#123	C₂²	1	2	yes	—
46	C₃×#123	C₂²	1	2	yes	—
47	C₃×#123	C₂²	1	2	yes	—
48	C₃×#123	C₂²	1	2	yes	complemented
49	C₃×#123	C₂²	1	2	yes	complemented
50	C₃×#123	C₂²	1	2	yes	complemented
51	C₃×#123	C₂²	1	2	yes	complemented
52	C₃×#123	C₂²	1	2	yes	complemented
53	C₃×#123	C₂²	1	2	yes	complemented
54	C₃×#123	C₂²	1	2	yes	complemented
55	C₃×#123	C₂²	1	2	yes	complemented
56	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₃×#121	C₂²	1	2	yes	—
65	C₃×#121	C₂²	1	2	yes	—
66	C₃×#121	C₂²	1	1	yes	characteristic
67	C₃×#121	C₂²	1	1	yes	characteristic
68	C₃×#121	C₂²	1	2	yes	—
69	C₃×#121	C₂²	1	2	yes	—
70	C₃×#121	C₂²	1	2	yes	—
71	C₃×#121	C₂²	1	2	yes	complemented
72	C₃×#121	C₂²	1	2	yes	complemented
73	C₃×#121	C₂²	1	2	yes	complemented
74	C₃×#121	C₂²	1	2	yes	complemented
75	C₃×#121	C₂²	1	1	yes	characteristic, complemented
76	C₃×#121	C₂²	1	2	yes	complemented
77	C₃×#121	C₂²	1	2	yes	complemented
78	C₃×#121	C₂²	1	2	yes	complemented
79	C₃×#120	C₂²	1	2	yes	—
80	C₃×#120	C₂²	1	2	yes	—
81	C₃×#120	C₂²	1	2	yes	—
82	C₃×#120	C₂²	1	2	yes	complemented
83	C₃×#120	C₂²	1	2	yes	complemented
84	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
86	C₃×C₄×D₄	C₂²	1	2	yes	complemented
87	C₃×C₄×D₄	C₂²	1	2	yes	complemented
88	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
89	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
90	C₃×C₄×D₄	C₂²	1	2	yes	complemented
91	C₃×C₄×D₄	C₂²	1	2	yes	complemented
92	C₃×C₄×D₄	C₂²	1	2	yes	complemented
93	C₃×C₄×D₄	C₂²	1	2	yes	complemented
94	C₃×C₄×D₄	C₂²	1	2	yes	complemented
95	C₃×C₄×D₄	C₂²	1	2	yes	complemented
96	C₃×#117	C₂²	1	2	yes	complemented
97	C₃×#117	C₂²	1	2	yes	complemented
98	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
103	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
106	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
108	#563	C₂×C₃	1	2	yes	complemented
109	#560	C₂×C₃	1	2	yes	complemented
110	#553	C₂×C₃	1	2	yes	complemented
111	#553	C₂×C₃	1	2	yes	complemented
112	#551	C₂×C₃	1	2	yes	complemented
113	#547	C₂×C₃	1	2	yes	complemented
114	#546	C₂×C₃	1	2	yes	complemented
115	#546	C₂×C₃	1	2	yes	complemented
116	#542	C₂×C₃	1	2	yes	complemented
117	#539	C₂×C₃	1	2	yes	complemented
118	#539	C₂×C₃	1	1	yes	characteristic, complemented
119	#538	C₂×C₃	1	1	yes	characteristic, complemented
120	#538	C₂×C₃	1	2	yes	complemented
121	#538	C₂×C₃	1	2	yes	complemented
122	#537	C₂×C₃	1	1	yes	characteristic, complemented
123	#534	C₂×C₃	1	1	yes	characteristic, complemented
124	#532	C₂×C₃	1	1	yes	characteristic, complemented
125	#529	C₂×C₃	1	1	yes	characteristic, complemented
126	C₂×#126	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂⁴×C₃	C₂³	1	1	yes	characteristic
128	C₂⁴×C₃	C₂³	1	2	yes	—
129	C₃×#41	—	4	4	no	—
130	C₃×#41	—	4	4	no	—
131	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
132	C₂×C₃×Q₈	C₂³	1	2	yes	—
133	C₂×C₃×Q₈	C₂³	1	2	yes	—
134	C₂×C₃×D₄	—	4	4	no	—
135	C₂×C₃×D₄	C₂³	1	2	yes	—
136	C₂×C₃×D₄	C₂³	1	2	yes	—
137	C₂×C₃×D₄	C₂³	1	2	yes	—
138	C₂×C₃×D₄	C₂³	1	2	yes	—
139	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
140	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
141	C₂×C₃×D₄	C₂³	1	2	yes	—
142	C₂×C₃×D₄	C₂³	1	2	yes	—
143	C₂×C₃×D₄	C₂³	1	2	yes	—
144	C₂×C₃×D₄	C₂³	1	2	yes	—
145	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
146	C₂×C₃×D₄	C₂³	1	2	yes	—
147	C₂×C₃×D₄	C₂³	1	2	yes	—
148	C₂×C₃×D₄	C₂³	1	2	yes	—
149	C₂×C₃×D₄	C₂³	1	2	yes	—
150	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
154	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂³	1	2	yes	—
157	C₂²×C₃×C₄	C₂³	1	2	yes	—
158	C₂²×C₃×C₄	C₂³	1	2	yes	—
159	C₂²×C₃×C₄	C₂³	1	2	yes	—
160	C₂²×C₃×C₄	C₂³	1	2	yes	—
161	C₂²×C₃×C₄	C₂³	1	2	yes	—
162	C₂²×C₃×C₄	C₂³	1	2	yes	—
163	C₂²×C₃×C₄	C₂³	1	2	yes	—
164	C₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
178	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₃×C₄⋊C₄	C₂³	1	2	yes	—
181	C₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃×C₄²	C₂³	1	1	yes	characteristic
211	C₃×C₄²	C₂³	1	1	yes	characteristic
212	C₃×C₄²	C₂³	1	1	yes	characteristic
213	C₃×C₄²	C₂³	1	1	yes	characteristic
214	C₃×C₄²	C₂³	1	2	yes	—
215	C₃×C₄²	C₂³	1	2	yes	—
216	C₃×C₄²	C₂³	1	2	yes	—
217	C₂×#41	C₂²×C₃	1	2	yes	complemented
218	C₂×#41	C₂²×C₃	1	2	yes	complemented
219	C₂²×D₄	C₂²×C₃	1	2	yes	—
220	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
222	#127	C₂²×C₃	1	1	yes	characteristic, complemented
223	#126	C₂²×C₃	1	2	yes	complemented
224	#126	C₂²×C₃	1	2	yes	complemented
225	#126	C₂²×C₃	1	2	yes	complemented
226	#126	C₂²×C₃	1	2	yes	complemented
227	#126	C₂²×C₃	1	2	yes	complemented
228	#126	C₂²×C₃	1	2	yes	complemented
229	#126	C₂²×C₃	1	2	yes	complemented
230	#126	C₂²×C₃	1	2	yes	complemented
231	#126	C₂²×C₃	1	2	yes	complemented
232	#125	C₂²×C₃	1	1	yes	characteristic, complemented
233	#125	C₂²×C₃	1	2	yes	complemented
234	#125	C₂²×C₃	1	2	yes	complemented
235	#124	C₂²×C₃	1	2	yes	—
236	#124	C₂²×C₃	1	2	yes	—
237	#124	C₂²×C₃	1	1	yes	characteristic, complemented
238	#124	C₂²×C₃	1	2	yes	complemented
239	#124	C₂²×C₃	1	2	yes	complemented
240	#123	C₂²×C₃	1	2	yes	—
241	#123	C₂²×C₃	1	2	yes	—
242	#123	C₂²×C₃	1	2	yes	—
243	#123	C₂²×C₃	1	2	yes	—
244	#123	C₂²×C₃	1	2	yes	complemented
245	#123	C₂²×C₃	1	2	yes	complemented
246	#123	C₂²×C₃	1	2	yes	complemented
247	#123	C₂²×C₃	1	2	yes	complemented
248	#123	C₂²×C₃	1	2	yes	complemented
249	#123	C₂²×C₃	1	2	yes	complemented
250	#123	C₂²×C₃	1	2	yes	complemented
251	#123	C₂²×C₃	1	2	yes	complemented
252	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
254	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
255	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
256	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
257	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
258	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
259	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
260	#121	C₂²×C₃	1	1	yes	characteristic
261	#121	C₂²×C₃	1	1	yes	characteristic
262	#121	C₂²×C₃	1	2	yes	—
263	#121	C₂²×C₃	1	2	yes	—
264	#121	C₂²×C₃	1	2	yes	—
265	#121	C₂²×C₃	1	2	yes	—
266	#121	C₂²×C₃	1	2	yes	—
267	#121	C₂²×C₃	1	1	yes	characteristic, complemented
268	#121	C₂²×C₃	1	2	yes	complemented
269	#121	C₂²×C₃	1	2	yes	complemented
270	#121	C₂²×C₃	1	2	yes	complemented
271	#121	C₂²×C₃	1	2	yes	complemented
272	#121	C₂²×C₃	1	2	yes	complemented
273	#121	C₂²×C₃	1	2	yes	complemented
274	#121	C₂²×C₃	1	2	yes	complemented
275	#120	C₂²×C₃	1	2	yes	—
276	#120	C₂²×C₃	1	2	yes	—
277	#120	C₂²×C₃	1	2	yes	—
278	#120	C₂²×C₃	1	2	yes	complemented
279	#120	C₂²×C₃	1	2	yes	complemented
280	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
281	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
282	C₄×D₄	C₂²×C₃	1	2	yes	complemented
283	C₄×D₄	C₂²×C₃	1	2	yes	complemented
284	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₄×D₄	C₂²×C₃	1	2	yes	complemented
287	C₄×D₄	C₂²×C₃	1	2	yes	complemented
288	C₄×D₄	C₂²×C₃	1	2	yes	complemented
289	C₄×D₄	C₂²×C₃	1	2	yes	complemented
290	C₄×D₄	C₂²×C₃	1	2	yes	complemented
291	C₄×D₄	C₂²×C₃	1	2	yes	complemented
292	#117	C₂²×C₃	1	2	yes	complemented
293	#117	C₂²×C₃	1	2	yes	complemented
294	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
296	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
298	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
302	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
303	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	4	2	no	—
306	C₂³×C₃	—	4	1	no	—
307	C₂³×C₃	—	4	1	no	—
308	C₂³×C₃	—	4	2	no	—
309	C₂³×C₃	—	4	2	no	—
310	C₂³×C₃	C₂⁴	1	2	yes	—
311	C₂³×C₃	C₂⁴	1	2	yes	—
312	C₂³×C₃	C₂⁴	1	2	yes	—
313	C₂³×C₃	C₂⁴	1	2	yes	—
314	C₂³×C₃	C₂⁴	1	1	yes	characteristic
315	C₃×Q₈	—	4	1	no	—
316	C₃×Q₈	—	4	2	no	—
317	C₃×Q₈	—	4	2	no	—
318	C₃×D₄	—	2	4	no	—
319	C₃×D₄	—	2	4	no	—
320	C₃×D₄	—	2	4	no	—
321	C₃×D₄	—	4	2	no	—
322	C₃×D₄	—	4	2	no	—
323	C₃×D₄	—	4	2	no	—
324	C₃×D₄	—	4	2	no	—
325	C₃×D₄	—	4	2	no	—
326	C₃×D₄	—	4	2	no	—
327	C₃×D₄	—	4	1	no	—
328	C₃×D₄	—	4	1	no	—
329	C₃×D₄	—	4	2	no	—
330	C₃×D₄	—	4	1	no	—
331	C₃×D₄	—	4	2	no	—
332	C₃×D₄	—	4	2	no	—
333	C₂×C₃×C₄	—	2	2	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	4	2	no	—
336	C₂×C₃×C₄	—	4	1	no	—
337	C₂×C₃×C₄	—	4	1	no	—
338	C₂×C₃×C₄	—	4	1	no	—
339	C₂×C₃×C₄	—	4	2	no	—
340	C₂×C₃×C₄	—	4	2	no	—
341	C₂×C₃×C₄	—	4	1	no	—
342	C₂×C₃×C₄	—	4	2	no	—
343	C₂×C₃×C₄	—	4	2	no	—
344	C₂×C₃×C₄	—	4	2	no	—
345	C₂×C₃×C₄	—	4	2	no	—
346	C₂×C₃×C₄	—	4	2	no	—
347	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂⁴	1	2	yes	—
350	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂⁴	1	2	yes	—
355	C₂×C₃×C₄	C₂⁴	1	2	yes	—
356	C₂×C₃×C₄	C₂⁴	1	2	yes	—
357	C₂×C₃×C₄	C₂⁴	1	2	yes	—
358	C₂×C₃×C₄	C₂⁴	1	2	yes	—
359	C₂×C₃×C₄	C₂⁴	1	2	yes	—
360	C₂×C₃×C₄	C₂⁴	1	2	yes	—
361	C₂⁴	C₂³×C₃	1	1	yes	characteristic
362	C₂⁴	C₂³×C₃	1	2	yes	—
363	#41	—	4	4	no	—
364	#41	—	4	4	no	—
365	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
366	C₂×Q₈	C₂³×C₃	1	2	yes	—
367	C₂×Q₈	C₂³×C₃	1	2	yes	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	C₂³×C₃	1	2	yes	—
370	C₂×D₄	C₂³×C₃	1	2	yes	—
371	C₂×D₄	C₂³×C₃	1	2	yes	—
372	C₂×D₄	C₂³×C₃	1	2	yes	—
373	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
374	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
375	C₂×D₄	C₂³×C₃	1	2	yes	—
376	C₂×D₄	C₂³×C₃	1	2	yes	—
377	C₂×D₄	C₂³×C₃	1	2	yes	—
378	C₂×D₄	C₂³×C₃	1	2	yes	—
379	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
380	C₂×D₄	C₂³×C₃	1	2	yes	—
381	C₂×D₄	C₂³×C₃	1	2	yes	—
382	C₂×D₄	C₂³×C₃	1	2	yes	—
383	C₂×D₄	C₂³×C₃	1	2	yes	—
384	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
385	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
386	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
387	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
388	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
389	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
390	C₂²×C₄	C₂³×C₃	1	2	yes	—
391	C₂²×C₄	C₂³×C₃	1	2	yes	—
392	C₂²×C₄	C₂³×C₃	1	2	yes	—
393	C₂²×C₄	C₂³×C₃	1	2	yes	—
394	C₂²×C₄	C₂³×C₃	1	2	yes	—
395	C₂²×C₄	C₂³×C₃	1	2	yes	—
396	C₂²×C₄	C₂³×C₃	1	2	yes	—
397	C₂²×C₄	C₂³×C₃	1	2	yes	—
398	C₄⋊C₄	C₂³×C₃	1	2	yes	—
399	C₄⋊C₄	C₂³×C₃	1	2	yes	—
400	C₄⋊C₄	C₂³×C₃	1	2	yes	—
401	C₄⋊C₄	C₂³×C₃	1	2	yes	—
402	C₄⋊C₄	C₂³×C₃	1	2	yes	—
403	C₄⋊C₄	C₂³×C₃	1	2	yes	—
404	C₄⋊C₄	C₂³×C₃	1	2	yes	—
405	C₄⋊C₄	C₂³×C₃	1	2	yes	—
406	C₄⋊C₄	C₂³×C₃	1	2	yes	—
407	C₄⋊C₄	C₂³×C₃	1	2	yes	—
408	C₄⋊C₄	C₂³×C₃	1	2	yes	—
409	C₄⋊C₄	C₂³×C₃	1	2	yes	—
410	C₄⋊C₄	C₂³×C₃	1	2	yes	—
411	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
412	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
413	C₄⋊C₄	C₂³×C₃	1	2	yes	—
414	C₄⋊C₄	C₂³×C₃	1	2	yes	—
415	C₄⋊C₄	C₂³×C₃	1	2	yes	—
416	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
417	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
418	C₄⋊C₄	C₂³×C₃	1	2	yes	—
419	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
420	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
421	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
422	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
423	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
424	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
425	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
426	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
427	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
428	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
429	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
430	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
431	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
432	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
433	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
434	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
435	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
436	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
437	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
438	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
439	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
440	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
441	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
442	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
443	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
444	C₄²	C₂³×C₃	1	1	yes	characteristic
445	C₄²	C₂³×C₃	1	1	yes	characteristic
446	C₄²	C₂³×C₃	1	1	yes	characteristic
447	C₄²	C₂³×C₃	1	1	yes	characteristic
448	C₄²	C₂³×C₃	1	2	yes	—
449	C₄²	C₂³×C₃	1	2	yes	—
450	C₄²	C₂³×C₃	1	2	yes	—
451	C₂²×C₃	—	2	1	no	—
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	2	2	no	—
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	2	2	no	—
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	2	2	no	—
465	C₂²×C₃	—	8	2	no	—
466	C₂²×C₃	—	8	4	no	—
467	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
468	C₂²×C₃	C₂⁵	1	1	yes	characteristic
469	C₃×C₄	—	2	1	no	—
470	C₃×C₄	—	2	2	no	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	2	2	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	1	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	2	2	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	1	no	—
480	C₃×C₄	—	2	1	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	1	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	C₂⁴×C₃	1	2	yes	—
490	C₂³	C₂⁴×C₃	1	2	yes	—
491	C₂³	C₂⁴×C₃	1	2	yes	—
492	C₂³	C₂⁴×C₃	1	2	yes	—
493	C₂³	C₂⁴×C₃	1	1	yes	characteristic
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	Q₈	—	4	1	no	—
497	D₄	—	2	4	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	4	no	—
500	D₄	—	4	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
527	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
528	C₂×C₄	C₂⁴×C₃	1	2	yes	—
529	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
530	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
531	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
532	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
533	C₂×C₄	C₂⁴×C₃	1	2	yes	—
534	C₂×C₄	C₂⁴×C₃	1	2	yes	—
535	C₂×C₄	C₂⁴×C₃	1	2	yes	—
536	C₂×C₄	C₂⁴×C₃	1	2	yes	—
537	C₂×C₄	C₂⁴×C₃	1	2	yes	—
538	C₂×C₄	C₂⁴×C₃	1	2	yes	—
539	C₂×C₄	C₂⁴×C₃	1	2	yes	—
540	C₂×C₃	—	2	2	no	—
541	C₂×C₃	—	4	2	no	—
542	C₂×C₃	—	4	2	no	—
543	C₂×C₃	—	4	2	no	—
544	C₂×C₃	—	4	2	no	—
545	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
546	C₂×C₃	#585	1	1	yes	characteristic
547	C₂×C₃	#585	1	1	yes	characteristic
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	8	2	no	—
563	C₂²	—	8	4	no	—
564	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
565	C₂²	C₂⁵×C₃	1	1	yes	characteristic
566	C₄	—	2	1	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	1	no	—
580	C₃	#3560	1	1	yes	characteristic, direct product factor, Sylow
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂	C₃×#585	1	1	yes	characteristic
588	C₂	C₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#563	C₂	semidirect
2. C₃×#560	C₂	semidirect
3. C₃×#553	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#551	C₂	semidirect
6. C₃×#547	C₂	semidirect
7. C₃×#546	C₂	semidirect
8. C₃×#546	C₂	semidirect
9. C₃×#542	C₂	semidirect
10. C₃×#539	C₂	semidirect
11. C₃×#539	C₂	semidirect
12. C₃×#538	C₂	semidirect
13. C₃×#538	C₂	semidirect
14. C₃×#538	C₂	semidirect
15. C₃×#537	C₂	semidirect
16. C₃×#534	C₂	semidirect
17. C₃×#532	C₂	semidirect
18. C₃×#529	C₂	semidirect
19. C₂×C₃×#126	C₂	semidirect
20. #3560	C₃	direct (N × H)
21. C₂×C₃×#41	C₂²	semidirect
22. C₂×C₃×#41	C₂²	semidirect
24. C₃×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₄⋊Q₈	C₂²	semidirect
26. C₃×#127	C₂²	semidirect
27. C₃×#126	C₂²	semidirect
28. C₃×#126	C₂²	semidirect
29. C₃×#126	C₂²	semidirect
30. C₃×#126	C₂²	semidirect
31. C₃×#126	C₂²	semidirect
32. C₃×#126	C₂²	semidirect
33. C₃×#126	C₂²	semidirect
34. C₃×#126	C₂²	semidirect
35. C₃×#126	C₂²	semidirect
36. C₃×#125	C₂²	semidirect
37. C₃×#125	C₂²	semidirect
38. C₃×#125	C₂²	semidirect
41. C₃×#124	C₂²	semidirect
42. C₃×#124	C₂²	semidirect
43. C₃×#124	C₂²	semidirect
48. C₃×#123	C₂²	semidirect
49. C₃×#123	C₂²	semidirect
50. C₃×#123	C₂²	semidirect
51. C₃×#123	C₂²	semidirect
52. C₃×#123	C₂²	semidirect
53. C₃×#123	C₂²	semidirect
54. C₃×#123	C₂²	semidirect
55. C₃×#123	C₂²	semidirect
56. C₃×C₂²⋊Q₈	C₂²	semidirect
57. C₃×C₂²⋊Q₈	C₂²	semidirect
58. C₃×C₂²⋊Q₈	C₂²	semidirect
59. C₃×C₂²⋊Q₈	C₂²	semidirect
60. C₃×C₂²⋊Q₈	C₂²	semidirect
61. C₃×C₂²⋊Q₈	C₂²	semidirect
62. C₃×C₂²⋊Q₈	C₂²	semidirect
63. C₃×C₂²⋊Q₈	C₂²	semidirect
71. C₃×#121	C₂²	semidirect
72. C₃×#121	C₂²	semidirect
73. C₃×#121	C₂²	semidirect
74. C₃×#121	C₂²	semidirect
75. C₃×#121	C₂²	semidirect
76. C₃×#121	C₂²	semidirect
77. C₃×#121	C₂²	semidirect
78. C₃×#121	C₂²	semidirect
82. C₃×#120	C₂²	semidirect
83. C₃×#120	C₂²	semidirect
84. C₃×C₄×Q₈	C₂²	semidirect
85. C₃×C₄×D₄	C₂²	semidirect
86. C₃×C₄×D₄	C₂²	semidirect
87. C₃×C₄×D₄	C₂²	semidirect
88. C₃×C₄×D₄	C₂²	semidirect
89. C₃×C₄×D₄	C₂²	semidirect
90. C₃×C₄×D₄	C₂²	semidirect
91. C₃×C₄×D₄	C₂²	semidirect
92. C₃×C₄×D₄	C₂²	semidirect
93. C₃×C₄×D₄	C₂²	semidirect
94. C₃×C₄×D₄	C₂²	semidirect
95. C₃×C₄×D₄	C₂²	semidirect
96. C₃×#117	C₂²	semidirect
97. C₃×#117	C₂²	semidirect
98. C₂×C₃×C₄⋊C₄	C₂²	semidirect
99. C₂×C₃×C₄⋊C₄	C₂²	semidirect
100. C₂×C₃×C₄⋊C₄	C₂²	semidirect
101. C₂×C₃×C₄⋊C₄	C₂²	semidirect
105. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
106. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
107. C₂×C₃×C₄²	C₂²	semidirect
108. #563	C₂×C₃	semidirect
109. #560	C₂×C₃	semidirect
110. #553	C₂×C₃	semidirect
111. #553	C₂×C₃	semidirect
112. #551	C₂×C₃	semidirect
113. #547	C₂×C₃	semidirect
114. #546	C₂×C₃	semidirect
115. #546	C₂×C₃	semidirect
116. #542	C₂×C₃	semidirect
117. #539	C₂×C₃	semidirect
118. #539	C₂×C₃	semidirect
119. #538	C₂×C₃	semidirect
120. #538	C₂×C₃	semidirect
121. #538	C₂×C₃	semidirect
122. #537	C₂×C₃	semidirect
123. #534	C₂×C₃	semidirect
124. #532	C₂×C₃	semidirect
125. #529	C₂×C₃	semidirect
126. C₂×#126	C₂×C₃	semidirect
217. C₂×#41	C₂²×C₃	semidirect
218. C₂×#41	C₂²×C₃	semidirect
220. C₄⋊Q₈	C₂²×C₃	semidirect
221. C₄⋊Q₈	C₂²×C₃	semidirect
222. #127	C₂²×C₃	semidirect
223. #126	C₂²×C₃	semidirect
224. #126	C₂²×C₃	semidirect
225. #126	C₂²×C₃	semidirect
226. #126	C₂²×C₃	semidirect
227. #126	C₂²×C₃	semidirect
228. #126	C₂²×C₃	semidirect
229. #126	C₂²×C₃	semidirect
230. #126	C₂²×C₃	semidirect
231. #126	C₂²×C₃	semidirect
232. #125	C₂²×C₃	semidirect
233. #125	C₂²×C₃	semidirect
234. #125	C₂²×C₃	semidirect
237. #124	C₂²×C₃	semidirect
238. #124	C₂²×C₃	semidirect
239. #124	C₂²×C₃	semidirect
244. #123	C₂²×C₃	semidirect
245. #123	C₂²×C₃	semidirect
246. #123	C₂²×C₃	semidirect
247. #123	C₂²×C₃	semidirect
248. #123	C₂²×C₃	semidirect
249. #123	C₂²×C₃	semidirect
250. #123	C₂²×C₃	semidirect
251. #123	C₂²×C₃	semidirect
252. C₂²⋊Q₈	C₂²×C₃	semidirect
253. C₂²⋊Q₈	C₂²×C₃	semidirect
254. C₂²⋊Q₈	C₂²×C₃	semidirect
255. C₂²⋊Q₈	C₂²×C₃	semidirect
256. C₂²⋊Q₈	C₂²×C₃	semidirect
257. C₂²⋊Q₈	C₂²×C₃	semidirect
258. C₂²⋊Q₈	C₂²×C₃	semidirect
259. C₂²⋊Q₈	C₂²×C₃	semidirect
267. #121	C₂²×C₃	semidirect
268. #121	C₂²×C₃	semidirect
269. #121	C₂²×C₃	semidirect
270. #121	C₂²×C₃	semidirect
271. #121	C₂²×C₃	semidirect
272. #121	C₂²×C₃	semidirect
273. #121	C₂²×C₃	semidirect
274. #121	C₂²×C₃	semidirect
278. #120	C₂²×C₃	semidirect
279. #120	C₂²×C₃	semidirect
280. C₄×Q₈	C₂²×C₃	semidirect
281. C₄×D₄	C₂²×C₃	semidirect
282. C₄×D₄	C₂²×C₃	semidirect
283. C₄×D₄	C₂²×C₃	semidirect
284. C₄×D₄	C₂²×C₃	semidirect
285. C₄×D₄	C₂²×C₃	semidirect
286. C₄×D₄	C₂²×C₃	semidirect
287. C₄×D₄	C₂²×C₃	semidirect
288. C₄×D₄	C₂²×C₃	semidirect
289. C₄×D₄	C₂²×C₃	semidirect
290. C₄×D₄	C₂²×C₃	semidirect
291. C₄×D₄	C₂²×C₃	semidirect
292. #117	C₂²×C₃	semidirect
293. #117	C₂²×C₃	semidirect
294. C₂×C₄⋊C₄	C₂²×C₃	semidirect
295. C₂×C₄⋊C₄	C₂²×C₃	semidirect
296. C₂×C₄⋊C₄	C₂²×C₃	semidirect
297. C₂×C₄⋊C₄	C₂²×C₃	semidirect
301. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
302. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
303. C₂×C₄²	C₂²×C₃	semidirect
580. C₃	#3560	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×#563	2
C₃×#560	2
C₃×#553	2
C₃×#551	2
C₃×#547	2
C₃×#546	2
C₃×#542	2
C₃×#539	2
C₃×#538	2
C₃×#537	2
C₃×#534	2
C₃×#532	2
C₃×#529	2
C₂×C₃×#126	2
#3560	3

Subgroups — C3×#3560 #87444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3560 #87444