Subgroups — C₃×#3519 #87403

Order 384.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#553	C₂	1	2	yes	maximal, complemented
4	C₃×#553	C₂	1	2	yes	maximal, complemented
5	C₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#546	C₂	1	4	yes	maximal, complemented
7	C₃×#546	C₂	1	2	yes	maximal, complemented
8	C₃×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄²	C₂	1	2	yes	maximal, complemented
10	C₃×#540	C₂	1	2	yes	maximal, complemented
11	C₃×#538	C₂	1	4	yes	maximal, complemented
12	C₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₃×#121	C₂	1	2	yes	maximal, complemented
16	C₃×#518	C₂	1	2	yes	maximal, complemented
17	C₂×C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	#3519	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₃×#41	C₂²	1	2	yes	complemented
20	C₂×C₃×#41	C₂²	1	2	yes	complemented
21	C₂²×C₃×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×D₄	C₂²	1	2	yes	—
23	C₂²×C₃×D₄	C₂²	1	2	yes	complemented
24	C₂²×C₃×D₄	C₂²	1	4	yes	complemented
25	C₂³×C₃×C₄	C₂²	1	2	yes	complemented
26	C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×#127	C₂²	1	1	yes	characteristic, complemented
28	C₃×#127	C₂²	1	2	yes	complemented
29	C₃×#126	C₂²	1	2	yes	complemented
30	C₃×#126	C₂²	1	4	yes	complemented
31	C₃×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃×#125	C₂²	1	2	yes	complemented
33	C₃×#124	C₂²	1	1	yes	characteristic, complemented
34	C₃×#124	C₂²	1	2	yes	complemented
35	C₃×#124	C₂²	1	4	yes	complemented
36	C₃×#123	C₂²	1	4	yes	complemented
37	C₃×#123	C₂²	1	2	yes	complemented
38	C₃×#123	C₂²	1	4	yes	complemented
39	C₃×#123	C₂²	1	4	yes	complemented
40	C₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
42	C₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
43	C₃×#121	C₂²	1	1	yes	characteristic
44	C₃×#121	C₂²	1	2	yes	complemented
45	C₃×#121	C₂²	1	4	yes	complemented
46	C₃×#121	C₂²	1	4	yes	complemented
47	C₃×#121	C₂²	1	2	yes	complemented
48	C₃×#121	C₂²	1	2	yes	complemented
49	C₃×#121	C₂²	1	2	yes	complemented
50	C₃×#121	C₂²	1	2	yes	complemented
51	C₃×#121	C₂²	1	4	yes	complemented
52	C₃×#121	C₂²	1	4	yes	complemented
53	C₃×#121	C₂²	1	2	yes	complemented
54	C₃×#121	C₂²	1	2	yes	complemented
55	C₃×#121	C₂²	1	4	yes	complemented
56	C₃×#120	C₂²	1	4	yes	complemented
57	C₃×#120	C₂²	1	4	yes	complemented
58	C₃×#120	C₂²	1	4	yes	complemented
59	C₃×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
61	C₃×C₄×D₄	C₂²	1	1	yes	characteristic
62	C₃×C₄×D₄	C₂²	1	2	yes	—
63	C₃×C₄×D₄	C₂²	1	2	yes	complemented
64	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
65	C₃×C₄×D₄	C₂²	1	2	yes	complemented
66	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
67	C₃×C₄×D₄	C₂²	1	4	yes	complemented
68	C₃×C₄×D₄	C₂²	1	2	yes	complemented
69	C₃×C₄×D₄	C₂²	1	4	yes	complemented
70	C₃×C₄×D₄	C₂²	1	2	yes	complemented
71	C₃×C₄×D₄	C₂²	1	4	yes	complemented
72	C₃×C₄×D₄	C₂²	1	2	yes	complemented
73	C₃×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
74	C₃×C₄×D₄	C₂²	1	2	yes	complemented
75	C₃×#117	C₂²	1	2	yes	complemented
76	C₃×#117	C₂²	1	2	yes	complemented
77	C₃×#117	C₂²	1	2	yes	complemented
78	C₂×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
80	C₂×C₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
81	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
82	C₂×C₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
83	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic, complemented
84	#555	C₂×C₃	1	1	yes	characteristic, complemented
85	#554	C₂×C₃	1	1	yes	characteristic, complemented
86	#553	C₂×C₃	1	2	yes	complemented
87	#553	C₂×C₃	1	2	yes	complemented
88	#550	C₂×C₃	1	1	yes	characteristic, complemented
89	#546	C₂×C₃	1	4	yes	complemented
90	#546	C₂×C₃	1	2	yes	complemented
91	D₄²	C₂×C₃	1	1	yes	characteristic, complemented
92	D₄²	C₂×C₃	1	2	yes	complemented
93	#540	C₂×C₃	1	2	yes	complemented
94	#538	C₂×C₃	1	4	yes	complemented
95	#532	C₂×C₃	1	1	yes	characteristic, complemented
96	#529	C₂×C₃	1	1	yes	characteristic, complemented
97	#525	C₂×C₃	1	2	yes	complemented
98	C₂×#121	C₂×C₃	1	2	yes	complemented
99	#518	C₂×C₃	1	2	yes	complemented
100	C₂×C₄×D₄	C₂×C₃	1	1	yes	characteristic, complemented
101	C₂⁴×C₃	C₂³	1	2	yes	—
102	C₂⁴×C₃	C₂³	1	4	yes	—
103	C₃×#41	—	4	4	no	—
104	C₃×#41	—	4	4	no	—
105	C₂×C₃×Q₈	C₂³	1	1	yes	characteristic
106	C₂×C₃×Q₈	C₂³	1	2	yes	—
107	C₂×C₃×D₄	—	2	4	no	—
108	C₂×C₃×D₄	—	2	8	no	—
109	C₂×C₃×D₄	—	4	4	no	—
110	C₂×C₃×D₄	—	4	8	no	—
111	C₂×C₃×D₄	C₂³	1	2	yes	—
112	C₂×C₃×D₄	C₂³	1	4	yes	—
113	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃×D₄	C₂³	1	2	yes	—
115	C₂×C₃×D₄	C₂³	1	4	yes	—
116	C₂×C₃×D₄	C₂³	1	2	yes	—
117	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
118	C₂×C₃×D₄	C₂³	1	2	yes	—
119	C₂×C₃×D₄	C₂³	1	4	yes	—
120	C₂×C₃×D₄	C₂³	1	2	yes	—
121	C₂×C₃×D₄	C₂³	1	4	yes	—
122	C₂×C₃×D₄	C₂³	1	4	yes	—
123	C₂×C₃×D₄	C₂³	1	4	yes	—
124	C₂×C₃×D₄	C₂³	1	1	yes	characteristic
125	C₂²×C₃×C₄	—	4	4	no	—
126	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
127	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
129	C₂²×C₃×C₄	C₂³	1	2	yes	—
130	C₂²×C₃×C₄	C₂³	1	2	yes	—
131	C₂²×C₃×C₄	C₂³	1	2	yes	—
132	C₂²×C₃×C₄	C₂³	1	2	yes	—
133	C₂²×C₃×C₄	C₂³	1	4	yes	—
134	C₂²×C₃×C₄	C₂³	1	2	yes	—
135	C₂²×C₃×C₄	C₂³	1	4	yes	—
136	C₂²×C₃×C₄	C₂³	1	4	yes	—
137	C₂²×C₃×C₄	C₂³	1	2	yes	—
138	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₃×C₄⋊C₄	C₂³	1	2	yes	—
141	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₃×C₄⋊C₄	C₂³	1	4	yes	—
144	C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₃×C₄⋊C₄	C₂³	1	4	yes	—
150	C₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
154	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
157	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
158	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
160	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
162	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₃×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₃×C₄²	C₂³	1	1	yes	characteristic
168	C₃×C₄²	C₂³	1	1	yes	characteristic
169	C₃×C₄²	C₂³	1	1	yes	characteristic
170	C₃×C₄²	C₂³	1	1	yes	characteristic
171	C₃×C₄²	C₂³	1	4	yes	—
172	C₃×C₄²	C₂³	1	2	yes	—
173	C₂×#41	C₂²×C₃	1	2	yes	complemented
174	C₂×#41	C₂²×C₃	1	2	yes	complemented
175	C₂²×D₄	C₂²×C₃	1	1	yes	characteristic
176	C₂²×D₄	C₂²×C₃	1	2	yes	—
177	C₂²×D₄	C₂²×C₃	1	2	yes	complemented
178	C₂²×D₄	C₂²×C₃	1	4	yes	complemented
179	C₂³×C₄	C₂²×C₃	1	2	yes	complemented
180	C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
181	#127	C₂²×C₃	1	1	yes	characteristic, complemented
182	#127	C₂²×C₃	1	2	yes	complemented
183	#126	C₂²×C₃	1	2	yes	complemented
184	#126	C₂²×C₃	1	4	yes	complemented
185	#125	C₂²×C₃	1	1	yes	characteristic, complemented
186	#125	C₂²×C₃	1	2	yes	complemented
187	#124	C₂²×C₃	1	1	yes	characteristic, complemented
188	#124	C₂²×C₃	1	2	yes	complemented
189	#124	C₂²×C₃	1	4	yes	complemented
190	#123	C₂²×C₃	1	4	yes	complemented
191	#123	C₂²×C₃	1	2	yes	complemented
192	#123	C₂²×C₃	1	4	yes	complemented
193	#123	C₂²×C₃	1	4	yes	complemented
194	C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
196	C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
197	#121	C₂²×C₃	1	1	yes	characteristic
198	#121	C₂²×C₃	1	2	yes	complemented
199	#121	C₂²×C₃	1	4	yes	complemented
200	#121	C₂²×C₃	1	4	yes	complemented
201	#121	C₂²×C₃	1	2	yes	complemented
202	#121	C₂²×C₃	1	2	yes	complemented
203	#121	C₂²×C₃	1	2	yes	complemented
204	#121	C₂²×C₃	1	2	yes	complemented
205	#121	C₂²×C₃	1	4	yes	complemented
206	#121	C₂²×C₃	1	4	yes	complemented
207	#121	C₂²×C₃	1	2	yes	complemented
208	#121	C₂²×C₃	1	2	yes	complemented
209	#121	C₂²×C₃	1	4	yes	complemented
210	#120	C₂²×C₃	1	4	yes	complemented
211	#120	C₂²×C₃	1	4	yes	complemented
212	#120	C₂²×C₃	1	4	yes	complemented
213	C₄×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
214	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
215	C₄×D₄	C₂²×C₃	1	1	yes	characteristic
216	C₄×D₄	C₂²×C₃	1	2	yes	—
217	C₄×D₄	C₂²×C₃	1	2	yes	complemented
218	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
219	C₄×D₄	C₂²×C₃	1	2	yes	complemented
220	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
221	C₄×D₄	C₂²×C₃	1	4	yes	complemented
222	C₄×D₄	C₂²×C₃	1	2	yes	complemented
223	C₄×D₄	C₂²×C₃	1	4	yes	complemented
224	C₄×D₄	C₂²×C₃	1	2	yes	complemented
225	C₄×D₄	C₂²×C₃	1	4	yes	complemented
226	C₄×D₄	C₂²×C₃	1	2	yes	complemented
227	C₄×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
228	C₄×D₄	C₂²×C₃	1	2	yes	complemented
229	#117	C₂²×C₃	1	2	yes	complemented
230	#117	C₂²×C₃	1	2	yes	complemented
231	#117	C₂²×C₃	1	2	yes	complemented
232	C₂×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
233	C₂×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
234	C₂×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
235	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
236	C₂×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
237	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic, complemented
238	C₂³×C₃	—	2	4	no	—
239	C₂³×C₃	—	2	4	no	—
240	C₂³×C₃	—	2	8	no	—
241	C₂³×C₃	—	4	2	no	—
242	C₂³×C₃	—	4	4	no	—
243	C₂³×C₃	—	4	4	no	—
244	C₂³×C₃	C₂⁴	1	2	yes	—
245	C₂³×C₃	C₂⁴	1	2	yes	—
246	C₂³×C₃	C₂⁴	1	4	yes	—
247	C₂³×C₃	C₂⁴	1	2	yes	—
248	C₂³×C₃	C₂⁴	1	1	yes	characteristic
249	C₃×Q₈	—	2	2	no	—
250	C₃×Q₈	—	4	2	no	—
251	C₃×D₄	—	2	4	no	—
252	C₃×D₄	—	2	8	no	—
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	8	no	—
255	C₃×D₄	—	2	2	no	—
256	C₃×D₄	—	2	4	no	—
257	C₃×D₄	—	2	2	no	—
258	C₃×D₄	—	2	4	no	—
259	C₃×D₄	—	4	4	no	—
260	C₃×D₄	—	4	4	no	—
261	C₃×D₄	—	4	4	no	—
262	C₃×D₄	—	4	2	no	—
263	C₃×D₄	—	4	4	no	—
264	C₃×D₄	#41	1	4	yes	complemented
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	2	no	—
267	C₂×C₃×C₄	—	2	4	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	4	no	—
270	C₂×C₃×C₄	—	2	4	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	4	2	no	—
274	C₂×C₃×C₄	—	4	4	no	—
275	C₂×C₃×C₄	—	4	4	no	—
276	C₂×C₃×C₄	—	4	4	no	—
277	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂⁴	1	2	yes	—
279	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂⁴	1	2	yes	—
282	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂⁴	1	4	yes	—
284	C₂×C₃×C₄	C₂⁴	1	2	yes	—
285	C₂×C₃×C₄	C₂⁴	1	2	yes	—
286	C₂×C₃×C₄	C₂⁴	1	2	yes	—
287	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
289	C₂⁴	C₂³×C₃	1	2	yes	—
290	C₂⁴	C₂³×C₃	1	4	yes	—
291	#41	—	4	4	no	—
292	#41	—	4	4	no	—
293	C₂×Q₈	C₂³×C₃	1	1	yes	characteristic
294	C₂×Q₈	C₂³×C₃	1	2	yes	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	C₂³×C₃	1	2	yes	—
300	C₂×D₄	C₂³×C₃	1	4	yes	—
301	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
302	C₂×D₄	C₂³×C₃	1	2	yes	—
303	C₂×D₄	C₂³×C₃	1	4	yes	—
304	C₂×D₄	C₂³×C₃	1	2	yes	—
305	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
306	C₂×D₄	C₂³×C₃	1	2	yes	—
307	C₂×D₄	C₂³×C₃	1	4	yes	—
308	C₂×D₄	C₂³×C₃	1	2	yes	—
309	C₂×D₄	C₂³×C₃	1	4	yes	—
310	C₂×D₄	C₂³×C₃	1	4	yes	—
311	C₂×D₄	C₂³×C₃	1	4	yes	—
312	C₂×D₄	C₂³×C₃	1	1	yes	characteristic
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
315	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₃	1	2	yes	—
318	C₂²×C₄	C₂³×C₃	1	2	yes	—
319	C₂²×C₄	C₂³×C₃	1	2	yes	—
320	C₂²×C₄	C₂³×C₃	1	2	yes	—
321	C₂²×C₄	C₂³×C₃	1	4	yes	—
322	C₂²×C₄	C₂³×C₃	1	2	yes	—
323	C₂²×C₄	C₂³×C₃	1	4	yes	—
324	C₂²×C₄	C₂³×C₃	1	4	yes	—
325	C₂²×C₄	C₂³×C₃	1	2	yes	—
326	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
327	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
328	C₄⋊C₄	C₂³×C₃	1	2	yes	—
329	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
330	C₄⋊C₄	C₂³×C₃	1	2	yes	—
331	C₄⋊C₄	C₂³×C₃	1	4	yes	—
332	C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
333	C₄⋊C₄	C₂³×C₃	1	2	yes	—
334	C₄⋊C₄	C₂³×C₃	1	2	yes	—
335	C₄⋊C₄	C₂³×C₃	1	2	yes	—
336	C₄⋊C₄	C₂³×C₃	1	2	yes	—
337	C₄⋊C₄	C₂³×C₃	1	4	yes	—
338	C₄⋊C₄	C₂³×C₃	1	2	yes	—
339	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
340	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
341	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
342	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
343	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
344	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
345	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
346	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
347	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
348	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
349	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
350	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
351	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
352	C₂²⋊C₄	C₂³×C₃	1	2	yes	—
353	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
354	C₂²⋊C₄	C₂³×C₃	1	4	yes	—
355	C₄²	C₂³×C₃	1	1	yes	characteristic
356	C₄²	C₂³×C₃	1	1	yes	characteristic
357	C₄²	C₂³×C₃	1	1	yes	characteristic
358	C₄²	C₂³×C₃	1	1	yes	characteristic
359	C₄²	C₂³×C₃	1	4	yes	—
360	C₄²	C₂³×C₃	1	2	yes	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	2	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	2	2	no	—
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	2	4	no	—
370	C₂²×C₃	—	2	4	no	—
371	C₂²×C₃	—	2	2	no	—
372	C₂²×C₃	—	2	2	no	—
373	C₂²×C₃	—	2	2	no	—
374	C₂²×C₃	—	4	8	no	—
375	C₂²×C₃	—	8	8	no	—
376	C₂²×C₃	C₂×#41	1	4	yes	—
377	C₂²×C₃	H(5,𝔽₂)	1	2	yes	—
378	C₂²×C₃	C₂⁵	1	1	yes	characteristic
379	C₃×C₄	—	2	1	no	—
380	C₃×C₄	—	2	2	no	—
381	C₃×C₄	—	2	1	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	2	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	4	no	—
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	C₂×#41	1	2	yes	—
390	C₃×C₄	H(5,𝔽₂)	1	2	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	C₂⁴×C₃	1	2	yes	—
398	C₂³	C₂⁴×C₃	1	2	yes	—
399	C₂³	C₂⁴×C₃	1	4	yes	—
400	C₂³	C₂⁴×C₃	1	2	yes	—
401	C₂³	C₂⁴×C₃	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	8	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	8	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	4	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	4	no	—
417	D₄	C₃×#41	1	4	yes	complemented
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
431	C₂×C₄	C₂⁴×C₃	1	2	yes	—
432	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
433	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
434	C₂×C₄	C₂⁴×C₃	1	2	yes	—
435	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
436	C₂×C₄	C₂⁴×C₃	1	4	yes	—
437	C₂×C₄	C₂⁴×C₃	1	2	yes	—
438	C₂×C₄	C₂⁴×C₃	1	2	yes	—
439	C₂×C₄	C₂⁴×C₃	1	2	yes	—
440	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
441	C₂×C₄	C₂⁴×C₃	1	1	yes	characteristic
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	2	4	no	—
444	C₂×C₃	—	4	2	no	—
445	C₂×C₃	—	4	4	no	—
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	C₂²×#41	1	1	yes	characteristic
448	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	2	4	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	8	8	no	—
465	C₂²	C₂×C₃×#41	1	4	yes	—
466	C₂²	C₃×H(5,𝔽₂)	1	2	yes	—
467	C₂²	C₂⁵×C₃	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	2	no	—
478	C₄	C₂×C₃×#41	1	2	yes	—
479	C₄	C₃×H(5,𝔽₂)	1	2	yes	—
480	C₃	#3519	1	1	yes	characteristic, direct product factor, Sylow
481	C₂	—	2	2	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	2	no	—
484	C₂	—	4	2	no	—
485	C₂	—	4	4	no	—
486	C₂	C₂²×C₃×#41	1	1	yes	characteristic
487	C₂	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
488	C₂	C₂×C₃×H(5,𝔽₂)	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×#555	C₂	semidirect
2. C₃×#554	C₂	semidirect
3. C₃×#553	C₂	semidirect
4. C₃×#553	C₂	semidirect
5. C₃×#550	C₂	semidirect
6. C₃×#546	C₂	semidirect
7. C₃×#546	C₂	semidirect
8. C₃×D₄²	C₂	semidirect
9. C₃×D₄²	C₂	semidirect
10. C₃×#540	C₂	semidirect
11. C₃×#538	C₂	semidirect
12. C₃×#532	C₂	semidirect
13. C₃×#529	C₂	semidirect
14. C₃×#525	C₂	semidirect
15. C₂×C₃×#121	C₂	semidirect
16. C₃×#518	C₂	semidirect
17. C₂×C₃×C₄×D₄	C₂	semidirect
18. #3519	C₃	direct (N × H)
19. C₂×C₃×#41	C₂²	semidirect
20. C₂×C₃×#41	C₂²	semidirect
23. C₂²×C₃×D₄	C₂²	semidirect
24. C₂²×C₃×D₄	C₂²	semidirect
25. C₂³×C₃×C₄	C₂²	semidirect
26. C₃×C₄⋊Q₈	C₂²	semidirect
27. C₃×#127	C₂²	semidirect
28. C₃×#127	C₂²	semidirect
29. C₃×#126	C₂²	semidirect
30. C₃×#126	C₂²	semidirect
31. C₃×#125	C₂²	semidirect
32. C₃×#125	C₂²	semidirect
33. C₃×#124	C₂²	semidirect
34. C₃×#124	C₂²	semidirect
35. C₃×#124	C₂²	semidirect
36. C₃×#123	C₂²	semidirect
37. C₃×#123	C₂²	semidirect
38. C₃×#123	C₂²	semidirect
39. C₃×#123	C₂²	semidirect
40. C₃×C₂²⋊Q₈	C₂²	semidirect
41. C₃×C₂²⋊Q₈	C₂²	semidirect
42. C₃×C₂²⋊Q₈	C₂²	semidirect
44. C₃×#121	C₂²	semidirect
45. C₃×#121	C₂²	semidirect
46. C₃×#121	C₂²	semidirect
47. C₃×#121	C₂²	semidirect
48. C₃×#121	C₂²	semidirect
49. C₃×#121	C₂²	semidirect
50. C₃×#121	C₂²	semidirect
51. C₃×#121	C₂²	semidirect
52. C₃×#121	C₂²	semidirect
53. C₃×#121	C₂²	semidirect
54. C₃×#121	C₂²	semidirect
55. C₃×#121	C₂²	semidirect
56. C₃×#120	C₂²	semidirect
57. C₃×#120	C₂²	semidirect
58. C₃×#120	C₂²	semidirect
59. C₃×C₄×Q₈	C₂²	semidirect
63. C₃×C₄×D₄	C₂²	semidirect
64. C₃×C₄×D₄	C₂²	semidirect
65. C₃×C₄×D₄	C₂²	semidirect
66. C₃×C₄×D₄	C₂²	semidirect
67. C₃×C₄×D₄	C₂²	semidirect
68. C₃×C₄×D₄	C₂²	semidirect
69. C₃×C₄×D₄	C₂²	semidirect
70. C₃×C₄×D₄	C₂²	semidirect
71. C₃×C₄×D₄	C₂²	semidirect
72. C₃×C₄×D₄	C₂²	semidirect
73. C₃×C₄×D₄	C₂²	semidirect
74. C₃×C₄×D₄	C₂²	semidirect
75. C₃×#117	C₂²	semidirect
76. C₃×#117	C₂²	semidirect
77. C₃×#117	C₂²	semidirect
78. C₂×C₃×C₄⋊C₄	C₂²	semidirect
79. C₂×C₃×C₄⋊C₄	C₂²	semidirect
80. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
81. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
82. C₂×C₃×C₂²⋊C₄	C₂²	semidirect
83. C₂×C₃×C₄²	C₂²	semidirect
84. #555	C₂×C₃	semidirect
85. #554	C₂×C₃	semidirect
86. #553	C₂×C₃	semidirect
87. #553	C₂×C₃	semidirect
88. #550	C₂×C₃	semidirect
89. #546	C₂×C₃	semidirect
90. #546	C₂×C₃	semidirect
91. D₄²	C₂×C₃	semidirect
92. D₄²	C₂×C₃	semidirect
93. #540	C₂×C₃	semidirect
94. #538	C₂×C₃	semidirect
95. #532	C₂×C₃	semidirect
96. #529	C₂×C₃	semidirect
97. #525	C₂×C₃	semidirect
98. C₂×#121	C₂×C₃	semidirect
99. #518	C₂×C₃	semidirect
100. C₂×C₄×D₄	C₂×C₃	semidirect
173. C₂×#41	C₂²×C₃	semidirect
174. C₂×#41	C₂²×C₃	semidirect
177. C₂²×D₄	C₂²×C₃	semidirect
178. C₂²×D₄	C₂²×C₃	semidirect
179. C₂³×C₄	C₂²×C₃	semidirect
180. C₄⋊Q₈	C₂²×C₃	semidirect
181. #127	C₂²×C₃	semidirect
182. #127	C₂²×C₃	semidirect
183. #126	C₂²×C₃	semidirect
184. #126	C₂²×C₃	semidirect
185. #125	C₂²×C₃	semidirect
186. #125	C₂²×C₃	semidirect
187. #124	C₂²×C₃	semidirect
188. #124	C₂²×C₃	semidirect
189. #124	C₂²×C₃	semidirect
190. #123	C₂²×C₃	semidirect
191. #123	C₂²×C₃	semidirect
192. #123	C₂²×C₃	semidirect
193. #123	C₂²×C₃	semidirect
194. C₂²⋊Q₈	C₂²×C₃	semidirect
195. C₂²⋊Q₈	C₂²×C₃	semidirect
196. C₂²⋊Q₈	C₂²×C₃	semidirect
198. #121	C₂²×C₃	semidirect
199. #121	C₂²×C₃	semidirect
200. #121	C₂²×C₃	semidirect
201. #121	C₂²×C₃	semidirect
202. #121	C₂²×C₃	semidirect
203. #121	C₂²×C₃	semidirect
204. #121	C₂²×C₃	semidirect
205. #121	C₂²×C₃	semidirect
206. #121	C₂²×C₃	semidirect
207. #121	C₂²×C₃	semidirect
208. #121	C₂²×C₃	semidirect
209. #121	C₂²×C₃	semidirect
210. #120	C₂²×C₃	semidirect
211. #120	C₂²×C₃	semidirect
212. #120	C₂²×C₃	semidirect
213. C₄×Q₈	C₂²×C₃	semidirect
217. C₄×D₄	C₂²×C₃	semidirect
218. C₄×D₄	C₂²×C₃	semidirect
219. C₄×D₄	C₂²×C₃	semidirect
220. C₄×D₄	C₂²×C₃	semidirect
221. C₄×D₄	C₂²×C₃	semidirect
222. C₄×D₄	C₂²×C₃	semidirect
223. C₄×D₄	C₂²×C₃	semidirect
224. C₄×D₄	C₂²×C₃	semidirect
225. C₄×D₄	C₂²×C₃	semidirect
226. C₄×D₄	C₂²×C₃	semidirect
227. C₄×D₄	C₂²×C₃	semidirect
228. C₄×D₄	C₂²×C₃	semidirect
229. #117	C₂²×C₃	semidirect
230. #117	C₂²×C₃	semidirect
231. #117	C₂²×C₃	semidirect
232. C₂×C₄⋊C₄	C₂²×C₃	semidirect
233. C₂×C₄⋊C₄	C₂²×C₃	semidirect
234. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
235. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
236. C₂×C₂²⋊C₄	C₂²×C₃	semidirect
237. C₂×C₄²	C₂²×C₃	semidirect
264. C₃×D₄	#41	semidirect
417. D₄	C₃×#41	semidirect
480. C₃	#3519	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×#555	2
C₃×#554	2
C₃×#553	2
C₃×#550	2
C₃×#546	2
C₃×D₄²	2
C₃×#540	2
C₃×#538	2
C₃×#532	2
C₃×#529	2
C₃×#525	2
C₂×C₃×#121	2
C₃×#518	2
C₂×C₃×C₄×D₄	2
#3519	3

Subgroups — C3×#3519 #87403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3519 #87403