Subgroups — C₂×C₃×#3210 #10679387

Order 768.

2186 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₃×#3210	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#464	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×#452	C₂	1	4	yes	maximal, complemented
10	C₂×C₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#3210	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₃×#41	C₂²	1	2	yes	—
13	C₂²×C₃×Q₁₆	C₂²	1	4	yes	—
14	C₂²×C₃×SD₁₆	C₂²	1	4	yes	—
15	C₃×#533	—	2	4	no	—
16	C₃×#533	C₂²	1	8	yes	complemented
17	C₃×#532	—	2	4	no	—
18	C₃×#532	C₂²	1	8	yes	—
19	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×#127	C₂²	1	1	yes	characteristic
23	C₂×C₃×#125	—	2	1	no	—
24	C₂×C₃×#124	C₂²	1	2	yes	—
25	C₂×C₃×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₃×#121	—	2	1	no	—
28	C₂×C₃×#121	—	2	1	no	—
29	C₂×C₃×C₄×Q₈	—	2	1	no	—
30	C₂×C₃×C₄×Q₈	C₂²	1	2	yes	—
31	C₂×C₃×C₄×D₄	—	2	1	no	—
32	C₂×C₃×C₄×D₄	—	2	1	no	—
33	C₂×C₃×#117	—	2	1	no	—
34	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
35	C₃×#494	C₂²	1	8	yes	complemented
36	C₃×#492	C₂²	1	8	yes	complemented
37	C₃×#487	C₂²	1	8	yes	complemented
38	C₃×#486	C₂²	1	8	yes	complemented
39	C₃×#464	C₂²	1	32	yes	complemented
40	C₃×#452	C₂²	1	32	yes	complemented
41	C₃×#431	C₂²	1	8	yes	complemented
42	C₂×C₃×C₄⋊C₈	C₂²	1	2	yes	—
43	C₂×C₃×#103	C₂²	1	4	yes	—
44	C₂×C₃×#102	C₂²	1	4	yes	—
45	C₂×C₃×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
47	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
48	C₂×#533	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#532	C₂×C₃	1	1	yes	characteristic
50	#3210	C₂×C₃	1	16	yes	direct product factor
51	C₂×#494	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#492	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×#487	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×#486	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#464	C₂×C₃	1	4	yes	complemented
56	C₂×#452	C₂×C₃	1	4	yes	complemented
57	C₂×#431	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×C₃×#41	—	2	4	no	—
59	C₂×C₃×#41	—	4	8	no	—
60	C₂×C₃×#41	C₂³	1	8	yes	—
61	C₂²×C₃×Q₈	—	2	1	no	—
62	C₂²×C₃×Q₈	C₂³	1	2	yes	—
63	C₂²×C₃×Q₈	C₂³	1	2	yes	—
64	C₂²×C₃×D₄	—	2	2	no	—
65	C₂²×C₃×D₄	—	2	1	no	—
66	C₂²×C₃×D₄	—	2	1	no	—
67	C₂²×C₃×D₄	C₂³	1	2	yes	—
68	C₂³×C₃×C₄	—	2	2	no	—
69	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
70	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
71	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
72	C₂×C₃×Q₁₆	—	4	8	no	—
73	C₂×C₃×Q₁₆	C₂³	1	16	yes	—
74	C₂×C₃×SD₁₆	—	4	8	no	—
75	C₂×C₃×SD₁₆	C₂³	1	16	yes	—
76	C₂²×C₃×C₈	C₂³	1	2	yes	—
77	C₂²×C₃×C₈	C₂³	1	2	yes	—
78	C₃×C₄⋊Q₈	—	2	2	no	—
79	C₃×C₄⋊Q₈	—	2	2	no	—
80	C₃×C₄⋊Q₈	—	2	2	no	—
81	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₃×C₄⋊Q₈	C₂³	1	4	yes	—
84	C₃×#127	—	2	2	no	—
85	C₃×#127	C₂³	1	4	yes	—
86	C₃×#125	—	2	8	no	—
87	C₃×#124	—	2	4	no	—
88	C₃×#124	C₂³	1	8	yes	—
89	C₃×C₂²⋊Q₈	—	2	8	no	—
90	C₃×C₂²⋊Q₈	—	2	4	no	—
91	C₃×C₂²⋊Q₈	C₂³	1	8	yes	—
92	C₃×#121	—	2	8	no	—
93	C₃×#121	—	2	8	no	—
94	C₃×C₄×Q₈	—	2	8	no	—
95	C₃×C₄×Q₈	—	2	4	no	—
96	C₃×C₄×Q₈	C₂³	1	8	yes	—
97	C₃×C₄×D₄	—	2	8	no	—
98	C₃×C₄×D₄	—	2	8	no	—
99	C₃×#117	—	2	8	no	—
100	C₂×C₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₃×C₄⋊C₄	—	2	2	no	—
106	C₂×C₃×C₄⋊C₄	—	2	2	no	—
107	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₃×C₄²	—	2	2	no	—
112	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
113	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
114	C₂×C₃×C₄²	D₄	1	4	yes	—
115	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
117	C₂×C₃×C₄²	C₂³	1	4	yes	—
118	C₃×C₄⋊C₈	C₂³	1	8	yes	—
119	C₃×#103	C₂³	1	16	yes	—
120	C₃×#102	C₂³	1	16	yes	—
121	C₃×C₂²⋊C₈	C₂³	1	8	yes	—
122	C₃×C₄×C₈	C₂³	1	4	yes	—
123	C₃×C₄×C₈	C₂³	1	4	yes	—
124	C₂²×#41	C₂²×C₃	1	2	yes	—
125	C₂²×Q₁₆	C₂²×C₃	1	4	yes	—
126	C₂²×SD₁₆	C₂²×C₃	1	4	yes	—
127	#533	—	2	4	no	—
128	#533	C₂²×C₃	1	8	yes	complemented
129	#532	—	2	4	no	—
130	#532	C₂²×C₃	1	8	yes	—
131	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
134	C₂×#127	C₂²×C₃	1	1	yes	characteristic
135	C₂×#125	—	2	1	no	—
136	C₂×#124	C₂²×C₃	1	2	yes	—
137	C₂×C₂²⋊Q₈	—	2	1	no	—
138	C₂×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
139	C₂×#121	—	2	1	no	—
140	C₂×#121	—	2	1	no	—
141	C₂×C₄×Q₈	—	2	1	no	—
142	C₂×C₄×Q₈	C₂²×C₃	1	2	yes	—
143	C₂×C₄×D₄	—	2	1	no	—
144	C₂×C₄×D₄	—	2	1	no	—
145	C₂×#117	—	2	1	no	—
146	C₂²×C₄²	C₂²×C₃	1	1	yes	characteristic
147	#494	C₂²×C₃	1	8	yes	complemented
148	#492	C₂²×C₃	1	8	yes	complemented
149	#487	C₂²×C₃	1	8	yes	complemented
150	#486	C₂²×C₃	1	8	yes	complemented
151	#464	C₂²×C₃	1	32	yes	complemented
152	#452	C₂²×C₃	1	32	yes	complemented
153	#431	C₂²×C₃	1	8	yes	complemented
154	C₂×C₄⋊C₈	C₂²×C₃	1	2	yes	—
155	C₂×#103	C₂²×C₃	1	4	yes	—
156	C₂×#102	C₂²×C₃	1	4	yes	—
157	C₂×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
158	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
160	C₂⁴×C₃	—	2	2	no	—
161	C₂⁴×C₃	C₂×D₄	1	1	yes	characteristic
162	C₃×#41	—	4	16	no	—
163	C₃×#41	—	4	16	no	—
164	C₂×C₃×Q₈	—	2	2	no	—
165	C₂×C₃×Q₈	—	2	4	no	—
166	C₂×C₃×Q₈	—	2	2	no	—
167	C₂×C₃×Q₈	—	2	8	no	—
168	C₂×C₃×Q₈	—	2	8	no	—
169	C₂×C₃×Q₈	—	4	4	no	—
170	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
171	C₂×C₃×Q₈	C₂⁴	1	4	yes	—
172	C₂×C₃×D₄	—	2	8	no	—
173	C₂×C₃×D₄	—	2	4	no	—
174	C₂×C₃×D₄	—	2	4	no	—
175	C₂×C₃×D₄	—	2	2	no	—
176	C₂×C₃×D₄	—	2	8	no	—
177	C₂×C₃×D₄	—	4	8	no	—
178	C₂×C₃×D₄	—	4	4	no	—
179	C₂×C₃×D₄	—	4	4	no	—
180	C₂×C₃×D₄	C₂⁴	1	4	yes	—
181	C₂²×C₃×C₄	—	2	4	no	—
182	C₂²×C₃×C₄	—	2	4	no	—
183	C₂²×C₃×C₄	—	2	4	no	—
184	C₂²×C₃×C₄	—	2	2	no	—
185	C₂²×C₃×C₄	—	2	2	no	—
186	C₂²×C₃×C₄	—	2	2	no	—
187	C₂²×C₃×C₄	—	2	8	no	—
188	C₂²×C₃×C₄	—	4	8	no	—
189	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
190	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
191	C₂²×C₃×C₄	C₂×D₄	1	4	yes	—
192	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
198	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
199	C₃×Q₁₆	—	4	16	no	—
200	C₃×SD₁₆	—	4	16	no	—
201	C₂×C₃×C₈	—	2	4	no	—
202	C₂×C₃×C₈	—	2	4	no	—
203	C₂×C₃×C₈	C₂⁴	1	4	yes	—
204	C₂×C₃×C₈	C₂⁴	1	4	yes	—
205	C₃×C₄⋊C₄	—	2	4	no	—
206	C₃×C₄⋊C₄	—	2	4	no	—
207	C₃×C₄⋊C₄	—	2	4	no	—
208	C₃×C₄⋊C₄	—	2	4	no	—
209	C₃×C₄⋊C₄	—	2	4	no	—
210	C₃×C₄⋊C₄	—	2	8	no	—
211	C₃×C₄⋊C₄	—	2	8	no	—
212	C₃×C₄⋊C₄	—	2	2	no	—
213	C₃×C₄⋊C₄	C₂⁴	1	4	yes	—
214	C₃×C₂²⋊C₄	—	2	8	no	—
215	C₃×C₂²⋊C₄	—	2	8	no	—
216	C₃×C₂²⋊C₄	—	2	8	no	—
217	C₃×C₄²	—	2	8	no	—
218	C₃×C₄²	C₂×D₄	1	4	yes	—
219	C₃×C₄²	C₂×D₄	1	4	yes	—
220	C₃×C₄²	C₂×D₄	1	2	yes	—
221	C₃×C₄²	C₂×D₄	1	2	yes	—
222	C₃×C₄²	C₂⁴	1	2	yes	—
223	C₃×C₄²	C₂⁴	1	2	yes	—
224	C₂×#41	—	2	4	no	—
225	C₂×#41	—	4	8	no	—
226	C₂×#41	C₂³×C₃	1	8	yes	—
227	C₂²×Q₈	—	2	1	no	—
228	C₂²×Q₈	C₂³×C₃	1	2	yes	—
229	C₂²×Q₈	C₂³×C₃	1	2	yes	—
230	C₂²×D₄	—	2	2	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	C₂³×C₃	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
236	C₂³×C₄	C₃×D₄	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
238	C₂×Q₁₆	—	4	8	no	—
239	C₂×Q₁₆	C₂³×C₃	1	16	yes	—
240	C₂×SD₁₆	—	4	8	no	—
241	C₂×SD₁₆	C₂³×C₃	1	16	yes	—
242	C₂²×C₈	C₂³×C₃	1	2	yes	—
243	C₂²×C₈	C₂³×C₃	1	2	yes	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	—	2	2	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
248	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
249	C₄⋊Q₈	C₂³×C₃	1	4	yes	—
250	#127	—	2	2	no	—
251	#127	C₂³×C₃	1	4	yes	—
252	#125	—	2	8	no	—
253	#124	—	2	4	no	—
254	#124	C₂³×C₃	1	8	yes	—
255	C₂²⋊Q₈	—	2	8	no	—
256	C₂²⋊Q₈	—	2	4	no	—
257	C₂²⋊Q₈	C₂³×C₃	1	8	yes	—
258	#121	—	2	8	no	—
259	#121	—	2	8	no	—
260	C₄×Q₈	—	2	8	no	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	C₂³×C₃	1	8	yes	—
263	C₄×D₄	—	2	8	no	—
264	C₄×D₄	—	2	8	no	—
265	#117	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
279	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
280	C₂×C₄²	C₃×D₄	1	4	yes	—
281	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₄²	C₂³×C₃	1	4	yes	—
284	C₄⋊C₈	C₂³×C₃	1	8	yes	—
285	#103	C₂³×C₃	1	16	yes	—
286	#102	C₂³×C₃	1	16	yes	—
287	C₂²⋊C₈	C₂³×C₃	1	8	yes	—
288	C₄×C₈	C₂³×C₃	1	4	yes	—
289	C₄×C₈	C₂³×C₃	1	4	yes	—
290	C₂³×C₃	—	2	2	no	—
291	C₂³×C₃	—	2	2	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	4	4	no	—
295	C₂³×C₃	—	4	4	no	—
296	C₂³×C₃	—	4	4	no	—
297	C₂³×C₃	C₂²×D₄	1	2	yes	—
298	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
299	C₃×Q₈	—	2	8	no	—
300	C₃×Q₈	—	2	8	no	—
301	C₃×Q₈	—	4	4	no	—
302	C₃×Q₈	—	4	4	no	—
303	C₃×Q₈	—	4	8	no	—
304	C₃×D₄	—	2	8	no	—
305	C₃×D₄	—	4	16	no	—
306	C₃×D₄	—	4	4	no	—
307	C₃×D₄	—	4	8	no	—
308	C₃×D₄	—	4	8	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	4	no	—
313	C₂×C₃×C₄	—	2	8	no	—
314	C₂×C₃×C₄	—	2	8	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	4	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	4	16	no	—
320	C₂×C₃×C₄	—	4	4	no	—
321	C₂×C₃×C₄	—	4	4	no	—
322	C₂×C₃×C₄	—	4	4	no	—
323	C₂×C₃×C₄	#135	1	4	yes	—
324	C₂×C₃×C₄	#137	1	4	yes	—
325	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
326	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
327	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
328	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
330	C₂×C₃×C₄	C₂²×D₄	1	2	yes	—
331	C₂×C₃×C₄	H(5,𝔽₂)	1	4	yes	—
332	C₂×C₃×C₄	C₂⁵	1	1	yes	characteristic
333	C₃×C₈	—	2	4	no	—
334	C₃×C₈	—	2	4	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	C₂×C₃×D₄	1	1	yes	characteristic
337	#41	—	4	16	no	—
338	#41	—	4	16	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
346	C₂×Q₈	C₂⁴×C₃	1	4	yes	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	4	8	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂⁴×C₃	1	4	yes	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
367	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
369	C₂²×C₄	C₂×C₃×D₄	1	4	yes	—
370	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
374	Q₁₆	—	4	16	no	—
375	SD₁₆	—	4	16	no	—
376	C₂×C₈	—	2	4	no	—
377	C₂×C₈	—	2	4	no	—
378	C₂×C₈	C₂⁴×C₃	1	4	yes	—
379	C₂×C₈	C₂⁴×C₃	1	4	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	C₂⁴×C₃	1	4	yes	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₄²	—	2	8	no	—
393	C₄²	C₂×C₃×D₄	1	4	yes	—
394	C₄²	C₂×C₃×D₄	1	4	yes	—
395	C₄²	C₂×C₃×D₄	1	2	yes	—
396	C₄²	C₂×C₃×D₄	1	2	yes	—
397	C₄²	C₂⁴×C₃	1	2	yes	—
398	C₄²	C₂⁴×C₃	1	2	yes	—
399	C₂²×C₃	—	2	2	no	—
400	C₂²×C₃	—	2	2	no	—
401	C₂²×C₃	—	2	2	no	—
402	C₂²×C₃	—	4	4	no	—
403	C₂²×C₃	—	4	4	no	—
404	C₂²×C₃	—	4	4	no	—
405	C₂²×C₃	—	4	4	no	—
406	C₂²×C₃	—	8	8	no	—
407	C₂²×C₃	#535	1	2	yes	—
408	C₂²×C₃	C₂×#135	1	2	yes	—
409	C₂²×C₃	C₂×#137	1	2	yes	—
410	C₂²×C₃	C₂³×D₄	1	1	yes	characteristic
411	C₃×C₄	—	2	2	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	4	4	no	—
415	C₃×C₄	—	4	4	no	—
416	C₃×C₄	—	4	4	no	—
417	C₃×C₄	#535	1	2	yes	—
418	C₃×C₄	C₂×#135	1	4	yes	—
419	C₃×C₄	C₂×#137	1	4	yes	—
420	C₃×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	C₂²×C₃×D₄	1	2	yes	—
429	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
430	Q₈	—	2	8	no	—
431	Q₈	—	2	8	no	—
432	Q₈	—	4	8	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	4	no	—
435	D₄	—	2	8	no	—
436	D₄	—	4	16	no	—
437	D₄	—	4	8	no	—
438	D₄	—	4	8	no	—
439	D₄	—	4	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	4	16	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	C₃×#135	1	4	yes	—
455	C₂×C₄	C₃×#137	1	4	yes	—
456	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
457	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
458	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
459	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
460	C₂×C₄	C₂²×C₃×D₄	1	2	yes	—
461	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
462	C₂×C₄	C₃×H(5,𝔽₂)	1	4	yes	—
463	C₂×C₄	C₂⁵×C₃	1	1	yes	characteristic
464	C₈	—	2	4	no	—
465	C₈	—	2	4	no	—
466	C₂×C₃	—	4	2	no	—
467	C₂×C₃	—	8	4	no	—
468	C₂×C₃	#3210	1	4	yes	direct product factor
469	C₂×C₃	C₂×#535	1	1	yes	characteristic
470	C₂×C₃	C₂²×#135	1	1	yes	characteristic
471	C₂×C₃	C₂²×#137	1	1	yes	characteristic
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	8	no	—
480	C₂²	C₃×#535	1	2	yes	—
481	C₂²	C₂×C₃×#135	1	2	yes	—
482	C₂²	C₂×C₃×#137	1	2	yes	—
483	C₂²	C₂³×C₃×D₄	1	1	yes	characteristic
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	C₃×#535	1	2	yes	—
491	C₄	C₂×C₃×#135	1	4	yes	—
492	C₄	C₂×C₃×#137	1	4	yes	—
493	C₄	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
494	C₃	C₂×#3210	1	1	yes	characteristic, direct product factor, Sylow
495	C₂	—	4	2	no	—
496	C₂	—	8	4	no	—
497	C₂	C₃×#3210	1	4	yes	direct product factor
498	C₂	C₂×C₃×#535	1	1	yes	characteristic
499	C₂	C₂²×C₃×#135	1	1	yes	characteristic
500	C₂	C₂²×C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃
prime radical	C₂×C₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#533	C₂	semidirect
3. C₃×#3210	C₂	direct (N × H)
4. C₂×C₃×#494	C₂	semidirect
5. C₂×C₃×#492	C₂	semidirect
6. C₂×C₃×#487	C₂	semidirect
7. C₂×C₃×#486	C₂	semidirect
8. C₂×C₃×#464	C₂	semidirect
9. C₂×C₃×#452	C₂	semidirect
10. C₂×C₃×#431	C₂	semidirect
11. C₂×#3210	C₃	direct (N × H)
16. C₃×#533	C₂²	semidirect
35. C₃×#494	C₂²	semidirect
36. C₃×#492	C₂²	semidirect
37. C₃×#487	C₂²	semidirect
38. C₃×#486	C₂²	semidirect
39. C₃×#464	C₂²	semidirect
40. C₃×#452	C₂²	semidirect
41. C₃×#431	C₂²	semidirect
48. C₂×#533	C₂×C₃	semidirect
50. #3210	C₂×C₃	direct (N × H)
51. C₂×#494	C₂×C₃	semidirect
52. C₂×#492	C₂×C₃	semidirect
53. C₂×#487	C₂×C₃	semidirect
54. C₂×#486	C₂×C₃	semidirect
55. C₂×#464	C₂×C₃	semidirect
56. C₂×#452	C₂×C₃	semidirect
57. C₂×#431	C₂×C₃	semidirect
128. #533	C₂²×C₃	semidirect
147. #494	C₂²×C₃	semidirect
148. #492	C₂²×C₃	semidirect
149. #487	C₂²×C₃	semidirect
150. #486	C₂²×C₃	semidirect
151. #464	C₂²×C₃	semidirect
152. #452	C₂²×C₃	semidirect
153. #431	C₂²×C₃	semidirect
468. C₂×C₃	#3210	direct (N × H)
494. C₃	C₂×#3210	direct (N × H)
497. C₂	C₃×#3210	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×#533	2
C₂×C₃×#532	2
C₃×#3210	2
C₂×C₃×#494	2
C₂×C₃×#492	2
C₂×C₃×#487	2
C₂×C₃×#486	2
C₂×C₃×#464	2
C₂×C₃×#452	2
C₂×C₃×#431	2
C₂×#3210	3

Subgroups — C2×C3×#3210 #10679387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#3210 #10679387