Subgroups — C₂×C₃×#2735 #10670777

Order 768.

3318 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2735	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃×#399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#397	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#396	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#388	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#388	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#379	C₂	1	2	yes	maximal
10	C₂×C₃×#379	C₂	1	1	yes	maximal, characteristic
11	C₂×#2735	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂⁶×C₃	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₄⋊C₄	C₂²	1	2	yes	complemented
16	C₂²×C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₃×C₄²	C₂²	1	2	yes	complemented
28	C₃×#399	C₂²	1	8	yes	complemented
29	C₃×#397	C₂²	1	8	yes	complemented
30	C₃×#397	C₂²	1	16	yes	complemented
31	C₃×#396	C₂²	1	16	yes	complemented
32	C₃×#388	C₂²	1	16	yes	complemented
33	C₃×#388	C₂²	1	16	yes	complemented
34	C₃×#388	C₂²	1	16	yes	complemented
35	C₃×#379	C₂²	1	8	yes	—
36	C₃×#379	C₂²	1	16	yes	—
37	C₂×C₃×#95	C₂²	1	2	yes	complemented
38	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₃×#95	C₂²	1	2	yes	complemented
40	C₂×C₃×#95	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₃×#95	C₂²	1	2	yes	complemented
42	#2735	C₂×C₃	1	16	yes	direct product factor
43	C₂×#399	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#397	C₂×C₃	1	2	yes	complemented
45	C₂×#397	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#396	C₂×C₃	1	2	yes	complemented
47	C₂×#388	C₂×C₃	1	2	yes	complemented
48	C₂×#388	C₂×C₃	1	2	yes	complemented
49	C₂×#388	C₂×C₃	1	2	yes	complemented
50	C₂×#379	C₂×C₃	1	2	yes	—
51	C₂×#379	C₂×C₃	1	1	yes	characteristic
52	C₂⁵×C₃	—	2	4	no	—
53	C₂⁵×C₃	—	2	8	no	—
54	C₂⁵×C₃	—	4	4	no	—
55	C₂⁵×C₃	—	4	2	no	—
56	C₂⁵×C₃	—	4	2	no	—
57	C₂⁵×C₃	C₂³	1	2	yes	—
58	C₂⁵×C₃	C₂³	1	1	yes	characteristic
59	C₂⁵×C₃	C₂³	1	4	yes	—
60	C₂³×C₃×C₄	C₂³	1	2	yes	—
61	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
62	C₂³×C₃×C₄	C₂³	1	2	yes	—
63	C₂³×C₃×C₄	C₂³	1	2	yes	—
64	C₂³×C₃×C₄	C₂³	1	2	yes	—
65	C₂³×C₃×C₄	C₂³	1	2	yes	—
66	C₂³×C₃×C₄	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄⋊C₄	—	4	2	no	—
68	C₂×C₃×C₄⋊C₄	—	4	4	no	—
69	C₂×C₃×C₄⋊C₄	—	4	4	no	—
70	C₂×C₃×C₄⋊C₄	—	4	2	no	—
71	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
72	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
73	C₂×C₃×C₄⋊C₄	C₂³	1	8	yes	complemented
74	C₂×C₃×C₄⋊C₄	C₂³	1	4	yes	complemented
75	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
76	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
79	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
80	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
81	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
82	C₂×C₃×C₂²⋊C₄	—	4	4	no	—
83	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
84	C₂×C₃×C₂²⋊C₄	—	4	2	no	—
85	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
93	C₂×C₃×C₂²⋊C₄	C₂³	1	8	yes	—
94	C₂×C₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₃×C₄²	—	4	4	no	—
96	C₂×C₃×C₄²	C₂³	1	8	yes	complemented
97	C₃×#95	C₂³	1	8	yes	complemented
98	C₃×#95	C₂³	1	4	yes	complemented
99	C₃×#95	C₂³	1	8	yes	complemented
100	C₃×#95	C₂³	1	8	yes	complemented
101	C₃×#95	C₂³	1	4	yes	complemented
102	C₂⁶	C₂²×C₃	1	1	yes	characteristic
103	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
105	C₂²×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
106	C₂²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
113	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
115	C₂²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
116	C₂²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂²×C₄²	C₂²×C₃	1	2	yes	complemented
118	#399	C₂²×C₃	1	8	yes	complemented
119	#397	C₂²×C₃	1	8	yes	complemented
120	#397	C₂²×C₃	1	16	yes	complemented
121	#396	C₂²×C₃	1	16	yes	complemented
122	#388	C₂²×C₃	1	16	yes	complemented
123	#388	C₂²×C₃	1	16	yes	complemented
124	#388	C₂²×C₃	1	16	yes	complemented
125	#379	C₂²×C₃	1	8	yes	—
126	#379	C₂²×C₃	1	16	yes	—
127	C₂×#95	C₂²×C₃	1	2	yes	complemented
128	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
129	C₂×#95	C₂²×C₃	1	2	yes	complemented
130	C₂×#95	C₂²×C₃	1	1	yes	characteristic, complemented
131	C₂×#95	C₂²×C₃	1	2	yes	complemented
132	C₂⁴×C₃	—	2	4	no	—
133	C₂⁴×C₃	—	2	4	no	—
134	C₂⁴×C₃	—	2	4	no	—
135	C₂⁴×C₃	—	2	4	no	—
136	C₂⁴×C₃	—	2	2	no	—
137	C₂⁴×C₃	—	2	4	no	—
138	C₂⁴×C₃	—	2	2	no	—
139	C₂⁴×C₃	—	2	4	no	—
140	C₂⁴×C₃	—	2	4	no	—
141	C₂⁴×C₃	—	2	4	no	—
142	C₂⁴×C₃	—	2	8	no	—
143	C₂⁴×C₃	—	2	16	no	—
144	C₂⁴×C₃	—	4	8	no	—
145	C₂⁴×C₃	—	4	4	no	—
146	C₂⁴×C₃	—	4	4	no	—
147	C₂⁴×C₃	—	4	32	no	—
148	C₂⁴×C₃	—	4	16	no	—
149	C₂⁴×C₃	—	4	32	no	—
150	C₂⁴×C₃	—	4	16	no	—
151	C₂⁴×C₃	—	4	16	no	—
152	C₂⁴×C₃	#41	1	8	yes	—
153	C₂⁴×C₃	#41	1	4	yes	—
154	C₂⁴×C₃	C₂⁴	1	4	yes	—
155	C₂⁴×C₃	C₂⁴	1	2	yes	—
156	C₂⁴×C₃	C₂⁴	1	1	yes	characteristic
157	C₂²×C₃×C₄	—	2	4	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	—	2	4	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	2	4	no	—
162	C₂²×C₃×C₄	—	2	4	no	—
163	C₂²×C₃×C₄	—	2	4	no	—
164	C₂²×C₃×C₄	—	2	4	no	—
165	C₂²×C₃×C₄	—	2	4	no	—
166	C₂²×C₃×C₄	—	2	4	no	—
167	C₂²×C₃×C₄	—	2	4	no	—
168	C₂²×C₃×C₄	—	2	4	no	—
169	C₂²×C₃×C₄	—	2	4	no	—
170	C₂²×C₃×C₄	—	2	4	no	—
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	2	4	no	—
174	C₂²×C₃×C₄	—	2	4	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
177	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
178	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
179	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
180	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
181	C₂²×C₃×C₄	C₂⁴	1	4	yes	—
182	C₂²×C₃×C₄	C₂⁴	1	2	yes	—
183	C₃×C₄⋊C₄	—	4	4	no	—
184	C₃×C₄⋊C₄	—	4	8	no	—
185	C₃×C₄⋊C₄	—	4	8	no	—
186	C₃×C₄⋊C₄	—	4	4	no	—
187	C₃×C₂²⋊C₄	—	2	16	no	—
188	C₃×C₂²⋊C₄	—	2	16	no	—
189	C₃×C₂²⋊C₄	—	2	16	no	—
190	C₃×C₂²⋊C₄	—	4	8	no	—
191	C₃×C₂²⋊C₄	—	4	8	no	—
192	C₃×C₂²⋊C₄	—	4	8	no	—
193	C₃×C₂²⋊C₄	—	4	4	no	—
194	C₃×C₂²⋊C₄	—	4	8	no	—
195	C₃×C₂²⋊C₄	—	4	8	no	—
196	C₃×C₂²⋊C₄	—	4	4	no	—
197	C₃×C₄²	—	4	8	no	—
198	C₂⁵	—	2	4	no	—
199	C₂⁵	—	2	8	no	—
200	C₂⁵	—	4	4	no	—
201	C₂⁵	—	4	2	no	—
202	C₂⁵	—	4	2	no	—
203	C₂⁵	C₂³×C₃	1	2	yes	—
204	C₂⁵	C₂³×C₃	1	1	yes	characteristic
205	C₂⁵	C₂³×C₃	1	4	yes	—
206	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₃	1	2	yes	—
208	C₂³×C₄	C₂³×C₃	1	2	yes	—
209	C₂³×C₄	C₂³×C₃	1	2	yes	—
210	C₂³×C₄	C₂³×C₃	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₃	1	2	yes	—
212	C₂³×C₄	C₂³×C₃	1	2	yes	—
213	C₂×C₄⋊C₄	—	4	2	no	—
214	C₂×C₄⋊C₄	—	4	4	no	—
215	C₂×C₄⋊C₄	—	4	4	no	—
216	C₂×C₄⋊C₄	—	4	2	no	—
217	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
218	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
219	C₂×C₄⋊C₄	C₂³×C₃	1	8	yes	complemented
220	C₂×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
221	C₂×C₂²⋊C₄	—	2	8	no	—
222	C₂×C₂²⋊C₄	—	2	8	no	—
223	C₂×C₂²⋊C₄	—	2	8	no	—
224	C₂×C₂²⋊C₄	—	4	4	no	—
225	C₂×C₂²⋊C₄	—	4	4	no	—
226	C₂×C₂²⋊C₄	—	4	4	no	—
227	C₂×C₂²⋊C₄	—	4	4	no	—
228	C₂×C₂²⋊C₄	—	4	4	no	—
229	C₂×C₂²⋊C₄	—	4	2	no	—
230	C₂×C₂²⋊C₄	—	4	2	no	—
231	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
234	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
235	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
236	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
237	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
241	C₂×C₄²	—	4	4	no	—
242	C₂×C₄²	C₂³×C₃	1	8	yes	complemented
243	#95	C₂³×C₃	1	8	yes	complemented
244	#95	C₂³×C₃	1	4	yes	complemented
245	#95	C₂³×C₃	1	8	yes	complemented
246	#95	C₂³×C₃	1	8	yes	complemented
247	#95	C₂³×C₃	1	4	yes	complemented
248	C₂³×C₃	—	2	16	no	—
249	C₂³×C₃	—	2	8	no	—
250	C₂³×C₃	—	2	16	no	—
251	C₂³×C₃	—	2	16	no	—
252	C₂³×C₃	—	2	16	no	—
253	C₂³×C₃	—	2	4	no	—
254	C₂³×C₃	—	2	4	no	—
255	C₂³×C₃	—	2	4	no	—
256	C₂³×C₃	—	2	2	no	—
257	C₂³×C₃	—	2	4	no	—
258	C₂³×C₃	—	2	4	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	—	2	4	no	—
261	C₂³×C₃	—	2	4	no	—
262	C₂³×C₃	—	2	4	no	—
263	C₂³×C₃	—	4	32	no	—
264	C₂³×C₃	—	4	16	no	—
265	C₂³×C₃	—	4	32	no	—
266	C₂³×C₃	—	4	16	no	—
267	C₂³×C₃	—	4	128	no	—
268	C₂³×C₃	—	4	16	no	—
269	C₂³×C₃	—	4	8	no	—
270	C₂³×C₃	—	4	8	no	—
271	C₂³×C₃	—	4	8	no	—
272	C₂³×C₃	—	4	8	no	—
273	C₂³×C₃	—	4	4	no	—
274	C₂³×C₃	—	4	8	no	—
275	C₂³×C₃	—	4	4	no	—
276	C₂³×C₃	C₂×#41	1	8	yes	—
277	C₂³×C₃	C₂×#41	1	4	yes	—
278	C₂³×C₃	C₂×#41	1	4	yes	—
279	C₂³×C₃	C₂×#41	1	2	yes	—
280	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
281	C₂³×C₃	H(5,𝔽₂)	1	4	yes	—
282	C₂³×C₃	H(5,𝔽₂)	1	2	yes	—
283	C₂³×C₃	C₂⁵	1	1	yes	characteristic
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	4	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	2	4	no	—
301	C₂×C₃×C₄	—	2	4	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	4	8	no	—
304	C₂×C₃×C₄	—	4	8	no	—
305	C₂×C₃×C₄	—	4	8	no	—
306	C₂×C₃×C₄	—	4	8	no	—
307	C₂×C₃×C₄	—	4	4	no	—
308	C₂×C₃×C₄	—	4	8	no	—
309	C₂×C₃×C₄	—	4	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	4	no	—
312	C₂⁴	—	2	4	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	8	no	—
321	C₂⁴	—	2	16	no	—
322	C₂⁴	—	4	8	no	—
323	C₂⁴	—	4	4	no	—
324	C₂⁴	—	4	4	no	—
325	C₂⁴	—	4	32	no	—
326	C₂⁴	—	4	16	no	—
327	C₂⁴	—	4	32	no	—
328	C₂⁴	—	4	16	no	—
329	C₂⁴	—	4	16	no	—
330	C₂⁴	C₃×#41	1	8	yes	—
331	C₂⁴	C₃×#41	1	4	yes	—
332	C₂⁴	C₂⁴×C₃	1	4	yes	—
333	C₂⁴	C₂⁴×C₃	1	2	yes	—
334	C₂⁴	C₂⁴×C₃	1	1	yes	characteristic
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
355	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₃	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₃	1	2	yes	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	8	no	—
363	C₄⋊C₄	—	4	8	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	2	16	no	—
366	C₂²⋊C₄	—	2	16	no	—
367	C₂²⋊C₄	—	2	16	no	—
368	C₂²⋊C₄	—	4	8	no	—
369	C₂²⋊C₄	—	4	8	no	—
370	C₂²⋊C₄	—	4	8	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	8	no	—
373	C₂²⋊C₄	—	4	8	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₄²	—	4	8	no	—
376	C₂²×C₃	—	2	8	no	—
377	C₂²×C₃	—	2	4	no	—
378	C₂²×C₃	—	2	8	no	—
379	C₂²×C₃	—	2	8	no	—
380	C₂²×C₃	—	2	8	no	—
381	C₂²×C₃	—	4	64	no	—
382	C₂²×C₃	—	4	4	no	—
383	C₂²×C₃	—	4	4	no	—
384	C₂²×C₃	—	4	4	no	—
385	C₂²×C₃	—	4	4	no	—
386	C₂²×C₃	—	4	2	no	—
387	C₂²×C₃	—	4	32	no	—
388	C₂²×C₃	—	4	16	no	—
389	C₂²×C₃	—	4	4	no	—
390	C₂²×C₃	—	4	2	no	—
391	C₂²×C₃	#538	1	8	yes	—
392	C₂²×C₃	#538	1	4	yes	—
393	C₂²×C₃	#551	1	8	yes	—
394	C₂²×C₃	#551	1	4	yes	—
395	C₂²×C₃	#560	1	4	yes	—
396	C₂²×C₃	C₂²×#41	1	2	yes	—
397	C₂²×C₃	C₂²×#41	1	1	yes	characteristic
398	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×C₃	C₂×H(5,𝔽₂)	1	2	yes	—
400	C₂²×C₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₃×C₄	—	4	4	no	—
402	C₃×C₄	—	4	4	no	—
403	C₃×C₄	—	4	4	no	—
404	C₃×C₄	—	4	4	no	—
405	C₃×C₄	—	4	2	no	—
406	C₃×C₄	—	4	4	no	—
407	C₃×C₄	—	4	2	no	—
408	C₂³	—	2	4	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	2	4	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	2	16	no	—
419	C₂³	—	2	8	no	—
420	C₂³	—	2	16	no	—
421	C₂³	—	2	16	no	—
422	C₂³	—	2	16	no	—
423	C₂³	—	4	32	no	—
424	C₂³	—	4	16	no	—
425	C₂³	—	4	32	no	—
426	C₂³	—	4	16	no	—
427	C₂³	—	4	16	no	—
428	C₂³	—	4	128	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	4	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	—	4	8	no	—
435	C₂³	—	4	4	no	—
436	C₂³	C₂×C₃×#41	1	8	yes	—
437	C₂³	C₂×C₃×#41	1	4	yes	—
438	C₂³	C₂×C₃×#41	1	2	yes	—
439	C₂³	C₂×C₃×#41	1	4	yes	—
440	C₂³	C₃×H(5,𝔽₂)	1	4	yes	—
441	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
442	C₂³	C₃×H(5,𝔽₂)	1	2	yes	—
443	C₂³	C₂⁵×C₃	1	1	yes	characteristic
444	C₂×C₄	—	2	4	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	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₃	—	4	8	no	—
471	C₂×C₃	—	4	4	no	—
472	C₂×C₃	#2735	1	8	yes	direct product factor
473	C₂×C₃	C₂×#538	1	2	yes	—
474	C₂×C₃	C₂×#538	1	1	yes	characteristic
475	C₂×C₃	C₂×#551	1	2	yes	—
476	C₂×C₃	C₂×#551	1	1	yes	characteristic
477	C₂×C₃	C₂×#560	1	1	yes	characteristic
478	C₂²	—	2	8	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	8	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	4	64	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	32	no	—
492	C₂²	—	4	16	no	—
493	C₂²	C₃×#538	1	8	yes	—
494	C₂²	C₃×#538	1	4	yes	—
495	C₂²	C₃×#551	1	8	yes	—
496	C₂²	C₃×#551	1	4	yes	—
497	C₂²	C₃×#560	1	4	yes	—
498	C₂²	C₂²×C₃×#41	1	2	yes	—
499	C₂²	C₂²×C₃×#41	1	1	yes	characteristic
500	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
502	C₂²	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
503	C₄	—	4	4	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	4	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	2	no	—
510	C₃	C₂×#2735	1	1	yes	characteristic, direct product factor, Sylow
511	C₂	—	4	8	no	—
512	C₂	—	4	4	no	—
513	C₂	C₃×#2735	1	8	yes	direct product factor
514	C₂	C₂×C₃×#538	1	2	yes	—
515	C₂	C₂×C₃×#538	1	1	yes	characteristic
516	C₂	C₂×C₃×#551	1	2	yes	—
517	C₂	C₂×C₃×#551	1	1	yes	characteristic
518	C₂	C₂×C₃×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃
prime radical	C₂⁶×C₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2735	C₂	direct (N × H)
2. C₂×C₃×#399	C₂	semidirect
3. C₂×C₃×#397	C₂	semidirect
4. C₂×C₃×#397	C₂	semidirect
5. C₂×C₃×#396	C₂	semidirect
6. C₂×C₃×#388	C₂	semidirect
7. C₂×C₃×#388	C₂	semidirect
8. C₂×C₃×#388	C₂	semidirect
11. C₂×#2735	C₃	direct (N × H)
13. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
14. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
15. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
16. C₂²×C₃×C₄⋊C₄	C₂²	semidirect
27. C₂²×C₃×C₄²	C₂²	semidirect
28. C₃×#399	C₂²	semidirect
29. C₃×#397	C₂²	semidirect
30. C₃×#397	C₂²	semidirect
31. C₃×#396	C₂²	semidirect
32. C₃×#388	C₂²	semidirect
33. C₃×#388	C₂²	semidirect
34. C₃×#388	C₂²	semidirect
37. C₂×C₃×#95	C₂²	semidirect
38. C₂×C₃×#95	C₂²	semidirect
39. C₂×C₃×#95	C₂²	semidirect
40. C₂×C₃×#95	C₂²	semidirect
41. C₂×C₃×#95	C₂²	semidirect
42. #2735	C₂×C₃	direct (N × H)
43. C₂×#399	C₂×C₃	semidirect
44. C₂×#397	C₂×C₃	semidirect
45. C₂×#397	C₂×C₃	semidirect
46. C₂×#396	C₂×C₃	semidirect
47. C₂×#388	C₂×C₃	semidirect
48. C₂×#388	C₂×C₃	semidirect
49. C₂×#388	C₂×C₃	semidirect
71. C₂×C₃×C₄⋊C₄	C₂³	semidirect
72. C₂×C₃×C₄⋊C₄	C₂³	semidirect
73. C₂×C₃×C₄⋊C₄	C₂³	semidirect
74. C₂×C₃×C₄⋊C₄	C₂³	semidirect
96. C₂×C₃×C₄²	C₂³	semidirect
97. C₃×#95	C₂³	semidirect
98. C₃×#95	C₂³	semidirect
99. C₃×#95	C₂³	semidirect
100. C₃×#95	C₂³	semidirect
101. C₃×#95	C₂³	semidirect
103. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
104. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
105. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
106. C₂²×C₄⋊C₄	C₂²×C₃	semidirect
117. C₂²×C₄²	C₂²×C₃	semidirect
118. #399	C₂²×C₃	semidirect
119. #397	C₂²×C₃	semidirect
120. #397	C₂²×C₃	semidirect
121. #396	C₂²×C₃	semidirect
122. #388	C₂²×C₃	semidirect
123. #388	C₂²×C₃	semidirect
124. #388	C₂²×C₃	semidirect
127. C₂×#95	C₂²×C₃	semidirect
128. C₂×#95	C₂²×C₃	semidirect
129. C₂×#95	C₂²×C₃	semidirect
130. C₂×#95	C₂²×C₃	semidirect
131. C₂×#95	C₂²×C₃	semidirect
217. C₂×C₄⋊C₄	C₂³×C₃	semidirect
218. C₂×C₄⋊C₄	C₂³×C₃	semidirect
219. C₂×C₄⋊C₄	C₂³×C₃	semidirect
220. C₂×C₄⋊C₄	C₂³×C₃	semidirect
242. C₂×C₄²	C₂³×C₃	semidirect
243. #95	C₂³×C₃	semidirect
244. #95	C₂³×C₃	semidirect
245. #95	C₂³×C₃	semidirect
246. #95	C₂³×C₃	semidirect
247. #95	C₂³×C₃	semidirect
472. C₂×C₃	#2735	direct (N × H)
510. C₃	C₂×#2735	direct (N × H)
513. C₂	C₃×#2735	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×#2735	2
C₂×C₃×#399	2
C₂×C₃×#397	2
C₂×C₃×#396	2
C₂×C₃×#388	2
C₂×C₃×#379	2
C₂×#2735	3

Subgroups — C2×C3×#2735 #10670777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#2735 #10670777