Subgroups — C₂×C₁₃×#3168 #15747009

Order 3328.

2070 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#529	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3168	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#529	—	2	8	no	—
19	C₁₃×#529	C₂²	1	16	yes	complemented
20	C₂×C₁₃×#126	—	2	2	no	—
21	C₂×C₁₃×#125	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	—	2	2	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	—	2	2	no	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#499	C₂²	1	8	yes	complemented
32	C₁₃×#495	C₂²	1	8	yes	complemented
33	C₁₃×#488	C₂²	1	16	yes	complemented
34	C₁₃×#467	C₂²	1	8	yes	complemented
35	C₁₃×#466	C₂²	1	8	yes	—
36	C₁₃×#465	C₂²	1	16	yes	complemented
37	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
38	C₄×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
39	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#106	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#103	C₂²	1	2	yes	—
45	C₂×C₁₃×#102	C₂²	1	2	yes	—
46	C₂×C₁₃×#102	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₁₃	C₂²	1	8	yes	complemented
52	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₁₃	—	2	2	no	—
54	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×Q₁₆	—	2	4	no	—
60	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
61	C₂×C₁₃×SD₁₆	—	2	8	no	—
62	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
63	C₂×C₁₃×D₈	—	2	4	no	—
64	C₂×C₁₃×D₈	C₂³	1	4	yes	—
65	C₂²×C₈×C₁₃	—	2	4	no	—
66	C₂²×C₈×C₁₃	—	2	4	no	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
70	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#126	—	2	16	no	—
74	C₁₃×#125	—	2	4	no	—
75	C₁₃×#125	C₂³	1	8	yes	—
76	C₁₃×#124	—	2	4	no	—
77	C₁₃×#124	C₂³	1	8	yes	—
78	C₁₃×#123	—	2	16	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
81	C₁₃×#121	—	2	4	no	—
82	C₁₃×#121	C₂³	1	8	yes	—
83	C₄×Q₈×C₁₃	—	2	4	no	—
84	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
85	C₄×D₄×C₁₃	—	2	16	no	—
86	C₄×D₄×C₁₃	—	2	4	no	—
87	C₄×D₄×C₁₃	C₂³	1	8	yes	—
88	C₁₃×#117	—	2	16	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₄²×C₁₃	—	2	2	no	—
101	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	D₄	1	4	yes	—
103	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	C₂³	1	4	yes	—
108	C₁₃×#107	C₂³	1	4	yes	—
109	C₁₃×#106	C₂³	1	8	yes	—
110	C₁₃×#103	C₂³	1	8	yes	—
111	C₁₃×#103	C₂³	1	8	yes	—
112	C₁₃×#102	C₂³	1	8	yes	—
113	C₁₃×#102	C₂³	1	8	yes	—
114	C₄×C₈×C₁₃	C₂³	1	4	yes	—
115	C₄×C₈×C₁₃	C₂³	1	4	yes	—
116	C₄×C₈×C₁₃	C₂³	1	4	yes	—
117	C₄×C₈×C₁₃	C₂³	1	4	yes	—
118	C₂×#3168	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	—	2	2	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	4	8	no	—
130	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	4	8	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×Q₁₆	—	2	8	no	—
151	C₁₃×SD₁₆	—	2	16	no	—
152	C₁₃×D₈	—	2	8	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	8	no	—
156	C₂×C₈×C₁₃	—	2	8	no	—
157	C₂×C₈×C₁₃	#41	1	4	yes	—
158	C₂×C₈×C₁₃	#41	1	4	yes	—
159	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
160	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
162	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	2	8	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	8	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	—	2	2	no	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	2	8	no	—
174	C₁₃×C₂²⋊C₄	—	2	8	no	—
175	C₁₃×C₂²⋊C₄	—	2	8	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₄²×C₁₃	C₂×D₄	1	4	yes	—
178	C₄²×C₁₃	C₂×D₄	1	2	yes	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂×D₄	1	4	yes	—
181	C₄²×C₁₃	C₂⁴	1	2	yes	—
182	C₄²×C₁₃	C₂⁴	1	2	yes	—
183	C₂×#529	C₂×C₁₃	1	2	yes	complemented
184	#3168	C₂×C₁₃	1	16	yes	direct product factor
185	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂×#488	C₂×C₁₃	1	2	yes	complemented
188	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
189	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
190	C₂×#465	C₂×C₁₃	1	2	yes	complemented
191	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂×C₄×SD₁₆	C₂×C₁₃	1	2	yes	complemented
193	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	#135	1	4	yes	—
202	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	—	2	4	no	—
206	Q₈×C₁₃	—	4	4	no	—
207	D₄×C₁₃	—	2	4	no	—
208	D₄×C₁₃	—	2	4	no	—
209	D₄×C₁₃	—	4	16	no	—
210	D₄×C₁₃	—	4	4	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	—	4	16	no	—
227	C₂×C₄×C₁₃	#135	1	4	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	C₂×#41	1	4	yes	—
240	C₈×C₁₃	C₂×#41	1	4	yes	—
241	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
242	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
243	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
246	#529	—	2	8	no	—
247	#529	C₂²×C₁₃	1	16	yes	complemented
248	C₂×#126	—	2	2	no	—
249	C₂×#125	C₂²×C₁₃	1	2	yes	—
250	C₂×#124	C₂²×C₁₃	1	2	yes	—
251	C₂×#123	—	2	2	no	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
253	C₂×#121	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×D₄	—	2	2	no	—
256	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
257	C₂×#117	—	2	2	no	—
258	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
259	#499	C₂²×C₁₃	1	8	yes	complemented
260	#495	C₂²×C₁₃	1	8	yes	complemented
261	#488	C₂²×C₁₃	1	16	yes	complemented
262	#467	C₂²×C₁₃	1	8	yes	complemented
263	#466	C₂²×C₁₃	1	8	yes	—
264	#465	C₂²×C₁₃	1	16	yes	complemented
265	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
266	C₄×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
267	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
268	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#106	C₂²×C₁₃	1	2	yes	—
271	C₂×#103	C₂²×C₁₃	1	2	yes	—
272	C₂×#103	C₂²×C₁₃	1	2	yes	—
273	C₂×#102	C₂²×C₁₃	1	2	yes	—
274	C₂×#102	C₂²×C₁₃	1	2	yes	—
275	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₁₃	1	8	yes	complemented
280	C₂²×C₁₃	—	2	8	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	4	4	no	—
285	C₂²×C₁₃	—	4	4	no	—
286	C₂²×C₁₃	—	8	8	no	—
287	C₂²×C₁₃	#532	1	2	yes	—
288	C₂²×C₁₃	C₂×#135	1	4	yes	—
289	C₂²×C₁₃	C₂×#135	1	2	yes	—
290	C₂²×C₁₃	C₂×#135	1	2	yes	—
291	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	2	2	no	—
295	C₄×C₁₃	—	2	2	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	—	4	4	no	—
299	C₄×C₁₃	#532	1	2	yes	—
300	C₄×C₁₃	C₂×#135	1	4	yes	—
301	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
302	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×Q₁₆	—	2	4	no	—
311	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
312	C₂×SD₁₆	—	2	8	no	—
313	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
314	C₂×D₈	—	2	4	no	—
315	C₂×D₈	C₂³×C₁₃	1	4	yes	—
316	C₂²×C₈	—	2	4	no	—
317	C₂²×C₈	—	2	4	no	—
318	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
321	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
322	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
324	#126	—	2	16	no	—
325	#125	—	2	4	no	—
326	#125	C₂³×C₁₃	1	8	yes	—
327	#124	—	2	4	no	—
328	#124	C₂³×C₁₃	1	8	yes	—
329	#123	—	2	16	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
332	#121	—	2	4	no	—
333	#121	C₂³×C₁₃	1	8	yes	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
336	C₄×D₄	—	2	16	no	—
337	C₄×D₄	—	2	4	no	—
338	C₄×D₄	C₂³×C₁₃	1	8	yes	—
339	#117	—	2	16	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄²	D₄×C₁₃	1	4	yes	—
355	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
358	#107	C₂³×C₁₃	1	4	yes	—
359	#107	C₂³×C₁₃	1	4	yes	—
360	#106	C₂³×C₁₃	1	8	yes	—
361	#103	C₂³×C₁₃	1	8	yes	—
362	#103	C₂³×C₁₃	1	8	yes	—
363	#102	C₂³×C₁₃	1	8	yes	—
364	#102	C₂³×C₁₃	1	8	yes	—
365	C₄×C₈	C₂³×C₁₃	1	4	yes	—
366	C₄×C₈	C₂³×C₁₃	1	4	yes	—
367	C₄×C₈	C₂³×C₁₃	1	4	yes	—
368	C₄×C₈	C₂³×C₁₃	1	4	yes	—
369	C₂×C₁₃	—	2	4	no	—
370	C₂×C₁₃	—	8	4	no	—
371	C₂×C₁₃	#3168	1	4	yes	direct product factor
372	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
373	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
374	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
375	C₂⁴	—	2	2	no	—
376	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	4	8	no	—
386	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	4	8	no	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
406	Q₁₆	—	2	8	no	—
407	SD₁₆	—	2	16	no	—
408	D₈	—	2	8	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	8	no	—
412	C₂×C₈	—	2	8	no	—
413	C₂×C₈	C₁₃×#41	1	4	yes	—
414	C₂×C₈	C₁₃×#41	1	4	yes	—
415	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
416	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
417	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
418	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
426	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₄²	—	2	8	no	—
433	C₄²	C₂×D₄×C₁₃	1	4	yes	—
434	C₄²	C₂×D₄×C₁₃	1	2	yes	—
435	C₄²	C₂×D₄×C₁₃	1	2	yes	—
436	C₄²	C₂×D₄×C₁₃	1	4	yes	—
437	C₄²	C₂⁴×C₁₃	1	2	yes	—
438	C₄²	C₂⁴×C₁₃	1	2	yes	—
439	C₁₃	C₂×#3168	1	1	yes	characteristic, direct product factor, Sylow
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	C₁₃×#135	1	4	yes	—
447	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
448	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
449	Q₈	—	2	4	no	—
450	Q₈	—	2	4	no	—
451	Q₈	—	4	4	no	—
452	D₄	—	2	4	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	16	no	—
455	D₄	—	4	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	C₁₃×#135	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
479	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
480	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
481	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	C₂×C₁₃×#41	1	4	yes	—
485	C₈	C₂×C₁₃×#41	1	4	yes	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	8	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	8	no	—
493	C₂²	C₁₃×#532	1	2	yes	—
494	C₂²	C₂×C₁₃×#135	1	4	yes	—
495	C₂²	C₂×C₁₃×#135	1	2	yes	—
496	C₂²	C₂×C₁₃×#135	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	4	no	—
505	C₄	C₁₃×#532	1	2	yes	—
506	C₄	C₂×C₁₃×#135	1	4	yes	—
507	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
508	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
509	C₂	—	2	4	no	—
510	C₂	—	8	4	no	—
511	C₂	C₁₃×#3168	1	4	yes	direct product factor
512	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
513	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
514	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂×C₁₃×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#529	C₂	semidirect
2. C₁₃×#3168	C₂	direct (N × H)
3. C₂×C₁₃×#499	C₂	semidirect
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#488	C₂	semidirect
6. C₂×C₁₃×#467	C₂	semidirect
8. C₂×C₁₃×#465	C₂	semidirect
9. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
10. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
12. C₂²×C₄×C₈×C₁₃	C₂	semidirect
19. C₁₃×#529	C₂²	semidirect
31. C₁₃×#499	C₂²	semidirect
32. C₁₃×#495	C₂²	semidirect
33. C₁₃×#488	C₂²	semidirect
34. C₁₃×#467	C₂²	semidirect
36. C₁₃×#465	C₂²	semidirect
37. C₄×C₁₃×Q₁₆	C₂²	semidirect
38. C₄×C₁₃×SD₁₆	C₂²	semidirect
39. C₄×C₁₃×D₈	C₂²	semidirect
51. C₂×C₄×C₈×C₁₃	C₂²	semidirect
118. C₂×#3168	C₁₃	direct (N × H)
183. C₂×#529	C₂×C₁₃	semidirect
184. #3168	C₂×C₁₃	direct (N × H)
185. C₂×#499	C₂×C₁₃	semidirect
186. C₂×#495	C₂×C₁₃	semidirect
187. C₂×#488	C₂×C₁₃	semidirect
188. C₂×#467	C₂×C₁₃	semidirect
190. C₂×#465	C₂×C₁₃	semidirect
191. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
192. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
193. C₂×C₄×D₈	C₂×C₁₃	semidirect
194. C₂²×C₄×C₈	C₂×C₁₃	semidirect
247. #529	C₂²×C₁₃	semidirect
259. #499	C₂²×C₁₃	semidirect
260. #495	C₂²×C₁₃	semidirect
261. #488	C₂²×C₁₃	semidirect
262. #467	C₂²×C₁₃	semidirect
264. #465	C₂²×C₁₃	semidirect
265. C₄×Q₁₆	C₂²×C₁₃	semidirect
266. C₄×SD₁₆	C₂²×C₁₃	semidirect
267. C₄×D₈	C₂²×C₁₃	semidirect
279. C₂×C₄×C₈	C₂²×C₁₃	semidirect
371. C₂×C₁₃	#3168	direct (N × H)
439. C₁₃	C₂×#3168	direct (N × H)
511. C₂	C₁₃×#3168	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×C₁₃×#529	2
C₁₃×#3168	2
C₂×C₁₃×#499	2
C₂×C₁₃×#495	2
C₂×C₁₃×#488	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₂×C₁₃×#465	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₄×C₁₃×D₈	2
C₂²×C₄×C₈×C₁₃	2
C₂×#3168	13

Subgroups — C2×C13×#3168 #15747009

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3168 #15747009