Subgroups — C₂×C₁₃×#3380 #15747692

Order 3328.

1918 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3380	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#478	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#476	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal
9	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₁₃×#554	—	2	8	no	—
12	C₁₃×#554	C₂²	1	16	yes	complemented
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×#125	C₂²	1	4	yes	—
15	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
16	C₂×C₁₃×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
20	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₁₃×#500	C₂²	1	8	yes	complemented
22	C₁₃×#499	C₂²	1	16	yes	complemented
23	C₁₃×#478	C₂²	1	32	yes	complemented
24	C₁₃×#476	C₂²	1	16	yes	complemented
25	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
26	C₄×C₁₃×D₈	C₂²	1	16	yes	—
27	C₄×C₁₃×D₈	C₂²	1	8	yes	—
28	C₂×C₁₃×#107	C₂²	1	2	yes	—
29	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#107	C₂²	1	2	yes	—
31	C₂×C₁₃×#106	C₂²	1	4	yes	—
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₃×#102	C₂²	1	4	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	—	2	4	no	—
43	C₂×C₁₃×D₈	Q₈	1	8	yes	complemented
44	C₂×C₁₃×D₈	C₂³	1	4	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	—	2	4	no	—
49	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
50	C₁₃×#125	—	2	8	no	—
51	C₁₃×#125	C₂³	1	16	yes	—
52	C₁₃×C₂²⋊Q₈	—	2	16	no	—
53	C₁₃×C₂²⋊Q₈	—	2	32	no	—
54	C₄×Q₈×C₁₃	D₄	1	4	yes	—
55	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
56	C₄×D₄×C₁₃	—	2	8	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	C₂³	1	8	yes	—
59	C₄×D₄×C₁₃	C₂³	1	16	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×#107	C₂³	1	4	yes	—
73	C₁₃×#107	C₂³	1	8	yes	—
74	C₁₃×#107	C₂³	1	8	yes	—
75	C₁₃×#106	C₂³	1	16	yes	—
76	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
77	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
78	C₁₃×#102	C₂³	1	16	yes	—
79	C₁₃×#102	C₂³	1	8	yes	—
80	C₄×C₈×C₁₃	C₂³	1	8	yes	—
81	C₄×C₈×C₁₃	C₂³	1	4	yes	—
82	C₂×#3380	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₃	—	2	8	no	—
86	C₂×Q₈×C₁₃	—	8	4	no	—
87	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
88	C₂×D₄×C₁₃	—	2	2	no	—
89	C₂×D₄×C₁₃	—	2	4	no	—
90	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	—
91	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	4	no	—
94	C₂²×C₄×C₁₃	—	2	8	no	—
95	C₂²×C₄×C₁₃	—	2	16	no	—
96	C₂²×C₄×C₁₃	—	4	8	no	—
97	C₂²×C₄×C₁₃	—	8	8	no	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₁₃×D₈	C₂×Q₈	1	16	yes	complemented
104	C₂×C₈×C₁₃	—	2	4	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
107	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
108	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
109	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
110	C₁₃×C₄⋊C₄	—	2	16	no	—
111	C₁₃×C₄⋊C₄	—	2	8	no	—
112	C₁₃×C₄⋊C₄	—	2	16	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
116	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
117	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
118	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
119	C₁₃×C₂²⋊C₄	—	2	8	no	—
120	C₁₃×C₂²⋊C₄	—	2	16	no	—
121	C₄²×C₁₃	C₂×D₄	1	4	yes	—
122	C₄²×C₁₃	C₂×D₄	1	2	yes	—
123	C₄²×C₁₃	C₂⁴	1	4	yes	—
124	C₄²×C₁₃	C₂⁴	1	2	yes	—
125	C₂×#554	C₂×C₁₃	1	2	yes	complemented
126	#3380	C₂×C₁₃	1	16	yes	direct product factor
127	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂×#499	C₂×C₁₃	1	2	yes	complemented
129	C₂×#478	C₂×C₁₃	1	4	yes	complemented
130	C₂×#476	C₂×C₁₃	1	2	yes	complemented
131	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	—
133	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
134	C₂³×C₁₃	—	2	8	no	—
135	C₂³×C₁₃	—	2	4	no	—
136	C₂³×C₁₃	—	4	4	no	—
137	C₂³×C₁₃	—	4	4	no	—
138	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₁₃	—	2	8	no	—
140	Q₈×C₁₃	—	8	8	no	—
141	D₄×C₁₃	—	2	8	no	—
142	D₄×C₁₃	—	2	4	no	—
143	D₄×C₁₃	C₂²×Q₈	1	8	yes	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	8	no	—
149	C₂×C₄×C₁₃	—	4	4	no	—
150	C₂×C₄×C₁₃	—	4	8	no	—
151	C₂×C₄×C₁₃	—	4	16	no	—
152	C₂×C₄×C₁₃	—	8	16	no	—
153	C₂×C₄×C₁₃	#135	1	4	yes	—
154	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
155	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
160	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
161	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
162	C₈×C₁₃	—	2	4	no	—
163	C₈×C₁₃	—	2	2	no	—
164	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
165	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
166	#554	—	2	8	no	—
167	#554	C₂²×C₁₃	1	16	yes	complemented
168	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
169	C₂×#125	C₂²×C₁₃	1	4	yes	—
170	C₂×C₂²⋊Q₈	—	2	2	no	—
171	C₂×C₂²⋊Q₈	—	2	4	no	—
172	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
174	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
175	C₂²×C₄⋊C₄	—	2	2	no	—
176	#500	C₂²×C₁₃	1	8	yes	complemented
177	#499	C₂²×C₁₃	1	16	yes	complemented
178	#478	C₂²×C₁₃	1	32	yes	complemented
179	#476	C₂²×C₁₃	1	16	yes	complemented
180	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
181	C₄×D₈	C₂²×C₁₃	1	16	yes	—
182	C₄×D₈	C₂²×C₁₃	1	8	yes	—
183	C₂×#107	C₂²×C₁₃	1	2	yes	—
184	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
185	C₂×#107	C₂²×C₁₃	1	2	yes	—
186	C₂×#106	C₂²×C₁₃	1	4	yes	—
187	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#102	C₂²×C₁₃	1	2	yes	—
190	C₂×#102	C₂²×C₁₃	1	4	yes	—
191	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	C₂²×C₁₃	—	2	8	no	—
194	C₂²×C₁₃	—	4	16	no	—
195	C₂²×C₁₃	—	4	4	no	—
196	C₂²×C₁₃	—	4	4	no	—
197	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
198	C₂²×C₁₃	C₂×#135	1	2	yes	—
199	C₂²×C₁₃	#576	1	2	yes	—
200	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	—	2	4	no	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	4	4	no	—
205	C₄×C₁₃	—	4	8	no	—
206	C₄×C₁₃	D₄×Q₈	1	2	yes	—
207	C₄×C₁₃	C₂×#135	1	4	yes	—
208	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
209	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
210	C₂²×Q₈	—	2	2	no	—
211	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
212	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	—	2	4	no	—
215	C₂×D₈	Q₈×C₁₃	1	8	yes	complemented
216	C₂×D₈	C₂³×C₁₃	1	4	yes	—
217	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
220	C₄⋊Q₈	—	2	4	no	—
221	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
222	#125	—	2	8	no	—
223	#125	C₂³×C₁₃	1	16	yes	—
224	C₂²⋊Q₈	—	2	16	no	—
225	C₂²⋊Q₈	—	2	32	no	—
226	C₄×Q₈	D₄×C₁₃	1	4	yes	—
227	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
228	C₄×D₄	—	2	8	no	—
229	C₄×D₄	—	2	4	no	—
230	C₄×D₄	C₂³×C₁₃	1	8	yes	—
231	C₄×D₄	C₂³×C₁₃	1	16	yes	—
232	C₂×C₄⋊C₄	—	2	4	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	16	no	—
236	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
237	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
243	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	#107	C₂³×C₁₃	1	4	yes	—
245	#107	C₂³×C₁₃	1	8	yes	—
246	#107	C₂³×C₁₃	1	8	yes	—
247	#106	C₂³×C₁₃	1	16	yes	—
248	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
249	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
250	#102	C₂³×C₁₃	1	16	yes	—
251	#102	C₂³×C₁₃	1	8	yes	—
252	C₄×C₈	C₂³×C₁₃	1	8	yes	—
253	C₄×C₈	C₂³×C₁₃	1	4	yes	—
254	C₂×C₁₃	—	4	8	no	—
255	C₂×C₁₃	#3380	1	4	yes	direct product factor
256	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
257	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
258	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
259	C₂⁴	—	2	2	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	8	4	no	—
263	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	C₂×Q₈×C₁₃	1	8	yes	—
267	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	16	no	—
272	C₂²×C₄	—	4	8	no	—
273	C₂²×C₄	—	8	8	no	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
279	D₈	C₂×Q₈×C₁₃	1	16	yes	complemented
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
283	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
284	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
285	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
286	C₄⋊C₄	—	2	16	no	—
287	C₄⋊C₄	—	2	8	no	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
292	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
293	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
294	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₄²	C₂×D₄×C₁₃	1	4	yes	—
298	C₄²	C₂×D₄×C₁₃	1	2	yes	—
299	C₄²	C₂⁴×C₁₃	1	4	yes	—
300	C₄²	C₂⁴×C₁₃	1	2	yes	—
301	C₁₃	C₂×#3380	1	1	yes	characteristic, direct product factor, Sylow
302	C₂³	—	2	8	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	4	4	no	—
305	C₂³	—	4	4	no	—
306	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	8	8	no	—
309	D₄	—	2	8	no	—
310	D₄	—	2	4	no	—
311	D₄	C₂²×Q₈×C₁₃	1	8	yes	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	8	no	—
319	C₂×C₄	—	4	16	no	—
320	C₂×C₄	—	8	16	no	—
321	C₂×C₄	C₁₃×#135	1	4	yes	—
322	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
324	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
325	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
327	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
328	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
330	C₈	—	2	4	no	—
331	C₈	—	2	2	no	—
332	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
333	C₂²	—	2	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	16	no	—
337	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
338	C₂²	C₂×C₁₃×#135	1	2	yes	—
339	C₂²	C₁₃×#576	1	2	yes	—
340	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	D₄×Q₈×C₁₃	1	2	yes	—
347	C₄	C₂×C₁₃×#135	1	4	yes	—
348	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
349	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂	—	4	8	no	—
351	C₂	C₁₃×#3380	1	4	yes	direct product factor
352	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
353	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
354	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
2. C₁₃×#3380	C₂	direct (N × H)
3. C₂×C₁₃×#500	C₂	semidirect
4. C₂×C₁₃×#499	C₂	semidirect
5. C₂×C₁₃×#478	C₂	semidirect
6. C₂×C₁₃×#476	C₂	semidirect
7. C₂×C₈×Q₈×C₁₃	C₂	semidirect
12. C₁₃×#554	C₂²	semidirect
21. C₁₃×#500	C₂²	semidirect
22. C₁₃×#499	C₂²	semidirect
23. C₁₃×#478	C₂²	semidirect
24. C₁₃×#476	C₂²	semidirect
25. C₈×Q₈×C₁₃	C₂²	semidirect
43. C₂×C₁₃×D₈	Q₈	semidirect
82. C₂×#3380	C₁₃	direct (N × H)
103. C₁₃×D₈	C₂×Q₈	semidirect
125. C₂×#554	C₂×C₁₃	semidirect
126. #3380	C₂×C₁₃	direct (N × H)
127. C₂×#500	C₂×C₁₃	semidirect
128. C₂×#499	C₂×C₁₃	semidirect
129. C₂×#478	C₂×C₁₃	semidirect
130. C₂×#476	C₂×C₁₃	semidirect
131. C₂×C₈×Q₈	C₂×C₁₃	semidirect
167. #554	C₂²×C₁₃	semidirect
176. #500	C₂²×C₁₃	semidirect
177. #499	C₂²×C₁₃	semidirect
178. #478	C₂²×C₁₃	semidirect
179. #476	C₂²×C₁₃	semidirect
180. C₈×Q₈	C₂²×C₁₃	semidirect
215. C₂×D₈	Q₈×C₁₃	semidirect
255. C₂×C₁₃	#3380	direct (N × H)
279. D₈	C₂×Q₈×C₁₃	semidirect
301. C₁₃	C₂×#3380	direct (N × H)
351. C₂	C₁₃×#3380	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×#554	2
C₁₃×#3380	2
C₂×C₁₃×#500	2
C₂×C₁₃×#499	2
C₂×C₁₃×#478	2
C₂×C₁₃×#476	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×D₈	2
C₂×#3380	13

Subgroups — C2×C13×#3380 #15747692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3380 #15747692