Subgroups — C₁₃×#21839 #15708178

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1992	C₂	1	4	yes	maximal, complemented
5	C₁₃×#1988	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1987	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1825	C₂	1	4	yes	maximal
8	C₁₃×#533	—	2	4	no	—
9	C₁₃×#533	C₄	1	8	yes	complemented
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#125	C₂²	1	2	yes	—
13	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
16	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
17	C₂×C₁₃×#117	—	2	1	no	—
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#432	—	2	4	no	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₁₃×#384	C₂²	1	2	yes	—
25	C₁₃×#382	—	2	1	no	—
26	C₁₃×#380	—	2	1	no	—
27	C₁₃×#380	C₂²	1	2	yes	—
28	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₁₃×#340	C₂²	1	8	yes	—
31	C₁₃×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	—	2	1	no	—
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
38	C₁₃×C₄⋊Q₈	—	2	2	no	—
39	C₁₃×C₄⋊Q₈	—	2	2	no	—
40	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
41	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
42	C₁₃×#125	—	2	4	no	—
43	C₁₃×#125	C₂×C₄	1	8	yes	—
44	C₁₃×C₂²⋊Q₈	—	2	8	no	—
45	C₁₃×C₂²⋊Q₈	—	2	8	no	—
46	C₄×Q₈×C₁₃	—	2	8	no	—
47	C₄×Q₈×C₁₃	—	2	8	no	—
48	C₁₃×#117	—	2	4	no	—
49	C₁₃×#117	—	4	4	no	—
50	C₁₃×#117	C₂×C₄	1	8	yes	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₄²×C₁₃	—	2	2	no	—
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	D₄	1	4	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₁₃×C₄⋊C₈	—	2	4	no	—
71	C₁₃×C₂²⋊C₈	—	2	4	no	—
72	C₁₃×#97	—	2	4	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	#21839	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	—	2	4	no	—
79	C₂×Q₈×C₁₃	—	4	4	no	—
80	C₂×Q₈×C₁₃	—	4	2	no	—
81	C₂×Q₈×C₁₃	—	4	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	4	2	no	—
89	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	8	no	—
101	C₁₃×C₄⋊C₄	—	2	8	no	—
102	C₁₃×C₄⋊C₄	—	2	8	no	—
103	C₁₃×C₄⋊C₄	—	2	4	no	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	2	8	no	—
108	C₁₃×C₄⋊C₄	—	4	4	no	—
109	C₁₃×C₄⋊C₄	—	4	4	no	—
110	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
111	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
112	C₁₃×C₂²⋊C₄	—	2	8	no	—
113	C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₄²×C₁₃	—	2	8	no	—
115	C₄²×C₁₃	—	4	4	no	—
116	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
117	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂×D₄	1	2	yes	—
121	C₄²×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
123	C₂×#432	C₂×C₁₃	1	1	yes	characteristic
124	#2285	C₂×C₁₃	1	1	yes	characteristic
125	#1992	C₂×C₁₃	1	4	yes	complemented
126	#1988	C₂×C₁₃	1	2	yes	complemented
127	#1987	C₂×C₁₃	1	2	yes	complemented
128	#1825	C₂×C₁₃	1	4	yes	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	1	no	—
131	C₂³×C₁₃	—	2	1	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₁₃	—	4	8	no	—
136	Q₈×C₁₃	—	4	8	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	8	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	4	4	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	4	no	—
151	C₂×C₄×C₁₃	—	4	4	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₁₃	#137	1	2	yes	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
164	C₈×C₁₃	—	4	4	no	—
165	#533	—	2	4	no	—
166	#533	C₄×C₁₃	1	8	yes	complemented
167	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
168	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
169	C₂×#125	C₂²×C₁₃	1	2	yes	—
170	C₂×C₂²⋊Q₈	—	2	1	no	—
171	C₂×C₂²⋊Q₈	—	2	1	no	—
172	C₂×C₄×Q₈	—	2	1	no	—
173	C₂×C₄×Q₈	—	2	1	no	—
174	C₂×#117	—	2	1	no	—
175	C₂×#117	C₂²×C₁₃	1	2	yes	—
176	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
177	#432	—	2	4	no	—
178	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
179	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×#97	C₂²×C₁₃	1	2	yes	—
181	#384	C₂²×C₁₃	1	2	yes	—
182	#382	—	2	1	no	—
183	#380	—	2	1	no	—
184	#380	C₂²×C₁₃	1	2	yes	—
185	C₄×C₄⋊C₄	—	2	1	no	—
186	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
187	#340	C₂²×C₁₃	1	8	yes	—
188	#340	C₂²×C₁₃	1	8	yes	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	4	2	no	—
193	C₂²×C₁₃	—	4	2	no	—
194	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₃	#536	1	2	yes	—
196	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
198	C₂²×C₁₃	#575	1	2	yes	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	4	4	no	—
204	C₄×C₁₃	—	4	4	no	—
205	C₄×C₁₃	—	8	4	no	—
206	C₄×C₁₃	#417	1	4	yes	—
207	C₄×C₁₃	#519	1	2	yes	—
208	C₄×C₁₃	#536	1	2	yes	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×Q₈	—	2	1	no	—
211	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
215	C₄⋊Q₈	—	2	2	no	—
216	C₄⋊Q₈	—	2	2	no	—
217	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
218	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
219	#125	—	2	4	no	—
220	#125	C₂×C₄×C₁₃	1	8	yes	—
221	C₂²⋊Q₈	—	2	8	no	—
222	C₂²⋊Q₈	—	2	8	no	—
223	C₄×Q₈	—	2	8	no	—
224	C₄×Q₈	—	2	8	no	—
225	#117	—	2	4	no	—
226	#117	—	4	4	no	—
227	#117	C₂×C₄×C₁₃	1	8	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
242	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
243	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₁₃	1	4	yes	—
245	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
247	C₄⋊C₈	—	2	4	no	—
248	C₂²⋊C₈	—	2	4	no	—
249	#97	—	2	4	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	C₂×C₁₃	—	4	2	no	—
253	C₂×C₁₃	#2310	1	1	yes	characteristic
254	C₂×C₁₃	C₂×#417	1	1	yes	characteristic
255	C₂×C₁₃	#2896	1	1	yes	characteristic
256	C₂×C₁₃	#3235	1	2	yes	—
257	C₂×C₁₃	#3237	1	2	yes	—
258	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	4	4	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
272	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	8	no	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
293	C₄⋊C₄	C₂²×C₄×C₁₃	1	4	yes	—
294	C₂²⋊C₄	—	2	8	no	—
295	C₂²⋊C₄	—	4	4	no	—
296	C₄²	—	2	8	no	—
297	C₄²	—	4	4	no	—
298	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
299	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
300	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
301	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
302	C₄²	C₂×D₄×C₁₃	1	2	yes	—
303	C₄²	C₂×D₄×C₁₃	1	2	yes	—
304	C₁₃	#21839	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	2	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
310	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
311	Q₈	—	4	8	no	—
312	Q₈	—	4	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
331	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
332	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
333	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
334	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
335	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
336	C₂×C₄	C₁₃×#137	1	2	yes	—
337	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
347	C₂²	C₁₃×#536	1	2	yes	—
348	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
349	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
350	C₂²	C₁₃×#575	1	2	yes	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	2	2	no	—
354	C₄	—	2	2	no	—
355	C₄	—	4	4	no	—
356	C₄	—	4	4	no	—
357	C₄	—	8	4	no	—
358	C₄	C₁₃×#417	1	4	yes	—
359	C₄	C₁₃×#519	1	2	yes	—
360	C₄	C₁₃×#536	1	2	yes	—
361	C₂	—	4	2	no	—
362	C₂	C₁₃×#2310	1	1	yes	characteristic
363	C₂	C₂×C₁₃×#417	1	1	yes	characteristic
364	C₂	C₁₃×#2896	1	1	yes	characteristic
365	C₂	C₁₃×#3235	1	2	yes	—
366	C₂	C₁₃×#3237	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1992	C₂	semidirect
5. C₁₃×#1988	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
9. C₁₃×#533	C₄	semidirect
75. #21839	C₁₃	direct (N × H)
125. #1992	C₂×C₁₃	semidirect
126. #1988	C₂×C₁₃	semidirect
127. #1987	C₂×C₁₃	semidirect
166. #533	C₄×C₁₃	semidirect
304. C₁₃	#21839	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×#533	2
C₂×C₁₃×#432	2
C₁₃×#2285	2
C₁₃×#1992	2
C₁₃×#1988	2
C₁₃×#1987	2
C₁₃×#1825	2
#21839	13

Subgroups — C13×#21839 #15708178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21839 #15708178