Subgroups — C₁₃×#21892 #15708231

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 366 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×#423	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2283	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1987	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1981	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1894	C₂	1	4	yes	maximal
7	C₁₃×#1805	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₁₃×#533	—	2	4	no	—
10	C₁₃×#533	C₄	1	8	yes	complemented
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#125	—	2	1	no	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₂×C₁₃×#117	—	2	1	no	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#423	—	2	4	no	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	8	yes	—
24	C₁₃×#383	—	2	1	no	—
25	C₁₃×#382	C₂²	1	2	yes	—
26	C₁₃×#381	—	2	1	no	—
27	C₁₃×#380	C₂²	1	2	yes	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
30	C₁₃×#376	—	2	1	no	—
31	C₁₃×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
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	C₂×C₁₃×M₁₆	—	2	4	no	—
38	C₂×C₁₃×M₁₆	—	4	4	no	—
39	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
40	C₁₃×C₄⋊Q₈	—	2	2	no	—
41	C₁₃×C₄⋊Q₈	—	2	2	no	—
42	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
43	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	—
44	C₁₃×#125	—	2	8	no	—
45	C₁₃×C₂²⋊Q₈	—	2	8	no	—
46	C₁₃×C₂²⋊Q₈	—	2	4	no	—
47	C₁₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₁₃	—	2	8	no	—
49	C₄×Q₈×C₁₃	—	2	4	no	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
51	C₁₃×#117	—	2	8	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	1	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×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₄²×C₁₃	—	2	2	no	—
62	C₂×C₄²×C₁₃	—	2	2	no	—
63	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	D₄	1	4	yes	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊C₈	—	2	4	no	—
70	C₁₃×C₄⋊C₈	—	2	4	no	—
71	C₁₃×#103	—	4	8	no	—
72	C₁₃×#95	—	2	2	no	—
73	C₁₃×#95	—	2	2	no	—
74	C₁₃×#95	—	2	2	no	—
75	C₁₃×#95	—	2	2	no	—
76	#21892	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₁₃	—	2	4	no	—
79	C₂×Q₈×C₁₃	—	2	2	no	—
80	C₂×Q₈×C₁₃	—	2	4	no	—
81	C₂×Q₈×C₁₃	—	2	4	no	—
82	C₂×Q₈×C₁₃	—	4	4	no	—
83	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
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	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₃	—	4	2	no	—
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₁₃×M₁₆	—	4	8	no	—
102	C₂×C₈×C₁₃	—	2	4	no	—
103	C₂×C₈×C₁₃	—	2	8	no	—
104	C₁₃×C₄⋊C₄	—	2	4	no	—
105	C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₁₃×C₄⋊C₄	—	2	4	no	—
107	C₁₃×C₄⋊C₄	—	2	8	no	—
108	C₁₃×C₄⋊C₄	—	2	8	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
113	C₁₃×C₂²⋊C₄	—	2	8	no	—
114	C₁₃×C₂²⋊C₄	—	4	4	no	—
115	C₄²×C₁₃	—	2	8	no	—
116	C₄²×C₁₃	—	4	4	no	—
117	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
119	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
121	C₄²×C₁₃	C₂×D₄	1	2	yes	—
122	C₄²×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×#533	C₂×C₁₃	1	1	yes	characteristic
124	C₂×#423	C₂×C₁₃	1	1	yes	characteristic
125	#2283	C₂×C₁₃	1	1	yes	characteristic
126	#1987	C₂×C₁₃	1	2	yes	complemented
127	#1981	C₂×C₁₃	1	2	yes	complemented
128	#1894	C₂×C₁₃	1	4	yes	—
129	#1805	C₂×C₁₃	1	4	yes	complemented
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	2	2	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	—	2	8	no	—
136	Q₈×C₁₃	—	4	8	no	—
137	Q₈×C₁₃	—	4	2	no	—
138	Q₈×C₁₃	—	4	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	4	4	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	—	4	4	no	—
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	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃	#137	1	4	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	H(5,𝔽₂)	1	2	yes	—
164	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
165	C₈×C₁₃	—	4	4	no	—
166	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
167	#533	—	2	4	no	—
168	#533	C₄×C₁₃	1	8	yes	complemented
169	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
170	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×#125	—	2	1	no	—
172	C₂×C₂²⋊Q₈	—	2	1	no	—
173	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
174	C₂×C₄×Q₈	—	2	1	no	—
175	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
176	C₂×#117	—	2	1	no	—
177	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
178	#423	—	2	4	no	—
179	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
181	C₂×#103	C₂²×C₁₃	1	8	yes	—
182	#383	—	2	1	no	—
183	#382	C₂²×C₁₃	1	2	yes	—
184	#381	—	2	1	no	—
185	#380	C₂²×C₁₃	1	2	yes	—
186	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
187	C₄×C₂²⋊C₄	—	2	1	no	—
188	#376	—	2	1	no	—
189	#340	C₂²×C₁₃	1	8	yes	—
190	C₂²×C₁₃	—	2	2	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	4	4	no	—
194	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₃	#537	1	2	yes	—
196	C₂²×C₁₃	C₂×#137	1	2	yes	—
197	C₂²×C₁₃	#575	1	2	yes	—
198	C₄×C₁₃	—	2	2	no	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	4	4	no	—
203	C₄×C₁₃	—	4	4	no	—
204	C₄×C₁₃	—	8	4	no	—
205	C₄×C₁₃	#419	1	4	yes	—
206	C₄×C₁₃	#520	1	2	yes	—
207	C₄×C₁₃	#535	1	1	yes	characteristic
208	C₄×C₁₃	#536	1	1	yes	characteristic
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
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	C₂×M₁₆	—	2	4	no	—
215	C₂×M₁₆	—	4	4	no	—
216	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
217	C₄⋊Q₈	—	2	2	no	—
218	C₄⋊Q₈	—	2	2	no	—
219	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
220	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
221	#125	—	2	8	no	—
222	C₂²⋊Q₈	—	2	8	no	—
223	C₂²⋊Q₈	—	2	4	no	—
224	C₂²⋊Q₈	C₂×C₄×C₁₃	1	8	yes	—
225	C₄×Q₈	—	2	8	no	—
226	C₄×Q₈	—	2	4	no	—
227	C₄×Q₈	C₂×C₄×C₁₃	1	8	yes	—
228	#117	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	1	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×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
241	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
243	C₂×C₄²	D₄×C₁₃	1	4	yes	—
244	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
246	C₄⋊C₈	—	2	4	no	—
247	C₄⋊C₈	—	2	4	no	—
248	#103	—	4	8	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	C₂×C₁₃	—	4	2	no	—
254	C₂×C₁₃	#2311	1	1	yes	characteristic
255	C₂×C₁₃	C₂×#419	1	1	yes	characteristic
256	C₂×C₁₃	#2896	1	1	yes	characteristic
257	C₂×C₁₃	#3252	1	4	yes	—
258	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
273	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
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	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
282	M₁₆	—	4	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	8	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
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	#21892	1	1	yes	characteristic, direct product factor, Sylow
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
309	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
310	Q₈	—	2	8	no	—
311	Q₈	—	4	8	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	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	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	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×#137	1	4	yes	—
336	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
338	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
339	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	4	no	—
345	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
346	C₂²	C₁₃×#537	1	2	yes	—
347	C₂²	C₂×C₁₃×#137	1	2	yes	—
348	C₂²	C₁₃×#575	1	2	yes	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	8	4	no	—
356	C₄	C₁₃×#419	1	4	yes	—
357	C₄	C₁₃×#520	1	2	yes	—
358	C₄	C₁₃×#535	1	1	yes	characteristic
359	C₄	C₁₃×#536	1	1	yes	characteristic
360	C₂	—	4	2	no	—
361	C₂	C₁₃×#2311	1	1	yes	characteristic
362	C₂	C₂×C₁₃×#419	1	1	yes	characteristic
363	C₂	C₁₃×#2896	1	1	yes	characteristic
364	C₂	C₁₃×#3252	1	4	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×#1987	C₂	semidirect
5. C₁₃×#1981	C₂	semidirect
7. C₁₃×#1805	C₂	semidirect
10. C₁₃×#533	C₄	semidirect
76. #21892	C₁₃	direct (N × H)
126. #1987	C₂×C₁₃	semidirect
127. #1981	C₂×C₁₃	semidirect
129. #1805	C₂×C₁₃	semidirect
168. #533	C₄×C₁₃	semidirect
304. C₁₃	#21892	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×#423	2
C₁₃×#2283	2
C₁₃×#1987	2
C₁₃×#1981	2
C₁₃×#1894	2
C₁₃×#1805	2
#21892	13

Subgroups — C13×#21892 #15708231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21892 #15708231