Subgroups — C₁₃×#9661 #15696000

Order 3328.

534 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×SD₁₆	C₄	1	1	yes	characteristic
9	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₄×C₁₃×SD₁₆	—	2	2	no	—
12	C₄×C₁₃×SD₁₆	—	2	2	no	—
13	C₂×C₁₃×#106	C₄	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#103	C₄	1	1	yes	characteristic
17	C₂×C₁₃×#102	C₄	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊C₈	—	2	2	no	—
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#336	—	2	2	no	—
23	C₁₃×#334	—	2	2	no	—
24	C₁₃×Q₈⋊C₈	—	2	2	no	—
25	C₁₃×D₄⋊C₈	—	2	2	no	—
26	C₁₃×#322	—	2	2	no	—
27	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	—	2	1	no	—
30	C₂×C₁₃×SD₁₆	—	2	2	no	—
31	C₂×C₁₃×SD₁₆	—	2	2	no	—
32	C₂×C₁₃×SD₁₆	—	2	2	no	—
33	C₂²×C₈×C₁₃	—	2	1	no	—
34	C₂²×C₈×C₁₃	—	2	1	no	—
35	C₂²×C₈×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₃	D₄	1	2	yes	—
39	C₄×Q₈×C₁₃	—	2	1	no	—
40	C₄×Q₈×C₁₃	—	2	1	no	—
41	C₄×Q₈×C₁₃	—	2	1	no	—
42	C₄×Q₈×C₁₃	—	2	1	no	—
43	C₄×D₄×C₁₃	—	2	1	no	—
44	C₄×D₄×C₁₃	—	2	1	no	—
45	C₄×D₄×C₁₃	—	2	1	no	—
46	C₄×D₄×C₁₃	—	2	1	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
51	C₂×C₄²×C₁₃	—	2	1	no	—
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#106	—	2	2	no	—
54	C₁₃×C₄⋊C₈	—	2	1	no	—
55	C₁₃×C₄⋊C₈	—	2	1	no	—
56	C₁₃×C₄⋊C₈	—	2	1	no	—
57	C₁₃×C₄⋊C₈	—	2	1	no	—
58	C₁₃×#103	—	2	2	no	—
59	C₁₃×#102	—	2	2	no	—
60	C₁₃×C₂²⋊C₈	—	4	4	no	—
61	C₄×C₈×C₁₃	—	2	1	no	—
62	C₄×C₈×C₁₃	—	2	1	no	—
63	C₄×C₈×C₁₃	—	2	1	no	—
64	C₄×C₈×C₁₃	D₄	1	2	yes	—
65	C₄×C₈×C₁₃	D₄	1	2	yes	—
66	C₄×C₈×C₁₃	D₄	1	2	yes	—
67	#9661	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	—	2	1	no	—
69	C₂×Q₈×C₁₃	—	2	1	no	—
70	C₂×Q₈×C₁₃	—	2	1	no	—
71	C₂×Q₈×C₁₃	—	2	1	no	—
72	C₂×Q₈×C₁₃	—	2	1	no	—
73	C₂×Q₈×C₁₃	—	2	1	no	—
74	C₂×Q₈×C₁₃	M₁₆	1	2	yes	—
75	C₂×D₄×C₁₃	—	2	1	no	—
76	C₂×D₄×C₁₃	—	2	1	no	—
77	C₂×D₄×C₁₃	—	2	1	no	—
78	C₂×D₄×C₁₃	—	2	1	no	—
79	C₂×D₄×C₁₃	—	2	1	no	—
80	C₂×D₄×C₁₃	M₁₆	1	2	yes	—
81	C₂²×C₄×C₁₃	—	2	1	no	—
82	C₂²×C₄×C₁₃	—	2	1	no	—
83	C₂²×C₄×C₁₃	—	2	1	no	—
84	C₂²×C₄×C₁₃	—	4	1	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	—	4	2	no	—
87	C₂²×C₄×C₁₃	—	4	2	no	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
91	C₁₃×SD₁₆	—	2	8	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₂×C₈×C₁₃	—	2	1	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	1	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	4	2	no	—
100	C₂×C₈×C₁₃	—	4	1	no	—
101	C₂×C₈×C₁₃	—	4	1	no	—
102	C₂×C₈×C₁₃	—	4	2	no	—
103	C₂×C₈×C₁₃	—	4	2	no	—
104	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
105	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
106	C₂×C₈×C₁₃	SD₁₆	1	4	yes	complemented
107	C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₁₃×C₄⋊C₄	—	4	1	no	—
112	C₁₃×C₄⋊C₄	—	4	1	no	—
113	C₁₃×C₂²⋊C₄	—	4	1	no	—
114	C₁₃×C₂²⋊C₄	—	4	1	no	—
115	C₄²×C₁₃	—	4	1	no	—
116	C₄²×C₁₃	—	4	1	no	—
117	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₁₃	#41	1	1	yes	characteristic
121	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
122	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
123	#1954	C₂×C₁₃	1	1	yes	characteristic
124	C₂×#334	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂×Q₈⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
126	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
127	C₂×#322	C₂×C₁₃	1	1	yes	characteristic, complemented
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	—	4	1	no	—
130	C₂³×C₁₃	—	4	1	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
134	Q₈×C₁₃	—	2	2	no	—
135	Q₈×C₁₃	—	2	2	no	—
136	Q₈×C₁₃	—	4	1	no	—
137	Q₈×C₁₃	—	4	1	no	—
138	D₄×C₁₃	—	2	2	no	—
139	D₄×C₁₃	—	2	2	no	—
140	D₄×C₁₃	—	4	1	no	—
141	D₄×C₁₃	—	4	1	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	4	1	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	8	2	no	—
151	C₂×C₄×C₁₃	—	8	1	no	—
152	C₂×C₄×C₁₃	—	8	1	no	—
153	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
161	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
162	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
164	C₂×C₄×C₁₃	#135	1	2	yes	—
165	C₈×C₁₃	—	2	2	no	—
166	C₈×C₁₃	—	2	2	no	—
167	C₈×C₁₃	—	2	4	no	—
168	C₈×C₁₃	—	4	2	no	—
169	C₈×C₁₃	—	8	1	no	—
170	C₈×C₁₃	—	8	1	no	—
171	C₂²×SD₁₆	C₄×C₁₃	1	1	yes	characteristic
172	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
174	C₄×SD₁₆	—	2	2	no	—
175	C₄×SD₁₆	—	2	2	no	—
176	C₂×#106	C₄×C₁₃	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×#103	C₄×C₁₃	1	1	yes	characteristic
180	C₂×#102	C₄×C₁₃	1	1	yes	characteristic
181	C₂×C₂²⋊C₈	—	2	2	no	—
182	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
185	#336	—	2	2	no	—
186	#334	—	2	2	no	—
187	Q₈⋊C₈	—	2	2	no	—
188	D₄⋊C₈	—	2	2	no	—
189	#322	—	2	2	no	—
190	C₂²×C₁₃	—	4	4	no	—
191	C₂²×C₁₃	—	4	2	no	—
192	C₂²×C₁₃	—	8	2	no	—
193	C₂²×C₁₃	—	8	1	no	—
194	C₂²×C₁₃	—	8	1	no	—
195	C₂²×C₁₃	#390	1	1	yes	characteristic
196	C₂²×C₁₃	#435	1	1	yes	characteristic
197	C₂²×C₁₃	#435	1	1	yes	characteristic
198	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
199	C₂²×C₁₃	#444	1	2	yes	—
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	4	2	no	—
203	C₄×C₁₃	—	8	1	no	—
204	C₄×C₁₃	—	8	1	no	—
205	C₄×C₁₃	#407	1	1	yes	characteristic
206	C₄×C₁₃	#408	1	1	yes	characteristic
207	C₄×C₁₃	#435	1	1	yes	characteristic
208	C₄×C₁₃	#435	1	1	yes	characteristic
209	C₄×C₁₃	#465	1	2	yes	—
210	C₄×C₁₃	#492	1	1	yes	characteristic
211	C₄×C₁₃	#495	1	1	yes	characteristic
212	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
213	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
214	C₂³×C₄	—	2	1	no	—
215	C₂×SD₁₆	—	2	2	no	—
216	C₂×SD₁₆	—	2	2	no	—
217	C₂×SD₁₆	—	2	2	no	—
218	C₂²×C₈	—	2	1	no	—
219	C₂²×C₈	—	2	1	no	—
220	C₂²×C₈	—	2	1	no	—
221	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
222	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂²×C₈	D₄×C₁₃	1	2	yes	—
224	C₄×Q₈	—	2	1	no	—
225	C₄×Q₈	—	2	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×D₄	—	2	1	no	—
229	C₄×D₄	—	2	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
238	#106	—	2	2	no	—
239	C₄⋊C₈	—	2	1	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	2	1	no	—
243	#103	—	2	2	no	—
244	#102	—	2	2	no	—
245	C₂²⋊C₈	—	4	4	no	—
246	C₄×C₈	—	2	1	no	—
247	C₄×C₈	—	2	1	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	D₄×C₁₃	1	2	yes	—
250	C₄×C₈	D₄×C₁₃	1	2	yes	—
251	C₄×C₈	D₄×C₁₃	1	2	yes	—
252	C₂×C₁₃	—	8	2	no	—
253	C₂×C₁₃	#1582	1	2	yes	—
254	C₂×C₁₃	#1583	1	2	yes	—
255	C₂×C₁₃	#1955	1	1	yes	characteristic
256	C₂×C₁₃	#1968	1	1	yes	characteristic
257	C₂×C₁₃	#1975	1	1	yes	characteristic
258	C₂⁴	—	2	1	no	—
259	C₂×Q₈	—	2	1	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	—	2	1	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	C₁₃×M₁₆	1	2	yes	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	—	2	1	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	C₁₃×M₁₆	1	2	yes	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	4	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
281	SD₁₆	—	2	8	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	1	no	—
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	1	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
295	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
296	C₂×C₈	C₁₃×SD₁₆	1	4	yes	complemented
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₂²⋊C₄	—	4	1	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
309	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₄²	C₁₃×#41	1	1	yes	characteristic
311	C₁₃	#9661	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³	—	2	2	no	—
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	4	1	no	—
322	D₄	—	2	2	no	—
323	D₄	—	2	2	no	—
324	D₄	—	4	1	no	—
325	D₄	—	4	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	1	no	—
336	C₂×C₄	—	8	1	no	—
337	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
340	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
341	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
342	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
343	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
344	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
345	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
346	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
347	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
348	C₂×C₄	C₁₃×#135	1	2	yes	—
349	C₈	—	2	2	no	—
350	C₈	—	2	2	no	—
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	—	8	1	no	—
354	C₈	—	8	1	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	1	no	—
360	C₂²	C₁₃×#390	1	1	yes	characteristic
361	C₂²	C₁₃×#435	1	1	yes	characteristic
362	C₂²	C₁₃×#435	1	1	yes	characteristic
363	C₂²	C₄×C₁₃×SD₁₆	1	2	yes	—
364	C₂²	C₁₃×#444	1	2	yes	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	4	2	no	—
368	C₄	—	8	1	no	—
369	C₄	—	8	1	no	—
370	C₄	C₁₃×#407	1	1	yes	characteristic
371	C₄	C₁₃×#408	1	1	yes	characteristic
372	C₄	C₁₃×#435	1	1	yes	characteristic
373	C₄	C₁₃×#435	1	1	yes	characteristic
374	C₄	C₁₃×#465	1	2	yes	—
375	C₄	C₁₃×#492	1	1	yes	characteristic
376	C₄	C₁₃×#495	1	1	yes	characteristic
377	C₂	—	8	2	no	—
378	C₂	C₁₃×#1582	1	2	yes	—
379	C₂	C₁₃×#1583	1	2	yes	—
380	C₂	C₁₃×#1955	1	1	yes	characteristic
381	C₂	C₁₃×#1968	1	1	yes	characteristic
382	C₂	C₁₃×#1975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂³×C₁₃	C₄×D₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#1984	C₂	semidirect
4. C₂×C₁₃×#334	C₂	semidirect
5. C₂×C₁₃×Q₈⋊C₈	C₂	semidirect
7. C₂×C₁₃×#322	C₂	semidirect
67. #9661	C₁₃	direct (N × H)
106. C₂×C₈×C₁₃	SD₁₆	semidirect
122. #1984	C₂×C₁₃	semidirect
124. C₂×#334	C₂×C₁₃	semidirect
125. C₂×Q₈⋊C₈	C₂×C₁₃	semidirect
127. C₂×#322	C₂×C₁₃	semidirect
296. C₂×C₈	C₁₃×SD₁₆	semidirect
311. C₁₃	#9661	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×C₄×C₁₃×SD₁₆	2
C₁₃×#1984	2
C₁₃×#1954	2
C₂×C₁₃×#334	2
C₂×C₁₃×Q₈⋊C₈	2
C₂×C₁₃×D₄⋊C₈	2
C₂×C₁₃×#322	2
#9661	13

Subgroups — C13×#9661 #15696000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9661 #15696000