Subgroups — C₁₃×#22451 #15708790

Order 3328.

1450 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2341	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1970	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1880	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1788	C₂	1	2	yes	maximal, complemented
8	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	2	yes	—
10	C₂×C₁₃×#135	—	2	8	no	—
11	C₂×C₁₃×#135	C₄	1	8	yes	complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
17	C₄×C₁₃×Q₁₆	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	4	yes	—
20	C₂×C₁₃×#102	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#390	—	2	4	no	—
24	C₁₃×#390	C₂²	1	4	yes	—
25	C₁₃×#380	—	2	2	no	—
26	C₁₃×#380	C₂²	1	2	yes	—
27	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#340	C₂²	1	2	yes	—
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	—	2	8	no	—
33	C₂×C₁₃×#41	—	4	4	no	—
34	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₁₃	—	2	2	no	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₁₃×#135	—	2	32	no	—
41	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
42	C₂×C₁₃×Q₁₆	D₄	1	8	yes	—
43	C₂×C₁₃×SD₁₆	—	2	8	no	—
44	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	—
45	C₂×C₁₃×D₈	—	2	4	no	—
46	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃	—	2	4	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	8	no	—
53	C₄×Q₈×C₁₃	—	4	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
60	C₂×C₄²×C₁₃	—	2	4	no	—
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₁₃×#107	—	2	4	no	—
63	C₁₃×#103	—	2	8	no	—
64	C₁₃×#102	—	4	4	no	—
65	C₁₃×C₂²⋊C₈	—	2	2	no	—
66	C₄×C₈×C₁₃	—	2	4	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	D₄	1	1	yes	characteristic
69	C₁₃×#95	D₄	1	1	yes	characteristic
70	#22451	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	2	2	no	—
72	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₁₃×#41	—	2	16	no	—
74	C₁₃×#41	—	4	8	no	—
75	C₁₃×#41	—	4	16	no	—
76	C₂×Q₈×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
79	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
80	C₂×D₄×C₁₃	—	2	8	no	—
81	C₂×D₄×C₁₃	—	2	4	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	4	no	—
84	C₂×D₄×C₁₃	—	4	8	no	—
85	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
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	8	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	4	8	no	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	#41	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₁₃×Q₁₆	C₂²⋊C₄	1	16	yes	complemented
99	C₁₃×SD₁₆	—	2	16	no	—
100	C₁₃×D₈	—	2	8	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	8	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	4	8	no	—
112	C₁₃×C₂²⋊C₄	—	2	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	8	no	—
114	C₁₃×C₂²⋊C₄	—	8	4	no	—
115	C₁₃×C₂²⋊C₄	—	8	2	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	2	2	no	—
118	C₄²×C₁₃	—	4	8	no	—
119	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic
120	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
121	#2341	C₂×C₁₃	1	2	yes	complemented
122	#1970	C₂×C₁₃	1	2	yes	complemented
123	#1880	C₂×C₁₃	1	4	yes	complemented
124	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#1788	C₂×C₁₃	1	2	yes	complemented
126	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	—	2	1	no	—
130	C₂³×C₁₃	—	2	1	no	—
131	C₂³×C₁₃	—	2	4	no	—
132	C₂³×C₁₃	—	4	4	no	—
133	C₂³×C₁₃	—	4	4	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	C₄×D₄	1	2	yes	—
137	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₁₃	—	2	4	no	—
139	Q₈×C₁₃	—	2	8	no	—
140	Q₈×C₁₃	C₂×C₂²⋊C₄	1	8	yes	—
141	D₄×C₁₃	—	2	4	no	—
142	D₄×C₁₃	—	2	4	no	—
143	D₄×C₁₃	—	4	16	no	—
144	D₄×C₁₃	—	4	4	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	8	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	4	16	no	—
157	C₂×C₄×C₁₃	—	4	4	no	—
158	C₂×C₄×C₁₃	—	4	4	no	—
159	C₂×C₄×C₁₃	—	4	4	no	—
160	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₁₃	#135	1	4	yes	complemented
162	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
166	C₈×C₁₃	—	2	2	no	—
167	C₈×C₁₃	—	4	2	no	—
168	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂²×#41	C₂²×C₁₃	1	2	yes	—
170	C₂×#135	—	2	8	no	—
171	C₂×#135	C₄×C₁₃	1	8	yes	complemented
172	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
173	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
174	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
177	C₄×Q₁₆	—	2	8	no	—
178	C₂×#107	C₂²×C₁₃	1	2	yes	—
179	C₂×#103	C₂²×C₁₃	1	4	yes	—
180	C₂×#102	C₂²×C₁₃	1	4	yes	—
181	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
183	#390	—	2	4	no	—
184	#390	C₂²×C₁₃	1	4	yes	—
185	#380	—	2	2	no	—
186	#380	C₂²×C₁₃	1	2	yes	—
187	C₄×C₂²⋊C₄	—	2	2	no	—
188	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
189	#340	C₂²×C₁₃	1	2	yes	—
190	#336	C₂²×C₁₃	1	2	yes	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	—	4	2	no	—
195	C₂²×C₁₃	—	4	2	no	—
196	C₂²×C₁₃	—	4	4	no	—
197	C₂²×C₁₃	—	4	4	no	—
198	C₂²×C₁₃	—	4	4	no	—
199	C₂²×C₁₃	—	8	4	no	—
200	C₂²×C₁₃	—	8	4	no	—
201	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂²×C₁₃	D₄²	1	2	yes	—
203	C₂²×C₁₃	C₂×#135	1	2	yes	—
204	C₂²×C₁₃	#576	1	1	yes	characteristic
205	C₂²×C₁₃	#578	1	1	yes	characteristic
206	C₄×C₁₃	—	2	2	no	—
207	C₄×C₁₃	—	2	8	no	—
208	C₄×C₁₃	—	2	4	no	—
209	C₄×C₁₃	—	4	2	no	—
210	C₄×C₁₃	—	8	4	no	—
211	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
212	C₄×C₁₃	#518	1	1	yes	characteristic
213	C₄×C₁₃	#546	1	2	yes	—
214	C₂×#41	—	2	4	no	—
215	C₂×#41	—	2	8	no	—
216	C₂×#41	—	4	4	no	—
217	C₂×#41	C₂×C₄×C₁₃	1	8	yes	—
218	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
219	C₂²×D₄	—	2	2	no	—
220	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
221	C₂³×C₄	—	2	2	no	—
222	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
223	#135	—	2	32	no	—
224	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
225	C₂×Q₁₆	D₄×C₁₃	1	8	yes	—
226	C₂×SD₁₆	—	2	8	no	—
227	C₂×SD₁₆	C₂×C₄×C₁₃	1	8	yes	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	C₂×C₄×C₁₃	1	4	yes	—
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
232	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
233	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
235	C₄×Q₈	—	2	8	no	—
236	C₄×Q₈	—	4	4	no	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	4	no	—
242	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
243	C₂×C₄²	—	2	4	no	—
244	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
245	#107	—	2	4	no	—
246	#103	—	2	8	no	—
247	#102	—	4	4	no	—
248	C₂²⋊C₈	—	2	2	no	—
249	C₄×C₈	—	2	4	no	—
250	#95	—	2	2	no	—
251	#95	D₄×C₁₃	1	1	yes	characteristic
252	#95	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₁₃	—	4	2	no	—
254	C₂×C₁₃	—	8	4	no	—
255	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₁₃	C₄×#135	1	1	yes	characteristic
257	C₂×C₁₃	#2951	1	1	yes	characteristic
258	C₂×C₁₃	#3285	1	2	yes	—
259	C₂×C₁₃	#3287	1	2	yes	—
260	C₂⁴	—	2	2	no	—
261	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
262	#41	—	2	16	no	—
263	#41	—	4	8	no	—
264	#41	—	4	16	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
268	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
269	C₂×D₄	—	2	8	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	4	8	no	—
274	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	4	8	no	—
281	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
285	C₂²×C₄	C₁₃×#41	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
287	Q₁₆	C₁₃×C₂²⋊C₄	1	16	yes	complemented
288	SD₁₆	—	2	16	no	—
289	D₈	—	2	8	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	8	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
296	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	4	8	no	—
301	C₂²⋊C₄	—	2	4	no	—
302	C₂²⋊C₄	—	4	8	no	—
303	C₂²⋊C₄	—	8	4	no	—
304	C₂²⋊C₄	—	8	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	4	8	no	—
308	C₁₃	#22451	1	1	yes	characteristic, direct product factor, Sylow
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	C₄×D₄×C₁₃	1	2	yes	—
319	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
320	Q₈	—	2	4	no	—
321	Q₈	—	2	8	no	—
322	Q₈	C₂×C₁₃×C₂²⋊C₄	1	8	yes	—
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	16	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	16	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
343	C₂×C₄	C₁₃×#135	1	4	yes	complemented
344	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
346	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
347	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
348	C₈	—	2	2	no	—
349	C₈	—	4	2	no	—
350	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	4	no	—
357	C₂²	—	4	4	no	—
358	C₂²	—	4	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
362	C₂²	D₄²×C₁₃	1	2	yes	—
363	C₂²	C₂×C₁₃×#135	1	2	yes	—
364	C₂²	C₁₃×#576	1	1	yes	characteristic
365	C₂²	C₁₃×#578	1	1	yes	characteristic
366	C₄	—	2	4	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	8	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	4	no	—
371	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
372	C₄	C₁₃×#518	1	1	yes	characteristic
373	C₄	C₁₃×#546	1	2	yes	—
374	C₂	—	4	2	no	—
375	C₂	—	8	4	no	—
376	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
377	C₂	C₄×C₁₃×#135	1	1	yes	characteristic
378	C₂	C₁₃×#2951	1	1	yes	characteristic
379	C₂	C₁₃×#3285	1	2	yes	—
380	C₂	C₁₃×#3287	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	C₂²×C₁₃×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
3. C₁₃×#2341	C₂	semidirect
4. C₁₃×#1970	C₂	semidirect
5. C₁₃×#1880	C₂	semidirect
6. C₁₃×#1808	C₂	semidirect
7. C₁₃×#1788	C₂	semidirect
8. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
11. C₂×C₁₃×#135	C₄	semidirect
70. #22451	C₁₃	direct (N × H)
98. C₁₃×Q₁₆	C₂²⋊C₄	semidirect
120. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
121. #2341	C₂×C₁₃	semidirect
122. #1970	C₂×C₁₃	semidirect
123. #1880	C₂×C₁₃	semidirect
124. #1808	C₂×C₁₃	semidirect
125. #1788	C₂×C₁₃	semidirect
126. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
161. C₂×C₄×C₁₃	#135	semidirect
171. C₂×#135	C₄×C₁₃	semidirect
287. Q₁₆	C₁₃×C₂²⋊C₄	semidirect
308. C₁₃	#22451	direct (N × H)
343. C₂×C₄	C₁₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₃×#135	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2341	2
C₁₃×#1970	2
C₁₃×#1880	2
C₁₃×#1808	2
C₁₃×#1788	2
C₈×C₁₃×C₂²⋊C₄	2
#22451	13

Subgroups — C13×#22451 #15708790

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22451 #15708790