Subgroups — C₁₃×#33488 #15719827

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2169	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2168	C₂	1	4	yes	maximal, complemented
4	D₄×C₁₃×C₁₆	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2112	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	2	yes	maximal, complemented
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₁₃×M₃₂	C₂²	1	4	yes	complemented
12	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	complemented
13	C₈×D₄×C₁₃	C₄	1	2	yes	—
14	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
15	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
16	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₈×D₄×C₁₃	C₂²	1	2	yes	—
18	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊C₈	C₄	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
23	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
24	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
26	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
28	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
29	C₁₃×#346	C₂²	1	2	yes	complemented
30	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
31	C₂²×D₄×C₁₃	C₈	1	1	yes	characteristic
32	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₃	—	4	4	no	—
34	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₄×D₄×C₁₃	C₈	1	2	yes	—
42	C₄×D₄×C₁₃	C₈	1	1	yes	characteristic
43	C₄×D₄×C₁₃	C₈	1	1	yes	characteristic
44	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
45	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₄	C₈	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₁₃×M₃₂	—	4	4	no	—
51	C₂×C₁₃×C₁₆	—	4	4	no	—
52	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
53	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
54	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
55	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
60	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
62	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	#33488	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₃	C₂×C₈	1	2	yes	—
68	C₂×D₄×C₁₃	—	2	4	no	—
69	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
70	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
71	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	—	4	2	no	—
73	C₂²×C₄×C₁₃	—	4	2	no	—
74	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₈×C₁₃	—	2	4	no	—
83	C₂×C₈×C₁₃	—	2	4	no	—
84	C₂×C₈×C₁₃	—	2	2	no	—
85	C₂×C₈×C₁₃	—	4	2	no	—
86	C₂×C₈×C₁₃	—	4	2	no	—
87	C₂×C₈×C₁₃	—	4	2	no	—
88	C₂×C₈×C₁₃	—	4	1	no	—
89	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
96	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
97	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
98	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
99	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
100	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
101	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
102	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
103	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
104	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₁₃×C₁₆	—	2	2	no	—
107	C₁₃×C₁₆	—	2	4	no	—
108	C₁₃×C₁₆	—	2	2	no	—
109	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
110	#2169	C₂×C₁₃	1	2	yes	complemented
111	#2168	C₂×C₁₃	1	4	yes	complemented
112	D₄×C₁₆	C₂×C₁₃	1	2	yes	complemented
113	#2163	C₂×C₁₃	1	1	yes	characteristic, complemented
114	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
115	#2112	C₂×C₁₃	1	2	yes	complemented
116	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	2	yes	complemented
117	C₂³×C₁₃	—	2	4	no	—
118	C₂³×C₁₃	—	2	4	no	—
119	C₂³×C₁₃	—	4	2	no	—
120	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
121	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
122	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
123	D₄×C₁₃	—	2	4	no	—
124	D₄×C₁₃	—	2	2	no	—
125	D₄×C₁₃	M₃₂	1	4	yes	complemented
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	4	2	no	—
135	C₂×C₄×C₁₃	—	4	2	no	—
136	C₂×C₄×C₁₃	—	4	2	no	—
137	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
138	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
139	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
143	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
145	C₈×C₁₃	—	2	1	no	—
146	C₈×C₁₃	—	2	2	no	—
147	C₈×C₁₃	—	2	2	no	—
148	C₈×C₁₃	—	2	1	no	—
149	C₈×C₁₃	—	2	1	no	—
150	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
151	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
152	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
153	C₂×M₃₂	C₂²×C₁₃	1	4	yes	complemented
154	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	complemented
155	C₈×D₄	C₄×C₁₃	1	2	yes	—
156	C₈×D₄	C₄×C₁₃	1	1	yes	characteristic
157	C₈×D₄	C₄×C₁₃	1	1	yes	characteristic
158	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
159	C₈×D₄	C₂²×C₁₃	1	2	yes	—
160	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₄×C₁₃	1	1	yes	characteristic
162	C₂×C₂²⋊C₈	C₄×C₁₃	1	2	yes	—
163	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
164	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
165	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
166	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
167	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
168	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
169	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
170	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
171	#346	C₂²×C₁₃	1	2	yes	complemented
172	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
173	C₂²×C₁₃	—	2	1	no	—
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	—	2	1	no	—
176	C₂²×C₁₃	—	2	2	no	—
177	C₂²×C₁₃	—	2	2	no	—
178	C₂²×C₁₃	—	2	2	no	—
179	C₂²×C₁₃	—	2	2	no	—
180	C₂²×C₁₃	—	4	8	no	—
181	C₂²×C₁₃	C₂×M₃₂	1	4	yes	—
182	C₂²×C₁₃	#504	1	2	yes	—
183	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
184	C₄×C₁₃	—	2	1	no	—
185	C₄×C₁₃	—	2	1	no	—
186	C₄×C₁₃	—	2	1	no	—
187	C₄×C₁₃	—	2	1	no	—
188	C₄×C₁₃	—	2	2	no	—
189	C₄×C₁₃	—	2	2	no	—
190	C₄×C₁₃	C₂×M₃₂	1	2	yes	—
191	C₄×C₁₃	#518	1	1	yes	characteristic
192	C₄×C₁₃	#568	1	1	yes	characteristic
193	C₂²×D₄	C₈×C₁₃	1	1	yes	characteristic
194	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
195	C₂²×C₈	—	4	4	no	—
196	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
197	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
198	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
199	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
200	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
201	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
202	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
203	C₄×D₄	C₈×C₁₃	1	2	yes	—
204	C₄×D₄	C₈×C₁₃	1	1	yes	characteristic
205	C₄×D₄	C₈×C₁₃	1	1	yes	characteristic
206	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
207	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
208	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
209	C₂×C₄⋊C₄	C₈×C₁₃	1	1	yes	characteristic
210	C₂×C₂²⋊C₄	C₈×C₁₃	1	2	yes	—
211	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
212	M₃₂	—	4	4	no	—
213	C₂×C₁₆	—	4	4	no	—
214	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
215	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
216	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
217	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
218	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
219	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
220	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
221	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
222	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
223	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
224	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
225	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
226	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
227	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×C₁₃	—	2	2	no	—
229	C₂×C₁₃	—	2	4	no	—
230	C₂×C₁₃	—	4	2	no	—
231	C₂×C₁₃	#2972	1	1	yes	characteristic
232	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
233	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
234	C₂⁴	C₂×C₈×C₁₃	1	2	yes	—
235	C₂×D₄	—	2	4	no	—
236	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
237	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
238	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
239	C₂²×C₄	—	4	2	no	—
240	C₂²×C₄	—	4	2	no	—
241	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
242	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
244	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
245	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
249	C₂×C₈	—	2	4	no	—
250	C₂×C₈	—	2	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	4	2	no	—
253	C₂×C₈	—	4	2	no	—
254	C₂×C₈	—	4	2	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
257	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
261	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
262	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
263	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
264	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
265	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
266	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
267	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
268	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
269	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
270	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
271	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
272	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	4	no	—
275	C₁₆	—	2	2	no	—
276	C₁₃	#33488	1	1	yes	characteristic, direct product factor, Sylow
277	C₂³	—	2	4	no	—
278	C₂³	—	2	4	no	—
279	C₂³	—	4	2	no	—
280	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
281	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
282	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
283	D₄	—	2	4	no	—
284	D₄	—	2	2	no	—
285	D₄	C₁₃×M₃₂	1	4	yes	complemented
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	2	no	—
296	C₂×C₄	—	4	2	no	—
297	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
298	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
299	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
300	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
302	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
303	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
304	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
305	C₈	—	2	1	no	—
306	C₈	—	2	2	no	—
307	C₈	—	2	2	no	—
308	C₈	—	2	1	no	—
309	C₈	—	2	1	no	—
310	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	1	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	4	8	no	—
319	C₂²	C₂×C₁₃×M₃₂	1	4	yes	—
320	C₂²	C₁₃×#504	1	2	yes	—
321	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
322	C₄	—	2	1	no	—
323	C₄	—	2	1	no	—
324	C₄	—	2	1	no	—
325	C₄	—	2	1	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	C₂×C₁₃×M₃₂	1	2	yes	—
329	C₄	C₁₃×#518	1	1	yes	characteristic
330	C₄	C₁₃×#568	1	1	yes	characteristic
331	C₂	—	2	2	no	—
332	C₂	—	2	4	no	—
333	C₂	—	4	2	no	—
334	C₂	C₁₃×#2972	1	1	yes	characteristic
335	C₂	C₂²×C₁₃×M₃₂	1	1	yes	characteristic
336	C₂	C₂×C₁₃×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂²×D₄×C₁₃	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2169	C₂	semidirect
3. C₁₃×#2168	C₂	semidirect
4. D₄×C₁₃×C₁₆	C₂	semidirect
5. C₁₃×#2163	C₂	semidirect
6. C₁₃×#2162	C₂	semidirect
7. C₁₃×#2112	C₂	semidirect
8. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
11. C₂×C₁₃×M₃₂	C₂²	semidirect
12. C₂²×C₁₃×C₁₆	C₂²	semidirect
22. C₁₃×C₄⋊C₁₆	C₂²	semidirect
23. C₁₃×C₄⋊C₁₆	C₂²	semidirect
27. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
28. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
29. C₁₃×#346	C₂²	semidirect
30. C₄×C₁₃×C₁₆	C₂²	semidirect
66. #33488	C₁₃	direct (N × H)
110. #2169	C₂×C₁₃	semidirect
111. #2168	C₂×C₁₃	semidirect
112. D₄×C₁₆	C₂×C₁₃	semidirect
113. #2163	C₂×C₁₃	semidirect
114. #2162	C₂×C₁₃	semidirect
115. #2112	C₂×C₁₃	semidirect
116. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
125. D₄×C₁₃	M₃₂	semidirect
153. C₂×M₃₂	C₂²×C₁₃	semidirect
154. C₂²×C₁₆	C₂²×C₁₃	semidirect
164. C₄⋊C₁₆	C₂²×C₁₃	semidirect
165. C₄⋊C₁₆	C₂²×C₁₃	semidirect
169. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
170. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
171. #346	C₂²×C₁₃	semidirect
172. C₄×C₁₆	C₂²×C₁₃	semidirect
276. C₁₃	#33488	direct (N × H)
285. D₄	C₁₃×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₃	2
C₁₃×#2169	2
C₁₃×#2168	2
D₄×C₁₃×C₁₆	2
C₁₃×#2163	2
C₁₃×#2162	2
C₁₃×#2112	2
C₂×C₁₃×C₂²⋊C₁₆	2
#33488	13

Subgroups — C13×#33488 #15719827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33488 #15719827