Subgroups — C₁₃×#33436 #15719775

Order 3328.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2169	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2168	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2168	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₃×C₁₆	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#525	C₄	1	1	yes	characteristic
15	C₁₃×#504	—	2	4	no	—
16	C₂×C₁₃×M₃₂	—	2	4	no	—
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
25	C₁₃×#435	C₄	1	2	yes	—
26	C₁₃×#435	C₄	1	2	yes	—
27	C₈×D₄×C₁₃	C₂²	1	2	yes	—
28	C₈×D₄×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#424	C₄	1	1	yes	characteristic
30	C₁₃×#408	C₄	1	1	yes	characteristic
31	C₁₃×#407	C₄	1	1	yes	characteristic
32	C₁₃×#405	C₂²	1	1	yes	characteristic
33	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
34	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
35	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₁₃×#346	C₂²	1	2	yes	complemented
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
43	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₁₃×#131	—	2	2	no	—
46	C₁₃×#131	—	2	2	no	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#123	C₈	1	2	yes	—
60	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
61	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
62	C₁₃×#121	C₈	1	1	yes	characteristic
63	C₁₃×#121	C₈	1	1	yes	characteristic
64	C₁₃×#120	C₈	1	2	yes	—
65	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
67	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
68	C₁₃×M₃₂	—	2	2	no	—
69	C₁₃×M₃₂	—	2	4	no	—
70	C₁₃×M₃₂	—	2	4	no	—
71	C₁₃×M₃₂	D₄	1	4	yes	complemented
72	C₂×C₁₃×C₁₆	—	2	2	no	—
73	C₂×C₁₃×C₁₆	—	2	2	no	—
74	C₂×C₁₃×C₁₆	—	2	4	no	—
75	C₂×C₁₃×C₁₆	—	2	4	no	—
76	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
82	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
83	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
84	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
85	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
86	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₃×#97	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₁₃	C₂³	1	2	yes	—
90	#33436	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
92	C₁₃×#41	—	2	2	no	—
93	C₁₃×#41	—	2	2	no	—
94	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
95	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
96	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
97	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₁₃×M₁₆	—	2	2	no	—
109	C₁₃×M₁₆	—	2	2	no	—
110	C₁₃×M₁₆	—	2	4	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	#41	1	2	yes	—
127	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
129	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
132	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
133	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
135	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
136	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
137	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
138	C₁₃×C₁₆	—	2	1	no	—
139	C₁₃×C₁₆	—	2	1	no	—
140	C₁₃×C₁₆	—	2	2	no	—
141	C₁₃×C₁₆	—	2	1	no	—
142	C₁₃×C₁₆	—	2	1	no	—
143	C₁₃×C₁₆	C₂×D₄	1	4	yes	—
144	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂²×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2929	C₂×C₁₃	1	1	yes	characteristic
147	#2169	C₂×C₁₃	1	2	yes	complemented
148	#2168	C₂×C₁₃	1	2	yes	complemented
149	#2168	C₂×C₁₃	1	2	yes	complemented
150	D₄×C₁₆	C₂×C₁₃	1	2	yes	complemented
151	#2151	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
153	C₂×C₂²⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2108	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
159	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
160	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
161	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	2	2	no	—
166	D₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#131	1	2	yes	—
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₈×C₁₃	—	2	1	no	—
186	C₈×C₁₃	—	2	1	no	—
187	C₈×C₁₃	—	2	2	no	—
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	C₄×D₄	1	2	yes	—
190	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
192	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
193	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
194	#525	C₄×C₁₃	1	1	yes	characteristic
195	#504	—	2	4	no	—
196	C₂×M₃₂	—	2	4	no	—
197	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
199	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
201	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
202	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
203	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
205	#435	C₄×C₁₃	1	2	yes	—
206	#435	C₄×C₁₃	1	2	yes	—
207	C₈×D₄	C₂²×C₁₃	1	2	yes	—
208	C₈×D₄	C₂²×C₁₃	1	2	yes	—
209	#424	C₄×C₁₃	1	1	yes	characteristic
210	#408	C₄×C₁₃	1	1	yes	characteristic
211	#407	C₄×C₁₃	1	1	yes	characteristic
212	#405	C₂²×C₁₃	1	1	yes	characteristic
213	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
214	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
215	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
218	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
220	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
221	#346	C₂²×C₁₃	1	2	yes	complemented
222	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	—	2	1	no	—
226	C₂²×C₁₃	—	2	1	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	2	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	4	4	no	—
234	C₂²×C₁₃	C₈×D₄	1	2	yes	—
235	C₂²×C₁₃	#504	1	2	yes	complemented
236	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	C₈×D₄	1	2	yes	—
243	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
245	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
246	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
247	#131	—	2	2	no	—
248	#131	—	2	2	no	—
249	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
250	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
251	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
255	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
260	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	#123	C₈×C₁₃	1	2	yes	—
262	C₂²⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
263	C₂²⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
264	#121	C₈×C₁₃	1	1	yes	characteristic
265	#121	C₈×C₁₃	1	1	yes	characteristic
266	#120	C₈×C₁₃	1	2	yes	—
267	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
268	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
269	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
270	M₃₂	—	2	2	no	—
271	M₃₂	—	2	4	no	—
272	M₃₂	—	2	4	no	—
273	M₃₂	D₄×C₁₃	1	4	yes	complemented
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	—	2	2	no	—
276	C₂×C₁₆	—	2	4	no	—
277	C₂×C₁₆	—	2	4	no	—
278	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
280	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
283	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
284	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
285	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
286	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
287	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
288	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
289	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
290	#97	C₂×C₄×C₁₃	1	2	yes	—
291	C₄×C₈	C₂³×C₁₃	1	2	yes	—
292	C₂×C₁₃	—	2	2	no	—
293	C₂×C₁₃	—	2	2	no	—
294	C₂×C₁₃	—	4	2	no	—
295	C₂×C₁₃	—	4	1	no	—
296	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
297	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
298	C₂×C₁₃	#3407	1	1	yes	characteristic
299	C₂⁴	C₂×C₈×C₁₃	1	1	yes	characteristic
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
303	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
304	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
305	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
306	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
330	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
331	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
334	C₂×C₈	C₁₃×#41	1	2	yes	—
335	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
336	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
339	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
340	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
341	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
342	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
343	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
344	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
345	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
346	C₁₆	—	2	1	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	2	no	—
349	C₁₆	—	2	1	no	—
350	C₁₆	—	2	1	no	—
351	C₁₆	C₂×D₄×C₁₃	1	4	yes	—
352	C₁₃	#33436	1	1	yes	characteristic, direct product factor, Sylow
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
357	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
358	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
359	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
375	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
376	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
377	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
380	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₁₃×#131	1	2	yes	—
382	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	C₄×D₄×C₁₃	1	2	yes	—
388	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
389	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	C₈×D₄×C₁₃	1	2	yes	—
402	C₂²	C₁₃×#504	1	2	yes	complemented
403	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	C₈×D₄×C₁₃	1	2	yes	—
410	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×C₈×D₄×C₁₃	1	1	yes	characteristic
417	C₂	C₂×C₁₃×#504	1	1	yes	characteristic
418	C₂	C₁₃×#3407	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	C₁₃×#525	C₄
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
1. C₂×C₁₃×#504	C₂	semidirect
2. C₂²×C₁₃×M₃₂	C₂	semidirect
4. C₁₃×#2169	C₂	semidirect
5. C₁₃×#2168	C₂	semidirect
6. C₁₃×#2168	C₂	semidirect
7. D₄×C₁₃×C₁₆	C₂	semidirect
8. C₁₃×#2151	C₂	semidirect
9. C₁₃×#2113	C₂	semidirect
10. C₂×C₁₃×C₂²⋊C₁₆	C₂	semidirect
11. C₁₃×#2108	C₂	semidirect
20. C₂×C₁₃×M₃₂	C₂²	semidirect
24. C₂²×C₁₃×C₁₆	C₂²	semidirect
33. C₁₃×C₄⋊C₁₆	C₂²	semidirect
34. C₁₃×C₄⋊C₁₆	C₂²	semidirect
39. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
40. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
41. C₁₃×#346	C₂²	semidirect
42. C₄×C₁₃×C₁₆	C₂²	semidirect
71. C₁₃×M₃₂	D₄	semidirect
90. #33436	C₁₃	direct (N × H)
144. C₂×#504	C₂×C₁₃	semidirect
145. C₂²×M₃₂	C₂×C₁₃	semidirect
147. #2169	C₂×C₁₃	semidirect
148. #2168	C₂×C₁₃	semidirect
149. #2168	C₂×C₁₃	semidirect
150. D₄×C₁₆	C₂×C₁₃	semidirect
151. #2151	C₂×C₁₃	semidirect
152. #2113	C₂×C₁₃	semidirect
153. C₂×C₂²⋊C₁₆	C₂×C₁₃	semidirect
154. #2108	C₂×C₁₃	semidirect
200. C₂×M₃₂	C₂²×C₁₃	semidirect
204. C₂²×C₁₆	C₂²×C₁₃	semidirect
213. C₄⋊C₁₆	C₂²×C₁₃	semidirect
214. C₄⋊C₁₆	C₂²×C₁₃	semidirect
219. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
220. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
221. #346	C₂²×C₁₃	semidirect
222. C₄×C₁₆	C₂²×C₁₃	semidirect
235. C₂²×C₁₃	#504	semidirect
273. M₃₂	D₄×C₁₃	semidirect
352. C₁₃	#33436	direct (N × H)
402. C₂²	C₁₃×#504	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#504	2
C₂²×C₁₃×M₃₂	2
C₁₃×#2929	2
C₁₃×#2169	2
C₁₃×#2168	2
D₄×C₁₃×C₁₆	2
C₁₃×#2151	2
C₁₃×#2113	2
C₂×C₁₃×C₂²⋊C₁₆	2
C₁₃×#2108	2
#33436	13

Subgroups — C13×#33436 #15719775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33436 #15719775