Subgroups — C₁₃×#32767 #15719106

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2621	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2620	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2074	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2073	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2072	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2016	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2001	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2000	C₂	1	2	yes	maximal
11	C₁₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	2	yes	—
21	C₂×C₁₃×#103	C₂²	1	2	yes	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
25	C₁₃×#398	—	2	2	no	—
26	C₁₃×#397	—	2	2	no	—
27	C₁₃×#396	—	2	2	no	—
28	C₁₃×#394	—	2	2	no	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#391	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#382	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×Q₁₆	—	4	2	no	—
45	C₂×C₁₃×Q₁₆	—	4	2	no	—
46	C₂×C₁₃×Q₁₆	—	4	2	no	—
47	C₂×C₁₃×SD₁₆	—	4	2	no	—
48	C₂×C₁₃×SD₁₆	—	4	2	no	—
49	C₂×C₁₃×SD₁₆	—	4	2	no	—
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	—	4	2	no	—
53	C₁₃×#124	—	4	2	no	—
54	C₁₃×C₂²⋊Q₈	—	4	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	2	no	—
56	C₁₃×C₂²⋊Q₈	—	4	2	no	—
57	C₁₃×#121	—	4	2	no	—
58	C₁₃×#117	—	4	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#103	—	4	2	no	—
76	C₁₃×#103	—	4	2	no	—
77	C₁₃×#103	—	4	2	no	—
78	C₁₃×#102	—	4	2	no	—
79	C₁₃×C₂²⋊C₈	—	4	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	4	no	—
83	#32767	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	1	no	—
85	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₁₃	—	2	1	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	—	2	2	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	2	no	—
94	C₂×Q₈×C₁₃	—	2	2	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	—	8	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	4	8	no	—
116	C₁₃×SD₁₆	—	4	8	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	4	2	no	—
128	C₁₃×C₄⋊C₄	—	4	2	no	—
129	C₁₃×C₄⋊C₄	—	4	4	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	8	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	4	no	—
135	C₁₃×C₂²⋊C₄	—	4	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	8	2	no	—
138	C₄²×C₁₃	—	2	2	no	—
139	C₄²×C₁₃	—	2	2	no	—
140	#2621	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2620	C₂×C₁₃	1	1	yes	characteristic
142	#2074	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2073	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2072	C₂×C₁₃	1	2	yes	complemented
145	#2016	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2015	C₂×C₁₃	1	2	yes	complemented
147	#2013	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#2001	C₂×C₁₃	1	2	yes	complemented
149	#2000	C₂×C₁₃	1	2	yes	—
150	#1818	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	2	1	no	—
152	C₂³×C₁₃	—	2	1	no	—
153	C₂³×C₁₃	—	2	1	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	4	1	no	—
157	C₂³×C₁₃	—	4	1	no	—
158	C₂³×C₁₃	—	4	1	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	4	2	no	—
163	Q₈×C₁₃	—	4	2	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	8	4	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	2	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
197	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₈×C₁₃	—	4	2	no	—
200	C₈×C₁₃	—	4	2	no	—
201	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
202	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
207	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#103	C₂²×C₁₃	1	2	yes	—
210	C₂×#103	C₂²×C₁₃	1	2	yes	—
211	C₂×#103	C₂²×C₁₃	1	2	yes	—
212	C₂×#102	C₂²×C₁₃	1	2	yes	—
213	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
214	#398	—	2	2	no	—
215	#397	—	2	2	no	—
216	#396	—	2	2	no	—
217	#394	—	2	2	no	—
218	#391	C₂²×C₁₃	1	2	yes	—
219	#391	C₂²×C₁₃	1	1	yes	characteristic
220	#390	C₂²×C₁₃	1	1	yes	characteristic
221	#384	C₂²×C₁₃	1	1	yes	characteristic
222	#382	C₂²×C₁₃	1	1	yes	characteristic
223	#340	C₂²×C₁₃	1	2	yes	—
224	#340	C₂²×C₁₃	1	2	yes	—
225	#336	C₂²×C₁₃	1	2	yes	—
226	#336	C₂²×C₁₃	1	1	yes	characteristic
227	#336	C₂²×C₁₃	1	1	yes	characteristic
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	4	1	no	—
230	C₂²×C₁₃	—	4	1	no	—
231	C₂²×C₁₃	—	4	2	no	—
232	C₂²×C₁₃	—	4	1	no	—
233	C₂²×C₁₃	—	8	2	no	—
234	C₂²×C₁₃	—	8	1	no	—
235	C₂²×C₁₃	—	8	1	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	#534	1	1	yes	characteristic
239	C₂²×C₁₃	#535	1	1	yes	characteristic
240	C₂²×C₁₃	#535	1	1	yes	characteristic
241	C₂²×C₁₃	#577	1	2	yes	—
242	C₂²×C₁₃	#578	1	2	yes	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	—	4	1	no	—
246	C₄×C₁₃	—	8	1	no	—
247	C₄×C₁₃	—	8	1	no	—
248	C₄×C₁₃	—	8	2	no	—
249	C₄×C₁₃	—	8	1	no	—
250	C₄×C₁₃	—	8	2	no	—
251	C₄×C₁₃	#560	1	2	yes	—
252	C₄×C₁₃	#560	1	2	yes	—
253	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
258	C₂×Q₁₆	—	4	2	no	—
259	C₂×Q₁₆	—	4	2	no	—
260	C₂×Q₁₆	—	4	2	no	—
261	C₂×SD₁₆	—	4	2	no	—
262	C₂×SD₁₆	—	4	2	no	—
263	C₂×SD₁₆	—	4	2	no	—
264	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
265	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
266	C₄⋊Q₈	—	4	2	no	—
267	#124	—	4	2	no	—
268	C₂²⋊Q₈	—	4	2	no	—
269	C₂²⋊Q₈	—	4	2	no	—
270	C₂²⋊Q₈	—	4	2	no	—
271	#121	—	4	2	no	—
272	#117	—	4	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
287	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
289	#103	—	4	2	no	—
290	#103	—	4	2	no	—
291	#103	—	4	2	no	—
292	#102	—	4	2	no	—
293	C₂²⋊C₈	—	4	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	4	no	—
297	C₂×C₁₃	—	8	1	no	—
298	C₂×C₁₃	—	16	1	no	—
299	C₂×C₁₃	#2815	1	1	yes	characteristic
300	C₂×C₁₃	#3201	1	2	yes	—
301	C₂×C₁₃	#3222	1	1	yes	characteristic
302	C₂×C₁₃	#3223	1	1	yes	characteristic
303	C₂×C₁₃	#3225	1	2	yes	—
304	C₂⁴	—	2	1	no	—
305	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
335	Q₁₆	—	4	8	no	—
336	SD₁₆	—	4	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₂²⋊C₄	—	4	4	no	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	8	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₁₃	#32767	1	1	yes	characteristic, direct product factor, Sylow
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	8	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
406	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
407	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	C₁₃×#534	1	1	yes	characteristic
422	C₂²	C₁₃×#535	1	1	yes	characteristic
423	C₂²	C₁₃×#535	1	1	yes	characteristic
424	C₂²	C₁₃×#577	1	2	yes	—
425	C₂²	C₁₃×#578	1	2	yes	—
426	C₄	—	4	1	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	2	no	—
434	C₄	C₁₃×#560	1	2	yes	—
435	C₄	C₁₃×#560	1	2	yes	—
436	C₂	—	8	1	no	—
437	C₂	—	16	1	no	—
438	C₂	C₁₃×#2815	1	1	yes	characteristic
439	C₂	C₁₃×#3201	1	2	yes	—
440	C₂	C₁₃×#3222	1	1	yes	characteristic
441	C₂	C₁₃×#3223	1	1	yes	characteristic
442	C₂	C₁₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2621	C₂	semidirect
3. C₁₃×#2074	C₂	semidirect
4. C₁₃×#2073	C₂	semidirect
5. C₁₃×#2072	C₂	semidirect
6. C₁₃×#2016	C₂	semidirect
7. C₁₃×#2015	C₂	semidirect
8. C₁₃×#2013	C₂	semidirect
9. C₁₃×#2001	C₂	semidirect
11. C₁₃×#1818	C₂	semidirect
83. #32767	C₁₃	direct (N × H)
140. #2621	C₂×C₁₃	semidirect
142. #2074	C₂×C₁₃	semidirect
143. #2073	C₂×C₁₃	semidirect
144. #2072	C₂×C₁₃	semidirect
145. #2016	C₂×C₁₃	semidirect
146. #2015	C₂×C₁₃	semidirect
147. #2013	C₂×C₁₃	semidirect
148. #2001	C₂×C₁₃	semidirect
150. #1818	C₂×C₁₃	semidirect
360. C₁₃	#32767	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2621	2
C₁₃×#2620	2
C₁₃×#2074	2
C₁₃×#2073	2
C₁₃×#2072	2
C₁₃×#2016	2
C₁₃×#2015	2
C₁₃×#2013	2
C₁₃×#2001	2
C₁₃×#2000	2
C₁₃×#1818	2
#32767	13

Subgroups — C13×#32767 #15719106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32767 #15719106