Subgroups — C₁₃×#32678 #15719017

Order 3328.

758 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2592	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2015	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2012	C₂	1	2	yes	maximal
5	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1971	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1926	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₁₃×#397	—	2	2	no	—
24	C₁₃×#393	—	2	2	no	—
25	C₁₃×#391	C₂²	1	2	yes	—
26	C₁₃×#391	C₂²	1	2	yes	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#390	C₂²	1	2	yes	—
29	C₁₃×#388	—	2	2	no	—
30	C₁₃×#388	—	2	2	no	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
38	C₂×C₁₃×Q₁₆	—	2	2	no	—
39	C₂×C₁₃×Q₁₆	—	4	1	no	—
40	C₂×C₁₃×Q₁₆	—	4	1	no	—
41	C₂×C₁₃×SD₁₆	—	4	2	no	—
42	C₂×C₁₃×SD₁₆	—	4	2	no	—
43	C₂×C₁₃×SD₁₆	—	4	2	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	4	1	no	—
46	C₂×C₁₃×D₈	—	4	1	no	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#124	—	4	2	no	—
51	C₁₃×#124	—	4	2	no	—
52	C₄×Q₈×C₁₃	—	4	1	no	—
53	C₄×Q₈×C₁₃	—	4	1	no	—
54	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#106	—	4	1	no	—
68	C₁₃×#106	—	4	1	no	—
69	C₁₃×C₄⋊C₈	—	4	1	no	—
70	C₁₃×#103	—	2	4	no	—
71	C₁₃×#103	—	4	2	no	—
72	C₁₃×#102	—	2	4	no	—
73	C₁₃×#102	—	4	2	no	—
74	C₁₃×#97	—	4	1	no	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	#32678	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂⁴×C₁₃	—	2	2	no	—
82	C₂×Q₈×C₁₃	—	2	2	no	—
83	C₂×Q₈×C₁₃	—	2	2	no	—
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	4	1	no	—
89	C₂×Q₈×C₁₃	—	4	2	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	2	2	no	—
93	C₂×D₄×C₁₃	—	2	2	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₁₃×Q₁₆	—	4	4	no	—
105	C₁₃×SD₁₆	—	4	8	no	—
106	C₁₃×D₈	—	4	4	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	1	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	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	#41	1	2	yes	—
115	C₂×C₈×C₁₃	#41	1	2	yes	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	2	no	—
122	C₁₃×C₂²⋊C₄	—	4	4	no	—
123	C₁₃×C₂²⋊C₄	—	4	4	no	—
124	C₁₃×C₂²⋊C₄	—	4	4	no	—
125	C₁₃×C₂²⋊C₄	—	4	4	no	—
126	C₁₃×C₂²⋊C₄	—	8	2	no	—
127	C₁₃×C₂²⋊C₄	—	8	2	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	8	2	no	—
133	#2592	C₂×C₁₃	1	2	yes	complemented
134	#2055	C₂×C₁₃	1	2	yes	complemented
135	#2015	C₂×C₁₃	1	2	yes	complemented
136	#2012	C₂×C₁₃	1	2	yes	—
137	#1985	C₂×C₁₃	1	1	yes	characteristic, complemented
138	#1972	C₂×C₁₃	1	1	yes	characteristic
139	#1971	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#1927	C₂×C₁₃	1	2	yes	complemented
141	#1926	C₂×C₁₃	1	2	yes	complemented
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	—	4	2	no	—
145	C₂³×C₁₃	—	4	2	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	2	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₁₃	—	4	4	no	—
151	Q₈×C₁₃	—	4	2	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	Q₈×C₁₃	—	4	2	no	—
154	Q₈×C₁₃	—	4	2	no	—
155	D₄×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	4	2	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	2	no	—
172	C₂×C₄×C₁₃	—	4	2	no	—
173	C₂×C₄×C₁₃	—	4	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	4	2	no	—
187	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
188	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
189	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×#124	C₂²×C₁₃	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
193	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
194	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#103	C₂²×C₁₃	1	2	yes	—
196	C₂×#103	C₂²×C₁₃	1	2	yes	—
197	C₂×#102	C₂²×C₁₃	1	2	yes	—
198	C₂×#102	C₂²×C₁₃	1	2	yes	—
199	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
200	#397	—	2	2	no	—
201	#393	—	2	2	no	—
202	#391	C₂²×C₁₃	1	2	yes	—
203	#391	C₂²×C₁₃	1	2	yes	—
204	#390	C₂²×C₁₃	1	2	yes	—
205	#390	C₂²×C₁₃	1	2	yes	—
206	#388	—	2	2	no	—
207	#388	—	2	2	no	—
208	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
209	#340	C₂²×C₁₃	1	2	yes	—
210	#336	C₂²×C₁₃	1	2	yes	—
211	#336	C₂²×C₁₃	1	2	yes	—
212	C₂²×C₁₃	—	8	2	no	—
213	C₂²×C₁₃	—	8	2	no	—
214	C₂²×C₁₃	—	8	2	no	—
215	C₂²×C₁₃	—	8	2	no	—
216	C₂²×C₁₃	—	8	2	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	2	no	—
219	C₂²×C₁₃	#534	1	1	yes	characteristic
220	C₂²×C₁₃	#550	1	1	yes	characteristic
221	C₂²×C₁₃	#550	1	1	yes	characteristic
222	C₂²×C₁₃	#575	1	2	yes	—
223	C₂²×C₁₃	#577	1	2	yes	—
224	C₄×C₁₃	—	4	2	no	—
225	C₄×C₁₃	—	4	1	no	—
226	C₄×C₁₃	—	4	2	no	—
227	C₄×C₁₃	—	4	1	no	—
228	C₄×C₁₃	—	8	2	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	#538	1	1	yes	characteristic
232	C₄×C₁₃	#538	1	1	yes	characteristic
233	C₄×C₁₃	#555	1	1	yes	characteristic
234	C₄×C₁₃	H(3,𝔽₄)	1	1	yes	characteristic
235	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
236	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
238	C₂×Q₁₆	—	2	2	no	—
239	C₂×Q₁₆	—	4	1	no	—
240	C₂×Q₁₆	—	4	1	no	—
241	C₂×SD₁₆	—	4	2	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂×D₈	—	4	1	no	—
246	C₂×D₈	—	4	1	no	—
247	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
250	#124	—	4	2	no	—
251	#124	—	4	2	no	—
252	C₄×Q₈	—	4	1	no	—
253	C₄×Q₈	—	4	1	no	—
254	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
255	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	#106	—	4	1	no	—
268	#106	—	4	1	no	—
269	C₄⋊C₈	—	4	1	no	—
270	#103	—	2	4	no	—
271	#103	—	4	2	no	—
272	#102	—	2	4	no	—
273	#102	—	4	2	no	—
274	#97	—	4	1	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	C₂×C₁₃	—	16	2	no	—
281	C₂×C₁₃	#2733	1	1	yes	characteristic
282	C₂×C₁₃	#3197	1	1	yes	characteristic
283	C₂×C₁₃	#3204	1	1	yes	characteristic
284	C₂×C₁₃	#3401	1	2	yes	—
285	C₂×C₁₃	#3401	1	2	yes	—
286	C₂⁴	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	4	1	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
309	Q₁₆	—	4	4	no	—
310	SD₁₆	—	4	8	no	—
311	D₈	—	4	4	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	C₁₃×#41	1	2	yes	—
320	C₂×C₈	C₁₃×#41	1	2	yes	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₂²⋊C₄	—	8	2	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	8	2	no	—
338	C₁₃	#32678	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
347	Q₈	—	4	4	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
377	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	C₁₃×#534	1	1	yes	characteristic
392	C₂²	C₁₃×#550	1	1	yes	characteristic
393	C₂²	C₁₃×#550	1	1	yes	characteristic
394	C₂²	C₁₃×#575	1	2	yes	—
395	C₂²	C₁₃×#577	1	2	yes	—
396	C₄	—	4	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₁₃×#538	1	1	yes	characteristic
404	C₄	C₁₃×#538	1	1	yes	characteristic
405	C₄	C₁₃×#555	1	1	yes	characteristic
406	C₄	C₁₃×H(3,𝔽₄)	1	1	yes	characteristic
407	C₂	—	16	2	no	—
408	C₂	C₁₃×#2733	1	1	yes	characteristic
409	C₂	C₁₃×#3197	1	1	yes	characteristic
410	C₂	C₁₃×#3204	1	1	yes	characteristic
411	C₂	C₁₃×#3401	1	2	yes	—
412	C₂	C₁₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2592	C₂	semidirect
2. C₁₃×#2055	C₂	semidirect
3. C₁₃×#2015	C₂	semidirect
5. C₁₃×#1985	C₂	semidirect
7. C₁₃×#1971	C₂	semidirect
8. C₁₃×#1927	C₂	semidirect
9. C₁₃×#1926	C₂	semidirect
80. #32678	C₁₃	direct (N × H)
133. #2592	C₂×C₁₃	semidirect
134. #2055	C₂×C₁₃	semidirect
135. #2015	C₂×C₁₃	semidirect
137. #1985	C₂×C₁₃	semidirect
139. #1971	C₂×C₁₃	semidirect
140. #1927	C₂×C₁₃	semidirect
141. #1926	C₂×C₁₃	semidirect
338. C₁₃	#32678	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×#2592	2
C₁₃×#2055	2
C₁₃×#2015	2
C₁₃×#2012	2
C₁₃×#1985	2
C₁₃×#1972	2
C₁₃×#1971	2
C₁₃×#1927	2
C₁₃×#1926	2
#32678	13

Subgroups — C13×#32678 #15719017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32678 #15719017