Subgroups — C₁₃×#21285 #15707624

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2319	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1973	C₂	1	2	yes	maximal
5	C₁₃×#1944	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1934	C₂	1	2	yes	maximal
7	C₁₃×#1933	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1762	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1726	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#391	C₂²	1	2	yes	—
27	C₁₃×#390	C₂²	1	2	yes	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#389	C₂²	1	2	yes	—
30	C₁₃×#388	—	2	2	no	—
31	C₁₃×#387	—	2	2	no	—
32	C₁₃×#383	—	2	1	no	—
33	C₁₃×#382	—	2	1	no	—
34	C₁₃×#381	—	2	1	no	—
35	C₁₃×#380	—	2	1	no	—
36	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₃×#376	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	1	no	—
45	C₂×C₁₃×SD₁₆	—	2	4	no	—
46	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₃	—	2	2	no	—
51	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
52	C₄×D₄×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#107	—	2	4	no	—
70	C₁₃×#106	C₂×C₄	1	4	yes	—
71	C₁₃×#103	—	2	4	no	—
72	C₁₃×#103	C₂×C₄	1	4	yes	—
73	C₁₃×#102	—	2	4	no	—
74	C₁₃×#102	C₂×C₄	1	4	yes	—
75	C₁₃×#97	—	2	4	no	—
76	C₁₃×#97	—	2	2	no	—
77	C₄×C₈×C₁₃	—	2	4	no	—
78	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
79	C₁₃×#95	—	2	1	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	D₄	1	1	yes	characteristic
86	C₁₃×#95	D₄	1	1	yes	characteristic
87	C₁₃×#95	D₄	1	2	yes	—
88	#21285	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	1	no	—
90	C₂×Q₈×C₁₃	—	2	1	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	8	2	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₁₃×SD₁₆	—	2	8	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	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃	#41	1	4	yes	—
117	C₂×C₈×C₁₃	#41	1	4	yes	—
118	C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	8	2	no	—
126	C₁₃×C₄⋊C₄	—	8	2	no	—
127	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₁₃×C₂²⋊C₄	—	8	2	no	—
131	C₁₃×C₂²⋊C₄	—	8	2	no	—
132	C₄²×C₁₃	—	2	4	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	8	1	no	—
136	C₄²×C₁₃	—	8	1	no	—
137	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
138	C₄²×C₁₃	#41	1	2	yes	—
139	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
140	#2320	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2319	C₂×C₁₃	1	1	yes	characteristic
142	#1973	C₂×C₁₃	1	2	yes	—
143	#1944	C₂×C₁₃	1	2	yes	complemented
144	#1934	C₂×C₁₃	1	2	yes	—
145	#1933	C₂×C₁₃	1	2	yes	complemented
146	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#1763	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#1762	C₂×C₁₃	1	1	yes	characteristic
149	#1726	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	2	2	no	—
157	Q₈×C₁₃	—	2	2	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	D₄×C₁₃	—	2	2	no	—
160	D₄×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	4	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	1	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	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	8	4	no	—
185	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	2	4	no	—
193	C₈×C₁₃	#117	1	4	yes	—
194	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
197	C₄×SD₁₆	C₄×C₁₃	1	8	yes	complemented
198	C₂×#107	C₂²×C₁₃	1	2	yes	—
199	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#103	C₂²×C₁₃	1	2	yes	—
201	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×#102	C₂²×C₁₃	1	2	yes	—
203	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#97	C₂²×C₁₃	1	2	yes	—
205	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
208	#391	C₂²×C₁₃	1	2	yes	—
209	#390	C₂²×C₁₃	1	2	yes	—
210	#389	C₂²×C₁₃	1	2	yes	—
211	#389	C₂²×C₁₃	1	2	yes	—
212	#388	—	2	2	no	—
213	#387	—	2	2	no	—
214	#383	—	2	1	no	—
215	#382	—	2	1	no	—
216	#381	—	2	1	no	—
217	#380	—	2	1	no	—
218	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
220	#376	C₂²×C₁₃	1	1	yes	characteristic
221	#340	C₂²×C₁₃	1	2	yes	—
222	#340	C₂²×C₁₃	1	2	yes	—
223	#340	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₁₃	—	4	2	no	—
225	C₂²×C₁₃	—	4	2	no	—
226	C₂²×C₁₃	—	4	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₁₃	#532	1	2	yes	—
231	C₂²×C₁₃	#576	1	1	yes	characteristic
232	C₂²×C₁₃	#577	1	2	yes	—
233	C₂²×C₁₃	#578	1	1	yes	characteristic
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	2	no	—
240	C₄×C₁₃	—	4	2	no	—
241	C₄×C₁₃	—	8	2	no	—
242	C₄×C₁₃	—	8	2	no	—
243	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
244	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
245	C₄×C₁₃	#529	1	2	yes	—
246	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₂³×C₄	—	2	1	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
272	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
273	#107	—	2	4	no	—
274	#106	C₂×C₄×C₁₃	1	4	yes	—
275	#103	—	2	4	no	—
276	#103	C₂×C₄×C₁₃	1	4	yes	—
277	#102	—	2	4	no	—
278	#102	C₂×C₄×C₁₃	1	4	yes	—
279	#97	—	2	4	no	—
280	#97	—	2	2	no	—
281	C₄×C₈	—	2	4	no	—
282	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
283	#95	—	2	1	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	D₄×C₁₃	1	1	yes	characteristic
290	#95	D₄×C₁₃	1	1	yes	characteristic
291	#95	D₄×C₁₃	1	2	yes	—
292	C₂×C₁₃	—	8	2	no	—
293	C₂×C₁₃	#2293	1	1	yes	characteristic
294	C₂×C₁₃	#2949	1	1	yes	characteristic
295	C₂×C₁₃	#2951	1	1	yes	characteristic
296	C₂×C₁₃	#3178	1	2	yes	—
297	C₂×C₁₃	#3179	1	2	yes	—
298	C₂⁴	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	8	2	no	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
319	SD₁₆	—	2	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
324	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
325	C₂×C₈	C₁₃×#41	1	4	yes	—
326	C₂×C₈	C₁₃×#41	1	4	yes	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	8	2	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
337	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₂²⋊C₄	—	8	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	8	1	no	—
345	C₄²	—	8	1	no	—
346	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
347	C₄²	C₁₃×#41	1	2	yes	—
348	C₁₃	#21285	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	1	no	—
354	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
355	Q₈	—	2	2	no	—
356	Q₈	—	2	2	no	—
357	Q₈	—	4	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	4	no	—
384	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
386	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
387	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
388	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
389	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	4	no	—
392	C₈	C₁₃×#117	1	4	yes	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
399	C₂²	C₁₃×#532	1	2	yes	—
400	C₂²	C₁₃×#576	1	1	yes	characteristic
401	C₂²	C₁₃×#577	1	2	yes	—
402	C₂²	C₁₃×#578	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	2	no	—
412	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
413	C₄	C₄×C₁₃×#41	1	1	yes	characteristic
414	C₄	C₁₃×#529	1	2	yes	—
415	C₂	—	8	2	no	—
416	C₂	C₁₃×#2293	1	1	yes	characteristic
417	C₂	C₁₃×#2949	1	1	yes	characteristic
418	C₂	C₁₃×#2951	1	1	yes	characteristic
419	C₂	C₁₃×#3178	1	2	yes	—
420	C₂	C₁₃×#3179	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×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2320	C₂	semidirect
5. C₁₃×#1944	C₂	semidirect
7. C₁₃×#1933	C₂	semidirect
8. C₄×C₁₃×#107	C₂	semidirect
9. C₁₃×#1763	C₂	semidirect
11. C₁₃×#1726	C₂	semidirect
15. C₄×C₁₃×SD₁₆	C₄	semidirect
88. #21285	C₁₃	direct (N × H)
140. #2320	C₂×C₁₃	semidirect
143. #1944	C₂×C₁₃	semidirect
145. #1933	C₂×C₁₃	semidirect
146. C₄×#107	C₂×C₁₃	semidirect
147. #1763	C₂×C₁₃	semidirect
149. #1726	C₂×C₁₃	semidirect
197. C₄×SD₁₆	C₄×C₁₃	semidirect
348. C₁₃	#21285	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2320	2
C₁₃×#2319	2
C₁₃×#1973	2
C₁₃×#1944	2
C₁₃×#1934	2
C₁₃×#1933	2
C₄×C₁₃×#107	2
C₁₃×#1763	2
C₁₃×#1762	2
C₁₃×#1726	2
#21285	13

Subgroups — C13×#21285 #15707624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21285 #15707624