Subgroups — C₁₃×#24496 #15710835

Order 3328.

924 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#485	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#419	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2434	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2043	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1981	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1928	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#485	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₃×#419	—	2	4	no	—
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×#103	C₂²	1	2	yes	—
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₃×#395	—	2	1	no	—
31	C₁₃×#395	—	2	1	no	—
32	C₁₃×#391	C₂²	1	2	yes	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#388	—	2	2	no	—
35	C₁₃×#385	—	2	2	no	—
36	C₁₃×#383	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	2	2	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	4	2	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	—	2	2	no	—
53	C₂×C₁₃×M₁₆	—	4	2	no	—
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×C₄⋊Q₈	—	2	4	no	—
58	C₁₃×C₄⋊Q₈	—	4	2	no	—
59	C₁₃×C₂²⋊Q₈	—	2	2	no	—
60	C₁₃×C₂²⋊Q₈	—	2	2	no	—
61	C₁₃×#117	—	2	2	no	—
62	C₁₃×#117	D₄	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#107	—	2	2	no	—
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	4	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	2	4	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	2	2	no	—
86	C₁₃×#103	—	4	2	no	—
87	C₁₃×#103	—	4	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	2	no	—
93	C₁₃×#95	—	2	2	no	—
94	C₁₃×#95	D₄	1	1	yes	characteristic
95	C₁₃×#95	D₄	1	1	yes	characteristic
96	#24496	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	4	4	no	—
109	C₂×Q₈×C₁₃	—	4	8	no	—
110	C₂×Q₈×C₁₃	—	4	4	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×Q₈×C₁₃	#41	1	4	yes	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	4	4	no	—
122	C₂²×C₄×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	#41	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₁₃×M₁₆	—	4	4	no	—
130	C₂×C₈×C₁₃	—	2	1	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	2	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	1	no	—
142	C₁₃×C₄⋊C₄	—	2	2	no	—
143	C₁₃×C₄⋊C₄	—	4	4	no	—
144	C₁₃×C₄⋊C₄	—	4	4	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	4	no	—
147	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₁₃×C₂²⋊C₄	—	2	4	no	—
150	C₁₃×C₂²⋊C₄	—	2	4	no	—
151	C₁₃×C₂²⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	8	1	no	—
153	C₄²×C₁₃	—	2	4	no	—
154	C₄²×C₁₃	—	2	2	no	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	8	2	no	—
157	C₂×#485	C₂×C₁₃	1	1	yes	characteristic
158	C₂×#419	C₂×C₁₃	1	1	yes	characteristic
159	#2434	C₂×C₁₃	1	1	yes	characteristic
160	#2347	C₂×C₁₃	1	1	yes	characteristic
161	#2066	C₂×C₁₃	1	2	yes	complemented
162	#2043	C₂×C₁₃	1	2	yes	complemented
163	#1981	C₂×C₁₃	1	2	yes	complemented
164	#1928	C₂×C₁₃	1	2	yes	complemented
165	#1894	C₂×C₁₃	1	1	yes	characteristic
166	#1851	C₂×C₁₃	1	1	yes	characteristic
167	#1787	C₂×C₁₃	1	1	yes	characteristic
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	1	no	—
171	C₂³×C₁₃	—	2	1	no	—
172	C₂³×C₁₃	#121	1	2	yes	—
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	4	no	—
175	Q₈×C₁₃	—	2	4	no	—
176	Q₈×C₁₃	—	4	8	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	Q₈×C₁₃	—	4	2	no	—
179	Q₈×C₁₃	—	4	1	no	—
180	Q₈×C₁₃	—	4	1	no	—
181	Q₈×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	#121	1	2	yes	—
209	C₂×C₄×C₁₃	#137	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	—	4	1	no	—
216	C₈×C₁₃	—	4	2	no	—
217	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
220	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
222	#485	—	2	4	no	—
223	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
226	#419	—	2	4	no	—
227	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#103	C₂²×C₁₃	1	2	yes	—
230	C₂×#103	C₂²×C₁₃	1	2	yes	—
231	C₂×#103	C₂²×C₁₃	1	2	yes	—
232	C₂×#103	C₂²×C₁₃	1	2	yes	—
233	C₂×#103	C₂²×C₁₃	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	#395	—	2	1	no	—
236	#395	—	2	1	no	—
237	#391	C₂²×C₁₃	1	2	yes	—
238	#389	C₂²×C₁₃	1	2	yes	—
239	#388	—	2	2	no	—
240	#385	—	2	2	no	—
241	#383	—	2	1	no	—
242	#380	C₂²×C₁₃	1	1	yes	characteristic
243	C₄×C₄⋊C₄	—	2	1	no	—
244	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
245	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	#340	C₂²×C₁₃	1	2	yes	—
247	#336	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₁₃	—	2	2	no	—
249	C₂²×C₁₃	—	2	2	no	—
250	C₂²×C₁₃	—	2	2	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
254	C₂²×C₁₃	#546	1	2	yes	—
255	C₂²×C₁₃	C₂×#137	1	2	yes	—
256	C₂²×C₁₃	#577	1	1	yes	characteristic
257	C₂²×C₁₃	#578	1	1	yes	characteristic
258	C₄×C₁₃	—	2	2	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	4	2	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	8	1	no	—
265	C₄×C₁₃	—	8	1	no	—
266	C₄×C₁₃	—	8	2	no	—
267	C₄×C₁₃	#525	1	1	yes	characteristic
268	C₄×C₁₃	#535	1	1	yes	characteristic
269	C₄×C₁₃	#551	1	2	yes	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	—	2	4	no	—
272	C₂²×Q₈	—	2	2	no	—
273	C₂²×Q₈	—	2	2	no	—
274	C₂²×Q₈	—	4	2	no	—
275	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	4	2	no	—
281	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	4	no	—
285	C₄⋊Q₈	—	4	2	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	#117	—	2	2	no	—
289	#117	D₄×C₁₃	1	4	yes	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	2	no	—
304	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
305	#107	—	2	2	no	—
306	#106	—	2	2	no	—
307	C₄⋊C₈	—	4	2	no	—
308	#103	—	2	4	no	—
309	#103	—	2	4	no	—
310	#103	—	2	4	no	—
311	#103	—	2	2	no	—
312	#103	—	2	2	no	—
313	#103	—	4	2	no	—
314	#103	—	4	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	#95	—	2	1	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	D₄×C₁₃	1	1	yes	characteristic
322	#95	D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₁₃	—	4	2	no	—
324	C₂×C₁₃	#2411	1	1	yes	characteristic
325	C₂×C₁₃	#3039	1	1	yes	characteristic
326	C₂×C₁₃	#3046	1	1	yes	characteristic
327	C₂×C₁₃	#3320	1	2	yes	—
328	C₂×C₁₃	#3328	1	2	yes	—
329	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	8	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	4	4	no	—
341	C₂×Q₈	—	4	8	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	C₁₃×#41	1	4	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂²×C₄	C₁₃×#41	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
361	M₁₆	—	4	4	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	4	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	8	1	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	8	2	no	—
389	C₁₃	#24496	1	1	yes	characteristic, direct product factor, Sylow
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	C₁₃×#121	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	8	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	C₁₃×#121	1	2	yes	—
431	C₂×C₄	C₁₃×#137	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
434	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
435	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
445	C₂²	C₁₃×#546	1	2	yes	—
446	C₂²	C₂×C₁₃×#137	1	2	yes	—
447	C₂²	C₁₃×#577	1	1	yes	characteristic
448	C₂²	C₁₃×#578	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	4	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	2	no	—
457	C₄	—	8	1	no	—
458	C₄	C₁₃×#525	1	1	yes	characteristic
459	C₄	C₁₃×#535	1	1	yes	characteristic
460	C₄	C₁₃×#551	1	2	yes	—
461	C₂	—	4	2	no	—
462	C₂	C₁₃×#2411	1	1	yes	characteristic
463	C₂	C₁₃×#3039	1	1	yes	characteristic
464	C₂	C₁₃×#3046	1	1	yes	characteristic
465	C₂	C₁₃×#3320	1	2	yes	—
466	C₂	C₁₃×#3328	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
5. C₁₃×#2066	C₂	semidirect
6. C₁₃×#2043	C₂	semidirect
7. C₁₃×#1981	C₂	semidirect
8. C₁₃×#1928	C₂	semidirect
96. #24496	C₁₃	direct (N × H)
161. #2066	C₂×C₁₃	semidirect
162. #2043	C₂×C₁₃	semidirect
163. #1981	C₂×C₁₃	semidirect
164. #1928	C₂×C₁₃	semidirect
389. C₁₃	#24496	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×C₁₃×#485	2
C₂×C₁₃×#419	2
C₁₃×#2434	2
C₁₃×#2347	2
C₁₃×#2066	2
C₁₃×#2043	2
C₁₃×#1981	2
C₁₃×#1928	2
C₁₃×#1894	2
C₁₃×#1851	2
C₁₃×#1787	2
#24496	13

Subgroups — C13×#24496 #15710835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24496 #15710835