Subgroups — C₁₃×#24597 #15710936

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2504	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2085	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₁₃×#482	—	2	4	no	—
17	C₁₃×#428	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₃×#397	—	2	1	no	—
28	C₁₃×#397	—	2	1	no	—
29	C₁₃×#390	C₂²	1	2	yes	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#388	—	2	2	no	—
32	C₁₃×#386	—	2	2	no	—
33	C₁₃×#383	—	2	1	no	—
34	C₁₃×#382	C₂²	1	2	yes	—
35	C₁₃×#380	C₂²	1	1	yes	characteristic
36	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	C₄×C₁₃×C₂²⋊C₄	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	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	4	no	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×#121	—	2	2	no	—
53	C₁₃×#121	—	2	2	no	—
54	C₁₃×#117	—	2	2	no	—
55	C₁₃×#117	D₄	1	4	yes	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	2	yes	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	—	2	2	no	—
73	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
74	C₁₃×#107	—	2	4	no	—
75	C₁₃×#107	—	2	2	no	—
76	C₁₃×#106	—	2	4	no	—
77	C₁₃×#106	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	4	no	—
79	C₁₃×#102	—	2	4	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×C₂²⋊C₈	—	2	2	no	—
83	C₁₃×#95	—	2	1	no	—
84	C₁₃×#95	—	2	2	no	—
85	C₁₃×#95	—	2	2	no	—
86	C₁₃×#95	—	2	2	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	D₄	1	1	yes	characteristic
89	C₁₃×#95	D₄	1	1	yes	characteristic
90	#24597	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	—	2	1	no	—
92	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	2	no	—
97	C₂×D₄×C₁₃	—	4	4	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	4	2	no	—
107	C₂²×C₄×C₁₃	—	8	1	no	—
108	C₂²×C₄×C₁₃	—	8	1	no	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	#41	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×M₁₆	—	2	8	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	#41	1	4	yes	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	2	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	2	no	—
133	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
134	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₁₃×C₂²⋊C₄	—	4	2	no	—
138	C₁₃×C₂²⋊C₄	—	8	2	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	—	8	1	no	—
141	C₄²×C₁₃	—	2	4	no	—
142	C₄²×C₁₃	—	2	2	no	—
143	C₄²×C₁₃	—	2	2	no	—
144	C₄²×C₁₃	—	8	2	no	—
145	C₂×#482	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#428	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2504	C₂×C₁₃	1	1	yes	characteristic
148	#2347	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#2085	C₂×C₁₃	1	2	yes	complemented
150	#2065	C₂×C₁₃	1	2	yes	complemented
151	#1949	C₂×C₁₃	1	2	yes	complemented
152	#1925	C₂×C₁₃	1	2	yes	complemented
153	#1895	C₂×C₁₃	1	1	yes	characteristic
154	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1823	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	4	1	no	—
161	C₂³×C₁₃	—	4	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	1	no	—
164	C₂³×C₁₃	—	4	1	no	—
165	C₂³×C₁₃	#121	1	2	yes	—
166	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
167	D₄×C₁₃	—	4	1	no	—
168	D₄×C₁₃	—	4	1	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	2	no	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	2	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	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	1	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	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	—	8	4	no	—
195	C₂×C₄×C₁₃	#121	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
200	C₈×C₁₃	—	2	4	no	—
201	C₈×C₁₃	—	4	1	no	—
202	C₈×C₁₃	—	4	1	no	—
203	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
204	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
207	#482	—	2	4	no	—
208	#428	—	2	4	no	—
209	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#107	C₂²×C₁₃	1	2	yes	—
211	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×#106	C₂²×C₁₃	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
214	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#102	C₂²×C₁₃	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
218	#397	—	2	1	no	—
219	#397	—	2	1	no	—
220	#390	C₂²×C₁₃	1	2	yes	—
221	#389	C₂²×C₁₃	1	2	yes	—
222	#388	—	2	2	no	—
223	#386	—	2	2	no	—
224	#383	—	2	1	no	—
225	#382	C₂²×C₁₃	1	2	yes	—
226	#380	C₂²×C₁₃	1	1	yes	characteristic
227	C₄×C₄⋊C₄	—	2	1	no	—
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	2	yes	—
232	#340	C₂²×C₁₃	1	2	yes	—
233	#336	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	2	no	—
241	C₂²×C₁₃	—	8	1	no	—
242	C₂²×C₁₃	—	8	1	no	—
243	C₂²×C₁₃	—	8	1	no	—
244	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₁₃	#547	1	2	yes	—
246	C₂²×C₁₃	#575	1	2	yes	—
247	C₂²×C₁₃	#576	1	1	yes	characteristic
248	C₂²×C₁₃	#577	1	1	yes	characteristic
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	#525	1	1	yes	characteristic
258	C₄×C₁₃	#536	1	1	yes	characteristic
259	C₄×C₁₃	#552	1	2	yes	—
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
262	C₂³×C₄	—	2	1	no	—
263	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
264	C₂×M₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	4	no	—
266	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
269	#121	—	2	2	no	—
270	#121	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	D₄×C₁₃	1	4	yes	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	C₂³×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
291	#107	—	2	4	no	—
292	#107	—	2	2	no	—
293	#106	—	2	4	no	—
294	#106	—	2	2	no	—
295	C₄⋊C₈	—	2	4	no	—
296	#102	—	2	4	no	—
297	#102	—	2	2	no	—
298	#102	—	2	2	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	D₄×C₁₃	1	1	yes	characteristic
306	#95	D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₁₃	—	4	2	no	—
308	C₂×C₁₃	—	16	1	no	—
309	C₂×C₁₃	#2413	1	1	yes	characteristic
310	C₂×C₁₃	#3040	1	1	yes	characteristic
311	C₂×C₁₃	#3045	1	1	yes	characteristic
312	C₂×C₁₃	#3350	1	2	yes	—
313	C₂×C₁₃	#3355	1	2	yes	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	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	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	8	1	no	—
331	C₂²×C₄	—	8	1	no	—
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
336	C₂²×C₄	C₁₃×#41	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	M₁₆	—	2	8	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₁₃×#41	1	4	yes	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
357	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₂²⋊C₄	—	8	1	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	8	2	no	—
368	C₁₃	#24597	1	1	yes	characteristic, direct product factor, Sylow
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	C₁₃×#121	1	2	yes	—
379	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
380	D₄	—	4	1	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	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	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	C₁₃×#121	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
410	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
411	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
412	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
413	C₈	—	2	4	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
427	C₂²	C₁₃×#547	1	2	yes	—
428	C₂²	C₁₃×#575	1	2	yes	—
429	C₂²	C₁₃×#576	1	1	yes	characteristic
430	C₂²	C₁₃×#577	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	2	no	—
439	C₄	C₁₃×#525	1	1	yes	characteristic
440	C₄	C₁₃×#536	1	1	yes	characteristic
441	C₄	C₁₃×#552	1	2	yes	—
442	C₂	—	4	2	no	—
443	C₂	—	16	1	no	—
444	C₂	C₁₃×#2413	1	1	yes	characteristic
445	C₂	C₁₃×#3040	1	1	yes	characteristic
446	C₂	C₁₃×#3045	1	1	yes	characteristic
447	C₂	C₁₃×#3350	1	2	yes	—
448	C₂	C₁₃×#3355	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 ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#428	C₂	semidirect
4. C₁₃×#2347	C₂	semidirect
5. C₁₃×#2085	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#1949	C₂	semidirect
8. C₁₃×#1925	C₂	semidirect
10. C₁₃×#1851	C₂	semidirect
11. C₁₃×#1823	C₂	semidirect
90. #24597	C₁₃	direct (N × H)
146. C₂×#428	C₂×C₁₃	semidirect
148. #2347	C₂×C₁₃	semidirect
149. #2085	C₂×C₁₃	semidirect
150. #2065	C₂×C₁₃	semidirect
151. #1949	C₂×C₁₃	semidirect
152. #1925	C₂×C₁₃	semidirect
154. #1851	C₂×C₁₃	semidirect
155. #1823	C₂×C₁₃	semidirect
368. C₁₃	#24597	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×#482	2
C₂×C₁₃×#428	2
C₁₃×#2504	2
C₁₃×#2347	2
C₁₃×#2085	2
C₁₃×#2065	2
C₁₃×#1949	2
C₁₃×#1925	2
C₁₃×#1895	2
C₁₃×#1851	2
C₁₃×#1823	2
#24597	13

Subgroups — C13×#24597 #15710936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24597 #15710936