Subgroups — C₁₃×#25048 #15711387

Order 3328.

888 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2420	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2073	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1862	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#121	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
16	C₁₃×#469	—	2	4	no	—
17	C₁₃×#442	—	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	1	yes	characteristic
22	C₂×C₁₃×#102	C₂²	1	2	yes	—
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#397	—	2	2	no	—
29	C₁₃×#394	—	2	2	no	—
30	C₁₃×#390	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#386	—	2	2	no	—
33	C₁₃×#382	C₂²	1	2	yes	—
34	C₁₃×#381	—	2	2	no	—
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	—	2	2	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×D₈	—	2	2	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	D₄	1	4	yes	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	2	no	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×#121	—	2	4	no	—
56	C₁₃×#121	—	4	2	no	—
57	C₄×D₄×C₁₃	—	2	4	no	—
58	C₄×D₄×C₁₃	—	4	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#107	—	4	2	no	—
73	C₁₃×#106	—	2	2	no	—
74	C₁₃×#106	—	2	2	no	—
75	C₁₃×#102	—	2	4	no	—
76	C₁₃×#102	—	2	4	no	—
77	C₁₃×#102	—	2	4	no	—
78	C₁₃×C₂²⋊C₈	—	2	2	no	—
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	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	2	yes	—
86	#25048	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	2	2	no	—
88	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₁₃	—	2	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	—	4	4	no	—
95	C₂×D₄×C₁₃	—	4	4	no	—
96	C₂×D₄×C₁₃	—	8	2	no	—
97	C₂×D₄×C₁₃	C₂×D₄	1	4	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	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	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	4	4	no	—
108	C₂²×C₄×C₁₃	—	4	4	no	—
109	C₂²×C₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
114	C₁₃×D₈	—	2	8	no	—
115	C₁₃×M₁₆	—	4	4	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₁₃	#41	1	2	yes	—
126	C₂×C₈×C₁₃	#41	1	2	yes	—
127	C₂×C₈×C₁₃	#41	1	2	yes	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	8	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	—	8	2	no	—
139	C₁₃×C₂²⋊C₄	—	8	2	no	—
140	C₁₃×C₂²⋊C₄	—	8	2	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₄²×C₁₃	—	2	1	no	—
145	C₂×#469	C₂×C₁₃	1	1	yes	characteristic
146	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#2420	C₂×C₁₃	1	2	yes	complemented
148	#2073	C₂×C₁₃	1	2	yes	complemented
149	#2033	C₂×C₁₃	1	2	yes	complemented
150	#1970	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1862	C₂×C₁₃	1	2	yes	complemented
153	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1809	C₂×C₁₃	1	1	yes	characteristic, complemented
155	#1753	C₂×C₁₃	1	1	yes	characteristic, complemented
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	—	2	1	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	—	4	2	no	—
164	C₂³×C₁₃	—	4	2	no	—
165	C₂³×C₁₃	—	4	2	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	—	4	2	no	—
168	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₁₃	—	2	4	no	—
170	D₄×C₁₃	—	2	4	no	—
171	D₄×C₁₃	—	4	2	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	8	8	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	1	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	1	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	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	8	8	no	—
197	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	4	1	no	—
205	C₈×C₁₃	—	4	1	no	—
206	C₈×C₁₃	#123	1	4	yes	—
207	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×#121	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
211	#469	—	2	4	no	—
212	#442	—	2	4	no	—
213	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#107	C₂²×C₁₃	1	2	yes	—
215	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#102	C₂²×C₁₃	1	2	yes	—
218	C₂×#102	C₂²×C₁₃	1	2	yes	—
219	C₂×#102	C₂²×C₁₃	1	2	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
223	#397	—	2	2	no	—
224	#394	—	2	2	no	—
225	#390	C₂²×C₁₃	1	2	yes	—
226	#389	C₂²×C₁₃	1	2	yes	—
227	#386	—	2	2	no	—
228	#382	C₂²×C₁₃	1	2	yes	—
229	#381	—	2	2	no	—
230	#380	C₂²×C₁₃	1	2	yes	—
231	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
232	#340	C₂²×C₁₃	1	2	yes	—
233	#340	C₂²×C₁₃	1	2	yes	—
234	#336	C₂²×C₁₃	1	1	yes	characteristic
235	#336	C₂²×C₁₃	1	1	yes	characteristic
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	1	no	—
238	C₂²×C₁₃	—	4	1	no	—
239	C₂²×C₁₃	—	4	1	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	8	2	no	—
245	C₂²×C₁₃	—	8	2	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	2	no	—
248	C₂²×C₁₃	#532	1	1	yes	characteristic
249	C₂²×C₁₃	D₄²	1	1	yes	characteristic
250	C₂²×C₁₃	#547	1	1	yes	characteristic
251	C₂²×C₁₃	#575	1	2	yes	—
252	C₂²×C₁₃	#576	1	2	yes	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
260	C₄×C₁₃	#542	1	1	yes	characteristic
261	C₄×C₁₃	#547	1	1	yes	characteristic
262	C₄×C₁₃	#553	1	1	yes	characteristic
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
265	C₂³×C₄	—	2	2	no	—
266	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×D₈	—	2	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	D₄×C₁₃	1	4	yes	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	#121	—	2	4	no	—
278	#121	—	4	2	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	4	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
293	#107	—	2	2	no	—
294	#107	—	4	2	no	—
295	#106	—	2	2	no	—
296	#106	—	2	2	no	—
297	#102	—	2	4	no	—
298	#102	—	2	4	no	—
299	#102	—	2	4	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	#97	—	2	2	no	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	D₄×C₁₃	1	2	yes	—
308	C₂×C₁₃	—	8	1	no	—
309	C₂×C₁₃	—	8	4	no	—
310	C₂×C₁₃	#2422	1	1	yes	characteristic
311	C₂×C₁₃	#3176	1	1	yes	characteristic
312	C₂×C₁₃	#3183	1	1	yes	characteristic
313	C₂×C₁₃	#3273	1	2	yes	—
314	C₂×C₁₃	#3347	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	8	2	no	—
325	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	D₈	—	2	8	no	—
343	M₁₆	—	4	4	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
353	C₂×C₈	C₁₃×#41	1	2	yes	—
354	C₂×C₈	C₁₃×#41	1	2	yes	—
355	C₂×C₈	C₁₃×#41	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	8	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	8	2	no	—
367	C₂²⋊C₄	—	8	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	1	no	—
373	C₁₃	#25048	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	1	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	8	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	8	8	no	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
417	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
420	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	C₁₃×#123	1	4	yes	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	C₁₃×#532	1	1	yes	characteristic
438	C₂²	D₄²×C₁₃	1	1	yes	characteristic
439	C₂²	C₁₃×#547	1	1	yes	characteristic
440	C₂²	C₁₃×#575	1	2	yes	—
441	C₂²	C₁₃×#576	1	2	yes	—
442	C₄	—	4	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
449	C₄	C₁₃×#542	1	1	yes	characteristic
450	C₄	C₁₃×#547	1	1	yes	characteristic
451	C₄	C₁₃×#553	1	1	yes	characteristic
452	C₂	—	8	1	no	—
453	C₂	—	8	4	no	—
454	C₂	C₁₃×#2422	1	1	yes	characteristic
455	C₂	C₁₃×#3176	1	1	yes	characteristic
456	C₂	C₁₃×#3183	1	1	yes	characteristic
457	C₂	C₁₃×#3273	1	2	yes	—
458	C₂	C₁₃×#3347	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#469	C₂
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×#442	C₂	semidirect
3. C₁₃×#2420	C₂	semidirect
4. C₁₃×#2073	C₂	semidirect
5. C₁₃×#2033	C₂	semidirect
6. C₁₃×#1970	C₂	semidirect
7. C₁₃×#1943	C₂	semidirect
8. C₁₃×#1862	C₂	semidirect
9. C₁₃×#1846	C₂	semidirect
10. C₁₃×#1809	C₂	semidirect
11. C₁₃×#1753	C₂	semidirect
86. #25048	C₁₃	direct (N × H)
146. C₂×#442	C₂×C₁₃	semidirect
147. #2420	C₂×C₁₃	semidirect
148. #2073	C₂×C₁₃	semidirect
149. #2033	C₂×C₁₃	semidirect
150. #1970	C₂×C₁₃	semidirect
151. #1943	C₂×C₁₃	semidirect
152. #1862	C₂×C₁₃	semidirect
153. #1846	C₂×C₁₃	semidirect
154. #1809	C₂×C₁₃	semidirect
155. #1753	C₂×C₁₃	semidirect
373. C₁₃	#25048	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×#469	2
C₂×C₁₃×#442	2
C₁₃×#2420	2
C₁₃×#2073	2
C₁₃×#2033	2
C₁₃×#1970	2
C₁₃×#1943	2
C₁₃×#1862	2
C₁₃×#1846	2
C₁₃×#1809	2
C₁₃×#1753	2
#25048	13

Subgroups — C13×#25048 #15711387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25048 #15711387