Subgroups — C₁₃×#25051 #15711390

Order 3328.

736 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3099	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3060	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2079	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2039	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1974	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1859	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₁₃×#537	C₂²	1	2	yes	—
15	C₁₃×#520	C₂²	1	2	yes	—
16	C₁₃×#485	—	2	2	no	—
17	C₁₃×#483	—	2	2	no	—
18	C₁₃×#482	—	2	2	no	—
19	C₁₃×#481	—	2	2	no	—
20	C₁₃×#470	—	2	1	no	—
21	C₁₃×#469	—	2	1	no	—
22	C₁₃×#465	—	2	2	no	—
23	C₁₃×#442	—	2	1	no	—
24	C₁₃×#441	—	2	1	no	—
25	C₄×C₁₃×SD₁₆	—	2	2	no	—
26	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
27	C₁₃×#428	C₂²	1	2	yes	—
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	2	yes	—
31	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#417	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₁₃×#417	C₂²	1	2	yes	—
36	C₁₃×#416	C₂²	1	1	yes	characteristic
37	C₁₃×#408	C₂²	1	2	yes	—
38	C₁₃×#405	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#384	C₂²	1	2	yes	—
41	C₁₃×#343	C₂²	1	2	yes	—
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#341	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
51	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
52	C₁₃×#131	—	2	2	no	—
53	C₁₃×#131	—	2	2	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	—	2	1	no	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	—	2	2	no	—
63	C₁₃×#121	—	2	2	no	—
64	C₁₃×#121	—	2	2	no	—
65	C₁₃×#121	—	4	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×D₄×C₁₃	—	2	2	no	—
68	C₄×D₄×C₁₃	—	4	2	no	—
69	C₁₃×#117	—	2	2	no	—
70	C₁₃×#117	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#108	—	2	2	no	—
77	C₁₃×#107	—	2	2	no	—
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#106	—	2	1	no	—
80	C₁₃×#106	—	2	1	no	—
81	C₁₃×#106	—	2	1	no	—
82	C₁₃×#106	—	2	2	no	—
83	C₁₃×#106	—	2	2	no	—
84	C₁₃×#106	—	2	2	no	—
85	C₁₃×#104	—	2	2	no	—
86	C₁₃×#104	—	2	4	no	—
87	C₁₃×#103	—	2	2	no	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#103	D₄	1	2	yes	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	D₄	1	2	yes	—
95	C₁₃×C₂²⋊C₈	—	2	2	no	—
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×#97	—	2	1	no	—
98	C₄×C₈×C₁₃	—	2	1	no	—
99	C₄×C₈×C₁₃	—	2	2	no	—
100	#25051	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	1	no	—
103	C₁₃×#41	—	2	1	no	—
104	C₁₃×#41	—	2	1	no	—
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	1	no	—
109	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	1	no	—
113	C₂×D₄×C₁₃	—	4	2	no	—
114	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
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	2	no	—
121	C₂²×C₄×C₁₃	—	4	2	no	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₁₃×Q₁₆	—	2	2	no	—
124	C₁₃×SD₁₆	—	2	4	no	—
125	C₁₃×D₈	—	2	2	no	—
126	C₁₃×M₁₆	—	2	2	no	—
127	C₁₃×M₁₆	—	2	1	no	—
128	C₁₃×M₁₆	—	2	2	no	—
129	C₁₃×M₁₆	—	2	1	no	—
130	C₁₃×M₁₆	—	2	1	no	—
131	C₁₃×M₁₆	—	2	1	no	—
132	C₁₃×M₁₆	—	4	2	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	4	2	no	—
139	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	#41	1	2	yes	—
143	C₂×C₈×C₁₃	#41	1	2	yes	—
144	C₁₃×C₄⋊C₄	—	2	2	no	—
145	C₁₃×C₄⋊C₄	—	2	2	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	4	2	no	—
149	C₁₃×C₄⋊C₄	—	4	2	no	—
150	C₁₃×C₄⋊C₄	—	8	4	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	4	2	no	—
159	C₄²×C₁₃	#41	1	2	yes	—
160	#3099	C₂×C₁₃	1	2	yes	complemented
161	#3060	C₂×C₁₃	1	1	yes	characteristic
162	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#2079	C₂×C₁₃	1	2	yes	complemented
164	#2039	C₂×C₁₃	1	2	yes	complemented
165	#1974	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1859	C₂×C₁₃	1	2	yes	complemented
168	#1844	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1764	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	2	1	no	—
176	Q₈×C₁₃	—	2	1	no	—
177	Q₈×C₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	2	no	—
179	D₄×C₁₃	—	2	1	no	—
180	D₄×C₁₃	—	2	1	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	1	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	1	no	—
186	D₄×C₁₃	—	16	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	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	8	2	no	—
200	C₂×C₄×C₁₃	—	16	2	no	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	—	4	1	no	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₈×C₁₃	#123	1	2	yes	—
212	C₈×C₁₃	#123	1	2	yes	—
213	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
215	#537	C₂²×C₁₃	1	2	yes	—
216	#520	C₂²×C₁₃	1	2	yes	—
217	#485	—	2	2	no	—
218	#483	—	2	2	no	—
219	#482	—	2	2	no	—
220	#481	—	2	2	no	—
221	#470	—	2	1	no	—
222	#469	—	2	1	no	—
223	#465	—	2	2	no	—
224	#442	—	2	1	no	—
225	#441	—	2	1	no	—
226	C₄×SD₁₆	—	2	2	no	—
227	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
228	#428	C₂²×C₁₃	1	2	yes	—
229	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#106	C₂²×C₁₃	1	2	yes	—
231	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#104	C₂²×C₁₃	1	2	yes	—
233	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
234	#417	C₂²×C₁₃	1	2	yes	—
235	#417	C₂²×C₁₃	1	2	yes	—
236	#417	C₂²×C₁₃	1	2	yes	—
237	#416	C₂²×C₁₃	1	1	yes	characteristic
238	#408	C₂²×C₁₃	1	2	yes	—
239	#405	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
241	#384	C₂²×C₁₃	1	2	yes	—
242	#343	C₂²×C₁₃	1	2	yes	—
243	#343	C₂²×C₁₃	1	2	yes	—
244	#341	C₂²×C₁₃	1	1	yes	characteristic
245	#339	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₁₃	—	2	2	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	—	4	2	no	—
249	C₂²×C₁₃	—	4	2	no	—
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	#542	1	1	yes	characteristic
253	C₂²×C₁₃	D₄²	1	1	yes	characteristic
254	C₂²×C₁₃	#553	1	1	yes	characteristic
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	4	2	no	—
257	C₄×C₁₃	—	4	1	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
262	C₄×C₁₃	#532	1	1	yes	characteristic
263	C₄×C₁₃	#547	1	1	yes	characteristic
264	C₄×C₁₃	#547	1	1	yes	characteristic
265	C₂×#41	C₂³×C₁₃	1	2	yes	—
266	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
267	#135	—	2	2	no	—
268	#135	—	2	2	no	—
269	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
270	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
271	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
272	#131	—	2	2	no	—
273	#131	—	2	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
277	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²⋊Q₈	—	2	2	no	—
282	C₂²⋊Q₈	—	2	2	no	—
283	#121	—	2	2	no	—
284	#121	—	2	2	no	—
285	#121	—	4	2	no	—
286	C₄×Q₈	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	4	2	no	—
289	#117	—	2	2	no	—
290	#117	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	4	2	no	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	#108	—	2	2	no	—
297	#107	—	2	2	no	—
298	#106	—	2	1	no	—
299	#106	—	2	1	no	—
300	#106	—	2	1	no	—
301	#106	—	2	1	no	—
302	#106	—	2	2	no	—
303	#106	—	2	2	no	—
304	#106	—	2	2	no	—
305	#104	—	2	4	no	—
306	#104	—	2	2	no	—
307	#103	—	2	2	no	—
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	D₄×C₁₃	1	2	yes	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	D₄×C₁₃	1	2	yes	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₂×C₁₃	—	2	1	no	—
321	C₂×C₁₃	—	2	1	no	—
322	C₂×C₁₃	—	8	2	no	—
323	C₂×C₁₃	—	8	1	no	—
324	C₂×C₁₃	#2422	1	1	yes	characteristic
325	C₂×C₁₃	#3291	1	2	yes	—
326	#41	—	2	2	no	—
327	#41	—	2	1	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	1	no	—
334	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
348	Q₁₆	—	2	2	no	—
349	SD₁₆	—	2	4	no	—
350	D₈	—	2	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	4	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₈	C₁₃×#41	1	2	yes	—
368	C₂×C₈	C₁₃×#41	1	2	yes	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	8	4	no	—
376	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	4	2	no	—
384	C₄²	C₁₃×#41	1	2	yes	—
385	C₁₃	#25051	1	1	yes	characteristic, direct product factor, Sylow
386	C₂³	—	2	2	no	—
387	C₂³	—	2	1	no	—
388	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	2	1	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	1	no	—
401	D₄	—	16	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	8	2	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	16	2	no	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₈	C₁₃×#123	1	2	yes	—
427	C₈	C₁₃×#123	1	2	yes	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₁₃×#542	1	1	yes	characteristic
435	C₂²	D₄²×C₁₃	1	1	yes	characteristic
436	C₂²	C₁₃×#553	1	1	yes	characteristic
437	C₄	—	2	4	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	2	no	—
443	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
444	C₄	C₁₃×#532	1	1	yes	characteristic
445	C₄	C₁₃×#547	1	1	yes	characteristic
446	C₄	C₁₃×#547	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	2	no	—
450	C₂	—	8	1	no	—
451	C₂	C₁₃×#2422	1	1	yes	characteristic
452	C₂	C₁₃×#3291	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3060	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3099	C₂	semidirect
3. C₁₃×#2952	C₂	semidirect
4. C₁₃×#2079	C₂	semidirect
5. C₁₃×#2039	C₂	semidirect
6. C₁₃×#1974	C₂	semidirect
7. C₁₃×#1951	C₂	semidirect
8. C₁₃×#1859	C₂	semidirect
9. C₁₃×#1844	C₂	semidirect
10. C₁₃×#1815	C₂	semidirect
11. C₁₃×#1764	C₂	semidirect
100. #25051	C₁₃	direct (N × H)
160. #3099	C₂×C₁₃	semidirect
162. #2952	C₂×C₁₃	semidirect
163. #2079	C₂×C₁₃	semidirect
164. #2039	C₂×C₁₃	semidirect
165. #1974	C₂×C₁₃	semidirect
166. #1951	C₂×C₁₃	semidirect
167. #1859	C₂×C₁₃	semidirect
168. #1844	C₂×C₁₃	semidirect
169. #1815	C₂×C₁₃	semidirect
170. #1764	C₂×C₁₃	semidirect
385. C₁₃	#25051	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×#3099	2
C₁₃×#3060	2
C₁₃×#2952	2
C₁₃×#2079	2
C₁₃×#2039	2
C₁₃×#1974	2
C₁₃×#1951	2
C₁₃×#1859	2
C₁₃×#1844	2
C₁₃×#1815	2
C₁₃×#1764	2
#25051	13

Subgroups — C13×#25051 #15711390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25051 #15711390