Subgroups — C₁₃×#24986 #15711325

Order 3328.

642 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×#3067	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2080	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2053	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1906	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1827	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1812	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#575	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×#41	C₂²	1	2	yes	—
16	C₁₃×#473	—	2	1	no	—
17	C₁₃×#472	—	2	1	no	—
18	C₁₃×#471	—	2	2	no	—
19	C₁₃×#442	—	2	1	no	—
20	C₁₃×#441	—	2	1	no	—
21	C₁₃×#440	—	2	2	no	—
22	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
23	C₁₃×#427	C₂²	1	1	yes	characteristic
24	C₁₃×#427	C₂²	1	1	yes	characteristic
25	C₁₃×#424	C₂²	1	2	yes	—
26	C₁₃×#421	C₂²	1	2	yes	—
27	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
28	C₁₃×#416	C₂²	1	1	yes	characteristic
29	C₁₃×#416	C₂²	1	2	yes	—
30	C₁₃×#413	C₂²	1	2	yes	—
31	C₁₃×#410	C₂²	1	2	yes	—
32	C₁₃×#410	C₂²	1	2	yes	—
33	C₁₃×#405	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
35	C₁₃×#344	C₂²	1	2	yes	—
36	C₁₃×#341	C₂²	1	1	yes	characteristic
37	C₁₃×#339	C₂²	1	1	yes	characteristic
38	C₁₃×#339	C₂²	1	2	yes	—
39	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	—
40	C₁₃×H(3,ℤ/4)	C₂²	1	2	yes	—
41	C₂×C₁₃×#41	C₂³	1	2	yes	—
42	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
43	C₁₃×#137	—	2	2	no	—
44	C₁₃×#137	—	2	2	no	—
45	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
46	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
47	C₁₃×#135	—	2	1	no	—
48	C₁₃×#135	—	2	1	no	—
49	C₁₃×#135	—	2	1	no	—
50	C₁₃×#135	—	2	1	no	—
51	C₁₃×#135	—	4	2	no	—
52	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
53	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
54	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
55	C₁₃×#131	—	2	1	no	—
56	C₁₃×#131	—	2	1	no	—
57	C₁₃×#131	—	2	1	no	—
58	C₁₃×#131	—	2	1	no	—
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₃	—	2	1	no	—
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#117	C₂³	1	2	yes	—
72	C₁₃×#117	C₂³	1	2	yes	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#108	—	2	1	no	—
76	C₁₃×#108	—	2	1	no	—
77	C₁₃×#107	—	2	1	no	—
78	C₁₃×#107	—	2	1	no	—
79	C₁₃×#106	—	2	1	no	—
80	C₁₃×#106	—	2	1	no	—
81	C₁₃×C₄⋊C₈	—	4	2	no	—
82	C₁₃×#104	—	2	2	no	—
83	C₁₃×#104	—	4	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	2	1	no	—
86	C₁₃×#102	—	2	2	no	—
87	C₁₃×#102	—	2	1	no	—
88	C₁₃×#101	—	2	2	no	—
89	C₁₃×#100	—	2	2	no	—
90	C₁₃×#99	—	4	2	no	—
91	C₁₃×#99	—	4	2	no	—
92	C₁₃×#97	—	2	1	no	—
93	C₁₃×#97	—	2	1	no	—
94	C₁₃×#97	—	2	1	no	—
95	C₄×C₈×C₁₃	—	2	1	no	—
96	#24986	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₁₃×#41	—	2	1	no	—
98	C₁₃×#41	—	2	1	no	—
99	C₁₃×#41	—	2	1	no	—
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	—	2	1	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₁₃×Q₁₆	—	2	1	no	—
117	C₁₃×Q₁₆	—	2	1	no	—
118	C₁₃×Q₁₆	—	4	2	no	—
119	C₁₃×SD₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	2	2	no	—
121	C₁₃×SD₁₆	—	4	2	no	—
122	C₁₃×SD₁₆	—	4	2	no	—
123	C₁₃×D₈	—	2	1	no	—
124	C₁₃×D₈	—	2	1	no	—
125	C₁₃×D₈	—	4	2	no	—
126	C₁₃×M₁₆	—	2	1	no	—
127	C₁₃×M₁₆	—	2	2	no	—
128	C₁₃×M₁₆	—	2	1	no	—
129	C₁₃×M₁₆	—	2	1	no	—
130	C₁₃×M₁₆	—	2	2	no	—
131	C₁₃×M₁₆	—	2	1	no	—
132	C₁₃×M₁₆	—	4	1	no	—
133	C₁₃×M₁₆	—	4	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	4	1	no	—
141	C₂×C₈×C₁₃	—	4	1	no	—
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
145	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
146	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
147	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₂²⋊C₄	—	2	2	no	—
153	C₁₃×C₂²⋊C₄	—	2	1	no	—
154	C₁₃×C₂²⋊C₄	—	2	2	no	—
155	C₁₃×C₂²⋊C₄	—	4	2	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	4	2	no	—
161	C₄²×C₁₃	#41	1	2	yes	—
162	#3067	C₂×C₁₃	1	1	yes	characteristic
163	#2943	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2080	C₂×C₁₃	1	2	yes	complemented
165	#2053	C₂×C₁₃	1	2	yes	complemented
166	#1976	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1946	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1906	C₂×C₁₃	1	2	yes	complemented
169	#1833	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1827	C₂×C₁₃	1	2	yes	complemented
171	#1812	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1765	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	1	no	—
175	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	—	2	1	no	—
178	Q₈×C₁₃	—	2	1	no	—
179	Q₈×C₁₃	—	2	2	no	—
180	D₄×C₁₃	—	2	2	no	—
181	D₄×C₁₃	—	2	1	no	—
182	D₄×C₁₃	—	2	1	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	4	1	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	1	no	—
187	D₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	2	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	8	1	no	—
199	C₂×C₄×C₁₃	—	8	4	no	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	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	H(5,𝔽₂)	1	1	yes	characteristic
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	—	4	1	no	—
208	C₈×C₁₃	—	4	2	no	—
209	C₈×C₁₃	—	4	1	no	—
210	C₈×C₁₃	#123	1	1	yes	characteristic
211	C₈×C₁₃	#123	1	1	yes	characteristic
212	C₈×C₁₃	#123	1	1	yes	characteristic
213	C₈×C₁₃	#123	1	1	yes	characteristic
214	#575	C₂²×C₁₃	1	2	yes	—
215	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
217	C₄×#41	C₂²×C₁₃	1	2	yes	—
218	#473	—	2	1	no	—
219	#472	—	2	1	no	—
220	#471	—	2	2	no	—
221	#442	—	2	1	no	—
222	#441	—	2	1	no	—
223	#440	—	2	2	no	—
224	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
225	#427	C₂²×C₁₃	1	1	yes	characteristic
226	#427	C₂²×C₁₃	1	1	yes	characteristic
227	#424	C₂²×C₁₃	1	2	yes	—
228	#421	C₂²×C₁₃	1	2	yes	—
229	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
230	#416	C₂²×C₁₃	1	1	yes	characteristic
231	#416	C₂²×C₁₃	1	2	yes	—
232	#413	C₂²×C₁₃	1	2	yes	—
233	#410	C₂²×C₁₃	1	2	yes	—
234	#410	C₂²×C₁₃	1	2	yes	—
235	#405	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
237	#344	C₂²×C₁₃	1	2	yes	—
238	#341	C₂²×C₁₃	1	1	yes	characteristic
239	#339	C₂²×C₁₃	1	1	yes	characteristic
240	#339	C₂²×C₁₃	1	2	yes	—
241	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	—
242	H(3,ℤ/4)	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	2	no	—
246	C₂²×C₁₃	—	8	2	no	—
247	C₂²×C₁₃	—	8	1	no	—
248	C₂²×C₁₃	#540	1	1	yes	characteristic
249	C₂²×C₁₃	#546	1	1	yes	characteristic
250	C₂²×C₁₃	#553	1	1	yes	characteristic
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	8	2	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
258	C₄×C₁₃	#529	1	1	yes	characteristic
259	C₄×C₁₃	#546	1	1	yes	characteristic
260	C₄×C₁₃	#555	1	1	yes	characteristic
261	C₂×#41	C₂³×C₁₃	1	2	yes	—
262	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
263	#137	—	2	2	no	—
264	#137	—	2	2	no	—
265	AGL(1,ℤ/8)	—	2	2	no	—
266	AGL(1,ℤ/8)	—	2	2	no	—
267	#135	—	2	1	no	—
268	#135	—	2	1	no	—
269	#135	—	2	1	no	—
270	#135	—	2	1	no	—
271	#135	—	4	2	no	—
272	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
273	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
274	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
275	#131	—	2	1	no	—
276	#131	—	2	1	no	—
277	#131	—	2	1	no	—
278	#131	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
282	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
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	2	yes	—
291	#117	C₂³×C₁₃	1	1	yes	characteristic
292	#117	C₂³×C₁₃	1	2	yes	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
295	#108	—	2	1	no	—
296	#108	—	2	1	no	—
297	#107	—	2	1	no	—
298	#107	—	2	1	no	—
299	#106	—	2	1	no	—
300	#106	—	2	1	no	—
301	C₄⋊C₈	—	4	2	no	—
302	#104	—	2	2	no	—
303	#104	—	4	2	no	—
304	#103	—	2	2	no	—
305	#103	—	2	1	no	—
306	#102	—	2	2	no	—
307	#102	—	2	1	no	—
308	#101	—	2	2	no	—
309	#100	—	2	2	no	—
310	#99	—	4	2	no	—
311	#99	—	4	2	no	—
312	#97	—	2	1	no	—
313	#97	—	2	1	no	—
314	#97	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₂×C₁₃	—	2	1	no	—
317	C₂×C₁₃	—	2	1	no	—
318	C₂×C₁₃	—	2	1	no	—
319	C₂×C₁₃	—	8	2	no	—
320	C₂×C₁₃	—	8	1	no	—
321	C₂×C₁₃	#2420	1	1	yes	characteristic
322	#41	—	2	1	no	—
323	#41	—	2	1	no	—
324	#41	—	2	1	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	1	no	—
330	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
331	C₂×Q₈	C₁₃×#41	1	1	yes	characteristic
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
335	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
341	Q₁₆	—	2	1	no	—
342	Q₁₆	—	2	1	no	—
343	Q₁₆	—	4	2	no	—
344	SD₁₆	—	2	2	no	—
345	SD₁₆	—	2	2	no	—
346	SD₁₆	—	4	2	no	—
347	SD₁₆	—	4	2	no	—
348	D₈	—	2	1	no	—
349	D₈	—	2	1	no	—
350	D₈	—	4	2	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	4	1	no	—
358	M₁₆	—	4	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	4	1	no	—
367	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
370	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
371	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
372	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	2	no	—
386	C₄²	C₁₃×#41	1	2	yes	—
387	C₁₃	#24986	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	—	2	2	no	—
389	C₂³	—	2	1	no	—
390	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	1	no	—
393	Q₈	—	2	1	no	—
394	Q₈	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	1	no	—
397	D₄	—	2	1	no	—
398	D₄	—	2	2	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	8	4	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	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	C₁₃×#123	1	1	yes	characteristic
426	C₈	C₁₃×#123	1	1	yes	characteristic
427	C₈	C₁₃×#123	1	1	yes	characteristic
428	C₈	C₁₃×#123	1	1	yes	characteristic
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	1	no	—
434	C₂²	C₁₃×#540	1	1	yes	characteristic
435	C₂²	C₁₃×#546	1	1	yes	characteristic
436	C₂²	C₁₃×#553	1	1	yes	characteristic
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
444	C₄	C₁₃×#529	1	1	yes	characteristic
445	C₄	C₁₃×#546	1	1	yes	characteristic
446	C₄	C₁₃×#555	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	1	no	—
452	C₂	C₁₃×#2420	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2420
prime radical	C₁₃×#3067	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2943	C₂	semidirect
3. C₁₃×#2080	C₂	semidirect
4. C₁₃×#2053	C₂	semidirect
5. C₁₃×#1976	C₂	semidirect
6. C₁₃×#1946	C₂	semidirect
7. C₁₃×#1906	C₂	semidirect
8. C₁₃×#1833	C₂	semidirect
9. C₁₃×#1827	C₂	semidirect
10. C₁₃×#1812	C₂	semidirect
11. C₁₃×#1765	C₂	semidirect
96. #24986	C₁₃	direct (N × H)
163. #2943	C₂×C₁₃	semidirect
164. #2080	C₂×C₁₃	semidirect
165. #2053	C₂×C₁₃	semidirect
166. #1976	C₂×C₁₃	semidirect
167. #1946	C₂×C₁₃	semidirect
168. #1906	C₂×C₁₃	semidirect
169. #1833	C₂×C₁₃	semidirect
170. #1827	C₂×C₁₃	semidirect
171. #1812	C₂×C₁₃	semidirect
172. #1765	C₂×C₁₃	semidirect
387. C₁₃	#24986	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×#3067	2
C₁₃×#2943	2
C₁₃×#2080	2
C₁₃×#2053	2
C₁₃×#1976	2
C₁₃×#1946	2
C₁₃×#1906	2
C₁₃×#1833	2
C₁₃×#1827	2
C₁₃×#1812	2
C₁₃×#1765	2
#24986	13

Subgroups — C13×#24986 #15711325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24986 #15711325