Subgroups — C₁₃×#32951 #15719290

Order 3328.

1298 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3573	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#472	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3021	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1914	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1903	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1814	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1813	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#585	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
12	C₁₃×#568	—	2	4	no	—
13	C₁₃×#568	—	2	2	no	—
14	C₁₃×#568	C₂²	1	2	yes	—
15	C₁₃×#568	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#131	—	2	4	no	—
17	C₂×C₁₃×#131	—	2	2	no	—
18	C₂×C₁₃×#131	C₂²	1	2	yes	—
19	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
20	C₁₃×#535	C₂²	1	2	yes	—
21	C₁₃×#472	—	2	4	no	—
22	C₁₃×#472	—	2	4	no	—
23	C₁₃×#469	—	2	2	no	—
24	C₁₃×#466	—	2	2	no	—
25	C₁₃×#454	—	2	4	no	—
26	C₁₃×#453	—	2	4	no	—
27	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
28	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#421	C₂²	1	4	yes	—
30	C₁₃×#418	C₂²	1	2	yes	complemented
31	C₁₃×#413	C₂²	1	2	yes	—
32	C₂×C₁₃×#100	C₂²	1	4	yes	complemented
33	C₁₃×#344	C₂²	1	4	yes	complemented
34	C₁₃×#338	C₂²	1	2	yes	complemented
35	C₁₃×2₋¹⁺⁴	—	2	2	no	—
36	C₁₃×2₋¹⁺⁴	D₄	1	2	yes	—
37	C₁₃×H(5,𝔽₂)	—	2	2	no	—
38	C₁₃×H(5,𝔽₂)	—	2	2	no	—
39	C₁₃×H(5,𝔽₂)	D₄	1	2	yes	—
40	C₂×C₁₃×#41	—	2	4	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
45	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
46	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
47	C₂×C₁₃×SD₁₆	—	2	4	no	—
48	C₂×C₁₃×D₈	—	2	4	no	—
49	C₂×C₁₃×D₈	—	2	1	no	—
50	C₂×C₁₃×D₈	—	2	1	no	—
51	C₂×C₁₃×D₈	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₁₃×#131	—	2	4	no	—
54	C₁₃×#131	—	2	8	no	—
55	C₁₃×#131	—	2	4	no	—
56	C₁₃×#131	—	2	4	no	—
57	C₁₃×#131	—	2	4	no	—
58	C₁₃×#131	—	2	2	no	—
59	C₁₃×#131	—	2	2	no	—
60	C₁₃×#131	—	2	4	no	—
61	C₁₃×#131	—	2	2	no	—
62	C₁₃×#131	—	2	2	no	—
63	C₁₃×#131	D₄	1	4	yes	complemented
64	C₁₃×#131	D₄	1	4	yes	complemented
65	C₂×C₁₃×M₁₆	—	2	8	no	—
66	C₂×C₁₃×M₁₆	—	2	4	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	—	2	4	no	—
69	C₂×C₁₃×M₁₆	—	2	2	no	—
70	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
71	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	—	2	4	no	—
75	C₂²×C₈×C₁₃	—	2	2	no	—
76	C₂²×C₈×C₁₃	D₄	1	2	yes	—
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#127	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₁₃×#121	—	2	4	no	—
81	C₁₃×#120	—	2	4	no	—
82	C₁₃×#117	C₂³	1	2	yes	—
83	C₁₃×#108	—	2	2	no	—
84	C₁₃×#108	—	2	2	no	—
85	C₁₃×#107	—	2	1	no	—
86	C₁₃×#106	—	2	1	no	—
87	C₁₃×#104	—	2	8	no	—
88	C₁₃×#102	—	2	4	no	—
89	C₁₃×#101	—	2	2	no	—
90	C₁₃×#100	—	2	2	no	—
91	C₁₃×#100	—	2	8	no	—
92	#32951	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	2	no	—
94	C₁₃×#41	—	2	4	no	—
95	C₁₃×#41	—	2	8	no	—
96	C₁₃×#41	—	2	4	no	—
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	2	4	no	—
99	C₁₃×#41	—	2	4	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	C₂×D₄	1	4	yes	—
105	C₁₃×#41	C₂×D₄	1	4	yes	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₁₃	#41	1	2	yes	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	4	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	4	4	no	—
120	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₁₃	#41	1	2	yes	—
122	C₂×D₄×C₁₃	#41	1	2	yes	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×SD₁₆	—	4	8	no	—
128	C₁₃×D₈	—	4	8	no	—
129	C₁₃×D₈	—	4	1	no	—
130	C₁₃×D₈	—	4	1	no	—
131	C₁₃×D₈	—	4	2	no	—
132	C₁₃×M₁₆	—	2	4	no	—
133	C₁₃×M₁₆	—	2	8	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	—	2	2	no	—
136	C₁₃×M₁₆	—	2	4	no	—
137	C₁₃×M₁₆	—	2	4	no	—
138	C₁₃×M₁₆	—	2	4	no	—
139	C₁₃×M₁₆	—	2	4	no	—
140	C₁₃×M₁₆	—	2	4	no	—
141	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₁₃	—	2	4	no	—
143	C₂×C₈×C₁₃	—	2	8	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	4	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	4	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	4	no	—
150	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
155	C₁₃×C₄⋊C₄	—	2	2	no	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	4	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	#3573	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×#472	C₂×C₁₃	1	2	yes	complemented
161	#3058	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#3021	C₂×C₁₃	1	2	yes	complemented
163	#1914	C₂×C₁₃	1	2	yes	complemented
164	#1903	C₂×C₁₃	1	4	yes	complemented
165	#1814	C₂×C₁₃	1	2	yes	complemented
166	#1813	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	4	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	4	2	no	—
170	C₂³×C₁₃	—	4	4	no	—
171	C₂³×C₁₃	—	16	2	no	—
172	C₂³×C₁₃	#121	1	2	yes	—
173	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
174	Q₈×C₁₃	—	2	4	no	—
175	Q₈×C₁₃	—	2	2	no	—
176	Q₈×C₁₃	—	2	2	no	—
177	Q₈×C₁₃	#121	1	4	yes	—
178	D₄×C₁₃	—	2	8	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	4	no	—
183	D₄×C₁₃	—	2	2	no	—
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	16	4	no	—
189	D₄×C₁₃	#121	1	4	yes	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	#121	1	2	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
203	C₈×C₁₃	—	2	4	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	4	4	no	—
206	C₈×C₁₃	#120	1	1	yes	characteristic
207	C₈×C₁₃	#120	1	2	yes	—
208	C₈×C₁₃	#120	1	1	yes	characteristic
209	#585	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
211	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
212	#568	—	2	4	no	—
213	#568	—	2	2	no	—
214	#568	C₂²×C₁₃	1	2	yes	—
215	#568	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×#131	—	2	4	no	—
217	C₂×#131	—	2	2	no	—
218	C₂×#131	C₂²×C₁₃	1	2	yes	—
219	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
220	#535	C₂²×C₁₃	1	2	yes	—
221	#472	—	2	4	no	—
222	#472	—	2	4	no	—
223	#469	—	2	2	no	—
224	#466	—	2	2	no	—
225	#454	—	2	4	no	—
226	#453	—	2	4	no	—
227	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
228	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
229	#421	C₂²×C₁₃	1	4	yes	—
230	#418	C₂²×C₁₃	1	2	yes	complemented
231	#413	C₂²×C₁₃	1	2	yes	—
232	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
233	#344	C₂²×C₁₃	1	4	yes	complemented
234	#338	C₂²×C₁₃	1	2	yes	complemented
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	4	1	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	8	2	no	—
240	C₂²×C₁₃	—	8	4	no	—
241	C₂²×C₁₃	—	8	4	no	—
242	C₂²×C₁₃	—	8	2	no	—
243	C₂²×C₁₃	—	16	4	no	—
244	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₁₃	#525	1	2	yes	—
246	C₄×C₁₃	—	2	4	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	8	2	no	—
249	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
250	C₄×C₁₃	C₂×#121	1	2	yes	—
251	C₄×C₁₃	#525	1	1	yes	characteristic
252	2₋¹⁺⁴	—	2	2	no	—
253	2₋¹⁺⁴	D₄×C₁₃	1	2	yes	—
254	H(5,𝔽₂)	—	2	2	no	—
255	H(5,𝔽₂)	—	2	2	no	—
256	H(5,𝔽₂)	D₄×C₁₃	1	2	yes	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	C₂³×C₁₃	1	2	yes	—
260	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
261	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
262	AGL(1,ℤ/8)	—	2	8	no	—
263	AGL(1,ℤ/8)	—	2	8	no	—
264	C₂×SD₁₆	—	2	4	no	—
265	C₂×D₈	—	2	4	no	—
266	C₂×D₈	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	—	2	2	no	—
270	#131	—	2	4	no	—
271	#131	—	2	8	no	—
272	#131	—	2	4	no	—
273	#131	—	2	4	no	—
274	#131	—	2	4	no	—
275	#131	—	2	2	no	—
276	#131	—	2	2	no	—
277	#131	—	2	4	no	—
278	#131	—	2	2	no	—
279	#131	—	2	2	no	—
280	#131	D₄×C₁₃	1	4	yes	complemented
281	#131	D₄×C₁₃	1	4	yes	complemented
282	C₂×M₁₆	—	2	8	no	—
283	C₂×M₁₆	—	2	4	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	4	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
288	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
289	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
290	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	D₄×C₁₃	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
295	#127	—	2	2	no	—
296	#124	—	2	2	no	—
297	#121	—	2	4	no	—
298	#120	—	2	4	no	—
299	#117	C₂³×C₁₃	1	2	yes	—
300	#108	—	2	2	no	—
301	#108	—	2	2	no	—
302	#107	—	2	1	no	—
303	#106	—	2	1	no	—
304	#104	—	2	8	no	—
305	#102	—	2	4	no	—
306	#101	—	2	2	no	—
307	#100	—	2	2	no	—
308	#100	—	2	8	no	—
309	C₂×C₁₃	—	2	1	no	—
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	—	4	2	no	—
312	C₂×C₁₃	—	4	4	no	—
313	C₂×C₁₃	—	16	2	no	—
314	C₂×C₁₃	#2847	1	1	yes	characteristic
315	C₂⁴	—	2	2	no	—
316	#41	—	2	4	no	—
317	#41	—	2	8	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	C₂×D₄×C₁₃	1	4	yes	—
327	#41	C₂×D₄×C₁₃	1	4	yes	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂×Q₈	C₁₃×#41	1	2	yes	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂×D₄	C₁₃×#41	1	2	yes	—
344	C₂×D₄	C₁₃×#41	1	2	yes	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
348	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
349	SD₁₆	—	4	8	no	—
350	D₈	—	4	8	no	—
351	D₈	—	4	1	no	—
352	D₈	—	4	1	no	—
353	D₈	—	4	2	no	—
354	M₁₆	—	2	4	no	—
355	M₁₆	—	2	8	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	2	4	no	—
361	M₁₆	—	2	4	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
373	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
376	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
377	C₄⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₄²	—	2	2	no	—
381	C₁₃	#32951	1	1	yes	characteristic, direct product factor, Sylow
382	C₂³	—	2	4	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	16	2	no	—
387	C₂³	C₁₃×#121	1	2	yes	—
388	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	C₁₃×#121	1	4	yes	—
393	D₄	—	2	8	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	4	no	—
402	D₄	—	4	2	no	—
403	D₄	—	16	4	no	—
404	D₄	C₁₃×#121	1	4	yes	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	C₁₃×#121	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
418	C₈	—	2	4	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	4	no	—
421	C₈	C₁₃×#120	1	1	yes	characteristic
422	C₈	C₁₃×#120	1	2	yes	—
423	C₈	C₁₃×#120	1	1	yes	characteristic
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	16	4	no	—
433	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
434	C₂²	C₁₃×#525	1	2	yes	—
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	8	2	no	—
438	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
439	C₄	C₂×C₁₃×#121	1	2	yes	—
440	C₄	C₁₃×#525	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	2	no	—
443	C₂	—	4	2	no	—
444	C₂	—	4	4	no	—
445	C₂	—	16	2	no	—
446	C₂	C₁₃×#2847	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2847
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3573	C₂	semidirect
2. C₂×C₁₃×#472	C₂	semidirect
3. C₁₃×#3058	C₂	semidirect
4. C₁₃×#3021	C₂	semidirect
5. C₁₃×#1914	C₂	semidirect
6. C₁₃×#1903	C₂	semidirect
7. C₁₃×#1814	C₂	semidirect
8. C₁₃×#1813	C₂	semidirect
11. C₂²×C₁₃×D₈	C₂²	semidirect
27. C₂×C₁₃×#108	C₂²	semidirect
28. C₁₃×#427	C₂²	semidirect
30. C₁₃×#418	C₂²	semidirect
32. C₂×C₁₃×#100	C₂²	semidirect
33. C₁₃×#344	C₂²	semidirect
34. C₁₃×#338	C₂²	semidirect
63. C₁₃×#131	D₄	semidirect
64. C₁₃×#131	D₄	semidirect
92. #32951	C₁₃	direct (N × H)
159. #3573	C₂×C₁₃	semidirect
160. C₂×#472	C₂×C₁₃	semidirect
161. #3058	C₂×C₁₃	semidirect
162. #3021	C₂×C₁₃	semidirect
163. #1914	C₂×C₁₃	semidirect
164. #1903	C₂×C₁₃	semidirect
165. #1814	C₂×C₁₃	semidirect
166. #1813	C₂×C₁₃	semidirect
211. C₂²×D₈	C₂²×C₁₃	semidirect
227. C₂×#108	C₂²×C₁₃	semidirect
228. #427	C₂²×C₁₃	semidirect
230. #418	C₂²×C₁₃	semidirect
232. C₂×#100	C₂²×C₁₃	semidirect
233. #344	C₂²×C₁₃	semidirect
234. #338	C₂²×C₁₃	semidirect
280. #131	D₄×C₁₃	semidirect
281. #131	D₄×C₁₃	semidirect
381. C₁₃	#32951	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×#3573	2
C₂×C₁₃×#472	2
C₁₃×#3058	2
C₁₃×#3021	2
C₁₃×#1914	2
C₁₃×#1903	2
C₁₃×#1814	2
C₁₃×#1813	2
#32951	13

Subgroups — C13×#32951 #15719290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32951 #15719290