Subgroups — C₁₃×#32698 #15719037

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2102	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2081	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2069	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2048	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2002	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1932	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1914	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1911	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1903	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1887	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1861	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1841	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1829	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₁₃×#568	C₂²	1	1	yes	characteristic
18	C₁₃×#535	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
20	C₁₃×#518	C₂²	1	1	yes	characteristic
21	C₁₃×#430	C₂²	1	1	yes	characteristic
22	C₁₃×#430	C₂²	1	1	yes	characteristic
23	C₁₃×#430	C₂²	1	1	yes	characteristic
24	C₁₃×#423	C₂²	1	1	yes	characteristic
25	C₁₃×#421	C₂²	1	1	yes	characteristic
26	C₁₃×#421	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
28	C₁₃×#418	C₂²	1	1	yes	characteristic
29	C₁₃×#418	C₂²	1	1	yes	characteristic
30	C₁₃×#418	C₂²	1	1	yes	characteristic
31	C₁₃×#413	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×#344	C₂²	1	1	yes	characteristic
40	C₁₃×#344	C₂²	1	1	yes	characteristic
41	C₁₃×#344	C₂²	1	1	yes	characteristic
42	C₁₃×#344	C₂²	1	1	yes	characteristic
43	C₁₃×#344	C₂²	1	1	yes	characteristic
44	C₁₃×#344	C₂²	1	1	yes	characteristic
45	C₁₃×#339	C₂²	1	1	yes	characteristic
46	C₁₃×#339	C₂²	1	1	yes	characteristic
47	C₁₃×#339	C₂²	1	1	yes	characteristic
48	C₁₃×#338	C₂²	1	1	yes	characteristic
49	C₁₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
50	C₁₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	2	no	—
53	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
56	C₁₃×AGL(1,ℤ/8)	—	4	1	no	—
57	C₂×C₁₃×SD₁₆	—	2	1	no	—
58	C₂×C₁₃×D₈	—	2	1	no	—
59	C₁₃×#131	—	4	1	no	—
60	C₁₃×#131	—	4	1	no	—
61	C₂×C₁₃×M₁₆	—	4	1	no	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
70	C₁₃×#127	—	2	1	no	—
71	C₁₃×#127	—	2	1	no	—
72	C₁₃×#127	—	2	1	no	—
73	C₁₃×#127	—	4	1	no	—
74	C₁₃×#124	—	2	1	no	—
75	C₁₃×#121	—	4	1	no	—
76	C₁₃×#120	—	2	2	no	—
77	C₄×D₄×C₁₃	—	4	1	no	—
78	C₄×D₄×C₁₃	—	4	1	no	—
79	C₁₃×#117	C₂³	1	1	yes	characteristic
80	C₁₃×#117	C₂³	1	1	yes	characteristic
81	C₁₃×#117	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#108	—	4	1	no	—
85	C₁₃×#108	—	4	1	no	—
86	C₁₃×#108	—	4	1	no	—
87	C₁₃×C₄⋊C₈	—	4	1	no	—
88	C₁₃×#104	—	2	1	no	—
89	C₁₃×#104	—	2	1	no	—
90	C₁₃×#104	—	4	1	no	—
91	C₁₃×#104	—	4	1	no	—
92	C₁₃×#102	—	4	1	no	—
93	C₁₃×#102	—	4	1	no	—
94	C₁₃×#102	—	4	1	no	—
95	C₁₃×#101	—	2	1	no	—
96	C₁₃×#100	—	2	1	no	—
97	C₁₃×#100	—	4	1	no	—
98	C₁₃×#100	—	4	1	no	—
99	C₁₃×#100	—	4	1	no	—
100	C₁₃×#100	—	4	1	no	—
101	C₁₃×#100	—	4	1	no	—
102	C₁₃×#100	—	4	1	no	—
103	C₁₃×#97	—	2	1	no	—
104	C₄×C₈×C₁₃	—	2	1	no	—
105	#32698	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂⁴×C₁₃	#41	1	2	yes	—
108	C₁₃×#41	—	2	1	no	—
109	C₁₃×#41	—	2	1	no	—
110	C₁₃×#41	—	2	1	no	—
111	C₁₃×#41	—	2	1	no	—
112	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	1	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	2	1	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	—	4	2	no	—
128	C₂×D₄×C₁₃	—	4	2	no	—
129	C₂×D₄×C₁₃	—	8	4	no	—
130	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₁₃×SD₁₆	—	4	2	no	—
136	C₁₃×D₈	—	4	2	no	—
137	C₁₃×M₁₆	—	2	1	no	—
138	C₁₃×M₁₆	—	2	1	no	—
139	C₁₃×M₁₆	—	2	1	no	—
140	C₁₃×M₁₆	—	2	1	no	—
141	C₁₃×M₁₆	—	2	1	no	—
142	C₁₃×M₁₆	—	2	1	no	—
143	C₁₃×M₁₆	—	2	1	no	—
144	C₁₃×M₁₆	—	2	1	no	—
145	C₁₃×M₁₆	—	2	1	no	—
146	C₁₃×M₁₆	—	2	1	no	—
147	C₁₃×M₁₆	—	2	1	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	—	2	1	no	—
150	C₁₃×M₁₆	—	2	1	no	—
151	C₁₃×M₁₆	—	2	1	no	—
152	C₁₃×M₁₆	—	2	1	no	—
153	C₁₃×M₁₆	—	4	2	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	4	2	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₂²⋊C₄	—	2	1	no	—
167	C₁₃×C₂²⋊C₄	—	2	1	no	—
168	C₁₃×C₂²⋊C₄	—	2	1	no	—
169	C₁₃×C₂²⋊C₄	—	4	2	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	2	1	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₄²×C₁₃	#41	1	1	yes	characteristic
176	C₄²×C₁₃	#41	1	1	yes	characteristic
177	#2102	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2081	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2081	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2069	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#2048	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#2002	C₂×C₁₃	1	1	yes	characteristic
183	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1932	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1914	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#1911	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1903	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1887	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#1861	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1841	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1829	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	4	1	no	—
197	C₂³×C₁₃	—	4	1	no	—
198	C₂³×C₁₃	—	4	1	no	—
199	C₂³×C₁₃	—	8	2	no	—
200	C₂³×C₁₃	—	8	2	no	—
201	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
202	Q₈×C₁₃	—	2	1	no	—
203	Q₈×C₁₃	—	2	1	no	—
204	D₄×C₁₃	—	2	1	no	—
205	D₄×C₁₃	—	2	1	no	—
206	D₄×C₁₃	—	4	1	no	—
207	D₄×C₁₃	—	4	1	no	—
208	D₄×C₁₃	—	4	1	no	—
209	D₄×C₁₃	—	4	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	1	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	1	no	—
216	D₄×C₁₃	—	8	4	no	—
217	D₄×C₁₃	—	8	4	no	—
218	D₄×C₁₃	—	16	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	16	2	no	—
229	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
235	C₈×C₁₃	—	4	1	no	—
236	C₈×C₁₃	—	4	1	no	—
237	C₈×C₁₃	—	4	1	no	—
238	C₈×C₁₃	—	4	1	no	—
239	C₈×C₁₃	—	4	1	no	—
240	C₈×C₁₃	—	4	1	no	—
241	C₈×C₁₃	—	4	1	no	—
242	C₈×C₁₃	—	4	1	no	—
243	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
244	#568	C₂²×C₁₃	1	1	yes	characteristic
245	#535	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
247	#518	C₂²×C₁₃	1	1	yes	characteristic
248	#430	C₂²×C₁₃	1	1	yes	characteristic
249	#430	C₂²×C₁₃	1	1	yes	characteristic
250	#430	C₂²×C₁₃	1	1	yes	characteristic
251	#423	C₂²×C₁₃	1	1	yes	characteristic
252	#421	C₂²×C₁₃	1	1	yes	characteristic
253	#421	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
255	#418	C₂²×C₁₃	1	1	yes	characteristic
256	#418	C₂²×C₁₃	1	1	yes	characteristic
257	#418	C₂²×C₁₃	1	1	yes	characteristic
258	#413	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
265	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
266	#344	C₂²×C₁₃	1	1	yes	characteristic
267	#344	C₂²×C₁₃	1	1	yes	characteristic
268	#344	C₂²×C₁₃	1	1	yes	characteristic
269	#344	C₂²×C₁₃	1	1	yes	characteristic
270	#344	C₂²×C₁₃	1	1	yes	characteristic
271	#344	C₂²×C₁₃	1	1	yes	characteristic
272	#339	C₂²×C₁₃	1	1	yes	characteristic
273	#339	C₂²×C₁₃	1	1	yes	characteristic
274	#339	C₂²×C₁₃	1	1	yes	characteristic
275	#338	C₂²×C₁₃	1	1	yes	characteristic
276	H(3,ℤ/4)	C₂²×C₁₃	1	1	yes	characteristic
277	H(3,ℤ/4)	C₂²×C₁₃	1	1	yes	characteristic
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	—	4	1	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	8	2	no	—
282	C₂²×C₁₃	—	8	2	no	—
283	C₂²×C₁₃	—	8	1	no	—
284	C₂²×C₁₃	—	8	2	no	—
285	C₂²×C₁₃	—	8	2	no	—
286	C₂²×C₁₃	—	8	1	no	—
287	C₂²×C₁₃	—	16	1	no	—
288	C₂²×C₁₃	—	16	1	no	—
289	C₂²×C₁₃	#538	1	1	yes	characteristic
290	C₂²×C₁₃	#551	1	1	yes	characteristic
291	C₂²×C₁₃	#551	1	1	yes	characteristic
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	4	1	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	8	1	no	—
296	C₄×C₁₃	—	8	1	no	—
297	C₄×C₁₃	—	8	1	no	—
298	C₄×C₁₃	#538	1	1	yes	characteristic
299	C₄×C₁₃	#540	1	1	yes	characteristic
300	C₄×C₁₃	#553	1	1	yes	characteristic
301	C₄×C₁₃	#560	1	1	yes	characteristic
302	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
306	AGL(1,ℤ/8)	—	4	1	no	—
307	AGL(1,ℤ/8)	—	4	1	no	—
308	C₂×SD₁₆	—	2	1	no	—
309	C₂×D₈	—	2	1	no	—
310	#131	—	4	1	no	—
311	#131	—	4	1	no	—
312	C₂×M₁₆	—	4	1	no	—
313	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
316	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
319	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
320	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
321	#127	—	2	1	no	—
322	#127	—	2	1	no	—
323	#127	—	2	1	no	—
324	#127	—	4	1	no	—
325	#124	—	2	1	no	—
326	#121	—	4	1	no	—
327	#120	—	2	2	no	—
328	C₄×D₄	—	4	1	no	—
329	C₄×D₄	—	4	1	no	—
330	#117	C₂³×C₁₃	1	1	yes	characteristic
331	#117	C₂³×C₁₃	1	1	yes	characteristic
332	#117	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	#108	—	4	1	no	—
336	#108	—	4	1	no	—
337	#108	—	4	1	no	—
338	C₄⋊C₈	—	4	1	no	—
339	#104	—	2	1	no	—
340	#104	—	2	1	no	—
341	#104	—	4	1	no	—
342	#104	—	4	1	no	—
343	#102	—	4	1	no	—
344	#102	—	4	1	no	—
345	#102	—	4	1	no	—
346	#101	—	2	1	no	—
347	#100	—	2	1	no	—
348	#100	—	4	1	no	—
349	#100	—	4	1	no	—
350	#100	—	4	1	no	—
351	#100	—	4	1	no	—
352	#100	—	4	1	no	—
353	#100	—	4	1	no	—
354	#97	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₂×C₁₃	—	2	1	no	—
357	C₂×C₁₃	—	2	1	no	—
358	C₂×C₁₃	—	2	1	no	—
359	C₂×C₁₃	—	8	1	no	—
360	C₂×C₁₃	—	8	2	no	—
361	C₂×C₁₃	—	16	1	no	—
362	C₂×C₁₃	#2749	1	1	yes	characteristic
363	C₂⁴	—	2	1	no	—
364	C₂⁴	C₁₃×#41	1	2	yes	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	C₂×Q₈	C₁₃×#41	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	8	4	no	—
387	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	SD₁₆	—	4	2	no	—
393	D₈	—	4	2	no	—
394	M₁₆	—	2	1	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	1	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	2	1	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	1	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	4	2	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	4	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	C₁₃×#41	1	1	yes	characteristic
433	C₄²	C₁₃×#41	1	1	yes	characteristic
434	C₁₃	#32698	1	1	yes	characteristic, direct product factor, Sylow
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	4	1	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	8	2	no	—
443	C₂³	—	8	2	no	—
444	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
445	Q₈	—	2	1	no	—
446	Q₈	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	2	1	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	1	no	—
458	D₄	—	4	1	no	—
459	D₄	—	8	4	no	—
460	D₄	—	8	4	no	—
461	D₄	—	16	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	16	2	no	—
472	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
473	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
474	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
478	C₈	—	4	1	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	1	no	—
481	C₈	—	4	1	no	—
482	C₈	—	4	1	no	—
483	C₈	—	4	1	no	—
484	C₈	—	4	1	no	—
485	C₈	—	4	1	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	16	1	no	—
496	C₂²	—	16	1	no	—
497	C₂²	C₁₃×#538	1	1	yes	characteristic
498	C₂²	C₁₃×#551	1	1	yes	characteristic
499	C₂²	C₁₃×#551	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	1	no	—
505	C₄	—	8	1	no	—
506	C₄	C₁₃×#538	1	1	yes	characteristic
507	C₄	C₁₃×#540	1	1	yes	characteristic
508	C₄	C₁₃×#553	1	1	yes	characteristic
509	C₄	C₁₃×#560	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	8	2	no	—
514	C₂	—	8	1	no	—
515	C₂	—	16	1	no	—
516	C₂	C₁₃×#2749	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2749
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2002	C₂
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×#2102	C₂	semidirect
2. C₁₃×#2081	C₂	semidirect
3. C₁₃×#2081	C₂	semidirect
4. C₁₃×#2069	C₂	semidirect
5. C₁₃×#2048	C₂	semidirect
7. C₁₃×#1965	C₂	semidirect
8. C₁₃×#1932	C₂	semidirect
9. C₁₃×#1914	C₂	semidirect
10. C₁₃×#1911	C₂	semidirect
11. C₁₃×#1903	C₂	semidirect
12. C₁₃×#1887	C₂	semidirect
13. C₁₃×#1861	C₂	semidirect
14. C₁₃×#1841	C₂	semidirect
15. C₁₃×#1829	C₂	semidirect
105. #32698	C₁₃	direct (N × H)
177. #2102	C₂×C₁₃	semidirect
178. #2081	C₂×C₁₃	semidirect
179. #2081	C₂×C₁₃	semidirect
180. #2069	C₂×C₁₃	semidirect
181. #2048	C₂×C₁₃	semidirect
183. #1965	C₂×C₁₃	semidirect
184. #1932	C₂×C₁₃	semidirect
185. #1914	C₂×C₁₃	semidirect
186. #1911	C₂×C₁₃	semidirect
187. #1903	C₂×C₁₃	semidirect
188. #1887	C₂×C₁₃	semidirect
189. #1861	C₂×C₁₃	semidirect
190. #1841	C₂×C₁₃	semidirect
191. #1829	C₂×C₁₃	semidirect
434. C₁₃	#32698	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×#2102	2
C₁₃×#2081	2
C₁₃×#2069	2
C₁₃×#2048	2
C₁₃×#2002	2
C₁₃×#1965	2
C₁₃×#1932	2
C₁₃×#1914	2
C₁₃×#1911	2
C₁₃×#1903	2
C₁₃×#1887	2
C₁₃×#1861	2
C₁₃×#1841	2
C₁₃×#1829	2
#32698	13

Subgroups — C13×#32698 #15719037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32698 #15719037