Subgroups — C₁₃×#24806 #15711145

Order 3328.

896 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3055	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1900	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₁₃×#525	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	2	yes	—
19	C₁₃×#472	—	2	4	no	—
20	C₁₃×#469	—	2	2	no	—
21	C₁₃×#469	—	2	2	no	—
22	C₁₃×#469	—	2	2	no	—
23	C₁₃×#468	—	2	2	no	—
24	C₁₃×#466	—	2	2	no	—
25	C₁₃×#465	—	2	2	no	—
26	C₁₃×#436	—	2	2	no	—
27	C₁₃×#435	—	2	2	no	—
28	C₁₃×#430	—	2	4	no	—
29	C₂×C₁₃×#108	C₂²	1	2	yes	—
30	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
32	C₁₃×#428	C₂²	1	2	yes	—
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₁₃×#424	C₂²	1	1	yes	characteristic
35	C₁₃×#418	C₂²	1	2	yes	—
36	C₁₃×#417	C₂²	1	2	yes	—
37	C₂×C₁₃×#102	C₂²	1	2	yes	—
38	C₂×C₁₃×#100	C₂²	1	2	yes	—
39	C₂×C₁₃×#100	C₂²	1	2	yes	—
40	C₁₃×#408	C₂²	1	1	yes	characteristic
41	C₁₃×#407	C₂²	1	1	yes	characteristic
42	C₁₃×#405	C₂²	1	1	yes	characteristic
43	C₁₃×#343	C₂²	1	2	yes	—
44	C₁₃×#343	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
50	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₁₃×#131	—	2	2	no	—
58	C₁₃×#131	—	2	2	no	—
59	C₂×C₁₃×M₁₆	—	2	2	no	—
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	—	2	4	no	—
64	C₂×C₁₃×M₁₆	—	4	2	no	—
65	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
66	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	2	no	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#123	—	2	1	no	—
76	C₁₃×C₂²⋊Q₈	D₄	1	2	yes	—
77	C₁₃×#121	—	2	2	no	—
78	C₁₃×#121	—	2	2	no	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	—	2	2	no	—
81	C₁₃×#121	D₄	1	2	yes	—
82	C₁₃×#120	—	2	1	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₁₃×#117	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₁₃×#108	—	2	4	no	—
88	C₁₃×#108	—	2	2	no	—
89	C₁₃×#108	D₄	1	4	yes	complemented
90	C₁₃×#107	—	2	2	no	—
91	C₁₃×#106	—	2	1	no	—
92	C₁₃×#106	—	2	1	no	—
93	C₁₃×#106	—	2	2	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	4	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	2	2	no	—
100	C₁₃×#100	—	2	4	no	—
101	C₁₃×#100	—	4	2	no	—
102	C₁₃×C₂²⋊C₈	—	2	2	no	—
103	C₁₃×C₂²⋊C₈	—	2	2	no	—
104	C₁₃×#97	—	2	1	no	—
105	C₄×C₈×C₁₃	—	2	1	no	—
106	#24806	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	#41	1	1	yes	characteristic
109	C₁₃×#41	—	2	1	no	—
110	C₁₃×#41	—	2	1	no	—
111	C₁₃×#41	—	2	1	no	—
112	C₁₃×#41	—	2	1	no	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	4	2	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	8	4	no	—
125	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
136	C₁₃×SD₁₆	—	4	4	no	—
137	C₁₃×D₈	—	4	4	no	—
138	C₁₃×D₈	—	4	2	no	—
139	C₁₃×D₈	—	4	2	no	—
140	C₁₃×M₁₆	—	2	2	no	—
141	C₁₃×M₁₆	—	2	4	no	—
142	C₁₃×M₁₆	—	2	4	no	—
143	C₁₃×M₁₆	—	2	1	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	1	no	—
146	C₁₃×M₁₆	—	2	1	no	—
147	C₁₃×M₁₆	—	2	2	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	—	4	4	no	—
150	C₁₃×M₁₆	—	4	2	no	—
151	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	1	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	2	no	—
158	C₂×C₈×C₁₃	—	4	4	no	—
159	C₂×C₈×C₁₃	—	4	2	no	—
160	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₃	#41	1	2	yes	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	2	no	—
167	C₁₃×C₄⋊C₄	—	2	2	no	—
168	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₁₃×C₂²⋊C₄	—	2	2	no	—
170	C₁₃×C₂²⋊C₄	—	2	1	no	—
171	C₁₃×C₂²⋊C₄	—	2	2	no	—
172	C₁₃×C₂²⋊C₄	—	4	2	no	—
173	C₁₃×C₂²⋊C₄	—	4	2	no	—
174	C₄²×C₁₃	—	2	1	no	—
175	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3055	C₂×C₁₃	1	2	yes	complemented
177	C₂×#469	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2930	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2063	C₂×C₁₃	1	2	yes	complemented
181	#2051	C₂×C₁₃	1	2	yes	complemented
182	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1900	C₂×C₁₃	1	2	yes	complemented
185	#1815	C₂×C₁₃	1	1	yes	characteristic, complemented
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	4	2	no	—
190	C₂³×C₁₃	—	4	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	8	2	no	—
194	C₂³×C₁₃	—	8	2	no	—
195	C₂³×C₁₃	#121	1	2	yes	—
196	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	1	no	—
198	Q₈×C₁₃	—	2	1	no	—
199	D₄×C₁₃	—	2	1	no	—
200	D₄×C₁₃	—	2	1	no	—
201	D₄×C₁₃	—	4	1	no	—
202	D₄×C₁₃	—	4	1	no	—
203	D₄×C₁₃	—	4	2	no	—
204	D₄×C₁₃	—	4	2	no	—
205	D₄×C₁₃	—	4	2	no	—
206	D₄×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	8	2	no	—
208	D₄×C₁₃	—	8	4	no	—
209	D₄×C₁₃	—	8	4	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	1	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	8	2	no	—
222	C₂×C₄×C₁₃	#121	1	2	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
228	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
229	C₈×C₁₃	—	2	2	no	—
230	C₈×C₁₃	—	2	4	no	—
231	C₈×C₁₃	—	4	1	no	—
232	C₈×C₁₃	—	4	1	no	—
233	C₈×C₁₃	—	4	2	no	—
234	C₈×C₁₃	#121	1	2	yes	—
235	C₈×C₁₃	#121	1	2	yes	—
236	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
237	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
240	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
241	#525	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#121	C₂²×C₁₃	1	2	yes	—
243	#472	—	2	4	no	—
244	#469	—	2	2	no	—
245	#469	—	2	2	no	—
246	#469	—	2	2	no	—
247	#468	—	2	2	no	—
248	#466	—	2	2	no	—
249	#465	—	2	2	no	—
250	#436	—	2	2	no	—
251	#435	—	2	2	no	—
252	#430	—	2	4	no	—
253	C₂×#108	C₂²×C₁₃	1	2	yes	—
254	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
256	#428	C₂²×C₁₃	1	2	yes	—
257	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
258	#424	C₂²×C₁₃	1	1	yes	characteristic
259	#418	C₂²×C₁₃	1	2	yes	—
260	#417	C₂²×C₁₃	1	2	yes	—
261	C₂×#102	C₂²×C₁₃	1	2	yes	—
262	C₂×#100	C₂²×C₁₃	1	2	yes	—
263	C₂×#100	C₂²×C₁₃	1	2	yes	—
264	#408	C₂²×C₁₃	1	1	yes	characteristic
265	#407	C₂²×C₁₃	1	1	yes	characteristic
266	#405	C₂²×C₁₃	1	1	yes	characteristic
267	#343	C₂²×C₁₃	1	2	yes	—
268	#343	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	4	1	no	—
274	C₂²×C₁₃	—	4	2	no	—
275	C₂²×C₁₃	—	8	1	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	—	8	2	no	—
278	C₂²×C₁₃	—	8	2	no	—
279	C₂²×C₁₃	—	8	2	no	—
280	C₂²×C₁₃	—	16	2	no	—
281	C₂²×C₁₃	—	16	2	no	—
282	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
283	C₂²×C₁₃	#548	1	1	yes	characteristic
284	C₂²×C₁₃	#553	1	1	yes	characteristic
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	4	2	no	—
288	C₄×C₁₃	—	8	2	no	—
289	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
290	C₄×C₁₃	#537	1	1	yes	characteristic
291	C₄×C₁₃	D₄²	1	1	yes	characteristic
292	C₄×C₁₃	#547	1	1	yes	characteristic
293	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
296	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
297	AGL(1,ℤ/8)	—	2	4	no	—
298	AGL(1,ℤ/8)	—	4	2	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×D₈	—	2	2	no	—
301	C₂×D₈	—	2	1	no	—
302	C₂×D₈	—	2	1	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂×D₈	—	2	2	no	—
305	#131	—	2	2	no	—
306	#131	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	4	no	—
312	C₂×M₁₆	—	4	2	no	—
313	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
314	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
315	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
316	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
317	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
318	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
319	C₂²×C₈	—	2	2	no	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
323	#123	—	2	1	no	—
324	C₂²⋊Q₈	D₄×C₁₃	1	2	yes	—
325	#121	—	2	2	no	—
326	#121	—	2	2	no	—
327	#121	—	2	2	no	—
328	#121	—	2	2	no	—
329	#121	D₄×C₁₃	1	2	yes	—
330	#120	—	2	1	no	—
331	C₄×D₄	—	2	2	no	—
332	#117	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	#108	—	2	4	no	—
336	#108	—	2	2	no	—
337	#108	D₄×C₁₃	1	4	yes	complemented
338	#107	—	2	2	no	—
339	#106	—	2	1	no	—
340	#106	—	2	1	no	—
341	#106	—	2	2	no	—
342	C₄⋊C₈	—	2	2	no	—
343	#103	—	2	2	no	—
344	#102	—	2	2	no	—
345	#102	—	2	4	no	—
346	#102	—	2	2	no	—
347	#102	—	2	2	no	—
348	#100	—	2	4	no	—
349	#100	—	4	2	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	#97	—	2	1	no	—
353	C₄×C₈	—	2	1	no	—
354	C₂×C₁₃	—	2	1	no	—
355	C₂×C₁₃	—	2	1	no	—
356	C₂×C₁₃	—	4	2	no	—
357	C₂×C₁₃	—	8	1	no	—
358	C₂×C₁₃	—	16	2	no	—
359	C₂×C₁₃	#2416	1	1	yes	characteristic
360	C₂×C₁₃	#3068	1	2	yes	—
361	C₂⁴	—	2	2	no	—
362	C₂⁴	C₁₃×#41	1	1	yes	characteristic
363	#41	—	2	1	no	—
364	#41	—	2	1	no	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	8	4	no	—
379	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
388	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
390	SD₁₆	—	4	4	no	—
391	D₈	—	4	4	no	—
392	D₈	—	4	2	no	—
393	D₈	—	4	2	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	4	no	—
396	M₁₆	—	2	4	no	—
397	M₁₆	—	2	1	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	1	no	—
403	M₁₆	—	4	4	no	—
404	M₁₆	—	4	2	no	—
405	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	2	1	no	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	4	4	no	—
413	C₂×C₈	—	4	2	no	—
414	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
415	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
418	C₂×C₈	C₁₃×#41	1	2	yes	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	1	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₄²	—	2	1	no	—
429	C₁₃	#24806	1	1	yes	characteristic, direct product factor, Sylow
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	8	2	no	—
438	C₂³	—	8	2	no	—
439	C₂³	C₁₃×#121	1	2	yes	—
440	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
441	Q₈	—	2	1	no	—
442	Q₈	—	2	1	no	—
443	D₄	—	2	1	no	—
444	D₄	—	2	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	1	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	8	2	no	—
452	D₄	—	8	4	no	—
453	D₄	—	8	4	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	C₁₃×#121	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
471	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
472	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	4	no	—
475	C₈	—	4	1	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	2	no	—
478	C₈	C₁₃×#121	1	2	yes	—
479	C₈	C₁₃×#121	1	2	yes	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	16	2	no	—
492	C₂²	—	16	2	no	—
493	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
494	C₂²	C₁₃×#548	1	1	yes	characteristic
495	C₂²	C₁₃×#553	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	8	2	no	—
500	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
501	C₄	C₁₃×#537	1	1	yes	characteristic
502	C₄	D₄²×C₁₃	1	1	yes	characteristic
503	C₄	C₁₃×#547	1	1	yes	characteristic
504	C₂	—	2	1	no	—
505	C₂	—	2	1	no	—
506	C₂	—	4	2	no	—
507	C₂	—	8	1	no	—
508	C₂	—	16	2	no	—
509	C₂	C₁₃×#2416	1	1	yes	characteristic
510	C₂	C₁₃×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#472	C₂	semidirect
2. C₁₃×#3055	C₂	semidirect
3. C₂×C₁₃×#469	C₂	semidirect
4. C₁₃×#2930	C₂	semidirect
5. C₂×C₁₃×#430	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2051	C₂	semidirect
8. C₁₃×#1978	C₂	semidirect
9. C₁₃×#1951	C₂	semidirect
10. C₁₃×#1900	C₂	semidirect
11. C₁₃×#1815	C₂	semidirect
89. C₁₃×#108	D₄	semidirect
106. #24806	C₁₃	direct (N × H)
175. C₂×#472	C₂×C₁₃	semidirect
176. #3055	C₂×C₁₃	semidirect
177. C₂×#469	C₂×C₁₃	semidirect
178. #2930	C₂×C₁₃	semidirect
179. C₂×#430	C₂×C₁₃	semidirect
180. #2063	C₂×C₁₃	semidirect
181. #2051	C₂×C₁₃	semidirect
182. #1978	C₂×C₁₃	semidirect
183. #1951	C₂×C₁₃	semidirect
184. #1900	C₂×C₁₃	semidirect
185. #1815	C₂×C₁₃	semidirect
337. #108	D₄×C₁₃	semidirect
429. C₁₃	#24806	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×#472	2
C₁₃×#3055	2
C₂×C₁₃×#469	2
C₁₃×#2930	2
C₂×C₁₃×#430	2
C₁₃×#2063	2
C₁₃×#2051	2
C₁₃×#1978	2
C₁₃×#1951	2
C₁₃×#1900	2
C₁₃×#1815	2
#24806	13

Subgroups — C13×#24806 #15711145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24806 #15711145