Subgroups — C₁₃×#24673 #15711012

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2019	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1977	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1931	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#460	—	2	1	no	—
19	C₁₃×#460	—	2	1	no	—
20	C₁₃×#460	—	2	1	no	—
21	C₁₃×#460	—	2	1	no	—
22	C₁₃×#460	—	2	2	no	—
23	C₁₃×#459	—	2	1	no	—
24	C₁₃×#459	—	2	1	no	—
25	C₁₃×#441	—	2	1	no	—
26	C₁₃×#440	—	2	1	no	—
27	C₄×C₁₃×Q₁₆	—	2	1	no	—
28	C₄×C₁₃×SD₁₆	—	2	1	no	—
29	C₁₃×#433	—	2	2	no	—
30	C₁₃×#432	—	2	1	no	—
31	C₁₃×#431	—	2	1	no	—
32	C₂×C₁₃×#108	C₂²	1	2	yes	—
33	C₁₃×#428	C₂²	1	1	yes	characteristic
34	C₁₃×#423	C₂²	1	1	yes	characteristic
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#419	C₂²	1	1	yes	characteristic
38	C₁₃×#418	C₂²	1	2	yes	—
39	C₁₃×#417	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	2	yes	—
41	C₂×C₁₃×#101	C₂²	1	2	yes	—
42	C₂×C₁₃×#100	C₂²	1	2	yes	—
43	C₂×C₁₃×#100	C₂²	1	2	yes	—
44	C₁₃×#408	C₂²	1	2	yes	—
45	C₁₃×#405	C₂²	1	2	yes	—
46	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
47	C₁₃×#343	C₂²	1	2	yes	—
48	C₁₃×#341	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₁₃×#137	—	2	2	no	—
55	C₁₃×#137	—	2	2	no	—
56	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
57	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
58	C₂×C₁₃×Q₁₆	—	2	1	no	—
59	C₂×C₁₃×SD₁₆	—	2	1	no	—
60	C₂×C₁₃×SD₁₆	—	2	2	no	—
61	C₂×C₁₃×SD₁₆	—	2	4	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	4	2	no	—
65	C₂×C₁₃×D₈	—	2	2	no	—
66	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
71	C₁₃×#127	—	2	1	no	—
72	C₁₃×#127	—	2	1	no	—
73	C₁₃×#127	—	2	1	no	—
74	C₁₃×#127	—	2	1	no	—
75	C₄×Q₈×C₁₃	—	2	1	no	—
76	C₄×Q₈×C₁₃	—	2	1	no	—
77	C₄×Q₈×C₁₃	—	2	1	no	—
78	C₄×Q₈×C₁₃	—	2	1	no	—
79	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
81	C₄×D₄×C₁₃	—	2	1	no	—
82	C₄×D₄×C₁₃	—	2	1	no	—
83	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
84	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
85	C₁₃×#117	—	2	1	no	—
86	C₁₃×#117	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#108	—	4	2	no	—
93	C₁₃×#107	—	2	1	no	—
94	C₁₃×#106	—	2	1	no	—
95	C₁₃×C₄⋊C₈	—	2	1	no	—
96	C₁₃×C₄⋊C₈	—	2	1	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
100	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
101	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
102	C₁₃×#103	—	2	1	no	—
103	C₁₃×#103	—	2	1	no	—
104	C₁₃×#103	—	2	1	no	—
105	C₁₃×#102	—	2	1	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	2	2	no	—
109	C₁₃×#102	—	2	2	no	—
110	C₁₃×#101	—	4	2	no	—
111	C₁₃×#100	—	2	4	no	—
112	C₁₃×#100	—	4	2	no	—
113	C₁₃×C₂²⋊C₈	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₁₃×#97	—	2	2	no	—
116	C₁₃×#97	—	2	1	no	—
117	C₄×C₈×C₁₃	—	2	2	no	—
118	C₄×C₈×C₁₃	—	2	1	no	—
119	#24673	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₁₃×#41	—	2	1	no	—
122	C₁₃×#41	—	2	1	no	—
123	C₁₃×#41	—	2	1	no	—
124	C₁₃×#41	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₃	#41	1	2	yes	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	2	no	—
139	C₂×D₄×C₁₃	—	4	1	no	—
140	C₂×D₄×C₁₃	—	4	1	no	—
141	C₂×D₄×C₁₃	—	4	1	no	—
142	C₂×D₄×C₁₃	—	4	1	no	—
143	C₂×D₄×C₁₃	—	8	2	no	—
144	C₂×D₄×C₁₃	—	8	2	no	—
145	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₁₃×Q₁₆	—	2	4	no	—
155	C₁₃×SD₁₆	—	2	4	no	—
156	C₁₃×SD₁₆	—	4	4	no	—
157	C₁₃×SD₁₆	—	4	4	no	—
158	C₁₃×SD₁₆	—	4	4	no	—
159	C₁₃×D₈	—	4	4	no	—
160	C₁₃×M₁₆	—	2	1	no	—
161	C₁₃×M₁₆	—	2	2	no	—
162	C₁₃×M₁₆	—	2	1	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	1	no	—
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	#41	1	2	yes	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	4	1	no	—
181	C₁₃×C₄⋊C₄	—	4	1	no	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₁₃×C₂²⋊C₄	—	2	1	no	—
185	C₁₃×C₂²⋊C₄	—	2	1	no	—
186	C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₄²×C₁₃	—	2	1	no	—
188	C₄²×C₁₃	—	2	1	no	—
189	C₄²×C₁₃	—	2	1	no	—
190	C₄²×C₁₃	—	4	1	no	—
191	C₄²×C₁₃	—	4	1	no	—
192	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	#3038	C₂×C₁₃	1	1	yes	characteristic
197	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#2925	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2051	C₂×C₁₃	1	2	yes	complemented
201	#2019	C₂×C₁₃	1	2	yes	complemented
202	#1977	C₂×C₁₃	1	2	yes	complemented
203	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1931	C₂×C₁₃	1	2	yes	complemented
206	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂³×C₁₃	—	2	1	no	—
208	C₂³×C₁₃	—	4	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	2	no	—
211	C₂³×C₁₃	—	8	2	no	—
212	C₂³×C₁₃	—	8	2	no	—
213	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	2	1	no	—
216	Q₈×C₁₃	—	2	1	no	—
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	4	1	no	—
219	Q₈×C₁₃	—	4	1	no	—
220	D₄×C₁₃	—	2	1	no	—
221	D₄×C₁₃	—	2	1	no	—
222	D₄×C₁₃	—	4	1	no	—
223	D₄×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	4	2	no	—
225	D₄×C₁₃	—	4	2	no	—
226	D₄×C₁₃	—	4	2	no	—
227	D₄×C₁₃	—	4	2	no	—
228	D₄×C₁₃	—	8	2	no	—
229	D₄×C₁₃	—	8	2	no	—
230	D₄×C₁₃	—	8	2	no	—
231	D₄×C₁₃	—	8	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	8	1	no	—
245	C₂×C₄×C₁₃	—	8	1	no	—
246	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₁₃	—	2	2	no	—
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	—	2	2	no	—
259	C₈×C₁₃	—	4	1	no	—
260	C₈×C₁₃	—	4	2	no	—
261	C₈×C₁₃	—	4	2	no	—
262	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
264	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
265	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
266	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	#460	—	2	1	no	—
269	#460	—	2	1	no	—
270	#460	—	2	1	no	—
271	#460	—	2	1	no	—
272	#460	—	2	2	no	—
273	#459	—	2	1	no	—
274	#459	—	2	1	no	—
275	#441	—	2	1	no	—
276	#440	—	2	1	no	—
277	C₄×Q₁₆	—	2	1	no	—
278	C₄×SD₁₆	—	2	1	no	—
279	#433	—	2	2	no	—
280	#432	—	2	1	no	—
281	#431	—	2	1	no	—
282	C₂×#108	C₂²×C₁₃	1	2	yes	—
283	#428	C₂²×C₁₃	1	1	yes	characteristic
284	#423	C₂²×C₁₃	1	1	yes	characteristic
285	#423	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	#419	C₂²×C₁₃	1	1	yes	characteristic
288	#418	C₂²×C₁₃	1	2	yes	—
289	#417	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#102	C₂²×C₁₃	1	2	yes	—
291	C₂×#101	C₂²×C₁₃	1	2	yes	—
292	C₂×#100	C₂²×C₁₃	1	2	yes	—
293	C₂×#100	C₂²×C₁₃	1	2	yes	—
294	#408	C₂²×C₁₃	1	2	yes	—
295	#405	C₂²×C₁₃	1	2	yes	—
296	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	#343	C₂²×C₁₃	1	2	yes	—
298	#341	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	1	no	—
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	—	8	2	no	—
305	C₂²×C₁₃	—	8	2	no	—
306	C₂²×C₁₃	—	8	2	no	—
307	C₂²×C₁₃	—	16	2	no	—
308	C₂²×C₁₃	—	16	2	no	—
309	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
310	C₂²×C₁₃	#553	1	1	yes	characteristic
311	C₂²×C₁₃	#555	1	1	yes	characteristic
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	2	1	no	—
314	C₄×C₁₃	—	2	1	no	—
315	C₄×C₁₃	—	4	1	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	4	1	no	—
319	C₄×C₁₃	—	8	1	no	—
320	C₄×C₁₃	#471	1	2	yes	—
321	C₄×C₁₃	#525	1	1	yes	characteristic
322	C₄×C₁₃	#535	1	1	yes	characteristic
323	C₄×C₁₃	#546	1	1	yes	characteristic
324	C₄×C₁₃	#550	1	1	yes	characteristic
325	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
326	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
330	#137	—	2	2	no	—
331	#137	—	2	2	no	—
332	AGL(1,ℤ/8)	—	4	2	no	—
333	AGL(1,ℤ/8)	—	4	2	no	—
334	C₂×Q₁₆	—	2	1	no	—
335	C₂×SD₁₆	—	2	1	no	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	4	2	no	—
341	C₂×D₈	—	2	2	no	—
342	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
343	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
344	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
347	#127	—	2	1	no	—
348	#127	—	2	1	no	—
349	#127	—	2	1	no	—
350	#127	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
356	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
360	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
361	#117	—	2	1	no	—
362	#117	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
368	#108	—	4	2	no	—
369	#107	—	2	1	no	—
370	#106	—	2	1	no	—
371	C₄⋊C₈	—	2	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	1	no	—
375	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
376	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
377	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
378	#103	—	2	1	no	—
379	#103	—	2	1	no	—
380	#103	—	2	1	no	—
381	#102	—	2	1	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#101	—	4	2	no	—
387	#100	—	2	4	no	—
388	#100	—	4	2	no	—
389	C₂²⋊C₈	—	2	2	no	—
390	C₂²⋊C₈	—	2	2	no	—
391	#97	—	2	2	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	—	2	2	no	—
394	C₄×C₈	—	2	1	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	8	1	no	—
398	C₂×C₁₃	—	16	2	no	—
399	C₂×C₁₃	#2414	1	1	yes	characteristic
400	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
401	C₂×C₁₃	#3068	1	1	yes	characteristic
402	C₂⁴	—	2	2	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	2	1	no	—
406	#41	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
413	C₂×Q₈	C₁₃×#41	1	2	yes	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	—	4	1	no	—
423	C₂×D₄	—	4	1	no	—
424	C₂×D₄	—	4	1	no	—
425	C₂×D₄	—	8	2	no	—
426	C₂×D₄	—	8	2	no	—
427	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
434	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
436	Q₁₆	—	2	4	no	—
437	SD₁₆	—	2	4	no	—
438	SD₁₆	—	4	4	no	—
439	SD₁₆	—	4	4	no	—
440	SD₁₆	—	4	4	no	—
441	D₈	—	4	4	no	—
442	M₁₆	—	2	1	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	2	1	no	—
445	M₁₆	—	2	2	no	—
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	1	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	C₁₃×#41	1	2	yes	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
457	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	1	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	4	1	no	—
473	C₄²	—	4	1	no	—
474	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₁₃	#24673	1	1	yes	characteristic, direct product factor, Sylow
479	C₂³	—	2	1	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	2	no	—
484	C₂³	—	8	2	no	—
485	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
486	Q₈	—	2	2	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	2	2	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	D₄	—	2	1	no	—
493	D₄	—	2	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	8	2	no	—
501	D₄	—	8	2	no	—
502	D₄	—	8	2	no	—
503	D₄	—	8	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	8	1	no	—
517	C₂×C₄	—	8	1	no	—
518	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
519	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
520	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
521	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
524	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
525	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
526	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
527	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	2	no	—
530	C₈	—	2	2	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	2	no	—
533	C₈	—	4	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	1	no	—
539	C₂²	—	8	2	no	—
540	C₂²	—	8	2	no	—
541	C₂²	—	8	2	no	—
542	C₂²	—	16	2	no	—
543	C₂²	—	16	2	no	—
544	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
545	C₂²	C₁₃×#553	1	1	yes	characteristic
546	C₂²	C₁₃×#555	1	1	yes	characteristic
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	4	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	C₁₃×#471	1	2	yes	—
556	C₄	C₁₃×#525	1	1	yes	characteristic
557	C₄	C₁₃×#535	1	1	yes	characteristic
558	C₄	C₁₃×#546	1	1	yes	characteristic
559	C₄	C₁₃×#550	1	1	yes	characteristic
560	C₂	—	2	1	no	—
561	C₂	—	2	1	no	—
562	C₂	—	8	1	no	—
563	C₂	—	16	2	no	—
564	C₂	C₁₃×#2414	1	1	yes	characteristic
565	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
566	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3038	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#460	C₂	semidirect
3. C₄×C₁₃×#137	C₂	semidirect
4. C₁₃×#2925	C₂	semidirect
5. C₁₃×#2051	C₂	semidirect
6. C₁₃×#2019	C₂	semidirect
7. C₁₃×#1977	C₂	semidirect
8. C₁₃×#1965	C₂	semidirect
9. C₁₃×#1950	C₂	semidirect
10. C₁₃×#1931	C₂	semidirect
11. C₁₃×#1801	C₂	semidirect
119. #24673	C₁₃	direct (N × H)
197. C₂×#460	C₂×C₁₃	semidirect
198. C₄×#137	C₂×C₁₃	semidirect
199. #2925	C₂×C₁₃	semidirect
200. #2051	C₂×C₁₃	semidirect
201. #2019	C₂×C₁₃	semidirect
202. #1977	C₂×C₁₃	semidirect
203. #1965	C₂×C₁₃	semidirect
204. #1950	C₂×C₁₃	semidirect
205. #1931	C₂×C₁₃	semidirect
206. #1801	C₂×C₁₃	semidirect
478. C₁₃	#24673	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×#3038	2
C₂×C₁₃×#460	2
C₄×C₁₃×#137	2
C₁₃×#2925	2
C₁₃×#2051	2
C₁₃×#2019	2
C₁₃×#1977	2
C₁₃×#1965	2
C₁₃×#1950	2
C₁₃×#1931	2
C₁₃×#1801	2
#24673	13

Subgroups — C13×#24673 #15711012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24673 #15711012