Subgroups — C₁₃×#24773 #15711112

Order 3328.

892 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#471	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3038	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2046	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×#1907	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×#131	C₂²	1	2	yes	—
16	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
17	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#471	—	2	8	no	—
20	C₁₃×#460	—	2	1	no	—
21	C₁₃×#460	—	2	1	no	—
22	C₁₃×#460	—	2	1	no	—
23	C₁₃×#460	—	2	1	no	—
24	C₁₃×#460	—	2	2	no	—
25	C₁₃×#459	—	2	1	no	—
26	C₁₃×#459	—	2	1	no	—
27	C₁₃×#441	—	2	1	no	—
28	C₁₃×#440	—	2	1	no	—
29	C₄×C₁₃×Q₁₆	—	2	1	no	—
30	C₄×C₁₃×SD₁₆	—	2	1	no	—
31	C₂×C₁₃×#108	C₂²	1	2	yes	—
32	C₁₃×#428	C₂²	1	1	yes	characteristic
33	C₁₃×#424	—	2	2	no	—
34	C₁₃×#424	C₂²	1	2	yes	—
35	C₁₃×#423	—	2	1	no	—
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₁₃×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₃×#419	C₂²	1	1	yes	characteristic
41	C₁₃×#418	C₂²	1	2	yes	—
42	C₁₃×#417	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#102	C₂²	1	2	yes	—
44	C₂×C₁₃×#101	C₂²	1	2	yes	—
45	C₂×C₁₃×#100	C₂²	1	2	yes	—
46	C₂×C₁₃×#100	C₂²	1	2	yes	—
47	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
48	C₁₃×#343	C₂²	1	2	yes	—
49	C₁₃×#341	C₂²	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#137	—	2	2	no	—
56	C₁₃×#137	D₄	1	4	yes	complemented
57	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
58	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
59	C₂×C₁₃×Q₁₆	—	2	1	no	—
60	C₂×C₁₃×SD₁₆	—	2	1	no	—
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×SD₁₆	—	2	4	no	—
63	C₂×C₁₃×SD₁₆	—	2	2	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₂×C₁₃×SD₁₆	—	4	2	no	—
66	C₂×C₁₃×D₈	—	2	2	no	—
67	C₁₃×#131	—	2	4	no	—
68	C₁₃×#131	—	4	2	no	—
69	C₂×C₁₃×M₁₆	—	2	2	no	—
70	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	—	2	2	no	—
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₁₃×#127	—	2	1	no	—
77	C₁₃×#127	—	2	1	no	—
78	C₁₃×#127	—	2	1	no	—
79	C₁₃×#127	—	2	1	no	—
80	C₄×Q₈×C₁₃	—	2	1	no	—
81	C₄×Q₈×C₁₃	—	2	1	no	—
82	C₄×Q₈×C₁₃	—	2	1	no	—
83	C₄×Q₈×C₁₃	—	2	1	no	—
84	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×D₄×C₁₃	—	2	1	no	—
87	C₄×D₄×C₁₃	—	2	1	no	—
88	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
89	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
90	C₁₃×#117	—	2	1	no	—
91	C₁₃×#117	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#108	—	2	4	no	—
98	C₁₃×#107	—	2	1	no	—
99	C₁₃×#106	—	2	1	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	1	no	—
103	C₁₃×C₄⋊C₈	—	2	1	no	—
104	C₁₃×C₄⋊C₈	—	2	1	no	—
105	C₁₃×C₄⋊C₈	—	2	1	no	—
106	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
107	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
109	C₁₃×#103	—	2	1	no	—
110	C₁₃×#103	—	2	1	no	—
111	C₁₃×#103	—	2	1	no	—
112	C₁₃×#102	—	2	1	no	—
113	C₁₃×#102	—	2	2	no	—
114	C₁₃×#102	—	2	2	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	2	2	no	—
117	C₁₃×#101	—	2	4	no	—
118	C₁₃×#100	—	2	4	no	—
119	C₁₃×#100	—	4	2	no	—
120	C₁₃×#97	—	2	1	no	—
121	C₄×C₈×C₁₃	—	2	1	no	—
122	#24773	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₂⁴×C₁₃	—	2	2	no	—
124	C₁₃×#41	—	2	1	no	—
125	C₁₃×#41	—	2	1	no	—
126	C₁₃×#41	C₂×D₄	1	2	yes	—
127	C₁₃×#41	#41	1	2	yes	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	1	no	—
130	C₂×Q₈×C₁₃	—	2	1	no	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₁₃	—	2	1	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	—	2	2	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	4	1	no	—
143	C₂×D₄×C₁₃	—	4	1	no	—
144	C₂×D₄×C₁₃	—	4	1	no	—
145	C₂×D₄×C₁₃	—	4	1	no	—
146	C₂×D₄×C₁₃	—	8	2	no	—
147	C₂×D₄×C₁₃	—	8	2	no	—
148	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×Q₁₆	—	2	4	no	—
158	C₁₃×SD₁₆	—	2	4	no	—
159	C₁₃×SD₁₆	—	4	4	no	—
160	C₁₃×SD₁₆	—	4	4	no	—
161	C₁₃×SD₁₆	—	4	4	no	—
162	C₁₃×D₈	—	4	4	no	—
163	C₁₃×M₁₆	—	2	1	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	—	2	1	no	—
168	C₁₃×M₁₆	—	2	2	no	—
169	C₁₃×M₁₆	—	2	1	no	—
170	C₁₃×M₁₆	—	4	4	no	—
171	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	2	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	2	no	—
177	C₂×C₈×C₁₃	—	2	2	no	—
178	C₂×C₈×C₁₃	—	4	4	no	—
179	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	4	1	no	—
186	C₁₃×C₄⋊C₄	—	4	1	no	—
187	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
188	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₁₃×C₂²⋊C₄	—	2	1	no	—
191	C₁₃×C₂²⋊C₄	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	4	1	no	—
196	C₄²×C₁₃	—	4	1	no	—
197	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
201	C₂×#471	C₂×C₁₃	1	2	yes	complemented
202	#3038	C₂×C₁₃	1	1	yes	characteristic
203	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₄×#137	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2906	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#2063	C₂×C₁₃	1	2	yes	complemented
207	#2046	C₂×C₁₃	1	2	yes	complemented
208	#1965	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1907	C₂×C₁₃	1	2	yes	complemented
211	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	4	2	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	2	no	—
216	C₂³×C₁₃	—	8	2	no	—
217	C₂³×C₁₃	—	8	2	no	—
218	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
219	Q₈×C₁₃	—	2	1	no	—
220	Q₈×C₁₃	—	2	2	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	4	1	no	—
223	Q₈×C₁₃	—	4	1	no	—
224	Q₈×C₁₃	#121	1	2	yes	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	2	no	—
227	D₄×C₁₃	—	2	1	no	—
228	D₄×C₁₃	—	4	2	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	4	2	no	—
232	D₄×C₁₃	—	8	2	no	—
233	D₄×C₁₃	—	8	2	no	—
234	D₄×C₁₃	—	8	2	no	—
235	D₄×C₁₃	—	8	2	no	—
236	D₄×C₁₃	#121	1	2	yes	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	8	1	no	—
250	C₂×C₄×C₁₃	—	8	1	no	—
251	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
261	C₈×C₁₃	—	2	2	no	—
262	C₈×C₁₃	—	2	2	no	—
263	C₈×C₁₃	—	2	2	no	—
264	C₈×C₁₃	—	4	2	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	2	no	—
267	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
269	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
270	C₂×#131	C₂²×C₁₃	1	2	yes	—
271	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
272	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	#471	—	2	8	no	—
275	#460	—	2	1	no	—
276	#460	—	2	1	no	—
277	#460	—	2	1	no	—
278	#460	—	2	1	no	—
279	#460	—	2	2	no	—
280	#459	—	2	1	no	—
281	#459	—	2	1	no	—
282	#441	—	2	1	no	—
283	#440	—	2	1	no	—
284	C₄×Q₁₆	—	2	1	no	—
285	C₄×SD₁₆	—	2	1	no	—
286	C₂×#108	C₂²×C₁₃	1	2	yes	—
287	#428	C₂²×C₁₃	1	1	yes	characteristic
288	#424	—	2	2	no	—
289	#424	C₂²×C₁₃	1	2	yes	—
290	#423	—	2	1	no	—
291	#423	C₂²×C₁₃	1	1	yes	characteristic
292	#423	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄⋊C₈	—	2	1	no	—
294	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
295	#419	C₂²×C₁₃	1	1	yes	characteristic
296	#418	C₂²×C₁₃	1	2	yes	—
297	#417	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#102	C₂²×C₁₃	1	2	yes	—
299	C₂×#101	C₂²×C₁₃	1	2	yes	—
300	C₂×#100	C₂²×C₁₃	1	2	yes	—
301	C₂×#100	C₂²×C₁₃	1	2	yes	—
302	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
303	#343	C₂²×C₁₃	1	2	yes	—
304	#341	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	4	1	no	—
309	C₂²×C₁₃	—	4	1	no	—
310	C₂²×C₁₃	—	8	2	no	—
311	C₂²×C₁₃	—	8	2	no	—
312	C₂²×C₁₃	—	8	2	no	—
313	C₂²×C₁₃	—	16	2	no	—
314	C₂²×C₁₃	—	16	2	no	—
315	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
316	C₂²×C₁₃	#547	1	1	yes	characteristic
317	C₂²×C₁₃	#553	1	1	yes	characteristic
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	—	4	1	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	#471	1	2	yes	complemented
327	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
328	C₄×C₁₃	#537	1	1	yes	characteristic
329	C₄×C₁₃	D₄²	1	1	yes	characteristic
330	C₄×C₁₃	#548	1	1	yes	characteristic
331	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
332	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
336	#137	—	2	2	no	—
337	#137	D₄×C₁₃	1	4	yes	complemented
338	AGL(1,ℤ/8)	—	2	4	no	—
339	AGL(1,ℤ/8)	—	2	4	no	—
340	C₂×Q₁₆	—	2	1	no	—
341	C₂×SD₁₆	—	2	1	no	—
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	2	2	no	—
345	C₂×SD₁₆	—	2	2	no	—
346	C₂×SD₁₆	—	4	2	no	—
347	C₂×D₈	—	2	2	no	—
348	#131	—	2	4	no	—
349	#131	—	4	2	no	—
350	C₂×M₁₆	—	2	2	no	—
351	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
352	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
353	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
355	C₂²×C₈	—	2	2	no	—
356	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
357	#127	—	2	1	no	—
358	#127	—	2	1	no	—
359	#127	—	2	1	no	—
360	#127	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
366	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
370	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
371	#117	—	2	1	no	—
372	#117	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	2	1	no	—
377	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	#108	—	2	4	no	—
379	#107	—	2	1	no	—
380	#106	—	2	1	no	—
381	C₄⋊C₈	—	2	2	no	—
382	C₄⋊C₈	—	2	2	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
388	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
389	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
390	#103	—	2	1	no	—
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
393	#102	—	2	1	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	2	no	—
398	#101	—	2	4	no	—
399	#100	—	2	4	no	—
400	#100	—	4	2	no	—
401	#97	—	2	1	no	—
402	C₄×C₈	—	2	1	no	—
403	C₂×C₁₃	—	2	1	no	—
404	C₂×C₁₃	—	2	1	no	—
405	C₂×C₁₃	—	4	2	no	—
406	C₂×C₁₃	—	16	2	no	—
407	C₂×C₁₃	#2416	1	1	yes	characteristic
408	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
409	C₂×C₁₃	#3068	1	1	yes	characteristic
410	C₂⁴	—	2	2	no	—
411	#41	—	2	1	no	—
412	#41	—	2	1	no	—
413	#41	C₂×D₄×C₁₃	1	2	yes	—
414	#41	C₁₃×#41	1	2	yes	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
421	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	—	4	1	no	—
433	C₂×D₄	—	8	2	no	—
434	C₂×D₄	—	8	2	no	—
435	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
442	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	Q₁₆	—	2	4	no	—
445	SD₁₆	—	2	4	no	—
446	SD₁₆	—	4	4	no	—
447	SD₁₆	—	4	4	no	—
448	SD₁₆	—	4	4	no	—
449	D₈	—	4	4	no	—
450	M₁₆	—	2	1	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	1	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	2	1	no	—
457	M₁₆	—	4	4	no	—
458	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	4	4	no	—
466	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
467	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	4	1	no	—
474	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	4	1	no	—
483	C₄²	—	4	1	no	—
484	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₁₃	#24773	1	1	yes	characteristic, direct product factor, Sylow
489	C₂³	—	2	1	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	8	2	no	—
494	C₂³	—	8	2	no	—
495	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
496	Q₈	—	2	1	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	C₁₃×#121	1	2	yes	—
502	D₄	—	2	2	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	8	2	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	D₄	—	8	2	no	—
513	D₄	C₁₃×#121	1	2	yes	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	8	1	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
529	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
530	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
531	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
535	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
536	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	—	2	2	no	—
541	C₈	—	4	2	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	16	2	no	—
553	C₂²	—	16	2	no	—
554	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
555	C₂²	C₁₃×#547	1	1	yes	characteristic
556	C₂²	C₁₃×#553	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	8	1	no	—
565	C₄	C₁₃×#471	1	2	yes	complemented
566	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
567	C₄	C₁₃×#537	1	1	yes	characteristic
568	C₄	D₄²×C₁₃	1	1	yes	characteristic
569	C₄	C₁₃×#548	1	1	yes	characteristic
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	4	2	no	—
573	C₂	—	16	2	no	—
574	C₂	C₁₃×#2416	1	1	yes	characteristic
575	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
576	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
1. C₂×C₁₃×#471	C₂	semidirect
3. C₂×C₁₃×#460	C₂	semidirect
4. C₄×C₁₃×#137	C₂	semidirect
5. C₁₃×#2906	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2046	C₂	semidirect
8. C₁₃×#1965	C₂	semidirect
9. C₁₃×#1950	C₂	semidirect
10. C₁₃×#1907	C₂	semidirect
11. C₁₃×#1801	C₂	semidirect
56. C₁₃×#137	D₄	semidirect
122. #24773	C₁₃	direct (N × H)
201. C₂×#471	C₂×C₁₃	semidirect
203. C₂×#460	C₂×C₁₃	semidirect
204. C₄×#137	C₂×C₁₃	semidirect
205. #2906	C₂×C₁₃	semidirect
206. #2063	C₂×C₁₃	semidirect
207. #2046	C₂×C₁₃	semidirect
208. #1965	C₂×C₁₃	semidirect
209. #1950	C₂×C₁₃	semidirect
210. #1907	C₂×C₁₃	semidirect
211. #1801	C₂×C₁₃	semidirect
326. C₄×C₁₃	#471	semidirect
337. #137	D₄×C₁₃	semidirect
488. C₁₃	#24773	direct (N × H)
565. C₄	C₁₃×#471	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#471	2
C₁₃×#3038	2
C₂×C₁₃×#460	2
C₄×C₁₃×#137	2
C₁₃×#2906	2
C₁₃×#2063	2
C₁₃×#2046	2
C₁₃×#1965	2
C₁₃×#1950	2
C₁₃×#1907	2
C₁₃×#1801	2
#24773	13

Subgroups — C13×#24773 #15711112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24773 #15711112