Subgroups — C₁₃×#24772 #15711111

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#473	C₂	1	2	yes	maximal
2	C₁₃×#3039	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2047	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1908	C₂	1	2	yes	maximal
11	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	2	yes	—
13	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊Q₈	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×#473	—	2	8	no	—
20	C₁₃×#462	—	2	1	no	—
21	C₁₃×#462	—	2	1	no	—
22	C₁₃×#462	—	2	1	no	—
23	C₁₃×#462	—	2	1	no	—
24	C₁₃×#462	—	2	2	no	—
25	C₁₃×#461	—	2	1	no	—
26	C₁₃×#461	—	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	2	yes	—
41	C₁₃×#419	C₂²	1	1	yes	characteristic
42	C₁₃×#417	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#103	C₂²	1	2	yes	—
44	C₂×C₁₃×#101	C₂²	1	2	yes	—
45	C₂×C₁₃×#101	C₂²	1	2	yes	—
46	C₂×C₁₃×#101	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	2	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×#137	—	2	2	no	—
54	C₁₃×#137	—	2	4	no	—
55	C₁₃×#137	—	2	4	no	—
56	C₁₃×#137	D₄	1	4	yes	—
57	C₂×C₁₃×Q₁₆	—	2	1	no	—
58	C₂×C₁₃×Q₁₆	—	2	2	no	—
59	C₂×C₁₃×Q₁₆	—	2	4	no	—
60	C₂×C₁₃×Q₁₆	—	2	2	no	—
61	C₂×C₁₃×Q₁₆	—	2	2	no	—
62	C₂×C₁₃×Q₁₆	—	4	2	no	—
63	C₂×C₁₃×SD₁₆	—	2	1	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₁₃×#131	—	2	4	no	—
66	C₁₃×#131	—	4	2	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
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	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	—	2	2	no	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	—	2	1	no	—
75	C₁₃×C₄⋊Q₈	—	2	1	no	—
76	C₁₃×C₄⋊Q₈	—	2	1	no	—
77	C₁₃×C₄⋊Q₈	—	2	1	no	—
78	C₄×Q₈×C₁₃	—	2	1	no	—
79	C₄×Q₈×C₁₃	—	2	1	no	—
80	C₄×Q₈×C₁₃	—	2	1	no	—
81	C₄×Q₈×C₁₃	—	2	1	no	—
82	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×D₄×C₁₃	—	2	1	no	—
85	C₄×D₄×C₁₃	—	2	1	no	—
86	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
87	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
88	C₁₃×#117	—	2	1	no	—
89	C₁₃×#117	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	1	no	—
113	C₁₃×#103	—	2	1	no	—
114	C₁₃×#103	—	2	2	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#102	—	2	1	no	—
117	C₁₃×#101	—	2	4	no	—
118	C₁₃×#101	—	2	4	no	—
119	C₁₃×#101	—	4	2	no	—
120	C₁₃×#97	—	2	1	no	—
121	C₄×C₈×C₁₃	—	2	1	no	—
122	#24772	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
123	C₁₃×#41	—	2	1	no	—
124	C₁₃×#41	—	2	1	no	—
125	C₁₃×#41	C₂×D₄	1	2	yes	—
126	C₁₃×#41	#41	1	2	yes	—
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	—	2	2	no	—
131	C₂×Q₈×C₁₃	—	2	2	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	2	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₁₃×Q₁₆	—	2	4	no	—
152	C₁₃×Q₁₆	—	4	4	no	—
153	C₁₃×Q₁₆	—	4	4	no	—
154	C₁₃×Q₁₆	—	4	4	no	—
155	C₁₃×SD₁₆	—	2	4	no	—
156	C₁₃×SD₁₆	—	4	4	no	—
157	C₁₃×M₁₆	—	2	1	no	—
158	C₁₃×M₁₆	—	2	2	no	—
159	C₁₃×M₁₆	—	2	2	no	—
160	C₁₃×M₁₆	—	2	2	no	—
161	C₁₃×M₁₆	—	2	1	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	—	2	1	no	—
164	C₁₃×M₁₆	—	4	4	no	—
165	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	4	4	no	—
173	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
180	C₁₃×C₄⋊C₄	—	4	1	no	—
181	C₁₃×C₄⋊C₄	—	4	1	no	—
182	C₁₃×C₄⋊C₄	—	4	1	no	—
183	C₁₃×C₄⋊C₄	—	4	1	no	—
184	C₁₃×C₄⋊C₄	—	4	1	no	—
185	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
186	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
187	C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₄²×C₁₃	—	2	1	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	4	1	no	—
194	C₄²×C₁₃	—	4	1	no	—
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₂×#473	C₂×C₁₃	1	2	yes	—
200	#3039	C₂×C₁₃	1	1	yes	characteristic
201	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
203	#2906	C₂×C₁₃	1	1	yes	characteristic
204	#2064	C₂×C₁₃	1	2	yes	complemented
205	#2047	C₂×C₁₃	1	2	yes	complemented
206	#1966	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1908	C₂×C₁₃	1	2	yes	—
209	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	1	no	—
211	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	1	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	2	2	no	—
215	Q₈×C₁₃	—	4	1	no	—
216	Q₈×C₁₃	—	4	1	no	—
217	Q₈×C₁₃	—	4	2	no	—
218	Q₈×C₁₃	—	4	2	no	—
219	Q₈×C₁₃	—	4	2	no	—
220	Q₈×C₁₃	—	4	2	no	—
221	Q₈×C₁₃	#121	1	2	yes	—
222	D₄×C₁₃	—	2	2	no	—
223	D₄×C₁₃	—	2	2	no	—
224	D₄×C₁₃	—	2	1	no	—
225	D₄×C₁₃	#121	1	2	yes	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	8	1	no	—
242	C₂×C₄×C₁₃	—	8	1	no	—
243	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
246	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
252	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
253	C₈×C₁₃	—	2	2	no	—
254	C₈×C₁₃	—	2	2	no	—
255	C₈×C₁₃	—	2	2	no	—
256	C₈×C₁₃	—	4	2	no	—
257	C₈×C₁₃	—	4	1	no	—
258	C₈×C₁₃	—	4	2	no	—
259	C₂×#137	C₂²×C₁₃	1	2	yes	—
260	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
262	C₂×#131	C₂²×C₁₃	1	2	yes	—
263	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
266	#473	—	2	8	no	—
267	#462	—	2	1	no	—
268	#462	—	2	1	no	—
269	#462	—	2	1	no	—
270	#462	—	2	1	no	—
271	#462	—	2	2	no	—
272	#461	—	2	1	no	—
273	#461	—	2	1	no	—
274	#441	—	2	1	no	—
275	#440	—	2	1	no	—
276	C₄×Q₁₆	—	2	1	no	—
277	C₄×SD₁₆	—	2	1	no	—
278	C₂×#108	C₂²×C₁₃	1	2	yes	—
279	#428	C₂²×C₁₃	1	1	yes	characteristic
280	#424	—	2	2	no	—
281	#424	C₂²×C₁₃	1	2	yes	—
282	#423	—	2	1	no	—
283	#423	C₂²×C₁₃	1	1	yes	characteristic
284	#423	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	—	2	1	no	—
286	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	#419	C₂²×C₁₃	1	2	yes	—
288	#419	C₂²×C₁₃	1	1	yes	characteristic
289	#417	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#103	C₂²×C₁₃	1	2	yes	—
291	C₂×#101	C₂²×C₁₃	1	2	yes	—
292	C₂×#101	C₂²×C₁₃	1	2	yes	—
293	C₂×#101	C₂²×C₁₃	1	2	yes	—
294	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
295	#343	C₂²×C₁₃	1	2	yes	—
296	#341	C₂²×C₁₃	1	2	yes	—
297	C₂²×C₁₃	—	2	1	no	—
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
303	C₂²×C₁₃	#547	1	1	yes	characteristic
304	C₂²×C₁₃	#553	1	1	yes	characteristic
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	1	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	—	4	2	no	—
310	C₄×C₁₃	—	4	1	no	—
311	C₄×C₁₃	—	4	1	no	—
312	C₄×C₁₃	—	8	2	no	—
313	C₄×C₁₃	—	8	1	no	—
314	C₄×C₁₃	#473	1	2	yes	complemented
315	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
316	C₄×C₁₃	#537	1	1	yes	characteristic
317	C₄×C₁₃	D₄²	1	1	yes	characteristic
318	C₄×C₁₃	#548	1	1	yes	characteristic
319	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
320	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
321	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
322	#137	—	2	2	no	—
323	#137	—	2	4	no	—
324	#137	—	2	4	no	—
325	#137	D₄×C₁₃	1	4	yes	—
326	C₂×Q₁₆	—	2	1	no	—
327	C₂×Q₁₆	—	2	4	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×Q₁₆	—	4	2	no	—
332	C₂×SD₁₆	—	2	1	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	#131	—	2	4	no	—
335	#131	—	4	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
338	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
339	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄×Q₈	—	2	1	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
352	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
356	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
357	#117	—	2	1	no	—
358	#117	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
366	#108	—	2	4	no	—
367	#107	—	2	1	no	—
368	#106	—	2	1	no	—
369	C₄⋊C₈	—	2	2	no	—
370	C₄⋊C₈	—	2	2	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	2	no	—
380	#103	—	2	2	no	—
381	#103	—	2	1	no	—
382	#103	—	2	1	no	—
383	#103	—	2	2	no	—
384	#103	—	2	2	no	—
385	#102	—	2	1	no	—
386	#101	—	2	4	no	—
387	#101	—	2	4	no	—
388	#101	—	4	2	no	—
389	#97	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₂×C₁₃	—	2	1	no	—
392	C₂×C₁₃	—	2	1	no	—
393	C₂×C₁₃	—	4	2	no	—
394	C₂×C₁₃	#2416	1	1	yes	characteristic
395	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
396	C₂×C₁₃	#3069	1	1	yes	characteristic
397	#41	—	2	1	no	—
398	#41	—	2	1	no	—
399	#41	C₂×D₄×C₁₃	1	2	yes	—
400	#41	C₁₃×#41	1	2	yes	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
413	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
423	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
425	Q₁₆	—	2	4	no	—
426	Q₁₆	—	4	4	no	—
427	Q₁₆	—	4	4	no	—
428	Q₁₆	—	4	4	no	—
429	SD₁₆	—	2	4	no	—
430	SD₁₆	—	4	4	no	—
431	M₁₆	—	2	1	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	2	no	—
434	M₁₆	—	2	2	no	—
435	M₁₆	—	2	1	no	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	1	no	—
438	M₁₆	—	4	4	no	—
439	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	4	4	no	—
447	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
448	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²⋊C₄	—	2	1	no	—
462	C₂²⋊C₄	—	2	1	no	—
463	C₂²⋊C₄	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	4	1	no	—
468	C₄²	—	4	1	no	—
469	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
473	C₁₃	#24772	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	1	no	—
475	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
476	Q₈	—	2	1	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	4	1	no	—
480	Q₈	—	4	1	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	C₁₃×#121	1	2	yes	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	1	no	—
489	D₄	C₁₃×#121	1	2	yes	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	1	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
508	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
509	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
510	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
515	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
517	C₈	—	2	2	no	—
518	C₈	—	2	2	no	—
519	C₈	—	2	2	no	—
520	C₈	—	4	2	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
529	C₂²	C₁₃×#547	1	1	yes	characteristic
530	C₂²	C₁₃×#553	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	8	1	no	—
539	C₄	—	8	2	no	—
540	C₄	C₁₃×#473	1	2	yes	complemented
541	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
542	C₄	C₁₃×#537	1	1	yes	characteristic
543	C₄	D₄²×C₁₃	1	1	yes	characteristic
544	C₄	C₁₃×#548	1	1	yes	characteristic
545	C₂	—	2	1	no	—
546	C₂	—	2	1	no	—
547	C₂	—	4	2	no	—
548	C₂	C₁₃×#2416	1	1	yes	characteristic
549	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
550	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#41	C₂³
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
3. C₂×C₁₃×#462	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
7. C₁₃×#2047	C₂	semidirect
8. C₁₃×#1966	C₂	semidirect
9. C₁₃×#1950	C₂	semidirect
11. C₁₃×#1801	C₂	semidirect
122. #24772	C₁₃	direct (N × H)
201. C₂×#462	C₂×C₁₃	semidirect
204. #2064	C₂×C₁₃	semidirect
205. #2047	C₂×C₁₃	semidirect
206. #1966	C₂×C₁₃	semidirect
207. #1950	C₂×C₁₃	semidirect
209. #1801	C₂×C₁₃	semidirect
314. C₄×C₁₃	#473	semidirect
473. C₁₃	#24772	direct (N × H)
540. C₄	C₁₃×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#473	2
C₁₃×#3039	2
C₂×C₁₃×#462	2
C₄×C₁₃×#137	2
C₁₃×#2906	2
C₁₃×#2064	2
C₁₃×#2047	2
C₁₃×#1966	2
C₁₃×#1950	2
C₁₃×#1908	2
C₁₃×#1801	2
#24772	13

Subgroups — C13×#24772 #15711111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24772 #15711111