Subgroups — C₁₃×#24857 #15711196

Order 3328.

720 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×#3079	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₁₃×#137	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2906	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2089	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2064	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1908	C₂	1	2	yes	maximal
10	C₁₃×#1816	C₂	1	2	yes	maximal
11	C₁₃×#1801	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#477	—	2	1	no	—
18	C₁₃×#477	—	2	1	no	—
19	C₁₃×#477	—	2	1	no	—
20	C₁₃×#477	—	2	2	no	—
21	C₁₃×#476	—	2	1	no	—
22	C₁₃×#475	—	2	1	no	—
23	C₁₃×#474	—	2	1	no	—
24	C₁₃×#441	—	2	1	no	—
25	C₁₃×#440	—	2	1	no	—
26	C₄×C₁₃×Q₁₆	—	2	1	no	—
27	C₄×C₁₃×SD₁₆	—	2	1	no	—
28	C₂×C₁₃×#108	C₂²	1	2	yes	—
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#428	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#107	C₂²	1	2	yes	—
32	C₁₃×#424	—	2	2	no	—
33	C₁₃×#424	C₂²	1	2	yes	—
34	C₁₃×#423	—	2	1	no	—
35	C₁₃×#423	C₂²	1	1	yes	characteristic
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	—	2	1	no	—
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#419	C₂²	1	1	yes	characteristic
40	C₁₃×#417	C₂²	1	2	yes	—
41	C₁₃×#417	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#103	C₂²	1	2	yes	—
43	C₂×C₁₃×#101	C₂²	1	2	yes	—
44	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
45	C₁₃×#343	C₂²	1	2	yes	—
46	C₁₃×#343	C₂²	1	2	yes	—
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	—	2	1	no	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#137	—	2	2	no	—
53	C₁₃×#137	Q₈	1	4	yes	complemented
54	C₂×C₁₃×Q₁₆	—	2	1	no	—
55	C₂×C₁₃×SD₁₆	—	2	1	no	—
56	C₁₃×#131	—	2	4	no	—
57	C₁₃×#131	—	4	2	no	—
58	C₂×C₁₃×M₁₆	—	2	2	no	—
59	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	—	2	2	no	—
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₁₃×C₄⋊Q₈	—	2	1	no	—
66	C₁₃×C₄⋊Q₈	—	2	1	no	—
67	C₁₃×C₄⋊Q₈	—	2	1	no	—
68	C₁₃×C₄⋊Q₈	—	2	1	no	—
69	C₄×Q₈×C₁₃	—	2	1	no	—
70	C₄×Q₈×C₁₃	—	2	1	no	—
71	C₄×Q₈×C₁₃	—	2	1	no	—
72	C₄×Q₈×C₁₃	—	2	1	no	—
73	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×D₄×C₁₃	—	2	1	no	—
76	C₄×D₄×C₁₃	—	2	1	no	—
77	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
78	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
79	C₁₃×#117	—	2	1	no	—
80	C₁₃×#117	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	—	2	1	no	—
86	C₂×C₄²×C₁₃	—	2	1	no	—
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#108	—	4	2	no	—
89	C₁₃×#107	—	2	2	no	—
90	C₁₃×#107	—	2	2	no	—
91	C₁₃×#107	—	2	1	no	—
92	C₁₃×#107	—	2	2	no	—
93	C₁₃×#106	—	2	1	no	—
94	C₁₃×#106	—	2	2	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×C₄⋊C₈	—	2	2	no	—
97	C₁₃×C₄⋊C₈	—	2	1	no	—
98	C₁₃×C₄⋊C₈	—	2	1	no	—
99	C₁₃×C₄⋊C₈	—	2	1	no	—
100	C₁₃×C₄⋊C₈	—	2	1	no	—
101	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
103	C₁₃×C₄⋊C₈	D₄	1	2	yes	—
104	C₁₃×#103	—	2	1	no	—
105	C₁₃×#103	—	2	2	no	—
106	C₁₃×#103	—	2	2	no	—
107	C₁₃×#103	—	2	2	no	—
108	C₁₃×#103	—	2	1	no	—
109	C₁₃×#103	—	2	1	no	—
110	C₁₃×#102	—	2	1	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#101	—	4	2	no	—
113	C₁₃×#97	—	2	1	no	—
114	C₄×C₈×C₁₃	—	2	1	no	—
115	#24857	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	—	2	1	no	—
118	C₁₃×#41	C₂×Q₈	1	2	yes	—
119	C₁₃×#41	#41	1	2	yes	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	4	1	no	—
126	C₂×Q₈×C₁₃	—	4	1	no	—
127	C₂×Q₈×C₁₃	—	8	2	no	—
128	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×Q₁₆	—	2	4	no	—
142	C₁₃×SD₁₆	—	2	4	no	—
143	C₁₃×M₁₆	—	2	1	no	—
144	C₁₃×M₁₆	—	2	2	no	—
145	C₁₃×M₁₆	—	2	2	no	—
146	C₁₃×M₁₆	—	2	2	no	—
147	C₁₃×M₁₆	—	2	1	no	—
148	C₁₃×M₁₆	—	2	1	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₁₃×M₁₆	—	4	4	no	—
151	C₁₃×M₁₆	C₂×Q₈	1	2	yes	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	—	4	4	no	—
159	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	2	2	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	4	1	no	—
168	C₁₃×C₄⋊C₄	—	4	1	no	—
169	C₁₃×C₄⋊C₄	—	4	1	no	—
170	C₁₃×C₄⋊C₄	—	4	1	no	—
171	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	—	2	1	no	—
174	C₁₃×C₂²⋊C₄	—	2	1	no	—
175	C₁₃×C₂²⋊C₄	—	2	1	no	—
176	C₄²×C₁₃	—	2	1	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	4	1	no	—
180	C₄²×C₁₃	—	4	1	no	—
181	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
185	#3079	C₂×C₁₃	1	1	yes	characteristic
186	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₄×#137	C₂×C₁₃	1	1	yes	characteristic
188	#2906	C₂×C₁₃	1	1	yes	characteristic
189	#2089	C₂×C₁₃	1	2	yes	complemented
190	#2064	C₂×C₁₃	1	2	yes	complemented
191	#1997	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1950	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1908	C₂×C₁₃	1	2	yes	—
194	#1816	C₂×C₁₃	1	2	yes	—
195	#1801	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂³×C₁₃	—	2	1	no	—
197	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
198	Q₈×C₁₃	—	2	1	no	—
199	Q₈×C₁₃	—	2	2	no	—
200	Q₈×C₁₃	—	2	2	no	—
201	Q₈×C₁₃	—	4	1	no	—
202	Q₈×C₁₃	—	4	1	no	—
203	Q₈×C₁₃	—	8	2	no	—
204	Q₈×C₁₃	—	8	2	no	—
205	Q₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	4	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	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	8	1	no	—
224	C₂×C₄×C₁₃	—	8	1	no	—
225	C₂×C₄×C₁₃	—	8	2	no	—
226	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
235	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₁₃	—	2	2	no	—
237	C₈×C₁₃	—	2	2	no	—
238	C₈×C₁₃	—	2	2	no	—
239	C₈×C₁₃	—	4	1	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₈×C₁₃	—	4	2	no	—
242	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×#131	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
247	#477	—	2	1	no	—
248	#477	—	2	1	no	—
249	#477	—	2	1	no	—
250	#477	—	2	2	no	—
251	#476	—	2	1	no	—
252	#475	—	2	1	no	—
253	#474	—	2	1	no	—
254	#441	—	2	1	no	—
255	#440	—	2	1	no	—
256	C₄×Q₁₆	—	2	1	no	—
257	C₄×SD₁₆	—	2	1	no	—
258	C₂×#108	C₂²×C₁₃	1	2	yes	—
259	#428	C₂²×C₁₃	1	2	yes	—
260	#428	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#107	C₂²×C₁₃	1	2	yes	—
262	#424	—	2	2	no	—
263	#424	C₂²×C₁₃	1	2	yes	—
264	#423	—	2	1	no	—
265	#423	C₂²×C₁₃	1	1	yes	characteristic
266	#423	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	—	2	1	no	—
268	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
269	#419	C₂²×C₁₃	1	1	yes	characteristic
270	#417	C₂²×C₁₃	1	2	yes	—
271	#417	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#103	C₂²×C₁₃	1	2	yes	—
273	C₂×#101	C₂²×C₁₃	1	2	yes	—
274	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
275	#343	C₂²×C₁₃	1	2	yes	—
276	#343	C₂²×C₁₃	1	2	yes	—
277	#343	C₂²×C₁₃	1	2	yes	—
278	#341	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	—	4	1	no	—
284	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
285	C₂²×C₁₃	#552	1	1	yes	characteristic
286	C₂²×C₁₃	#554	1	1	yes	characteristic
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	2	1	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	4	1	no	—
294	C₄×C₁₃	—	8	1	no	—
295	C₄×C₁₃	—	8	2	no	—
296	C₄×C₁₃	#473	1	2	yes	—
297	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
298	C₄×C₁₃	#537	1	1	yes	characteristic
299	C₄×C₁₃	#546	1	1	yes	characteristic
300	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
301	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
304	#137	—	2	2	no	—
305	#137	Q₈×C₁₃	1	4	yes	complemented
306	C₂×Q₁₆	—	2	1	no	—
307	C₂×SD₁₆	—	2	1	no	—
308	#131	—	2	4	no	—
309	#131	—	4	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
313	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	—	2	1	no	—
319	C₄⋊Q₈	—	2	1	no	—
320	C₄⋊Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
326	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
330	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
331	#117	—	2	1	no	—
332	#117	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	—	2	1	no	—
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	#108	—	4	2	no	—
341	#107	—	2	2	no	—
342	#107	—	2	2	no	—
343	#107	—	2	1	no	—
344	#107	—	2	2	no	—
345	#106	—	2	1	no	—
346	#106	—	2	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	1	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	2	1	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
354	C₄⋊C₈	D₄×C₁₃	1	1	yes	characteristic
355	C₄⋊C₈	D₄×C₁₃	1	2	yes	—
356	#103	—	2	1	no	—
357	#103	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	—	2	1	no	—
361	#103	—	2	1	no	—
362	#102	—	2	1	no	—
363	#102	—	2	2	no	—
364	#101	—	4	2	no	—
365	#97	—	2	1	no	—
366	C₄×C₈	—	2	1	no	—
367	C₂×C₁₃	—	2	1	no	—
368	C₂×C₁₃	—	2	1	no	—
369	C₂×C₁₃	—	4	2	no	—
370	C₂×C₁₃	#2417	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#473	1	1	yes	characteristic
372	C₂×C₁₃	#3068	1	1	yes	characteristic
373	#41	—	2	1	no	—
374	#41	—	2	1	no	—
375	#41	C₂×Q₈×C₁₃	1	2	yes	—
376	#41	C₁₃×#41	1	2	yes	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	4	1	no	—
383	C₂×Q₈	—	4	1	no	—
384	C₂×Q₈	—	8	2	no	—
385	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
396	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	Q₁₆	—	2	4	no	—
399	SD₁₆	—	2	4	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	4	4	no	—
408	M₁₆	C₂×Q₈×C₁₃	1	2	yes	—
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	4	4	no	—
416	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
417	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₄⋊C₄	—	4	1	no	—
428	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂²⋊C₄	—	2	1	no	—
431	C₂²⋊C₄	—	2	1	no	—
432	C₂²⋊C₄	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₄²	—	4	1	no	—
437	C₄²	—	4	1	no	—
438	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₁₃	#24857	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	1	no	—
444	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
445	Q₈	—	2	1	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	2	2	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	1	no	—
450	Q₈	—	8	2	no	—
451	Q₈	—	8	2	no	—
452	Q₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	1	no	—
456	D₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
457	C₂×C₄	—	2	1	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	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	2	no	—
473	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
474	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
475	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
476	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
479	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
480	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
481	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
482	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	2	2	no	—
486	C₈	—	4	1	no	—
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	1	no	—
494	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
495	C₂²	C₁₃×#552	1	1	yes	characteristic
496	C₂²	C₁₃×#554	1	1	yes	characteristic
497	C₄	—	2	1	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	8	1	no	—
505	C₄	—	8	2	no	—
506	C₄	C₁₃×#473	1	2	yes	—
507	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
508	C₄	C₁₃×#537	1	1	yes	characteristic
509	C₄	C₁₃×#546	1	1	yes	characteristic
510	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	4	2	no	—
514	C₂	C₁₃×#2417	1	1	yes	characteristic
515	C₂	C₂×C₁₃×#473	1	1	yes	characteristic
516	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	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
2. C₂×C₁₃×#477	C₂	semidirect
5. C₁₃×#2089	C₂	semidirect
6. C₁₃×#2064	C₂	semidirect
7. C₁₃×#1997	C₂	semidirect
8. C₁₃×#1950	C₂	semidirect
11. C₁₃×#1801	C₂	semidirect
53. C₁₃×#137	Q₈	semidirect
115. #24857	C₁₃	direct (N × H)
186. C₂×#477	C₂×C₁₃	semidirect
189. #2089	C₂×C₁₃	semidirect
190. #2064	C₂×C₁₃	semidirect
191. #1997	C₂×C₁₃	semidirect
192. #1950	C₂×C₁₃	semidirect
195. #1801	C₂×C₁₃	semidirect
305. #137	Q₈×C₁₃	semidirect
442. C₁₃	#24857	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×#3079	2
C₂×C₁₃×#477	2
C₄×C₁₃×#137	2
C₁₃×#2906	2
C₁₃×#2089	2
C₁₃×#2064	2
C₁₃×#1997	2
C₁₃×#1950	2
C₁₃×#1908	2
C₁₃×#1816	2
C₁₃×#1801	2
#24857	13

Subgroups — C13×#24857 #15711196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24857 #15711196