Subgroups — C₁₃×#21009 #15707348

Order 3328.

1708 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2896	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#410	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1910	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1909	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
8	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₁₃×#568	—	2	2	no	—
11	C₁₃×#568	—	2	4	no	—
12	C₁₃×#568	C₂²	1	4	yes	—
13	C₂×C₁₃×#131	—	2	4	no	—
14	C₂²×C₁₃×M₁₆	—	2	2	no	—
15	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
16	C₁₃×#537	—	2	2	no	—
17	C₁₃×#536	C₄	1	2	yes	complemented
18	C₁₃×#536	C₂²	1	2	yes	—
19	C₁₃×#535	C₄	1	2	yes	complemented
20	C₁₃×#535	C₂²	1	2	yes	—
21	C₁₃×#534	—	2	2	no	—
22	C₁₃×#532	C₄	1	4	yes	complemented
23	C₁₃×#525	—	2	2	no	—
24	C₁₃×#525	—	2	2	no	—
25	C₂×C₁₃×#117	C₂²	1	2	yes	—
26	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₁₃×#419	C₂²	1	4	yes	complemented
28	C₁₃×#418	C₂²	1	4	yes	complemented
29	C₁₃×#417	—	2	4	no	—
30	C₁₃×#416	—	2	4	no	—
31	C₁₃×#410	—	2	2	no	—
32	C₁₃×#410	C₂²	1	4	yes	—
33	C₂×C₁₃×#99	—	2	2	no	—
34	C₁₃×H(3,ℤ/4)	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#41	—	2	2	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	2	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	2	no	—
42	C₂×C₁₃×#41	—	2	2	no	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
46	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
47	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×#41	D₄	1	2	yes	—
49	C₂×C₁₃×#41	D₄	1	2	yes	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₁₃	D₄	1	2	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	—	2	1	no	—
58	C₂³×C₄×C₁₃	D₄	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#131	—	2	16	no	—
61	C₁₃×#131	—	2	16	no	—
62	C₂×C₁₃×M₁₆	—	2	4	no	—
63	C₂×C₁₃×M₁₆	—	2	8	no	—
64	C₂×C₁₃×M₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	8	no	—
66	C₂×C₁₃×M₁₆	—	2	2	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
68	C₂×C₁₃×M₁₆	—	2	2	no	—
69	C₂×C₁₃×M₁₆	D₄	1	4	yes	complemented
70	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
71	C₂²×C₈×C₁₃	—	2	4	no	—
72	C₂²×C₈×C₁₃	D₄	1	4	yes	complemented
73	C₁₃×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
74	C₁₃×#127	C₂×C₄	1	4	yes	complemented
75	C₁₃×#124	C₂×C₄	1	4	yes	complemented
76	C₁₃×#124	C₂×C₄	1	4	yes	complemented
77	C₁₃×#123	—	2	4	no	—
78	C₁₃×#123	—	2	4	no	—
79	C₁₃×C₂²⋊Q₈	—	2	4	no	—
80	C₁₃×C₂²⋊Q₈	—	2	4	no	—
81	C₁₃×#121	—	2	4	no	—
82	C₁₃×#121	—	2	8	no	—
83	C₁₃×#121	—	2	4	no	—
84	C₁₃×#120	—	2	4	no	—
85	C₁₃×#120	—	2	4	no	—
86	C₄×D₄×C₁₃	—	2	8	no	—
87	C₁₃×#117	—	2	1	no	—
88	C₁₃×#117	—	2	1	no	—
89	C₁₃×#117	—	2	2	no	—
90	C₁₃×#117	—	2	2	no	—
91	C₁₃×#117	—	2	2	no	—
92	C₁₃×#117	C₂×C₄	1	2	yes	—
93	C₁₃×#117	C₂³	1	4	yes	—
94	C₁₃×#117	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₄²×C₁₃	—	2	2	no	—
100	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
101	C₁₃×#103	—	2	8	no	—
102	C₁₃×#102	—	2	8	no	—
103	C₁₃×#99	—	2	8	no	—
104	#21009	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₂⁴×C₁₃	—	2	1	no	—
106	C₂⁴×C₁₃	C₂²⋊C₄	1	2	yes	—
107	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	—	2	4	no	—
110	C₁₃×#41	—	2	4	no	—
111	C₁₃×#41	—	2	4	no	—
112	C₁₃×#41	—	2	4	no	—
113	C₁₃×#41	—	2	4	no	—
114	C₁₃×#41	—	2	4	no	—
115	C₁₃×#41	—	2	4	no	—
116	C₁₃×#41	—	2	4	no	—
117	C₁₃×#41	—	2	4	no	—
118	C₁₃×#41	—	2	4	no	—
119	C₁₃×#41	—	2	4	no	—
120	C₁₃×#41	—	4	2	no	—
121	C₁₃×#41	—	4	1	no	—
122	C₁₃×#41	—	4	1	no	—
123	C₁₃×#41	—	4	1	no	—
124	C₁₃×#41	—	4	2	no	—
125	C₁₃×#41	—	4	1	no	—
126	C₂×Q₈×C₁₃	—	2	2	no	—
127	C₂×Q₈×C₁₃	—	2	2	no	—
128	C₂×Q₈×C₁₃	—	2	1	no	—
129	C₂×Q₈×C₁₃	—	2	2	no	—
130	C₂×Q₈×C₁₃	—	2	2	no	—
131	C₂×Q₈×C₁₃	C₂²⋊C₄	1	2	yes	—
132	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
133	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
134	C₂×D₄×C₁₃	—	2	4	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	8	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	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	4	2	no	—
145	C₂×D₄×C₁₃	—	4	2	no	—
146	C₂×D₄×C₁₃	C₂²⋊C₄	1	2	yes	—
147	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
148	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	#41	1	2	yes	—
173	C₂²×C₄×C₁₃	#41	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₁₃×M₁₆	—	2	16	no	—
176	C₁₃×M₁₆	—	2	4	no	—
177	C₁₃×M₁₆	—	2	4	no	—
178	C₁₃×M₁₆	—	2	4	no	—
179	C₁₃×M₁₆	—	2	4	no	—
180	C₂×C₈×C₁₃	—	2	16	no	—
181	C₂×C₈×C₁₃	—	2	4	no	—
182	C₂×C₈×C₁₃	—	2	4	no	—
183	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	4	2	no	—
189	C₁₃×C₂²⋊C₄	—	2	2	no	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	2	no	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	4	2	no	—
195	C₄²×C₁₃	—	2	2	no	—
196	C₄²×C₁₃	—	2	4	no	—
197	C₄²×C₁₃	—	4	2	no	—
198	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
199	C₂×#568	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3449	C₂×C₁₃	1	1	yes	characteristic
201	#2896	C₂×C₁₃	1	2	yes	complemented
202	C₂×#410	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1910	C₂×C₁₃	1	4	yes	complemented
204	#1909	C₂×C₁₃	1	4	yes	complemented
205	C₂×H(3,ℤ/4)	C₂×C₁₃	1	2	yes	complemented
206	C₂³×C₁₃	—	2	2	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	8	1	no	—
211	C₂³×C₁₃	—	8	2	no	—
212	C₂³×C₁₃	—	8	2	no	—
213	C₂³×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
214	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×C₁₃	#121	1	2	yes	—
217	C₂³×C₁₃	#121	1	2	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₃	—	2	4	no	—
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	4	1	no	—
223	Q₈×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	2	8	no	—
225	D₄×C₁₃	—	2	8	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	4	no	—
229	D₄×C₁₃	—	4	2	no	—
230	D₄×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	4	1	no	—
233	D₄×C₁₃	—	4	1	no	—
234	D₄×C₁₃	—	8	8	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	4	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	4	no	—
248	C₂×C₄×C₁₃	—	8	2	no	—
249	C₂×C₄×C₁₃	—	8	4	no	—
250	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
256	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
257	C₂×C₄×C₁₃	#120	1	2	yes	—
258	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
259	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
260	C₂×C₄×C₁₃	#121	1	2	yes	—
261	C₂×C₄×C₁₃	#121	1	2	yes	—
262	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
263	C₂×C₄×C₁₃	#123	1	2	yes	—
264	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
269	C₈×C₁₃	—	2	8	no	—
270	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
271	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
272	#568	—	2	2	no	—
273	#568	—	2	4	no	—
274	#568	C₂²×C₁₃	1	4	yes	—
275	C₂×#131	—	2	4	no	—
276	C₂²×M₁₆	—	2	2	no	—
277	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
278	#537	—	2	2	no	—
279	#536	C₄×C₁₃	1	2	yes	complemented
280	#536	C₂²×C₁₃	1	2	yes	—
281	#535	C₄×C₁₃	1	2	yes	complemented
282	#535	C₂²×C₁₃	1	2	yes	—
283	#534	—	2	2	no	—
284	#532	C₄×C₁₃	1	4	yes	complemented
285	#525	—	2	2	no	—
286	#525	—	2	2	no	—
287	C₂×#117	C₂²×C₁₃	1	2	yes	—
288	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
289	#419	C₂²×C₁₃	1	4	yes	complemented
290	#418	C₂²×C₁₃	1	4	yes	complemented
291	#417	—	2	4	no	—
292	#416	—	2	4	no	—
293	#410	—	2	2	no	—
294	#410	C₂²×C₁₃	1	4	yes	—
295	C₂×#99	—	2	2	no	—
296	H(3,ℤ/4)	C₂²×C₁₃	1	8	yes	complemented
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	4	1	no	—
299	C₂²×C₁₃	—	4	2	no	—
300	C₂²×C₁₃	—	4	1	no	—
301	C₂²×C₁₃	—	4	1	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	2	no	—
307	C₂²×C₁₃	—	8	2	no	—
308	C₂²×C₁₃	—	8	4	no	—
309	C₂²×C₁₃	#386	1	1	yes	characteristic
310	C₂²×C₁₃	#386	1	1	yes	characteristic
311	C₂²×C₁₃	#386	1	2	yes	—
312	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×#121	1	2	yes	—
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	8	4	no	—
318	C₄×C₁₃	#386	1	1	yes	characteristic
319	C₄×C₁₃	#386	1	2	yes	—
320	C₄×C₁₃	#386	1	1	yes	characteristic
321	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
322	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
323	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	2	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
335	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
336	C₂×#41	C₂×C₄×C₁₃	1	2	yes	—
337	C₂×#41	D₄×C₁₃	1	2	yes	—
338	C₂×#41	D₄×C₁₃	1	2	yes	—
339	C₂×#41	C₂³×C₁₃	1	2	yes	—
340	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
341	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
344	C₂²×D₄	D₄×C₁₃	1	2	yes	—
345	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	D₄×C₁₃	1	2	yes	—
348	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
349	#131	—	2	16	no	—
350	#131	—	2	16	no	—
351	C₂×M₁₆	—	2	4	no	—
352	C₂×M₁₆	—	2	8	no	—
353	C₂×M₁₆	—	2	2	no	—
354	C₂×M₁₆	—	2	8	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	2	2	no	—
357	C₂×M₁₆	—	2	2	no	—
358	C₂×M₁₆	D₄×C₁₃	1	4	yes	complemented
359	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
360	C₂²×C₈	—	2	4	no	—
361	C₂²×C₈	D₄×C₁₃	1	4	yes	complemented
362	C₄⋊Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
363	#127	C₂×C₄×C₁₃	1	4	yes	complemented
364	#124	C₂×C₄×C₁₃	1	4	yes	complemented
365	#124	C₂×C₄×C₁₃	1	4	yes	complemented
366	#123	—	2	4	no	—
367	#123	—	2	4	no	—
368	C₂²⋊Q₈	—	2	4	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	2	8	no	—
372	#121	—	2	4	no	—
373	#120	—	2	4	no	—
374	#120	—	2	4	no	—
375	C₄×D₄	—	2	8	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	#117	—	2	2	no	—
381	#117	C₂×C₄×C₁₃	1	2	yes	—
382	#117	C₂³×C₁₃	1	4	yes	—
383	#117	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
390	#103	—	2	8	no	—
391	#102	—	2	8	no	—
392	#99	—	2	8	no	—
393	C₂×C₁₃	—	2	1	no	—
394	C₂×C₁₃	—	2	2	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	—	2	2	no	—
398	C₂×C₁₃	—	4	4	no	—
399	C₂×C₁₃	—	8	2	no	—
400	C₂×C₁₃	C₂×#386	1	1	yes	characteristic
401	C₂⁴	—	2	1	no	—
402	C₂⁴	C₁₃×C₂²⋊C₄	1	2	yes	—
403	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
404	#41	—	2	4	no	—
405	#41	—	2	4	no	—
406	#41	—	2	4	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	4	no	—
411	#41	—	2	4	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	4	no	—
416	#41	—	4	1	no	—
417	#41	—	4	2	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	C₁₃×C₂²⋊C₄	1	2	yes	—
428	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
429	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	C₁₃×C₂²⋊C₄	1	2	yes	—
443	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
444	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
445	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	C₁₃×C₂²⋊C₄	1	4	yes	—
459	C₂²×C₄	C₁₃×C₂²⋊C₄	1	2	yes	—
460	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
463	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
467	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
468	C₂²×C₄	C₁₃×#41	1	2	yes	—
469	C₂²×C₄	C₁₃×#41	1	2	yes	—
470	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
471	M₁₆	—	2	16	no	—
472	M₁₆	—	2	4	no	—
473	M₁₆	—	2	4	no	—
474	M₁₆	—	2	4	no	—
475	M₁₆	—	2	4	no	—
476	C₂×C₈	—	2	16	no	—
477	C₂×C₈	—	2	4	no	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	C₂×D₄×C₁₃	1	8	yes	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	4	2	no	—
494	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
495	C₁₃	#21009	1	1	yes	characteristic, direct product factor, Sylow
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	8	1	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
504	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
505	C₂³	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
506	C₂³	C₁₃×#121	1	2	yes	—
507	C₂³	C₁₃×#121	1	2	yes	—
508	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	4	no	—
511	Q₈	—	2	4	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	D₄	—	2	8	no	—
515	D₄	—	2	8	no	—
516	D₄	—	2	4	no	—
517	D₄	—	2	4	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	4	no	—
540	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
541	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
542	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
543	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
544	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
545	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
546	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
547	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
548	C₂×C₄	C₁₃×#120	1	2	yes	—
549	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
550	C₂×C₄	C₁₃×#121	1	2	yes	—
551	C₂×C₄	C₁₃×#121	1	2	yes	—
552	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
553	C₂×C₄	C₁₃×#123	1	1	yes	characteristic
554	C₂×C₄	C₁₃×#123	1	2	yes	—
555	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
559	C₈	—	2	8	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	4	no	—
572	C₂²	C₁₃×#386	1	1	yes	characteristic
573	C₂²	C₁₃×#386	1	1	yes	characteristic
574	C₂²	C₁₃×#386	1	2	yes	—
575	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
576	C₂²	C₂×C₁₃×#121	1	2	yes	—
577	C₄	—	2	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	8	4	no	—
581	C₄	C₁₃×#386	1	1	yes	characteristic
582	C₄	C₁₃×#386	1	2	yes	—
583	C₄	C₁₃×#386	1	1	yes	characteristic
584	C₄	C₂×C₄×D₄×C₁₃	1	2	yes	—
585	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
586	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	2	no	—
592	C₂	—	4	4	no	—
593	C₂	—	8	2	no	—
594	C₂	C₂×C₁₃×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#386
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×#386
prime radical	C₁₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#568	C₂	semidirect
3. C₁₃×#2896	C₂	semidirect
4. C₂×C₁₃×#410	C₂	semidirect
5. C₁₃×#1910	C₂	semidirect
6. C₁₃×#1909	C₂	semidirect
7. C₂×C₁₃×H(3,ℤ/4)	C₂	semidirect
17. C₁₃×#536	C₄	semidirect
19. C₁₃×#535	C₄	semidirect
22. C₁₃×#532	C₄	semidirect
27. C₁₃×#419	C₂²	semidirect
28. C₁₃×#418	C₂²	semidirect
34. C₁₃×H(3,ℤ/4)	C₂²	semidirect
69. C₂×C₁₃×M₁₆	D₄	semidirect
72. C₂²×C₈×C₁₃	D₄	semidirect
73. C₁₃×C₄⋊Q₈	C₂×C₄	semidirect
74. C₁₃×#127	C₂×C₄	semidirect
75. C₁₃×#124	C₂×C₄	semidirect
76. C₁₃×#124	C₂×C₄	semidirect
104. #21009	C₁₃	direct (N × H)
199. C₂×#568	C₂×C₁₃	semidirect
201. #2896	C₂×C₁₃	semidirect
202. C₂×#410	C₂×C₁₃	semidirect
203. #1910	C₂×C₁₃	semidirect
204. #1909	C₂×C₁₃	semidirect
205. C₂×H(3,ℤ/4)	C₂×C₁₃	semidirect
279. #536	C₄×C₁₃	semidirect
281. #535	C₄×C₁₃	semidirect
284. #532	C₄×C₁₃	semidirect
289. #419	C₂²×C₁₃	semidirect
290. #418	C₂²×C₁₃	semidirect
296. H(3,ℤ/4)	C₂²×C₁₃	semidirect
358. C₂×M₁₆	D₄×C₁₃	semidirect
361. C₂²×C₈	D₄×C₁₃	semidirect
362. C₄⋊Q₈	C₂×C₄×C₁₃	semidirect
363. #127	C₂×C₄×C₁₃	semidirect
364. #124	C₂×C₄×C₁₃	semidirect
365. #124	C₂×C₄×C₁₃	semidirect
495. C₁₃	#21009	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×#568	2
C₁₃×#3449	2
C₁₃×#2896	2
C₂×C₁₃×#410	2
C₁₃×#1910	2
C₁₃×#1909	2
C₂×C₁₃×H(3,ℤ/4)	2
#21009	13

Subgroups — C13×#21009 #15707348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21009 #15707348