Subgroups — C₁₃×#19820 #15706159

Order 3328.

676 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3330	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1719	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1701	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1680	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1679	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1665	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1647	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1642	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1625	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	—	2	1	no	—
17	C₁₃×#550	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#547	C₂²	1	1	yes	characteristic
20	C₁₃×#547	C₂²	1	1	yes	characteristic
21	C₁₃×#500	C₂²	1	1	yes	characteristic
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#487	C₂²	1	1	yes	characteristic
24	C₁₃×#487	C₂²	1	1	yes	characteristic
25	C₁₃×#486	—	2	1	no	—
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#484	—	2	1	no	—
29	C₁₃×#483	—	2	1	no	—
30	C₁₃×#475	C₂²	1	1	yes	characteristic
31	C₁₃×#474	—	2	1	no	—
32	C₁₃×#474	C₂²	1	1	yes	characteristic
33	C₁₃×#474	C₂²	1	1	yes	characteristic
34	C₁₃×#468	—	2	1	no	—
35	C₁₃×#465	—	2	1	no	—
36	C₁₃×#465	—	2	1	no	—
37	C₁₃×#462	C₂²	1	1	yes	characteristic
38	C₁₃×#461	C₂²	1	1	yes	characteristic
39	C₁₃×#461	C₂²	1	1	yes	characteristic
40	C₁₃×#459	—	2	1	no	—
41	C₁₃×#459	C₂²	1	1	yes	characteristic
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#452	—	2	1	no	—
44	C₁₃×#449	—	2	1	no	—
45	C₁₃×#449	—	2	1	no	—
46	C₁₃×#448	—	2	1	no	—
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×D₈	—	2	1	no	—
50	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
51	C₁₃×#436	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
54	C₁₃×#417	—	2	1	no	—
55	C₂×C₁₃×#103	—	2	1	no	—
56	C₁₃×#334	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#332	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#332	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₃×#322	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	1	no	—
68	C₂×C₁₃×#41	—	2	1	no	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂²×Q₈×C₁₃	—	2	1	no	—
71	C₁₃×#135	—	4	4	no	—
72	C₂×C₁₃×Q₁₆	—	2	1	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×SD₁₆	—	2	1	no	—
75	C₂×C₁₃×SD₁₆	—	2	1	no	—
76	C₂×C₁₃×SD₁₆	—	2	1	no	—
77	C₂×C₁₃×SD₁₆	D₄	1	1	yes	characteristic
78	C₂×C₁₃×D₈	—	2	1	no	—
79	C₂×C₁₃×D₈	—	2	1	no	—
80	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	—	2	1	no	—
82	C₂²×C₈×C₁₃	—	2	1	no	—
83	C₂²×C₈×C₁₃	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₃×#127	—	2	1	no	—
89	C₁₃×#127	C₂³	1	1	yes	characteristic
90	C₁₃×#123	—	4	1	no	—
91	C₁₃×#123	—	4	1	no	—
92	C₁₃×C₂²⋊Q₈	—	2	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×C₂²⋊Q₈	—	2	1	no	—
95	C₁₃×C₂²⋊Q₈	—	4	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	2	1	no	—
98	C₁₃×#121	—	2	1	no	—
99	C₁₃×#121	—	4	1	no	—
100	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₁₃	—	2	1	no	—
102	C₄×D₄×C₁₃	—	2	1	no	—
103	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
104	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	4	1	no	—
111	C₁₃×#107	D₄	1	1	yes	characteristic
112	C₁₃×#106	—	2	1	no	—
113	C₁₃×#106	D₄	1	1	yes	characteristic
114	C₁₃×C₄⋊C₈	—	2	1	no	—
115	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₃×#103	—	2	1	no	—
120	C₁₃×#103	—	2	1	no	—
121	C₁₃×#103	—	2	1	no	—
122	C₁₃×#103	—	2	1	no	—
123	C₁₃×#103	—	2	1	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	—	2	1	no	—
126	C₁₃×#103	—	2	1	no	—
127	C₁₃×#103	D₄	1	1	yes	characteristic
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	4	1	no	—
135	C₁₃×#102	D₄	1	1	yes	characteristic
136	C₁₃×#102	D₄	1	1	yes	characteristic
137	C₁₃×#102	D₄	1	1	yes	characteristic
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×C₂²⋊C₈	—	2	1	no	—
141	C₄×C₈×C₁₃	—	2	1	no	—
142	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
145	#19820	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₁₃×#41	—	4	2	no	—
147	C₁₃×#41	—	4	2	no	—
148	C₁₃×#41	—	4	2	no	—
149	C₁₃×#41	—	8	1	no	—
150	C₁₃×#41	—	8	1	no	—
151	C₁₃×#41	—	8	1	no	—
152	C₂×Q₈×C₁₃	—	2	1	no	—
153	C₂×Q₈×C₁₃	—	2	1	no	—
154	C₂×Q₈×C₁₃	—	2	1	no	—
155	C₂×Q₈×C₁₃	—	4	1	no	—
156	C₂×Q₈×C₁₃	—	4	2	no	—
157	C₂×Q₈×C₁₃	—	8	1	no	—
158	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	2	1	no	—
162	C₂×D₄×C₁₃	—	4	1	no	—
163	C₂×D₄×C₁₃	—	4	1	no	—
164	C₂×D₄×C₁₃	—	4	1	no	—
165	C₂×D₄×C₁₃	—	4	1	no	—
166	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	4	1	no	—
173	C₂²×C₄×C₁₃	—	4	1	no	—
174	C₂²×C₄×C₁₃	—	4	1	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₁₃×Q₁₆	—	4	2	no	—
177	C₁₃×SD₁₆	—	2	2	no	—
178	C₁₃×SD₁₆	—	4	2	no	—
179	C₁₃×SD₁₆	—	8	1	no	—
180	C₁₃×SD₁₆	—	8	1	no	—
181	C₁₃×SD₁₆	—	8	1	no	—
182	C₁₃×D₈	—	2	2	no	—
183	C₁₃×D₈	—	4	2	no	—
184	C₁₃×D₈	—	4	2	no	—
185	C₁₃×M₁₆	—	8	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	4	2	no	—
192	C₂×C₈×C₁₃	—	8	1	no	—
193	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₁₃×C₄⋊C₄	—	2	1	no	—
198	C₁₃×C₄⋊C₄	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	4	1	no	—
205	C₁₃×C₄⋊C₄	—	4	1	no	—
206	C₁₃×C₄⋊C₄	—	4	1	no	—
207	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
210	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	—	2	1	no	—
212	C₁₃×C₂²⋊C₄	—	2	1	no	—
213	C₁₃×C₂²⋊C₄	—	2	1	no	—
214	C₁₃×C₂²⋊C₄	—	4	1	no	—
215	C₁₃×C₂²⋊C₄	—	4	1	no	—
216	C₁₃×C₂²⋊C₄	—	4	1	no	—
217	C₁₃×C₂²⋊C₄	—	4	1	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
220	#3358	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3330	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#3298	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1719	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1701	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1680	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1679	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1665	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1649	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1647	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1642	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1625	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1580	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂³×C₁₃	—	2	1	no	—
236	C₂³×C₁₃	—	2	1	no	—
237	C₂³×C₁₃	—	2	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	2	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	Q₈×C₁₃	—	4	1	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	1	no	—
246	Q₈×C₁₃	—	8	2	no	—
247	Q₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
248	D₄×C₁₃	—	2	1	no	—
249	D₄×C₁₃	—	2	1	no	—
250	D₄×C₁₃	—	2	1	no	—
251	D₄×C₁₃	—	2	1	no	—
252	D₄×C₁₃	—	2	1	no	—
253	D₄×C₁₃	—	4	1	no	—
254	D₄×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	4	1	no	—
256	D₄×C₁₃	—	4	1	no	—
257	D₄×C₁₃	—	8	2	no	—
258	D₄×C₁₃	—	8	1	no	—
259	D₄×C₁₃	—	8	2	no	—
260	D₄×C₁₃	—	8	2	no	—
261	D₄×C₁₃	—	16	1	no	—
262	D₄×C₁₃	#135	1	2	yes	complemented
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	—	8	2	no	—
279	C₂×C₄×C₁₃	—	8	2	no	—
280	C₂×C₄×C₁₃	—	8	2	no	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	—	2	1	no	—
287	C₈×C₁₃	—	2	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₈×C₁₃	—	4	1	no	—
292	C₈×C₁₃	—	4	1	no	—
293	C₂×#135	—	2	1	no	—
294	#550	C₂²×C₁₃	1	1	yes	characteristic
295	D₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	#547	C₂²×C₁₃	1	1	yes	characteristic
297	#547	C₂²×C₁₃	1	1	yes	characteristic
298	#500	C₂²×C₁₃	1	1	yes	characteristic
299	#492	C₂²×C₁₃	1	1	yes	characteristic
300	#487	C₂²×C₁₃	1	1	yes	characteristic
301	#487	C₂²×C₁₃	1	1	yes	characteristic
302	#486	—	2	1	no	—
303	#486	C₂²×C₁₃	1	1	yes	characteristic
304	#486	C₂²×C₁₃	1	1	yes	characteristic
305	#484	—	2	1	no	—
306	#483	—	2	1	no	—
307	#475	C₂²×C₁₃	1	1	yes	characteristic
308	#474	—	2	1	no	—
309	#474	C₂²×C₁₃	1	1	yes	characteristic
310	#474	C₂²×C₁₃	1	1	yes	characteristic
311	#468	—	2	1	no	—
312	#465	—	2	1	no	—
313	#465	—	2	1	no	—
314	#462	C₂²×C₁₃	1	1	yes	characteristic
315	#461	C₂²×C₁₃	1	1	yes	characteristic
316	#461	C₂²×C₁₃	1	1	yes	characteristic
317	#459	—	2	1	no	—
318	#459	C₂²×C₁₃	1	1	yes	characteristic
319	#459	C₂²×C₁₃	1	1	yes	characteristic
320	#452	—	2	1	no	—
321	#449	—	2	1	no	—
322	#449	—	2	1	no	—
323	#448	—	2	1	no	—
324	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
326	C₄×D₈	—	2	1	no	—
327	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
328	#436	C₂²×C₁₃	1	1	yes	characteristic
329	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
331	#417	—	2	1	no	—
332	C₂×#103	—	2	1	no	—
333	#334	C₂²×C₁₃	1	1	yes	characteristic
334	#334	C₂²×C₁₃	1	1	yes	characteristic
335	#332	C₂²×C₁₃	1	1	yes	characteristic
336	#332	C₂²×C₁₃	1	1	yes	characteristic
337	#332	C₂²×C₁₃	1	1	yes	characteristic
338	#331	C₂²×C₁₃	1	1	yes	characteristic
339	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
343	#322	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	1	no	—
350	C₂²×C₁₃	—	4	1	no	—
351	C₂²×C₁₃	—	4	1	no	—
352	C₂²×C₁₃	—	4	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	—	8	1	no	—
355	C₂²×C₁₃	—	8	1	no	—
356	C₂²×C₁₃	D₄²	1	1	yes	characteristic
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	1	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	4	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	1	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
367	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
368	C₄×C₁₃	#576	1	1	yes	characteristic
369	C₄×C₁₃	#577	1	1	yes	characteristic
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂²×Q₈	—	2	1	no	—
374	#135	—	4	4	no	—
375	C₂×Q₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	—	2	1	no	—
378	C₂×SD₁₆	—	2	1	no	—
379	C₂×SD₁₆	—	2	1	no	—
380	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
381	C₂×D₈	—	2	1	no	—
382	C₂×D₈	—	2	1	no	—
383	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
384	C₂×M₁₆	—	2	1	no	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	1	no	—
388	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
391	#127	—	2	1	no	—
392	#127	C₂³×C₁₃	1	1	yes	characteristic
393	#123	—	4	1	no	—
394	#123	—	4	1	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	1	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	C₂²⋊Q₈	—	4	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	—	2	1	no	—
402	#121	—	4	1	no	—
403	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	—	2	1	no	—
406	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	#107	—	2	1	no	—
412	#107	—	2	1	no	—
413	#107	—	4	1	no	—
414	#107	D₄×C₁₃	1	1	yes	characteristic
415	#106	—	2	1	no	—
416	#106	D₄×C₁₃	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#103	—	2	1	no	—
427	#103	—	2	1	no	—
428	#103	—	2	1	no	—
429	#103	—	2	1	no	—
430	#103	D₄×C₁₃	1	1	yes	characteristic
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#102	—	4	1	no	—
438	#102	D₄×C₁₃	1	1	yes	characteristic
439	#102	D₄×C₁₃	1	1	yes	characteristic
440	#102	D₄×C₁₃	1	1	yes	characteristic
441	C₂²⋊C₈	—	2	1	no	—
442	C₂²⋊C₈	—	2	1	no	—
443	C₂²⋊C₈	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
447	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₁₃	—	4	2	no	—
449	C₂×C₁₃	—	8	1	no	—
450	C₂×C₁₃	—	8	1	no	—
451	C₂×C₁₃	—	16	1	no	—
452	C₂×C₁₃	#3264	1	1	yes	characteristic
453	C₂×C₁₃	#3282	1	1	yes	characteristic
454	C₂×C₁₃	#3289	1	1	yes	characteristic
455	#41	—	4	2	no	—
456	#41	—	4	2	no	—
457	#41	—	4	2	no	—
458	#41	—	8	1	no	—
459	#41	—	8	1	no	—
460	#41	—	8	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	4	1	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	8	1	no	—
467	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	4	1	no	—
472	C₂×D₄	—	4	1	no	—
473	C₂×D₄	—	4	1	no	—
474	C₂×D₄	—	4	1	no	—
475	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	Q₁₆	—	4	2	no	—
486	SD₁₆	—	2	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	8	1	no	—
489	SD₁₆	—	8	1	no	—
490	SD₁₆	—	8	1	no	—
491	D₈	—	2	2	no	—
492	D₈	—	4	2	no	—
493	D₈	—	4	2	no	—
494	M₁₆	—	8	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	4	2	no	—
501	C₂×C₈	—	8	1	no	—
502	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
505	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	4	1	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
518	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
519	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	4	1	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₂²⋊C₄	—	4	1	no	—
526	C₂²⋊C₄	—	4	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₁₃	#19820	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	4	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	4	1	no	—
536	Q₈	—	4	1	no	—
537	Q₈	—	4	1	no	—
538	Q₈	—	4	1	no	—
539	Q₈	—	4	1	no	—
540	Q₈	—	4	1	no	—
541	Q₈	—	8	2	no	—
542	Q₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	8	1	no	—
554	D₄	—	8	2	no	—
555	D₄	—	8	2	no	—
556	D₄	—	16	1	no	—
557	D₄	C₁₃×#135	1	2	yes	complemented
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	2	no	—
573	C₂×C₄	—	8	2	no	—
574	C₂×C₄	—	8	2	no	—
575	C₂×C₄	—	8	2	no	—
576	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
579	C₈	—	2	1	no	—
580	C₈	—	2	1	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	1	no	—
583	C₈	—	4	1	no	—
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	—	4	1	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	8	1	no	—
598	C₂²	—	8	1	no	—
599	C₂²	—	8	1	no	—
600	C₂²	D₄²×C₁₃	1	1	yes	characteristic
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	8	1	no	—
608	C₄	—	8	1	no	—
609	C₄	—	8	1	no	—
610	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
611	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
612	C₄	C₁₃×#576	1	1	yes	characteristic
613	C₄	C₁₃×#577	1	1	yes	characteristic
614	C₂	—	4	2	no	—
615	C₂	—	8	1	no	—
616	C₂	—	8	1	no	—
617	C₂	—	16	1	no	—
618	C₂	C₁₃×#3264	1	1	yes	characteristic
619	C₂	C₁₃×#3282	1	1	yes	characteristic
620	C₂	C₁₃×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3358	C₂	semidirect
2. C₁₃×#3330	C₂	semidirect
3. C₁₃×#3298	C₂	semidirect
4. C₁₃×#3284	C₂	semidirect
5. C₁₃×#1719	C₂	semidirect
6. C₁₃×#1701	C₂	semidirect
7. C₁₃×#1680	C₂	semidirect
8. C₁₃×#1679	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1649	C₂	semidirect
11. C₁₃×#1647	C₂	semidirect
12. C₁₃×#1642	C₂	semidirect
13. C₁₃×#1625	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×#1580	C₂	semidirect
145. #19820	C₁₃	direct (N × H)
220. #3358	C₂×C₁₃	semidirect
221. #3330	C₂×C₁₃	semidirect
222. #3298	C₂×C₁₃	semidirect
223. #3284	C₂×C₁₃	semidirect
224. #1719	C₂×C₁₃	semidirect
225. #1701	C₂×C₁₃	semidirect
226. #1680	C₂×C₁₃	semidirect
227. #1679	C₂×C₁₃	semidirect
228. #1665	C₂×C₁₃	semidirect
229. #1649	C₂×C₁₃	semidirect
230. #1647	C₂×C₁₃	semidirect
231. #1642	C₂×C₁₃	semidirect
232. #1625	C₂×C₁₃	semidirect
233. #1583	C₂×C₁₃	semidirect
234. #1580	C₂×C₁₃	semidirect
262. D₄×C₁₃	#135	semidirect
529. C₁₃	#19820	direct (N × H)
557. D₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3358	2
C₁₃×#3330	2
C₁₃×#3298	2
C₁₃×#3284	2
C₁₃×#1719	2
C₁₃×#1701	2
C₁₃×#1680	2
C₁₃×#1679	2
C₁₃×#1665	2
C₁₃×#1649	2
C₁₃×#1647	2
C₁₃×#1642	2
C₁₃×#1625	2
C₁₃×#1583	2
C₁₃×#1580	2
#19820	13

Subgroups — C13×#19820 #15706159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19820 #15706159