Subgroups — C₁₃×#19827 #15706166

Order 3328.

668 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1717	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1697	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1682	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1635	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1621	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#135	—	2	1	no	—
17	Q₈²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#550	C₂²	1	1	yes	characteristic
19	C₁₃×#550	C₂²	1	1	yes	characteristic
20	C₁₃×#547	C₂²	1	1	yes	characteristic
21	C₁₃×#493	C₂²	1	1	yes	characteristic
22	C₁₃×#492	C₂²	1	1	yes	characteristic
23	C₁₃×#487	C₂²	1	1	yes	characteristic
24	C₁₃×#486	—	2	1	no	—
25	C₁₃×#486	—	2	1	no	—
26	C₁₃×#486	C₂²	1	1	yes	characteristic
27	C₁₃×#486	C₂²	1	1	yes	characteristic
28	C₁₃×#486	C₂²	1	1	yes	characteristic
29	C₁₃×#481	—	2	1	no	—
30	C₁₃×#476	—	2	1	no	—
31	C₁₃×#476	—	2	1	no	—
32	C₁₃×#476	C₂²	1	1	yes	characteristic
33	C₁₃×#476	C₂²	1	1	yes	characteristic
34	C₁₃×#475	C₂²	1	1	yes	characteristic
35	C₁₃×#469	—	2	1	no	—
36	C₁₃×#465	—	2	1	no	—
37	C₁₃×#462	C₂²	1	1	yes	characteristic
38	C₁₃×#460	—	2	1	no	—
39	C₁₃×#460	—	2	1	no	—
40	C₁₃×#460	C₂²	1	1	yes	characteristic
41	C₁₃×#460	C₂²	1	1	yes	characteristic
42	C₁₃×#459	C₂²	1	1	yes	characteristic
43	C₁₃×#459	C₂²	1	1	yes	characteristic
44	C₁₃×#452	—	2	1	no	—
45	C₁₃×#449	—	2	1	no	—
46	C₁₃×#449	—	2	1	no	—
47	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
49	C₄×C₁₃×SD₁₆	—	2	1	no	—
50	C₄×C₁₃×SD₁₆	—	2	1	no	—
51	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
53	C₁₃×#436	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
55	C₁₃×#417	—	2	1	no	—
56	C₁₃×#335	C₂²	1	1	yes	characteristic
57	C₁₃×#334	C₂²	1	1	yes	characteristic
58	C₁₃×#333	C₂²	1	1	yes	characteristic
59	C₁₃×#332	C₂²	1	1	yes	characteristic
60	C₁₃×#331	C₂²	1	1	yes	characteristic
61	C₁₃×#331	C₂²	1	1	yes	characteristic
62	C₁₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₃×Q₈⋊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	C₁₃×#135	—	4	4	no	—
71	C₂×C₁₃×Q₁₆	—	2	1	no	—
72	C₂×C₁₃×SD₁₆	—	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	D₄	1	1	yes	characteristic
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	—	4	1	no	—
81	C₂×C₁₃×M₁₆	—	2	1	no	—
82	C₂²×C₈×C₁₃	—	2	1	no	—
83	C₁₃×C₄⋊Q₈	—	2	1	no	—
84	C₁₃×C₄⋊Q₈	—	2	1	no	—
85	C₁₃×C₄⋊Q₈	—	4	1	no	—
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	—	2	1	no	—
90	C₁₃×#127	C₂³	1	1	yes	characteristic
91	C₁₃×#127	C₂³	1	1	yes	characteristic
92	C₁₃×#123	—	4	1	no	—
93	C₁₃×C₂²⋊Q₈	—	2	1	no	—
94	C₁₃×#121	—	2	1	no	—
95	C₁₃×#121	—	2	1	no	—
96	C₁₃×#121	—	2	1	no	—
97	C₁₃×#121	—	4	1	no	—
98	C₁₃×#121	—	4	1	no	—
99	C₄×Q₈×C₁₃	—	2	1	no	—
100	C₄×Q₈×C₁₃	—	2	1	no	—
101	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₃	—	2	1	no	—
104	C₄×D₄×C₁₃	—	2	1	no	—
105	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
106	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₁₃×#106	—	2	1	no	—
109	C₁₃×#106	—	2	1	no	—
110	C₁₃×#106	—	2	1	no	—
111	C₁₃×#106	D₄	1	1	yes	characteristic
112	C₁₃×#106	D₄	1	1	yes	characteristic
113	C₁₃×C₄⋊C₈	—	2	1	no	—
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	—	4	1	no	—
122	C₁₃×#103	D₄	1	1	yes	characteristic
123	C₁₃×#103	D₄	1	1	yes	characteristic
124	C₁₃×#102	—	2	1	no	—
125	C₁₃×#102	—	2	1	no	—
126	C₁₃×#102	—	2	1	no	—
127	C₁₃×#102	—	2	1	no	—
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	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
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	C₄×C₈×C₁₃	—	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	#19827	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	—	4	1	no	—
155	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
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	—	2	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	—	4	1	no	—
167	C₂×D₄×C₁₃	—	4	1	no	—
168	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₁₃×Q₁₆	—	4	2	no	—
176	C₁₃×SD₁₆	—	2	2	no	—
177	C₁₃×SD₁₆	—	2	2	no	—
178	C₁₃×SD₁₆	—	4	2	no	—
179	C₁₃×SD₁₆	—	4	2	no	—
180	C₁₃×SD₁₆	—	4	2	no	—
181	C₁₃×SD₁₆	—	8	1	no	—
182	C₁₃×D₈	—	4	2	no	—
183	C₁₃×D₈	—	8	1	no	—
184	C₁₃×D₈	—	8	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	C₂×D₄	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	—	2	1	no	—
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	—	4	1	no	—
203	C₁₃×C₄⋊C₄	—	4	1	no	—
204	C₁₃×C₄⋊C₄	—	4	1	no	—
205	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
206	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
207	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
209	C₁₃×C₂²⋊C₄	—	2	1	no	—
210	C₁₃×C₂²⋊C₄	—	2	1	no	—
211	C₁₃×C₂²⋊C₄	—	4	1	no	—
212	C₁₃×C₂²⋊C₄	—	4	1	no	—
213	C₁₃×C₂²⋊C₄	—	4	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	4	1	no	—
217	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
218	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#3362	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#3332	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#3284	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1717	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1697	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1682	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1677	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1666	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1645	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#1635	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1621	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1621	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1583	C₂×C₁₃	1	1	yes	characteristic, complemented
232	SD₁₆⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	—	2	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	2	1	no	—
238	Q₈×C₁₃	—	2	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	4	1	no	—
241	Q₈×C₁₃	—	8	1	no	—
242	Q₈×C₁₃	—	16	1	no	—
243	Q₈×C₁₃	#135	1	2	yes	complemented
244	Q₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
245	D₄×C₁₃	—	2	1	no	—
246	D₄×C₁₃	—	2	1	no	—
247	D₄×C₁₃	—	2	1	no	—
248	D₄×C₁₃	—	2	1	no	—
249	D₄×C₁₃	—	4	1	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	D₄×C₁₃	—	4	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	2	no	—
259	D₄×C₁₃	—	8	1	no	—
260	D₄×C₁₃	—	8	1	no	—
261	D₄×C₁₃	—	8	2	no	—
262	D₄×C₁₃	—	16	1	no	—
263	D₄×C₁₃	—	16	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	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	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	—	8	2	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	—	8	2	no	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
282	C₈×C₁₃	—	2	1	no	—
283	C₈×C₁₃	—	2	1	no	—
284	C₈×C₁₃	—	2	1	no	—
285	C₈×C₁₃	—	2	1	no	—
286	C₈×C₁₃	—	4	1	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	—	4	1	no	—
290	C₈×C₁₃	—	4	1	no	—
291	C₂×#135	—	2	1	no	—
292	Q₈²	C₂²×C₁₃	1	1	yes	characteristic
293	#550	C₂²×C₁₃	1	1	yes	characteristic
294	#550	C₂²×C₁₃	1	1	yes	characteristic
295	#547	C₂²×C₁₃	1	1	yes	characteristic
296	#493	C₂²×C₁₃	1	1	yes	characteristic
297	#492	C₂²×C₁₃	1	1	yes	characteristic
298	#487	C₂²×C₁₃	1	1	yes	characteristic
299	#486	—	2	1	no	—
300	#486	—	2	1	no	—
301	#486	C₂²×C₁₃	1	1	yes	characteristic
302	#486	C₂²×C₁₃	1	1	yes	characteristic
303	#486	C₂²×C₁₃	1	1	yes	characteristic
304	#481	—	2	1	no	—
305	#476	—	2	1	no	—
306	#476	—	2	1	no	—
307	#476	C₂²×C₁₃	1	1	yes	characteristic
308	#476	C₂²×C₁₃	1	1	yes	characteristic
309	#475	C₂²×C₁₃	1	1	yes	characteristic
310	#469	—	2	1	no	—
311	#465	—	2	1	no	—
312	#462	C₂²×C₁₃	1	1	yes	characteristic
313	#460	—	2	1	no	—
314	#460	—	2	1	no	—
315	#460	C₂²×C₁₃	1	1	yes	characteristic
316	#460	C₂²×C₁₃	1	1	yes	characteristic
317	#459	C₂²×C₁₃	1	1	yes	characteristic
318	#459	C₂²×C₁₃	1	1	yes	characteristic
319	#452	—	2	1	no	—
320	#449	—	2	1	no	—
321	#449	—	2	1	no	—
322	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₄×SD₁₆	—	2	1	no	—
325	C₄×SD₁₆	—	2	1	no	—
326	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
327	C₄×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
328	#436	C₂²×C₁₃	1	1	yes	characteristic
329	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	#417	—	2	1	no	—
331	#335	C₂²×C₁₃	1	1	yes	characteristic
332	#334	C₂²×C₁₃	1	1	yes	characteristic
333	#333	C₂²×C₁₃	1	1	yes	characteristic
334	#332	C₂²×C₁₃	1	1	yes	characteristic
335	#331	C₂²×C₁₃	1	1	yes	characteristic
336	#331	C₂²×C₁₃	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
339	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
340	D₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	#322	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₁₃	—	4	1	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	—	8	1	no	—
350	C₂²×C₁₃	—	8	1	no	—
351	C₂²×C₁₃	—	8	1	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	D₄²	1	1	yes	characteristic
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	1	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	1	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	1	no	—
362	C₄×C₁₃	—	8	1	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
365	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
366	C₄×C₁₃	#577	1	1	yes	characteristic
367	C₄×C₁₃	#577	1	1	yes	characteristic
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	#135	—	4	4	no	—
372	C₂×Q₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	—	2	1	no	—
377	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
378	C₂×SD₁₆	D₄×C₁₃	1	1	yes	characteristic
379	C₂×D₈	—	2	1	no	—
380	C₂×D₈	—	2	1	no	—
381	C₂×D₈	—	4	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂²×C₈	—	2	1	no	—
384	C₄⋊Q₈	—	2	1	no	—
385	C₄⋊Q₈	—	2	1	no	—
386	C₄⋊Q₈	—	4	1	no	—
387	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
388	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
389	#127	—	2	1	no	—
390	#127	—	2	1	no	—
391	#127	C₂³×C₁₃	1	1	yes	characteristic
392	#127	C₂³×C₁₃	1	1	yes	characteristic
393	#123	—	4	1	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	1	no	—
397	#121	—	2	1	no	—
398	#121	—	4	1	no	—
399	#121	—	4	1	no	—
400	C₄×Q₈	—	2	1	no	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
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	C₂×C₄⋊C₄	—	2	1	no	—
409	#106	—	2	1	no	—
410	#106	—	2	1	no	—
411	#106	—	2	1	no	—
412	#106	D₄×C₁₃	1	1	yes	characteristic
413	#106	D₄×C₁₃	1	1	yes	characteristic
414	C₄⋊C₈	—	2	1	no	—
415	C₄⋊C₈	—	2	1	no	—
416	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
420	#103	—	2	1	no	—
421	#103	—	2	1	no	—
422	#103	—	4	1	no	—
423	#103	D₄×C₁₃	1	1	yes	characteristic
424	#103	D₄×C₁₃	1	1	yes	characteristic
425	#102	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
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	D₄×C₁₃	1	1	yes	characteristic
438	#102	D₄×C₁₃	1	1	yes	characteristic
439	C₂²⋊C₈	—	2	1	no	—
440	C₂²⋊C₈	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
444	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
446	C₂×C₁₃	—	8	1	no	—
447	C₂×C₁₃	—	8	1	no	—
448	C₂×C₁₃	—	16	1	no	—
449	C₂×C₁₃	—	16	1	no	—
450	C₂×C₁₃	#3265	1	1	yes	characteristic
451	C₂×C₁₃	#3282	1	1	yes	characteristic
452	C₂×C₁₃	#3288	1	1	yes	characteristic
453	#41	—	4	2	no	—
454	#41	—	4	2	no	—
455	#41	—	4	2	no	—
456	#41	—	8	1	no	—
457	#41	—	8	1	no	—
458	#41	—	8	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	4	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	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	Q₁₆	—	4	2	no	—
483	SD₁₆	—	2	2	no	—
484	SD₁₆	—	2	2	no	—
485	SD₁₆	—	4	2	no	—
486	SD₁₆	—	4	2	no	—
487	SD₁₆	—	4	2	no	—
488	SD₁₆	—	8	1	no	—
489	D₈	—	4	2	no	—
490	D₈	—	8	1	no	—
491	D₈	—	8	2	no	—
492	M₁₆	—	8	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	4	2	no	—
499	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	4	1	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	4	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	4	1	no	—
524	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
525	C₁₃	#19827	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	—	4	1	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	1	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	Q₈	—	8	1	no	—
535	Q₈	—	16	1	no	—
536	Q₈	C₁₃×#135	1	2	yes	complemented
537	Q₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
538	D₄	—	2	1	no	—
539	D₄	—	2	1	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	1	no	—
542	D₄	—	4	1	no	—
543	D₄	—	4	1	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	1	no	—
546	D₄	—	4	1	no	—
547	D₄	—	4	1	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	8	2	no	—
551	D₄	—	8	2	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	1	no	—
554	D₄	—	8	2	no	—
555	D₄	—	16	1	no	—
556	D₄	—	16	1	no	—
557	C₂×C₄	—	2	1	no	—
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	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	—	8	2	no	—
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
574	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
575	C₈	—	2	1	no	—
576	C₈	—	2	1	no	—
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	4	1	no	—
580	C₈	—	4	1	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	1	no	—
583	C₈	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	8	1	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	—	8	1	no	—
596	C₂²	D₄²×C₁₃	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
607	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
608	C₄	C₁₃×#577	1	1	yes	characteristic
609	C₄	C₁₃×#577	1	1	yes	characteristic
610	C₂	—	8	1	no	—
611	C₂	—	8	1	no	—
612	C₂	—	16	1	no	—
613	C₂	—	16	1	no	—
614	C₂	C₁₃×#3265	1	1	yes	characteristic
615	C₂	C₁₃×#3282	1	1	yes	characteristic
616	C₂	C₁₃×#3288	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×#3362	C₂	semidirect
2. C₁₃×#3362	C₂	semidirect
3. C₁₃×#3332	C₂	semidirect
4. C₁₃×#3284	C₂	semidirect
5. C₁₃×#1717	C₂	semidirect
6. C₁₃×#1697	C₂	semidirect
7. C₁₃×#1682	C₂	semidirect
8. C₁₃×#1677	C₂	semidirect
9. C₁₃×#1666	C₂	semidirect
10. C₁₃×#1645	C₂	semidirect
11. C₁₃×#1635	C₂	semidirect
12. C₁₃×#1621	C₂	semidirect
13. C₁₃×#1621	C₂	semidirect
14. C₁₃×#1583	C₂	semidirect
15. C₁₃×SD₁₆⋊C₈	C₂	semidirect
145. #19827	C₁₃	direct (N × H)
218. #3362	C₂×C₁₃	semidirect
219. #3362	C₂×C₁₃	semidirect
220. #3332	C₂×C₁₃	semidirect
221. #3284	C₂×C₁₃	semidirect
222. #1717	C₂×C₁₃	semidirect
223. #1697	C₂×C₁₃	semidirect
224. #1682	C₂×C₁₃	semidirect
225. #1677	C₂×C₁₃	semidirect
226. #1666	C₂×C₁₃	semidirect
227. #1645	C₂×C₁₃	semidirect
228. #1635	C₂×C₁₃	semidirect
229. #1621	C₂×C₁₃	semidirect
230. #1621	C₂×C₁₃	semidirect
231. #1583	C₂×C₁₃	semidirect
232. SD₁₆⋊C₈	C₂×C₁₃	semidirect
243. Q₈×C₁₃	#135	semidirect
525. C₁₃	#19827	direct (N × H)
536. Q₈	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×#3362	2
C₁₃×#3332	2
C₁₃×#3284	2
C₁₃×#1717	2
C₁₃×#1697	2
C₁₃×#1682	2
C₁₃×#1677	2
C₁₃×#1666	2
C₁₃×#1645	2
C₁₃×#1635	2
C₁₃×#1621	2
C₁₃×#1583	2
C₁₃×SD₁₆⋊C₈	2
#19827	13

Subgroups — C13×#19827 #15706166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19827 #15706166