Subgroups — C₁₃×#60821 #15747160

Order 3328.

2002 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3223	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3210	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3209	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3044	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3011	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₁₃×#137	C₂²	1	4	yes	—
15	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
16	C₁₃×#557	—	2	2	no	—
17	C₁₃×#556	—	2	2	no	—
18	C₁₃×#552	—	2	4	no	—
19	D₄×Q₈×C₁₃	—	2	2	no	—
20	C₁₃×#547	—	2	4	no	—
21	C₁₃×#547	—	2	2	no	—
22	C₁₃×#541	C₂²	1	4	yes	—
23	C₁₃×#536	C₂²	1	2	yes	—
24	C₁₃×#536	C₂²	1	4	yes	—
25	C₁₃×#536	C₂²	1	2	yes	—
26	C₁₃×#533	C₂²	1	4	yes	—
27	C₁₃×#533	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₁₃×#519	C₂²	1	2	yes	—
34	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
35	C₁₃×#497	C₂²	1	4	yes	—
36	C₁₃×#494	C₂²	1	4	yes	—
37	C₁₃×#494	C₂²	1	4	yes	—
38	C₁₃×#494	C₂²	1	2	yes	—
39	C₁₃×#492	C₂²	1	2	yes	—
40	C₁₃×#491	C₂²	1	4	yes	—
41	C₁₃×#488	C₂²	1	4	yes	—
42	C₁₃×#487	C₂²	1	2	yes	—
43	C₁₃×#487	C₂²	1	4	yes	—
44	C₁₃×#486	C₂²	1	2	yes	—
45	C₁₃×#464	C₂²	1	16	yes	—
46	C₁₃×#462	C₂²	1	16	yes	—
47	C₁₃×#452	C₂²	1	16	yes	—
48	C₁₃×#451	C₂²	1	16	yes	—
49	C₁₃×#433	C₂²	1	4	yes	—
50	C₁₃×#431	C₂²	1	4	yes	—
51	C₁₃×#424	C₂²	1	2	yes	—
52	C₁₃×#419	C₂²	1	4	yes	—
53	C₁₃×#416	C₂²	1	4	yes	—
54	C₁₃×#408	C₂²	1	2	yes	—
55	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×2₋¹⁺⁴	—	4	8	no	—
58	C₂×C₁₃×#41	—	2	4	no	—
59	C₂×C₁₃×#41	—	2	2	no	—
60	C₂×C₁₃×#41	C₂³	1	2	yes	—
61	C₂×C₁₃×#41	C₂³	1	4	yes	—
62	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	2	no	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
67	C₁₃×#137	—	4	8	no	—
68	C₂×C₁₃×Q₁₆	—	4	8	no	—
69	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
70	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
71	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
72	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₁₃×C₄⋊Q₈	—	2	2	no	—
75	C₁₃×C₄⋊Q₈	—	2	4	no	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
85	C₁₃×#127	C₂³	1	1	yes	characteristic
86	C₁₃×#126	—	2	8	no	—
87	C₁₃×#125	—	2	8	no	—
88	C₁₃×#125	—	2	4	no	—
89	C₁₃×#125	C₂³	1	2	yes	—
90	C₁₃×#124	—	2	2	no	—
91	C₁₃×#124	C₂³	1	4	yes	—
92	C₁₃×#124	C₂³	1	2	yes	—
93	C₁₃×#123	—	2	4	no	—
94	C₁₃×#123	—	2	4	no	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	4	no	—
99	C₁₃×C₂²⋊Q₈	—	2	8	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	4	no	—
103	C₄×Q₈×C₁₃	—	2	4	no	—
104	C₄×Q₈×C₁₃	—	2	4	no	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	D₄	1	2	yes	—
107	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	D₄	1	4	yes	—
111	C₄×D₄×C₁₃	D₄	1	2	yes	—
112	C₁₃×#117	—	2	4	no	—
113	C₁₃×#117	—	2	4	no	—
114	C₁₃×#117	C₂³	1	2	yes	—
115	C₁₃×#117	C₂³	1	1	yes	characteristic
116	C₁₃×#117	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#103	C₂³	1	16	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₁₃×#97	C₂³	1	2	yes	—
128	C₄×C₈×C₁₃	C₂³	1	2	yes	—
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	2	yes	—
131	#60821	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₁₃×#41	—	2	4	no	—
133	C₁₃×#41	—	2	8	no	—
134	C₁₃×#41	—	4	8	no	—
135	C₁₃×#41	—	4	16	no	—
136	C₁₃×#41	—	4	8	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	8	no	—
142	C₂×Q₈×C₁₃	—	2	8	no	—
143	C₂×Q₈×C₁₃	—	4	8	no	—
144	C₂×Q₈×C₁₃	—	4	8	no	—
145	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
147	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₁₃×Q₁₆	—	4	16	no	—
165	C₁₃×Q₁₆	—	4	8	no	—
166	C₁₃×SD₁₆	—	4	8	no	—
167	C₁₃×M₁₆	—	2	4	no	—
168	C₂×C₈×C₁₃	—	2	4	no	—
169	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
171	C₁₃×C₄⋊C₄	—	2	4	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	2	4	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	—	2	4	no	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	2	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	4	no	—
180	C₁₃×C₄⋊C₄	—	2	8	no	—
181	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
184	C₁₃×C₂²⋊C₄	—	2	2	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	—	2	8	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
189	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
190	C₄²×C₁₃	—	2	8	no	—
191	C₄²×C₁₃	—	2	2	no	—
192	C₄²×C₁₃	C₂×D₄	1	4	yes	—
193	C₄²×C₁₃	C₂×D₄	1	2	yes	—
194	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₄²×C₁₃	C₂⁴	1	2	yes	—
197	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
198	#3499	C₂×C₁₃	1	1	yes	characteristic
199	#3223	C₂×C₁₃	1	8	yes	complemented
200	#3210	C₂×C₁₃	1	4	yes	complemented
201	#3209	C₂×C₁₃	1	4	yes	complemented
202	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3044	C₂×C₁₃	1	4	yes	complemented
207	#3011	C₂×C₁₃	1	4	yes	complemented
208	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	8	no	—
214	Q₈×C₁₃	—	2	8	no	—
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	4	8	no	—
217	Q₈×C₁₃	—	4	4	no	—
218	Q₈×C₁₃	—	4	4	no	—
219	Q₈×C₁₃	—	4	4	no	—
220	D₄×C₁₃	—	2	4	no	—
221	D₄×C₁₃	—	2	2	no	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	4	8	no	—
224	D₄×C₁₃	—	4	4	no	—
225	D₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	8	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	—	4	4	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
244	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
245	C₈×C₁₃	—	2	4	no	—
246	C₈×C₁₃	—	2	4	no	—
247	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
248	C₂×#137	C₂²×C₁₃	1	4	yes	—
249	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
250	#557	—	2	2	no	—
251	#556	—	2	2	no	—
252	#552	—	2	4	no	—
253	D₄×Q₈	—	2	2	no	—
254	#547	—	2	4	no	—
255	#547	—	2	2	no	—
256	#541	C₂²×C₁₃	1	4	yes	—
257	#536	C₂²×C₁₃	1	4	yes	—
258	#536	C₂²×C₁₃	1	2	yes	—
259	#536	C₂²×C₁₃	1	2	yes	—
260	#533	C₂²×C₁₃	1	4	yes	—
261	#533	C₂²×C₁₃	1	1	yes	characteristic
262	#532	C₂²×C₁₃	1	1	yes	characteristic
263	#532	C₂²×C₁₃	1	2	yes	—
264	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
267	#519	C₂²×C₁₃	1	2	yes	—
268	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
269	#497	C₂²×C₁₃	1	4	yes	—
270	#494	C₂²×C₁₃	1	4	yes	—
271	#494	C₂²×C₁₃	1	4	yes	—
272	#494	C₂²×C₁₃	1	2	yes	—
273	#492	C₂²×C₁₃	1	2	yes	—
274	#491	C₂²×C₁₃	1	4	yes	—
275	#488	C₂²×C₁₃	1	4	yes	—
276	#487	C₂²×C₁₃	1	2	yes	—
277	#487	C₂²×C₁₃	1	4	yes	—
278	#486	C₂²×C₁₃	1	2	yes	—
279	#464	C₂²×C₁₃	1	16	yes	—
280	#462	C₂²×C₁₃	1	16	yes	—
281	#452	C₂²×C₁₃	1	16	yes	—
282	#451	C₂²×C₁₃	1	16	yes	—
283	#433	C₂²×C₁₃	1	4	yes	—
284	#431	C₂²×C₁₃	1	4	yes	—
285	#424	C₂²×C₁₃	1	2	yes	—
286	#419	C₂²×C₁₃	1	4	yes	—
287	#416	C₂²×C₁₃	1	4	yes	—
288	#408	C₂²×C₁₃	1	2	yes	—
289	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	#535	1	2	yes	—
297	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	—	4	2	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	#535	1	2	yes	—
306	C₄×C₁₃	#578	1	4	yes	—
307	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
308	2₋¹⁺⁴	—	4	8	no	—
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	C₂³×C₁₃	1	2	yes	—
312	C₂×#41	C₂³×C₁₃	1	4	yes	—
313	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
314	C₂²×Q₈	—	2	2	no	—
315	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
317	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
318	#137	—	4	8	no	—
319	C₂×Q₁₆	—	4	8	no	—
320	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
321	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
322	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
323	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
324	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	4	no	—
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
330	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
332	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
333	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
334	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
335	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
336	#127	C₂³×C₁₃	1	1	yes	characteristic
337	#126	—	2	8	no	—
338	#125	—	2	8	no	—
339	#125	—	2	4	no	—
340	#125	C₂³×C₁₃	1	2	yes	—
341	#124	—	2	2	no	—
342	#124	C₂³×C₁₃	1	4	yes	—
343	#124	C₂³×C₁₃	1	2	yes	—
344	#123	—	2	4	no	—
345	#123	—	2	4	no	—
346	#123	—	2	8	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	—	2	4	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	8	no	—
351	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
352	#121	—	2	2	no	—
353	#121	—	2	4	no	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	D₄×C₁₃	1	2	yes	—
358	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
359	C₄×D₄	—	2	4	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	D₄×C₁₃	1	4	yes	—
362	C₄×D₄	D₄×C₁₃	1	2	yes	—
363	#117	—	2	4	no	—
364	#117	—	2	4	no	—
365	#117	C₂³×C₁₃	1	2	yes	—
366	#117	C₂³×C₁₃	1	1	yes	characteristic
367	#117	C₂³×C₁₃	1	2	yes	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
373	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
374	#103	C₂³×C₁₃	1	8	yes	—
375	#103	C₂³×C₁₃	1	16	yes	—
376	#102	C₂³×C₁₃	1	8	yes	—
377	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
378	#97	C₂³×C₁₃	1	2	yes	—
379	C₄×C₈	C₂³×C₁₃	1	2	yes	—
380	C₄×C₈	C₂³×C₁₃	1	2	yes	—
381	C₄×C₈	C₂³×C₁₃	1	2	yes	—
382	C₂×C₁₃	—	2	2	no	—
383	C₂×C₁₃	—	4	2	no	—
384	C₂×C₁₃	—	8	2	no	—
385	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
386	C₂×C₁₃	C₂×#578	1	2	yes	—
387	#41	—	2	4	no	—
388	#41	—	2	8	no	—
389	#41	—	4	8	no	—
390	#41	—	4	16	no	—
391	#41	—	4	8	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	8	no	—
397	C₂×Q₈	—	2	8	no	—
398	C₂×Q₈	—	4	8	no	—
399	C₂×Q₈	—	4	8	no	—
400	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
402	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
403	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
409	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	Q₁₆	—	4	16	no	—
420	Q₁₆	—	4	8	no	—
421	SD₁₆	—	4	8	no	—
422	M₁₆	—	2	4	no	—
423	C₂×C₈	—	2	4	no	—
424	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
425	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	8	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
438	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
444	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
445	C₄²	—	2	8	no	—
446	C₄²	—	2	2	no	—
447	C₄²	C₂×D₄×C₁₃	1	4	yes	—
448	C₄²	C₂×D₄×C₁₃	1	2	yes	—
449	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
451	C₄²	C₂⁴×C₁₃	1	2	yes	—
452	C₁₃	#60821	1	1	yes	characteristic, direct product factor, Sylow
453	C₂³	—	2	2	no	—
454	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
455	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
456	Q₈	—	2	2	no	—
457	Q₈	—	2	8	no	—
458	Q₈	—	2	8	no	—
459	Q₈	—	2	4	no	—
460	Q₈	—	4	8	no	—
461	Q₈	—	4	4	no	—
462	Q₈	—	4	4	no	—
463	Q₈	—	4	4	no	—
464	D₄	—	2	4	no	—
465	D₄	—	2	2	no	—
466	D₄	—	2	4	no	—
467	D₄	—	4	8	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
487	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
488	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
489	C₈	—	2	4	no	—
490	C₈	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	2	no	—
496	C₂²	C₁₃×#535	1	2	yes	—
497	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
498	C₄	—	2	4	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	C₁₃×#535	1	2	yes	—
506	C₄	C₁₃×#578	1	4	yes	—
507	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
508	C₂	—	2	2	no	—
509	C₂	—	4	2	no	—
510	C₂	—	8	2	no	—
511	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
512	C₂	C₂×C₁₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3509	C₂	semidirect
3. C₁₃×#3223	C₂	semidirect
4. C₁₃×#3210	C₂	semidirect
5. C₁₃×#3209	C₂	semidirect
6. C₁₃×#3152	C₂	semidirect
7. C₂×C₁₃×#494	C₂	semidirect
8. C₁₃×#3139	C₂	semidirect
9. C₁₃×#3131	C₂	semidirect
10. C₁₃×#3044	C₂	semidirect
11. C₁₃×#3011	C₂	semidirect
12. C₁₃×#2922	C₂	semidirect
131. #60821	C₁₃	direct (N × H)
197. #3509	C₂×C₁₃	semidirect
199. #3223	C₂×C₁₃	semidirect
200. #3210	C₂×C₁₃	semidirect
201. #3209	C₂×C₁₃	semidirect
202. #3152	C₂×C₁₃	semidirect
203. C₂×#494	C₂×C₁₃	semidirect
204. #3139	C₂×C₁₃	semidirect
205. #3131	C₂×C₁₃	semidirect
206. #3044	C₂×C₁₃	semidirect
207. #3011	C₂×C₁₃	semidirect
208. #2922	C₂×C₁₃	semidirect
452. C₁₃	#60821	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×#3509	2
C₁₃×#3499	2
C₁₃×#3223	2
C₁₃×#3210	2
C₁₃×#3209	2
C₁₃×#3152	2
C₂×C₁₃×#494	2
C₁₃×#3139	2
C₁₃×#3131	2
C₁₃×#3044	2
C₁₃×#3011	2
C₁₃×#2922	2
#60821	13

Subgroups — C13×#60821 #15747160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60821 #15747160