Subgroups — C₁₃×#61081 #15747420

Order 3328.

2658 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#578	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3497	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3271	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3270	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3060	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3037	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3013	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	—
12	C₁₃×#578	—	2	16	no	—
13	C₂×C₁₃×#137	C₂²	1	4	yes	—
14	C₂×C₁₃×#137	C₂²	1	8	yes	—
15	C₂×C₁₃×#135	C₂²	1	4	yes	—
16	C₂×C₁₃×#135	C₂²	1	2	yes	—
17	C₂×C₁₃×#135	C₂²	1	2	yes	—
18	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#131	C₂²	1	2	yes	—
21	C₁₃×#550	—	2	2	no	—
22	C₁₃×#550	C₂²	1	4	yes	—
23	D₄×Q₈×C₁₃	—	2	2	no	—
24	D₄×Q₈×C₁₃	C₂²	1	4	yes	—
25	C₁₃×#548	—	2	4	no	—
26	C₁₃×#548	C₂²	1	8	yes	—
27	C₁₃×#537	—	2	4	no	—
28	C₁₃×#537	C₂²	1	4	yes	—
29	C₁₃×#532	—	2	4	no	—
30	C₁₃×#532	C₂²	1	2	yes	—
31	C₁₃×#532	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
33	C₁₃×#497	C₂²	1	4	yes	—
34	C₁₃×#496	C₂²	1	4	yes	—
35	C₁₃×#470	C₂²	1	4	yes	—
36	C₁₃×#469	C₂²	1	4	yes	—
37	C₁₃×#465	C₂²	1	8	yes	—
38	C₁₃×#464	C₂²	1	8	yes	—
39	C₁₃×#462	C₂²	1	4	yes	—
40	C₁₃×#460	C₂²	1	4	yes	—
41	C₁₃×#452	C₂²	1	8	yes	—
42	C₁₃×#451	C₂²	1	8	yes	—
43	C₁₃×#449	C₂²	1	8	yes	—
44	C₁₃×#448	C₂²	1	8	yes	—
45	C₁₃×#441	C₂²	1	8	yes	—
46	C₁₃×#435	C₂²	1	8	yes	—
47	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
48	C₁₃×#423	C₂²	1	1	yes	characteristic
49	C₁₃×#417	C₂²	1	4	yes	—
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₁₃×#408	C₂²	1	2	yes	—
52	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
53	C₁₃×2₋¹⁺⁴	—	2	16	no	—
54	C₁₃×2₋¹⁺⁴	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	8	no	—
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	C₂³	1	4	yes	—
58	C₂×C₁₃×#41	C₂³	1	8	yes	—
59	C₂×C₁₃×#41	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₃	—	2	4	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₁₃×#137	—	2	16	no	—
64	C₁₃×#137	—	2	32	no	—
65	C₁₃×#135	—	2	16	no	—
66	C₁₃×#135	—	2	8	no	—
67	C₁₃×#135	—	4	4	no	—
68	C₂×C₁₃×Q₁₆	—	2	16	no	—
69	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
70	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
77	C₂×C₁₃×D₈	C₂³	1	2	yes	—
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₁₃×#131	—	2	8	no	—
80	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
81	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
82	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊Q₈	—	2	4	no	—
86	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
88	C₁₃×#127	—	2	4	no	—
89	C₁₃×#127	D₄	1	1	yes	characteristic
90	C₁₃×#127	C₂³	1	2	yes	—
91	C₁₃×#124	—	2	8	no	—
92	C₁₃×#124	D₄	1	2	yes	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×C₂²⋊Q₈	—	2	4	no	—
95	C₁₃×C₂²⋊Q₈	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
98	C₁₃×#121	—	2	8	no	—
99	C₁₃×#121	—	2	8	no	—
100	C₁₃×#121	—	2	4	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	2	no	—
103	C₁₃×#121	—	2	8	no	—
104	C₁₃×#121	D₄	1	4	yes	—
105	C₁₃×#121	C₂³	1	8	yes	—
106	C₄×Q₈×C₁₃	—	2	2	no	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
109	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	4	no	—
112	C₄×D₄×C₁₃	—	2	8	no	—
113	C₄×D₄×C₁₃	—	2	2	no	—
114	C₄×D₄×C₁₃	—	2	2	no	—
115	C₄×D₄×C₁₃	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	—	2	2	no	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₁₃×#106	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
122	C₁₃×#103	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	8	yes	—
125	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
126	C₁₃×#97	C₂³	1	4	yes	—
127	#61081	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₁₃×#41	—	2	4	no	—
129	C₁₃×#41	—	2	4	no	—
130	C₁₃×#41	—	2	16	no	—
131	C₁₃×#41	—	2	8	no	—
132	C₁₃×#41	—	2	8	no	—
133	C₁₃×#41	—	4	8	no	—
134	C₁₃×#41	—	4	32	no	—
135	C₁₃×#41	—	4	16	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	8	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	16	no	—
140	C₂×Q₈×C₁₃	—	4	8	no	—
141	C₂×Q₈×C₁₃	—	4	16	no	—
142	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
143	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
145	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	8	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
152	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	8	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	8	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×Q₁₆	—	2	16	no	—
164	C₁₃×Q₁₆	—	2	4	no	—
165	C₁₃×Q₁₆	—	4	2	no	—
166	C₁₃×Q₁₆	C₂×D₄	1	16	yes	—
167	C₁₃×SD₁₆	—	2	16	no	—
168	C₁₃×SD₁₆	—	2	8	no	—
169	C₁₃×SD₁₆	—	4	4	no	—
170	C₁₃×D₈	—	2	4	no	—
171	C₁₃×D₈	—	4	2	no	—
172	C₁₃×M₁₆	—	2	4	no	—
173	C₁₃×M₁₆	—	2	8	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	8	no	—
176	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
177	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
178	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
179	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	2	no	—
183	C₁₃×C₄⋊C₄	—	2	2	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	—	2	8	no	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
193	C₄²×C₁₃	—	2	4	no	—
194	C₄²×C₁₃	—	2	4	no	—
195	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₁₃	C₂⁴	1	2	yes	—
198	C₂×#578	C₂×C₁₃	1	2	yes	complemented
199	#3497	C₂×C₁₃	1	2	yes	complemented
200	#3271	C₂×C₁₃	1	8	yes	complemented
201	#3270	C₂×C₁₃	1	8	yes	complemented
202	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#3060	C₂×C₁₃	1	2	yes	complemented
204	#3037	C₂×C₁₃	1	2	yes	complemented
205	#3013	C₂×C₁₃	1	4	yes	complemented
206	C₂×#441	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2932	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	4	no	—
209	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	8	no	—
212	Q₈×C₁₃	—	2	4	no	—
213	Q₈×C₁₃	—	2	4	no	—
214	Q₈×C₁₃	—	2	4	no	—
215	Q₈×C₁₃	—	2	4	no	—
216	Q₈×C₁₃	—	4	16	no	—
217	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
218	D₄×C₁₃	—	2	8	no	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	—	2	4	no	—
221	D₄×C₁₃	—	2	4	no	—
222	D₄×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	4	16	no	—
224	D₄×C₁₃	—	4	4	no	—
225	D₄×C₁₃	—	4	8	no	—
226	D₄×C₁₃	—	8	2	no	—
227	D₄×C₁₃	—	8	8	no	—
228	C₂×C₄×C₁₃	—	2	8	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	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	16	no	—
236	C₂×C₄×C₁₃	—	4	16	no	—
237	C₂×C₄×C₁₃	—	4	8	no	—
238	C₂×C₄×C₁₃	—	8	2	no	—
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	4	yes	—
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
246	C₈×C₁₃	—	2	4	no	—
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	C₂²×D₄	1	4	yes	—
249	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	—
250	#578	—	2	16	no	—
251	C₂×#137	C₂²×C₁₃	1	4	yes	—
252	C₂×#137	C₂²×C₁₃	1	8	yes	—
253	C₂×#135	C₂²×C₁₃	1	2	yes	—
254	C₂×#135	C₂²×C₁₃	1	4	yes	—
255	C₂×#135	C₂²×C₁₃	1	2	yes	—
256	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
257	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#131	C₂²×C₁₃	1	2	yes	—
259	#550	—	2	2	no	—
260	#550	C₂²×C₁₃	1	4	yes	—
261	D₄×Q₈	—	2	2	no	—
262	D₄×Q₈	C₂²×C₁₃	1	4	yes	—
263	#548	—	2	4	no	—
264	#548	C₂²×C₁₃	1	8	yes	—
265	#537	—	2	4	no	—
266	#537	C₂²×C₁₃	1	4	yes	—
267	#532	—	2	4	no	—
268	#532	C₂²×C₁₃	1	2	yes	—
269	#532	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
271	#497	C₂²×C₁₃	1	4	yes	—
272	#496	C₂²×C₁₃	1	4	yes	—
273	#470	C₂²×C₁₃	1	4	yes	—
274	#469	C₂²×C₁₃	1	4	yes	—
275	#465	C₂²×C₁₃	1	8	yes	—
276	#464	C₂²×C₁₃	1	8	yes	—
277	#462	C₂²×C₁₃	1	4	yes	—
278	#460	C₂²×C₁₃	1	4	yes	—
279	#452	C₂²×C₁₃	1	8	yes	—
280	#451	C₂²×C₁₃	1	8	yes	—
281	#449	C₂²×C₁₃	1	8	yes	—
282	#448	C₂²×C₁₃	1	8	yes	—
283	#441	C₂²×C₁₃	1	8	yes	—
284	#435	C₂²×C₁₃	1	8	yes	—
285	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
286	#423	C₂²×C₁₃	1	1	yes	characteristic
287	#417	C₂²×C₁₃	1	4	yes	—
288	C₂×#103	C₂²×C₁₃	1	2	yes	—
289	#408	C₂²×C₁₃	1	2	yes	—
290	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	8	no	—
293	C₂²×C₁₃	—	2	4	no	—
294	C₂²×C₁₃	—	4	4	no	—
295	C₂²×C₁₃	—	4	4	no	—
296	C₂²×C₁₃	—	4	4	no	—
297	C₂²×C₁₃	D₄²	1	2	yes	—
298	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	8	no	—
302	C₄×C₁₃	—	2	4	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	D₄²	1	2	yes	—
306	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
307	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
308	2₋¹⁺⁴	—	2	16	no	—
309	2₋¹⁺⁴	—	4	8	no	—
310	C₂×#41	—	2	8	no	—
311	C₂×#41	—	2	4	no	—
312	C₂×#41	C₂³×C₁₃	1	4	yes	—
313	C₂×#41	C₂³×C₁₃	1	8	yes	—
314	C₂×#41	C₂³×C₁₃	1	2	yes	—
315	C₂²×Q₈	—	2	4	no	—
316	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
317	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
318	#137	—	2	16	no	—
319	#137	—	2	32	no	—
320	#135	—	2	16	no	—
321	#135	—	2	8	no	—
322	#135	—	4	4	no	—
323	C₂×Q₁₆	—	2	16	no	—
324	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
325	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
326	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
327	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
328	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
329	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
330	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
331	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
332	C₂×D₈	C₂³×C₁₃	1	2	yes	—
333	C₂×D₈	C₂³×C₁₃	1	2	yes	—
334	#131	—	2	8	no	—
335	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
336	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
337	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₄⋊Q₈	—	2	4	no	—
341	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
342	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
343	#127	—	2	4	no	—
344	#127	D₄×C₁₃	1	1	yes	characteristic
345	#127	C₂³×C₁₃	1	2	yes	—
346	#124	—	2	8	no	—
347	#124	D₄×C₁₃	1	2	yes	—
348	#124	C₂³×C₁₃	1	4	yes	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	8	no	—
351	C₂²⋊Q₈	—	2	8	no	—
352	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
353	#121	—	2	8	no	—
354	#121	—	2	8	no	—
355	#121	—	2	4	no	—
356	#121	—	2	2	no	—
357	#121	—	2	2	no	—
358	#121	—	2	8	no	—
359	#121	D₄×C₁₃	1	4	yes	—
360	#121	C₂³×C₁₃	1	8	yes	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
364	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	4	no	—
367	C₄×D₄	—	2	8	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	C₂³×C₁₃	1	4	yes	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
373	C₂×C₄²	—	2	2	no	—
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	#106	C₂³×C₁₃	1	4	yes	—
376	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
377	#103	C₂³×C₁₃	1	8	yes	—
378	#103	C₂³×C₁₃	1	8	yes	—
379	#102	C₂³×C₁₃	1	8	yes	—
380	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
381	#97	C₂³×C₁₃	1	4	yes	—
382	C₂×C₁₃	—	2	2	no	—
383	C₂×C₁₃	—	4	4	no	—
384	C₂×C₁₃	—	8	4	no	—
385	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
386	C₂×C₁₃	#3586	1	2	yes	—
387	#41	—	2	4	no	—
388	#41	—	2	4	no	—
389	#41	—	2	16	no	—
390	#41	—	2	8	no	—
391	#41	—	2	8	no	—
392	#41	—	4	8	no	—
393	#41	—	4	32	no	—
394	#41	—	4	16	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	8	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	16	no	—
399	C₂×Q₈	—	4	8	no	—
400	C₂×Q₈	—	4	16	no	—
401	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
402	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
403	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
404	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
411	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
412	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
422	Q₁₆	—	2	16	no	—
423	Q₁₆	—	2	4	no	—
424	Q₁₆	—	4	2	no	—
425	Q₁₆	C₂×D₄×C₁₃	1	16	yes	—
426	SD₁₆	—	2	16	no	—
427	SD₁₆	—	2	8	no	—
428	SD₁₆	—	4	4	no	—
429	D₈	—	2	4	no	—
430	D₈	—	4	2	no	—
431	M₁₆	—	2	4	no	—
432	M₁₆	—	2	8	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	8	no	—
435	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
436	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
437	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
438	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
452	C₄²	—	2	4	no	—
453	C₄²	—	2	4	no	—
454	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
455	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₄²	C₂⁴×C₁₃	1	2	yes	—
457	C₁₃	#61081	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	4	no	—
459	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
460	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
461	Q₈	—	2	8	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	4	16	no	—
467	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
468	D₄	—	2	8	no	—
469	D₄	—	2	4	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	4	4	no	—
473	D₄	—	4	16	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	8	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	8	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
490	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
492	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
494	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
496	C₈	—	2	4	no	—
497	C₈	—	2	2	no	—
498	C₈	C₂²×D₄×C₁₃	1	4	yes	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	D₄²×C₁₃	1	2	yes	—
506	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	8	no	—
510	C₄	—	2	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₄	D₄²×C₁₃	1	2	yes	—
514	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
515	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂	—	2	2	no	—
517	C₂	—	4	4	no	—
518	C₂	—	8	4	no	—
519	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
520	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#578	C₂	semidirect
2. C₁₃×#3497	C₂	semidirect
3. C₁₃×#3271	C₂	semidirect
4. C₁₃×#3270	C₂	semidirect
5. C₁₃×#3150	C₂	semidirect
6. C₁₃×#3060	C₂	semidirect
7. C₁₃×#3037	C₂	semidirect
8. C₁₃×#3013	C₂	semidirect
9. C₂×C₁₃×#441	C₂	semidirect
10. C₁₃×#2932	C₂	semidirect
69. C₂×C₁₃×Q₁₆	D₄	semidirect
127. #61081	C₁₃	direct (N × H)
198. C₂×#578	C₂×C₁₃	semidirect
199. #3497	C₂×C₁₃	semidirect
200. #3271	C₂×C₁₃	semidirect
201. #3270	C₂×C₁₃	semidirect
202. #3150	C₂×C₁₃	semidirect
203. #3060	C₂×C₁₃	semidirect
204. #3037	C₂×C₁₃	semidirect
205. #3013	C₂×C₁₃	semidirect
206. C₂×#441	C₂×C₁₃	semidirect
207. #2932	C₂×C₁₃	semidirect
324. C₂×Q₁₆	D₄×C₁₃	semidirect
457. C₁₃	#61081	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×#578	2
C₁₃×#3497	2
C₁₃×#3271	2
C₁₃×#3270	2
C₁₃×#3150	2
C₁₃×#3060	2
C₁₃×#3037	2
C₁₃×#3013	2
C₂×C₁₃×#441	2
C₁₃×#2932	2
#61081	13

Subgroups — C13×#61081 #15747420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61081 #15747420