Subgroups — C₁₃×#60920 #15747259

Order 3328.

1886 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3260	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3259	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3257	C₂	1	8	yes	maximal, complemented
6	C₁₃×#3080	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3077	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3055	C₂	1	4	yes	maximal, complemented
9	C₁₃×#3038	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₁₃×#542	C₂²	1	4	yes	complemented
15	C₁₃×#541	C₂²	1	2	yes	complemented
16	C₁₃×#540	—	2	4	no	—
17	C₁₃×#540	C₂²	1	4	yes	—
18	C₁₃×#540	C₂²	1	4	yes	—
19	C₁₃×#540	C₂²	1	2	yes	complemented
20	C₁₃×#539	—	2	2	no	—
21	C₁₃×#538	—	2	2	no	—
22	C₁₃×#533	C₂²	1	1	yes	characteristic
23	C₁₃×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
25	C₁₃×#529	—	2	4	no	—
26	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₁₃×#525	C₂²	1	2	yes	—
28	C₂×C₁₃×#123	—	2	2	no	—
29	C₂×C₁₃×#121	—	2	2	no	—
30	C₂×C₁₃×#121	C₂²	1	2	yes	—
31	C₄×C₁₃×#41	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₁₃×#479	C₂²	1	8	yes	complemented
35	C₁₃×#478	C₂²	1	8	yes	complemented
36	C₁₃×#478	C₂²	1	8	yes	complemented
37	C₁₃×#476	C₂²	1	4	yes	complemented
38	C₁₃×#474	C₂²	1	4	yes	complemented
39	C₁₃×#469	C₂²	1	8	yes	complemented
40	C₁₃×#468	C₂²	1	8	yes	complemented
41	C₁₃×#466	C₂²	1	8	yes	complemented
42	C₁₃×#465	C₂²	1	8	yes	complemented
43	C₁₃×#463	C₂²	1	8	yes	complemented
44	C₁₃×#461	C₂²	1	4	yes	complemented
45	C₁₃×#460	C₂²	1	8	yes	complemented
46	C₁₃×#459	C₂²	1	4	yes	complemented
47	C₁₃×#459	C₂²	1	8	yes	complemented
48	C₁₃×#428	C₂²	1	4	yes	—
49	C₁₃×#424	C₂²	1	4	yes	complemented
50	C₁₃×#424	C₂²	1	4	yes	complemented
51	C₁₃×#423	C₂²	1	2	yes	—
52	C₁₃×#423	C₂²	1	2	yes	—
53	C₁₃×#418	C₂²	1	4	yes	—
54	C₁₃×#417	C₂²	1	4	yes	—
55	C₂×C₁₃×#41	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	—	2	2	no	—
57	C₂²×D₄×C₁₃	—	2	2	no	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	—	2	2	no	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
62	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
63	C₂×C₁₃×D₈	C₂³	1	8	yes	—
64	C₂×C₁₃×M₁₆	—	4	4	no	—
65	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
66	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₁₃×#127	—	2	2	no	—
71	C₁₃×#127	C₂³	1	1	yes	characteristic
72	C₁₃×#127	C₂³	1	4	yes	—
73	C₁₃×#126	—	2	4	no	—
74	C₁₃×#126	—	2	4	no	—
75	C₁₃×#125	—	2	4	no	—
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	C₂³	1	2	yes	—
78	C₁₃×#125	C₂³	1	4	yes	—
79	C₁₃×#124	—	2	4	no	—
80	C₁₃×#124	C₂³	1	2	yes	—
81	C₁₃×#123	—	2	2	no	—
82	C₁₃×#123	—	2	8	no	—
83	C₁₃×#123	—	2	8	no	—
84	C₁₃×#123	—	2	4	no	—
85	C₁₃×#123	—	2	4	no	—
86	C₁₃×C₂²⋊Q₈	—	2	2	no	—
87	C₁₃×C₂²⋊Q₈	—	2	4	no	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
89	C₁₃×#121	—	2	4	no	—
90	C₁₃×#121	—	2	2	no	—
91	C₁₃×#121	—	2	8	no	—
92	C₁₃×#121	—	2	8	no	—
93	C₁₃×#121	—	2	4	no	—
94	C₁₃×#121	C₂³	1	8	yes	—
95	C₁₃×#121	C₂³	1	4	yes	—
96	C₁₃×#120	—	2	2	no	—
97	C₄×Q₈×C₁₃	—	2	2	no	—
98	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
99	C₄×D₄×C₁₃	—	2	4	no	—
100	C₄×D₄×C₁₃	—	2	4	no	—
101	C₄×D₄×C₁₃	—	2	2	no	—
102	C₄×D₄×C₁₃	—	2	2	no	—
103	C₄×D₄×C₁₃	—	2	2	no	—
104	C₄×D₄×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	C₂³	1	4	yes	—
106	C₄×D₄×C₁₃	C₂³	1	4	yes	—
107	C₁₃×#117	—	2	2	no	—
108	C₁₃×#117	D₄	1	4	yes	—
109	C₁₃×#117	C₂³	1	2	yes	—
110	C₁₃×#117	C₂³	1	2	yes	—
111	C₁₃×#117	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
118	C₂×C₄²×C₁₃	—	2	2	no	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	C₂³	1	8	yes	—
122	C₁₃×#106	C₂³	1	8	yes	—
123	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
124	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
125	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
126	C₁₃×#103	C₂³	1	8	yes	—
127	C₁₃×#102	C₂³	1	8	yes	—
128	C₁₃×#102	C₂³	1	8	yes	—
129	C₁₃×#102	C₂³	1	8	yes	—
130	#60920	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₁₃×#41	—	2	4	no	—
134	C₁₃×#41	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	2	4	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	2	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	4	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	8	4	no	—
146	C₂×D₄×C₁₃	—	8	4	no	—
147	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	8	4	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₁₃×SD₁₆	—	4	8	no	—
164	C₁₃×D₈	—	4	8	no	—
165	C₁₃×M₁₆	—	2	8	no	—
166	C₁₃×M₁₆	—	4	4	no	—
167	C₂×C₈×C₁₃	—	4	4	no	—
168	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
169	C₁₃×C₄⋊C₄	—	2	8	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
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	4	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
180	C₁₃×C₂²⋊C₄	—	2	2	no	—
181	C₁₃×C₂²⋊C₄	—	2	4	no	—
182	C₁₃×C₂²⋊C₄	—	2	4	no	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	4	no	—
186	C₁₃×C₂²⋊C₄	—	2	4	no	—
187	C₁₃×C₂²⋊C₄	—	2	4	no	—
188	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
189	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	4	no	—
192	C₄²×C₁₃	C₂×D₄	1	2	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	#3455	C₂×C₁₃	1	1	yes	characteristic, complemented
198	C₂×#540	C₂×C₁₃	1	1	yes	characteristic, complemented
199	#3260	C₂×C₁₃	1	4	yes	complemented
200	#3259	C₂×C₁₃	1	4	yes	complemented
201	#3257	C₂×C₁₃	1	8	yes	complemented
202	#3080	C₂×C₁₃	1	2	yes	complemented
203	#3077	C₂×C₁₃	1	2	yes	complemented
204	#3055	C₂×C₁₃	1	4	yes	complemented
205	#3038	C₂×C₁₃	1	2	yes	complemented
206	#3036	C₂×C₁₃	1	2	yes	complemented
207	#2905	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	4	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	—	4	4	no	—
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	8	2	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	2	4	no	—
222	D₄×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	2	2	no	—
224	D₄×C₁₃	—	4	4	no	—
225	D₄×C₁₃	—	4	4	no	—
226	D₄×C₁₃	—	8	2	no	—
227	D₄×C₁₃	—	8	8	no	—
228	D₄×C₁₃	—	8	4	no	—
229	D₄×C₁₃	—	8	8	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	4	no	—
240	C₂×C₄×C₁₃	—	4	4	no	—
241	C₂×C₄×C₁₃	—	8	4	no	—
242	C₂×C₄×C₁₃	—	8	4	no	—
243	C₂×C₄×C₁₃	—	8	4	no	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
250	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
252	C₈×C₁₃	—	2	8	no	—
253	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
254	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
255	#542	C₂²×C₁₃	1	4	yes	complemented
256	#541	C₂²×C₁₃	1	2	yes	complemented
257	#540	—	2	4	no	—
258	#540	C₂²×C₁₃	1	4	yes	—
259	#540	C₂²×C₁₃	1	4	yes	—
260	#540	C₂²×C₁₃	1	2	yes	complemented
261	#539	—	2	2	no	—
262	#538	—	2	2	no	—
263	#533	C₂²×C₁₃	1	1	yes	characteristic
264	#532	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
266	#529	—	2	4	no	—
267	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
268	#525	C₂²×C₁₃	1	2	yes	—
269	C₂×#123	—	2	2	no	—
270	C₂×#121	—	2	2	no	—
271	C₂×#121	C₂²×C₁₃	1	2	yes	—
272	C₄×#41	C₂²×C₁₃	1	2	yes	—
273	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
274	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
275	#479	C₂²×C₁₃	1	8	yes	complemented
276	#478	C₂²×C₁₃	1	8	yes	complemented
277	#478	C₂²×C₁₃	1	8	yes	complemented
278	#476	C₂²×C₁₃	1	4	yes	complemented
279	#474	C₂²×C₁₃	1	4	yes	complemented
280	#469	C₂²×C₁₃	1	8	yes	complemented
281	#468	C₂²×C₁₃	1	8	yes	complemented
282	#466	C₂²×C₁₃	1	8	yes	complemented
283	#465	C₂²×C₁₃	1	8	yes	complemented
284	#463	C₂²×C₁₃	1	8	yes	complemented
285	#461	C₂²×C₁₃	1	4	yes	complemented
286	#460	C₂²×C₁₃	1	8	yes	complemented
287	#459	C₂²×C₁₃	1	8	yes	complemented
288	#459	C₂²×C₁₃	1	4	yes	complemented
289	#428	C₂²×C₁₃	1	4	yes	—
290	#424	C₂²×C₁₃	1	4	yes	complemented
291	#424	C₂²×C₁₃	1	4	yes	complemented
292	#423	C₂²×C₁₃	1	2	yes	—
293	#423	C₂²×C₁₃	1	2	yes	—
294	#418	C₂²×C₁₃	1	4	yes	—
295	#417	C₂²×C₁₃	1	4	yes	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	4	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	4	no	—
301	C₂²×C₁₃	—	4	4	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	8	2	no	—
305	C₂²×C₁₃	—	8	8	no	—
306	C₂²×C₁₃	#537	1	2	yes	—
307	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	—	4	2	no	—
315	C₄×C₁₃	#537	1	2	yes	—
316	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
317	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
318	C₂×#41	C₂³×C₁₃	1	2	yes	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	AGL(1,ℤ/8)	—	4	8	no	—
325	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
326	C₂×D₈	C₂³×C₁₃	1	8	yes	—
327	C₂×M₁₆	—	4	4	no	—
328	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
329	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
330	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
331	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
332	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
333	#127	—	2	2	no	—
334	#127	C₂³×C₁₃	1	4	yes	—
335	#127	C₂³×C₁₃	1	1	yes	characteristic
336	#126	—	2	4	no	—
337	#126	—	2	4	no	—
338	#125	—	2	4	no	—
339	#125	—	2	2	no	—
340	#125	C₂³×C₁₃	1	4	yes	—
341	#125	C₂³×C₁₃	1	2	yes	—
342	#124	—	2	4	no	—
343	#124	C₂³×C₁₃	1	2	yes	—
344	#123	—	2	2	no	—
345	#123	—	2	8	no	—
346	#123	—	2	8	no	—
347	#123	—	2	4	no	—
348	#123	—	2	4	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
352	#121	—	2	4	no	—
353	#121	—	2	2	no	—
354	#121	—	2	8	no	—
355	#121	—	2	8	no	—
356	#121	—	2	4	no	—
357	#121	C₂³×C₁₃	1	8	yes	—
358	#121	C₂³×C₁₃	1	4	yes	—
359	#120	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
362	C₄×D₄	—	2	4	no	—
363	C₄×D₄	—	2	4	no	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	C₂³×C₁₃	1	4	yes	—
368	C₄×D₄	C₂³×C₁₃	1	4	yes	—
369	C₄×D₄	C₂³×C₁₃	1	4	yes	—
370	#117	—	2	2	no	—
371	#117	D₄×C₁₃	1	4	yes	—
372	#117	C₂³×C₁₃	1	2	yes	—
373	#117	C₂³×C₁₃	1	2	yes	—
374	#117	C₂³×C₁₃	1	2	yes	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
381	C₂×C₄²	—	2	2	no	—
382	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
384	#107	C₂³×C₁₃	1	8	yes	—
385	#106	C₂³×C₁₃	1	8	yes	—
386	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
387	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
388	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
389	#103	C₂³×C₁₃	1	8	yes	—
390	#102	C₂³×C₁₃	1	8	yes	—
391	#102	C₂³×C₁₃	1	8	yes	—
392	#102	C₂³×C₁₃	1	8	yes	—
393	C₂×C₁₃	—	2	2	no	—
394	C₂×C₁₃	—	4	2	no	—
395	C₂×C₁₃	—	8	2	no	—
396	C₂×C₁₃	—	8	4	no	—
397	C₂×C₁₃	C₂×#537	1	1	yes	characteristic
398	C₂×C₁₃	#3585	1	2	yes	—
399	C₂⁴	—	2	2	no	—
400	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
401	#41	—	2	4	no	—
402	#41	—	2	4	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	8	4	no	—
414	C₂×D₄	—	8	4	no	—
415	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
416	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	8	4	no	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
431	SD₁₆	—	4	8	no	—
432	D₈	—	4	8	no	—
433	M₁₆	—	2	8	no	—
434	M₁₆	—	4	4	no	—
435	C₂×C₈	—	4	4	no	—
436	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
445	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
447	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
448	C₂²⋊C₄	—	2	2	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
457	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	4	no	—
460	C₄²	C₂×D₄×C₁₃	1	2	yes	—
461	C₄²	C₂×D₄×C₁₃	1	2	yes	—
462	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₄²	C₂⁴×C₁₃	1	2	yes	—
465	C₁₃	#60920	1	1	yes	characteristic, direct product factor, Sylow
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	4	no	—
473	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
474	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	Q₈	—	2	2	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	8	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	2	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	8	8	no	—
485	D₄	—	8	2	no	—
486	D₄	—	8	8	no	—
487	D₄	—	8	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	8	4	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
506	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
508	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
509	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
510	C₈	—	2	8	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	4	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	8	no	—
521	C₂²	C₁₃×#537	1	2	yes	—
522	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	4	no	—
526	C₄	—	2	2	no	—
527	C₄	—	4	4	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	2	no	—
530	C₄	C₁₃×#537	1	2	yes	—
531	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
532	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂	—	2	2	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	4	no	—
536	C₂	—	8	2	no	—
537	C₂	C₂×C₁₃×#537	1	1	yes	characteristic
538	C₂	C₁₃×#3585	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 ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3455	C₂	semidirect
2. C₂×C₁₃×#540	C₂	semidirect
3. C₁₃×#3260	C₂	semidirect
4. C₁₃×#3259	C₂	semidirect
5. C₁₃×#3257	C₂	semidirect
6. C₁₃×#3080	C₂	semidirect
7. C₁₃×#3077	C₂	semidirect
8. C₁₃×#3055	C₂	semidirect
9. C₁₃×#3038	C₂	semidirect
10. C₁₃×#3036	C₂	semidirect
11. C₁₃×#2905	C₂	semidirect
14. C₁₃×#542	C₂²	semidirect
15. C₁₃×#541	C₂²	semidirect
19. C₁₃×#540	C₂²	semidirect
34. C₁₃×#479	C₂²	semidirect
35. C₁₃×#478	C₂²	semidirect
36. C₁₃×#478	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#474	C₂²	semidirect
39. C₁₃×#469	C₂²	semidirect
40. C₁₃×#468	C₂²	semidirect
41. C₁₃×#466	C₂²	semidirect
42. C₁₃×#465	C₂²	semidirect
43. C₁₃×#463	C₂²	semidirect
44. C₁₃×#461	C₂²	semidirect
45. C₁₃×#460	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
47. C₁₃×#459	C₂²	semidirect
49. C₁₃×#424	C₂²	semidirect
50. C₁₃×#424	C₂²	semidirect
130. #60920	C₁₃	direct (N × H)
197. #3455	C₂×C₁₃	semidirect
198. C₂×#540	C₂×C₁₃	semidirect
199. #3260	C₂×C₁₃	semidirect
200. #3259	C₂×C₁₃	semidirect
201. #3257	C₂×C₁₃	semidirect
202. #3080	C₂×C₁₃	semidirect
203. #3077	C₂×C₁₃	semidirect
204. #3055	C₂×C₁₃	semidirect
205. #3038	C₂×C₁₃	semidirect
206. #3036	C₂×C₁₃	semidirect
207. #2905	C₂×C₁₃	semidirect
255. #542	C₂²×C₁₃	semidirect
256. #541	C₂²×C₁₃	semidirect
260. #540	C₂²×C₁₃	semidirect
275. #479	C₂²×C₁₃	semidirect
276. #478	C₂²×C₁₃	semidirect
277. #478	C₂²×C₁₃	semidirect
278. #476	C₂²×C₁₃	semidirect
279. #474	C₂²×C₁₃	semidirect
280. #469	C₂²×C₁₃	semidirect
281. #468	C₂²×C₁₃	semidirect
282. #466	C₂²×C₁₃	semidirect
283. #465	C₂²×C₁₃	semidirect
284. #463	C₂²×C₁₃	semidirect
285. #461	C₂²×C₁₃	semidirect
286. #460	C₂²×C₁₃	semidirect
287. #459	C₂²×C₁₃	semidirect
288. #459	C₂²×C₁₃	semidirect
290. #424	C₂²×C₁₃	semidirect
291. #424	C₂²×C₁₃	semidirect
465. C₁₃	#60920	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×#3455	2
C₂×C₁₃×#540	2
C₁₃×#3260	2
C₁₃×#3259	2
C₁₃×#3257	2
C₁₃×#3080	2
C₁₃×#3077	2
C₁₃×#3055	2
C₁₃×#3038	2
C₁₃×#3036	2
C₁₃×#2905	2
#60920	13

Subgroups — C13×#60920 #15747259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60920 #15747259