Subgroups — C₁₃×#14054 #15700393

Order 3328.

1566 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1445	C₂	1	2	yes	maximal
5	C₁₃×#1441	C₂	1	2	yes	maximal
6	C₁₃×#1436	C₂	1	2	yes	maximal
7	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₁₃×C₄⋊#95	C₂	1	2	yes	maximal
9	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	—	2	4	no	—
13	C₂×C₁₃×#125	—	2	4	no	—
14	C₂×C₁₃×#125	C₄	1	8	yes	complemented
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×#389	—	2	4	no	—
27	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
28	C₂×C₁₃×#95	C₂²	1	2	yes	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#125	—	2	32	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
71	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
72	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
73	C₂×C₄²×C₁₃	—	2	2	no	—
74	C₂×C₄²×C₁₃	—	2	2	no	—
75	C₂×C₄²×C₁₃	—	2	2	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	4	no	—
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	—	2	4	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	4	2	no	—
83	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
84	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
85	C₁₃×#95	—	2	4	no	—
86	C₁₃×#95	—	2	4	no	—
87	C₁₃×#95	—	2	2	no	—
88	C₁₃×#95	—	2	4	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	—	2	4	no	—
93	C₁₃×#95	—	4	2	no	—
94	C₁₃×#95	—	4	2	no	—
95	C₁₃×#95	—	4	2	no	—
96	C₁₃×#95	—	4	2	no	—
97	#14054	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
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	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
170	C₂²×C₄×C₁₃	#41	1	2	yes	—
171	C₂²×C₄×C₁₃	#41	1	2	yes	—
172	C₂²×C₄×C₁₃	#41	1	2	yes	—
173	C₂²×C₄×C₁₃	#41	1	2	yes	—
174	C₂²×C₄×C₁₃	#41	1	2	yes	—
175	C₂²×C₄×C₁₃	#41	1	2	yes	—
176	C₁₃×C₄⋊C₄	—	2	16	no	—
177	C₁₃×C₄⋊C₄	—	2	16	no	—
178	C₁₃×C₄⋊C₄	—	2	8	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	4	8	no	—
181	C₁₃×C₄⋊C₄	—	4	4	no	—
182	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	16	yes	—
183	C₄²×C₁₃	—	2	8	no	—
184	C₄²×C₁₃	—	2	8	no	—
185	C₄²×C₁₃	—	4	8	no	—
186	C₄²×C₁₃	—	4	4	no	—
187	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic
188	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
189	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
190	#1445	C₂×C₁₃	1	2	yes	—
191	#1441	C₂×C₁₃	1	2	yes	—
192	#1436	C₂×C₁₃	1	2	yes	—
193	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
194	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
195	C₄⋊#95	C₂×C₁₃	1	2	yes	—
196	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
197	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
198	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
201	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
202	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
203	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
204	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
205	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
206	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
207	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
212	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	2	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	2	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	2	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	2	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	2	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	8	yes	—
282	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
283	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
284	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
285	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
287	C₂×C₄×C₁₃	#124	1	4	yes	—
288	C₂×C₄×C₁₃	#125	1	4	yes	complemented
289	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
290	C₂×#125	—	2	4	no	—
291	C₂×#125	—	2	4	no	—
292	C₂×#125	C₄×C₁₃	1	8	yes	complemented
293	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
295	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
297	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
299	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
300	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#389	—	2	4	no	—
305	C₄×C₄⋊C₄	—	2	4	no	—
306	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#95	C₂²×C₁₃	1	2	yes	—
311	C₂×#95	C₂²×C₁₃	1	2	yes	—
312	C₂×#95	C₂²×C₁₃	1	2	yes	—
313	C₂×#95	C₂²×C₁₃	1	2	yes	—
314	C₂×#95	C₂²×C₁₃	1	2	yes	—
315	C₂×#95	C₂²×C₁₃	1	2	yes	—
316	C₂×#95	C₂²×C₁₃	1	2	yes	—
317	C₂×#95	C₂²×C₁₃	1	2	yes	—
318	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
320	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
321	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
322	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
323	C₂²×C₁₃	#520	1	1	yes	characteristic
324	C₂²×C₁₃	#520	1	1	yes	characteristic
325	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
328	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
329	C₂²×C₁₃	#529	1	1	yes	characteristic
330	C₂²×C₁₃	#529	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
332	C₂²×C₁₃	#533	1	1	yes	characteristic
333	C₂²×C₁₃	#540	1	1	yes	characteristic
334	C₂²×C₁₃	#541	1	1	yes	characteristic
335	C₂²×C₁₃	#544	1	1	yes	characteristic
336	C₂²×C₁₃	#544	1	1	yes	characteristic
337	C₂²×C₁₃	#546	1	1	yes	characteristic
338	C₂²×C₁₃	#546	1	1	yes	characteristic
339	C₂²×C₁₃	#547	1	1	yes	characteristic
340	C₂²×C₁₃	#547	1	1	yes	characteristic
341	C₂²×C₁₃	#548	1	1	yes	characteristic
342	C₂²×C₁₃	#548	1	1	yes	characteristic
343	C₂²×C₁₃	#550	1	1	yes	characteristic
344	C₂²×C₁₃	#550	1	1	yes	characteristic
345	C₂²×C₁₃	#552	1	1	yes	characteristic
346	C₂²×C₁₃	#552	1	1	yes	characteristic
347	C₂²×C₁₃	#553	1	1	yes	characteristic
348	C₂²×C₁₃	#553	1	1	yes	characteristic
349	C₂²×C₁₃	#554	1	1	yes	characteristic
350	C₂²×C₁₃	#554	1	1	yes	characteristic
351	C₂²×C₁₃	#557	1	1	yes	characteristic
352	C₂²×C₁₃	#557	1	1	yes	characteristic
353	C₄×C₁₃	—	2	8	no	—
354	C₄×C₁₃	—	2	4	no	—
355	C₄×C₁₃	—	4	2	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	4	4	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	—	4	4	no	—
360	C₄×C₁₃	—	4	2	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	—	8	2	no	—
363	C₄×C₁₃	#391	1	8	yes	—
364	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
369	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
370	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	#125	—	2	32	no	—
376	C₂×C₄⋊C₄	—	2	4	no	—
377	C₂×C₄⋊C₄	—	2	4	no	—
378	C₂×C₄⋊C₄	—	2	4	no	—
379	C₂×C₄⋊C₄	—	2	4	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	4	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	4	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	4	2	no	—
390	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
391	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
392	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
393	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
394	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
395	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
396	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	—	2	2	no	—
399	C₂×C₄²	—	2	2	no	—
400	C₂×C₄²	—	2	2	no	—
401	C₂×C₄²	—	2	4	no	—
402	C₂×C₄²	—	2	2	no	—
403	C₂×C₄²	—	2	4	no	—
404	C₂×C₄²	—	2	2	no	—
405	C₂×C₄²	—	2	2	no	—
406	C₂×C₄²	—	4	2	no	—
407	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
408	C₂×C₄²	Q₈×C₁₃	1	4	yes	—
409	#95	—	2	4	no	—
410	#95	—	2	4	no	—
411	#95	—	2	2	no	—
412	#95	—	2	4	no	—
413	#95	—	2	2	no	—
414	#95	—	2	2	no	—
415	#95	—	2	2	no	—
416	#95	—	2	4	no	—
417	#95	—	4	2	no	—
418	#95	—	4	2	no	—
419	#95	—	4	2	no	—
420	#95	—	4	2	no	—
421	C₂×C₁₃	C₂×#391	1	1	yes	characteristic
422	C₂×C₁₃	C₄×#125	1	1	yes	characteristic
423	C₂×C₁₃	#2330	1	1	yes	characteristic
424	C₂×C₁₃	#2339	1	1	yes	characteristic
425	C₂×C₁₃	#2341	1	1	yes	characteristic
426	C₂×C₁₃	#2370	1	1	yes	characteristic
427	C₂×C₁₃	#2370	1	1	yes	characteristic
428	C₂×C₁₃	#2441	1	1	yes	characteristic
429	C₂×C₁₃	#2442	1	1	yes	characteristic
430	C₂×C₁₃	#2453	1	1	yes	characteristic
431	C₂×C₁₃	#2454	1	1	yes	characteristic
432	C₂×C₁₃	#2489	1	1	yes	characteristic
433	C₂×C₁₃	#2490	1	1	yes	characteristic
434	C₂×C₁₃	#2550	1	1	yes	characteristic
435	C₂×C₁₃	#2552	1	1	yes	characteristic
436	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
497	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
499	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
502	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
504	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
505	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
506	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
508	C₂²×C₄	C₁₃×#41	1	2	yes	—
509	C₂²×C₄	C₁₃×#41	1	2	yes	—
510	C₂²×C₄	C₁₃×#41	1	2	yes	—
511	C₂²×C₄	C₁₃×#41	1	2	yes	—
512	C₂²×C₄	C₁₃×#41	1	2	yes	—
513	C₂²×C₄	C₁₃×#41	1	2	yes	—
514	C₄⋊C₄	—	2	16	no	—
515	C₄⋊C₄	—	2	16	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₄⋊C₄	—	2	8	no	—
518	C₄⋊C₄	—	4	8	no	—
519	C₄⋊C₄	—	4	4	no	—
520	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	16	yes	—
521	C₄²	—	2	8	no	—
522	C₄²	—	2	8	no	—
523	C₄²	—	4	8	no	—
524	C₄²	—	4	4	no	—
525	C₁₃	#14054	1	1	yes	characteristic, direct product factor, Sylow
526	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
527	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
528	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
529	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
530	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
531	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
532	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
533	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
534	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
535	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
536	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
537	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
540	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	2	no	—
603	C₂×C₄	—	4	2	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	2	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	8	yes	—
610	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
611	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
612	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
613	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
614	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
615	C₂×C₄	C₁₃×#124	1	4	yes	—
616	C₂×C₄	C₁₃×#125	1	4	yes	complemented
617	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
618	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
619	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
620	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
621	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
622	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
623	C₂²	C₁₃×#520	1	1	yes	characteristic
624	C₂²	C₁₃×#520	1	1	yes	characteristic
625	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
626	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
627	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
628	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
629	C₂²	C₁₃×#529	1	1	yes	characteristic
630	C₂²	C₁₃×#529	1	1	yes	characteristic
631	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
632	C₂²	C₁₃×#533	1	1	yes	characteristic
633	C₂²	C₁₃×#540	1	1	yes	characteristic
634	C₂²	C₁₃×#541	1	1	yes	characteristic
635	C₂²	C₁₃×#544	1	1	yes	characteristic
636	C₂²	C₁₃×#544	1	1	yes	characteristic
637	C₂²	C₁₃×#546	1	1	yes	characteristic
638	C₂²	C₁₃×#546	1	1	yes	characteristic
639	C₂²	C₁₃×#547	1	1	yes	characteristic
640	C₂²	C₁₃×#547	1	1	yes	characteristic
641	C₂²	C₁₃×#548	1	1	yes	characteristic
642	C₂²	C₁₃×#548	1	1	yes	characteristic
643	C₂²	C₁₃×#550	1	1	yes	characteristic
644	C₂²	C₁₃×#550	1	1	yes	characteristic
645	C₂²	C₁₃×#552	1	1	yes	characteristic
646	C₂²	C₁₃×#552	1	1	yes	characteristic
647	C₂²	C₁₃×#553	1	1	yes	characteristic
648	C₂²	C₁₃×#553	1	1	yes	characteristic
649	C₂²	C₁₃×#554	1	1	yes	characteristic
650	C₂²	C₁₃×#554	1	1	yes	characteristic
651	C₂²	C₁₃×#557	1	1	yes	characteristic
652	C₂²	C₁₃×#557	1	1	yes	characteristic
653	C₄	—	2	8	no	—
654	C₄	—	2	4	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	2	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	8	2	no	—
663	C₄	C₁₃×#391	1	8	yes	—
664	C₂	C₂×C₁₃×#391	1	1	yes	characteristic
665	C₂	C₄×C₁₃×#125	1	1	yes	characteristic
666	C₂	C₁₃×#2330	1	1	yes	characteristic
667	C₂	C₁₃×#2339	1	1	yes	characteristic
668	C₂	C₁₃×#2341	1	1	yes	characteristic
669	C₂	C₁₃×#2370	1	1	yes	characteristic
670	C₂	C₁₃×#2370	1	1	yes	characteristic
671	C₂	C₁₃×#2441	1	1	yes	characteristic
672	C₂	C₁₃×#2442	1	1	yes	characteristic
673	C₂	C₁₃×#2453	1	1	yes	characteristic
674	C₂	C₁₃×#2454	1	1	yes	characteristic
675	C₂	C₁₃×#2489	1	1	yes	characteristic
676	C₂	C₁₃×#2490	1	1	yes	characteristic
677	C₂	C₁₃×#2550	1	1	yes	characteristic
678	C₂	C₁₃×#2552	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₂×C₁₃×#125	C₄	semidirect
97. #14054	C₁₃	direct (N × H)
288. C₂×C₄×C₁₃	#125	semidirect
292. C₂×#125	C₄×C₁₃	semidirect
525. C₁₃	#14054	direct (N × H)
616. C₂×C₄	C₁₃×#125	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#125	2
C₂×C₁₃×#389	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1445	2
C₁₃×#1441	2
C₁₃×#1436	2
C₁₃×C₄⋊#95	2
C₄×C₁₃×#95	2
#14054	13

Subgroups — C13×#14054 #15700393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14054 #15700393