Subgroups — C₁₃×#14053 #15700392

Order 3328.

1838 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#391	C₂	1	2	yes	maximal
3	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1446	C₂	1	2	yes	maximal
6	C₁₃×#1441	C₂	1	2	yes	maximal
7	C₁₃×#1436	C₂	1	2	yes	maximal
8	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
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	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₄	1	8	yes	complemented
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×#391	—	2	8	no	—
27	C₁₃×#389	—	2	4	no	—
28	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	2	yes	—
31	C₂×C₁₃×#95	C₂²	1	2	yes	—
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
40	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	—	2	4	no	—
42	C₂²×Q₈×C₁₃	—	2	4	no	—
43	C₂²×Q₈×C₁₃	—	2	4	no	—
44	C₂²×Q₈×C₁₃	—	2	4	no	—
45	C₂²×Q₈×C₁₃	—	4	2	no	—
46	C₂²×Q₈×C₁₃	—	4	2	no	—
47	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	32	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	4	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	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	complemented
78	C₂×C₄²×C₁₃	—	2	2	no	—
79	C₂×C₄²×C₁₃	—	2	2	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	4	no	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	—	2	2	no	—
86	C₂×C₄²×C₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	4	2	no	—
88	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
89	C₂×C₄²×C₁₃	Q₈	1	4	yes	complemented
90	C₁₃×#95	—	2	4	no	—
91	C₁₃×#95	—	2	4	no	—
92	C₁₃×#95	—	2	4	no	—
93	C₁₃×#95	—	2	4	no	—
94	C₁₃×#95	—	2	4	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	4	no	—
98	C₁₃×#95	—	4	2	no	—
99	C₁₃×#95	—	4	2	no	—
100	C₁₃×#95	D₄	1	4	yes	—
101	C₁₃×#95	Q₈	1	4	yes	complemented
102	#14053	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₂×Q₈×C₁₃	—	2	16	no	—
105	C₂×Q₈×C₁₃	—	2	16	no	—
106	C₂×Q₈×C₁₃	—	4	8	no	—
107	C₂×Q₈×C₁₃	—	4	8	no	—
108	C₂×Q₈×C₁₃	—	4	8	no	—
109	C₂×Q₈×C₁₃	—	4	8	no	—
110	C₂×Q₈×C₁₃	—	4	8	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	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	1	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	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	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	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	2	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	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	2	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	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
165	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
184	C₂²×C₄×C₁₃	#41	1	2	yes	—
185	C₂²×C₄×C₁₃	#41	1	2	yes	—
186	C₂²×C₄×C₁₃	#41	1	2	yes	—
187	C₂²×C₄×C₁₃	#41	1	2	yes	—
188	C₁₃×C₄⋊C₄	—	2	16	no	—
189	C₁₃×C₄⋊C₄	—	2	8	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	4	8	no	—
192	C₁₃×C₄⋊C₄	—	4	4	no	—
193	C₁₃×C₄⋊C₄	C₂²⋊C₄	1	16	yes	—
194	C₄²×C₁₃	—	2	8	no	—
195	C₄²×C₁₃	—	2	8	no	—
196	C₄²×C₁₃	—	4	8	no	—
197	C₄²×C₁₃	—	4	4	no	—
198	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
199	C₂×#391	C₂×C₁₃	1	2	yes	—
200	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
201	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
202	#1446	C₂×C₁₃	1	2	yes	—
203	#1441	C₂×C₁₃	1	2	yes	—
204	#1436	C₂×C₁₃	1	2	yes	—
205	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
206	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
207	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
208	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
209	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
214	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
215	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
216	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
218	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
224	Q₈×C₁₃	—	4	32	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	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	4	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	4	no	—
239	C₂×C₄×C₁₃	—	2	4	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	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	4	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	2	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	2	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	—	4	2	no	—
286	C₂×C₄×C₁₃	—	4	2	no	—
287	C₂×C₄×C₁₃	—	4	2	no	—
288	C₂×C₄×C₁₃	—	4	2	no	—
289	C₂×C₄×C₁₃	—	4	2	no	—
290	C₂×C₄×C₁₃	—	4	2	no	—
291	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	8	yes	—
292	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
293	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
294	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
295	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
296	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
297	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
298	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
299	C₂×C₄×C₁₃	#124	1	4	yes	—
300	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
301	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	complemented
302	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
303	C₂×C₄⋊Q₈	—	2	4	no	—
304	C₂×C₄⋊Q₈	—	2	4	no	—
305	C₂×C₄⋊Q₈	C₄×C₁₃	1	8	yes	complemented
306	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
312	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
313	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
316	#391	—	2	8	no	—
317	#389	—	2	4	no	—
318	C₄×C₄⋊C₄	—	2	4	no	—
319	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#95	C₂²×C₁₃	1	2	yes	—
322	C₂×#95	C₂²×C₁₃	1	2	yes	—
323	C₂×#95	C₂²×C₁₃	1	2	yes	—
324	C₂×#95	C₂²×C₁₃	1	2	yes	—
325	C₂×#95	C₂²×C₁₃	1	2	yes	—
326	C₂×#95	C₂²×C₁₃	1	2	yes	—
327	C₂×#95	C₂²×C₁₃	1	2	yes	—
328	C₂×#95	C₂²×C₁₃	1	2	yes	—
329	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
334	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
335	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
336	C₂²×C₁₃	#518	1	1	yes	characteristic
337	C₂²×C₁₃	#519	1	1	yes	characteristic
338	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
339	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
340	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
341	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
342	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
343	C₂²×C₁₃	#532	1	1	yes	characteristic
344	C₂²×C₁₃	#533	1	1	yes	characteristic
345	C₂²×C₁₃	#533	1	1	yes	characteristic
346	C₂²×C₁₃	#542	1	1	yes	characteristic
347	C₂²×C₁₃	#542	1	1	yes	characteristic
348	C₂²×C₁₃	#544	1	1	yes	characteristic
349	C₂²×C₁₃	#544	1	1	yes	characteristic
350	C₂²×C₁₃	D₄²	1	1	yes	characteristic
351	C₂²×C₁₃	D₄²	1	1	yes	characteristic
352	C₂²×C₁₃	#546	1	1	yes	characteristic
353	C₂²×C₁₃	#546	1	1	yes	characteristic
354	C₂²×C₁₃	#547	1	1	yes	characteristic
355	C₂²×C₁₃	#548	1	1	yes	characteristic
356	C₂²×C₁₃	#548	1	1	yes	characteristic
357	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
358	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
359	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
360	C₂²×C₁₃	#554	1	1	yes	characteristic
361	C₂²×C₁₃	#554	1	1	yes	characteristic
362	C₂²×C₁₃	#555	1	1	yes	characteristic
363	C₂²×C₁₃	#556	1	1	yes	characteristic
364	C₂²×C₁₃	#557	1	1	yes	characteristic
365	C₂²×C₁₃	Q₈²	1	1	yes	characteristic
366	C₄×C₁₃	—	2	8	no	—
367	C₄×C₁₃	—	2	4	no	—
368	C₄×C₁₃	—	2	4	no	—
369	C₄×C₁₃	—	2	4	no	—
370	C₄×C₁₃	—	4	4	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	4	4	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	8	2	no	—
376	C₄×C₁₃	#391	1	8	yes	complemented
377	C₂²×Q₈	—	2	4	no	—
378	C₂²×Q₈	—	2	4	no	—
379	C₂²×Q₈	—	2	4	no	—
380	C₂²×Q₈	—	2	4	no	—
381	C₂²×Q₈	—	4	2	no	—
382	C₂²×Q₈	—	4	2	no	—
383	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	—
384	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
385	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
391	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₄⋊Q₈	—	2	32	no	—
396	C₂×C₄⋊C₄	—	2	4	no	—
397	C₂×C₄⋊C₄	—	2	4	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	4	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	—	2	4	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	2	no	—
407	C₂×C₄⋊C₄	—	4	2	no	—
408	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
409	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
410	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
411	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
412	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
413	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	complemented
414	C₂×C₄²	—	2	2	no	—
415	C₂×C₄²	—	2	2	no	—
416	C₂×C₄²	—	2	2	no	—
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	—	2	2	no	—
420	C₂×C₄²	—	2	4	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	—	4	2	no	—
424	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
425	C₂×C₄²	Q₈×C₁₃	1	4	yes	complemented
426	#95	—	2	4	no	—
427	#95	—	2	4	no	—
428	#95	—	2	4	no	—
429	#95	—	2	4	no	—
430	#95	—	2	4	no	—
431	#95	—	2	2	no	—
432	#95	—	2	2	no	—
433	#95	—	2	4	no	—
434	#95	—	4	2	no	—
435	#95	—	4	2	no	—
436	#95	D₄×C₁₃	1	4	yes	—
437	#95	Q₈×C₁₃	1	4	yes	complemented
438	C₂×C₁₃	C₂×#391	1	1	yes	characteristic
439	C₂×C₁₃	C₄×C₄⋊Q₈	1	1	yes	characteristic
440	C₂×C₁₃	#2331	1	1	yes	characteristic
441	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×C₁₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
443	C₂×C₁₃	#2365	1	1	yes	characteristic
444	C₂×C₁₃	#2369	1	1	yes	characteristic
445	C₂×C₁₃	#2439	1	1	yes	characteristic
446	C₂×C₁₃	#2440	1	1	yes	characteristic
447	C₂×C₁₃	#2451	1	1	yes	characteristic
448	C₂×C₁₃	#2452	1	1	yes	characteristic
449	C₂×C₁₃	#2491	1	1	yes	characteristic
450	C₂×C₁₃	#2492	1	1	yes	characteristic
451	C₂×C₁₃	#2550	1	1	yes	characteristic
452	C₂×C₁₃	#2551	1	1	yes	characteristic
453	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
454	C₂×Q₈	—	2	16	no	—
455	C₂×Q₈	—	2	16	no	—
456	C₂×Q₈	—	4	8	no	—
457	C₂×Q₈	—	4	8	no	—
458	C₂×Q₈	—	4	8	no	—
459	C₂×Q₈	—	4	8	no	—
460	C₂×Q₈	—	4	8	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	2	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
515	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
516	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
517	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
518	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
519	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
521	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
523	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
524	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
526	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
528	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
529	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
530	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
531	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
534	C₂²×C₄	C₁₃×#41	1	2	yes	—
535	C₂²×C₄	C₁₃×#41	1	2	yes	—
536	C₂²×C₄	C₁₃×#41	1	2	yes	—
537	C₂²×C₄	C₁₃×#41	1	2	yes	—
538	C₄⋊C₄	—	2	16	no	—
539	C₄⋊C₄	—	2	8	no	—
540	C₄⋊C₄	—	2	8	no	—
541	C₄⋊C₄	—	4	8	no	—
542	C₄⋊C₄	—	4	4	no	—
543	C₄⋊C₄	C₁₃×C₂²⋊C₄	1	16	yes	—
544	C₄²	—	2	8	no	—
545	C₄²	—	2	8	no	—
546	C₄²	—	4	8	no	—
547	C₄²	—	4	4	no	—
548	C₁₃	#14053	1	1	yes	characteristic, direct product factor, Sylow
549	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
550	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
551	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
552	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
553	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
554	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
555	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
556	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
557	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
558	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
559	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
560	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
561	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
562	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
563	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
564	Q₈	—	4	32	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	2	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	4	2	no	—
631	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	8	yes	—
632	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
633	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
634	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
635	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
636	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
637	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
638	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
639	C₂×C₄	C₁₃×#124	1	4	yes	—
640	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
641	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	complemented
642	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
643	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
644	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
645	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
646	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
647	C₂²	C₁₃×#518	1	1	yes	characteristic
648	C₂²	C₁₃×#519	1	1	yes	characteristic
649	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
650	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
651	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
652	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
653	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
654	C₂²	C₁₃×#532	1	1	yes	characteristic
655	C₂²	C₁₃×#533	1	1	yes	characteristic
656	C₂²	C₁₃×#533	1	1	yes	characteristic
657	C₂²	C₁₃×#542	1	1	yes	characteristic
658	C₂²	C₁₃×#542	1	1	yes	characteristic
659	C₂²	C₁₃×#544	1	1	yes	characteristic
660	C₂²	C₁₃×#544	1	1	yes	characteristic
661	C₂²	D₄²×C₁₃	1	1	yes	characteristic
662	C₂²	D₄²×C₁₃	1	1	yes	characteristic
663	C₂²	C₁₃×#546	1	1	yes	characteristic
664	C₂²	C₁₃×#546	1	1	yes	characteristic
665	C₂²	C₁₃×#547	1	1	yes	characteristic
666	C₂²	C₁₃×#548	1	1	yes	characteristic
667	C₂²	C₁₃×#548	1	1	yes	characteristic
668	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
669	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
670	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
671	C₂²	C₁₃×#554	1	1	yes	characteristic
672	C₂²	C₁₃×#554	1	1	yes	characteristic
673	C₂²	C₁₃×#555	1	1	yes	characteristic
674	C₂²	C₁₃×#556	1	1	yes	characteristic
675	C₂²	C₁₃×#557	1	1	yes	characteristic
676	C₂²	Q₈²×C₁₃	1	1	yes	characteristic
677	C₄	—	2	8	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	4	no	—
681	C₄	—	4	4	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	4	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	2	no	—
686	C₄	—	8	2	no	—
687	C₄	C₁₃×#391	1	8	yes	complemented
688	C₂	C₂×C₁₃×#391	1	1	yes	characteristic
689	C₂	C₄×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
690	C₂	C₁₃×#2331	1	1	yes	characteristic
691	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
692	C₂	Q₈×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
693	C₂	C₁₃×#2365	1	1	yes	characteristic
694	C₂	C₁₃×#2369	1	1	yes	characteristic
695	C₂	C₁₃×#2439	1	1	yes	characteristic
696	C₂	C₁₃×#2440	1	1	yes	characteristic
697	C₂	C₁₃×#2451	1	1	yes	characteristic
698	C₂	C₁₃×#2452	1	1	yes	characteristic
699	C₂	C₁₃×#2491	1	1	yes	characteristic
700	C₂	C₁₃×#2492	1	1	yes	characteristic
701	C₂	C₁₃×#2550	1	1	yes	characteristic
702	C₂	C₁₃×#2551	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
15. C₂×C₁₃×C₄⋊Q₈	C₄	semidirect
77. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
89. C₂×C₄²×C₁₃	Q₈	semidirect
101. C₁₃×#95	Q₈	semidirect
102. #14053	C₁₃	direct (N × H)
301. C₂×C₄×C₁₃	C₄⋊Q₈	semidirect
305. C₂×C₄⋊Q₈	C₄×C₁₃	semidirect
376. C₄×C₁₃	#391	semidirect
413. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
425. C₂×C₄²	Q₈×C₁₃	semidirect
437. #95	Q₈×C₁₃	semidirect
548. C₁₃	#14053	direct (N × H)
641. C₂×C₄	C₁₃×C₄⋊Q₈	semidirect
687. C₄	C₁₃×#391	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×C₄⋊Q₈	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1446	2
C₁₃×#1441	2
C₁₃×#1436	2
C₁₃×C₄⋊#95	2
C₄×C₁₃×#95	2
#14053	13

Subgroups — C13×#14053 #15700392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14053 #15700392