Subgroups — C₁₃×#35012 #15721351

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2851	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2848	C₂	1	2	yes	maximal
3	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2626	C₂	1	2	yes	maximal
6	C₁₃×#2574	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2556	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2522	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2465	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2312	C₂	1	2	yes	maximal
12	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#399	C₂²	1	4	yes	—
26	C₁₃×#398	C₂²	1	4	yes	complemented
27	C₁₃×#398	C₂²	1	4	yes	complemented
28	C₁₃×#396	C₂²	1	4	yes	—
29	C₁₃×#396	C₂²	1	4	yes	—
30	C₁₃×#395	C₂²	1	4	yes	complemented
31	C₁₃×#395	C₂²	1	4	yes	complemented
32	C₁₃×#393	C₂²	1	4	yes	—
33	C₁₃×#391	C₂²	1	4	yes	complemented
34	C₁₃×#391	C₂²	1	2	yes	complemented
35	C₁₃×#389	C₂²	1	2	yes	complemented
36	C₁₃×#389	C₂²	1	4	yes	complemented
37	C₁₃×#389	C₂²	1	2	yes	complemented
38	C₁₃×#389	C₂²	1	2	yes	complemented
39	C₁₃×#388	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	4	yes	—
41	C₁₃×#388	C₂²	1	4	yes	—
42	C₁₃×#388	C₂²	1	4	yes	—
43	C₁₃×#387	C₂²	1	4	yes	complemented
44	C₁₃×#387	C₂²	1	4	yes	complemented
45	C₁₃×#387	C₂²	1	4	yes	complemented
46	C₁₃×#387	C₂²	1	4	yes	complemented
47	C₁₃×#387	C₂²	1	4	yes	complemented
48	C₁₃×#385	C₂²	1	4	yes	—
49	C₁₃×#385	C₂²	1	4	yes	—
50	C₁₃×#385	C₂²	1	4	yes	—
51	C₁₃×#385	C₂²	1	4	yes	—
52	C₁₃×#382	C₂²	1	2	yes	complemented
53	C₁₃×#380	C₂²	1	2	yes	—
54	C₁₃×#380	C₂²	1	2	yes	—
55	C₁₃×#380	C₂²	1	2	yes	—
56	C₁₃×#380	C₂²	1	2	yes	—
57	C₁₃×#380	C₂²	1	2	yes	—
58	C₁₃×#380	C₂²	1	2	yes	—
59	C₁₃×#379	C₂²	1	4	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
62	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
65	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
67	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
69	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	—	2	4	no	—
71	C₂³×C₄×C₁₃	—	4	2	no	—
72	C₂³×C₄×C₁₃	—	4	2	no	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×#125	—	4	4	no	—
82	C₁₃×C₂²⋊Q₈	—	2	8	no	—
83	C₁₃×C₂²⋊Q₈	—	2	8	no	—
84	C₁₃×C₂²⋊Q₈	—	4	4	no	—
85	C₁₃×C₂²⋊Q₈	—	4	4	no	—
86	C₄×Q₈×C₁₃	—	4	4	no	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
104	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃	—	4	2	no	—
114	C₂×C₄²×C₁₃	—	4	2	no	—
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
121	C₁₃×#95	C₂³	1	4	yes	—
122	C₁₃×#95	C₂³	1	4	yes	—
123	C₁₃×#95	C₂³	1	4	yes	—
124	C₁₃×#95	C₂³	1	4	yes	—
125	C₁₃×#95	C₂³	1	4	yes	—
126	C₁₃×#95	C₂³	1	4	yes	—
127	C₁₃×#95	C₂³	1	4	yes	—
128	C₁₃×#95	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	#35012	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₂⁴×C₁₃	—	2	2	no	—
136	C₂⁴×C₁₃	—	4	1	no	—
137	C₂⁴×C₁₃	—	4	1	no	—
138	C₂⁴×C₁₃	—	4	1	no	—
139	C₂⁴×C₁₃	—	4	1	no	—
140	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
142	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	4	no	—
145	C₂×Q₈×C₁₃	—	4	2	no	—
146	C₂×Q₈×C₁₃	—	4	2	no	—
147	C₂×Q₈×C₁₃	—	4	2	no	—
148	C₂×Q₈×C₁₃	—	4	2	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	4	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	4	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	4	1	no	—
158	C₂²×C₄×C₁₃	—	4	1	no	—
159	C₂²×C₄×C₁₃	—	4	1	no	—
160	C₂²×C₄×C₁₃	—	4	1	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	4	1	no	—
164	C₂²×C₄×C₁₃	—	4	1	no	—
165	C₂²×C₄×C₁₃	—	4	1	no	—
166	C₂²×C₄×C₁₃	—	4	1	no	—
167	C₂²×C₄×C₁₃	—	4	1	no	—
168	C₂²×C₄×C₁₃	—	4	1	no	—
169	C₂²×C₄×C₁₃	—	4	16	no	—
170	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
172	C₂²×C₄×C₁₃	#41	1	4	yes	—
173	C₂²×C₄×C₁₃	#41	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	8	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	8	no	—
190	C₁₃×C₄⋊C₄	—	2	8	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₄⋊C₄	—	4	2	no	—
193	C₁₃×C₄⋊C₄	—	4	2	no	—
194	C₁₃×C₄⋊C₄	—	4	4	no	—
195	C₁₃×C₄⋊C₄	—	4	2	no	—
196	C₁₃×C₄⋊C₄	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	4	2	no	—
200	C₁₃×C₄⋊C₄	—	4	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	4	4	no	—
205	C₁₃×C₂²⋊C₄	—	4	4	no	—
206	C₁₃×C₂²⋊C₄	—	4	4	no	—
207	C₁₃×C₂²⋊C₄	—	4	4	no	—
208	C₁₃×C₂²⋊C₄	C₂×Q₈	1	16	yes	—
209	C₄²×C₁₃	—	2	4	no	—
210	C₄²×C₁₃	—	2	4	no	—
211	C₄²×C₁₃	—	4	2	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₄²×C₁₃	—	4	4	no	—
214	C₄²×C₁₃	—	4	4	no	—
215	#2851	C₂×C₁₃	1	2	yes	complemented
216	#2848	C₂×C₁₃	1	2	yes	—
217	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2626	C₂×C₁₃	1	2	yes	—
220	#2574	C₂×C₁₃	1	4	yes	complemented
221	#2556	C₂×C₁₃	1	4	yes	complemented
222	#2522	C₂×C₁₃	1	4	yes	complemented
223	#2465	C₂×C₁₃	1	4	yes	complemented
224	#2329	C₂×C₁₃	1	2	yes	complemented
225	#2312	C₂×C₁₃	1	2	yes	—
226	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
227	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	8	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	2	no	—
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	4	4	no	—
240	C₂³×C₁₃	—	4	4	no	—
241	C₂³×C₁₃	—	4	4	no	—
242	C₂³×C₁₃	—	4	4	no	—
243	C₂³×C₁₃	—	4	4	no	—
244	C₂³×C₁₃	—	4	4	no	—
245	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
246	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
247	C₂³×C₁₃	C₂×#41	1	2	yes	—
248	C₂³×C₁₃	C₂×#41	1	2	yes	—
249	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
250	Q₈×C₁₃	—	4	8	no	—
251	Q₈×C₁₃	—	8	4	no	—
252	C₂×C₄×C₁₃	—	2	8	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	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	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	2	no	—
280	C₂×C₄×C₁₃	—	4	4	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	4	4	no	—
284	C₂×C₄×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	—	4	8	no	—
286	C₂×C₄×C₁₃	—	4	4	no	—
287	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
288	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
290	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
292	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
293	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
295	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
296	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
297	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
300	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	#399	C₂²×C₁₃	1	4	yes	—
305	#398	C₂²×C₁₃	1	4	yes	complemented
306	#398	C₂²×C₁₃	1	4	yes	complemented
307	#396	C₂²×C₁₃	1	4	yes	—
308	#396	C₂²×C₁₃	1	4	yes	—
309	#395	C₂²×C₁₃	1	4	yes	complemented
310	#395	C₂²×C₁₃	1	4	yes	complemented
311	#393	C₂²×C₁₃	1	4	yes	—
312	#391	C₂²×C₁₃	1	2	yes	complemented
313	#391	C₂²×C₁₃	1	4	yes	complemented
314	#389	C₂²×C₁₃	1	4	yes	complemented
315	#389	C₂²×C₁₃	1	2	yes	complemented
316	#389	C₂²×C₁₃	1	2	yes	complemented
317	#389	C₂²×C₁₃	1	2	yes	complemented
318	#388	C₂²×C₁₃	1	4	yes	—
319	#388	C₂²×C₁₃	1	4	yes	—
320	#388	C₂²×C₁₃	1	4	yes	—
321	#388	C₂²×C₁₃	1	4	yes	—
322	#387	C₂²×C₁₃	1	4	yes	complemented
323	#387	C₂²×C₁₃	1	4	yes	complemented
324	#387	C₂²×C₁₃	1	4	yes	complemented
325	#387	C₂²×C₁₃	1	4	yes	complemented
326	#387	C₂²×C₁₃	1	4	yes	complemented
327	#385	C₂²×C₁₃	1	4	yes	—
328	#385	C₂²×C₁₃	1	4	yes	—
329	#385	C₂²×C₁₃	1	4	yes	—
330	#385	C₂²×C₁₃	1	4	yes	—
331	#382	C₂²×C₁₃	1	2	yes	complemented
332	#380	C₂²×C₁₃	1	2	yes	—
333	#380	C₂²×C₁₃	1	2	yes	—
334	#380	C₂²×C₁₃	1	2	yes	—
335	#380	C₂²×C₁₃	1	2	yes	—
336	#380	C₂²×C₁₃	1	2	yes	—
337	#380	C₂²×C₁₃	1	2	yes	—
338	#379	C₂²×C₁₃	1	4	yes	—
339	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
340	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
341	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
342	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
343	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
344	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	2	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	2	no	—
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	4	no	—
353	C₂²×C₁₃	—	2	4	no	—
354	C₂²×C₁₃	—	2	4	no	—
355	C₂²×C₁₃	—	4	16	no	—
356	C₂²×C₁₃	—	4	2	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	#533	1	4	yes	—
361	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
362	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂²×C₁₃	#585	1	1	yes	characteristic
367	C₂²×C₁₃	#585	1	1	yes	characteristic
368	C₄×C₁₃	—	2	4	no	—
369	C₄×C₁₃	—	2	2	no	—
370	C₄×C₁₃	—	2	2	no	—
371	C₄×C₁₃	—	2	4	no	—
372	C₄×C₁₃	—	2	4	no	—
373	C₄×C₁₃	—	2	4	no	—
374	C₄×C₁₃	—	4	4	no	—
375	C₄×C₁₃	—	4	4	no	—
376	C₄×C₁₃	—	4	2	no	—
377	C₄×C₁₃	—	4	4	no	—
378	C₄×C₁₃	—	4	4	no	—
379	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
381	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
382	C₂³×C₄	—	2	4	no	—
383	C₂³×C₄	—	4	2	no	—
384	C₂³×C₄	—	4	2	no	—
385	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
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	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
392	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
393	#125	—	4	4	no	—
394	C₂²⋊Q₈	—	2	8	no	—
395	C₂²⋊Q₈	—	2	8	no	—
396	C₂²⋊Q₈	—	4	4	no	—
397	C₂²⋊Q₈	—	4	4	no	—
398	C₄×Q₈	—	4	4	no	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	—	2	4	no	—
416	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄²	—	4	2	no	—
426	C₂×C₄²	—	4	2	no	—
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
432	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
433	#95	C₂³×C₁₃	1	4	yes	—
434	#95	C₂³×C₁₃	1	4	yes	—
435	#95	C₂³×C₁₃	1	4	yes	—
436	#95	C₂³×C₁₃	1	4	yes	—
437	#95	C₂³×C₁₃	1	4	yes	—
438	#95	C₂³×C₁₃	1	4	yes	—
439	#95	C₂³×C₁₃	1	4	yes	—
440	#95	C₂³×C₁₃	1	4	yes	—
441	#95	C₂³×C₁₃	1	4	yes	—
442	#95	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	4	yes	—
444	#95	C₂³×C₁₃	1	4	yes	—
445	C₂×C₁₃	—	2	4	no	—
446	C₂×C₁₃	—	4	4	no	—
447	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
448	C₂×C₁₃	#3459	1	1	yes	characteristic
449	C₂×C₁₃	#3460	1	1	yes	characteristic
450	C₂×C₁₃	#3490	1	1	yes	characteristic
451	C₂×C₁₃	#3493	1	1	yes	characteristic
452	C₂×C₁₃	#3501	1	1	yes	characteristic
453	C₂×C₁₃	#3501	1	1	yes	characteristic
454	C₂⁴	—	2	2	no	—
455	C₂⁴	—	2	2	no	—
456	C₂⁴	—	4	1	no	—
457	C₂⁴	—	4	1	no	—
458	C₂⁴	—	4	1	no	—
459	C₂⁴	—	4	1	no	—
460	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
461	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
462	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₂×Q₈	—	2	4	no	—
464	C₂×Q₈	—	2	4	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	4	2	no	—
467	C₂×Q₈	—	4	2	no	—
468	C₂×Q₈	—	4	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	4	1	no	—
478	C₂²×C₄	—	4	1	no	—
479	C₂²×C₄	—	4	1	no	—
480	C₂²×C₄	—	4	1	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	—	4	1	no	—
487	C₂²×C₄	—	4	1	no	—
488	C₂²×C₄	—	4	1	no	—
489	C₂²×C₄	—	4	16	no	—
490	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
492	C₂²×C₄	C₁₃×#41	1	4	yes	—
493	C₂²×C₄	C₁₃×#41	1	4	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
502	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	8	no	—
508	C₄⋊C₄	—	2	8	no	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	4	2	no	—
515	C₄⋊C₄	—	4	2	no	—
516	C₄⋊C₄	—	4	4	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	4	4	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	4	4	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	4	no	—
527	C₂²⋊C₄	—	4	4	no	—
528	C₂²⋊C₄	C₂×Q₈×C₁₃	1	16	yes	—
529	C₄²	—	2	4	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	4	2	no	—
532	C₄²	—	4	2	no	—
533	C₄²	—	4	4	no	—
534	C₄²	—	4	4	no	—
535	C₁₃	#35012	1	1	yes	characteristic, direct product factor, Sylow
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	8	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	4	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	4	4	no	—
553	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
554	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
555	C₂³	C₂×C₁₃×#41	1	2	yes	—
556	C₂³	C₂×C₁₃×#41	1	2	yes	—
557	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
558	Q₈	—	4	8	no	—
559	Q₈	—	8	4	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	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	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	4	4	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	—	4	4	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
596	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
597	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
598	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
599	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
600	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	4	16	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	C₁₃×#533	1	4	yes	—
616	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
617	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
618	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
619	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂²	C₁₃×#585	1	1	yes	characteristic
622	C₂²	C₁₃×#585	1	1	yes	characteristic
623	C₄	—	2	4	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	4	no	—
627	C₄	—	2	4	no	—
628	C₄	—	2	4	no	—
629	C₄	—	4	4	no	—
630	C₄	—	4	4	no	—
631	C₄	—	4	2	no	—
632	C₄	—	4	4	no	—
633	C₄	—	4	4	no	—
634	C₂	—	2	4	no	—
635	C₂	—	4	4	no	—
636	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
637	C₂	C₁₃×#3459	1	1	yes	characteristic
638	C₂	C₁₃×#3460	1	1	yes	characteristic
639	C₂	C₁₃×#3490	1	1	yes	characteristic
640	C₂	C₁₃×#3493	1	1	yes	characteristic
641	C₂	C₁₃×#3501	1	1	yes	characteristic
642	C₂	C₁₃×#3501	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2851	C₂	semidirect
3. C₁₃×#2659	C₂	semidirect
4. C₁₃×#2659	C₂	semidirect
6. C₁₃×#2574	C₂	semidirect
7. C₁₃×#2556	C₂	semidirect
8. C₁₃×#2522	C₂	semidirect
9. C₁₃×#2465	C₂	semidirect
10. C₁₃×#2329	C₂	semidirect
12. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
15. C₂×C₁₃×#125	C₂²	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₁₃×#398	C₂²	semidirect
27. C₁₃×#398	C₂²	semidirect
30. C₁₃×#395	C₂²	semidirect
31. C₁₃×#395	C₂²	semidirect
33. C₁₃×#391	C₂²	semidirect
34. C₁₃×#391	C₂²	semidirect
35. C₁₃×#389	C₂²	semidirect
36. C₁₃×#389	C₂²	semidirect
37. C₁₃×#389	C₂²	semidirect
38. C₁₃×#389	C₂²	semidirect
43. C₁₃×#387	C₂²	semidirect
44. C₁₃×#387	C₂²	semidirect
45. C₁₃×#387	C₂²	semidirect
46. C₁₃×#387	C₂²	semidirect
47. C₁₃×#387	C₂²	semidirect
52. C₁₃×#382	C₂²	semidirect
60. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
61. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
104. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
133. #35012	C₁₃	direct (N × H)
215. #2851	C₂×C₁₃	semidirect
217. #2659	C₂×C₁₃	semidirect
218. #2659	C₂×C₁₃	semidirect
220. #2574	C₂×C₁₃	semidirect
221. #2556	C₂×C₁₃	semidirect
222. #2522	C₂×C₁₃	semidirect
223. #2465	C₂×C₁₃	semidirect
224. #2329	C₂×C₁₃	semidirect
226. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
294. C₂×#125	C₂²×C₁₃	semidirect
299. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
305. #398	C₂²×C₁₃	semidirect
306. #398	C₂²×C₁₃	semidirect
309. #395	C₂²×C₁₃	semidirect
310. #395	C₂²×C₁₃	semidirect
312. #391	C₂²×C₁₃	semidirect
313. #391	C₂²×C₁₃	semidirect
314. #389	C₂²×C₁₃	semidirect
315. #389	C₂²×C₁₃	semidirect
316. #389	C₂²×C₁₃	semidirect
317. #389	C₂²×C₁₃	semidirect
322. #387	C₂²×C₁₃	semidirect
323. #387	C₂²×C₁₃	semidirect
324. #387	C₂²×C₁₃	semidirect
325. #387	C₂²×C₁₃	semidirect
326. #387	C₂²×C₁₃	semidirect
331. #382	C₂²×C₁₃	semidirect
339. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
340. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
416. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
535. C₁₃	#35012	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×#2851	2
C₁₃×#2848	2
C₁₃×#2659	2
C₁₃×#2626	2
C₁₃×#2574	2
C₁₃×#2556	2
C₁₃×#2522	2
C₁₃×#2465	2
C₁₃×#2329	2
C₁₃×#2312	2
C₄×C₁₃×C₂²⋊Q₈	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
#35012	13

Subgroups — C13×#35012 #15721351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35012 #15721351