Subgroups — C₁₃×#34947 #15721286

Order 3328.

2522 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2566	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2565	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2564	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2417	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2297	C₂	1	2	yes	maximal
14	C₁₃×#2285	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₁₃×#533	—	2	8	no	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₄×C₁₃×#41	—	2	8	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
33	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#117	C₂²	1	2	yes	—
35	C₂×C₁₃×#117	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#400	C₂²	1	4	yes	—
41	C₁₃×#399	C₂²	1	4	yes	—
42	C₁₃×#398	C₂²	1	8	yes	—
43	C₁₃×#396	C₂²	1	8	yes	—
44	C₁₃×#395	C₂²	1	4	yes	—
45	C₁₃×#393	C₂²	1	4	yes	—
46	C₁₃×#391	C₂²	1	2	yes	—
47	C₁₃×#391	C₂²	1	2	yes	—
48	C₁₃×#391	C₂²	1	4	yes	—
49	C₁₃×#390	C₂²	1	2	yes	—
50	C₁₃×#390	C₂²	1	2	yes	—
51	C₁₃×#389	C₂²	1	4	yes	—
52	C₁₃×#387	C₂²	1	8	yes	—
53	C₁₃×#386	C₂²	1	8	yes	—
54	C₁₃×#385	C₂²	1	8	yes	—
55	C₁₃×#384	C₂²	1	2	yes	—
56	C₁₃×#384	C₂²	1	2	yes	—
57	C₁₃×#382	C₂²	1	2	yes	—
58	C₁₃×#382	C₂²	1	2	yes	—
59	C₁₃×#380	C₂²	1	8	yes	—
60	C₁₃×#380	C₂²	1	4	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
68	C₂×C₁₃×#95	C₂²	1	2	yes	—
69	C₂×C₁₃×#41	—	2	4	no	—
70	C₂×C₁₃×#41	—	2	4	no	—
71	C₂×C₁₃×#41	Q₈	1	8	yes	complemented
72	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
73	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×C₄⋊Q₈	—	2	4	no	—
85	C₁₃×C₄⋊Q₈	—	2	4	no	—
86	C₁₃×#125	—	2	8	no	—
87	C₁₃×C₂²⋊Q₈	—	2	8	no	—
88	C₁₃×C₂²⋊Q₈	—	2	8	no	—
89	C₁₃×C₂²⋊Q₈	—	2	16	no	—
90	C₄×Q₈×C₁₃	—	2	4	no	—
91	C₄×Q₈×C₁₃	—	2	4	no	—
92	C₄×Q₈×C₁₃	—	2	8	no	—
93	C₄×Q₈×C₁₃	—	2	8	no	—
94	C₄×D₄×C₁₃	—	2	8	no	—
95	C₄×D₄×C₁₃	—	2	8	no	—
96	C₄×D₄×C₁₃	—	2	4	no	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₁₃×#117	—	2	4	no	—
99	C₁₃×#117	—	2	8	no	—
100	C₁₃×#117	—	2	8	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
123	C₂×C₄²×C₁₃	—	2	8	no	—
124	C₂×C₄²×C₁₃	—	2	8	no	—
125	C₂×C₄²×C₁₃	D₄	1	8	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₁₃×#95	C₂³	1	8	yes	—
138	C₁₃×#95	C₂³	1	8	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	2	yes	—
141	C₁₃×#95	C₂³	1	2	yes	—
142	C₁₃×#95	C₂³	1	8	yes	—
143	C₁₃×#95	C₂³	1	8	yes	—
144	#34947	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₁₃×#41	—	2	32	no	—
148	C₂×Q₈×C₁₃	—	2	2	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	8	no	—
153	C₂×Q₈×C₁₃	—	4	4	no	—
154	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
155	C₂×D₄×C₁₃	—	2	4	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂×D₄×C₁₃	—	2	2	no	—
159	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	—
160	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	4	4	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	—	4	4	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
176	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
177	C₂²×C₄×C₁₃	#41	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	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×C₄⋊C₄	—	2	4	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	2	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	4	no	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	8	no	—
198	C₁₃×C₄⋊C₄	—	2	8	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	8	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	16	no	—
204	C₁₃×C₄⋊C₄	—	4	8	no	—
205	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	8	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	16	no	—
211	C₁₃×C₂²⋊C₄	—	4	8	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	4	no	—
215	C₄²×C₁₃	—	2	8	no	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	—	2	8	no	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	C₂×D₄	1	4	yes	—
220	C₄²×C₁₃	C₂×D₄	1	4	yes	—
221	C₄²×C₁₃	C₂×D₄	1	4	yes	—
222	C₄²×C₁₃	C₂×D₄	1	4	yes	—
223	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic
225	#2568	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2566	C₂×C₁₃	1	2	yes	complemented
228	#2565	C₂×C₁₃	1	2	yes	complemented
229	#2564	C₂×C₁₃	1	4	yes	complemented
230	#2563	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2542	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2417	C₂×C₁₃	1	4	yes	complemented
233	#2396	C₂×C₁₃	1	4	yes	complemented
234	C₄×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
235	#2297	C₂×C₁₃	1	2	yes	—
236	#2285	C₂×C₁₃	1	2	yes	complemented
237	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	2	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
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	C₂⁵	1	1	yes	characteristic
249	Q₈×C₁₃	—	2	8	no	—
250	Q₈×C₁₃	—	4	8	no	—
251	Q₈×C₁₃	—	4	8	no	—
252	D₄×C₁₃	—	2	16	no	—
253	D₄×C₁₃	—	2	8	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	16	no	—
262	C₂×C₄×C₁₃	—	2	8	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	8	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	8	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	16	no	—
276	C₂×C₄×C₁₃	—	4	8	no	—
277	C₂×C₄×C₁₃	—	4	8	no	—
278	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
288	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
290	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
291	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
292	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
293	#533	—	2	8	no	—
294	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#125	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×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
300	C₄×#41	—	2	8	no	—
301	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
304	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
307	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
309	C₂×#117	C₂²×C₁₃	1	2	yes	—
310	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#117	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
313	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
314	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
315	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
316	#400	C₂²×C₁₃	1	4	yes	—
317	#399	C₂²×C₁₃	1	4	yes	—
318	#398	C₂²×C₁₃	1	8	yes	—
319	#396	C₂²×C₁₃	1	8	yes	—
320	#395	C₂²×C₁₃	1	4	yes	—
321	#393	C₂²×C₁₃	1	4	yes	—
322	#391	C₂²×C₁₃	1	2	yes	—
323	#391	C₂²×C₁₃	1	2	yes	—
324	#391	C₂²×C₁₃	1	4	yes	—
325	#390	C₂²×C₁₃	1	2	yes	—
326	#390	C₂²×C₁₃	1	2	yes	—
327	#389	C₂²×C₁₃	1	4	yes	—
328	#387	C₂²×C₁₃	1	8	yes	—
329	#386	C₂²×C₁₃	1	8	yes	—
330	#385	C₂²×C₁₃	1	8	yes	—
331	#384	C₂²×C₁₃	1	2	yes	—
332	#384	C₂²×C₁₃	1	2	yes	—
333	#382	C₂²×C₁₃	1	2	yes	—
334	#382	C₂²×C₁₃	1	2	yes	—
335	#380	C₂²×C₁₃	1	4	yes	—
336	#380	C₂²×C₁₃	1	8	yes	—
337	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
339	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
340	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
341	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
342	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
343	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
344	C₂×#95	C₂²×C₁₃	1	2	yes	—
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	4	no	—
348	C₂²×C₁₃	—	2	4	no	—
349	C₂²×C₁₃	—	2	4	no	—
350	C₂²×C₁₃	—	2	8	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	4	2	no	—
353	C₂²×C₁₃	—	4	4	no	—
354	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
355	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
356	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
357	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
358	C₂²×C₁₃	C₂²×#41	1	2	yes	—
359	C₂²×C₁₃	#585	1	2	yes	—
360	C₄×C₁₃	—	2	4	no	—
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	2	2	no	—
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	2	8	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	4	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	4	no	—
369	C₄×C₁₃	—	4	4	no	—
370	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
371	C₄×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
372	C₄×C₁₃	#532	1	4	yes	—
373	C₂×#41	—	2	4	no	—
374	C₂×#41	—	2	4	no	—
375	C₂×#41	Q₈×C₁₃	1	8	yes	complemented
376	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
377	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
379	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
380	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
382	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
383	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
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	1	yes	characteristic
388	C₄⋊Q₈	—	2	4	no	—
389	C₄⋊Q₈	—	2	4	no	—
390	#125	—	2	8	no	—
391	C₂²⋊Q₈	—	2	8	no	—
392	C₂²⋊Q₈	—	2	8	no	—
393	C₂²⋊Q₈	—	2	16	no	—
394	C₄×Q₈	—	2	4	no	—
395	C₄×Q₈	—	2	4	no	—
396	C₄×Q₈	—	2	8	no	—
397	C₄×Q₈	—	2	8	no	—
398	C₄×D₄	—	2	8	no	—
399	C₄×D₄	—	2	8	no	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	4	no	—
402	#117	—	2	4	no	—
403	#117	—	2	8	no	—
404	#117	—	2	8	no	—
405	C₂×C₄⋊C₄	—	2	8	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	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×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
420	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
427	C₂×C₄²	—	2	8	no	—
428	C₂×C₄²	—	2	8	no	—
429	C₂×C₄²	D₄×C₁₃	1	8	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
431	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
432	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
434	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
435	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
436	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
437	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
439	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
441	#95	C₂³×C₁₃	1	4	yes	—
442	#95	C₂³×C₁₃	1	2	yes	—
443	#95	C₂³×C₁₃	1	2	yes	—
444	#95	C₂³×C₁₃	1	8	yes	—
445	#95	C₂³×C₁₃	1	8	yes	—
446	#95	C₂³×C₁₃	1	8	yes	—
447	#95	C₂³×C₁₃	1	8	yes	—
448	C₂×C₁₃	—	2	4	no	—
449	C₂×C₁₃	—	4	4	no	—
450	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
451	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
452	C₂×C₁₃	#3449	1	1	yes	characteristic
453	C₂×C₁₃	#3475	1	2	yes	—
454	C₂×C₁₃	Q₈×#41	1	2	yes	—
455	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
457	#41	—	2	32	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	4	no	—
460	C₂×Q₈	—	2	4	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	8	no	—
463	C₂×Q₈	—	4	4	no	—
464	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	C₂×Q₈×C₁₃	1	8	yes	—
470	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	8	no	—
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
483	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
485	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
486	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
487	C₂²×C₄	C₁₃×#41	1	4	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
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	4	no	—
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	8	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	16	no	—
514	C₄⋊C₄	—	4	8	no	—
515	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	4	8	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	8	no	—
526	C₄²	—	2	4	no	—
527	C₄²	—	2	8	no	—
528	C₄²	—	2	4	no	—
529	C₄²	C₂×D₄×C₁₃	1	4	yes	—
530	C₄²	C₂×D₄×C₁₃	1	4	yes	—
531	C₄²	C₂×D₄×C₁₃	1	4	yes	—
532	C₄²	C₂×D₄×C₁₃	1	4	yes	—
533	C₁₃	#34947	1	1	yes	characteristic, direct product factor, Sylow
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
541	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
542	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
543	C₂³	C₂×C₁₃×#41	1	2	yes	—
544	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
545	Q₈	—	2	8	no	—
546	Q₈	—	4	8	no	—
547	Q₈	—	4	8	no	—
548	D₄	—	2	16	no	—
549	D₄	—	2	8	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	16	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	8	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	16	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
575	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
576	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
581	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
582	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
583	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
584	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
585	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
586	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
587	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	4	no	—
591	C₂²	—	2	4	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	8	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	4	no	—
597	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
598	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
599	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
600	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
601	C₂²	C₂²×C₁₃×#41	1	2	yes	—
602	C₂²	C₁₃×#585	1	2	yes	—
603	C₄	—	2	4	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	2	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	8	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	4	no	—
613	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
614	C₄	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
615	C₄	C₁₃×#532	1	4	yes	—
616	C₂	—	2	4	no	—
617	C₂	—	4	4	no	—
618	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
619	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
620	C₂	C₁₃×#3449	1	1	yes	characteristic
621	C₂	C₁₃×#3475	1	2	yes	—
622	C₂	Q₈×C₁₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#2568	C₂	semidirect
4. C₁₃×#2567	C₂	semidirect
5. C₁₃×#2566	C₂	semidirect
6. C₁₃×#2565	C₂	semidirect
7. C₁₃×#2564	C₂	semidirect
8. C₁₃×#2563	C₂	semidirect
9. C₁₃×#2542	C₂	semidirect
10. C₁₃×#2417	C₂	semidirect
11. C₁₃×#2396	C₂	semidirect
12. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₁₃×#2285	C₂	semidirect
15. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
71. C₂×C₁₃×#41	Q₈	semidirect
144. #34947	C₁₃	direct (N × H)
205. C₁₃×C₄⋊C₄	#41	semidirect
223. C₂×#533	C₂×C₁₃	semidirect
225. #2568	C₂×C₁₃	semidirect
226. #2567	C₂×C₁₃	semidirect
227. #2566	C₂×C₁₃	semidirect
228. #2565	C₂×C₁₃	semidirect
229. #2564	C₂×C₁₃	semidirect
230. #2563	C₂×C₁₃	semidirect
231. #2542	C₂×C₁₃	semidirect
232. #2417	C₂×C₁₃	semidirect
233. #2396	C₂×C₁₃	semidirect
234. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
236. #2285	C₂×C₁₃	semidirect
237. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
278. C₂×C₄×C₁₃	C₂²⋊Q₈	semidirect
375. C₂×#41	Q₈×C₁₃	semidirect
515. C₄⋊C₄	C₁₃×#41	semidirect
533. C₁₃	#34947	direct (N × H)
574. C₂×C₄	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#533	2
C₂×C₄×C₁₃×#41	2
C₁₃×#2568	2
C₁₃×#2567	2
C₁₃×#2566	2
C₁₃×#2565	2
C₁₃×#2564	2
C₁₃×#2563	2
C₁₃×#2542	2
C₁₃×#2417	2
C₁₃×#2396	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2297	2
C₁₃×#2285	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34947	13

Subgroups — C13×#34947 #15721286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34947 #15721286