Subgroups — C₁₃×#34946 #15721285

Order 3328.

2834 conjugacy classes of subgroups.

The subgroup lattice has 500 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	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2563	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2562	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2561	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2547	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2503	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2435	C₂	1	2	yes	maximal
9	C₁₃×#2398	C₂	1	4	yes	maximal, complemented
10	C₄×C₁₃×#124	C₂	1	4	yes	maximal, complemented
11	C₁₃×#2280	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
15	C₁₃×#533	—	2	8	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#124	C₂²	1	4	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
23	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
24	C₂×C₄×D₄×C₁₃	—	2	8	no	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₁₃×#117	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#400	C₂²	1	8	yes	complemented
35	C₁₃×#397	C₂²	1	8	yes	complemented
36	C₁₃×#394	C₂²	1	8	yes	—
37	C₁₃×#393	C₂²	1	8	yes	complemented
38	C₁₃×#391	C₂²	1	4	yes	complemented
39	C₁₃×#390	C₂²	1	4	yes	—
40	C₁₃×#388	C₂²	1	16	yes	complemented
41	C₁₃×#382	C₂²	1	4	yes	complemented
42	C₁₃×#381	C₂²	1	8	yes	—
43	C₁₃×#380	C₂²	1	8	yes	complemented
44	C₁₃×#380	C₂²	1	8	yes	complemented
45	C₁₃×#379	C₂²	1	8	yes	—
46	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
47	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
48	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
50	C₄×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
51	C₁₃×#376	C₂²	1	2	yes	complemented
52	C₄³×C₁₃	C₂²	1	2	yes	complemented
53	C₂⁵×C₁₃	C₂³	1	2	yes	—
54	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×D₄×C₁₃	—	2	8	no	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	—	2	16	no	—
62	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	—	2	4	no	—
69	C₁₃×C₄⋊Q₈	—	2	4	no	—
70	C₁₃×#125	—	2	8	no	—
71	C₁₃×#124	—	2	16	no	—
72	C₁₃×C₂²⋊Q₈	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	8	no	—
74	C₄×Q₈×C₁₃	—	2	8	no	—
75	C₄×Q₈×C₁₃	—	2	8	no	—
76	C₄×D₄×C₁₃	—	2	8	no	—
77	C₄×D₄×C₁₃	—	2	8	no	—
78	C₄×D₄×C₁₃	—	2	8	no	—
79	C₄×D₄×C₁₃	—	2	8	no	—
80	C₁₃×#117	—	2	8	no	—
81	C₁₃×#117	—	2	8	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
99	C₂×C₄²×C₁₃	D₄	1	8	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	16	yes	—
111	C₁₃×#95	C₂³	1	16	yes	—
112	#34946	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	2	8	no	—
115	C₂⁴×C₁₃	—	2	8	no	—
116	C₂⁴×C₁₃	—	4	4	no	—
117	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₁₃	—	2	4	no	—
120	C₂×Q₈×C₁₃	—	2	4	no	—
121	C₂×Q₈×C₁₃	—	2	8	no	—
122	C₂×Q₈×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	2	32	no	—
124	C₂×D₄×C₁₃	—	2	8	no	—
125	C₂×D₄×C₁₃	—	2	4	no	—
126	C₂×D₄×C₁₃	—	2	4	no	—
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	#41	1	8	yes	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	8	no	—
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	2	16	no	—
135	C₂²×C₄×C₁₃	—	2	16	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	32	no	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	#41	1	8	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	32	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	4	16	no	—
167	C₄²×C₁₃	—	2	8	no	—
168	C₄²×C₁₃	—	2	8	no	—
169	C₄²×C₁₃	—	2	8	no	—
170	C₄²×C₁₃	—	4	4	no	—
171	C₄²×C₁₃	C₂×D₄	1	4	yes	—
172	C₄²×C₁₃	C₂×D₄	1	4	yes	—
173	C₄²×C₁₃	C₂×D₄	1	4	yes	—
174	C₄²×C₁₃	C₂×D₄	1	4	yes	—
175	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
177	#2563	C₂×C₁₃	1	2	yes	complemented
178	#2562	C₂×C₁₃	1	4	yes	complemented
179	#2561	C₂×C₁₃	1	4	yes	complemented
180	#2547	C₂×C₁₃	1	2	yes	complemented
181	#2503	C₂×C₁₃	1	2	yes	complemented
182	#2435	C₂×C₁₃	1	2	yes	—
183	#2398	C₂×C₁₃	1	4	yes	complemented
184	C₄×#124	C₂×C₁₃	1	4	yes	complemented
185	#2280	C₂×C₁₃	1	4	yes	complemented
186	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	16	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	8	no	—
194	C₂³×C₁₃	—	4	32	no	—
195	C₂³×C₁₃	—	4	8	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂³×C₁₃	C₂×#41	1	8	yes	—
199	C₂³×C₁₃	C₂×#41	1	4	yes	—
200	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
201	Q₈×C₁₃	—	4	8	no	—
202	Q₈×C₁₃	—	4	8	no	—
203	D₄×C₁₃	—	2	16	no	—
204	D₄×C₁₃	—	2	16	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	8	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	8	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	8	no	—
220	C₂×C₄×C₁₃	—	4	16	no	—
221	C₂×C₄×C₁₃	—	4	16	no	—
222	C₂×C₄×C₁₃	#124	1	16	yes	complemented
223	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
230	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
231	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
232	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
234	#533	—	2	8	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
237	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
238	C₂×#124	C₂²×C₁₃	1	4	yes	—
239	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
242	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
243	C₂×C₄×D₄	—	2	8	no	—
244	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
248	C₂×#117	C₂²×C₁₃	1	2	yes	—
249	C₂×#117	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
253	#400	C₂²×C₁₃	1	8	yes	complemented
254	#397	C₂²×C₁₃	1	8	yes	complemented
255	#394	C₂²×C₁₃	1	8	yes	—
256	#393	C₂²×C₁₃	1	8	yes	complemented
257	#391	C₂²×C₁₃	1	4	yes	complemented
258	#390	C₂²×C₁₃	1	4	yes	—
259	#388	C₂²×C₁₃	1	16	yes	complemented
260	#382	C₂²×C₁₃	1	4	yes	complemented
261	#381	C₂²×C₁₃	1	8	yes	—
262	#380	C₂²×C₁₃	1	8	yes	complemented
263	#380	C₂²×C₁₃	1	8	yes	complemented
264	#379	C₂²×C₁₃	1	8	yes	—
265	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
266	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
267	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
269	C₄×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	complemented
270	#376	C₂²×C₁₃	1	2	yes	complemented
271	C₄³	C₂²×C₁₃	1	2	yes	complemented
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	8	no	—
275	C₂²×C₁₃	—	2	8	no	—
276	C₂²×C₁₃	—	2	16	no	—
277	C₂²×C₁₃	—	4	32	no	—
278	C₂²×C₁₃	—	4	4	no	—
279	C₂²×C₁₃	—	4	4	no	—
280	C₂²×C₁₃	—	4	8	no	—
281	C₂²×C₁₃	C₂×#124	1	4	yes	—
282	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
283	C₂²×C₁₃	C₂²×#41	1	2	yes	—
284	C₂²×C₁₃	C₂²×#41	1	2	yes	—
285	C₂²×C₁₃	#585	1	2	yes	—
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	4	4	no	—
290	C₄×C₁₃	—	4	4	no	—
291	C₄×C₁₃	—	4	4	no	—
292	C₄×C₁₃	—	4	8	no	—
293	C₄×C₁₃	#525	1	4	yes	—
294	C₄×C₁₃	C₂×#124	1	4	yes	—
295	C₄×C₁₃	C₂×#124	1	4	yes	—
296	C₂⁵	C₂³×C₁₃	1	2	yes	—
297	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
298	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
299	C₂²×D₄	—	2	8	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
302	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
303	C₂³×C₄	—	2	8	no	—
304	C₂³×C₄	—	2	16	no	—
305	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
307	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
308	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	4	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	#125	—	2	8	no	—
314	#124	—	2	16	no	—
315	C₂²⋊Q₈	—	2	8	no	—
316	C₂²⋊Q₈	—	2	8	no	—
317	C₄×Q₈	—	2	8	no	—
318	C₄×Q₈	—	2	8	no	—
319	C₄×D₄	—	2	8	no	—
320	C₄×D₄	—	2	8	no	—
321	C₄×D₄	—	2	8	no	—
322	C₄×D₄	—	2	8	no	—
323	#117	—	2	8	no	—
324	#117	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
342	C₂×C₄²	D₄×C₁₃	1	8	yes	—
343	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
344	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
345	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
346	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
347	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
351	#95	C₂³×C₁₃	1	4	yes	—
352	#95	C₂³×C₁₃	1	4	yes	—
353	#95	C₂³×C₁₃	1	16	yes	—
354	#95	C₂³×C₁₃	1	16	yes	—
355	C₂×C₁₃	—	2	4	no	—
356	C₂×C₁₃	—	4	8	no	—
357	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
358	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
359	C₂×C₁₃	#3449	1	1	yes	characteristic
360	C₂×C₁₃	#3475	1	4	yes	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	8	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	4	4	no	—
365	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
366	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	8	no	—
370	C₂×Q₈	—	4	4	no	—
371	C₂×D₄	—	2	32	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	—	2	4	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	C₁₃×#41	1	8	yes	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	16	no	—
383	C₂²×C₄	—	2	16	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	32	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
389	C₂²×C₄	C₁₃×#41	1	8	yes	—
390	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	32	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	4	16	no	—
415	C₄²	—	2	8	no	—
416	C₄²	—	2	8	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	4	4	no	—
419	C₄²	C₂×D₄×C₁₃	1	4	yes	—
420	C₄²	C₂×D₄×C₁₃	1	4	yes	—
421	C₄²	C₂×D₄×C₁₃	1	4	yes	—
422	C₄²	C₂×D₄×C₁₃	1	4	yes	—
423	C₁₃	#34946	1	1	yes	characteristic, direct product factor, Sylow
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	16	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	8	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	8	no	—
431	C₂³	—	4	32	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	8	no	—
434	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
435	C₂³	C₂×C₁₃×#41	1	8	yes	—
436	C₂³	C₂×C₁₃×#41	1	4	yes	—
437	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
438	Q₈	—	4	8	no	—
439	Q₈	—	4	8	no	—
440	D₄	—	2	16	no	—
441	D₄	—	2	16	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	16	no	—
459	C₂×C₄	C₁₃×#124	1	16	yes	complemented
460	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
466	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
467	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
468	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	8	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	16	no	—
474	C₂²	—	4	32	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	8	no	—
478	C₂²	C₂×C₁₃×#124	1	4	yes	—
479	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
480	C₂²	C₂²×C₁₃×#41	1	2	yes	—
481	C₂²	C₂²×C₁₃×#41	1	2	yes	—
482	C₂²	C₁₃×#585	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	8	no	—
490	C₄	C₁₃×#525	1	4	yes	—
491	C₄	C₂×C₁₃×#124	1	4	yes	—
492	C₄	C₂×C₁₃×#124	1	4	yes	—
493	C₂	—	2	4	no	—
494	C₂	—	4	8	no	—
495	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
496	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
497	C₂	C₁₃×#3449	1	1	yes	characteristic
498	C₂	C₁₃×#3475	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂³×D₄×C₁₃	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×#2563	C₂	semidirect
4. C₁₃×#2562	C₂	semidirect
5. C₁₃×#2561	C₂	semidirect
6. C₁₃×#2547	C₂	semidirect
7. C₁₃×#2503	C₂	semidirect
9. C₁₃×#2398	C₂	semidirect
10. C₄×C₁₃×#124	C₂	semidirect
11. C₁₃×#2280	C₂	semidirect
12. C₄×C₁₃×#117	C₂	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
23. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
34. C₁₃×#400	C₂²	semidirect
35. C₁₃×#397	C₂²	semidirect
37. C₁₃×#393	C₂²	semidirect
38. C₁₃×#391	C₂²	semidirect
40. C₁₃×#388	C₂²	semidirect
41. C₁₃×#382	C₂²	semidirect
43. C₁₃×#380	C₂²	semidirect
44. C₁₃×#380	C₂²	semidirect
46. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
50. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
51. C₁₃×#376	C₂²	semidirect
52. C₄³×C₁₃	C₂²	semidirect
112. #34946	C₁₃	direct (N × H)
175. C₂×#533	C₂×C₁₃	semidirect
177. #2563	C₂×C₁₃	semidirect
178. #2562	C₂×C₁₃	semidirect
179. #2561	C₂×C₁₃	semidirect
180. #2547	C₂×C₁₃	semidirect
181. #2503	C₂×C₁₃	semidirect
183. #2398	C₂×C₁₃	semidirect
184. C₄×#124	C₂×C₁₃	semidirect
185. #2280	C₂×C₁₃	semidirect
186. C₄×#117	C₂×C₁₃	semidirect
222. C₂×C₄×C₁₃	#124	semidirect
235. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
236. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
237. C₂×#125	C₂²×C₁₃	semidirect
241. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
242. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
253. #400	C₂²×C₁₃	semidirect
254. #397	C₂²×C₁₃	semidirect
256. #393	C₂²×C₁₃	semidirect
257. #391	C₂²×C₁₃	semidirect
259. #388	C₂²×C₁₃	semidirect
260. #382	C₂²×C₁₃	semidirect
262. #380	C₂²×C₁₃	semidirect
263. #380	C₂²×C₁₃	semidirect
265. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
266. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
269. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
270. #376	C₂²×C₁₃	semidirect
271. C₄³	C₂²×C₁₃	semidirect
423. C₁₃	#34946	direct (N × H)
459. C₂×C₄	C₁₃×#124	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
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2563	2
C₁₃×#2562	2
C₁₃×#2561	2
C₁₃×#2547	2
C₁₃×#2503	2
C₁₃×#2435	2
C₁₃×#2398	2
C₄×C₁₃×#124	2
C₁₃×#2280	2
C₄×C₁₃×#117	2
#34946	13

Subgroups — C13×#34946 #15721285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34946 #15721285