Subgroups — C₂×C₁₃×#2545 #15721239

Order 3328.

3310 conjugacy classes of subgroups.

The subgroup lattice has 464 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, complemented
2	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2545	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#396	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#388	C₂	1	4	yes	maximal, complemented
10	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
16	C₂×C₁₃×#124	—	2	8	no	—
17	C₂×C₁₃×#124	—	2	8	no	—
18	C₂×C₁₃×#124	C₂²	1	8	yes	—
19	C₂×C₁₃×#124	C₂²	1	8	yes	—
20	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#396	C₂²	1	32	yes	complemented
35	C₁₃×#391	C₂²	1	8	yes	complemented
36	C₁₃×#390	C₂²	1	8	yes	—
37	C₁₃×#388	C₂²	1	32	yes	complemented
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	4	yes	—
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
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	—	2	4	no	—
46	C₂²×Q₈×C₁₃	—	2	4	no	—
47	C₂²×Q₈×C₁₃	D₄	1	8	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	2	4	no	—
52	C₂²×D₄×C₁₃	—	2	4	no	—
53	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	—	2	32	no	—
63	C₁₃×#124	—	2	32	no	—
64	C₁₃×#124	—	2	32	no	—
65	C₄×Q₈×C₁₃	—	2	32	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₄²×C₁₃	—	2	8	no	—
83	C₂×C₄²×C₁₃	—	2	4	no	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	D₄	1	8	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
90	C₁₃×#95	C₂³	1	8	yes	—
91	C₁₃×#95	C₂³	1	16	yes	—
92	C₂×#2545	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	8	no	—
96	C₂⁴×C₁₃	—	2	4	no	—
97	C₂⁴×C₁₃	—	2	8	no	—
98	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
100	C₂×Q₈×C₁₃	—	2	32	no	—
101	C₂×Q₈×C₁₃	—	2	8	no	—
102	C₂×Q₈×C₁₃	—	2	8	no	—
103	C₂×Q₈×C₁₃	—	2	8	no	—
104	C₂×Q₈×C₁₃	—	2	8	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₃	—	4	16	no	—
107	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	—
108	C₂×D₄×C₁₃	—	2	8	no	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	4	16	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	#41	1	8	yes	—
132	C₂²×C₄×C₁₃	#41	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
141	C₁₃×C₄⋊C₄	—	2	16	no	—
142	C₁₃×C₄⋊C₄	—	2	8	no	—
143	C₁₃×C₄⋊C₄	—	2	32	no	—
144	C₁₃×C₄⋊C₄	—	2	16	no	—
145	C₁₃×C₂²⋊C₄	—	2	32	no	—
146	C₁₃×C₂²⋊C₄	—	2	16	no	—
147	C₁₃×C₂²⋊C₄	—	2	16	no	—
148	C₁₃×C₂²⋊C₄	—	2	32	no	—
149	C₄²×C₁₃	—	2	16	no	—
150	C₄²×C₁₃	—	2	8	no	—
151	C₄²×C₁₃	—	2	8	no	—
152	C₄²×C₁₃	C₂×D₄	1	16	yes	—
153	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
155	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic
156	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
157	#2545	C₂×C₁₃	1	16	yes	direct product factor
158	C₂×#396	C₂×C₁₃	1	4	yes	complemented
159	C₂×#391	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
161	C₂×#388	C₂×C₁₃	1	4	yes	complemented
162	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	8	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	2	8	no	—
168	C₂³×C₁₃	—	4	8	no	—
169	C₂³×C₁₃	—	4	8	no	—
170	C₂³×C₁₃	—	4	8	no	—
171	C₂³×C₁₃	—	4	16	no	—
172	C₂³×C₁₃	—	4	16	no	—
173	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
174	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
175	C₂³×C₁₃	C₂×#41	1	2	yes	—
176	C₂³×C₁₃	C₂×#41	1	4	yes	—
177	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
178	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	32	no	—
180	Q₈×C₁₃	—	4	16	no	—
181	D₄×C₁₃	—	4	16	no	—
182	C₂×C₄×C₁₃	—	2	16	no	—
183	C₂×C₄×C₁₃	—	2	8	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	16	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	#121	1	16	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
210	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
211	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
212	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	—	2	8	no	—
215	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
216	C₂×#124	—	2	8	no	—
217	C₂×#124	—	2	8	no	—
218	C₂×#124	C₂²×C₁₃	1	8	yes	—
219	C₂×#124	C₂²×C₁₃	1	8	yes	—
220	C₂×C₄×Q₈	—	2	8	no	—
221	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
222	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
228	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
229	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
230	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
231	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
234	#396	C₂²×C₁₃	1	32	yes	complemented
235	#391	C₂²×C₁₃	1	8	yes	complemented
236	#390	C₂²×C₁₃	1	8	yes	—
237	#388	C₂²×C₁₃	1	32	yes	complemented
238	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
239	C₂×#95	C₂²×C₁₃	1	4	yes	—
240	C₂×#95	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	4	8	no	—
245	C₂²×C₁₃	—	4	8	no	—
246	C₂²×C₁₃	—	8	16	no	—
247	C₂²×C₁₃	C₂×#121	1	4	yes	—
248	C₂²×C₁₃	#532	1	4	yes	—
249	C₂²×C₁₃	#536	1	4	yes	—
250	C₂²×C₁₃	#548	1	8	yes	—
251	C₂²×C₁₃	#556	1	8	yes	—
252	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
253	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
254	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
255	C₂²×C₁₃	C₂²×#41	1	2	yes	—
256	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
257	C₄×C₁₃	—	2	8	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	2	8	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₄×C₁₃	C₂×#121	1	8	yes	—
265	C₂⁵	C₂³×C₁₃	1	2	yes	—
266	C₂²×Q₈	—	2	4	no	—
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	—	2	4	no	—
269	C₂²×Q₈	—	2	4	no	—
270	C₂²×Q₈	—	2	4	no	—
271	C₂²×Q₈	D₄×C₁₃	1	8	yes	—
272	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
273	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
274	C₂²×D₄	—	2	4	no	—
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
278	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₄⋊Q₈	—	2	32	no	—
287	#124	—	2	32	no	—
288	#124	—	2	32	no	—
289	C₄×Q₈	—	2	32	no	—
290	C₂×C₄⋊C₄	—	2	8	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	16	no	—
293	C₂×C₄⋊C₄	—	2	8	no	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
298	C₂×C₂²⋊C₄	—	2	16	no	—
299	C₂×C₂²⋊C₄	—	2	8	no	—
300	C₂×C₂²⋊C₄	—	2	8	no	—
301	C₂×C₂²⋊C₄	—	2	16	no	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
306	C₂×C₄²	—	2	8	no	—
307	C₂×C₄²	—	2	4	no	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	D₄×C₁₃	1	8	yes	—
310	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
311	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
312	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
313	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
314	#95	C₂³×C₁₃	1	8	yes	—
315	#95	C₂³×C₁₃	1	16	yes	—
316	C₂×C₁₃	—	8	4	no	—
317	C₂×C₁₃	#2545	1	8	yes	direct product factor
318	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
321	C₂×C₁₃	C₂×#548	1	2	yes	—
322	C₂×C₁₃	C₂×#556	1	2	yes	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	8	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	2	8	no	—
328	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
329	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
330	C₂×Q₈	—	2	32	no	—
331	C₂×Q₈	—	2	8	no	—
332	C₂×Q₈	—	2	8	no	—
333	C₂×Q₈	—	2	8	no	—
334	C₂×Q₈	—	2	8	no	—
335	C₂×Q₈	—	2	8	no	—
336	C₂×Q₈	—	4	16	no	—
337	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	4	16	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
361	C₂²×C₄	C₁₃×#41	1	8	yes	—
362	C₂²×C₄	C₁₃×#41	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
369	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
370	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
371	C₄⋊C₄	—	2	16	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	32	no	—
374	C₄⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	—	2	32	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₂²⋊C₄	—	2	16	no	—
378	C₂²⋊C₄	—	2	32	no	—
379	C₄²	—	2	16	no	—
380	C₄²	—	2	8	no	—
381	C₄²	—	2	8	no	—
382	C₄²	C₂×D₄×C₁₃	1	16	yes	—
383	C₁₃	C₂×#2545	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	8	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	4	8	no	—
392	C₂³	—	4	16	no	—
393	C₂³	—	4	16	no	—
394	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
396	C₂³	C₂×C₁₃×#41	1	2	yes	—
397	C₂³	C₂×C₁₃×#41	1	4	yes	—
398	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
399	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
400	Q₈	—	2	32	no	—
401	Q₈	—	4	16	no	—
402	D₄	—	4	16	no	—
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	C₁₃×#121	1	16	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
430	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
431	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	8	no	—
437	C₂²	—	8	16	no	—
438	C₂²	C₂×C₁₃×#121	1	4	yes	—
439	C₂²	C₁₃×#532	1	4	yes	—
440	C₂²	C₁₃×#536	1	4	yes	—
441	C₂²	C₁₃×#548	1	8	yes	—
442	C₂²	C₁₃×#556	1	8	yes	—
443	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
444	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
445	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
446	C₂²	C₂²×C₁₃×#41	1	2	yes	—
447	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
448	C₄	—	2	8	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	8	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	C₂×C₁₃×#121	1	8	yes	—
456	C₂	—	8	4	no	—
457	C₂	C₁₃×#2545	1	8	yes	direct product factor
458	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
460	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#548	1	2	yes	—
462	C₂	C₂×C₁₃×#556	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
4. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
5. C₁₃×#2545	C₂	direct (N × H)
6. C₂×C₁₃×#396	C₂	semidirect
7. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#388	C₂	semidirect
10. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
34. C₁₃×#396	C₂²	semidirect
35. C₁₃×#391	C₂²	semidirect
37. C₁₃×#388	C₂²	semidirect
38. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
92. C₂×#2545	C₁₃	direct (N × H)
153. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
156. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
157. #2545	C₂×C₁₃	direct (N × H)
158. C₂×#396	C₂×C₁₃	semidirect
159. C₂×#391	C₂×C₁₃	semidirect
161. C₂×#388	C₂×C₁₃	semidirect
162. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
215. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
221. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
234. #396	C₂²×C₁₃	semidirect
235. #391	C₂²×C₁₃	semidirect
237. #388	C₂²×C₁₃	semidirect
238. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
317. C₂×C₁₃	#2545	direct (N × H)
383. C₁₃	C₂×#2545	direct (N × H)
457. C₂	C₁₃×#2545	direct (N × H)

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
C₂²×C₁₃×#124	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2545	2
C₂×C₁₃×#396	2
C₂×C₁₃×#391	2
C₂×C₁₃×#390	2
C₂×C₁₃×#388	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2545	13

Subgroups — C2×C13×#2545 #15721239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2545 #15721239