Subgroups — C₂×C₁₃×#2550 #15721227

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 508 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	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2550	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#398	C₂	1	2	yes	maximal
5	C₂×C₁₃×#395	C₂	1	2	yes	maximal
6	C₂×C₁₃×#391	C₂	1	2	yes	maximal
7	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#389	C₂	1	2	yes	maximal
10	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	—
16	C₂×C₁₃×#125	—	2	8	no	—
17	C₂×C₁₃×#125	C₂²	1	8	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#398	C₂²	1	16	yes	—
34	C₁₃×#395	C₂²	1	16	yes	—
35	C₁₃×#391	C₂²	1	16	yes	—
36	C₁₃×#389	C₂²	1	16	yes	—
37	C₁₃×#389	C₂²	1	8	yes	—
38	C₁₃×#389	C₂²	1	8	yes	—
39	C₁₃×#382	C₂²	1	8	yes	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	—
42	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#95	C₂²	1	2	yes	—
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₃	—	2	8	no	—
50	C₂²×Q₈×C₁₃	—	2	8	no	—
51	C₂²×Q₈×C₁₃	—	4	4	no	—
52	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	—	2	32	no	—
65	C₁₃×#125	—	2	32	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
76	C₂×C₁₃×C₄⋊C₄	Q₈	1	8	yes	complemented
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	—	2	4	no	—
89	C₂×C₄²×C₁₃	—	2	4	no	—
90	C₂×C₄²×C₁₃	—	4	4	no	—
91	C₂×C₄²×C₁₃	Q₈	1	8	yes	complemented
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
96	C₁₃×#95	C₂³	1	4	yes	—
97	C₁₃×#95	C₂³	1	4	yes	—
98	C₁₃×#95	C₂³	1	8	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₂×#2550	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₂×Q₈×C₁₃	—	2	16	no	—
106	C₂×Q₈×C₁₃	—	2	16	no	—
107	C₂×Q₈×C₁₃	—	4	8	no	—
108	C₂×Q₈×C₁₃	—	4	32	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
138	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
140	C₂²×C₄×C₁₃	#41	1	4	yes	—
141	C₂²×C₄×C₁₃	#41	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₁₃×C₄⋊C₄	—	2	16	no	—
154	C₁₃×C₄⋊C₄	—	2	16	no	—
155	C₁₃×C₄⋊C₄	—	2	8	no	—
156	C₁₃×C₄⋊C₄	—	2	16	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	16	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	4	8	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
163	C₁₃×C₄⋊C₄	C₂×Q₈	1	16	yes	complemented
164	C₄²×C₁₃	—	2	8	no	—
165	C₄²×C₁₃	—	2	8	no	—
166	C₄²×C₁₃	—	4	8	no	—
167	C₄²×C₁₃	C₂×Q₈	1	16	yes	complemented
168	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic
169	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic
170	#2550	C₂×C₁₃	1	16	yes	direct product factor
171	C₂×#398	C₂×C₁₃	1	2	yes	—
172	C₂×#395	C₂×C₁₃	1	2	yes	—
173	C₂×#391	C₂×C₁₃	1	2	yes	—
174	C₂×#389	C₂×C₁₃	1	2	yes	—
175	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
176	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
177	C₂×#382	C₂×C₁₃	1	1	yes	characteristic
178	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
179	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
180	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
182	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
183	C₂³×C₁₃	C₂×#41	1	2	yes	—
184	C₂³×C₁₃	C₂×#41	1	2	yes	—
185	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
186	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
187	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
188	Q₈×C₁₃	—	4	32	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	16	no	—
192	C₂×C₄×C₁₃	—	2	8	no	—
193	C₂×C₄×C₁₃	—	2	8	no	—
194	C₂×C₄×C₁₃	—	2	16	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	4	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	2	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	2	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	4	4	no	—
220	C₂×C₄×C₁₃	—	4	8	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	8	no	—
223	C₂×C₄×C₁₃	C₄⋊Q₈	1	16	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
227	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
228	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
229	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
230	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
231	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
232	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
233	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄⋊Q₈	—	2	8	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	—
236	C₂×#125	—	2	8	no	—
237	C₂×#125	C₂²×C₁₃	1	8	yes	—
238	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
244	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
253	#398	C₂²×C₁₃	1	16	yes	—
254	#395	C₂²×C₁₃	1	16	yes	—
255	#391	C₂²×C₁₃	1	16	yes	—
256	#389	C₂²×C₁₃	1	16	yes	—
257	#389	C₂²×C₁₃	1	8	yes	—
258	#389	C₂²×C₁₃	1	8	yes	—
259	#382	C₂²×C₁₃	1	8	yes	—
260	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
261	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	—
262	C₂×#95	C₂²×C₁₃	1	2	yes	—
263	C₂×#95	C₂²×C₁₃	1	2	yes	—
264	C₂×#95	C₂²×C₁₃	1	2	yes	—
265	C₂×#95	C₂²×C₁₃	1	2	yes	—
266	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#95	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
270	C₂²×C₁₃	#533	1	4	yes	—
271	C₂²×C₁₃	#544	1	4	yes	—
272	C₂²×C₁₃	#546	1	4	yes	—
273	C₂²×C₁₃	#548	1	4	yes	—
274	C₂²×C₁₃	#554	1	4	yes	—
275	C₂²×C₁₃	#557	1	4	yes	—
276	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
277	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
278	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
279	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
280	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
281	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
282	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
283	C₄×C₁₃	—	2	4	no	—
284	C₄×C₁₃	—	2	4	no	—
285	C₄×C₁₃	—	2	8	no	—
286	C₄×C₁₃	—	2	4	no	—
287	C₄×C₁₃	—	2	4	no	—
288	C₄×C₁₃	—	2	8	no	—
289	C₄×C₁₃	—	4	2	no	—
290	C₄×C₁₃	—	4	4	no	—
291	C₄×C₁₃	—	4	2	no	—
292	C₄×C₁₃	—	4	4	no	—
293	C₄×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
294	C₂²×Q₈	—	2	8	no	—
295	C₂²×Q₈	—	2	8	no	—
296	C₂²×Q₈	—	4	4	no	—
297	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
298	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
301	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
303	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
304	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₄⋊Q₈	—	2	32	no	—
310	#125	—	2	32	no	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	—	2	8	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	8	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	4	4	no	—
320	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
321	C₂×C₄⋊C₄	Q₈×C₁₃	1	8	yes	complemented
322	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₄²	—	2	4	no	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	—	4	4	no	—
336	C₂×C₄²	Q₈×C₁₃	1	8	yes	complemented
337	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
338	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
339	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
340	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
341	#95	C₂³×C₁₃	1	4	yes	—
342	#95	C₂³×C₁₃	1	4	yes	—
343	#95	C₂³×C₁₃	1	8	yes	—
344	#95	C₂³×C₁₃	1	8	yes	—
345	#95	C₂³×C₁₃	1	8	yes	—
346	#95	C₂³×C₁₃	1	8	yes	—
347	#95	C₂³×C₁₃	1	8	yes	—
348	C₂×C₁₃	#2550	1	8	yes	direct product factor
349	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
350	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
351	C₂×C₁₃	C₂×#544	1	1	yes	characteristic
352	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
354	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
355	C₂×C₁₃	C₂×#557	1	1	yes	characteristic
356	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
357	C₂×Q₈	—	2	16	no	—
358	C₂×Q₈	—	2	16	no	—
359	C₂×Q₈	—	4	8	no	—
360	C₂×Q₈	—	4	32	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
387	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
389	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
390	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
392	C₂²×C₄	C₁₃×#41	1	4	yes	—
393	C₂²×C₄	C₁₃×#41	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
405	C₄⋊C₄	—	2	16	no	—
406	C₄⋊C₄	—	2	16	no	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	16	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	16	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	4	8	no	—
414	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
415	C₄⋊C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
416	C₄²	—	2	8	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	4	8	no	—
419	C₄²	C₂×Q₈×C₁₃	1	16	yes	complemented
420	C₁₃	C₂×#2550	1	1	yes	characteristic, direct product factor, Sylow
421	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
422	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
423	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
424	C₂³	C₂×C₁₃×#41	1	2	yes	—
425	C₂³	C₂×C₁₃×#41	1	2	yes	—
426	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
427	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
428	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
429	Q₈	—	4	32	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	16	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	16	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	C₁₃×C₄⋊Q₈	1	16	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
467	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
468	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
469	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
470	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
471	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
472	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
473	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
474	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
475	C₂²	C₁₃×#533	1	4	yes	—
476	C₂²	C₁₃×#544	1	4	yes	—
477	C₂²	C₁₃×#546	1	4	yes	—
478	C₂²	C₁₃×#548	1	4	yes	—
479	C₂²	C₁₃×#554	1	4	yes	—
480	C₂²	C₁₃×#557	1	4	yes	—
481	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
482	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
483	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
484	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
485	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
486	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
487	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
488	C₄	—	2	4	no	—
489	C₄	—	2	4	no	—
490	C₄	—	2	8	no	—
491	C₄	—	2	4	no	—
492	C₄	—	2	4	no	—
493	C₄	—	2	8	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	4	no	—
498	C₄	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
499	C₂	C₁₃×#2550	1	8	yes	direct product factor
500	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
501	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
502	C₂	C₂×C₁₃×#544	1	1	yes	characteristic
503	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
504	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
505	C₂	C₂×C₁₃×#554	1	1	yes	characteristic
506	C₂	C₂×C₁₃×#557	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×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
3. C₁₃×#2550	C₂	direct (N × H)
76. C₂×C₁₃×C₄⋊C₄	Q₈	semidirect
91. C₂×C₄²×C₁₃	Q₈	semidirect
103. C₂×#2550	C₁₃	direct (N × H)
163. C₁₃×C₄⋊C₄	C₂×Q₈	semidirect
167. C₄²×C₁₃	C₂×Q₈	semidirect
170. #2550	C₂×C₁₃	direct (N × H)
321. C₂×C₄⋊C₄	Q₈×C₁₃	semidirect
336. C₂×C₄²	Q₈×C₁₃	semidirect
348. C₂×C₁₃	#2550	direct (N × H)
415. C₄⋊C₄	C₂×Q₈×C₁₃	semidirect
419. C₄²	C₂×Q₈×C₁₃	semidirect
420. C₁₃	C₂×#2550	direct (N × H)
499. C₂	C₁₃×#2550	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×#125	2
C₁₃×#2550	2
C₂×C₁₃×#398	2
C₂×C₁₃×#395	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#382	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2550	13

Subgroups — C2×C13×#2550 #15721227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2550 #15721227