Subgroups — C₂×C₁₃×#2439 #15721051

Order 3328.

2854 conjugacy classes of subgroups.

The subgroup lattice has 564 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×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2439	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#396	C₂	1	2	yes	maximal
5	C₂×C₁₃×#393	C₂	1	2	yes	maximal
6	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊Q₈	—	2	8	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
17	C₂×C₁₃×#117	—	2	8	no	—
18	C₂×C₁₃×#117	C₂²	1	8	yes	—
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	1	yes	characteristic
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	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	C₁₃×#396	C₂²	1	16	yes	—
34	C₁₃×#393	C₂²	1	16	yes	—
35	C₁₃×#391	C₂²	1	16	yes	complemented
36	C₁₃×#389	C₂²	1	8	yes	complemented
37	C₁₃×#389	C₂²	1	8	yes	complemented
38	C₁₃×#387	C₂²	1	16	yes	complemented
39	C₁₃×#382	C₂²	1	8	yes	complemented
40	C₁₃×#380	C₂²	1	8	yes	—
41	C₄×C₁₃×C₂²⋊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	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	—	2	8	no	—
51	C₂²×Q₈×C₁₃	—	2	8	no	—
52	C₂²×Q₈×C₁₃	—	4	4	no	—
53	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
54	C₂³×C₄×C₁₃	—	2	4	no	—
55	C₂³×C₄×C₁₃	—	2	4	no	—
56	C₂³×C₄×C₁₃	Q₈	1	8	yes	complemented
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	32	no	—
69	C₁₃×#117	—	2	32	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
75	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
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	8	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	4	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₂×C₄²×C₁₃	—	2	8	no	—
93	C₂×C₄²×C₁₃	—	2	4	no	—
94	C₂×C₄²×C₁₃	—	2	4	no	—
95	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
98	C₁₃×#95	C₂³	1	4	yes	—
99	C₁₃×#95	C₂³	1	4	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₁₃×#95	C₂³	1	8	yes	—
102	C₁₃×#95	C₂³	1	8	yes	—
103	C₁₃×#95	C₂³	1	8	yes	—
104	C₁₃×#95	C₂³	1	8	yes	—
105	C₂×#2439	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	—	2	2	no	—
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	2	no	—
112	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
113	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
114	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₂×Q₈×C₁₃	—	2	16	no	—
116	C₂×Q₈×C₁₃	—	2	16	no	—
117	C₂×Q₈×C₁₃	—	4	8	no	—
118	C₂×Q₈×C₁₃	—	4	32	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	32	no	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	4	no	—
141	C₂²×C₄×C₁₃	—	2	4	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	complemented
150	C₂²×C₄×C₁₃	#41	1	4	yes	—
151	C₂²×C₄×C₁₃	#41	1	4	yes	—
152	C₂²×C₄×C₁₃	#41	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	2	16	no	—
165	C₁₃×C₄⋊C₄	—	2	8	no	—
166	C₁₃×C₄⋊C₄	—	2	16	no	—
167	C₁₃×C₄⋊C₄	—	2	8	no	—
168	C₁₃×C₄⋊C₄	—	4	8	no	—
169	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
170	C₁₃×C₂²⋊C₄	—	2	16	no	—
171	C₁₃×C₂²⋊C₄	—	2	8	no	—
172	C₁₃×C₂²⋊C₄	—	2	8	no	—
173	C₁₃×C₂²⋊C₄	—	4	8	no	—
174	C₄²×C₁₃	—	2	16	no	—
175	C₄²×C₁₃	—	2	8	no	—
176	C₄²×C₁₃	—	2	8	no	—
177	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic
179	#2439	C₂×C₁₃	1	16	yes	direct product factor
180	C₂×#396	C₂×C₁₃	1	2	yes	—
181	C₂×#393	C₂×C₁₃	1	2	yes	—
182	C₂×#391	C₂×C₁₃	1	2	yes	complemented
183	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#387	C₂×C₁₃	1	2	yes	complemented
186	C₂×#382	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
188	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	2	8	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	4	4	no	—
202	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
204	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
205	C₂³×C₁₃	C₂×#41	1	2	yes	—
206	C₂³×C₁₃	C₂×#41	1	2	yes	—
207	C₂³×C₁₃	C₂×#41	1	2	yes	—
208	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
209	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
210	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
211	Q₈×C₁₃	—	4	32	no	—
212	C₂×C₄×C₁₃	—	2	8	no	—
213	C₂×C₄×C₁₃	—	2	16	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	32	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	4	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	C₂²⋊Q₈	1	16	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
249	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
251	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
252	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
253	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
254	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	—	2	8	no	—
256	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
257	C₂×#117	—	2	8	no	—
258	C₂×#117	C₂²×C₁₃	1	8	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
265	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
268	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
270	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
272	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
273	#396	C₂²×C₁₃	1	16	yes	—
274	#393	C₂²×C₁₃	1	16	yes	—
275	#391	C₂²×C₁₃	1	16	yes	complemented
276	#389	C₂²×C₁₃	1	8	yes	complemented
277	#389	C₂²×C₁₃	1	8	yes	complemented
278	#387	C₂²×C₁₃	1	16	yes	complemented
279	#382	C₂²×C₁₃	1	8	yes	complemented
280	#380	C₂²×C₁₃	1	8	yes	—
281	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
282	C₂×#95	C₂²×C₁₃	1	2	yes	—
283	C₂×#95	C₂²×C₁₃	1	2	yes	—
284	C₂×#95	C₂²×C₁₃	1	2	yes	—
285	C₂×#95	C₂²×C₁₃	1	2	yes	—
286	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#95	C₂²×C₁₃	1	2	yes	—
289	C₂²×C₁₃	—	2	4	no	—
290	C₂²×C₁₃	—	2	4	no	—
291	C₂²×C₁₃	—	2	4	no	—
292	C₂²×C₁₃	—	4	16	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	—	4	2	no	—
296	C₂²×C₁₃	—	4	2	no	—
297	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
298	C₂²×C₁₃	#533	1	4	yes	—
299	C₂²×C₁₃	#544	1	4	yes	—
300	C₂²×C₁₃	#546	1	4	yes	—
301	C₂²×C₁₃	#548	1	4	yes	—
302	C₂²×C₁₃	#555	1	4	yes	—
303	C₂²×C₁₃	#556	1	4	yes	—
304	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
305	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
306	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
307	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
308	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
309	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
310	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₄×C₁₃	—	2	4	no	—
312	C₄×C₁₃	—	2	8	no	—
313	C₄×C₁₃	—	2	4	no	—
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	4	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	4	4	no	—
319	C₄×C₁₃	—	4	2	no	—
320	C₄×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
321	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
322	C₂²×Q₈	—	2	8	no	—
323	C₂²×Q₈	—	2	8	no	—
324	C₂²×Q₈	—	4	4	no	—
325	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
326	C₂³×C₄	—	2	4	no	—
327	C₂³×C₄	—	2	4	no	—
328	C₂³×C₄	Q₈×C₁₃	1	8	yes	complemented
329	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
330	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
331	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
332	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
335	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
337	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
340	C₄⋊Q₈	—	2	32	no	—
341	#117	—	2	32	no	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	—	2	8	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	8	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	4	4	no	—
348	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
356	C₂×C₂²⋊C₄	—	2	8	no	—
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₂²⋊C₄	—	4	4	no	—
360	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
364	C₂×C₄²	—	2	8	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	—	2	4	no	—
367	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
368	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
369	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
370	#95	C₂³×C₁₃	1	4	yes	—
371	#95	C₂³×C₁₃	1	4	yes	—
372	#95	C₂³×C₁₃	1	8	yes	—
373	#95	C₂³×C₁₃	1	8	yes	—
374	#95	C₂³×C₁₃	1	8	yes	—
375	#95	C₂³×C₁₃	1	8	yes	—
376	#95	C₂³×C₁₃	1	8	yes	—
377	C₂×C₁₃	—	4	4	no	—
378	C₂×C₁₃	#2439	1	8	yes	direct product factor
379	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
380	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
381	C₂×C₁₃	C₂×#544	1	1	yes	characteristic
382	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
383	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#555	1	1	yes	characteristic
385	C₂×C₁₃	C₂×#556	1	1	yes	characteristic
386	C₂⁴	—	2	2	no	—
387	C₂⁴	—	2	2	no	—
388	C₂⁴	—	2	2	no	—
389	C₂⁴	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	—	2	2	no	—
392	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
393	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
394	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
395	C₂×Q₈	—	2	16	no	—
396	C₂×Q₈	—	2	16	no	—
397	C₂×Q₈	—	4	8	no	—
398	C₂×Q₈	—	4	32	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	32	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
426	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
427	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
428	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
429	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
430	C₂²×C₄	C₁₃×#41	1	4	yes	—
431	C₂²×C₄	C₁₃×#41	1	4	yes	—
432	C₂²×C₄	C₁₃×#41	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	16	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	16	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	4	8	no	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
450	C₂²⋊C₄	—	2	16	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	4	8	no	—
454	C₄²	—	2	16	no	—
455	C₄²	—	2	8	no	—
456	C₄²	—	2	8	no	—
457	C₁₃	C₂×#2439	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	8	no	—
459	C₂³	—	2	8	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
472	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
473	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
474	C₂³	C₂×C₁₃×#41	1	2	yes	—
475	C₂³	C₂×C₁₃×#41	1	2	yes	—
476	C₂³	C₂×C₁₃×#41	1	2	yes	—
477	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
478	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
479	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
480	Q₈	—	4	32	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	16	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	32	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	C₁₃×C₂²⋊Q₈	1	16	yes	—
515	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
516	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
517	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
518	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
519	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
520	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
521	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	16	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
531	C₂²	C₁₃×#533	1	4	yes	—
532	C₂²	C₁₃×#544	1	4	yes	—
533	C₂²	C₁₃×#546	1	4	yes	—
534	C₂²	C₁₃×#548	1	4	yes	—
535	C₂²	C₁₃×#555	1	4	yes	—
536	C₂²	C₁₃×#556	1	4	yes	—
537	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
538	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
539	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
540	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
541	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
542	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
543	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
544	C₄	—	2	4	no	—
545	C₄	—	2	8	no	—
546	C₄	—	2	4	no	—
547	C₄	—	2	4	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	2	no	—
553	C₄	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
554	C₂	—	4	4	no	—
555	C₂	C₁₃×#2439	1	8	yes	direct product factor
556	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
558	C₂	C₂×C₁₃×#544	1	1	yes	characteristic
559	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
560	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
561	C₂	C₂×C₁₃×#555	1	1	yes	characteristic
562	C₂	C₂×C₁₃×#556	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
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
3. C₁₃×#2439	C₂	direct (N × H)
6. C₂×C₁₃×#391	C₂	semidirect
7. C₂×C₁₃×#389	C₂	semidirect
8. C₂×C₁₃×#389	C₂	semidirect
9. C₂×C₁₃×#387	C₂	semidirect
10. C₂×C₁₃×#382	C₂	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
35. C₁₃×#391	C₂²	semidirect
36. C₁₃×#389	C₂²	semidirect
37. C₁₃×#389	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
39. C₁₃×#382	C₂²	semidirect
56. C₂³×C₄×C₁₃	Q₈	semidirect
105. C₂×#2439	C₁₃	direct (N × H)
149. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
177. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
179. #2439	C₂×C₁₃	direct (N × H)
182. C₂×#391	C₂×C₁₃	semidirect
183. C₂×#389	C₂×C₁₃	semidirect
184. C₂×#389	C₂×C₁₃	semidirect
185. C₂×#387	C₂×C₁₃	semidirect
186. C₂×#382	C₂×C₁₃	semidirect
256. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
275. #391	C₂²×C₁₃	semidirect
276. #389	C₂²×C₁₃	semidirect
277. #389	C₂²×C₁₃	semidirect
278. #387	C₂²×C₁₃	semidirect
279. #382	C₂²×C₁₃	semidirect
328. C₂³×C₄	Q₈×C₁₃	semidirect
378. C₂×C₁₃	#2439	direct (N × H)
429. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
457. C₁₃	C₂×#2439	direct (N × H)
555. C₂	C₁₃×#2439	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×#117	2
C₁₃×#2439	2
C₂×C₁₃×#396	2
C₂×C₁₃×#393	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₁₃×#382	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2439	13

Subgroups — C2×C13×#2439 #15721051

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2439 #15721051