Subgroups — C₂×C₁₃×#2409 #15721021

Order 3328.

5566 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	C₂⁴×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2409	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#395	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#393	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#386	C₂	1	2	yes	maximal
9	C₂×C₁₃×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	—	2	16	no	—
12	C₂³×Q₈×C₁₃	—	2	8	no	—
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂³×Q₈×C₁₃	C₂²	1	8	yes	complemented
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊Q₈	—	2	16	no	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	16	yes	complemented
22	C₂×C₄×D₄×C₁₃	—	2	8	no	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#395	C₂²	1	16	yes	complemented
33	C₁₃×#393	C₂²	1	16	yes	complemented
34	C₁₃×#391	C₂²	1	16	yes	complemented
35	C₁₃×#386	C₂²	1	16	yes	—
36	C₁₃×#385	C₂²	1	16	yes	complemented
37	C₁₃×#380	C₂²	1	8	yes	complemented
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	4	yes	—
40	C₂×C₁₃×#95	C₂²	1	4	yes	—
41	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	128	no	—
44	C₂²×Q₈×C₁₃	—	2	64	no	—
45	C₂²×Q₈×C₁₃	—	2	16	no	—
46	C₂²×Q₈×C₁₃	—	2	8	no	—
47	C₂²×Q₈×C₁₃	—	2	8	no	—
48	C₂²×Q₈×C₁₃	—	2	8	no	—
49	C₂²×Q₈×C₁₃	—	2	32	no	—
50	C₂²×Q₈×C₁₃	D₄	1	16	yes	complemented
51	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
52	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
53	C₂²×D₄×C₁₃	—	2	4	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	Q₈	1	8	yes	complemented
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	—	2	8	no	—
58	C₂³×C₄×C₁₃	—	2	16	no	—
59	C₂³×C₄×C₁₃	—	2	8	no	—
60	C₂³×C₄×C₁₃	—	2	4	no	—
61	C₂³×C₄×C₁₃	—	2	8	no	—
62	C₂³×C₄×C₁₃	D₄	1	8	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×C₂²⋊Q₈	—	2	64	no	—
74	C₄×D₄×C₁₃	—	2	32	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₃	—	2	4	no	—
90	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
91	C₁₃×#95	C₂³	1	8	yes	—
92	C₁₃×#95	C₂³	1	16	yes	—
93	C₁₃×#95	C₂³	1	16	yes	—
94	C₂×#2409	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	4	no	—
97	C₂⁴×C₁₃	—	2	4	no	—
98	C₂⁴×C₁₃	—	2	2	no	—
99	C₂⁴×C₁₃	—	2	2	no	—
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
102	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
103	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	complemented
104	C₂⁴×C₁₃	#41	1	4	yes	—
105	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
106	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
107	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
108	C₂×Q₈×C₁₃	—	2	256	no	—
109	C₂×Q₈×C₁₃	—	2	64	no	—
110	C₂×Q₈×C₁₃	—	2	64	no	—
111	C₂×Q₈×C₁₃	—	2	32	no	—
112	C₂×Q₈×C₁₃	—	2	16	no	—
113	C₂×Q₈×C₁₃	—	2	16	no	—
114	C₂×Q₈×C₁₃	—	2	16	no	—
115	C₂×Q₈×C₁₃	C₂×D₄	1	32	yes	complemented
116	C₂×D₄×C₁₃	—	2	32	no	—
117	C₂×D₄×C₁₃	—	2	8	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	complemented
120	C₂²×C₄×C₁₃	—	2	64	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	16	no	—
123	C₂²×C₄×C₁₃	—	2	8	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	32	no	—
128	C₂²×C₄×C₁₃	—	2	32	no	—
129	C₂²×C₄×C₁₃	—	2	16	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	8	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	2	16	no	—
139	C₂²×C₄×C₁₃	—	4	16	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
145	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	complemented
146	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	8	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	8	no	—
154	C₁₃×C₄⋊C₄	—	2	16	no	—
155	C₁₃×C₄⋊C₄	—	2	32	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	16	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	32	no	—
160	C₄²×C₁₃	—	2	8	no	—
161	C₂⁴×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
163	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
164	#2409	C₂×C₁₃	1	16	yes	direct product factor
165	C₂×#395	C₂×C₁₃	1	2	yes	complemented
166	C₂×#393	C₂×C₁₃	1	2	yes	complemented
167	C₂×#391	C₂×C₁₃	1	2	yes	complemented
168	C₂×#386	C₂×C₁₃	1	2	yes	—
169	C₂×#385	C₂×C₁₃	1	2	yes	complemented
170	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
171	C₂³×C₁₃	—	2	8	no	—
172	C₂³×C₁₃	—	2	8	no	—
173	C₂³×C₁₃	—	2	16	no	—
174	C₂³×C₁₃	—	2	16	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	4	no	—
177	C₂³×C₁₃	—	2	8	no	—
178	C₂³×C₁₃	—	2	16	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	2	no	—
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	4	no	—
183	C₂³×C₁₃	—	4	4	no	—
184	C₂³×C₁₃	—	4	4	no	—
185	C₂³×C₁₃	—	4	8	no	—
186	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
187	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
188	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
189	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
190	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
191	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
192	C₂³×C₁₃	C₂²×Q₈	1	4	yes	complemented
193	C₂³×C₁₃	C₂×#41	1	4	yes	—
194	C₂³×C₁₃	C₂×#41	1	2	yes	—
195	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
196	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	64	no	—
198	Q₈×C₁₃	—	2	64	no	—
199	D₄×C₁₃	—	2	32	no	—
200	C₂×C₄×C₁₃	—	2	64	no	—
201	C₂×C₄×C₁₃	—	2	32	no	—
202	C₂×C₄×C₁₃	—	2	8	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	32	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	8	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	4	4	no	—
218	C₂×C₄×C₁₃	—	4	4	no	—
219	C₂×C₄×C₁₃	—	4	16	no	—
220	C₂×C₄×C₁₃	—	4	16	no	—
221	C₂×C₄×C₁₃	#120	1	16	yes	—
222	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
223	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
226	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	complemented
227	C₂³×Q₈	—	2	16	no	—
228	C₂³×Q₈	—	2	8	no	—
229	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
230	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
231	C₂³×Q₈	C₂²×C₁₃	1	8	yes	complemented
232	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
234	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
235	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	—	2	16	no	—
237	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	16	yes	complemented
238	C₂×C₄×D₄	—	2	8	no	—
239	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
242	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
245	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
248	#395	C₂²×C₁₃	1	16	yes	complemented
249	#393	C₂²×C₁₃	1	16	yes	complemented
250	#391	C₂²×C₁₃	1	16	yes	complemented
251	#386	C₂²×C₁₃	1	16	yes	—
252	#385	C₂²×C₁₃	1	16	yes	complemented
253	#380	C₂²×C₁₃	1	8	yes	complemented
254	C₂×#95	C₂²×C₁₃	1	2	yes	—
255	C₂×#95	C₂²×C₁₃	1	4	yes	—
256	C₂×#95	C₂²×C₁₃	1	4	yes	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	2	32	no	—
259	C₂²×C₁₃	—	2	4	no	—
260	C₂²×C₁₃	—	2	8	no	—
261	C₂²×C₁₃	—	2	8	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	8	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	16	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	4	no	—
268	C₂²×C₁₃	C₂×#120	1	4	yes	—
269	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
270	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	complemented
271	C₂²×C₁₃	#536	1	4	yes	—
272	C₂²×C₁₃	#548	1	8	yes	—
273	C₂²×C₁₃	D₄×Q₈	1	8	yes	—
274	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
275	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
276	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
277	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
278	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
279	C₄×C₁₃	—	2	16	no	—
280	C₄×C₁₃	—	2	4	no	—
281	C₄×C₁₃	—	2	4	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	8	no	—
285	C₄×C₁₃	C₂×#120	1	8	yes	—
286	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
287	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×Q₈	—	2	128	no	—
289	C₂²×Q₈	—	2	64	no	—
290	C₂²×Q₈	—	2	16	no	—
291	C₂²×Q₈	—	2	8	no	—
292	C₂²×Q₈	—	2	8	no	—
293	C₂²×Q₈	—	2	8	no	—
294	C₂²×Q₈	—	2	32	no	—
295	C₂²×Q₈	D₄×C₁₃	1	16	yes	complemented
296	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
297	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	—	2	4	no	—
300	C₂²×D₄	Q₈×C₁₃	1	8	yes	complemented
301	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
302	C₂³×C₄	—	2	8	no	—
303	C₂³×C₄	—	2	16	no	—
304	C₂³×C₄	—	2	8	no	—
305	C₂³×C₄	—	2	4	no	—
306	C₂³×C₄	—	2	8	no	—
307	C₂³×C₄	D₄×C₁₃	1	8	yes	—
308	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
309	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
312	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
313	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²⋊Q₈	—	2	64	no	—
319	C₄×D₄	—	2	32	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	2	8	no	—
322	C₂×C₄⋊C₄	—	2	16	no	—
323	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
326	C₂×C₂²⋊C₄	—	2	4	no	—
327	C₂×C₂²⋊C₄	—	2	8	no	—
328	C₂×C₂²⋊C₄	—	2	4	no	—
329	C₂×C₂²⋊C₄	—	2	16	no	—
330	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
334	C₂×C₄²	—	2	4	no	—
335	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
336	#95	C₂³×C₁₃	1	8	yes	—
337	#95	C₂³×C₁₃	1	16	yes	—
338	#95	C₂³×C₁₃	1	16	yes	—
339	C₂×C₁₃	—	2	8	no	—
340	C₂×C₁₃	—	4	4	no	—
341	C₂×C₁₃	#2409	1	8	yes	direct product factor
342	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
343	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
344	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
345	C₂×C₁₃	C₂×#548	1	2	yes	—
346	C₂×C₁₃	C₂×D₄×Q₈	1	2	yes	—
347	C₂⁴	—	2	4	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
354	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
355	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	complemented
356	C₂⁴	C₁₃×#41	1	4	yes	—
357	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
358	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
359	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
360	C₂×Q₈	—	2	256	no	—
361	C₂×Q₈	—	2	64	no	—
362	C₂×Q₈	—	2	64	no	—
363	C₂×Q₈	—	2	32	no	—
364	C₂×Q₈	—	2	16	no	—
365	C₂×Q₈	—	2	16	no	—
366	C₂×Q₈	—	2	16	no	—
367	C₂×Q₈	C₂×D₄×C₁₃	1	32	yes	complemented
368	C₂×D₄	—	2	32	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	complemented
372	C₂²×C₄	—	2	64	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	16	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	32	no	—
380	C₂²×C₄	—	2	32	no	—
381	C₂²×C₄	—	2	16	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	16	no	—
391	C₂²×C₄	—	4	16	no	—
392	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
397	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	complemented
398	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	8	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	8	no	—
406	C₄⋊C₄	—	2	16	no	—
407	C₄⋊C₄	—	2	32	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	16	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	32	no	—
412	C₄²	—	2	8	no	—
413	C₁₃	C₂×#2409	1	1	yes	characteristic, direct product factor, Sylow
414	C₂³	—	2	8	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	2	16	no	—
417	C₂³	—	2	16	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	8	no	—
421	C₂³	—	2	16	no	—
422	C₂³	—	2	4	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
430	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
431	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
432	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
433	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
434	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
435	C₂³	C₂²×Q₈×C₁₃	1	4	yes	complemented
436	C₂³	C₂×C₁₃×#41	1	4	yes	—
437	C₂³	C₂×C₁₃×#41	1	2	yes	—
438	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
439	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
440	Q₈	—	2	64	no	—
441	Q₈	—	2	64	no	—
442	D₄	—	2	32	no	—
443	C₂×C₄	—	2	64	no	—
444	C₂×C₄	—	2	32	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	32	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	—	4	16	no	—
464	C₂×C₄	C₁₃×#120	1	16	yes	—
465	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
466	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
468	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
469	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	complemented
470	C₂²	—	2	4	no	—
471	C₂²	—	2	32	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	8	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	8	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	16	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	4	no	—
481	C₂²	C₂×C₁₃×#120	1	4	yes	—
482	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
483	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	complemented
484	C₂²	C₁₃×#536	1	4	yes	—
485	C₂²	C₁₃×#548	1	8	yes	—
486	C₂²	D₄×Q₈×C₁₃	1	8	yes	—
487	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
488	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
489	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
490	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
491	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
492	C₄	—	2	16	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	8	no	—
498	C₄	C₂×C₁₃×#120	1	8	yes	—
499	C₂	—	2	8	no	—
500	C₂	—	4	4	no	—
501	C₂	C₁₃×#2409	1	8	yes	direct product factor
502	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
503	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
504	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
505	C₂	C₂×C₁₃×#548	1	2	yes	—
506	C₂	C₂×D₄×Q₈×C₁₃	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. C₂⁴×Q₈×C₁₃	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
4. C₁₃×#2409	C₂	direct (N × H)
5. C₂×C₁₃×#395	C₂	semidirect
6. C₂×C₁₃×#393	C₂	semidirect
7. C₂×C₁₃×#391	C₂	semidirect
9. C₂×C₁₃×#385	C₂	semidirect
10. C₂×C₁₃×#380	C₂	semidirect
15. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×#395	C₂²	semidirect
33. C₁₃×#393	C₂²	semidirect
34. C₁₃×#391	C₂²	semidirect
36. C₁₃×#385	C₂²	semidirect
37. C₁₃×#380	C₂²	semidirect
50. C₂²×Q₈×C₁₃	D₄	semidirect
55. C₂²×D₄×C₁₃	Q₈	semidirect
94. C₂×#2409	C₁₃	direct (N × H)
103. C₂⁴×C₁₃	C₂×Q₈	semidirect
115. C₂×Q₈×C₁₃	C₂×D₄	semidirect
119. C₂×D₄×C₁₃	C₂×Q₈	semidirect
145. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
161. C₂⁴×Q₈	C₂×C₁₃	semidirect
162. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
164. #2409	C₂×C₁₃	direct (N × H)
165. C₂×#395	C₂×C₁₃	semidirect
166. C₂×#393	C₂×C₁₃	semidirect
167. C₂×#391	C₂×C₁₃	semidirect
169. C₂×#385	C₂×C₁₃	semidirect
170. C₂×#380	C₂×C₁₃	semidirect
186. C₂³×C₁₃	C₂²⋊Q₈	semidirect
192. C₂³×C₁₃	C₂²×Q₈	semidirect
226. C₂×C₄×C₁₃	C₂²×Q₈	semidirect
231. C₂³×Q₈	C₂²×C₁₃	semidirect
237. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
248. #395	C₂²×C₁₃	semidirect
249. #393	C₂²×C₁₃	semidirect
250. #391	C₂²×C₁₃	semidirect
252. #385	C₂²×C₁₃	semidirect
253. #380	C₂²×C₁₃	semidirect
270. C₂²×C₁₃	C₂×C₂²⋊Q₈	semidirect
295. C₂²×Q₈	D₄×C₁₃	semidirect
300. C₂²×D₄	Q₈×C₁₃	semidirect
341. C₂×C₁₃	#2409	direct (N × H)
355. C₂⁴	C₂×Q₈×C₁₃	semidirect
367. C₂×Q₈	C₂×D₄×C₁₃	semidirect
371. C₂×D₄	C₂×Q₈×C₁₃	semidirect
397. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
413. C₁₃	C₂×#2409	direct (N × H)
429. C₂³	C₁₃×C₂²⋊Q₈	semidirect
435. C₂³	C₂²×Q₈×C₁₃	semidirect
469. C₂×C₄	C₂²×Q₈×C₁₃	semidirect
483. C₂²	C₂×C₁₃×C₂²⋊Q₈	semidirect
501. C₂	C₁₃×#2409	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₁₃	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2409	2
C₂×C₁₃×#395	2
C₂×C₁₃×#393	2
C₂×C₁₃×#391	2
C₂×C₁₃×#386	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂×#2409	13

Subgroups — C2×C13×#2409 #15721021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2409 #15721021