Subgroups — C₂×C₁₃×#2426 #15721044

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2426	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₁₃×#396	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#394	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#390	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#124	—	2	8	no	—
18	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
19	C₂×C₁₃×C₂²⋊Q₈	—	2	8	no	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#121	—	2	8	no	—
22	C₂×C₁₃×#121	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₁₃	—	2	8	no	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
41	C₁₃×#396	C₂²	1	16	yes	complemented
42	C₁₃×#394	C₂²	1	16	yes	complemented
43	C₁₃×#390	C₂²	1	8	yes	complemented
44	C₁₃×#390	C₂²	1	16	yes	complemented
45	C₁₃×#389	C₂²	1	8	yes	complemented
46	C₁₃×#388	C₂²	1	16	yes	complemented
47	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#95	C₂²	1	2	yes	—
51	C₂⁵×C₁₃	C₂³	1	2	yes	—
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×Q₈×C₁₃	—	2	4	no	—
54	C₂²×Q₈×C₁₃	—	2	4	no	—
55	C₂²×Q₈×C₁₃	D₄	1	8	yes	complemented
56	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	4	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	2	4	no	—
62	C₂²×D₄×C₁₃	—	4	4	no	—
63	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
65	C₂³×C₄×C₁₃	—	2	4	no	—
66	C₂³×C₄×C₁₃	—	2	4	no	—
67	C₂³×C₄×C₁₃	—	2	4	no	—
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×#124	—	2	32	no	—
79	C₁₃×C₂²⋊Q₈	—	2	32	no	—
80	C₁₃×#121	—	2	32	no	—
81	C₄×Q₈×C₁₃	—	2	32	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
85	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
86	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₄²×C₁₃	—	2	8	no	—
109	C₂×C₄²×C₁₃	—	2	4	no	—
110	C₂×C₄²×C₁₃	—	2	4	no	—
111	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
114	C₁₃×#95	C₂³	1	4	yes	—
115	C₁₃×#95	C₂³	1	4	yes	—
116	C₁₃×#95	C₂³	1	8	yes	—
117	C₂×#2426	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂⁴×C₁₃	—	2	2	no	—
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₂⁴×C₁₃	—	2	2	no	—
122	C₂⁴×C₁₃	—	2	2	no	—
123	C₂⁴×C₁₃	—	2	2	no	—
124	C₂⁴×C₁₃	—	2	4	no	—
125	C₂⁴×C₁₃	—	2	4	no	—
126	C₂⁴×C₁₃	—	2	4	no	—
127	C₂⁴×C₁₃	—	2	4	no	—
128	C₂⁴×C₁₃	—	2	4	no	—
129	C₂⁴×C₁₃	—	2	4	no	—
130	C₂⁴×C₁₃	—	2	4	no	—
131	C₂⁴×C₁₃	#41	1	4	yes	—
132	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
133	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×Q₈×C₁₃	—	2	32	no	—
136	C₂×Q₈×C₁₃	—	2	8	no	—
137	C₂×Q₈×C₁₃	—	2	8	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	16	yes	complemented
139	C₂×D₄×C₁₃	—	2	16	no	—
140	C₂×D₄×C₁₃	—	2	16	no	—
141	C₂×D₄×C₁₃	—	2	8	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	4	8	no	—
145	C₂×D₄×C₁₃	—	4	32	no	—
146	C₂×D₄×C₁₃	—	4	16	no	—
147	C₂²×C₄×C₁₃	—	2	2	no	—
148	C₂²×C₄×C₁₃	—	2	4	no	—
149	C₂²×C₄×C₁₃	—	2	4	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	4	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	2	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	8	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	4	16	no	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
173	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₁₃	#41	1	4	yes	—
177	C₂²×C₄×C₁₃	#41	1	4	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
187	C₁₃×C₄⋊C₄	—	2	16	no	—
188	C₁₃×C₄⋊C₄	—	2	8	no	—
189	C₁₃×C₄⋊C₄	—	2	16	no	—
190	C₁₃×C₄⋊C₄	—	4	8	no	—
191	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
192	C₁₃×C₂²⋊C₄	—	2	8	no	—
193	C₁₃×C₂²⋊C₄	—	2	16	no	—
194	C₁₃×C₂²⋊C₄	—	2	16	no	—
195	C₁₃×C₂²⋊C₄	—	2	16	no	—
196	C₁₃×C₂²⋊C₄	—	2	16	no	—
197	C₁₃×C₂²⋊C₄	—	2	8	no	—
198	C₁₃×C₂²⋊C₄	—	2	16	no	—
199	C₁₃×C₂²⋊C₄	—	4	8	no	—
200	C₄²×C₁₃	—	2	16	no	—
201	C₄²×C₁₃	—	2	8	no	—
202	C₄²×C₁₃	—	2	8	no	—
203	C₂²×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic
206	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#2426	C₂×C₁₃	1	16	yes	direct product factor
208	C₂×#396	C₂×C₁₃	1	2	yes	complemented
209	C₂×#394	C₂×C₁₃	1	2	yes	complemented
210	C₂×#390	C₂×C₁₃	1	2	yes	complemented
211	C₂×#390	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×#388	C₂×C₁₃	1	2	yes	complemented
214	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	8	no	—
216	C₂³×C₁₃	—	2	8	no	—
217	C₂³×C₁₃	—	2	8	no	—
218	C₂³×C₁₃	—	2	2	no	—
219	C₂³×C₁₃	—	2	2	no	—
220	C₂³×C₁₃	—	2	2	no	—
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	4	4	no	—
232	C₂³×C₁₃	—	4	4	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	4	8	no	—
236	C₂³×C₁₃	—	4	8	no	—
237	C₂³×C₁₃	—	4	8	no	—
238	C₂³×C₁₃	—	4	8	no	—
239	C₂³×C₁₃	—	4	8	no	—
240	C₂³×C₁₃	—	4	8	no	—
241	C₂³×C₁₃	—	4	8	no	—
242	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂³×C₁₃	C₂×#41	1	4	yes	—
245	C₂³×C₁₃	C₂×#41	1	2	yes	—
246	C₂³×C₁₃	C₂×#41	1	2	yes	—
247	C₂³×C₁₃	C₂×#41	1	2	yes	—
248	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
249	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
250	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	32	no	—
252	D₄×C₁₃	—	4	32	no	—
253	D₄×C₁₃	—	4	16	no	—
254	C₂×C₄×C₁₃	—	2	16	no	—
255	C₂×C₄×C₁₃	—	2	16	no	—
256	C₂×C₄×C₁₃	—	2	8	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	2	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	4	4	no	—
279	C₂×C₄×C₁₃	—	4	4	no	—
280	C₂×C₄×C₁₃	—	4	4	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	8	no	—
283	C₂×C₄×C₁₃	—	4	16	no	—
284	C₂×C₄×C₁₃	#121	1	16	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
290	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
291	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
292	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
294	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#124	—	2	8	no	—
296	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
297	C₂×C₂²⋊Q₈	—	2	8	no	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
299	C₂×#121	—	2	8	no	—
300	C₂×#121	C₂²×C₁₃	1	8	yes	—
301	C₂×C₄×Q₈	—	2	8	no	—
302	C₂×C₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
303	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
304	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
310	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
315	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
316	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
317	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
318	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
319	#396	C₂²×C₁₃	1	16	yes	complemented
320	#394	C₂²×C₁₃	1	16	yes	complemented
321	#390	C₂²×C₁₃	1	8	yes	complemented
322	#390	C₂²×C₁₃	1	16	yes	complemented
323	#389	C₂²×C₁₃	1	8	yes	complemented
324	#388	C₂²×C₁₃	1	16	yes	complemented
325	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
326	C₂×#95	C₂²×C₁₃	1	2	yes	—
327	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	4	no	—
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	4	2	no	—
333	C₂²×C₁₃	—	4	16	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	4	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	4	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	8	16	no	—
345	C₂²×C₁₃	C₂×#121	1	4	yes	—
346	C₂²×C₁₃	#529	1	4	yes	—
347	C₂²×C₁₃	#542	1	4	yes	—
348	C₂²×C₁₃	#546	1	4	yes	—
349	C₂²×C₁₃	#548	1	4	yes	—
350	C₂²×C₁₃	#548	1	4	yes	—
351	C₂²×C₁₃	#550	1	4	yes	—
352	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
353	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
354	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
355	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
356	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
357	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
359	C₄×C₁₃	—	2	8	no	—
360	C₄×C₁₃	—	2	8	no	—
361	C₄×C₁₃	—	2	4	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	2	no	—
364	C₄×C₁₃	—	4	2	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	4	no	—
367	C₄×C₁₃	C₂×#121	1	8	yes	—
368	C₂⁵	C₂³×C₁₃	1	2	yes	—
369	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×Q₈	—	2	4	no	—
371	C₂²×Q₈	—	2	4	no	—
372	C₂²×Q₈	D₄×C₁₃	1	8	yes	complemented
373	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
374	C₂²×D₄	—	2	8	no	—
375	C₂²×D₄	—	2	8	no	—
376	C₂²×D₄	—	2	4	no	—
377	C₂²×D₄	—	2	4	no	—
378	C₂²×D₄	—	2	4	no	—
379	C₂²×D₄	—	4	4	no	—
380	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
381	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
382	C₂³×C₄	—	2	4	no	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	4	no	—
385	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
391	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
392	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
395	#124	—	2	32	no	—
396	C₂²⋊Q₈	—	2	32	no	—
397	#121	—	2	32	no	—
398	C₄×Q₈	—	2	32	no	—
399	C₂×C₄⋊C₄	—	2	8	no	—
400	C₂×C₄⋊C₄	—	2	4	no	—
401	C₂×C₄⋊C₄	—	2	8	no	—
402	C₂×C₄⋊C₄	—	4	4	no	—
403	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₂²⋊C₄	—	2	8	no	—
411	C₂×C₂²⋊C₄	—	2	8	no	—
412	C₂×C₂²⋊C₄	—	2	8	no	—
413	C₂×C₂²⋊C₄	—	2	8	no	—
414	C₂×C₂²⋊C₄	—	2	4	no	—
415	C₂×C₂²⋊C₄	—	2	8	no	—
416	C₂×C₂²⋊C₄	—	4	4	no	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
425	C₂×C₄²	—	2	8	no	—
426	C₂×C₄²	—	2	4	no	—
427	C₂×C₄²	—	2	4	no	—
428	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
431	#95	C₂³×C₁₃	1	4	yes	—
432	#95	C₂³×C₁₃	1	4	yes	—
433	#95	C₂³×C₁₃	1	8	yes	—
434	C₂×C₁₃	—	4	4	no	—
435	C₂×C₁₃	—	8	4	no	—
436	C₂×C₁₃	#2426	1	8	yes	direct product factor
437	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
438	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
439	C₂×C₁₃	C₂×#542	1	1	yes	characteristic
440	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
441	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
442	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
443	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
444	C₂⁴	—	2	2	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	—	2	2	no	—
447	C₂⁴	—	2	2	no	—
448	C₂⁴	—	2	2	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	2	4	no	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	4	no	—
455	C₂⁴	—	2	4	no	—
456	C₂⁴	—	2	4	no	—
457	C₂⁴	C₁₃×#41	1	4	yes	—
458	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
459	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
460	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
461	C₂×Q₈	—	2	32	no	—
462	C₂×Q₈	—	2	8	no	—
463	C₂×Q₈	—	2	8	no	—
464	C₂×Q₈	C₂×D₄×C₁₃	1	16	yes	complemented
465	C₂×D₄	—	2	16	no	—
466	C₂×D₄	—	2	16	no	—
467	C₂×D₄	—	2	8	no	—
468	C₂×D₄	—	2	8	no	—
469	C₂×D₄	—	2	8	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	32	no	—
472	C₂×D₄	—	4	16	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	2	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	8	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	4	16	no	—
498	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
499	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
502	C₂²×C₄	C₁₃×#41	1	4	yes	—
503	C₂²×C₄	C₁₃×#41	1	4	yes	—
504	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
509	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
511	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
513	C₄⋊C₄	—	2	16	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	16	no	—
516	C₄⋊C₄	—	4	8	no	—
517	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	16	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	2	16	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	16	no	—
525	C₂²⋊C₄	—	4	8	no	—
526	C₄²	—	2	16	no	—
527	C₄²	—	2	8	no	—
528	C₄²	—	2	8	no	—
529	C₁₃	C₂×#2426	1	1	yes	characteristic, direct product factor, Sylow
530	C₂³	—	2	8	no	—
531	C₂³	—	2	8	no	—
532	C₂³	—	2	8	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	8	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	4	8	no	—
555	C₂³	—	4	8	no	—
556	C₂³	—	4	8	no	—
557	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
558	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂³	C₂×C₁₃×#41	1	4	yes	—
560	C₂³	C₂×C₁₃×#41	1	2	yes	—
561	C₂³	C₂×C₁₃×#41	1	2	yes	—
562	C₂³	C₂×C₁₃×#41	1	2	yes	—
563	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
564	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
565	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
566	Q₈	—	2	32	no	—
567	D₄	—	4	32	no	—
568	D₄	—	4	16	no	—
569	C₂×C₄	—	2	16	no	—
570	C₂×C₄	—	2	16	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	—	4	16	no	—
599	C₂×C₄	C₁₃×#121	1	16	yes	—
600	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
601	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
602	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
603	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
604	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
605	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
606	C₂²	—	2	4	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	16	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	4	no	—
621	C₂²	—	8	16	no	—
622	C₂²	C₂×C₁₃×#121	1	4	yes	—
623	C₂²	C₁₃×#529	1	4	yes	—
624	C₂²	C₁₃×#542	1	4	yes	—
625	C₂²	C₁₃×#546	1	4	yes	—
626	C₂²	C₁₃×#548	1	4	yes	—
627	C₂²	C₁₃×#548	1	4	yes	—
628	C₂²	C₁₃×#550	1	4	yes	—
629	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
630	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
631	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
632	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
633	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
634	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
635	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
636	C₄	—	2	8	no	—
637	C₄	—	2	8	no	—
638	C₄	—	2	4	no	—
639	C₄	—	4	2	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	4	no	—
644	C₄	C₂×C₁₃×#121	1	8	yes	—
645	C₂	—	4	4	no	—
646	C₂	—	8	4	no	—
647	C₂	C₁₃×#2426	1	8	yes	direct product factor
648	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
649	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
650	C₂	C₂×C₁₃×#542	1	1	yes	characteristic
651	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
652	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
653	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
654	C₂	C₂×C₁₃×#550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#121	C₂
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×#124	C₂	semidirect
2. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
4. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
5. C₁₃×#2426	C₂	direct (N × H)
6. C₂×C₁₃×#396	C₂	semidirect
7. C₂×C₁₃×#394	C₂	semidirect
8. C₂×C₁₃×#390	C₂	semidirect
9. C₂×C₁₃×#390	C₂	semidirect
10. C₂×C₁₃×#389	C₂	semidirect
11. C₂×C₁₃×#388	C₂	semidirect
12. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
18. C₂×C₁₃×#124	C₂²	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
41. C₁₃×#396	C₂²	semidirect
42. C₁₃×#394	C₂²	semidirect
43. C₁₃×#390	C₂²	semidirect
44. C₁₃×#390	C₂²	semidirect
45. C₁₃×#389	C₂²	semidirect
46. C₁₃×#388	C₂²	semidirect
47. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
55. C₂²×Q₈×C₁₃	D₄	semidirect
117. C₂×#2426	C₁₃	direct (N × H)
138. C₂×Q₈×C₁₃	C₂×D₄	semidirect
203. C₂²×#124	C₂×C₁₃	semidirect
204. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
206. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
207. #2426	C₂×C₁₃	direct (N × H)
208. C₂×#396	C₂×C₁₃	semidirect
209. C₂×#394	C₂×C₁₃	semidirect
210. C₂×#390	C₂×C₁₃	semidirect
211. C₂×#390	C₂×C₁₃	semidirect
212. C₂×#389	C₂×C₁₃	semidirect
213. C₂×#388	C₂×C₁₃	semidirect
214. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
296. C₂×#124	C₂²×C₁₃	semidirect
298. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
302. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
319. #396	C₂²×C₁₃	semidirect
320. #394	C₂²×C₁₃	semidirect
321. #390	C₂²×C₁₃	semidirect
322. #390	C₂²×C₁₃	semidirect
323. #389	C₂²×C₁₃	semidirect
324. #388	C₂²×C₁₃	semidirect
325. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
372. C₂²×Q₈	D₄×C₁₃	semidirect
436. C₂×C₁₃	#2426	direct (N × H)
464. C₂×Q₈	C₂×D₄×C₁₃	semidirect
529. C₁₃	C₂×#2426	direct (N × H)
647. C₂	C₁₃×#2426	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×#124	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₁₃×#121	2
C₂²×C₄×Q₈×C₁₃	2
C₁₃×#2426	2
C₂×C₁₃×#396	2
C₂×C₁₃×#394	2
C₂×C₁₃×#390	2
C₂×C₁₃×#389	2
C₂×C₁₃×#388	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2426	13

Subgroups — C2×C13×#2426 #15721044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2426 #15721044