Subgroups — C₂×C₁₃×#3491 #15749114

Order 3328.

7390 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3491	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#552	C₂	1	8	yes	maximal, complemented
3	C₂×C₁₃×#551	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#539	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#534	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#123	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#552	C₂²	1	128	yes	complemented
14	C₁₃×#551	C₂²	1	128	yes	complemented
15	C₁₃×#543	C₂²	1	16	yes	complemented
16	C₁₃×#539	C₂²	1	64	yes	complemented
17	C₁₃×#534	C₂²	1	16	yes	—
18	C₁₃×#529	C₂²	1	64	yes	complemented
19	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
20	C₂×C₁₃×#126	C₂²	1	8	yes	complemented
21	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
22	C₂×C₁₃×#125	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#123	C₂²	1	8	yes	—
25	C₂×C₁₃×#123	C₂²	1	4	yes	—
26	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
28	C₂×C₁₃×#123	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#123	C₂²	1	32	yes	complemented
30	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#121	C₂²	1	4	yes	—
34	C₂×C₁₃×#120	C₂²	1	4	yes	—
35	C₁₃×#518	C₂²	1	32	yes	complemented
36	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
37	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
39	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
40	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
41	C₂×C₁₃×#117	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
44	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
45	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	complemented
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
48	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
50	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
51	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
52	C₂⁵×C₁₃	C₂³	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
55	C₂²×D₄×C₁₃	—	2	16	no	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	—	2	8	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
70	C₁₃×#126	C₂³	1	64	yes	complemented
71	C₁₃×#126	C₂³	1	64	yes	complemented
72	C₁₃×#125	C₂³	1	32	yes	complemented
73	C₁₃×#125	C₂³	1	64	yes	complemented
74	C₁₃×#124	C₂³	1	32	yes	complemented
75	C₁₃×#123	C₂³	1	64	yes	—
76	C₁₃×#123	C₂³	1	32	yes	—
77	C₁₃×#123	C₂³	1	32	yes	complemented
78	C₁₃×#123	C₂³	1	32	yes	complemented
79	C₁₃×#123	C₂³	1	64	yes	complemented
80	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	complemented
81	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
82	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
83	C₁₃×#121	C₂³	1	32	yes	—
84	C₁₃×#120	C₂³	1	32	yes	—
85	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
86	C₄×D₄×C₁₃	C₂³	1	64	yes	—
87	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
88	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
89	C₁₃×#117	C₂³	1	64	yes	complemented
90	C₁₃×#117	C₂³	1	32	yes	complemented
91	C₁₃×#117	C₂³	1	64	yes	complemented
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	complemented
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
114	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
118	C₂×#3491	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	8	no	—
120	C₂⁴×C₁₃	—	4	4	no	—
121	C₂⁴×C₁₃	—	4	8	no	—
122	C₂⁴×C₁₃	#41	1	8	yes	—
123	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
125	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
126	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
127	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
128	C₂×Q₈×C₁₃	—	4	8	no	—
129	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
130	C₂×D₄×C₁₃	—	2	16	no	—
131	C₂×D₄×C₁₃	—	2	16	no	—
132	C₂×D₄×C₁₃	—	2	64	no	—
133	C₂×D₄×C₁₃	—	4	8	no	—
134	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
135	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
136	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
137	C₂²×C₄×C₁₃	—	2	16	no	—
138	C₂²×C₄×C₁₃	—	2	4	no	—
139	C₂²×C₄×C₁₃	—	2	4	no	—
140	C₂²×C₄×C₁₃	—	2	32	no	—
141	C₂²×C₄×C₁₃	—	2	8	no	—
142	C₂²×C₄×C₁₃	—	4	4	no	—
143	C₂²×C₄×C₁₃	—	4	16	no	—
144	C₂²×C₄×C₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
160	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
161	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
162	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
163	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
164	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
167	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
168	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
169	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
170	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
171	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
172	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
173	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
174	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
175	C₄²×C₁₃	C₂⁴	1	16	yes	—
176	C₄²×C₁₃	C₂⁴	1	16	yes	—
177	C₄²×C₁₃	C₂⁴	1	32	yes	—
178	#3491	C₂×C₁₃	1	32	yes	direct product factor
179	C₂×#552	C₂×C₁₃	1	8	yes	complemented
180	C₂×#551	C₂×C₁₃	1	8	yes	complemented
181	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
182	C₂×#539	C₂×C₁₃	1	4	yes	complemented
183	C₂×#534	C₂×C₁₃	1	1	yes	characteristic
184	C₂×#529	C₂×C₁₃	1	4	yes	complemented
185	C₂²×#123	C₂×C₁₃	1	2	yes	complemented
186	C₂×#518	C₂×C₁₃	1	2	yes	complemented
187	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	2	8	no	—
190	C₂³×C₁₃	—	2	8	no	—
191	C₂³×C₁₃	—	2	16	no	—
192	C₂³×C₁₃	—	2	16	no	—
193	C₂³×C₁₃	—	4	16	no	—
194	C₂³×C₁₃	—	4	8	no	—
195	C₂³×C₁₃	—	4	16	no	—
196	C₂³×C₁₃	—	8	16	no	—
197	C₂³×C₁₃	C₂×#41	1	8	yes	—
198	C₂³×C₁₃	C₂×#41	1	4	yes	—
199	C₂³×C₁₃	C₂×#41	1	16	yes	—
200	C₂³×C₁₃	C₂⁵	1	8	yes	—
201	C₂³×C₁₃	C₂⁵	1	4	yes	—
202	C₂³×C₁₃	C₂⁵	1	2	yes	—
203	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
204	Q₈×C₁₃	—	4	16	no	—
205	D₄×C₁₃	—	2	32	no	—
206	D₄×C₁₃	—	2	32	no	—
207	D₄×C₁₃	—	4	16	no	—
208	C₂×C₄×C₁₃	—	2	32	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	8	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	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	16	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	4	8	no	—
219	C₂×C₄×C₁₃	—	4	32	no	—
220	C₂×C₄×C₁₃	—	4	16	no	—
221	C₂×C₄×C₁₃	—	4	8	no	—
222	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
225	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
226	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
227	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
228	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
229	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#552	C₂²×C₁₃	1	128	yes	complemented
231	#551	C₂²×C₁₃	1	128	yes	complemented
232	#543	C₂²×C₁₃	1	16	yes	complemented
233	#539	C₂²×C₁₃	1	64	yes	complemented
234	#534	C₂²×C₁₃	1	16	yes	—
235	#529	C₂²×C₁₃	1	64	yes	complemented
236	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
237	C₂×#126	C₂²×C₁₃	1	8	yes	complemented
238	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
239	C₂×#125	C₂²×C₁₃	1	8	yes	complemented
240	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
241	C₂×#123	C₂²×C₁₃	1	8	yes	—
242	C₂×#123	C₂²×C₁₃	1	4	yes	—
243	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
244	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
245	C₂×#123	C₂²×C₁₃	1	8	yes	complemented
246	C₂×#123	C₂²×C₁₃	1	32	yes	complemented
247	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
248	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
249	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
250	C₂×#121	C₂²×C₁₃	1	4	yes	—
251	C₂×#120	C₂²×C₁₃	1	4	yes	—
252	#518	C₂²×C₁₃	1	32	yes	complemented
253	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
254	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
256	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	complemented
257	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
258	C₂×#117	C₂²×C₁₃	1	4	yes	complemented
259	C₂×#117	C₂²×C₁₃	1	8	yes	complemented
260	C₂×#117	C₂²×C₁₃	1	16	yes	complemented
261	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
262	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	complemented
263	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
266	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
267	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
268	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
269	C₂²×C₁₃	—	2	4	no	—
270	C₂²×C₁₃	—	2	8	no	—
271	C₂²×C₁₃	—	2	16	no	—
272	C₂²×C₁₃	—	2	8	no	—
273	C₂²×C₁₃	—	2	8	no	—
274	C₂²×C₁₃	—	2	16	no	—
275	C₂²×C₁₃	—	4	16	no	—
276	C₂²×C₁₃	—	4	16	no	—
277	C₂²×C₁₃	—	8	16	no	—
278	C₂²×C₁₃	C₂²×#41	1	8	yes	—
279	C₂²×C₁₃	C₂²×#41	1	4	yes	—
280	C₂²×C₁₃	C₂²×#41	1	2	yes	—
281	C₂²×C₁₃	#585	1	4	yes	—
282	C₂²×C₁₃	C₂⁶	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	8	no	—
287	C₄×C₁₃	—	2	16	no	—
288	C₄×C₁₃	—	2	8	no	—
289	C₂⁵	C₂³×C₁₃	1	2	yes	—
290	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
292	C₂²×D₄	—	2	16	no	—
293	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
294	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
295	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
296	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
297	C₂³×C₄	—	2	8	no	—
298	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
302	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
304	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
305	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
306	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
307	#126	C₂³×C₁₃	1	64	yes	complemented
308	#126	C₂³×C₁₃	1	64	yes	complemented
309	#125	C₂³×C₁₃	1	32	yes	complemented
310	#125	C₂³×C₁₃	1	64	yes	complemented
311	#124	C₂³×C₁₃	1	32	yes	complemented
312	#123	C₂³×C₁₃	1	64	yes	—
313	#123	C₂³×C₁₃	1	32	yes	—
314	#123	C₂³×C₁₃	1	32	yes	complemented
315	#123	C₂³×C₁₃	1	32	yes	complemented
316	#123	C₂³×C₁₃	1	64	yes	complemented
317	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	complemented
318	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
319	C₂²⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
320	#121	C₂³×C₁₃	1	32	yes	—
321	#120	C₂³×C₁₃	1	32	yes	—
322	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
323	C₄×D₄	C₂³×C₁₃	1	64	yes	—
324	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
325	C₄×D₄	C₂³×C₁₃	1	32	yes	complemented
326	#117	C₂³×C₁₃	1	64	yes	complemented
327	#117	C₂³×C₁₃	1	32	yes	complemented
328	#117	C₂³×C₁₃	1	64	yes	complemented
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	8	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	complemented
338	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
351	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
352	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
353	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
355	C₂×C₁₃	—	2	8	no	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	—	4	8	no	—
358	C₂×C₁₃	#3491	1	4	yes	direct product factor
359	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#585	1	2	yes	—
361	C₂⁴	—	2	8	no	—
362	C₂⁴	—	4	4	no	—
363	C₂⁴	—	4	8	no	—
364	C₂⁴	C₁₃×#41	1	8	yes	—
365	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
366	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
367	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
368	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
369	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
370	C₂×Q₈	—	4	8	no	—
371	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
372	C₂×D₄	—	2	16	no	—
373	C₂×D₄	—	2	16	no	—
374	C₂×D₄	—	2	64	no	—
375	C₂×D₄	—	4	8	no	—
376	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
377	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
378	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
379	C₂²×C₄	—	2	16	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	32	no	—
383	C₂²×C₄	—	2	8	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	16	no	—
386	C₂²×C₄	—	4	8	no	—
387	C₂²×C₄	—	4	4	no	—
388	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
390	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
393	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
402	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
403	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
404	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
405	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
406	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
407	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
408	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
409	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
410	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
411	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
412	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
413	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
414	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
415	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
416	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
417	C₄²	C₂⁴×C₁₃	1	16	yes	—
418	C₄²	C₂⁴×C₁₃	1	16	yes	—
419	C₄²	C₂⁴×C₁₃	1	32	yes	—
420	C₁₃	C₂×#3491	1	1	yes	characteristic, direct product factor, Sylow
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	16	no	—
426	C₂³	—	4	16	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	16	no	—
429	C₂³	—	8	16	no	—
430	C₂³	C₂×C₁₃×#41	1	8	yes	—
431	C₂³	C₂×C₁₃×#41	1	4	yes	—
432	C₂³	C₂×C₁₃×#41	1	16	yes	—
433	C₂³	C₂⁵×C₁₃	1	8	yes	—
434	C₂³	C₂⁵×C₁₃	1	4	yes	—
435	C₂³	C₂⁵×C₁₃	1	2	yes	—
436	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
437	Q₈	—	4	16	no	—
438	D₄	—	2	32	no	—
439	D₄	—	2	32	no	—
440	D₄	—	4	16	no	—
441	C₂×C₄	—	2	32	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	16	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	2	16	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	32	no	—
453	C₂×C₄	—	4	16	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
456	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
457	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
458	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
459	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
460	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	16	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	2	16	no	—
467	C₂²	—	4	16	no	—
468	C₂²	—	4	16	no	—
469	C₂²	—	8	16	no	—
470	C₂²	C₂²×C₁₃×#41	1	8	yes	—
471	C₂²	C₂²×C₁₃×#41	1	4	yes	—
472	C₂²	C₂²×C₁₃×#41	1	2	yes	—
473	C₂²	C₁₃×#585	1	4	yes	—
474	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	8	no	—
478	C₄	—	2	8	no	—
479	C₄	—	2	16	no	—
480	C₄	—	2	8	no	—
481	C₂	—	2	8	no	—
482	C₂	—	2	4	no	—
483	C₂	—	4	8	no	—
484	C₂	C₁₃×#3491	1	4	yes	direct product factor
485	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
486	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂×C₁₃×#534	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₃×#3491	C₂	direct (N × H)
2. C₂×C₁₃×#552	C₂	semidirect
3. C₂×C₁₃×#551	C₂	semidirect
4. C₂×C₁₃×#543	C₂	semidirect
5. C₂×C₁₃×#539	C₂	semidirect
7. C₂×C₁₃×#529	C₂	semidirect
8. C₂²×C₁₃×#123	C₂	semidirect
9. C₂×C₁₃×#518	C₂	semidirect
10. C₂²×C₁₃×#117	C₂	semidirect
13. C₁₃×#552	C₂²	semidirect
14. C₁₃×#551	C₂²	semidirect
15. C₁₃×#543	C₂²	semidirect
16. C₁₃×#539	C₂²	semidirect
18. C₁₃×#529	C₂²	semidirect
19. C₂×C₁₃×#126	C₂²	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
23. C₂×C₁₃×#124	C₂²	semidirect
26. C₂×C₁₃×#123	C₂²	semidirect
27. C₂×C₁₃×#123	C₂²	semidirect
28. C₂×C₁₃×#123	C₂²	semidirect
29. C₂×C₁₃×#123	C₂²	semidirect
30. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₁₃×#518	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
38. C₂×C₄×D₄×C₁₃	C₂²	semidirect
39. C₂×C₄×D₄×C₁₃	C₂²	semidirect
40. C₂×C₁₃×#117	C₂²	semidirect
41. C₂×C₁₃×#117	C₂²	semidirect
42. C₂×C₁₃×#117	C₂²	semidirect
43. C₂×C₁₃×#117	C₂²	semidirect
44. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
45. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
49. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
50. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
51. C₂²×C₄²×C₁₃	C₂²	semidirect
70. C₁₃×#126	C₂³	semidirect
71. C₁₃×#126	C₂³	semidirect
72. C₁₃×#125	C₂³	semidirect
73. C₁₃×#125	C₂³	semidirect
74. C₁₃×#124	C₂³	semidirect
77. C₁₃×#123	C₂³	semidirect
78. C₁₃×#123	C₂³	semidirect
79. C₁₃×#123	C₂³	semidirect
80. C₁₃×C₂²⋊Q₈	C₂³	semidirect
81. C₁₃×C₂²⋊Q₈	C₂³	semidirect
82. C₁₃×C₂²⋊Q₈	C₂³	semidirect
85. C₄×Q₈×C₁₃	C₂³	semidirect
87. C₄×D₄×C₁₃	C₂³	semidirect
88. C₄×D₄×C₁₃	C₂³	semidirect
89. C₁₃×#117	C₂³	semidirect
90. C₁₃×#117	C₂³	semidirect
91. C₁₃×#117	C₂³	semidirect
99. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
100. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
112. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
113. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
117. C₂×C₄²×C₁₃	C₂³	semidirect
118. C₂×#3491	C₁₃	direct (N × H)
178. #3491	C₂×C₁₃	direct (N × H)
179. C₂×#552	C₂×C₁₃	semidirect
180. C₂×#551	C₂×C₁₃	semidirect
181. C₂×#543	C₂×C₁₃	semidirect
182. C₂×#539	C₂×C₁₃	semidirect
184. C₂×#529	C₂×C₁₃	semidirect
185. C₂²×#123	C₂×C₁₃	semidirect
186. C₂×#518	C₂×C₁₃	semidirect
187. C₂²×#117	C₂×C₁₃	semidirect
230. #552	C₂²×C₁₃	semidirect
231. #551	C₂²×C₁₃	semidirect
232. #543	C₂²×C₁₃	semidirect
233. #539	C₂²×C₁₃	semidirect
235. #529	C₂²×C₁₃	semidirect
236. C₂×#126	C₂²×C₁₃	semidirect
237. C₂×#126	C₂²×C₁₃	semidirect
238. C₂×#125	C₂²×C₁₃	semidirect
239. C₂×#125	C₂²×C₁₃	semidirect
240. C₂×#124	C₂²×C₁₃	semidirect
243. C₂×#123	C₂²×C₁₃	semidirect
244. C₂×#123	C₂²×C₁₃	semidirect
245. C₂×#123	C₂²×C₁₃	semidirect
246. C₂×#123	C₂²×C₁₃	semidirect
247. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
248. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
249. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
252. #518	C₂²×C₁₃	semidirect
253. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
255. C₂×C₄×D₄	C₂²×C₁₃	semidirect
256. C₂×C₄×D₄	C₂²×C₁₃	semidirect
257. C₂×#117	C₂²×C₁₃	semidirect
258. C₂×#117	C₂²×C₁₃	semidirect
259. C₂×#117	C₂²×C₁₃	semidirect
260. C₂×#117	C₂²×C₁₃	semidirect
261. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
262. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
266. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
267. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
268. C₂²×C₄²	C₂²×C₁₃	semidirect
307. #126	C₂³×C₁₃	semidirect
308. #126	C₂³×C₁₃	semidirect
309. #125	C₂³×C₁₃	semidirect
310. #125	C₂³×C₁₃	semidirect
311. #124	C₂³×C₁₃	semidirect
314. #123	C₂³×C₁₃	semidirect
315. #123	C₂³×C₁₃	semidirect
316. #123	C₂³×C₁₃	semidirect
317. C₂²⋊Q₈	C₂³×C₁₃	semidirect
318. C₂²⋊Q₈	C₂³×C₁₃	semidirect
319. C₂²⋊Q₈	C₂³×C₁₃	semidirect
322. C₄×Q₈	C₂³×C₁₃	semidirect
324. C₄×D₄	C₂³×C₁₃	semidirect
325. C₄×D₄	C₂³×C₁₃	semidirect
326. #117	C₂³×C₁₃	semidirect
327. #117	C₂³×C₁₃	semidirect
328. #117	C₂³×C₁₃	semidirect
336. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
337. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
349. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
350. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
354. C₂×C₄²	C₂³×C₁₃	semidirect
358. C₂×C₁₃	#3491	direct (N × H)
420. C₁₃	C₂×#3491	direct (N × H)
484. C₂	C₁₃×#3491	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3491	2
C₂×C₁₃×#552	2
C₂×C₁₃×#551	2
C₂×C₁₃×#543	2
C₂×C₁₃×#539	2
C₂×C₁₃×#534	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#123	2
C₂×C₁₃×#518	2
C₂²×C₁₃×#117	2
C₂×#3491	13

Subgroups — C2×C13×#3491 #15749114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3491 #15749114