Subgroups — C₂×C₁₃×#3512 #15749148

Order 3328.

7238 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#553	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#553	C₂	1	8	yes	maximal, complemented
4	C₂×C₁₃×#552	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#541	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#537	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#529	C₂	1	4	yes	maximal, complemented
10	C₂²×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#520	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₁₃×#553	C₂²	1	64	yes	complemented
16	C₁₃×#553	C₂²	1	128	yes	complemented
17	C₁₃×#552	C₂²	1	64	yes	complemented
18	C₁₃×#541	C₂²	1	32	yes	complemented
19	C₁₃×#540	C₂²	1	32	yes	complemented
20	C₁₃×#537	C₂²	1	32	yes	complemented
21	C₁₃×#532	C₂²	1	16	yes	complemented
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
24	C₁₃×#529	C₂²	1	64	yes	complemented
25	C₂×C₁₃×#126	C₂²	1	8	yes	—
26	C₂×C₁₃×#126	C₂²	1	8	yes	—
27	C₂×C₁₃×#125	C₂²	1	2	yes	—
28	C₂×C₁₃×#125	C₂²	1	2	yes	—
29	C₂×C₁₃×#125	C₂²	1	4	yes	—
30	C₂×C₁₃×#125	C₂²	1	8	yes	—
31	C₂×C₁₃×#125	C₂²	1	16	yes	complemented
32	C₂×C₁₃×#124	C₂²	1	2	yes	—
33	C₂×C₁₃×#123	C₂²	1	8	yes	—
34	C₂×C₁₃×#123	C₂²	1	8	yes	—
35	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
36	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
37	C₂×C₁₃×#121	C₂²	1	4	yes	—
38	C₂×C₁₃×#121	C₂²	1	4	yes	—
39	C₂×C₁₃×#121	C₂²	1	8	yes	—
40	C₂×C₁₃×#121	C₂²	1	4	yes	—
41	C₂×C₁₃×#121	C₂²	1	8	yes	—
42	C₁₃×#520	C₂²	1	32	yes	complemented
43	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
44	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
46	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
52	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#117	C₂²	1	2	yes	—
54	C₂×C₁₃×#117	C₂²	1	4	yes	—
55	C₂×C₁₃×#117	C₂²	1	8	yes	—
56	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
57	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
58	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
59	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
60	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
61	C₂×C₁₃×#41	—	2	8	no	—
62	C₂×C₁₃×#41	—	2	16	no	—
63	C₂×C₁₃×#41	C₂³	1	8	yes	—
64	C₂×C₁₃×#41	C₂³	1	16	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
81	C₁₃×#127	C₂³	1	8	yes	—
82	C₁₃×#126	C₂³	1	64	yes	—
83	C₁₃×#126	C₂³	1	64	yes	—
84	C₁₃×#125	C₂³	1	16	yes	—
85	C₁₃×#125	C₂³	1	16	yes	—
86	C₁₃×#125	C₂³	1	32	yes	—
87	C₁₃×#125	C₂³	1	64	yes	—
88	C₁₃×#124	C₂³	1	16	yes	—
89	C₁₃×#123	C₂³	1	64	yes	—
90	C₁₃×#123	C₂³	1	64	yes	—
91	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
92	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
93	C₁₃×#121	C₂³	1	32	yes	—
94	C₁₃×#121	C₂³	1	32	yes	—
95	C₁₃×#121	C₂³	1	64	yes	—
96	C₁₃×#121	C₂³	1	32	yes	—
97	C₁₃×#121	C₂³	1	64	yes	—
98	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
99	C₄×Q₈×C₁₃	C₂³	1	32	yes	—
100	C₄×D₄×C₁₃	C₂³	1	32	yes	—
101	C₄×D₄×C₁₃	C₂³	1	16	yes	—
102	C₄×D₄×C₁₃	C₂³	1	32	yes	—
103	C₄×D₄×C₁₃	C₂³	1	64	yes	—
104	C₄×D₄×C₁₃	C₂³	1	64	yes	—
105	C₄×D₄×C₁₃	C₂³	1	32	yes	—
106	C₁₃×#117	C₂³	1	8	yes	—
107	C₁₃×#117	C₂³	1	16	yes	—
108	C₁₃×#117	C₂³	1	32	yes	—
109	C₁₃×#117	C₂³	1	64	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	32	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
137	C₂×#3512	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
139	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
140	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×#41	—	2	32	no	—
142	C₁₃×#41	—	2	64	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	8	no	—
145	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
146	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	16	no	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	4	16	no	—
152	C₂×D₄×C₁₃	—	4	8	no	—
153	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
154	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
155	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
156	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
159	C₂²×C₄×C₁₃	—	2	16	no	—
160	C₂²×C₄×C₁₃	—	2	8	no	—
161	C₂²×C₄×C₁₃	—	4	8	no	—
162	C₂²×C₄×C₁₃	—	4	16	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	4	8	no	—
165	C₂²×C₄×C₁₃	#41	1	8	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
184	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
186	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
187	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
188	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
190	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
191	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
192	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
193	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
194	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
195	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
196	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
197	C₄²×C₁₃	C₂⁴	1	4	yes	—
198	C₄²×C₁₃	C₂⁴	1	8	yes	—
199	C₄²×C₁₃	C₂⁴	1	16	yes	—
200	C₄²×C₁₃	C₂⁴	1	4	yes	—
201	C₄²×C₁₃	C₂⁴	1	8	yes	—
202	C₄²×C₁₃	C₂⁴	1	32	yes	—
203	#3512	C₂×C₁₃	1	32	yes	direct product factor
204	C₂×#553	C₂×C₁₃	1	4	yes	complemented
205	C₂×#553	C₂×C₁₃	1	8	yes	complemented
206	C₂×#552	C₂×C₁₃	1	4	yes	complemented
207	C₂×#541	C₂×C₁₃	1	2	yes	complemented
208	C₂×#540	C₂×C₁₃	1	2	yes	complemented
209	C₂×#537	C₂×C₁₃	1	2	yes	complemented
210	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#529	C₂×C₁₃	1	4	yes	complemented
212	C₂²×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂×#520	C₂×C₁₃	1	2	yes	complemented
214	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	8	no	—
217	C₂³×C₁₃	—	2	4	no	—
218	C₂³×C₁₃	—	2	8	no	—
219	C₂³×C₁₃	—	2	8	no	—
220	C₂³×C₁₃	—	2	8	no	—
221	C₂³×C₁₃	C₂×#41	1	4	yes	—
222	C₂³×C₁₃	C₂⁵	1	8	yes	—
223	C₂³×C₁₃	C₂⁵	1	4	yes	—
224	C₂³×C₁₃	C₂⁵	1	2	yes	—
225	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
226	Q₈×C₁₃	—	2	8	no	—
227	Q₈×C₁₃	—	2	16	no	—
228	D₄×C₁₃	—	2	16	no	—
229	D₄×C₁₃	—	2	32	no	—
230	D₄×C₁₃	—	2	8	no	—
231	D₄×C₁₃	—	2	16	no	—
232	D₄×C₁₃	—	4	32	no	—
233	D₄×C₁₃	—	4	16	no	—
234	C₂×C₄×C₁₃	—	2	8	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	8	no	—
238	C₂×C₄×C₁₃	—	2	16	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	32	no	—
241	C₂×C₄×C₁₃	—	2	16	no	—
242	C₂×C₄×C₁₃	—	4	16	no	—
243	C₂×C₄×C₁₃	—	4	32	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	4	16	no	—
246	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
247	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
248	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
250	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
252	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
254	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
257	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×#41	C₂²×C₁₃	1	2	yes	—
259	#553	C₂²×C₁₃	1	64	yes	complemented
260	#553	C₂²×C₁₃	1	128	yes	complemented
261	#552	C₂²×C₁₃	1	64	yes	complemented
262	#541	C₂²×C₁₃	1	32	yes	complemented
263	#540	C₂²×C₁₃	1	32	yes	complemented
264	#537	C₂²×C₁₃	1	32	yes	complemented
265	#532	C₂²×C₁₃	1	16	yes	complemented
266	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
268	#529	C₂²×C₁₃	1	64	yes	complemented
269	C₂×#126	C₂²×C₁₃	1	8	yes	—
270	C₂×#126	C₂²×C₁₃	1	8	yes	—
271	C₂×#125	C₂²×C₁₃	1	2	yes	—
272	C₂×#125	C₂²×C₁₃	1	2	yes	—
273	C₂×#125	C₂²×C₁₃	1	4	yes	—
274	C₂×#125	C₂²×C₁₃	1	8	yes	—
275	C₂×#125	C₂²×C₁₃	1	16	yes	complemented
276	C₂×#124	C₂²×C₁₃	1	2	yes	—
277	C₂×#123	C₂²×C₁₃	1	8	yes	—
278	C₂×#123	C₂²×C₁₃	1	8	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
280	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
281	C₂×#121	C₂²×C₁₃	1	4	yes	—
282	C₂×#121	C₂²×C₁₃	1	4	yes	—
283	C₂×#121	C₂²×C₁₃	1	8	yes	—
284	C₂×#121	C₂²×C₁₃	1	4	yes	—
285	C₂×#121	C₂²×C₁₃	1	8	yes	—
286	#520	C₂²×C₁₃	1	32	yes	complemented
287	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
288	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
290	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
291	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
292	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
293	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
294	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
295	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
296	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#117	C₂²×C₁₃	1	2	yes	—
298	C₂×#117	C₂²×C₁₃	1	4	yes	—
299	C₂×#117	C₂²×C₁₃	1	8	yes	—
300	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
301	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
302	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
303	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	8	no	—
307	C₂²×C₁₃	—	2	8	no	—
308	C₂²×C₁₃	—	2	4	no	—
309	C₂²×C₁₃	—	2	8	no	—
310	C₂²×C₁₃	—	2	8	no	—
311	C₂²×C₁₃	—	2	8	no	—
312	C₂²×C₁₃	—	4	16	no	—
313	C₂²×C₁₃	—	4	8	no	—
314	C₂²×C₁₃	C₂²×#41	1	4	yes	—
315	C₂²×C₁₃	C₂²×#41	1	2	yes	—
316	C₂²×C₁₃	#585	1	4	yes	—
317	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
318	C₄×C₁₃	—	2	8	no	—
319	C₄×C₁₃	—	2	4	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	8	no	—
322	C₄×C₁₃	—	2	16	no	—
323	C₄×C₁₃	—	2	4	no	—
324	C₄×C₁₃	C₂²×#41	1	4	yes	—
325	C₄×C₁₃	C₂²×#41	1	4	yes	—
326	C₂×#41	—	2	8	no	—
327	C₂×#41	—	2	16	no	—
328	C₂×#41	C₂³×C₁₃	1	8	yes	—
329	C₂×#41	C₂³×C₁₃	1	16	yes	—
330	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
334	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
337	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
338	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
339	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
343	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
344	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
346	#127	C₂³×C₁₃	1	8	yes	—
347	#126	C₂³×C₁₃	1	64	yes	—
348	#126	C₂³×C₁₃	1	64	yes	—
349	#125	C₂³×C₁₃	1	16	yes	—
350	#125	C₂³×C₁₃	1	16	yes	—
351	#125	C₂³×C₁₃	1	32	yes	—
352	#125	C₂³×C₁₃	1	64	yes	—
353	#124	C₂³×C₁₃	1	16	yes	—
354	#123	C₂³×C₁₃	1	64	yes	—
355	#123	C₂³×C₁₃	1	64	yes	—
356	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
357	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
358	#121	C₂³×C₁₃	1	32	yes	—
359	#121	C₂³×C₁₃	1	32	yes	—
360	#121	C₂³×C₁₃	1	64	yes	—
361	#121	C₂³×C₁₃	1	32	yes	—
362	#121	C₂³×C₁₃	1	64	yes	—
363	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
364	C₄×Q₈	C₂³×C₁₃	1	32	yes	—
365	C₄×D₄	C₂³×C₁₃	1	32	yes	—
366	C₄×D₄	C₂³×C₁₃	1	16	yes	—
367	C₄×D₄	C₂³×C₁₃	1	32	yes	—
368	C₄×D₄	C₂³×C₁₃	1	64	yes	—
369	C₄×D₄	C₂³×C₁₃	1	64	yes	—
370	C₄×D₄	C₂³×C₁₃	1	32	yes	—
371	#117	C₂³×C₁₃	1	8	yes	—
372	#117	C₂³×C₁₃	1	16	yes	—
373	#117	C₂³×C₁₃	1	32	yes	—
374	#117	C₂³×C₁₃	1	64	yes	—
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
378	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	32	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
394	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
395	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
396	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
397	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
400	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
401	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₁₃	—	2	4	no	—
403	C₂×C₁₃	—	4	8	no	—
404	C₂×C₁₃	—	4	4	no	—
405	C₂×C₁₃	#3512	1	4	yes	direct product factor
406	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
407	C₂×C₁₃	C₂×#585	1	2	yes	—
408	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
409	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
410	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
411	#41	—	2	32	no	—
412	#41	—	2	64	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	8	no	—
415	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
416	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	16	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	4	16	no	—
422	C₂×D₄	—	4	8	no	—
423	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
424	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
425	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
428	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
429	C₂²×C₄	—	2	16	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	4	8	no	—
432	C₂²×C₄	—	4	16	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	C₁₃×#41	1	8	yes	—
436	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	2	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	8	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
444	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
445	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
446	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
447	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
452	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
453	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
454	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
455	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
456	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
457	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
458	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
459	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
460	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
461	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
462	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
463	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
464	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
465	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
466	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
467	C₄²	C₂⁴×C₁₃	1	4	yes	—
468	C₄²	C₂⁴×C₁₃	1	8	yes	—
469	C₄²	C₂⁴×C₁₃	1	16	yes	—
470	C₄²	C₂⁴×C₁₃	1	4	yes	—
471	C₄²	C₂⁴×C₁₃	1	8	yes	—
472	C₄²	C₂⁴×C₁₃	1	32	yes	—
473	C₁₃	C₂×#3512	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	8	no	—
480	C₂³	C₂×C₁₃×#41	1	4	yes	—
481	C₂³	C₂⁵×C₁₃	1	8	yes	—
482	C₂³	C₂⁵×C₁₃	1	4	yes	—
483	C₂³	C₂⁵×C₁₃	1	2	yes	—
484	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
485	Q₈	—	2	8	no	—
486	Q₈	—	2	16	no	—
487	D₄	—	2	16	no	—
488	D₄	—	2	32	no	—
489	D₄	—	2	8	no	—
490	D₄	—	2	16	no	—
491	D₄	—	4	32	no	—
492	D₄	—	4	16	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	16	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	32	no	—
500	C₂×C₄	—	2	16	no	—
501	C₂×C₄	—	4	16	no	—
502	C₂×C₄	—	4	32	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	16	no	—
505	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
506	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
507	C₂×C₄	C₂×C₁₃×#41	1	16	yes	—
508	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
509	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
510	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
511	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
512	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
513	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
514	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
515	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	8	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	4	8	no	—
525	C₂²	C₂²×C₁₃×#41	1	4	yes	—
526	C₂²	C₂²×C₁₃×#41	1	2	yes	—
527	C₂²	C₁₃×#585	1	4	yes	—
528	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
529	C₄	—	2	8	no	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	8	no	—
533	C₄	—	2	16	no	—
534	C₄	—	2	4	no	—
535	C₄	C₂²×C₁₃×#41	1	4	yes	—
536	C₄	C₂²×C₁₃×#41	1	4	yes	—
537	C₂	—	2	4	no	—
538	C₂	—	4	8	no	—
539	C₂	—	4	4	no	—
540	C₂	C₁₃×#3512	1	4	yes	direct product factor
541	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
542	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
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×#3512	C₂	direct (N × H)
2. C₂×C₁₃×#553	C₂	semidirect
3. C₂×C₁₃×#553	C₂	semidirect
4. C₂×C₁₃×#552	C₂	semidirect
5. C₂×C₁₃×#541	C₂	semidirect
6. C₂×C₁₃×#540	C₂	semidirect
7. C₂×C₁₃×#537	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂×C₁₃×#529	C₂	semidirect
10. C₂²×C₁₃×#125	C₂	semidirect
11. C₂×C₁₃×#520	C₂	semidirect
12. C₂×C₄×C₁₃×#41	C₂	semidirect
15. C₁₃×#553	C₂²	semidirect
16. C₁₃×#553	C₂²	semidirect
17. C₁₃×#552	C₂²	semidirect
18. C₁₃×#541	C₂²	semidirect
19. C₁₃×#540	C₂²	semidirect
20. C₁₃×#537	C₂²	semidirect
21. C₁₃×#532	C₂²	semidirect
24. C₁₃×#529	C₂²	semidirect
31. C₂×C₁₃×#125	C₂²	semidirect
42. C₁₃×#520	C₂²	semidirect
43. C₄×C₁₃×#41	C₂²	semidirect
137. C₂×#3512	C₁₃	direct (N × H)
203. #3512	C₂×C₁₃	direct (N × H)
204. C₂×#553	C₂×C₁₃	semidirect
205. C₂×#553	C₂×C₁₃	semidirect
206. C₂×#552	C₂×C₁₃	semidirect
207. C₂×#541	C₂×C₁₃	semidirect
208. C₂×#540	C₂×C₁₃	semidirect
209. C₂×#537	C₂×C₁₃	semidirect
210. C₂×#532	C₂×C₁₃	semidirect
211. C₂×#529	C₂×C₁₃	semidirect
212. C₂²×#125	C₂×C₁₃	semidirect
213. C₂×#520	C₂×C₁₃	semidirect
214. C₂×C₄×#41	C₂×C₁₃	semidirect
259. #553	C₂²×C₁₃	semidirect
260. #553	C₂²×C₁₃	semidirect
261. #552	C₂²×C₁₃	semidirect
262. #541	C₂²×C₁₃	semidirect
263. #540	C₂²×C₁₃	semidirect
264. #537	C₂²×C₁₃	semidirect
265. #532	C₂²×C₁₃	semidirect
268. #529	C₂²×C₁₃	semidirect
275. C₂×#125	C₂²×C₁₃	semidirect
286. #520	C₂²×C₁₃	semidirect
287. C₄×#41	C₂²×C₁₃	semidirect
405. C₂×C₁₃	#3512	direct (N × H)
473. C₁₃	C₂×#3512	direct (N × H)
540. C₂	C₁₃×#3512	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×#3512	2
C₂×C₁₃×#553	2
C₂×C₁₃×#552	2
C₂×C₁₃×#541	2
C₂×C₁₃×#540	2
C₂×C₁₃×#537	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂²×C₁₃×#125	2
C₂×C₁₃×#520	2
C₂×C₄×C₁₃×#41	2
C₂×#3512	13

Subgroups — C2×C13×#3512 #15749148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3512 #15749148