Subgroups — C₂×C₁₃×#3517 #15749129

Order 3328.

7854 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3517	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#553	C₂	1	6	yes	maximal, complemented
4	C₂×C₁₃×#550	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#550	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#547	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×#540	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₃×#532	C₂	1	3	yes	maximal, complemented
10	C₂×C₁₃×#529	C₂	1	3	yes	maximal, 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	C₂²×C₁₃×#41	C₂²	1	6	yes	—
16	C₁₃×#557	C₂²	1	16	yes	complemented
17	C₁₃×#553	C₂²	1	96	yes	complemented
18	C₁₃×#550	C₂²	1	48	yes	complemented
19	C₁₃×#550	C₂²	1	16	yes	complemented
20	C₁₃×#550	C₂²	1	32	yes	complemented
21	C₁₃×#547	C₂²	1	48	yes	complemented
22	C₁₃×#540	C₂²	1	96	yes	complemented
23	C₁₃×#532	C₂²	1	48	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₂×C₁₃×#127	C₂²	1	3	yes	—
26	C₂×C₁₃×#127	C₂²	1	6	yes	—
27	C₁₃×#529	C₂²	1	48	yes	complemented
28	C₂×C₁₃×#126	C₂²	1	6	yes	—
29	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#125	C₂²	1	6	yes	—
31	C₂×C₁₃×#124	C₂²	1	3	yes	—
32	C₂×C₁₃×#123	C₂²	1	6	yes	—
33	C₂×C₁₃×#123	C₂²	1	12	yes	—
34	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	—
35	C₂×C₁₃×#121	C₂²	1	3	yes	—
36	C₂×C₁₃×#121	C₂²	1	6	yes	—
37	C₂×C₁₃×#121	C₂²	1	6	yes	—
38	C₂×C₁₃×#121	C₂²	1	6	yes	—
39	C₂×C₁₃×#121	C₂²	1	12	yes	—
40	C₂×C₁₃×#121	C₂²	1	6	yes	—
41	C₁₃×#520	C₂²	1	32	yes	complemented
42	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
43	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
47	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
48	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
49	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
50	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
51	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
52	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
53	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	—
54	C₂×C₁₃×#117	C₂²	1	3	yes	—
55	C₂×C₁₃×#117	C₂²	1	6	yes	—
56	C₂²×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
57	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
58	C₂×C₁₃×#41	—	2	8	no	—
59	C₂×C₁₃×#41	—	2	16	no	—
60	C₂×C₁₃×#41	—	4	24	no	—
61	C₂×C₁₃×#41	C₂³	1	8	yes	—
62	C₂×C₁₃×#41	C₂³	1	16	yes	—
63	C₂×C₁₃×#41	C₂³	1	48	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
77	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	—
78	C₁₃×#127	C₂³	1	24	yes	—
79	C₁₃×#127	C₂³	1	48	yes	—
80	C₁₃×#126	C₂³	1	48	yes	—
81	C₁₃×#125	C₂³	1	8	yes	—
82	C₁₃×#125	C₂³	1	48	yes	—
83	C₁₃×#124	C₂³	1	24	yes	—
84	C₁₃×#123	C₂³	1	48	yes	—
85	C₁₃×#123	C₂³	1	96	yes	—
86	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
87	C₁₃×#121	C₂³	1	24	yes	—
88	C₁₃×#121	C₂³	1	48	yes	—
89	C₁₃×#121	C₂³	1	48	yes	—
90	C₁₃×#121	C₂³	1	48	yes	—
91	C₁₃×#121	C₂³	1	96	yes	—
92	C₁₃×#121	C₂³	1	48	yes	—
93	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
94	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
95	C₄×Q₈×C₁₃	C₂³	1	16	yes	—
96	C₄×Q₈×C₁₃	C₂³	1	24	yes	—
97	C₄×D₄×C₁₃	C₂³	1	24	yes	—
98	C₄×D₄×C₁₃	C₂³	1	24	yes	—
99	C₄×D₄×C₁₃	C₂³	1	48	yes	—
100	C₄×D₄×C₁₃	C₂³	1	48	yes	—
101	C₄×D₄×C₁₃	C₂³	1	24	yes	—
102	C₄×D₄×C₁₃	C₂³	1	48	yes	—
103	C₄×D₄×C₁₃	C₂³	1	48	yes	—
104	C₁₃×#117	C₂³	1	24	yes	—
105	C₁₃×#117	C₂³	1	48	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
125	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
126	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
129	C₂×#3517	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
131	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
132	C₁₃×#41	—	2	32	no	—
133	C₁₃×#41	—	2	64	no	—
134	C₁₃×#41	—	4	96	no	—
135	C₂×Q₈×C₁₃	—	2	12	no	—
136	C₂×Q₈×C₁₃	#41	1	8	yes	complemented
137	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
139	C₂×D₄×C₁₃	—	2	12	no	—
140	C₂×D₄×C₁₃	—	2	24	no	—
141	C₂×D₄×C₁₃	—	2	12	no	—
142	C₂×D₄×C₁₃	—	4	12	no	—
143	C₂×D₄×C₁₃	—	4	12	no	—
144	C₂×D₄×C₁₃	—	4	24	no	—
145	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
149	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
150	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
151	C₂²×C₄×C₁₃	—	2	12	no	—
152	C₂²×C₄×C₁₃	—	2	24	no	—
153	C₂²×C₄×C₁₃	—	2	12	no	—
154	C₂²×C₄×C₁₃	—	4	6	no	—
155	C₂²×C₄×C₁₃	—	4	24	no	—
156	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	48	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
172	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
173	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
174	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
175	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
177	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
179	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
180	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
181	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
182	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
183	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
184	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
185	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
186	C₄²×C₁₃	C₂⁴	1	4	yes	—
187	C₄²×C₁₃	C₂⁴	1	12	yes	—
188	C₄²×C₁₃	C₂⁴	1	12	yes	—
189	C₄²×C₁₃	C₂⁴	1	12	yes	—
190	C₄²×C₁₃	C₂⁴	1	24	yes	—
191	#3517	C₂×C₁₃	1	32	yes	direct product factor
192	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
193	C₂×#553	C₂×C₁₃	1	6	yes	complemented
194	C₂×#550	C₂×C₁₃	1	3	yes	complemented
195	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
196	C₂×#550	C₂×C₁₃	1	2	yes	complemented
197	C₂×#547	C₂×C₁₃	1	3	yes	complemented
198	C₂×#540	C₂×C₁₃	1	6	yes	complemented
199	C₂×#532	C₂×C₁₃	1	3	yes	complemented
200	C₂×#529	C₂×C₁₃	1	3	yes	complemented
201	C₂×#520	C₂×C₁₃	1	2	yes	complemented
202	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂³×C₁₃	—	2	6	no	—
204	C₂³×C₁₃	—	2	12	no	—
205	C₂³×C₁₃	—	2	6	no	—
206	C₂³×C₁₃	—	2	12	no	—
207	C₂³×C₁₃	—	2	6	no	—
208	C₂³×C₁₃	—	2	12	no	—
209	C₂³×C₁₃	C₂⁵	1	6	yes	—
210	C₂³×C₁₃	C₂⁵	1	12	yes	—
211	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	24	no	—
213	Q₈×C₁₃	C₂×#41	1	16	yes	complemented
214	D₄×C₁₃	—	2	24	no	—
215	D₄×C₁₃	—	2	48	no	—
216	D₄×C₁₃	—	2	24	no	—
217	D₄×C₁₃	—	4	24	no	—
218	D₄×C₁₃	—	4	24	no	—
219	D₄×C₁₃	—	4	48	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	6	no	—
223	C₂×C₄×C₁₃	—	2	12	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	6	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	24	no	—
228	C₂×C₄×C₁₃	—	2	48	no	—
229	C₂×C₄×C₁₃	—	2	24	no	—
230	C₂×C₄×C₁₃	—	4	12	no	—
231	C₂×C₄×C₁₃	—	4	48	no	—
232	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
233	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
234	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
235	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
237	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
239	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
240	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
243	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×#41	C₂²×C₁₃	1	2	yes	—
245	C₂²×#41	C₂²×C₁₃	1	6	yes	—
246	#557	C₂²×C₁₃	1	16	yes	complemented
247	#553	C₂²×C₁₃	1	96	yes	complemented
248	#550	C₂²×C₁₃	1	48	yes	complemented
249	#550	C₂²×C₁₃	1	16	yes	complemented
250	#550	C₂²×C₁₃	1	32	yes	complemented
251	#547	C₂²×C₁₃	1	48	yes	complemented
252	#540	C₂²×C₁₃	1	96	yes	complemented
253	#532	C₂²×C₁₃	1	48	yes	complemented
254	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
255	C₂×#127	C₂²×C₁₃	1	3	yes	—
256	C₂×#127	C₂²×C₁₃	1	6	yes	—
257	#529	C₂²×C₁₃	1	48	yes	complemented
258	C₂×#126	C₂²×C₁₃	1	6	yes	—
259	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#125	C₂²×C₁₃	1	6	yes	—
261	C₂×#124	C₂²×C₁₃	1	3	yes	—
262	C₂×#123	C₂²×C₁₃	1	6	yes	—
263	C₂×#123	C₂²×C₁₃	1	12	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	—
265	C₂×#121	C₂²×C₁₃	1	3	yes	—
266	C₂×#121	C₂²×C₁₃	1	6	yes	—
267	C₂×#121	C₂²×C₁₃	1	6	yes	—
268	C₂×#121	C₂²×C₁₃	1	6	yes	—
269	C₂×#121	C₂²×C₁₃	1	12	yes	—
270	C₂×#121	C₂²×C₁₃	1	6	yes	—
271	#520	C₂²×C₁₃	1	32	yes	complemented
272	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
273	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
277	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
278	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
279	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
280	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
281	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
282	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
283	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	—
284	C₂×#117	C₂²×C₁₃	1	3	yes	—
285	C₂×#117	C₂²×C₁₃	1	6	yes	—
286	C₂²×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
287	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
288	C₂²×C₁₃	—	2	6	no	—
289	C₂²×C₁₃	—	2	12	no	—
290	C₂²×C₁₃	—	2	6	no	—
291	C₂²×C₁₃	—	2	12	no	—
292	C₂²×C₁₃	—	2	6	no	—
293	C₂²×C₁₃	—	2	12	no	—
294	C₂²×C₁₃	—	4	12	no	—
295	C₂²×C₁₃	—	4	24	no	—
296	C₂²×C₁₃	C₂²×#41	1	2	yes	—
297	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
298	C₂²×C₁₃	#585	1	2	yes	—
299	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	4	no	—
302	C₄×C₁₃	—	2	6	no	—
303	C₄×C₁₃	—	2	12	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	6	no	—
306	C₄×C₁₃	—	2	4	no	—
307	C₄×C₁₃	C₂²×#41	1	12	yes	—
308	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
309	C₂×#41	—	2	8	no	—
310	C₂×#41	—	2	16	no	—
311	C₂×#41	—	4	24	no	—
312	C₂×#41	C₂³×C₁₃	1	8	yes	—
313	C₂×#41	C₂³×C₁₃	1	16	yes	—
314	C₂×#41	C₂³×C₁₃	1	48	yes	—
315	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
316	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
318	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
319	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
321	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
322	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
324	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
325	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
326	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
327	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
328	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	—
329	#127	C₂³×C₁₃	1	24	yes	—
330	#127	C₂³×C₁₃	1	48	yes	—
331	#126	C₂³×C₁₃	1	48	yes	—
332	#125	C₂³×C₁₃	1	8	yes	—
333	#125	C₂³×C₁₃	1	48	yes	—
334	#124	C₂³×C₁₃	1	24	yes	—
335	#123	C₂³×C₁₃	1	48	yes	—
336	#123	C₂³×C₁₃	1	96	yes	—
337	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
338	#121	C₂³×C₁₃	1	24	yes	—
339	#121	C₂³×C₁₃	1	48	yes	—
340	#121	C₂³×C₁₃	1	48	yes	—
341	#121	C₂³×C₁₃	1	48	yes	—
342	#121	C₂³×C₁₃	1	96	yes	—
343	#121	C₂³×C₁₃	1	48	yes	—
344	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
345	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
346	C₄×Q₈	C₂³×C₁₃	1	16	yes	—
347	C₄×Q₈	C₂³×C₁₃	1	24	yes	—
348	C₄×D₄	C₂³×C₁₃	1	24	yes	—
349	C₄×D₄	C₂³×C₁₃	1	24	yes	—
350	C₄×D₄	C₂³×C₁₃	1	48	yes	—
351	C₄×D₄	C₂³×C₁₃	1	48	yes	—
352	C₄×D₄	C₂³×C₁₃	1	24	yes	—
353	C₄×D₄	C₂³×C₁₃	1	48	yes	—
354	C₄×D₄	C₂³×C₁₃	1	48	yes	—
355	#117	C₂³×C₁₃	1	24	yes	—
356	#117	C₂³×C₁₃	1	48	yes	—
357	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
374	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
375	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
376	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
377	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
378	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
379	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
380	C₂×C₁₃	—	4	6	no	—
381	C₂×C₁₃	—	4	12	no	—
382	C₂×C₁₃	#3517	1	4	yes	direct product factor
383	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
384	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
385	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
386	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
387	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
388	#41	—	2	32	no	—
389	#41	—	2	64	no	—
390	#41	—	4	96	no	—
391	C₂×Q₈	—	2	12	no	—
392	C₂×Q₈	C₁₃×#41	1	8	yes	complemented
393	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
394	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
395	C₂×D₄	—	2	12	no	—
396	C₂×D₄	—	2	24	no	—
397	C₂×D₄	—	2	12	no	—
398	C₂×D₄	—	4	24	no	—
399	C₂×D₄	—	4	12	no	—
400	C₂×D₄	—	4	12	no	—
401	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
402	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
403	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
404	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
405	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
406	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
407	C₂²×C₄	—	2	24	no	—
408	C₂²×C₄	—	2	12	no	—
409	C₂²×C₄	—	2	12	no	—
410	C₂²×C₄	—	4	24	no	—
411	C₂²×C₄	—	4	6	no	—
412	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
419	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	48	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
426	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
427	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
428	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
429	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
430	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
431	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
433	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
434	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
435	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
436	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
437	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
438	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
439	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
440	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
441	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
442	C₄²	C₂⁴×C₁₃	1	4	yes	—
443	C₄²	C₂⁴×C₁₃	1	12	yes	—
444	C₄²	C₂⁴×C₁₃	1	12	yes	—
445	C₄²	C₂⁴×C₁₃	1	12	yes	—
446	C₄²	C₂⁴×C₁₃	1	24	yes	—
447	C₁₃	C₂×#3517	1	1	yes	characteristic, direct product factor, Sylow
448	C₂³	—	2	6	no	—
449	C₂³	—	2	12	no	—
450	C₂³	—	2	6	no	—
451	C₂³	—	2	12	no	—
452	C₂³	—	2	6	no	—
453	C₂³	—	2	12	no	—
454	C₂³	C₂⁵×C₁₃	1	6	yes	—
455	C₂³	C₂⁵×C₁₃	1	12	yes	—
456	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
457	Q₈	—	2	24	no	—
458	Q₈	C₂×C₁₃×#41	1	16	yes	complemented
459	D₄	—	2	24	no	—
460	D₄	—	2	48	no	—
461	D₄	—	2	24	no	—
462	D₄	—	4	24	no	—
463	D₄	—	4	24	no	—
464	D₄	—	4	48	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	6	no	—
468	C₂×C₄	—	2	12	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	6	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	24	no	—
473	C₂×C₄	—	2	48	no	—
474	C₂×C₄	—	2	24	no	—
475	C₂×C₄	—	4	12	no	—
476	C₂×C₄	—	4	48	no	—
477	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
478	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
479	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
480	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
481	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
482	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
483	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
484	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
485	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
486	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
487	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
488	C₂²	—	2	6	no	—
489	C₂²	—	2	12	no	—
490	C₂²	—	2	6	no	—
491	C₂²	—	2	12	no	—
492	C₂²	—	2	6	no	—
493	C₂²	—	2	12	no	—
494	C₂²	—	4	12	no	—
495	C₂²	—	4	24	no	—
496	C₂²	C₂²×C₁₃×#41	1	2	yes	—
497	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
498	C₂²	C₁₃×#585	1	2	yes	—
499	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	4	no	—
502	C₄	—	2	6	no	—
503	C₄	—	2	12	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	6	no	—
506	C₄	—	2	4	no	—
507	C₄	C₂²×C₁₃×#41	1	12	yes	—
508	C₄	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
509	C₂	—	4	6	no	—
510	C₂	—	4	12	no	—
511	C₂	C₁₃×#3517	1	4	yes	direct product factor
512	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
513	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂	C₂×C₁₃×#585	1	1	yes	characteristic

	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×#3517	C₂	direct (N × H)
2. C₂×C₁₃×#557	C₂	semidirect
3. C₂×C₁₃×#553	C₂	semidirect
4. C₂×C₁₃×#550	C₂	semidirect
5. C₂×C₁₃×#550	C₂	semidirect
6. C₂×C₁₃×#550	C₂	semidirect
7. C₂×C₁₃×#547	C₂	semidirect
8. C₂×C₁₃×#540	C₂	semidirect
9. C₂×C₁₃×#532	C₂	semidirect
10. C₂×C₁₃×#529	C₂	semidirect
11. C₂×C₁₃×#520	C₂	semidirect
12. C₂×C₄×C₁₃×#41	C₂	semidirect
16. C₁₃×#557	C₂²	semidirect
17. C₁₃×#553	C₂²	semidirect
18. C₁₃×#550	C₂²	semidirect
19. C₁₃×#550	C₂²	semidirect
20. C₁₃×#550	C₂²	semidirect
21. C₁₃×#547	C₂²	semidirect
22. C₁₃×#540	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
27. C₁₃×#529	C₂²	semidirect
41. C₁₃×#520	C₂²	semidirect
42. C₄×C₁₃×#41	C₂²	semidirect
129. C₂×#3517	C₁₃	direct (N × H)
136. C₂×Q₈×C₁₃	#41	semidirect
191. #3517	C₂×C₁₃	direct (N × H)
192. C₂×#557	C₂×C₁₃	semidirect
193. C₂×#553	C₂×C₁₃	semidirect
194. C₂×#550	C₂×C₁₃	semidirect
195. C₂×#550	C₂×C₁₃	semidirect
196. C₂×#550	C₂×C₁₃	semidirect
197. C₂×#547	C₂×C₁₃	semidirect
198. C₂×#540	C₂×C₁₃	semidirect
199. C₂×#532	C₂×C₁₃	semidirect
200. C₂×#529	C₂×C₁₃	semidirect
201. C₂×#520	C₂×C₁₃	semidirect
202. C₂×C₄×#41	C₂×C₁₃	semidirect
213. Q₈×C₁₃	C₂×#41	semidirect
246. #557	C₂²×C₁₃	semidirect
247. #553	C₂²×C₁₃	semidirect
248. #550	C₂²×C₁₃	semidirect
249. #550	C₂²×C₁₃	semidirect
250. #550	C₂²×C₁₃	semidirect
251. #547	C₂²×C₁₃	semidirect
252. #540	C₂²×C₁₃	semidirect
253. #532	C₂²×C₁₃	semidirect
257. #529	C₂²×C₁₃	semidirect
271. #520	C₂²×C₁₃	semidirect
272. C₄×#41	C₂²×C₁₃	semidirect
382. C₂×C₁₃	#3517	direct (N × H)
392. C₂×Q₈	C₁₃×#41	semidirect
447. C₁₃	C₂×#3517	direct (N × H)
458. Q₈	C₂×C₁₃×#41	semidirect
511. C₂	C₁₃×#3517	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×#3517	2
C₂×C₁₃×#557	2
C₂×C₁₃×#553	2
C₂×C₁₃×#550	2
C₂×C₁₃×#547	2
C₂×C₁₃×#540	2
C₂×C₁₃×#532	2
C₂×C₁₃×#529	2
C₂×C₁₃×#520	2
C₂×C₄×C₁₃×#41	2
C₂×#3517	13

Subgroups — C2×C13×#3517 #15749129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3517 #15749129