Subgroups — C₂×C₁₃×#3500 #15749145

Order 3328.

11534 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3500	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₁₃×#548	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#546	C₂	1	12	yes	maximal, complemented
6	C₂×C₁₃×#536	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#535	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×#532	C₂	1	3	yes	maximal, complemented
9	C₂²×C₁₃×#124	C₂	1	3	yes	maximal, complemented
10	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×2₋¹⁺⁴	—	2	16	no	—
12	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	16	yes	complemented
13	C₂×C₁₃×H(5,𝔽₂)	—	2	16	no	—
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
15	C₂²×C₁₃×#41	C₂²	1	3	yes	—
16	C₂²×C₁₃×#41	C₂²	1	2	yes	—
17	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
19	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
20	C₂³×Q₈×C₁₃	C₂²	1	3	yes	complemented
21	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
22	C₂³×D₄×C₁₃	C₂²	1	3	yes	—
23	C₂³×D₄×C₁₃	C₂²	1	6	yes	—
24	C₁₃×#548	C₂²	1	64	yes	complemented
25	C₁₃×#546	C₂²	1	192	yes	complemented
26	C₁₃×#536	C₂²	1	48	yes	complemented
27	C₁₃×#535	C₂²	1	48	yes	complemented
28	C₁₃×#532	C₂²	1	48	yes	complemented
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
30	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
31	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
32	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
33	C₂×C₁₃×#124	C₂²	1	12	yes	complemented
34	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#124	C₂²	1	48	yes	complemented
36	C₂×C₁₃×#123	C₂²	1	12	yes	complemented
37	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
38	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
39	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
40	C₂×C₁₃×#120	C₂²	1	12	yes	complemented
41	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
42	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
44	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	complemented
45	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
46	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	12	yes	complemented
47	C₂²×C₄²×C₁₃	C₂²	1	3	yes	complemented
48	C₂⁵×C₁₃	C₂³	1	6	yes	—
49	C₁₃×2₋¹⁺⁴	—	2	128	no	—
50	C₁₃×H(5,𝔽₂)	—	2	128	no	—
51	C₂×C₁₃×#41	—	2	16	no	—
52	C₂×C₁₃×#41	—	2	48	no	—
53	C₂×C₁₃×#41	—	2	24	no	—
54	C₂×C₁₃×#41	—	2	24	no	—
55	C₂×C₁₃×#41	D₄	1	16	yes	complemented
56	C₂×C₁₃×#41	C₂³	1	24	yes	—
57	C₂×C₁₃×#41	C₂³	1	16	yes	—
58	C₂×C₁₃×#41	C₂³	1	8	yes	—
59	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
60	C₂×C₁₃×#41	C₂³	1	48	yes	complemented
61	C₂²×Q₈×C₁₃	—	2	16	no	—
62	C₂²×Q₈×C₁₃	—	2	24	no	—
63	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×Q₈×C₁₃	C₂³	1	24	yes	complemented
68	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
69	C₂²×D₄×C₁₃	—	2	48	no	—
70	C₂²×D₄×C₁₃	—	2	24	no	—
71	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
74	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₁₃	C₂³	1	48	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
82	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
85	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	complemented
86	C₁₃×#127	C₂³	1	24	yes	complemented
87	C₁₃×#124	C₂³	1	24	yes	complemented
88	C₁₃×#124	C₂³	1	48	yes	complemented
89	C₁₃×#124	C₂³	1	96	yes	complemented
90	C₁₃×#124	C₂³	1	8	yes	complemented
91	C₁₃×#123	C₂³	1	96	yes	complemented
92	C₁₃×C₂²⋊Q₈	C₂³	1	96	yes	complemented
93	C₁₃×#121	C₂³	1	96	yes	complemented
94	C₁₃×#121	C₂³	1	96	yes	complemented
95	C₁₃×#120	C₂³	1	96	yes	complemented
96	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
97	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
98	C₄×D₄×C₁₃	C₂³	1	96	yes	complemented
99	C₁₃×#117	C₂³	1	24	yes	complemented
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	96	yes	complemented
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
109	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
110	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
111	C₂×#3500	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	24	no	—
113	C₂⁴×C₁₃	—	4	24	no	—
114	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
115	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
117	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
118	C₁₃×#41	—	2	64	no	—
119	C₁₃×#41	—	2	192	no	—
120	C₁₃×#41	—	2	96	no	—
121	C₁₃×#41	—	2	96	no	—
122	C₁₃×#41	C₂×D₄	1	64	yes	complemented
123	C₂×Q₈×C₁₃	—	2	64	no	—
124	C₂×Q₈×C₁₃	—	2	24	no	—
125	C₂×Q₈×C₁₃	—	2	12	no	—
126	C₂×Q₈×C₁₃	—	2	96	no	—
127	C₂×Q₈×C₁₃	—	2	4	no	—
128	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
129	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
130	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
131	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
132	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
133	C₂×D₄×C₁₃	—	2	24	no	—
134	C₂×D₄×C₁₃	—	2	24	no	—
135	C₂×D₄×C₁₃	—	2	192	no	—
136	C₂×D₄×C₁₃	—	2	24	no	—
137	C₂×D₄×C₁₃	—	2	12	no	—
138	C₂×D₄×C₁₃	—	2	96	no	—
139	C₂×D₄×C₁₃	—	2	4	no	—
140	C₂×D₄×C₁₃	—	4	24	no	—
141	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	—
142	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
148	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
149	C₂²×C₄×C₁₃	—	2	24	no	—
150	C₂²×C₄×C₁₃	—	2	24	no	—
151	C₂²×C₄×C₁₃	—	2	24	no	—
152	C₂²×C₄×C₁₃	—	4	12	no	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
163	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
167	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
168	C₁₃×C₂²⋊C₄	C₂⁴	1	96	yes	—
169	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
170	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
171	C₄²×C₁₃	C₂⁴	1	4	yes	—
172	C₄²×C₁₃	C₂⁴	1	12	yes	—
173	C₄²×C₁₃	C₂⁴	1	24	yes	—
174	C₂²×2₋¹⁺⁴	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂²×H(5,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
176	#3500	C₂×C₁₃	1	32	yes	direct product factor
177	C₂×#548	C₂×C₁₃	1	4	yes	complemented
178	C₂×#546	C₂×C₁₃	1	12	yes	complemented
179	C₂×#536	C₂×C₁₃	1	3	yes	complemented
180	C₂×#535	C₂×C₁₃	1	3	yes	complemented
181	C₂×#532	C₂×C₁₃	1	3	yes	complemented
182	C₂²×#124	C₂×C₁₃	1	3	yes	complemented
183	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	12	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	2	12	no	—
187	C₂³×C₁₃	—	2	8	no	—
188	C₂³×C₁₃	—	2	24	no	—
189	C₂³×C₁₃	—	2	48	no	—
190	C₂³×C₁₃	—	4	48	no	—
191	C₂³×C₁₃	—	8	48	no	—
192	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
193	C₂³×C₁₃	C₂⁵	1	12	yes	—
194	C₂³×C₁₃	C₂⁵	1	4	yes	—
195	C₂³×C₁₃	C₂⁵	1	6	yes	—
196	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
197	Q₈×C₁₃	—	2	48	no	—
198	Q₈×C₁₃	—	2	24	no	—
199	Q₈×C₁₃	—	2	8	no	—
200	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
201	D₄×C₁₃	—	2	48	no	—
202	D₄×C₁₃	—	2	48	no	—
203	D₄×C₁₃	—	2	48	no	—
204	D₄×C₁₃	—	2	24	no	—
205	D₄×C₁₃	—	2	8	no	—
206	D₄×C₁₃	—	4	48	no	—
207	D₄×C₁₃	C₂²×D₄	1	48	yes	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	12	no	—
210	C₂×C₄×C₁₃	—	2	48	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	12	no	—
213	C₂×C₄×C₁₃	—	2	48	no	—
214	C₂×C₄×C₁₃	—	2	48	no	—
215	C₂×C₄×C₁₃	—	4	24	no	—
216	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	48	yes	—
219	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
220	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
221	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
222	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
225	C₂×2₋¹⁺⁴	—	2	16	no	—
226	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	16	yes	complemented
227	C₂×H(5,𝔽₂)	—	2	16	no	—
228	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	16	yes	complemented
229	C₂²×#41	C₂²×C₁₃	1	3	yes	—
230	C₂²×#41	C₂²×C₁₃	1	2	yes	—
231	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
232	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
233	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
234	C₂³×Q₈	C₂²×C₁₃	1	3	yes	complemented
235	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
236	C₂³×D₄	C₂²×C₁₃	1	3	yes	—
237	C₂³×D₄	C₂²×C₁₃	1	6	yes	—
238	#548	C₂²×C₁₃	1	64	yes	complemented
239	#546	C₂²×C₁₃	1	192	yes	complemented
240	#536	C₂²×C₁₃	1	48	yes	complemented
241	#535	C₂²×C₁₃	1	48	yes	complemented
242	#532	C₂²×C₁₃	1	48	yes	complemented
243	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
244	C₂×#127	C₂²×C₁₃	1	3	yes	complemented
245	C₂×#124	C₂²×C₁₃	1	3	yes	complemented
246	C₂×#124	C₂²×C₁₃	1	6	yes	complemented
247	C₂×#124	C₂²×C₁₃	1	12	yes	complemented
248	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic, complemented
249	C₂×#124	C₂²×C₁₃	1	48	yes	complemented
250	C₂×#123	C₂²×C₁₃	1	12	yes	complemented
251	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	complemented
252	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
253	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
254	C₂×#120	C₂²×C₁₃	1	12	yes	complemented
255	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
256	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
257	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
258	C₂×C₄×D₄	C₂²×C₁₃	1	12	yes	complemented
259	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
260	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	12	yes	complemented
261	C₂²×C₄²	C₂²×C₁₃	1	3	yes	complemented
262	C₂²×C₁₃	—	2	12	no	—
263	C₂²×C₁₃	—	2	24	no	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	2	12	no	—
266	C₂²×C₁₃	—	2	8	no	—
267	C₂²×C₁₃	—	2	24	no	—
268	C₂²×C₁₃	—	4	8	no	—
269	C₂²×C₁₃	—	4	24	no	—
270	C₂²×C₁₃	—	8	48	no	—
271	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
272	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
273	C₂²×C₁₃	#585	1	4	yes	—
274	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
275	C₄×C₁₃	—	2	4	no	—
276	C₄×C₁₃	—	2	12	no	—
277	C₄×C₁₃	—	2	4	no	—
278	C₄×C₁₃	—	2	12	no	—
279	C₄×C₁₃	C₂³×D₄	1	12	yes	—
280	C₄×C₁₃	C₂³×D₄	1	4	yes	—
281	C₂⁵	C₂³×C₁₃	1	6	yes	—
282	2₋¹⁺⁴	—	2	128	no	—
283	H(5,𝔽₂)	—	2	128	no	—
284	C₂×#41	—	2	16	no	—
285	C₂×#41	—	2	48	no	—
286	C₂×#41	—	2	24	no	—
287	C₂×#41	—	2	24	no	—
288	C₂×#41	D₄×C₁₃	1	16	yes	complemented
289	C₂×#41	C₂³×C₁₃	1	24	yes	—
290	C₂×#41	C₂³×C₁₃	1	16	yes	—
291	C₂×#41	C₂³×C₁₃	1	8	yes	—
292	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
293	C₂×#41	C₂³×C₁₃	1	48	yes	complemented
294	C₂²×Q₈	—	2	16	no	—
295	C₂²×Q₈	—	2	24	no	—
296	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
297	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
298	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
299	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₁₃	1	24	yes	complemented
301	C₂²×Q₈	C₂³×C₁₃	1	16	yes	complemented
302	C₂²×D₄	—	2	48	no	—
303	C₂²×D₄	—	2	24	no	—
304	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
305	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
306	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
307	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
308	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
309	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂²×D₄	C₂³×C₁₃	1	48	yes	—
311	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
312	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
313	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
317	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
318	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
319	#127	C₂³×C₁₃	1	24	yes	complemented
320	#124	C₂³×C₁₃	1	24	yes	complemented
321	#124	C₂³×C₁₃	1	48	yes	complemented
322	#124	C₂³×C₁₃	1	96	yes	complemented
323	#124	C₂³×C₁₃	1	8	yes	complemented
324	#123	C₂³×C₁₃	1	96	yes	complemented
325	C₂²⋊Q₈	C₂³×C₁₃	1	96	yes	complemented
326	#121	C₂³×C₁₃	1	96	yes	complemented
327	#121	C₂³×C₁₃	1	96	yes	complemented
328	#120	C₂³×C₁₃	1	96	yes	complemented
329	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
330	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
331	C₄×D₄	C₂³×C₁₃	1	96	yes	complemented
332	#117	C₂³×C₁₃	1	24	yes	complemented
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	96	yes	complemented
340	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
341	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
342	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₃	1	24	yes	complemented
344	C₂×C₁₃	—	2	12	no	—
345	C₂×C₁₃	—	4	4	no	—
346	C₂×C₁₃	—	4	12	no	—
347	C₂×C₁₃	#3500	1	4	yes	direct product factor
348	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
349	C₂×C₁₃	C₂×#585	1	2	yes	—
350	C₂⁴	—	2	24	no	—
351	C₂⁴	—	4	24	no	—
352	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
353	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
354	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
355	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
356	#41	—	2	64	no	—
357	#41	—	2	192	no	—
358	#41	—	2	96	no	—
359	#41	—	2	96	no	—
360	#41	C₂×D₄×C₁₃	1	64	yes	complemented
361	C₂×Q₈	—	2	64	no	—
362	C₂×Q₈	—	2	24	no	—
363	C₂×Q₈	—	2	12	no	—
364	C₂×Q₈	—	2	96	no	—
365	C₂×Q₈	—	2	4	no	—
366	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
367	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
368	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
369	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
370	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
371	C₂×D₄	—	2	24	no	—
372	C₂×D₄	—	2	24	no	—
373	C₂×D₄	—	2	192	no	—
374	C₂×D₄	—	2	24	no	—
375	C₂×D₄	—	2	12	no	—
376	C₂×D₄	—	2	96	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	24	no	—
379	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	—
380	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
381	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
382	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
383	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
384	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
385	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
386	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
387	C₂²×C₄	—	2	24	no	—
388	C₂²×C₄	—	2	24	no	—
389	C₂²×C₄	—	2	24	no	—
390	C₂²×C₄	—	4	12	no	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
392	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
394	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
395	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
401	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
403	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
404	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
405	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
406	C₂²⋊C₄	C₂⁴×C₁₃	1	96	yes	—
407	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
408	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
409	C₄²	C₂⁴×C₁₃	1	4	yes	—
410	C₄²	C₂⁴×C₁₃	1	12	yes	—
411	C₄²	C₂⁴×C₁₃	1	24	yes	—
412	C₁₃	C₂×#3500	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	12	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	12	no	—
416	C₂³	—	2	8	no	—
417	C₂³	—	2	24	no	—
418	C₂³	—	2	48	no	—
419	C₂³	—	4	48	no	—
420	C₂³	—	8	48	no	—
421	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
422	C₂³	C₂⁵×C₁₃	1	12	yes	—
423	C₂³	C₂⁵×C₁₃	1	4	yes	—
424	C₂³	C₂⁵×C₁₃	1	6	yes	—
425	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
426	Q₈	—	2	48	no	—
427	Q₈	—	2	24	no	—
428	Q₈	—	2	8	no	—
429	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
430	D₄	—	2	48	no	—
431	D₄	—	2	48	no	—
432	D₄	—	2	48	no	—
433	D₄	—	2	24	no	—
434	D₄	—	2	8	no	—
435	D₄	—	4	48	no	—
436	D₄	C₂²×D₄×C₁₃	1	48	yes	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	12	no	—
439	C₂×C₄	—	2	48	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	12	no	—
442	C₂×C₄	—	2	48	no	—
443	C₂×C₄	—	2	48	no	—
444	C₂×C₄	—	4	24	no	—
445	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
446	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₁₃	1	48	yes	—
448	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
449	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
450	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
451	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
452	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
453	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	24	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	12	no	—
458	C₂²	—	2	8	no	—
459	C₂²	—	2	24	no	—
460	C₂²	—	4	8	no	—
461	C₂²	—	4	24	no	—
462	C₂²	—	8	48	no	—
463	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
464	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
465	C₂²	C₁₃×#585	1	4	yes	—
466	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	12	no	—
469	C₄	—	2	4	no	—
470	C₄	—	2	12	no	—
471	C₄	C₂³×D₄×C₁₃	1	12	yes	—
472	C₄	C₂³×D₄×C₁₃	1	4	yes	—
473	C₂	—	2	12	no	—
474	C₂	—	4	12	no	—
475	C₂	—	4	4	no	—
476	C₂	C₁₃×#3500	1	4	yes	direct product factor
477	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
478	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. C₂²×C₁₃×2₋¹⁺⁴	C₂	semidirect
2. C₂²×C₁₃×H(5,𝔽₂)	C₂	semidirect
3. C₁₃×#3500	C₂	direct (N × H)
4. C₂×C₁₃×#548	C₂	semidirect
5. C₂×C₁₃×#546	C₂	semidirect
6. C₂×C₁₃×#536	C₂	semidirect
7. C₂×C₁₃×#535	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂²×C₁₃×#124	C₂	semidirect
10. C₂×C₄×C₁₃×#41	C₂	semidirect
12. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
14. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×C₁₃×#41	C₂²	semidirect
19. C₂²×C₁₃×#41	C₂²	semidirect
20. C₂³×Q₈×C₁₃	C₂²	semidirect
21. C₂³×Q₈×C₁₃	C₂²	semidirect
24. C₁₃×#548	C₂²	semidirect
25. C₁₃×#546	C₂²	semidirect
26. C₁₃×#536	C₂²	semidirect
27. C₁₃×#535	C₂²	semidirect
28. C₁₃×#532	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₂×C₁₃×#127	C₂²	semidirect
31. C₂×C₁₃×#124	C₂²	semidirect
32. C₂×C₁₃×#124	C₂²	semidirect
33. C₂×C₁₃×#124	C₂²	semidirect
34. C₂×C₁₃×#124	C₂²	semidirect
35. C₂×C₁₃×#124	C₂²	semidirect
36. C₂×C₁₃×#123	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₂×C₁₃×#121	C₂²	semidirect
39. C₂×C₁₃×#121	C₂²	semidirect
40. C₂×C₁₃×#120	C₂²	semidirect
41. C₄×C₁₃×#41	C₂²	semidirect
42. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂×C₁₃×#117	C₂²	semidirect
46. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
47. C₂²×C₄²×C₁₃	C₂²	semidirect
55. C₂×C₁₃×#41	D₄	semidirect
59. C₂×C₁₃×#41	C₂³	semidirect
60. C₂×C₁₃×#41	C₂³	semidirect
67. C₂²×Q₈×C₁₃	C₂³	semidirect
68. C₂²×Q₈×C₁₃	C₂³	semidirect
85. C₁₃×C₄⋊Q₈	C₂³	semidirect
86. C₁₃×#127	C₂³	semidirect
87. C₁₃×#124	C₂³	semidirect
88. C₁₃×#124	C₂³	semidirect
89. C₁₃×#124	C₂³	semidirect
90. C₁₃×#124	C₂³	semidirect
91. C₁₃×#123	C₂³	semidirect
92. C₁₃×C₂²⋊Q₈	C₂³	semidirect
93. C₁₃×#121	C₂³	semidirect
94. C₁₃×#121	C₂³	semidirect
95. C₁₃×#120	C₂³	semidirect
96. C₄×Q₈×C₁₃	C₂³	semidirect
97. C₄×D₄×C₁₃	C₂³	semidirect
98. C₄×D₄×C₁₃	C₂³	semidirect
99. C₁₃×#117	C₂³	semidirect
106. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
110. C₂×C₄²×C₁₃	C₂³	semidirect
111. C₂×#3500	C₁₃	direct (N × H)
122. C₁₃×#41	C₂×D₄	semidirect
174. C₂²×2₋¹⁺⁴	C₂×C₁₃	semidirect
175. C₂²×H(5,𝔽₂)	C₂×C₁₃	semidirect
176. #3500	C₂×C₁₃	direct (N × H)
177. C₂×#548	C₂×C₁₃	semidirect
178. C₂×#546	C₂×C₁₃	semidirect
179. C₂×#536	C₂×C₁₃	semidirect
180. C₂×#535	C₂×C₁₃	semidirect
181. C₂×#532	C₂×C₁₃	semidirect
182. C₂²×#124	C₂×C₁₃	semidirect
183. C₂×C₄×#41	C₂×C₁₃	semidirect
226. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
228. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
232. C₂²×#41	C₂²×C₁₃	semidirect
233. C₂²×#41	C₂²×C₁₃	semidirect
234. C₂³×Q₈	C₂²×C₁₃	semidirect
235. C₂³×Q₈	C₂²×C₁₃	semidirect
238. #548	C₂²×C₁₃	semidirect
239. #546	C₂²×C₁₃	semidirect
240. #536	C₂²×C₁₃	semidirect
241. #535	C₂²×C₁₃	semidirect
242. #532	C₂²×C₁₃	semidirect
243. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
244. C₂×#127	C₂²×C₁₃	semidirect
245. C₂×#124	C₂²×C₁₃	semidirect
246. C₂×#124	C₂²×C₁₃	semidirect
247. C₂×#124	C₂²×C₁₃	semidirect
248. C₂×#124	C₂²×C₁₃	semidirect
249. C₂×#124	C₂²×C₁₃	semidirect
250. C₂×#123	C₂²×C₁₃	semidirect
251. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
252. C₂×#121	C₂²×C₁₃	semidirect
253. C₂×#121	C₂²×C₁₃	semidirect
254. C₂×#120	C₂²×C₁₃	semidirect
255. C₄×#41	C₂²×C₁₃	semidirect
256. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
257. C₂×C₄×D₄	C₂²×C₁₃	semidirect
258. C₂×C₄×D₄	C₂²×C₁₃	semidirect
259. C₂×#117	C₂²×C₁₃	semidirect
260. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
261. C₂²×C₄²	C₂²×C₁₃	semidirect
288. C₂×#41	D₄×C₁₃	semidirect
292. C₂×#41	C₂³×C₁₃	semidirect
293. C₂×#41	C₂³×C₁₃	semidirect
300. C₂²×Q₈	C₂³×C₁₃	semidirect
301. C₂²×Q₈	C₂³×C₁₃	semidirect
318. C₄⋊Q₈	C₂³×C₁₃	semidirect
319. #127	C₂³×C₁₃	semidirect
320. #124	C₂³×C₁₃	semidirect
321. #124	C₂³×C₁₃	semidirect
322. #124	C₂³×C₁₃	semidirect
323. #124	C₂³×C₁₃	semidirect
324. #123	C₂³×C₁₃	semidirect
325. C₂²⋊Q₈	C₂³×C₁₃	semidirect
326. #121	C₂³×C₁₃	semidirect
327. #121	C₂³×C₁₃	semidirect
328. #120	C₂³×C₁₃	semidirect
329. C₄×Q₈	C₂³×C₁₃	semidirect
330. C₄×D₄	C₂³×C₁₃	semidirect
331. C₄×D₄	C₂³×C₁₃	semidirect
332. #117	C₂³×C₁₃	semidirect
339. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
343. C₂×C₄²	C₂³×C₁₃	semidirect
347. C₂×C₁₃	#3500	direct (N × H)
360. #41	C₂×D₄×C₁₃	semidirect
412. C₁₃	C₂×#3500	direct (N × H)
476. C₂	C₁₃×#3500	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×C₁₃×2₋¹⁺⁴	2
C₂²×C₁₃×H(5,𝔽₂)	2
C₁₃×#3500	2
C₂×C₁₃×#548	2
C₂×C₁₃×#546	2
C₂×C₁₃×#536	2
C₂×C₁₃×#535	2
C₂×C₁₃×#532	2
C₂²×C₁₃×#124	2
C₂×C₄×C₁₃×#41	2
C₂×#3500	13

Subgroups — C2×C13×#3500 #15749145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3500 #15749145