Subgroups — C₂×C₁₃×#3280 #15747379

Order 3328.

3074 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#546	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3280	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	—	2	8	no	—
16	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×D₈	—	2	8	no	—
21	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
22	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×D₈	C₂²	1	8	yes	complemented
25	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#546	—	2	8	no	—
28	C₁₃×#546	C₂²	1	16	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#123	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#120	—	2	2	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₂²×C₁₃×C₂²⋊C₄	—	2	2	no	—
38	C₁₃×#495	C₂²	1	8	yes	complemented
39	C₁₃×#467	C₂²	1	8	yes	complemented
40	C₁₃×#466	C₂²	1	8	yes	complemented
41	C₁₃×#463	C₂²	1	16	yes	complemented
42	C₁₃×#450	C₂²	1	16	yes	complemented
43	C₁₃×#449	C₂²	1	16	yes	complemented
44	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
45	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
49	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
50	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
51	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
54	C₂⁵×C₁₃	—	2	2	no	—
55	C₂×C₁₃×#41	—	2	4	no	—
56	C₂×C₁₃×#41	—	2	8	no	—
57	C₂×C₁₃×#41	—	4	4	no	—
58	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	2	2	no	—
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	—	2	2	no	—
64	C₂²×D₄×C₁₃	—	2	4	no	—
65	C₂²×D₄×C₁₃	—	4	4	no	—
66	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	—	2	2	no	—
71	C₂³×C₄×C₁₃	—	2	2	no	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×#135	—	2	32	no	—
75	C₂×C₁₃×Q₁₆	—	2	4	no	—
76	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	complemented
77	C₂×C₁₃×SD₁₆	—	2	8	no	—
78	C₂×C₁₃×SD₁₆	—	4	4	no	—
79	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
80	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
81	C₂×C₁₃×D₈	—	2	8	no	—
82	C₂×C₁₃×D₈	—	2	32	no	—
83	C₂×C₁₃×D₈	—	2	4	no	—
84	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
85	C₂×C₁₃×D₈	C₂³	1	8	yes	—
86	C₂×C₁₃×D₈	C₂³	1	4	yes	—
87	C₂×C₁₃×D₈	C₂³	1	4	yes	—
88	C₂²×C₈×C₁₃	—	2	4	no	—
89	C₂²×C₈×C₁₃	—	2	4	no	—
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	4	yes	complemented
96	C₁₃×#124	—	2	4	no	—
97	C₁₃×#124	C₂³	1	8	yes	complemented
98	C₁₃×#123	—	2	16	no	—
99	C₁₃×C₂²⋊Q₈	—	2	4	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	—	2	16	no	—
103	C₁₃×#121	C₂³	1	8	yes	complemented
104	C₁₃×#120	—	2	16	no	—
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	D₄	1	4	yes	—
107	C₄×D₄×C₁₃	C₂³	1	4	yes	—
108	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
118	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	C₂³	1	4	yes	complemented
122	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
123	C₁₃×#103	C₂³	1	8	yes	complemented
124	C₁₃×#102	C₂³	1	8	yes	complemented
125	C₁₃×#102	C₂³	1	8	yes	complemented
126	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
127	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
128	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
129	C₂×#3280	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂⁴×C₁₃	—	2	2	no	—
132	C₂⁴×C₁₃	—	2	8	no	—
133	C₂⁴×C₁₃	—	4	8	no	—
134	C₂⁴×C₁₃	—	4	8	no	—
135	C₂⁴×C₁₃	—	8	4	no	—
136	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×#41	—	2	16	no	—
139	C₁₃×#41	—	4	8	no	—
140	C₁₃×#41	—	4	16	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	16	no	—
147	C₂×D₄×C₁₃	—	2	8	no	—
148	C₂×D₄×C₁₃	—	2	8	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	4	no	—
151	C₂×D₄×C₁₃	—	2	8	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	16	no	—
157	C₂×D₄×C₁₃	—	4	8	no	—
158	C₂×D₄×C₁₃	—	4	8	no	—
159	C₂×D₄×C₁₃	—	8	4	no	—
160	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
161	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
162	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	2	no	—
168	C₂²×C₄×C₁₃	—	2	2	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	2	8	no	—
172	C₂²×C₄×C₁₃	—	4	8	no	—
173	C₂²×C₄×C₁₃	—	8	4	no	—
174	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₁₃×Q₁₆	—	2	8	no	—
184	C₁₃×SD₁₆	—	2	16	no	—
185	C₁₃×SD₁₆	—	4	8	no	—
186	C₁₃×D₈	—	2	16	no	—
187	C₁₃×D₈	—	2	8	no	—
188	C₁₃×D₈	C₂×D₄	1	16	yes	complemented
189	C₂×C₈×C₁₃	—	2	2	no	—
190	C₂×C₈×C₁₃	—	2	2	no	—
191	C₂×C₈×C₁₃	—	2	2	no	—
192	C₂×C₈×C₁₃	—	2	8	no	—
193	C₂×C₈×C₁₃	—	2	8	no	—
194	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
195	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
196	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
197	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
198	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
199	C₁₃×C₄⋊C₄	—	2	8	no	—
200	C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
202	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	—	2	8	no	—
206	C₁₃×C₂²⋊C₄	—	2	8	no	—
207	C₁₃×C₂²⋊C₄	—	2	8	no	—
208	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
209	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
210	C₄²×C₁₃	C₂×D₄	1	2	yes	—
211	C₄²×C₁₃	C₂⁴	1	2	yes	—
212	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂³×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#546	C₂×C₁₃	1	2	yes	complemented
215	#3280	C₂×C₁₃	1	16	yes	direct product factor
216	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
217	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
218	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
219	C₂×#463	C₂×C₁₃	1	2	yes	complemented
220	C₂×#449	C₂×C₁₃	1	2	yes	complemented
221	C₂×#450	C₂×C₁₃	1	2	yes	complemented
222	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	2	2	no	—
227	C₂³×C₁₃	—	2	8	no	—
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	4	16	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	4	4	no	—
236	C₂³×C₁₃	—	4	4	no	—
237	C₂³×C₁₃	—	4	16	no	—
238	C₂³×C₁₃	—	4	4	no	—
239	C₂³×C₁₃	—	8	8	no	—
240	C₂³×C₁₃	—	8	32	no	—
241	C₂³×C₁₃	#135	1	4	yes	complemented
242	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
244	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
245	Q₈×C₁₃	—	2	4	no	—
246	Q₈×C₁₃	—	2	4	no	—
247	Q₈×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	2	8	no	—
249	D₄×C₁₃	—	2	8	no	—
250	D₄×C₁₃	—	2	4	no	—
251	D₄×C₁₃	—	2	4	no	—
252	D₄×C₁₃	—	2	4	no	—
253	D₄×C₁₃	—	4	16	no	—
254	D₄×C₁₃	—	4	16	no	—
255	D₄×C₁₃	—	4	4	no	—
256	D₄×C₁₃	—	8	8	no	—
257	D₄×C₁₃	C₂²×D₄	1	8	yes	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	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	2	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	4	16	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	4	no	—
273	C₂×C₄×C₁₃	—	8	8	no	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
281	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
282	C₈×C₁₃	—	2	2	no	—
283	C₈×C₁₃	—	2	2	no	—
284	C₈×C₁₃	—	2	2	no	—
285	C₈×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂²×#41	C₂²×C₁₃	1	2	yes	complemented
287	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
288	C₂×#135	—	2	8	no	—
289	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
290	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
292	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
293	C₂²×D₈	—	2	8	no	—
294	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
295	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
296	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂²×D₈	C₂²×C₁₃	1	8	yes	complemented
298	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
300	#546	—	2	8	no	—
301	#546	C₂²×C₁₃	1	16	yes	complemented
302	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
303	C₂×#123	—	2	2	no	—
304	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
305	C₂×#121	—	2	2	no	—
306	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
307	C₂×#120	—	2	2	no	—
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
310	C₂²×C₂²⋊C₄	—	2	2	no	—
311	#495	C₂²×C₁₃	1	8	yes	complemented
312	#467	C₂²×C₁₃	1	8	yes	complemented
313	#466	C₂²×C₁₃	1	8	yes	complemented
314	#463	C₂²×C₁₃	1	16	yes	complemented
315	#450	C₂²×C₁₃	1	16	yes	complemented
316	#449	C₂²×C₁₃	1	16	yes	complemented
317	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
318	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
319	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
322	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
323	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
324	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	8	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	2	no	—
331	C₂²×C₁₃	—	2	8	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	4	4	no	—
335	C₂²×C₁₃	—	4	16	no	—
336	C₂²×C₁₃	—	4	4	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	—	8	32	no	—
342	C₂²×C₁₃	—	8	8	no	—
343	C₂²×C₁₃	D₄²	1	2	yes	—
344	C₂²×C₁₃	C₂×#135	1	2	yes	—
345	C₂²×C₁₃	C₂×#135	1	4	yes	complemented
346	C₂²×C₁₃	#576	1	2	yes	—
347	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
348	C₄×C₁₃	—	2	2	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	4	4	no	—
353	C₄×C₁₃	—	4	4	no	—
354	C₄×C₁₃	D₄²	1	2	yes	—
355	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂⁵	—	2	2	no	—
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	2	8	no	—
360	C₂×#41	—	4	4	no	—
361	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
362	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
363	C₂²×D₄	—	2	8	no	—
364	C₂²×D₄	—	2	2	no	—
365	C₂²×D₄	—	2	2	no	—
366	C₂²×D₄	—	2	2	no	—
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	4	4	no	—
369	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
370	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
371	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
372	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	—	2	2	no	—
374	C₂³×C₄	—	2	2	no	—
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
377	#135	—	2	32	no	—
378	C₂×Q₁₆	—	2	4	no	—
379	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	complemented
380	C₂×SD₁₆	—	2	8	no	—
381	C₂×SD₁₆	—	4	4	no	—
382	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
383	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
384	C₂×D₈	—	2	8	no	—
385	C₂×D₈	—	2	32	no	—
386	C₂×D₈	—	2	4	no	—
387	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
388	C₂×D₈	C₂³×C₁₃	1	8	yes	—
389	C₂×D₈	C₂³×C₁₃	1	4	yes	—
390	C₂×D₈	C₂³×C₁₃	1	4	yes	—
391	C₂²×C₈	—	2	4	no	—
392	C₂²×C₈	—	2	4	no	—
393	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₃	1	4	yes	complemented
399	#124	—	2	4	no	—
400	#124	C₂³×C₁₃	1	8	yes	complemented
401	#123	—	2	16	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
404	#121	—	2	4	no	—
405	#121	—	2	16	no	—
406	#121	C₂³×C₁₃	1	8	yes	complemented
407	#120	—	2	16	no	—
408	C₄×D₄	—	2	4	no	—
409	C₄×D₄	D₄×C₁₃	1	4	yes	—
410	C₄×D₄	C₂³×C₁₃	1	4	yes	—
411	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
412	C₂×C₄⋊C₄	—	2	2	no	—
413	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
415	C₂×C₂²⋊C₄	—	2	2	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	2	no	—
418	C₂×C₂²⋊C₄	—	2	2	no	—
419	C₂×C₂²⋊C₄	—	2	2	no	—
420	C₂×C₂²⋊C₄	—	2	16	no	—
421	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	#107	C₂³×C₁₃	1	4	yes	complemented
425	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
426	#103	C₂³×C₁₃	1	8	yes	complemented
427	#102	C₂³×C₁₃	1	8	yes	complemented
428	#102	C₂³×C₁₃	1	8	yes	complemented
429	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
430	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	complemented
431	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
432	C₂×C₁₃	—	2	4	no	—
433	C₂×C₁₃	—	4	2	no	—
434	C₂×C₁₃	—	4	8	no	—
435	C₂×C₁₃	—	8	4	no	—
436	C₂×C₁₃	#3280	1	4	yes	direct product factor
437	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
438	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
439	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
440	C₂⁴	—	2	2	no	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	8	no	—
443	C₂⁴	—	4	8	no	—
444	C₂⁴	—	4	8	no	—
445	C₂⁴	—	8	4	no	—
446	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
448	#41	—	2	16	no	—
449	#41	—	4	8	no	—
450	#41	—	4	16	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	4	no	—
453	C₂×Q₈	—	2	4	no	—
454	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	16	no	—
457	C₂×D₄	—	2	8	no	—
458	C₂×D₄	—	2	8	no	—
459	C₂×D₄	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	4	8	no	—
466	C₂×D₄	—	4	16	no	—
467	C₂×D₄	—	4	8	no	—
468	C₂×D₄	—	4	8	no	—
469	C₂×D₄	—	8	4	no	—
470	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
471	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
472	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
473	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	4	8	no	—
483	C₂²×C₄	—	8	4	no	—
484	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	Q₁₆	—	2	8	no	—
494	SD₁₆	—	2	16	no	—
495	SD₁₆	—	4	8	no	—
496	D₈	—	2	16	no	—
497	D₈	—	2	8	no	—
498	D₈	C₂×D₄×C₁₃	1	16	yes	complemented
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	8	no	—
503	C₂×C₈	—	2	8	no	—
504	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
505	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
506	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
507	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
508	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
509	C₄⋊C₄	—	2	8	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
512	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	8	no	—
518	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
519	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
520	C₄²	C₂×D₄×C₁₃	1	2	yes	—
521	C₄²	C₂⁴×C₁₃	1	2	yes	—
522	C₁₃	C₂×#3280	1	1	yes	characteristic, direct product factor, Sylow
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	4	16	no	—
532	C₂³	—	4	4	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	4	4	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	4	16	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	8	8	no	—
539	C₂³	—	8	32	no	—
540	C₂³	C₁₃×#135	1	4	yes	complemented
541	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
542	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
543	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
544	Q₈	—	2	4	no	—
545	Q₈	—	2	4	no	—
546	Q₈	—	4	4	no	—
547	D₄	—	2	8	no	—
548	D₄	—	2	8	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	4	no	—
551	D₄	—	2	4	no	—
552	D₄	—	4	16	no	—
553	D₄	—	4	16	no	—
554	D₄	—	4	4	no	—
555	D₄	—	8	8	no	—
556	D₄	C₂²×D₄×C₁₃	1	8	yes	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	4	16	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	8	8	no	—
573	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
574	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
575	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
576	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
579	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
580	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
581	C₈	—	2	2	no	—
582	C₈	—	2	2	no	—
583	C₈	—	2	2	no	—
584	C₈	C₂²×D₄×C₁₃	1	4	yes	—
585	C₂²	—	2	8	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	2	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	8	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	16	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	—	8	32	no	—
600	C₂²	—	8	8	no	—
601	C₂²	D₄²×C₁₃	1	2	yes	—
602	C₂²	C₂×C₁₃×#135	1	2	yes	—
603	C₂²	C₂×C₁₃×#135	1	4	yes	complemented
604	C₂²	C₁₃×#576	1	2	yes	—
605	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	4	no	—
611	C₄	—	4	4	no	—
612	C₄	D₄²×C₁₃	1	2	yes	—
613	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
614	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂	—	2	4	no	—
616	C₂	—	4	2	no	—
617	C₂	—	4	8	no	—
618	C₂	—	8	4	no	—
619	C₂	C₁₃×#3280	1	4	yes	direct product factor
620	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
621	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
622	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂³×C₁₃×D₈	C₂	semidirect
3. C₂×C₁₃×#546	C₂	semidirect
4. C₁₃×#3280	C₂	direct (N × H)
5. C₂×C₁₃×#495	C₂	semidirect
6. C₂×C₁₃×#467	C₂	semidirect
7. C₂×C₁₃×#466	C₂	semidirect
8. C₂×C₁₃×#463	C₂	semidirect
9. C₂×C₁₃×#449	C₂	semidirect
10. C₂×C₁₃×#450	C₂	semidirect
11. C₂×C₄×C₁₃×D₈	C₂	semidirect
12. C₂×C₈×D₄×C₁₃	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
17. C₂²×C₁₃×Q₁₆	C₂²	semidirect
18. C₂²×C₁₃×SD₁₆	C₂²	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
24. C₂²×C₁₃×D₈	C₂²	semidirect
26. C₂³×C₈×C₁₃	C₂²	semidirect
28. C₁₃×#546	C₂²	semidirect
29. C₂×C₁₃×#124	C₂²	semidirect
33. C₂×C₁₃×#121	C₂²	semidirect
36. C₂×C₄×D₄×C₁₃	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₁₃×#467	C₂²	semidirect
40. C₁₃×#466	C₂²	semidirect
41. C₁₃×#463	C₂²	semidirect
42. C₁₃×#450	C₂²	semidirect
43. C₁₃×#449	C₂²	semidirect
44. C₄×C₁₃×D₈	C₂²	semidirect
45. C₈×D₄×C₁₃	C₂²	semidirect
46. C₂×C₁₃×#107	C₂²	semidirect
47. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
48. C₂×C₁₃×#103	C₂²	semidirect
49. C₂×C₁₃×#102	C₂²	semidirect
50. C₂×C₁₃×#102	C₂²	semidirect
52. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
53. C₂×C₄×C₈×C₁₃	C₂²	semidirect
58. C₂×C₁₃×#41	C₂³	semidirect
76. C₂×C₁₃×Q₁₆	C₂³	semidirect
79. C₂×C₁₃×SD₁₆	C₂³	semidirect
80. C₂×C₁₃×SD₁₆	C₂³	semidirect
84. C₂×C₁₃×D₈	D₄	semidirect
95. C₂²×C₈×C₁₃	C₂³	semidirect
97. C₁₃×#124	C₂³	semidirect
103. C₁₃×#121	C₂³	semidirect
108. C₄×D₄×C₁₃	C₂³	semidirect
121. C₁₃×#107	C₂³	semidirect
122. C₁₃×C₄⋊C₈	C₂³	semidirect
123. C₁₃×#103	C₂³	semidirect
124. C₁₃×#102	C₂³	semidirect
125. C₁₃×#102	C₂³	semidirect
127. C₁₃×C₂²⋊C₈	C₂³	semidirect
128. C₄×C₈×C₁₃	C₂³	semidirect
129. C₂×#3280	C₁₃	direct (N × H)
188. C₁₃×D₈	C₂×D₄	semidirect
212. C₂²×#135	C₂×C₁₃	semidirect
213. C₂³×D₈	C₂×C₁₃	semidirect
214. C₂×#546	C₂×C₁₃	semidirect
215. #3280	C₂×C₁₃	direct (N × H)
216. C₂×#495	C₂×C₁₃	semidirect
217. C₂×#467	C₂×C₁₃	semidirect
218. C₂×#466	C₂×C₁₃	semidirect
219. C₂×#463	C₂×C₁₃	semidirect
220. C₂×#449	C₂×C₁₃	semidirect
221. C₂×#450	C₂×C₁₃	semidirect
222. C₂×C₄×D₈	C₂×C₁₃	semidirect
223. C₂×C₈×D₄	C₂×C₁₃	semidirect
241. C₂³×C₁₃	#135	semidirect
286. C₂²×#41	C₂²×C₁₃	semidirect
289. C₂×#135	C₂²×C₁₃	semidirect
290. C₂²×Q₁₆	C₂²×C₁₃	semidirect
291. C₂²×SD₁₆	C₂²×C₁₃	semidirect
292. C₂²×SD₁₆	C₂²×C₁₃	semidirect
297. C₂²×D₈	C₂²×C₁₃	semidirect
299. C₂³×C₈	C₂²×C₁₃	semidirect
301. #546	C₂²×C₁₃	semidirect
302. C₂×#124	C₂²×C₁₃	semidirect
306. C₂×#121	C₂²×C₁₃	semidirect
309. C₂×C₄×D₄	C₂²×C₁₃	semidirect
311. #495	C₂²×C₁₃	semidirect
312. #467	C₂²×C₁₃	semidirect
313. #466	C₂²×C₁₃	semidirect
314. #463	C₂²×C₁₃	semidirect
315. #450	C₂²×C₁₃	semidirect
316. #449	C₂²×C₁₃	semidirect
317. C₄×D₈	C₂²×C₁₃	semidirect
318. C₈×D₄	C₂²×C₁₃	semidirect
319. C₂×#107	C₂²×C₁₃	semidirect
320. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
321. C₂×#103	C₂²×C₁₃	semidirect
322. C₂×#102	C₂²×C₁₃	semidirect
323. C₂×#102	C₂²×C₁₃	semidirect
325. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
326. C₂×C₄×C₈	C₂²×C₁₃	semidirect
345. C₂²×C₁₃	C₂×#135	semidirect
361. C₂×#41	C₂³×C₁₃	semidirect
379. C₂×Q₁₆	C₂³×C₁₃	semidirect
382. C₂×SD₁₆	C₂³×C₁₃	semidirect
383. C₂×SD₁₆	C₂³×C₁₃	semidirect
387. C₂×D₈	D₄×C₁₃	semidirect
398. C₂²×C₈	C₂³×C₁₃	semidirect
400. #124	C₂³×C₁₃	semidirect
406. #121	C₂³×C₁₃	semidirect
411. C₄×D₄	C₂³×C₁₃	semidirect
424. #107	C₂³×C₁₃	semidirect
425. C₄⋊C₈	C₂³×C₁₃	semidirect
426. #103	C₂³×C₁₃	semidirect
427. #102	C₂³×C₁₃	semidirect
428. #102	C₂³×C₁₃	semidirect
430. C₂²⋊C₈	C₂³×C₁₃	semidirect
431. C₄×C₈	C₂³×C₁₃	semidirect
436. C₂×C₁₃	#3280	direct (N × H)
498. D₈	C₂×D₄×C₁₃	semidirect
522. C₁₃	C₂×#3280	direct (N × H)
540. C₂³	C₁₃×#135	semidirect
603. C₂²	C₂×C₁₃×#135	semidirect
619. C₂	C₁₃×#3280	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×#135	2
C₂³×C₁₃×D₈	2
C₂×C₁₃×#546	2
C₁₃×#3280	2
C₂×C₁₃×#495	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₂×C₁₃×#463	2
C₂×C₁₃×#449	2
C₂×C₁₃×#450	2
C₂×C₄×C₁₃×D₈	2
C₂×C₈×D₄×C₁₃	2
C₂×#3280	13

Subgroups — C2×C13×#3280 #15747379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3280 #15747379