Subgroups — C₂×C₁₃×#3508 #15749137

Order 3328.

8622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#559	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#550	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₃×#546	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#540	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#535	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#532	C₂	1	4	yes	maximal, complemented
9	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#518	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
16	C₁₃×#559	C₂²	1	64	yes	complemented
17	C₁₃×#550	C₂²	1	64	yes	complemented
18	C₁₃×#546	C₂²	1	128	yes	complemented
19	C₁₃×#540	C₂²	1	64	yes	complemented
20	C₁₃×#535	C₂²	1	32	yes	complemented
21	C₁₃×#533	C₂²	1	16	yes	complemented
22	C₁₃×#532	C₂²	1	64	yes	complemented
23	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#127	C₂²	1	2	yes	—
25	C₂×C₁₃×#127	C₂²	1	2	yes	—
26	C₂×C₁₃×#127	C₂²	1	4	yes	—
27	C₂×C₁₃×#127	C₂²	1	16	yes	complemented
28	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
30	C₂×C₁₃×#124	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#124	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#123	C₂²	1	16	yes	complemented
33	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
34	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
36	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
37	C₂×C₁₃×#120	C₂²	1	8	yes	—
38	C₁₃×#518	C₂²	1	32	yes	complemented
39	C₄×C₁₃×#41	C₂²	1	16	yes	complemented
40	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
41	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
42	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
43	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
44	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
45	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
46	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
47	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#117	C₂²	1	2	yes	—
49	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
50	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
51	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
53	C₂⁵×C₁₃	C₂³	1	4	yes	—
54	C₂×C₁₃×#41	—	2	8	no	—
55	C₂×C₁₃×#41	—	4	32	no	—
56	C₂×C₁₃×#41	C₂³	1	8	yes	—
57	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
60	C₂²×D₄×C₁₃	—	2	16	no	—
61	C₂²×D₄×C₁₃	—	4	16	no	—
62	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	32	yes	—
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
73	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
77	C₁₃×#127	C₂³	1	16	yes	—
78	C₁₃×#127	C₂³	1	16	yes	—
79	C₁₃×#127	C₂³	1	32	yes	—
80	C₁₃×#127	C₂³	1	32	yes	complemented
81	C₁₃×#125	C₂³	1	16	yes	complemented
82	C₁₃×#124	C₂³	1	64	yes	complemented
83	C₁₃×#124	C₂³	1	32	yes	complemented
84	C₁₃×#123	C₂³	1	128	yes	complemented
85	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
86	C₁₃×#121	C₂³	1	64	yes	complemented
87	C₁₃×#121	C₂³	1	64	yes	complemented
88	C₁₃×#121	C₂³	1	128	yes	complemented
89	C₁₃×#120	C₂³	1	64	yes	—
90	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
91	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
92	C₄×D₄×C₁₃	C₂³	1	32	yes	—
93	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
94	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
95	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
96	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
97	C₁₃×#117	C₂³	1	8	yes	—
98	C₁₃×#117	C₂³	1	16	yes	—
99	C₁₃×#117	C₂³	1	16	yes	complemented
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	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	64	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
115	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
119	C₂×#3508	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂⁴×C₁₃	—	2	16	no	—
121	C₂⁴×C₁₃	—	4	16	no	—
122	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
123	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
124	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
126	C₁₃×#41	—	2	32	no	—
127	C₁₃×#41	—	4	128	no	—
128	C₂×Q₈×C₁₃	—	2	4	no	—
129	C₂×Q₈×C₁₃	—	2	16	no	—
130	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
131	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
132	C₂×D₄×C₁₃	—	2	8	no	—
133	C₂×D₄×C₁₃	—	2	16	no	—
134	C₂×D₄×C₁₃	—	2	16	no	—
135	C₂×D₄×C₁₃	—	2	4	no	—
136	C₂×D₄×C₁₃	—	2	64	no	—
137	C₂×D₄×C₁₃	—	2	32	no	—
138	C₂×D₄×C₁₃	—	4	64	no	—
139	C₂×D₄×C₁₃	—	4	16	no	—
140	C₂×D₄×C₁₃	—	4	32	no	—
141	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
142	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
143	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
144	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
146	C₂×D₄×C₁₃	C₂⁴	1	64	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
148	C₂²×C₄×C₁₃	—	2	8	no	—
149	C₂²×C₄×C₁₃	—	2	8	no	—
150	C₂²×C₄×C₁₃	—	2	16	no	—
151	C₂²×C₄×C₁₃	—	4	32	no	—
152	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
153	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	64	yes	—
161	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
168	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
169	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
170	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
171	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
172	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
173	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
174	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
175	C₄²×C₁₃	C₂⁴	1	4	yes	—
176	C₄²×C₁₃	C₂⁴	1	4	yes	—
177	C₄²×C₁₃	C₂⁴	1	8	yes	—
178	C₄²×C₁₃	C₂⁴	1	8	yes	—
179	C₄²×C₁₃	C₂⁴	1	16	yes	—
180	C₄²×C₁₃	C₂⁴	1	16	yes	—
181	#3508	C₂×C₁₃	1	32	yes	direct product factor
182	C₂×#559	C₂×C₁₃	1	4	yes	complemented
183	C₂×#550	C₂×C₁₃	1	4	yes	complemented
184	C₂×#546	C₂×C₁₃	1	8	yes	complemented
185	C₂×#540	C₂×C₁₃	1	4	yes	complemented
186	C₂×#535	C₂×C₁₃	1	2	yes	complemented
187	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂×#532	C₂×C₁₃	1	4	yes	complemented
189	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂×#518	C₂×C₁₃	1	2	yes	complemented
191	C₂×C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	16	no	—
195	C₂³×C₁₃	—	2	8	no	—
196	C₂³×C₁₃	—	2	32	no	—
197	C₂³×C₁₃	—	2	32	no	—
198	C₂³×C₁₃	—	4	32	no	—
199	C₂³×C₁₃	—	8	32	no	—
200	C₂³×C₁₃	C₂×#41	1	4	yes	—
201	C₂³×C₁₃	C₂⁵	1	16	yes	—
202	C₂³×C₁₃	C₂⁵	1	4	yes	—
203	C₂³×C₁₃	C₂⁵	1	2	yes	—
204	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
205	Q₈×C₁₃	—	2	8	no	—
206	Q₈×C₁₃	—	2	32	no	—
207	D₄×C₁₃	—	2	16	no	—
208	D₄×C₁₃	—	2	32	no	—
209	D₄×C₁₃	—	2	32	no	—
210	D₄×C₁₃	—	2	8	no	—
211	D₄×C₁₃	—	2	64	no	—
212	D₄×C₁₃	—	4	32	no	—
213	D₄×C₁₃	—	4	64	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	16	no	—
218	C₂×C₄×C₁₃	—	2	16	no	—
219	C₂×C₄×C₁₃	—	2	16	no	—
220	C₂×C₄×C₁₃	—	2	32	no	—
221	C₂×C₄×C₁₃	—	4	64	no	—
222	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
223	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
224	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
225	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	—
226	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
227	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
228	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
229	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
230	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
231	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
233	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
234	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
235	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
236	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
237	#559	C₂²×C₁₃	1	64	yes	complemented
238	#550	C₂²×C₁₃	1	64	yes	complemented
239	#546	C₂²×C₁₃	1	128	yes	complemented
240	#540	C₂²×C₁₃	1	64	yes	complemented
241	#535	C₂²×C₁₃	1	32	yes	complemented
242	#533	C₂²×C₁₃	1	16	yes	complemented
243	#532	C₂²×C₁₃	1	64	yes	complemented
244	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
245	C₂×#127	C₂²×C₁₃	1	2	yes	—
246	C₂×#127	C₂²×C₁₃	1	2	yes	—
247	C₂×#127	C₂²×C₁₃	1	4	yes	—
248	C₂×#127	C₂²×C₁₃	1	16	yes	complemented
249	C₂×#127	C₂²×C₁₃	1	4	yes	complemented
250	C₂×#125	C₂²×C₁₃	1	2	yes	complemented
251	C₂×#124	C₂²×C₁₃	1	8	yes	complemented
252	C₂×#124	C₂²×C₁₃	1	4	yes	complemented
253	C₂×#123	C₂²×C₁₃	1	16	yes	complemented
254	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
255	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
256	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
257	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
258	C₂×#120	C₂²×C₁₃	1	8	yes	—
259	#518	C₂²×C₁₃	1	32	yes	complemented
260	C₄×#41	C₂²×C₁₃	1	16	yes	complemented
261	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
262	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
263	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
264	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
265	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
266	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
267	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
268	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#117	C₂²×C₁₃	1	2	yes	—
270	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
271	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
272	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
273	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	8	no	—
276	C₂²×C₁₃	—	2	4	no	—
277	C₂²×C₁₃	—	2	16	no	—
278	C₂²×C₁₃	—	2	8	no	—
279	C₂²×C₁₃	—	2	32	no	—
280	C₂²×C₁₃	—	4	8	no	—
281	C₂²×C₁₃	—	4	32	no	—
282	C₂²×C₁₃	—	8	32	no	—
283	C₂²×C₁₃	C₂²×#41	1	4	yes	—
284	C₂²×C₁₃	C₂²×#41	1	2	yes	—
285	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
286	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
287	C₄×C₁₃	—	2	4	no	—
288	C₄×C₁₃	—	2	8	no	—
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	2	16	no	—
291	C₄×C₁₃	C₂²×#41	1	4	yes	—
292	C₄×C₁₃	C₂²×#41	1	4	yes	—
293	C₄×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
294	C₂⁵	C₂³×C₁₃	1	4	yes	—
295	C₂×#41	—	2	8	no	—
296	C₂×#41	—	4	32	no	—
297	C₂×#41	C₂³×C₁₃	1	8	yes	—
298	C₂×#41	C₂³×C₁₃	1	64	yes	complemented
299	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
301	C₂²×D₄	—	2	16	no	—
302	C₂²×D₄	—	4	16	no	—
303	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
305	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
306	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
308	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
309	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
310	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
311	C₂²×D₄	C₂³×C₁₃	1	32	yes	—
312	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
313	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
314	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
317	C₄⋊Q₈	C₂³×C₁₃	1	16	yes	complemented
318	#127	C₂³×C₁₃	1	16	yes	—
319	#127	C₂³×C₁₃	1	16	yes	—
320	#127	C₂³×C₁₃	1	32	yes	—
321	#127	C₂³×C₁₃	1	32	yes	complemented
322	#125	C₂³×C₁₃	1	16	yes	complemented
323	#124	C₂³×C₁₃	1	64	yes	complemented
324	#124	C₂³×C₁₃	1	32	yes	complemented
325	#123	C₂³×C₁₃	1	128	yes	complemented
326	C₂²⋊Q₈	C₂³×C₁₃	1	32	yes	—
327	#121	C₂³×C₁₃	1	64	yes	complemented
328	#121	C₂³×C₁₃	1	64	yes	complemented
329	#121	C₂³×C₁₃	1	128	yes	complemented
330	#120	C₂³×C₁₃	1	64	yes	—
331	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
332	C₄×Q₈	C₂³×C₁₃	1	32	yes	complemented
333	C₄×D₄	C₂³×C₁₃	1	32	yes	—
334	C₄×D₄	C₂³×C₁₃	1	16	yes	complemented
335	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
336	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
337	C₄×D₄	C₂³×C₁₃	1	64	yes	complemented
338	#117	C₂³×C₁₃	1	8	yes	—
339	#117	C₂³×C₁₃	1	16	yes	—
340	#117	C₂³×C₁₃	1	16	yes	complemented
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	64	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
352	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
353	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
357	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
358	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₁₃	1	16	yes	complemented
360	C₂×C₁₃	—	2	4	no	—
361	C₂×C₁₃	—	4	4	no	—
362	C₂×C₁₃	—	4	16	no	—
363	C₂×C₁₃	#3508	1	4	yes	direct product factor
364	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
365	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
366	C₂⁴	—	2	16	no	—
367	C₂⁴	—	4	16	no	—
368	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
369	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
370	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
371	C₂⁴	C₂⁴×C₁₃	1	16	yes	—
372	#41	—	2	32	no	—
373	#41	—	4	128	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	16	no	—
376	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
377	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	16	no	—
380	C₂×D₄	—	2	16	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	64	no	—
383	C₂×D₄	—	2	32	no	—
384	C₂×D₄	—	4	64	no	—
385	C₂×D₄	—	4	16	no	—
386	C₂×D₄	—	4	32	no	—
387	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
388	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
389	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
390	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
391	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
392	C₂×D₄	C₂⁴×C₁₃	1	64	yes	—
393	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	4	32	no	—
398	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
399	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	64	yes	—
407	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
411	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
412	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
413	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
414	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
415	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
416	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
417	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
418	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
419	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
420	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
421	C₄²	C₂⁴×C₁₃	1	4	yes	—
422	C₄²	C₂⁴×C₁₃	1	4	yes	—
423	C₄²	C₂⁴×C₁₃	1	8	yes	—
424	C₄²	C₂⁴×C₁₃	1	8	yes	—
425	C₄²	C₂⁴×C₁₃	1	16	yes	—
426	C₄²	C₂⁴×C₁₃	1	16	yes	—
427	C₁₃	C₂×#3508	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	4	no	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	16	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	32	no	—
433	C₂³	—	2	32	no	—
434	C₂³	—	4	32	no	—
435	C₂³	—	8	32	no	—
436	C₂³	C₂×C₁₃×#41	1	4	yes	—
437	C₂³	C₂⁵×C₁₃	1	16	yes	—
438	C₂³	C₂⁵×C₁₃	1	4	yes	—
439	C₂³	C₂⁵×C₁₃	1	2	yes	—
440	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
441	Q₈	—	2	8	no	—
442	Q₈	—	2	32	no	—
443	D₄	—	2	16	no	—
444	D₄	—	2	32	no	—
445	D₄	—	2	32	no	—
446	D₄	—	2	8	no	—
447	D₄	—	2	64	no	—
448	D₄	—	4	32	no	—
449	D₄	—	4	64	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	16	no	—
454	C₂×C₄	—	2	16	no	—
455	C₂×C₄	—	2	16	no	—
456	C₂×C₄	—	2	32	no	—
457	C₂×C₄	—	4	64	no	—
458	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
459	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
460	C₂×C₄	C₂×C₁₃×#41	1	16	yes	complemented
461	C₂×C₄	C₁₃×H(5,𝔽₂)	1	8	yes	—
462	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
463	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
464	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
465	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
466	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
467	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	8	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	16	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	32	no	—
475	C₂²	—	4	8	no	—
476	C₂²	—	4	32	no	—
477	C₂²	—	8	32	no	—
478	C₂²	C₂²×C₁₃×#41	1	4	yes	—
479	C₂²	C₂²×C₁₃×#41	1	2	yes	—
480	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
481	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	2	8	no	—
484	C₄	—	2	4	no	—
485	C₄	—	2	16	no	—
486	C₄	C₂²×C₁₃×#41	1	4	yes	—
487	C₄	C₂²×C₁₃×#41	1	4	yes	—
488	C₄	C₂×C₁₃×H(5,𝔽₂)	1	8	yes	—
489	C₂	—	2	4	no	—
490	C₂	—	4	16	no	—
491	C₂	—	4	4	no	—
492	C₂	C₁₃×#3508	1	4	yes	direct product factor
493	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
494	C₂	C₂²×C₁₃×H(5,𝔽₂)	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×#3508	C₂	direct (N × H)
2. C₂×C₁₃×#559	C₂	semidirect
3. C₂×C₁₃×#550	C₂	semidirect
4. C₂×C₁₃×#546	C₂	semidirect
5. C₂×C₁₃×#540	C₂	semidirect
6. C₂×C₁₃×#535	C₂	semidirect
7. C₂×C₁₃×#533	C₂	semidirect
8. C₂×C₁₃×#532	C₂	semidirect
9. C₂²×C₁₃×#127	C₂	semidirect
10. C₂×C₁₃×#518	C₂	semidirect
11. C₂×C₄×C₁₃×#41	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
16. C₁₃×#559	C₂²	semidirect
17. C₁₃×#550	C₂²	semidirect
18. C₁₃×#546	C₂²	semidirect
19. C₁₃×#540	C₂²	semidirect
20. C₁₃×#535	C₂²	semidirect
21. C₁₃×#533	C₂²	semidirect
22. C₁₃×#532	C₂²	semidirect
23. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₁₃×#127	C₂²	semidirect
28. C₂×C₁₃×#127	C₂²	semidirect
29. C₂×C₁₃×#125	C₂²	semidirect
30. C₂×C₁₃×#124	C₂²	semidirect
31. C₂×C₁₃×#124	C₂²	semidirect
32. C₂×C₁₃×#123	C₂²	semidirect
34. C₂×C₁₃×#121	C₂²	semidirect
35. C₂×C₁₃×#121	C₂²	semidirect
36. C₂×C₁₃×#121	C₂²	semidirect
38. C₁₃×#518	C₂²	semidirect
39. C₄×C₁₃×#41	C₂²	semidirect
40. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
41. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
43. C₂×C₄×D₄×C₁₃	C₂²	semidirect
44. C₂×C₄×D₄×C₁₃	C₂²	semidirect
45. C₂×C₄×D₄×C₁₃	C₂²	semidirect
46. C₂×C₄×D₄×C₁₃	C₂²	semidirect
49. C₂×C₁₃×#117	C₂²	semidirect
52. C₂²×C₄²×C₁₃	C₂²	semidirect
57. C₂×C₁₃×#41	C₂³	semidirect
76. C₁₃×C₄⋊Q₈	C₂³	semidirect
80. C₁₃×#127	C₂³	semidirect
81. C₁₃×#125	C₂³	semidirect
82. C₁₃×#124	C₂³	semidirect
83. C₁₃×#124	C₂³	semidirect
84. C₁₃×#123	C₂³	semidirect
86. C₁₃×#121	C₂³	semidirect
87. C₁₃×#121	C₂³	semidirect
88. C₁₃×#121	C₂³	semidirect
90. C₄×Q₈×C₁₃	C₂³	semidirect
91. C₄×Q₈×C₁₃	C₂³	semidirect
93. C₄×D₄×C₁₃	C₂³	semidirect
94. C₄×D₄×C₁₃	C₂³	semidirect
95. C₄×D₄×C₁₃	C₂³	semidirect
96. C₄×D₄×C₁₃	C₂³	semidirect
99. C₁₃×#117	C₂³	semidirect
118. C₂×C₄²×C₁₃	C₂³	semidirect
119. C₂×#3508	C₁₃	direct (N × H)
152. C₂²×C₄×C₁₃	#41	semidirect
181. #3508	C₂×C₁₃	direct (N × H)
182. C₂×#559	C₂×C₁₃	semidirect
183. C₂×#550	C₂×C₁₃	semidirect
184. C₂×#546	C₂×C₁₃	semidirect
185. C₂×#540	C₂×C₁₃	semidirect
186. C₂×#535	C₂×C₁₃	semidirect
187. C₂×#533	C₂×C₁₃	semidirect
188. C₂×#532	C₂×C₁₃	semidirect
189. C₂²×#127	C₂×C₁₃	semidirect
190. C₂×#518	C₂×C₁₃	semidirect
191. C₂×C₄×#41	C₂×C₁₃	semidirect
224. C₂×C₄×C₁₃	C₂×#41	semidirect
234. C₂²×#41	C₂²×C₁₃	semidirect
237. #559	C₂²×C₁₃	semidirect
238. #550	C₂²×C₁₃	semidirect
239. #546	C₂²×C₁₃	semidirect
240. #540	C₂²×C₁₃	semidirect
241. #535	C₂²×C₁₃	semidirect
242. #533	C₂²×C₁₃	semidirect
243. #532	C₂²×C₁₃	semidirect
244. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
248. C₂×#127	C₂²×C₁₃	semidirect
249. C₂×#127	C₂²×C₁₃	semidirect
250. C₂×#125	C₂²×C₁₃	semidirect
251. C₂×#124	C₂²×C₁₃	semidirect
252. C₂×#124	C₂²×C₁₃	semidirect
253. C₂×#123	C₂²×C₁₃	semidirect
255. C₂×#121	C₂²×C₁₃	semidirect
256. C₂×#121	C₂²×C₁₃	semidirect
257. C₂×#121	C₂²×C₁₃	semidirect
259. #518	C₂²×C₁₃	semidirect
260. C₄×#41	C₂²×C₁₃	semidirect
261. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
262. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
264. C₂×C₄×D₄	C₂²×C₁₃	semidirect
265. C₂×C₄×D₄	C₂²×C₁₃	semidirect
266. C₂×C₄×D₄	C₂²×C₁₃	semidirect
267. C₂×C₄×D₄	C₂²×C₁₃	semidirect
270. C₂×#117	C₂²×C₁₃	semidirect
273. C₂²×C₄²	C₂²×C₁₃	semidirect
298. C₂×#41	C₂³×C₁₃	semidirect
317. C₄⋊Q₈	C₂³×C₁₃	semidirect
321. #127	C₂³×C₁₃	semidirect
322. #125	C₂³×C₁₃	semidirect
323. #124	C₂³×C₁₃	semidirect
324. #124	C₂³×C₁₃	semidirect
325. #123	C₂³×C₁₃	semidirect
327. #121	C₂³×C₁₃	semidirect
328. #121	C₂³×C₁₃	semidirect
329. #121	C₂³×C₁₃	semidirect
331. C₄×Q₈	C₂³×C₁₃	semidirect
332. C₄×Q₈	C₂³×C₁₃	semidirect
334. C₄×D₄	C₂³×C₁₃	semidirect
335. C₄×D₄	C₂³×C₁₃	semidirect
336. C₄×D₄	C₂³×C₁₃	semidirect
337. C₄×D₄	C₂³×C₁₃	semidirect
340. #117	C₂³×C₁₃	semidirect
359. C₂×C₄²	C₂³×C₁₃	semidirect
363. C₂×C₁₃	#3508	direct (N × H)
398. C₂²×C₄	C₁₃×#41	semidirect
427. C₁₃	C₂×#3508	direct (N × H)
460. C₂×C₄	C₂×C₁₃×#41	semidirect
492. C₂	C₁₃×#3508	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×#3508	2
C₂×C₁₃×#559	2
C₂×C₁₃×#550	2
C₂×C₁₃×#546	2
C₂×C₁₃×#540	2
C₂×C₁₃×#535	2
C₂×C₁₃×#533	2
C₂×C₁₃×#532	2
C₂²×C₁₃×#127	2
C₂×C₁₃×#518	2
C₂×C₄×C₁₃×#41	2
C₂×#3508	13

Subgroups — C2×C13×#3508 #15749137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3508 #15749137