Subgroups — C₂×C₁₃×#2617 #15720893

Order 3328.

5222 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#120	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2617	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#394	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#392	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#121	—	2	8	no	—
17	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
18	C₂×C₁₃×#120	—	2	16	no	—
19	C₂×C₁₃×#120	C₂²	1	16	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
30	C₁₃×#397	C₂²	1	16	yes	complemented
31	C₁₃×#394	C₂²	1	32	yes	complemented
32	C₁₃×#392	C₂²	1	16	yes	complemented
33	C₁₃×#386	C₂²	1	16	yes	complemented
34	C₁₃×#380	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#95	C₂²	1	4	yes	complemented
37	C₂⁵×C₁₃	—	2	4	no	—
38	C₂⁵×C₁₃	—	2	4	no	—
39	C₂⁵×C₁₃	—	4	4	no	—
40	C₂⁵×C₁₃	—	4	4	no	—
41	C₂⁵×C₁₃	D₄	1	8	yes	complemented
42	C₂⁵×C₁₃	C₂³	1	2	yes	—
43	C₂⁵×C₁₃	C₂³	1	2	yes	—
44	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
45	C₂⁵×C₁₃	C₂³	1	4	yes	—
46	C₂²×D₄×C₁₃	—	2	16	no	—
47	C₂²×D₄×C₁₃	—	2	8	no	—
48	C₂²×D₄×C₁₃	—	2	8	no	—
49	C₂²×D₄×C₁₃	—	2	8	no	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	4	8	no	—
52	C₂²×D₄×C₁₃	—	4	8	no	—
53	C₂²×D₄×C₁₃	—	4	4	no	—
54	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
55	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
56	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
57	C₂³×C₄×C₁₃	—	2	4	no	—
58	C₂³×C₄×C₁₃	—	4	4	no	—
59	C₂³×C₄×C₁₃	—	4	4	no	—
60	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
68	C₁₃×#121	—	2	32	no	—
69	C₁₃×#120	—	2	64	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
74	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
87	C₁₃×#95	C₂³	1	8	yes	complemented
88	C₁₃×#95	C₂³	1	16	yes	complemented
89	C₂×#2617	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	32	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	8	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	—	2	8	no	—
97	C₂⁴×C₁₃	—	2	8	no	—
98	C₂⁴×C₁₃	—	2	8	no	—
99	C₂⁴×C₁₃	—	2	4	no	—
100	C₂⁴×C₁₃	—	2	4	no	—
101	C₂⁴×C₁₃	—	2	4	no	—
102	C₂⁴×C₁₃	—	2	8	no	—
103	C₂⁴×C₁₃	—	2	8	no	—
104	C₂⁴×C₁₃	—	4	32	no	—
105	C₂⁴×C₁₃	—	4	8	no	—
106	C₂⁴×C₁₃	—	4	8	no	—
107	C₂⁴×C₁₃	—	4	16	no	—
108	C₂⁴×C₁₃	—	4	16	no	—
109	C₂⁴×C₁₃	—	4	32	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
111	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
112	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
113	C₂⁴×C₁₃	C₂×D₄	1	16	yes	complemented
114	C₂⁴×C₁₃	#41	1	4	yes	—
115	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
117	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂×D₄×C₁₃	—	2	32	no	—
120	C₂×D₄×C₁₃	—	2	16	no	—
121	C₂×D₄×C₁₃	—	2	16	no	—
122	C₂×D₄×C₁₃	—	2	16	no	—
123	C₂×D₄×C₁₃	—	2	8	no	—
124	C₂×D₄×C₁₃	—	4	16	no	—
125	C₂×D₄×C₁₃	—	4	16	no	—
126	C₂×D₄×C₁₃	—	4	8	no	—
127	C₂×D₄×C₁₃	—	4	16	no	—
128	C₂×D₄×C₁₃	—	4	64	no	—
129	C₂×D₄×C₁₃	—	4	32	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	8	no	—
140	C₂²×C₄×C₁₃	—	2	8	no	—
141	C₂²×C₄×C₁₃	—	4	16	no	—
142	C₂²×C₄×C₁₃	—	4	8	no	—
143	C₂²×C₄×C₁₃	—	4	8	no	—
144	C₂²×C₄×C₁₃	—	4	16	no	—
145	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₁₃×C₄⋊C₄	—	2	8	no	—
154	C₁₃×C₄⋊C₄	—	4	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	32	no	—
156	C₁₃×C₂²⋊C₄	—	2	16	no	—
157	C₁₃×C₂²⋊C₄	—	2	16	no	—
158	C₁₃×C₂²⋊C₄	—	2	16	no	—
159	C₁₃×C₂²⋊C₄	—	2	16	no	—
160	C₁₃×C₂²⋊C₄	—	4	16	no	—
161	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂²×#120	C₂×C₁₃	1	2	yes	complemented
163	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#2617	C₂×C₁₃	1	16	yes	direct product factor
165	C₂×#397	C₂×C₁₃	1	2	yes	complemented
166	C₂×#394	C₂×C₁₃	1	4	yes	complemented
167	C₂×#392	C₂×C₁₃	1	2	yes	complemented
168	C₂×#386	C₂×C₁₃	1	2	yes	complemented
169	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	8	no	—
171	C₂³×C₁₃	—	2	16	no	—
172	C₂³×C₁₃	—	2	8	no	—
173	C₂³×C₁₃	—	2	16	no	—
174	C₂³×C₁₃	—	2	4	no	—
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	2	16	no	—
177	C₂³×C₁₃	—	2	32	no	—
178	C₂³×C₁₃	—	2	32	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	2	4	no	—
181	C₂³×C₁₃	—	2	8	no	—
182	C₂³×C₁₃	—	2	8	no	—
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	2	8	no	—
187	C₂³×C₁₃	—	2	8	no	—
188	C₂³×C₁₃	—	4	32	no	—
189	C₂³×C₁₃	—	4	128	no	—
190	C₂³×C₁₃	—	4	16	no	—
191	C₂³×C₁₃	—	4	16	no	—
192	C₂³×C₁₃	—	4	32	no	—
193	C₂³×C₁₃	—	4	8	no	—
194	C₂³×C₁₃	—	4	8	no	—
195	C₂³×C₁₃	—	4	16	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	8	no	—
198	C₂³×C₁₃	—	4	16	no	—
199	C₂³×C₁₃	—	4	8	no	—
200	C₂³×C₁₃	—	4	16	no	—
201	C₂³×C₁₃	#121	1	16	yes	—
202	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
203	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
204	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
205	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
207	C₂³×C₁₃	C₂×#41	1	4	yes	—
208	C₂³×C₁₃	C₂×#41	1	2	yes	—
209	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
210	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
211	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
212	D₄×C₁₃	—	4	16	no	—
213	D₄×C₁₃	—	4	64	no	—
214	D₄×C₁₃	—	4	32	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	8	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	8	no	—
225	C₂×C₄×C₁₃	—	2	8	no	—
226	C₂×C₄×C₁₃	—	2	8	no	—
227	C₂×C₄×C₁₃	—	4	16	no	—
228	C₂×C₄×C₁₃	—	4	16	no	—
229	C₂×C₄×C₁₃	—	4	8	no	—
230	C₂×C₄×C₁₃	—	4	16	no	—
231	C₂×C₄×C₁₃	—	4	8	no	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
234	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
235	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
236	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
237	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
238	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#121	—	2	8	no	—
241	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
242	C₂×#120	—	2	16	no	—
243	C₂×#120	C₂²×C₁₃	1	16	yes	complemented
244	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
245	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
246	C₂²×C₂²⋊C₄	—	2	8	no	—
247	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
249	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
252	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
253	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
254	#397	C₂²×C₁₃	1	16	yes	complemented
255	#394	C₂²×C₁₃	1	32	yes	complemented
256	#392	C₂²×C₁₃	1	16	yes	complemented
257	#386	C₂²×C₁₃	1	16	yes	complemented
258	#380	C₂²×C₁₃	1	8	yes	complemented
259	C₂×#95	C₂²×C₁₃	1	2	yes	complemented
260	C₂×#95	C₂²×C₁₃	1	4	yes	complemented
261	C₂²×C₁₃	—	2	32	no	—
262	C₂²×C₁₃	—	2	4	no	—
263	C₂²×C₁₃	—	2	8	no	—
264	C₂²×C₁₃	—	2	4	no	—
265	C₂²×C₁₃	—	2	8	no	—
266	C₂²×C₁₃	—	2	8	no	—
267	C₂²×C₁₃	—	2	16	no	—
268	C₂²×C₁₃	—	4	64	no	—
269	C₂²×C₁₃	—	4	32	no	—
270	C₂²×C₁₃	—	4	4	no	—
271	C₂²×C₁₃	—	4	4	no	—
272	C₂²×C₁₃	—	4	8	no	—
273	C₂²×C₁₃	—	4	4	no	—
274	C₂²×C₁₃	—	4	4	no	—
275	C₂²×C₁₃	—	4	8	no	—
276	C₂²×C₁₃	—	4	4	no	—
277	C₂²×C₁₃	—	4	8	no	—
278	C₂²×C₁₃	—	8	16	no	—
279	C₂²×C₁₃	C₂×#121	1	8	yes	—
280	C₂²×C₁₃	C₂×#121	1	4	yes	—
281	C₂²×C₁₃	#534	1	4	yes	—
282	C₂²×C₁₃	#534	1	8	yes	—
283	C₂²×C₁₃	#535	1	4	yes	—
284	C₂²×C₁₃	#538	1	8	yes	—
285	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
286	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
287	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
288	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
289	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	2	4	no	—
292	C₄×C₁₃	—	4	4	no	—
293	C₄×C₁₃	—	4	8	no	—
294	C₄×C₁₃	—	4	4	no	—
295	C₂⁵	—	2	4	no	—
296	C₂⁵	—	2	4	no	—
297	C₂⁵	—	4	4	no	—
298	C₂⁵	—	4	4	no	—
299	C₂⁵	D₄×C₁₃	1	8	yes	complemented
300	C₂⁵	C₂³×C₁₃	1	2	yes	—
301	C₂⁵	C₂³×C₁₃	1	2	yes	—
302	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
303	C₂⁵	C₂³×C₁₃	1	4	yes	—
304	C₂²×D₄	—	2	16	no	—
305	C₂²×D₄	—	2	8	no	—
306	C₂²×D₄	—	2	8	no	—
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	—	2	4	no	—
309	C₂²×D₄	—	4	8	no	—
310	C₂²×D₄	—	4	8	no	—
311	C₂²×D₄	—	4	4	no	—
312	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
313	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
314	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	4	4	no	—
317	C₂³×C₄	—	4	4	no	—
318	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
319	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
322	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
325	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
326	#121	—	2	32	no	—
327	#120	—	2	64	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	4	4	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
332	C₂×C₂²⋊C₄	—	2	16	no	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	2	8	no	—
336	C₂×C₂²⋊C₄	—	2	8	no	—
337	C₂×C₂²⋊C₄	—	2	32	no	—
338	C₂×C₂²⋊C₄	—	4	8	no	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
345	#95	C₂³×C₁₃	1	8	yes	complemented
346	#95	C₂³×C₁₃	1	16	yes	complemented
347	C₂×C₁₃	—	2	8	no	—
348	C₂×C₁₃	—	4	8	no	—
349	C₂×C₁₃	—	8	4	no	—
350	C₂×C₁₃	#2617	1	8	yes	direct product factor
351	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
352	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#534	1	2	yes	—
354	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
355	C₂×C₁₃	C₂×#538	1	2	yes	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	4	no	—
358	C₂⁴	—	2	32	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	2	8	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	8	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	8	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	4	32	no	—
371	C₂⁴	—	4	8	no	—
372	C₂⁴	—	4	8	no	—
373	C₂⁴	—	4	16	no	—
374	C₂⁴	—	4	16	no	—
375	C₂⁴	—	4	32	no	—
376	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
377	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
378	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
379	C₂⁴	C₂×D₄×C₁₃	1	16	yes	complemented
380	C₂⁴	C₁₃×#41	1	4	yes	—
381	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
382	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
383	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
384	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂×D₄	—	2	32	no	—
386	C₂×D₄	—	2	16	no	—
387	C₂×D₄	—	2	16	no	—
388	C₂×D₄	—	2	16	no	—
389	C₂×D₄	—	2	8	no	—
390	C₂×D₄	—	4	16	no	—
391	C₂×D₄	—	4	16	no	—
392	C₂×D₄	—	4	8	no	—
393	C₂×D₄	—	4	16	no	—
394	C₂×D₄	—	4	64	no	—
395	C₂×D₄	—	4	32	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	8	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	4	16	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	16	no	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
414	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
415	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	4	8	no	—
421	C₂²⋊C₄	—	2	32	no	—
422	C₂²⋊C₄	—	2	16	no	—
423	C₂²⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	2	16	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	4	16	no	—
427	C₁₃	C₂×#2617	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	—	2	8	no	—
429	C₂³	—	2	16	no	—
430	C₂³	—	2	8	no	—
431	C₂³	—	2	16	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	16	no	—
435	C₂³	—	2	32	no	—
436	C₂³	—	2	32	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	4	32	no	—
447	C₂³	—	4	128	no	—
448	C₂³	—	4	16	no	—
449	C₂³	—	4	16	no	—
450	C₂³	—	4	32	no	—
451	C₂³	—	4	8	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	16	no	—
454	C₂³	—	4	8	no	—
455	C₂³	—	4	8	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	4	8	no	—
458	C₂³	—	4	16	no	—
459	C₂³	C₁₃×#121	1	16	yes	—
460	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
461	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
462	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
463	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
464	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
465	C₂³	C₂×C₁₃×#41	1	4	yes	—
466	C₂³	C₂×C₁₃×#41	1	2	yes	—
467	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
468	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
469	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
470	D₄	—	4	16	no	—
471	D₄	—	4	64	no	—
472	D₄	—	4	32	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	8	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	16	no	—
489	C₂×C₄	—	4	8	no	—
490	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
491	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
492	C₂²	—	2	32	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	8	no	—
497	C₂²	—	2	8	no	—
498	C₂²	—	2	16	no	—
499	C₂²	—	4	64	no	—
500	C₂²	—	4	32	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	8	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	8	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	8	no	—
509	C₂²	—	8	16	no	—
510	C₂²	C₂×C₁₃×#121	1	8	yes	—
511	C₂²	C₂×C₁₃×#121	1	4	yes	—
512	C₂²	C₁₃×#534	1	4	yes	—
513	C₂²	C₁₃×#534	1	8	yes	—
514	C₂²	C₁₃×#535	1	4	yes	—
515	C₂²	C₁₃×#538	1	8	yes	—
516	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
517	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
518	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
519	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
520	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
521	C₄	—	2	4	no	—
522	C₄	—	2	4	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	8	no	—
525	C₄	—	4	4	no	—
526	C₂	—	2	8	no	—
527	C₂	—	4	8	no	—
528	C₂	—	8	4	no	—
529	C₂	C₁₃×#2617	1	8	yes	direct product factor
530	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
531	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#534	1	2	yes	—
533	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
534	C₂	C₂×C₁₃×#538	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#121	C₂	semidirect
2. C₂²×C₁₃×#120	C₂	semidirect
3. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
4. C₁₃×#2617	C₂	direct (N × H)
5. C₂×C₁₃×#397	C₂	semidirect
6. C₂×C₁₃×#394	C₂	semidirect
7. C₂×C₁₃×#392	C₂	semidirect
8. C₂×C₁₃×#386	C₂	semidirect
9. C₂×C₁₃×#380	C₂	semidirect
13. C₂³×D₄×C₁₃	C₂²	semidirect
17. C₂×C₁₃×#121	C₂²	semidirect
19. C₂×C₁₃×#120	C₂²	semidirect
20. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
21. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
27. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
29. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
30. C₁₃×#397	C₂²	semidirect
31. C₁₃×#394	C₂²	semidirect
32. C₁₃×#392	C₂²	semidirect
33. C₁₃×#386	C₂²	semidirect
34. C₁₃×#380	C₂²	semidirect
35. C₂×C₁₃×#95	C₂²	semidirect
36. C₂×C₁₃×#95	C₂²	semidirect
41. C₂⁵×C₁₃	D₄	semidirect
56. C₂²×D₄×C₁₃	C₂³	semidirect
60. C₂³×C₄×C₁₃	D₄	semidirect
72. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
73. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
85. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
86. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
87. C₁₃×#95	C₂³	semidirect
88. C₁₃×#95	C₂³	semidirect
89. C₂×#2617	C₁₃	direct (N × H)
113. C₂⁴×C₁₃	C₂×D₄	semidirect
147. C₂²×C₄×C₁₃	C₂×D₄	semidirect
161. C₂²×#121	C₂×C₁₃	semidirect
162. C₂²×#120	C₂×C₁₃	semidirect
163. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
164. #2617	C₂×C₁₃	direct (N × H)
165. C₂×#397	C₂×C₁₃	semidirect
166. C₂×#394	C₂×C₁₃	semidirect
167. C₂×#392	C₂×C₁₃	semidirect
168. C₂×#386	C₂×C₁₃	semidirect
169. C₂×#380	C₂×C₁₃	semidirect
237. C₂³×D₄	C₂²×C₁₃	semidirect
241. C₂×#121	C₂²×C₁₃	semidirect
243. C₂×#120	C₂²×C₁₃	semidirect
244. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
245. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
251. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
252. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
253. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
254. #397	C₂²×C₁₃	semidirect
255. #394	C₂²×C₁₃	semidirect
256. #392	C₂²×C₁₃	semidirect
257. #386	C₂²×C₁₃	semidirect
258. #380	C₂²×C₁₃	semidirect
259. C₂×#95	C₂²×C₁₃	semidirect
260. C₂×#95	C₂²×C₁₃	semidirect
299. C₂⁵	D₄×C₁₃	semidirect
314. C₂²×D₄	C₂³×C₁₃	semidirect
318. C₂³×C₄	D₄×C₁₃	semidirect
330. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
331. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
343. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
344. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
345. #95	C₂³×C₁₃	semidirect
346. #95	C₂³×C₁₃	semidirect
350. C₂×C₁₃	#2617	direct (N × H)
379. C₂⁴	C₂×D₄×C₁₃	semidirect
413. C₂²×C₄	C₂×D₄×C₁₃	semidirect
427. C₁₃	C₂×#2617	direct (N × H)
529. C₂	C₁₃×#2617	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×#121	2
C₂²×C₁₃×#120	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2617	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#392	2
C₂×C₁₃×#386	2
C₂×C₁₃×#380	2
C₂×#2617	13

Subgroups — C2×C13×#2617 #15720893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2617 #15720893