Subgroups — C₂×C₁₃×#2593 #15721190

Order 3328.

2334 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2593	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₁₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#394	C₂	1	2	yes	maximal
5	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#400	C₂²	1	8	yes	complemented
27	C₁₃×#398	C₂²	1	8	yes	complemented
28	C₁₃×#394	C₂²	1	16	yes	—
29	C₁₃×#390	C₂²	1	8	yes	—
30	C₁₃×#388	C₂²	1	16	yes	complemented
31	C₁₃×#388	C₂²	1	16	yes	complemented
32	C₁₃×#388	C₂²	1	16	yes	complemented
33	C₁₃×#388	C₂²	1	16	yes	complemented
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	16	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	2	yes	—
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#95	C₂²	1	2	yes	—
40	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₃	—	4	2	no	—
44	C₂²×D₄×C₁₃	—	4	2	no	—
45	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
56	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₄²×C₁₃	—	2	8	no	—
77	C₂×C₄²×C₁₃	—	4	2	no	—
78	C₂×C₄²×C₁₃	—	4	4	no	—
79	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
82	C₁₃×#95	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	8	yes	—
84	C₁₃×#95	C₂³	1	8	yes	—
85	C₁₃×#95	C₂³	1	4	yes	—
86	C₁₃×#95	C₂³	1	8	yes	—
87	C₁₃×#95	C₂³	1	4	yes	—
88	C₂×#2593	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	4	no	—
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂×D₄×C₁₃	—	2	8	no	—
99	C₂×D₄×C₁₃	—	4	4	no	—
100	C₂×D₄×C₁₃	—	4	4	no	—
101	C₂×D₄×C₁₃	—	4	16	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	#41	1	8	yes	—
122	C₂²×C₄×C₁₃	#41	1	8	yes	—
123	C₂²×C₄×C₁₃	#41	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
132	C₁₃×C₄⋊C₄	—	2	16	no	—
133	C₁₃×C₄⋊C₄	—	2	16	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	—	4	4	no	—
136	C₁₃×C₄⋊C₄	—	4	4	no	—
137	C₁₃×C₂²⋊C₄	—	2	16	no	—
138	C₁₃×C₂²⋊C₄	—	2	16	no	—
139	C₁₃×C₂²⋊C₄	—	2	16	no	—
140	C₁₃×C₂²⋊C₄	—	2	16	no	—
141	C₁₃×C₂²⋊C₄	—	4	8	no	—
142	C₁₃×C₂²⋊C₄	—	4	8	no	—
143	C₄²×C₁₃	—	2	16	no	—
144	C₄²×C₁₃	—	4	4	no	—
145	C₄²×C₁₃	—	4	8	no	—
146	#2593	C₂×C₁₃	1	16	yes	direct product factor
147	C₂×#400	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂×#394	C₂×C₁₃	1	2	yes	—
150	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
151	C₂×#388	C₂×C₁₃	1	2	yes	complemented
152	C₂×#388	C₂×C₁₃	1	2	yes	complemented
153	C₂×#388	C₂×C₁₃	1	2	yes	complemented
154	C₂×#388	C₂×C₁₃	1	2	yes	complemented
155	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
156	C₂³×C₁₃	—	2	4	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	2	4	no	—
160	C₂³×C₁₃	—	2	4	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	4	8	no	—
164	C₂³×C₁₃	—	4	8	no	—
165	C₂³×C₁₃	—	4	8	no	—
166	C₂³×C₁₃	—	4	8	no	—
167	C₂³×C₁₃	—	4	8	no	—
168	C₂³×C₁₃	—	4	8	no	—
169	C₂³×C₁₃	—	4	8	no	—
170	C₂³×C₁₃	C₂×#41	1	2	yes	—
171	C₂³×C₁₃	C₂×#41	1	4	yes	—
172	C₂³×C₁₃	C₂×#41	1	4	yes	—
173	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
175	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
176	D₄×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	—	2	16	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	16	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	4	8	no	—
200	C₂×C₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	4	4	no	—
203	C₂×C₄×C₁₃	—	4	4	no	—
204	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
205	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
207	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
216	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
222	#400	C₂²×C₁₃	1	8	yes	complemented
223	#398	C₂²×C₁₃	1	8	yes	complemented
224	#394	C₂²×C₁₃	1	16	yes	—
225	#390	C₂²×C₁₃	1	8	yes	—
226	#388	C₂²×C₁₃	1	16	yes	complemented
227	#388	C₂²×C₁₃	1	16	yes	complemented
228	#388	C₂²×C₁₃	1	16	yes	complemented
229	#388	C₂²×C₁₃	1	16	yes	complemented
230	C₄×C₄⋊C₄	C₂²×C₁₃	1	16	yes	complemented
231	C₂×#95	C₂²×C₁₃	1	2	yes	—
232	C₂×#95	C₂²×C₁₃	1	2	yes	—
233	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#95	C₂²×C₁₃	1	2	yes	—
235	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#95	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	4	4	no	—
238	C₂²×C₁₃	—	4	4	no	—
239	C₂²×C₁₃	—	4	4	no	—
240	C₂²×C₁₃	—	4	4	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	4	4	no	—
244	C₂²×C₁₃	—	8	16	no	—
245	C₂²×C₁₃	#529	1	8	yes	—
246	C₂²×C₁₃	#538	1	4	yes	—
247	C₂²×C₁₃	#553	1	8	yes	—
248	C₂²×C₁₃	#555	1	4	yes	—
249	C₂²×C₁₃	#559	1	4	yes	—
250	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
251	C₂²×C₁₃	C₂²×#41	1	2	yes	—
252	C₂²×C₁₃	C₂²×#41	1	2	yes	—
253	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
255	C₄×C₁₃	—	2	8	no	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	2	8	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	4	2	no	—
262	C₄×C₁₃	—	4	2	no	—
263	C₂⁵	C₂³×C₁₃	1	2	yes	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	4	2	no	—
266	C₂²×D₄	—	4	2	no	—
267	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
268	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
271	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
272	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
273	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
274	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	2	8	no	—
277	C₂×C₄⋊C₄	—	2	8	no	—
278	C₂×C₄⋊C₄	—	4	2	no	—
279	C₂×C₄⋊C₄	—	4	2	no	—
280	C₂×C₄⋊C₄	—	4	2	no	—
281	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
282	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
286	C₂×C₂²⋊C₄	—	2	8	no	—
287	C₂×C₂²⋊C₄	—	2	8	no	—
288	C₂×C₂²⋊C₄	—	2	8	no	—
289	C₂×C₂²⋊C₄	—	2	8	no	—
290	C₂×C₂²⋊C₄	—	4	4	no	—
291	C₂×C₂²⋊C₄	—	4	4	no	—
292	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
295	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
296	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
298	C₂×C₄²	—	2	8	no	—
299	C₂×C₄²	—	4	2	no	—
300	C₂×C₄²	—	4	4	no	—
301	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
302	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
303	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
304	#95	C₂³×C₁₃	1	8	yes	—
305	#95	C₂³×C₁₃	1	8	yes	—
306	#95	C₂³×C₁₃	1	8	yes	—
307	#95	C₂³×C₁₃	1	4	yes	—
308	#95	C₂³×C₁₃	1	8	yes	—
309	#95	C₂³×C₁₃	1	4	yes	—
310	C₂×C₁₃	—	8	4	no	—
311	C₂×C₁₃	#2593	1	8	yes	direct product factor
312	C₂×C₁₃	C₂×#529	1	2	yes	—
313	C₂×C₁₃	C₂×#538	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#553	1	2	yes	—
315	C₂×C₁₃	C₂×#555	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#559	1	1	yes	characteristic
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
325	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	16	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	C₁₃×#41	1	8	yes	—
350	C₂²×C₄	C₁₃×#41	1	8	yes	—
351	C₂²×C₄	C₁₃×#41	1	4	yes	—
352	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
360	C₄⋊C₄	—	2	16	no	—
361	C₄⋊C₄	—	2	16	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	4	no	—
365	C₂²⋊C₄	—	2	16	no	—
366	C₂²⋊C₄	—	2	16	no	—
367	C₂²⋊C₄	—	2	16	no	—
368	C₂²⋊C₄	—	2	16	no	—
369	C₂²⋊C₄	—	4	8	no	—
370	C₂²⋊C₄	—	4	8	no	—
371	C₄²	—	2	16	no	—
372	C₄²	—	4	4	no	—
373	C₄²	—	4	8	no	—
374	C₁₃	C₂×#2593	1	1	yes	characteristic, direct product factor, Sylow
375	C₂³	—	2	4	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	4	8	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	4	8	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	8	no	—
389	C₂³	C₂×C₁₃×#41	1	2	yes	—
390	C₂³	C₂×C₁₃×#41	1	4	yes	—
391	C₂³	C₂×C₁₃×#41	1	4	yes	—
392	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
393	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
394	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
395	D₄	—	4	16	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
424	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
425	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	8	16	no	—
434	C₂²	C₁₃×#529	1	8	yes	—
435	C₂²	C₁₃×#538	1	4	yes	—
436	C₂²	C₁₃×#553	1	8	yes	—
437	C₂²	C₁₃×#555	1	4	yes	—
438	C₂²	C₁₃×#559	1	4	yes	—
439	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
440	C₂²	C₂²×C₁₃×#41	1	2	yes	—
441	C₂²	C₂²×C₁₃×#41	1	2	yes	—
442	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
444	C₄	—	2	8	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	8	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₂	—	8	4	no	—
453	C₂	C₁₃×#2593	1	8	yes	direct product factor
454	C₂	C₂×C₁₃×#529	1	2	yes	—
455	C₂	C₂×C₁₃×#538	1	1	yes	characteristic
456	C₂	C₂×C₁₃×#553	1	2	yes	—
457	C₂	C₂×C₁₃×#555	1	1	yes	characteristic
458	C₂	C₂×C₁₃×#559	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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. C₁₃×#2593	C₂	direct (N × H)
2. C₂×C₁₃×#400	C₂	semidirect
3. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#388	C₂	semidirect
7. C₂×C₁₃×#388	C₂	semidirect
8. C₂×C₁₃×#388	C₂	semidirect
9. C₂×C₁₃×#388	C₂	semidirect
10. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
26. C₁₃×#400	C₂²	semidirect
27. C₁₃×#398	C₂²	semidirect
30. C₁₃×#388	C₂²	semidirect
31. C₁₃×#388	C₂²	semidirect
32. C₁₃×#388	C₂²	semidirect
33. C₁₃×#388	C₂²	semidirect
34. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
88. C₂×#2593	C₁₃	direct (N × H)
146. #2593	C₂×C₁₃	direct (N × H)
147. C₂×#400	C₂×C₁₃	semidirect
148. C₂×#398	C₂×C₁₃	semidirect
151. C₂×#388	C₂×C₁₃	semidirect
152. C₂×#388	C₂×C₁₃	semidirect
153. C₂×#388	C₂×C₁₃	semidirect
154. C₂×#388	C₂×C₁₃	semidirect
155. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
222. #400	C₂²×C₁₃	semidirect
223. #398	C₂²×C₁₃	semidirect
226. #388	C₂²×C₁₃	semidirect
227. #388	C₂²×C₁₃	semidirect
228. #388	C₂²×C₁₃	semidirect
229. #388	C₂²×C₁₃	semidirect
230. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
311. C₂×C₁₃	#2593	direct (N × H)
374. C₁₃	C₂×#2593	direct (N × H)
453. C₂	C₁₃×#2593	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×#2593	2
C₂×C₁₃×#400	2
C₂×C₁₃×#398	2
C₂×C₁₃×#394	2
C₂×C₁₃×#390	2
C₂×C₁₃×#388	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×#2593	13

Subgroups — C2×C13×#2593 #15721190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2593 #15721190