Subgroups — C₂×C₁₃×#2339 #15720438

Order 3328.

6150 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2339	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#386	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#381	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#95	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×#41	—	2	16	no	—
11	C₂²×C₁₃×#41	C₄	1	16	yes	complemented
12	C₂²×C₁₃×#41	C₂²	1	8	yes	—
13	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	16	no	—
20	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#391	C₂²	1	16	yes	complemented
27	C₁₃×#386	C₂²	1	32	yes	complemented
28	C₁₃×#381	C₂²	1	16	yes	complemented
29	C₁₃×#380	C₂²	1	8	yes	complemented
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	4	yes	—
34	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#95	C₂²	1	4	yes	—
36	C₂×C₁₃×#95	C₂²	1	16	yes	complemented
37	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
38	C₂⁵×C₁₃	C₂³	1	2	yes	—
39	C₂×C₁₃×#41	—	2	128	no	—
40	C₂×C₁₃×#41	—	2	64	no	—
41	C₂×C₁₃×#41	C₂×C₄	1	64	yes	complemented
42	C₂²×Q₈×C₁₃	—	2	8	no	—
43	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
44	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
45	C₂²×D₄×C₁₃	—	2	16	no	—
46	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
47	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
48	C₂²×D₄×C₁₃	D₄	1	16	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃	—	2	16	no	—
52	C₂³×C₄×C₁₃	—	2	8	no	—
53	C₂³×C₄×C₁₃	—	2	16	no	—
54	C₂³×C₄×C₁₃	—	2	16	no	—
55	C₂³×C₄×C₁₃	—	4	8	no	—
56	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
57	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₁₃	—	2	64	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₄²×C₁₃	—	2	8	no	—
77	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
78	C₁₃×#95	C₂³	1	4	yes	—
79	C₁₃×#95	C₂³	1	4	yes	—
80	C₁₃×#95	C₂³	1	8	yes	—
81	C₁₃×#95	C₂³	1	16	yes	—
82	C₁₃×#95	C₂³	1	16	yes	—
83	C₂×#2339	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₃	—	2	8	no	—
85	C₂⁴×C₁₃	—	2	4	no	—
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	4	no	—
88	C₂⁴×C₁₃	—	2	4	no	—
89	C₂⁴×C₁₃	—	2	2	no	—
90	C₂⁴×C₁₃	—	2	2	no	—
91	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
92	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
93	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
94	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
95	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
96	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₁₃×#41	—	2	256	no	—
98	C₂×Q₈×C₁₃	—	2	32	no	—
99	C₂×Q₈×C₁₃	—	2	16	no	—
100	C₂×Q₈×C₁₃	C₂²×C₄	1	16	yes	complemented
101	C₂×D₄×C₁₃	—	2	64	no	—
102	C₂×D₄×C₁₃	—	2	32	no	—
103	C₂×D₄×C₁₃	C₂²⋊C₄	1	64	yes	complemented
104	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
105	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
106	C₂×D₄×C₁₃	C₂×D₄	1	32	yes	—
107	C₂²×C₄×C₁₃	—	2	64	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	32	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	32	no	—
114	C₂²×C₄×C₁₃	—	2	16	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	32	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	32	no	—
123	C₂²×C₄×C₁₃	—	4	16	no	—
124	C₂²×C₄×C₁₃	—	4	64	no	—
125	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂²×C₄	1	32	yes	complemented
129	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	complemented
130	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
131	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
132	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₁₃×C₄⋊C₄	—	2	16	no	—
139	C₁₃×C₂²⋊C₄	—	2	32	no	—
140	C₁₃×C₂²⋊C₄	—	2	16	no	—
141	C₁₃×C₂²⋊C₄	—	4	8	no	—
142	C₄²×C₁₃	—	2	16	no	—
143	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic
144	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	complemented
145	#2339	C₂×C₁₃	1	16	yes	direct product factor
146	C₂×#391	C₂×C₁₃	1	2	yes	complemented
147	C₂×#386	C₂×C₁₃	1	4	yes	complemented
148	C₂×#381	C₂×C₁₃	1	2	yes	complemented
149	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂²×#95	C₂×C₁₃	1	2	yes	complemented
152	C₂³×C₁₃	—	2	16	no	—
153	C₂³×C₁₃	—	2	16	no	—
154	C₂³×C₁₃	—	2	32	no	—
155	C₂³×C₁₃	—	2	32	no	—
156	C₂³×C₁₃	—	2	8	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	4	no	—
159	C₂³×C₁₃	—	2	8	no	—
160	C₂³×C₁₃	—	2	8	no	—
161	C₂³×C₁₃	—	2	8	no	—
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	2	no	—
165	C₂³×C₁₃	—	2	2	no	—
166	C₂³×C₁₃	—	4	8	no	—
167	C₂³×C₁₃	—	4	8	no	—
168	C₂³×C₁₃	C₂×C₂²⋊C₄	1	32	yes	—
169	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
170	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
171	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
172	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
173	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
174	C₂³×C₁₃	C₂×#41	1	4	yes	—
175	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
176	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
177	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
178	Q₈×C₁₃	—	2	32	no	—
179	D₄×C₁₃	—	2	64	no	—
180	D₄×C₁₃	C₂×C₂²⋊C₄	1	64	yes	complemented
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	16	no	—
183	C₂×C₄×C₁₃	—	2	64	no	—
184	C₂×C₄×C₁₃	—	2	16	no	—
185	C₂×C₄×C₁₃	—	2	4	no	—
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	8	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	32	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	8	no	—
194	C₂×C₄×C₁₃	—	2	8	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	4	64	no	—
197	C₂×C₄×C₁₃	—	4	16	no	—
198	C₂×C₄×C₁₃	—	4	8	no	—
199	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
200	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
201	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
202	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
204	C₂×C₄×C₁₃	C₂×#41	1	8	yes	complemented
205	C₂²×#41	—	2	16	no	—
206	C₂²×#41	C₄×C₁₃	1	16	yes	complemented
207	C₂²×#41	C₂²×C₁₃	1	8	yes	—
208	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
210	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	—
212	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
213	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×C₄×D₄	—	2	16	no	—
215	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	complemented
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
218	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
221	#391	C₂²×C₁₃	1	16	yes	complemented
222	#386	C₂²×C₁₃	1	32	yes	complemented
223	#381	C₂²×C₁₃	1	16	yes	complemented
224	#380	C₂²×C₁₃	1	8	yes	complemented
225	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
226	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#95	C₂²×C₁₃	1	2	yes	—
228	C₂×#95	C₂²×C₁₃	1	4	yes	—
229	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#95	C₂²×C₁₃	1	4	yes	—
231	C₂×#95	C₂²×C₁₃	1	16	yes	complemented
232	C₂²×C₁₃	—	2	64	no	—
233	C₂²×C₁₃	—	2	8	no	—
234	C₂²×C₁₃	—	2	8	no	—
235	C₂²×C₁₃	—	2	16	no	—
236	C₂²×C₁₃	—	2	16	no	—
237	C₂²×C₁₃	—	2	4	no	—
238	C₂²×C₁₃	—	2	4	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	4	16	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	16	yes	—
244	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
245	C₂²×C₁₃	C₄×#41	1	4	yes	—
246	C₂²×C₁₃	#520	1	4	yes	—
247	C₂²×C₁₃	#546	1	8	yes	—
248	C₂²×C₁₃	#547	1	8	yes	—
249	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
250	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
251	C₂²×C₁₃	C₂²×#41	1	2	yes	—
252	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	8	no	—
256	C₄×C₁₃	—	2	8	no	—
257	C₄×C₁₃	—	4	8	no	—
258	C₄×C₁₃	—	4	4	no	—
259	C₄×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
260	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
261	C₂⁵	C₂³×C₁₃	1	2	yes	—
262	C₂×#41	—	2	128	no	—
263	C₂×#41	—	2	64	no	—
264	C₂×#41	C₂×C₄×C₁₃	1	64	yes	complemented
265	C₂²×Q₈	—	2	8	no	—
266	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	complemented
267	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
268	C₂²×D₄	—	2	16	no	—
269	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
270	C₂²×D₄	C₂×C₄×C₁₃	1	16	yes	complemented
271	C₂²×D₄	D₄×C₁₃	1	16	yes	—
272	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
274	C₂³×C₄	—	2	16	no	—
275	C₂³×C₄	—	2	8	no	—
276	C₂³×C₄	—	2	16	no	—
277	C₂³×C₄	—	2	16	no	—
278	C₂³×C₄	—	4	8	no	—
279	C₂³×C₄	C₂×C₄×C₁₃	1	16	yes	complemented
280	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
281	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
282	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
284	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
286	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
287	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
288	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₄×D₄	—	2	64	no	—
291	C₂×C₄⋊C₄	—	2	8	no	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
293	C₂×C₂²⋊C₄	—	2	16	no	—
294	C₂×C₂²⋊C₄	—	2	8	no	—
295	C₂×C₂²⋊C₄	—	4	4	no	—
296	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
297	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
298	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
299	C₂×C₄²	—	2	8	no	—
300	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
301	#95	C₂³×C₁₃	1	4	yes	—
302	#95	C₂³×C₁₃	1	8	yes	—
303	#95	C₂³×C₁₃	1	16	yes	—
304	#95	C₂³×C₁₃	1	4	yes	—
305	#95	C₂³×C₁₃	1	16	yes	—
306	C₂×C₁₃	—	2	16	no	—
307	C₂×C₁₃	—	4	4	no	—
308	C₂×C₁₃	#2339	1	8	yes	direct product factor
309	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
312	C₂×C₁₃	C₂×#546	1	2	yes	—
313	C₂×C₁₃	C₂×#547	1	2	yes	—
314	C₂⁴	—	2	8	no	—
315	C₂⁴	—	2	4	no	—
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
322	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
323	C₂⁴	C₂×D₄×C₁₃	1	16	yes	—
324	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
325	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
326	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
327	#41	—	2	256	no	—
328	C₂×Q₈	—	2	32	no	—
329	C₂×Q₈	—	2	16	no	—
330	C₂×Q₈	C₂²×C₄×C₁₃	1	16	yes	complemented
331	C₂×D₄	—	2	64	no	—
332	C₂×D₄	—	2	32	no	—
333	C₂×D₄	C₁₃×C₂²⋊C₄	1	64	yes	complemented
334	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
335	C₂×D₄	C₂²×C₄×C₁₃	1	32	yes	complemented
336	C₂×D₄	C₂×D₄×C₁₃	1	32	yes	—
337	C₂²×C₄	—	2	64	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	32	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	32	no	—
344	C₂²×C₄	—	2	16	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	32	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	32	no	—
353	C₂²×C₄	—	4	16	no	—
354	C₂²×C₄	—	4	64	no	—
355	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
359	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
360	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
361	C₂²×C₄	C₁₃×#41	1	8	yes	complemented
362	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
368	C₄⋊C₄	—	2	16	no	—
369	C₂²⋊C₄	—	2	32	no	—
370	C₂²⋊C₄	—	2	16	no	—
371	C₂²⋊C₄	—	4	8	no	—
372	C₄²	—	2	16	no	—
373	C₁₃	C₂×#2339	1	1	yes	characteristic, direct product factor, Sylow
374	C₂³	—	2	16	no	—
375	C₂³	—	2	16	no	—
376	C₂³	—	2	32	no	—
377	C₂³	—	2	32	no	—
378	C₂³	—	2	8	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	4	8	no	—
390	C₂³	C₂×C₁₃×C₂²⋊C₄	1	32	yes	—
391	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
392	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
393	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	16	yes	—
395	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
396	C₂³	C₂×C₁₃×#41	1	4	yes	—
397	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
398	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
399	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
400	Q₈	—	2	32	no	—
401	D₄	—	2	64	no	—
402	D₄	C₂×C₁₃×C₂²⋊C₄	1	64	yes	complemented
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	—	2	64	no	—
406	C₂×C₄	—	2	16	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	32	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	64	no	—
419	C₂×C₄	—	4	16	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	16	yes	—
422	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
424	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
426	C₂×C₄	C₂×C₁₃×#41	1	8	yes	complemented
427	C₂²	—	2	64	no	—
428	C₂²	—	2	8	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	2	16	no	—
431	C₂²	—	2	16	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	16	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	16	yes	—
439	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	4	yes	—
440	C₂²	C₄×C₁₃×#41	1	4	yes	—
441	C₂²	C₁₃×#520	1	4	yes	—
442	C₂²	C₁₃×#546	1	8	yes	—
443	C₂²	C₁₃×#547	1	8	yes	—
444	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
445	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
446	C₂²	C₂²×C₁₃×#41	1	2	yes	—
447	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
449	C₄	—	2	4	no	—
450	C₄	—	2	8	no	—
451	C₄	—	2	8	no	—
452	C₄	—	4	8	no	—
453	C₄	—	4	4	no	—
454	C₄	C₂²×C₁₃×C₂²⋊C₄	1	8	yes	—
455	C₂	—	2	16	no	—
456	C₂	—	4	4	no	—
457	C₂	C₁₃×#2339	1	8	yes	direct product factor
458	C₂	C₂³×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
459	C₂	C₂×C₄×C₁₃×#41	1	1	yes	characteristic
460	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
461	C₂	C₂×C₁₃×#546	1	2	yes	—
462	C₂	C₂×C₁₃×#547	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×C₁₃×#41	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2339	C₂	direct (N × H)
4. C₂×C₁₃×#391	C₂	semidirect
5. C₂×C₁₃×#386	C₂	semidirect
6. C₂×C₁₃×#381	C₂	semidirect
7. C₂×C₁₃×#380	C₂	semidirect
8. C₂×C₄×C₁₃×C₂²⋊C₄	C₂	semidirect
9. C₂²×C₁₃×#95	C₂	semidirect
11. C₂²×C₁₃×#41	C₄	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₁₃×#391	C₂²	semidirect
27. C₁₃×#386	C₂²	semidirect
28. C₁₃×#381	C₂²	semidirect
29. C₁₃×#380	C₂²	semidirect
30. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₁₃×#95	C₂²	semidirect
41. C₂×C₁₃×#41	C₂×C₄	semidirect
43. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
47. C₂²×D₄×C₁₃	C₂×C₄	semidirect
56. C₂³×C₄×C₁₃	C₂×C₄	semidirect
57. C₂³×C₄×C₁₃	C₂×C₄	semidirect
83. C₂×#2339	C₁₃	direct (N × H)
100. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
103. C₂×D₄×C₁₃	C₂²⋊C₄	semidirect
105. C₂×D₄×C₁₃	C₂²×C₄	semidirect
128. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
129. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
131. C₂²×C₄×C₁₃	#41	semidirect
144. C₂²×C₄×D₄	C₂×C₁₃	semidirect
145. #2339	C₂×C₁₃	direct (N × H)
146. C₂×#391	C₂×C₁₃	semidirect
147. C₂×#386	C₂×C₁₃	semidirect
148. C₂×#381	C₂×C₁₃	semidirect
149. C₂×#380	C₂×C₁₃	semidirect
150. C₂×C₄×C₂²⋊C₄	C₂×C₁₃	semidirect
151. C₂²×#95	C₂×C₁₃	semidirect
180. D₄×C₁₃	C₂×C₂²⋊C₄	semidirect
204. C₂×C₄×C₁₃	C₂×#41	semidirect
206. C₂²×#41	C₄×C₁₃	semidirect
215. C₂×C₄×D₄	C₂²×C₁₃	semidirect
221. #391	C₂²×C₁₃	semidirect
222. #386	C₂²×C₁₃	semidirect
223. #381	C₂²×C₁₃	semidirect
224. #380	C₂²×C₁₃	semidirect
225. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
231. C₂×#95	C₂²×C₁₃	semidirect
264. C₂×#41	C₂×C₄×C₁₃	semidirect
266. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
270. C₂²×D₄	C₂×C₄×C₁₃	semidirect
279. C₂³×C₄	C₂×C₄×C₁₃	semidirect
280. C₂³×C₄	C₂×C₄×C₁₃	semidirect
308. C₂×C₁₃	#2339	direct (N × H)
330. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
333. C₂×D₄	C₁₃×C₂²⋊C₄	semidirect
335. C₂×D₄	C₂²×C₄×C₁₃	semidirect
358. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
359. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
361. C₂²×C₄	C₁₃×#41	semidirect
373. C₁₃	C₂×#2339	direct (N × H)
402. D₄	C₂×C₁₃×C₂²⋊C₄	semidirect
426. C₂×C₄	C₂×C₁₃×#41	semidirect
457. C₂	C₁₃×#2339	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₃×#41	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2339	2
C₂×C₁₃×#391	2
C₂×C₁₃×#386	2
C₂×C₁₃×#381	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂²×C₁₃×#95	2
C₂×#2339	13

Subgroups — C2×C13×#2339 #15720438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2339 #15720438