Subgroups — C₂×C₁₃×#2549 #15721159

Order 3328.

3094 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	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal
2	C₁₃×#2549	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#395	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#391	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#385	C₂	1	2	yes	maximal
8	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₂²⋊Q₈	—	2	16	no	—
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	16	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
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	1	yes	characteristic
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#398	C₂²	1	16	yes	complemented
27	C₁₃×#395	C₂²	1	16	yes	complemented
28	C₁₃×#391	C₂²	1	16	yes	complemented
29	C₁₃×#389	C₂²	1	16	yes	complemented
30	C₁₃×#385	C₂²	1	16	yes	—
31	C₁₃×#380	C₂²	1	8	yes	—
32	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂×C₁₃×#95	C₂²	1	8	yes	—
35	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#95	C₂²	1	2	yes	—
41	C₂×C₁₃×#95	C₂²	1	2	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₁₃	—	2	8	no	—
44	C₂²×Q₈×C₁₃	—	2	8	no	—
45	C₂²×Q₈×C₁₃	—	4	4	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
47	C₂³×C₄×C₁₃	—	2	8	no	—
48	C₂³×C₄×C₁₃	—	2	8	no	—
49	C₂³×C₄×C₁₃	—	4	4	no	—
50	C₂³×C₄×C₁₃	—	4	4	no	—
51	C₂³×C₄×C₁₃	Q₈	1	8	yes	complemented
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
62	C₁₃×C₂²⋊Q₈	—	2	64	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
77	C₂×C₁₃×C₂²⋊C₄	Q₈	1	8	yes	complemented
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₃	—	4	4	no	—
82	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	8	yes	—
84	C₁₃×#95	C₂³	1	4	yes	—
85	C₁₃×#95	C₂³	1	4	yes	—
86	C₁₃×#95	C₂³	1	8	yes	—
87	C₁₃×#95	C₂³	1	8	yes	—
88	C₁₃×#95	C₂³	1	8	yes	—
89	C₁₃×#95	C₂³	1	4	yes	—
90	C₁₃×#95	C₂³	1	4	yes	—
91	C₂×#2549	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
95	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
96	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂×Q₈×C₁₃	—	2	16	no	—
100	C₂×Q₈×C₁₃	—	2	16	no	—
101	C₂×Q₈×C₁₃	—	4	8	no	—
102	C₂×Q₈×C₁₃	—	4	32	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	4	no	—
107	C₂²×C₄×C₁₃	—	2	4	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	16	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	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	16	no	—
122	C₂²×C₄×C₁₃	—	4	16	no	—
123	C₂²×C₄×C₁₃	—	4	8	no	—
124	C₂²×C₄×C₁₃	—	4	8	no	—
125	C₂²×C₄×C₁₃	—	4	32	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
128	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×Q₈	1	16	yes	complemented
131	C₂²×C₄×C₁₃	#41	1	8	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₁₃×C₄⋊C₄	—	2	16	no	—
141	C₁₃×C₄⋊C₄	—	2	16	no	—
142	C₁₃×C₄⋊C₄	—	2	16	no	—
143	C₁₃×C₄⋊C₄	—	2	16	no	—
144	C₁₃×C₄⋊C₄	—	4	8	no	—
145	C₁₃×C₄⋊C₄	—	4	8	no	—
146	C₁₃×C₂²⋊C₄	—	2	16	no	—
147	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
148	C₁₃×C₂²⋊C₄	C₂×Q₈	1	16	yes	complemented
149	C₄²×C₁₃	—	4	8	no	—
150	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	—
151	#2549	C₂×C₁₃	1	16	yes	direct product factor
152	C₂×#398	C₂×C₁₃	1	2	yes	complemented
153	C₂×#395	C₂×C₁₃	1	2	yes	complemented
154	C₂×#391	C₂×C₁₃	1	2	yes	complemented
155	C₂×#389	C₂×C₁₃	1	2	yes	complemented
156	C₂×#385	C₂×C₁₃	1	2	yes	—
157	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
158	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
159	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic
160	C₂³×C₁₃	—	2	8	no	—
161	C₂³×C₁₃	—	2	8	no	—
162	C₂³×C₁₃	—	2	16	no	—
163	C₂³×C₁₃	—	2	16	no	—
164	C₂³×C₁₃	—	2	4	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	C₄⋊Q₈	1	16	yes	—
167	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
168	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
169	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
170	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
171	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
172	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
173	C₂³×C₁₃	C₂×#41	1	4	yes	—
174	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
175	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
176	Q₈×C₁₃	—	4	32	no	—
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	16	no	—
180	C₂×C₄×C₁₃	—	2	16	no	—
181	C₂×C₄×C₁₃	—	2	16	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	4	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	4	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	4	no	—
198	C₂×C₄×C₁₃	—	2	4	no	—
199	C₂×C₄×C₁₃	—	4	16	no	—
200	C₂×C₄×C₁₃	—	4	32	no	—
201	C₂×C₄×C₁₃	—	4	8	no	—
202	C₂×C₄×C₁₃	—	4	8	no	—
203	C₂×C₄×C₁₃	—	4	8	no	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
205	C₂×C₄×C₁₃	C₂²×Q₈	1	8	yes	—
206	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
207	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
208	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
209	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
210	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
211	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₂²⋊Q₈	—	2	16	no	—
213	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	16	yes	—
214	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
215	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
219	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
224	#398	C₂²×C₁₃	1	16	yes	complemented
225	#395	C₂²×C₁₃	1	16	yes	complemented
226	#391	C₂²×C₁₃	1	16	yes	complemented
227	#389	C₂²×C₁₃	1	16	yes	complemented
228	#385	C₂²×C₁₃	1	16	yes	—
229	#380	C₂²×C₁₃	1	8	yes	—
230	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
231	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×#95	C₂²×C₁₃	1	2	yes	—
233	C₂×#95	C₂²×C₁₃	1	2	yes	—
234	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#95	C₂²×C₁₃	1	2	yes	—
236	C₂×#95	C₂²×C₁₃	1	2	yes	—
237	C₂×#95	C₂²×C₁₃	1	8	yes	—
238	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
240	C₂²×C₁₃	—	2	4	no	—
241	C₂²×C₁₃	—	2	4	no	—
242	C₂²×C₁₃	—	2	8	no	—
243	C₂²×C₁₃	—	2	8	no	—
244	C₂²×C₁₃	—	2	32	no	—
245	C₂²×C₁₃	C₂×C₄⋊Q₈	1	8	yes	—
246	C₂²×C₁₃	C₂×C₄⋊Q₈	1	4	yes	—
247	C₂²×C₁₃	#533	1	4	yes	—
248	C₂²×C₁₃	#543	1	4	yes	—
249	C₂²×C₁₃	#546	1	8	yes	—
250	C₂²×C₁₃	#554	1	8	yes	—
251	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
252	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
253	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
254	C₂²×C₁₃	C₂²×#41	1	2	yes	—
255	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
256	C₄×C₁₃	—	2	4	no	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	8	no	—
259	C₄×C₁₃	—	2	8	no	—
260	C₄×C₁₃	—	2	8	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	4	4	no	—
264	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×Q₈	—	2	8	no	—
266	C₂²×Q₈	—	2	8	no	—
267	C₂²×Q₈	—	4	4	no	—
268	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
269	C₂³×C₄	—	2	8	no	—
270	C₂³×C₄	—	2	8	no	—
271	C₂³×C₄	—	4	4	no	—
272	C₂³×C₄	—	4	4	no	—
273	C₂³×C₄	Q₈×C₁₃	1	8	yes	complemented
274	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
276	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
278	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
283	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
284	C₂²⋊Q₈	—	2	64	no	—
285	C₂×C₄⋊C₄	—	2	8	no	—
286	C₂×C₄⋊C₄	—	2	8	no	—
287	C₂×C₄⋊C₄	—	2	8	no	—
288	C₂×C₄⋊C₄	—	2	8	no	—
289	C₂×C₄⋊C₄	—	4	4	no	—
290	C₂×C₄⋊C₄	—	4	4	no	—
291	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
292	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
297	C₂×C₂²⋊C₄	—	2	8	no	—
298	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
299	C₂×C₂²⋊C₄	Q₈×C₁₃	1	8	yes	complemented
300	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
301	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
303	C₂×C₄²	—	4	4	no	—
304	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
305	#95	C₂³×C₁₃	1	8	yes	—
306	#95	C₂³×C₁₃	1	4	yes	—
307	#95	C₂³×C₁₃	1	4	yes	—
308	#95	C₂³×C₁₃	1	8	yes	—
309	#95	C₂³×C₁₃	1	4	yes	—
310	#95	C₂³×C₁₃	1	4	yes	—
311	#95	C₂³×C₁₃	1	8	yes	—
312	#95	C₂³×C₁₃	1	8	yes	—
313	C₂×C₁₃	—	2	8	no	—
314	C₂×C₁₃	#2549	1	8	yes	direct product factor
315	C₂×C₁₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
317	C₂×C₁₃	C₂×#543	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#546	1	2	yes	—
319	C₂×C₁₃	C₂×#554	1	2	yes	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
323	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
324	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
325	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
326	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
327	C₂×Q₈	—	2	16	no	—
328	C₂×Q₈	—	2	16	no	—
329	C₂×Q₈	—	4	8	no	—
330	C₂×Q₈	—	4	32	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	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	16	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	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	16	no	—
350	C₂²×C₄	—	4	16	no	—
351	C₂²×C₄	—	4	8	no	—
352	C₂²×C₄	—	4	8	no	—
353	C₂²×C₄	—	4	32	no	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
355	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
356	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
359	C₂²×C₄	C₁₃×#41	1	8	yes	—
360	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
368	C₄⋊C₄	—	2	16	no	—
369	C₄⋊C₄	—	2	16	no	—
370	C₄⋊C₄	—	2	16	no	—
371	C₄⋊C₄	—	2	16	no	—
372	C₄⋊C₄	—	4	8	no	—
373	C₄⋊C₄	—	4	8	no	—
374	C₂²⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
376	C₂²⋊C₄	C₂×Q₈×C₁₃	1	16	yes	complemented
377	C₄²	—	4	8	no	—
378	C₁₃	C₂×#2549	1	1	yes	characteristic, direct product factor, Sylow
379	C₂³	—	2	8	no	—
380	C₂³	—	2	8	no	—
381	C₂³	—	2	16	no	—
382	C₂³	—	2	16	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	C₁₃×C₄⋊Q₈	1	16	yes	—
386	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
387	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
388	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
389	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
390	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
391	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
392	C₂³	C₂×C₁₃×#41	1	4	yes	—
393	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
394	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
395	Q₈	—	4	32	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	2	16	no	—
400	C₂×C₄	—	2	16	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	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	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	16	no	—
419	C₂×C₄	—	4	32	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	8	no	—
423	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
424	C₂×C₄	C₂²×Q₈×C₁₃	1	8	yes	—
425	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
426	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
427	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
428	C₂²	—	2	32	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	8	no	—
432	C₂²	—	2	8	no	—
433	C₂²	C₂×C₁₃×C₄⋊Q₈	1	8	yes	—
434	C₂²	C₂×C₁₃×C₄⋊Q₈	1	4	yes	—
435	C₂²	C₁₃×#533	1	4	yes	—
436	C₂²	C₁₃×#543	1	4	yes	—
437	C₂²	C₁₃×#546	1	8	yes	—
438	C₂²	C₁₃×#554	1	8	yes	—
439	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
440	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
441	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
442	C₂²	C₂²×C₁₃×#41	1	2	yes	—
443	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	8	no	—
448	C₄	—	2	8	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₂	—	2	8	no	—
453	C₂	C₁₃×#2549	1	8	yes	direct product factor
454	C₂	C₂²×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
455	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
456	C₂	C₂×C₁₃×#543	1	1	yes	characteristic
457	C₂	C₂×C₁₃×#546	1	2	yes	—
458	C₂	C₂×C₁₃×#554	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
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
2. C₁₃×#2549	C₂	direct (N × H)
3. C₂×C₁₃×#398	C₂	semidirect
4. C₂×C₁₃×#395	C₂	semidirect
5. C₂×C₁₃×#391	C₂	semidirect
6. C₂×C₁₃×#389	C₂	semidirect
26. C₁₃×#398	C₂²	semidirect
27. C₁₃×#395	C₂²	semidirect
28. C₁₃×#391	C₂²	semidirect
29. C₁₃×#389	C₂²	semidirect
51. C₂³×C₄×C₁₃	Q₈	semidirect
77. C₂×C₁₃×C₂²⋊C₄	Q₈	semidirect
91. C₂×#2549	C₁₃	direct (N × H)
130. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
148. C₁₃×C₂²⋊C₄	C₂×Q₈	semidirect
151. #2549	C₂×C₁₃	direct (N × H)
152. C₂×#398	C₂×C₁₃	semidirect
153. C₂×#395	C₂×C₁₃	semidirect
154. C₂×#391	C₂×C₁₃	semidirect
155. C₂×#389	C₂×C₁₃	semidirect
224. #398	C₂²×C₁₃	semidirect
225. #395	C₂²×C₁₃	semidirect
226. #391	C₂²×C₁₃	semidirect
227. #389	C₂²×C₁₃	semidirect
273. C₂³×C₄	Q₈×C₁₃	semidirect
299. C₂×C₂²⋊C₄	Q₈×C₁₃	semidirect
314. C₂×C₁₃	#2549	direct (N × H)
358. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
376. C₂²⋊C₄	C₂×Q₈×C₁₃	semidirect
378. C₁₃	C₂×#2549	direct (N × H)
453. C₂	C₁₃×#2549	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×C₂²⋊Q₈	2
C₁₃×#2549	2
C₂×C₁₃×#398	2
C₂×C₁₃×#395	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂²×C₁₃×#95	2
C₂×#2549	13

Subgroups — C2×C13×#2549 #15721159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2549 #15721159