Subgroups — C₁₃×#34982 #15721321

Order 3328.

4046 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2848	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2626	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2437	C₂	1	16	yes	maximal, complemented
6	C₁₃×#2315	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2315	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#379	C₂	1	2	yes	maximal
9	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
11	C₁₃×#543	—	2	8	no	—
12	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
15	C₂²×C₁₃×C₂²⋊C₄	—	2	8	no	—
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₁₃×#399	C₂²	1	8	yes	complemented
24	C₁₃×#396	C₂²	1	16	yes	complemented
25	C₁₃×#393	C₂²	1	8	yes	complemented
26	C₁₃×#385	C₂²	1	8	yes	complemented
27	C₁₃×#385	C₂²	1	8	yes	complemented
28	C₁₃×#385	C₂²	1	8	yes	complemented
29	C₁₃×#385	C₂²	1	16	yes	complemented
30	C₁₃×#380	C₂²	1	4	yes	complemented
31	C₁₃×#380	C₂²	1	8	yes	complemented
32	C₁₃×#380	C₂²	1	8	yes	complemented
33	C₁₃×#379	C₂²	1	4	yes	—
34	C₁₃×#379	C₂²	1	4	yes	—
35	C₁₃×#379	C₂²	1	8	yes	—
36	C₂⁵×C₁₃	—	2	4	no	—
37	C₂⁵×C₁₃	—	2	4	no	—
38	C₂⁵×C₁₃	—	4	8	no	—
39	C₂⁵×C₁₃	Q₈	1	8	yes	complemented
40	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
41	C₂⁵×C₁₃	C₂³	1	4	yes	—
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃	C₂³	1	4	yes	complemented
45	C₂³×C₄×C₁₃	—	2	8	no	—
46	C₂³×C₄×C₁₃	—	4	8	no	—
47	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₂²⋊Q₈	—	2	16	no	—
53	C₁₃×C₂²⋊Q₈	—	2	32	no	—
54	C₁₃×C₂²⋊Q₈	—	4	16	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
59	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
63	C₂×C₁₃×C₂²⋊C₄	—	2	32	no	—
64	C₂×C₁₃×C₂²⋊C₄	—	4	16	no	—
65	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
66	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₁₃×#95	C₂³	1	16	yes	complemented
76	C₁₃×#95	C₂³	1	8	yes	complemented
77	#34982	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₃	—	2	2	no	—
79	C₂⁴×C₁₃	—	2	2	no	—
80	C₂⁴×C₁₃	—	2	8	no	—
81	C₂⁴×C₁₃	—	2	32	no	—
82	C₂⁴×C₁₃	—	2	8	no	—
83	C₂⁴×C₁₃	—	2	2	no	—
84	C₂⁴×C₁₃	—	2	8	no	—
85	C₂⁴×C₁₃	—	2	2	no	—
86	C₂⁴×C₁₃	—	2	16	no	—
87	C₂⁴×C₁₃	—	4	32	no	—
88	C₂⁴×C₁₃	—	4	4	no	—
89	C₂⁴×C₁₃	—	4	8	no	—
90	C₂⁴×C₁₃	—	4	4	no	—
91	C₂⁴×C₁₃	—	4	32	no	—
92	C₂⁴×C₁₃	—	4	32	no	—
93	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
94	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
95	C₂⁴×C₁₃	C₂×Q₈	1	16	yes	—
96	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
97	C₂⁴×C₁₃	C₂×Q₈	1	4	yes	—
98	C₂⁴×C₁₃	#41	1	4	yes	—
99	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
103	C₂×Q₈×C₁₃	—	2	8	no	—
104	C₂×Q₈×C₁₃	—	4	8	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	16	no	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	16	no	—
110	C₂²×C₄×C₁₃	—	4	4	no	—
111	C₂²×C₄×C₁₃	—	4	8	no	—
112	C₂²×C₄×C₁₃	—	4	4	no	—
113	C₂²×C₄×C₁₃	—	4	8	no	—
114	C₂²×C₄×C₁₃	—	4	8	no	—
115	C₂²×C₄×C₁₃	—	4	32	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
121	C₁₃×C₄⋊C₄	—	2	8	no	—
122	C₁₃×C₄⋊C₄	—	2	16	no	—
123	C₁₃×C₄⋊C₄	—	4	8	no	—
124	C₁₃×C₄⋊C₄	—	4	16	no	—
125	C₁₃×C₂²⋊C₄	—	2	8	no	—
126	C₁₃×C₂²⋊C₄	—	2	8	no	—
127	C₁₃×C₂²⋊C₄	—	2	8	no	—
128	C₁₃×C₂²⋊C₄	—	2	8	no	—
129	C₁₃×C₂²⋊C₄	—	2	8	no	—
130	C₁₃×C₂²⋊C₄	—	2	32	no	—
131	C₁₃×C₂²⋊C₄	—	2	16	no	—
132	C₁₃×C₂²⋊C₄	—	4	16	no	—
133	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
134	C₂×#543	C₂×C₁₃	1	1	yes	characteristic, complemented
135	C₂³×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
136	#2848	C₂×C₁₃	1	4	yes	complemented
137	#2626	C₂×C₁₃	1	4	yes	complemented
138	#2437	C₂×C₁₃	1	16	yes	complemented
139	#2315	C₂×C₁₃	1	2	yes	complemented
140	#2315	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#379	C₂×C₁₃	1	2	yes	—
142	C₂³×C₁₃	—	2	16	no	—
143	C₂³×C₁₃	—	2	16	no	—
144	C₂³×C₁₃	—	2	8	no	—
145	C₂³×C₁₃	—	2	16	no	—
146	C₂³×C₁₃	—	2	2	no	—
147	C₂³×C₁₃	—	2	2	no	—
148	C₂³×C₁₃	—	2	4	no	—
149	C₂³×C₁₃	—	2	4	no	—
150	C₂³×C₁₃	—	2	8	no	—
151	C₂³×C₁₃	—	2	32	no	—
152	C₂³×C₁₃	—	2	8	no	—
153	C₂³×C₁₃	—	2	32	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	2	no	—
156	C₂³×C₁₃	—	2	8	no	—
157	C₂³×C₁₃	—	4	8	no	—
158	C₂³×C₁₃	—	4	8	no	—
159	C₂³×C₁₃	—	4	16	no	—
160	C₂³×C₁₃	—	4	8	no	—
161	C₂³×C₁₃	—	4	8	no	—
162	C₂³×C₁₃	—	4	32	no	—
163	C₂³×C₁₃	—	4	32	no	—
164	C₂³×C₁₃	—	4	128	no	—
165	C₂³×C₁₃	—	4	8	no	—
166	C₂³×C₁₃	—	4	8	no	—
167	C₂³×C₁₃	C₂²⋊Q₈	1	16	yes	complemented
168	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
169	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
171	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
172	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
173	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
174	C₂³×C₁₃	C₂×#41	1	2	yes	—
175	C₂³×C₁₃	C₂×#41	1	4	yes	—
176	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
177	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
178	Q₈×C₁₃	—	8	8	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	8	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	16	no	—
184	C₂×C₄×C₁₃	—	2	16	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	4	8	no	—
187	C₂×C₄×C₁₃	—	4	32	no	—
188	C₂×C₄×C₁₃	—	4	8	no	—
189	C₂×C₄×C₁₃	—	8	8	no	—
190	C₂×C₄×C₁₃	—	8	8	no	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
192	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
193	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
194	#543	—	2	8	no	—
195	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
196	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
197	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
198	C₂²×C₂²⋊C₄	—	2	8	no	—
199	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
200	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
201	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
202	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
203	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
204	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
206	#399	C₂²×C₁₃	1	8	yes	complemented
207	#396	C₂²×C₁₃	1	16	yes	complemented
208	#393	C₂²×C₁₃	1	8	yes	complemented
209	#385	C₂²×C₁₃	1	8	yes	complemented
210	#385	C₂²×C₁₃	1	8	yes	complemented
211	#385	C₂²×C₁₃	1	8	yes	complemented
212	#385	C₂²×C₁₃	1	16	yes	complemented
213	#380	C₂²×C₁₃	1	4	yes	complemented
214	#380	C₂²×C₁₃	1	8	yes	complemented
215	#380	C₂²×C₁₃	1	8	yes	complemented
216	#379	C₂²×C₁₃	1	4	yes	—
217	#379	C₂²×C₁₃	1	4	yes	—
218	#379	C₂²×C₁₃	1	8	yes	—
219	C₂²×C₁₃	—	2	32	no	—
220	C₂²×C₁₃	—	2	4	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	2	8	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	2	8	no	—
226	C₂²×C₁₃	—	2	8	no	—
227	C₂²×C₁₃	—	2	8	no	—
228	C₂²×C₁₃	—	2	4	no	—
229	C₂²×C₁₃	—	2	8	no	—
230	C₂²×C₁₃	—	2	4	no	—
231	C₂²×C₁₃	—	2	8	no	—
232	C₂²×C₁₃	—	4	16	no	—
233	C₂²×C₁₃	—	4	64	no	—
234	C₂²×C₁₃	—	4	16	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	4	yes	—
238	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	8	yes	—
239	C₂²×C₁₃	#543	1	8	yes	complemented
240	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
241	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
242	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
244	C₄×C₁₃	—	2	8	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	—	4	8	no	—
247	C₄×C₁₃	—	4	8	no	—
248	C₂⁵	—	2	4	no	—
249	C₂⁵	—	2	4	no	—
250	C₂⁵	—	4	8	no	—
251	C₂⁵	Q₈×C₁₃	1	8	yes	complemented
252	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
253	C₂⁵	C₂³×C₁₃	1	4	yes	—
254	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
255	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₁₃	1	4	yes	complemented
257	C₂³×C₄	—	2	8	no	—
258	C₂³×C₄	—	4	8	no	—
259	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
260	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
261	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
262	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
264	C₂²⋊Q₈	—	2	16	no	—
265	C₂²⋊Q₈	—	2	32	no	—
266	C₂²⋊Q₈	—	4	16	no	—
267	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	complemented
268	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
270	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	complemented
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	—	2	8	no	—
273	C₂×C₂²⋊C₄	—	2	8	no	—
274	C₂×C₂²⋊C₄	—	2	8	no	—
275	C₂×C₂²⋊C₄	—	2	32	no	—
276	C₂×C₂²⋊C₄	—	4	16	no	—
277	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
287	#95	C₂³×C₁₃	1	16	yes	complemented
288	#95	C₂³×C₁₃	1	8	yes	complemented
289	C₂×C₁₃	—	2	4	no	—
290	C₂×C₁₃	—	2	8	no	—
291	C₂×C₁₃	—	2	8	no	—
292	C₂×C₁₃	—	4	4	no	—
293	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
294	C₂×C₁₃	C₂×#543	1	2	yes	—
295	C₂×C₁₃	#3484	1	2	yes	—
296	C₂×C₁₃	#3490	1	2	yes	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	2	2	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	32	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	16	no	—
306	C₂⁴	—	4	32	no	—
307	C₂⁴	—	4	4	no	—
308	C₂⁴	—	4	8	no	—
309	C₂⁴	—	4	4	no	—
310	C₂⁴	—	4	32	no	—
311	C₂⁴	—	4	32	no	—
312	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
313	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
314	C₂⁴	C₂×Q₈×C₁₃	1	16	yes	—
315	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
316	C₂⁴	C₂×Q₈×C₁₃	1	4	yes	—
317	C₂⁴	C₁₃×#41	1	4	yes	—
318	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
319	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
320	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
321	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	—	4	8	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	16	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	16	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	—	4	32	no	—
335	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
336	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	4	8	no	—
343	C₄⋊C₄	—	4	16	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	32	no	—
350	C₂²⋊C₄	—	2	16	no	—
351	C₂²⋊C₄	—	4	16	no	—
352	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
353	C₁₃	#34982	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³	—	2	16	no	—
355	C₂³	—	2	16	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	16	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	32	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	32	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	8	no	—
369	C₂³	—	4	8	no	—
370	C₂³	—	4	8	no	—
371	C₂³	—	4	16	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	8	no	—
374	C₂³	—	4	32	no	—
375	C₂³	—	4	32	no	—
376	C₂³	—	4	128	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	4	8	no	—
379	C₂³	C₁₃×C₂²⋊Q₈	1	16	yes	complemented
380	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
381	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
382	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
383	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
384	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
385	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
386	C₂³	C₂×C₁₃×#41	1	2	yes	—
387	C₂³	C₂×C₁₃×#41	1	4	yes	—
388	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
389	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
390	Q₈	—	8	8	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	32	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	8	8	no	—
402	C₂×C₄	—	8	8	no	—
403	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
404	C₂²	—	2	32	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	16	no	—
418	C₂²	—	4	64	no	—
419	C₂²	—	4	16	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	4	yes	—
423	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	8	yes	—
424	C₂²	C₁₃×#543	1	8	yes	complemented
425	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
426	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
427	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
428	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
429	C₄	—	2	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	8	no	—
432	C₄	—	4	8	no	—
433	C₂	—	2	4	no	—
434	C₂	—	2	8	no	—
435	C₂	—	2	8	no	—
436	C₂	—	4	4	no	—
437	C₂	C₂²×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂	C₂×C₁₃×#543	1	2	yes	—
439	C₂	C₁₃×#3484	1	2	yes	—
440	C₂	C₁₃×#3490	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁶×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#543	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2626	C₂	semidirect
5. C₁₃×#2437	C₂	semidirect
6. C₁₃×#2315	C₂	semidirect
7. C₁₃×#2315	C₂	semidirect
12. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
13. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
14. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
23. C₁₃×#399	C₂²	semidirect
24. C₁₃×#396	C₂²	semidirect
25. C₁₃×#393	C₂²	semidirect
26. C₁₃×#385	C₂²	semidirect
27. C₁₃×#385	C₂²	semidirect
28. C₁₃×#385	C₂²	semidirect
29. C₁₃×#385	C₂²	semidirect
30. C₁₃×#380	C₂²	semidirect
31. C₁₃×#380	C₂²	semidirect
32. C₁₃×#380	C₂²	semidirect
39. C₂⁵×C₁₃	Q₈	semidirect
44. C₂²×Q₈×C₁₃	C₂³	semidirect
55. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
56. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
57. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
58. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
75. C₁₃×#95	C₂³	semidirect
76. C₁₃×#95	C₂³	semidirect
77. #34982	C₁₃	direct (N × H)
134. C₂×#543	C₂×C₁₃	semidirect
136. #2848	C₂×C₁₃	semidirect
137. #2626	C₂×C₁₃	semidirect
138. #2437	C₂×C₁₃	semidirect
139. #2315	C₂×C₁₃	semidirect
140. #2315	C₂×C₁₃	semidirect
167. C₂³×C₁₃	C₂²⋊Q₈	semidirect
195. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
196. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
197. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
206. #399	C₂²×C₁₃	semidirect
207. #396	C₂²×C₁₃	semidirect
208. #393	C₂²×C₁₃	semidirect
209. #385	C₂²×C₁₃	semidirect
210. #385	C₂²×C₁₃	semidirect
211. #385	C₂²×C₁₃	semidirect
212. #385	C₂²×C₁₃	semidirect
213. #380	C₂²×C₁₃	semidirect
214. #380	C₂²×C₁₃	semidirect
215. #380	C₂²×C₁₃	semidirect
239. C₂²×C₁₃	#543	semidirect
251. C₂⁵	Q₈×C₁₃	semidirect
256. C₂²×Q₈	C₂³×C₁₃	semidirect
267. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
268. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
269. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
270. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
287. #95	C₂³×C₁₃	semidirect
288. #95	C₂³×C₁₃	semidirect
353. C₁₃	#34982	direct (N × H)
379. C₂³	C₁₃×C₂²⋊Q₈	semidirect
424. C₂²	C₁₃×#543	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#543	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2848	2
C₁₃×#2626	2
C₁₃×#2437	2
C₁₃×#2315	2
C₂×C₁₃×#379	2
#34982	13

Subgroups — C13×#34982 #15721321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34982 #15721321