Subgroups — C₁₃×#34980 #15721319

Order 3328.

7786 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#534	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2849	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2846	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2613	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2410	C₂	1	8	yes	maximal, complemented
8	C₁₃×#2405	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2403	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2308	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₃	—	2	8	no	—
15	C₂³×D₄×C₁₃	—	2	16	no	—
16	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
20	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
22	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#534	—	2	16	no	—
24	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
27	C₂×C₁₃×#120	—	2	8	no	—
28	C₂×C₁₃×#120	C₂²	1	2	yes	—
29	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
32	C₂×C₁₃×#120	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
38	C₁₃×#394	C₂²	1	16	yes	complemented
39	C₁₃×#392	C₂²	1	16	yes	complemented
40	C₁₃×#386	C₂²	1	8	yes	complemented
41	C₁₃×#386	C₂²	1	8	yes	complemented
42	C₁₃×#386	C₂²	1	8	yes	complemented
43	C₁₃×#385	C₂²	1	8	yes	complemented
44	C₁₃×#381	C₂²	1	4	yes	complemented
45	C₁₃×#379	C₂²	1	2	yes	complemented
46	C₁₃×#379	C₂²	1	2	yes	complemented
47	C₁₃×#379	C₂²	1	4	yes	complemented
48	C₁₃×#379	C₂²	1	4	yes	complemented
49	C₁₃×#379	C₂²	1	8	yes	complemented
50	C₂⁵×C₁₃	—	2	8	no	—
51	C₂⁵×C₁₃	—	2	4	no	—
52	C₂⁵×C₁₃	—	2	8	no	—
53	C₂⁵×C₁₃	—	4	8	no	—
54	C₂⁵×C₁₃	—	4	8	no	—
55	C₂⁵×C₁₃	D₄	1	8	yes	complemented
56	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
57	C₂⁵×C₁₃	C₂³	1	4	yes	—
58	C₂⁵×C₁₃	C₂³	1	2	yes	—
59	C₂⁵×C₁₃	C₂³	1	2	yes	—
60	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
61	C₂⁵×C₁₃	C₂³	1	2	yes	—
62	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
63	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic, complemented
64	C₂²×D₄×C₁₃	—	2	128	no	—
65	C₂²×D₄×C₁₃	—	2	16	no	—
66	C₂²×D₄×C₁₃	—	2	8	no	—
67	C₂²×D₄×C₁₃	—	2	8	no	—
68	C₂²×D₄×C₁₃	—	2	16	no	—
69	C₂²×D₄×C₁₃	—	2	8	no	—
70	C₂²×D₄×C₁₃	—	2	8	no	—
71	C₂²×D₄×C₁₃	—	2	32	no	—
72	C₂²×D₄×C₁₃	—	2	32	no	—
73	C₂²×D₄×C₁₃	—	2	8	no	—
74	C₂²×D₄×C₁₃	—	2	4	no	—
75	C₂²×D₄×C₁₃	—	2	8	no	—
76	C₂²×D₄×C₁₃	—	2	8	no	—
77	C₂²×D₄×C₁₃	—	4	8	no	—
78	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
79	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
85	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
86	C₂²×D₄×C₁₃	C₂³	1	8	yes	complemented
87	C₂³×C₄×C₁₃	—	2	4	no	—
88	C₂³×C₄×C₁₃	—	2	8	no	—
89	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
92	C₂³×C₄×C₁₃	C₂³	1	2	yes	complemented
93	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
94	C₁₃×#123	—	2	16	no	—
95	C₁₃×#123	—	2	16	no	—
96	C₁₃×#121	—	2	32	no	—
97	C₁₃×#120	—	2	8	no	—
98	C₁₃×#120	—	2	16	no	—
99	C₁₃×#120	—	2	8	no	—
100	C₁₃×#120	—	2	16	no	—
101	C₁₃×#120	—	2	16	no	—
102	C₁₃×#120	—	4	16	no	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
104	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	4	8	no	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
113	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
114	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
116	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
117	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
118	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
119	C₁₃×#95	C₂³	1	16	yes	complemented
120	#34980	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	8	no	—
123	C₂⁴×C₁₃	—	2	32	no	—
124	C₂⁴×C₁₃	—	2	32	no	—
125	C₂⁴×C₁₃	—	2	16	no	—
126	C₂⁴×C₁₃	—	2	8	no	—
127	C₂⁴×C₁₃	—	2	8	no	—
128	C₂⁴×C₁₃	—	2	8	no	—
129	C₂⁴×C₁₃	—	2	4	no	—
130	C₂⁴×C₁₃	—	2	4	no	—
131	C₂⁴×C₁₃	—	2	4	no	—
132	C₂⁴×C₁₃	—	2	8	no	—
133	C₂⁴×C₁₃	—	2	8	no	—
134	C₂⁴×C₁₃	—	2	2	no	—
135	C₂⁴×C₁₃	—	2	16	no	—
136	C₂⁴×C₁₃	—	2	4	no	—
137	C₂⁴×C₁₃	—	4	32	no	—
138	C₂⁴×C₁₃	—	4	4	no	—
139	C₂⁴×C₁₃	—	4	4	no	—
140	C₂⁴×C₁₃	—	4	4	no	—
141	C₂⁴×C₁₃	—	4	4	no	—
142	C₂⁴×C₁₃	—	4	8	no	—
143	C₂⁴×C₁₃	—	4	8	no	—
144	C₂⁴×C₁₃	—	4	4	no	—
145	C₂⁴×C₁₃	—	4	64	no	—
146	C₂⁴×C₁₃	—	4	64	no	—
147	C₂⁴×C₁₃	—	4	32	no	—
148	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
149	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
150	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
151	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
152	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
153	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
154	C₂⁴×C₁₃	C₂×D₄	1	8	yes	complemented
155	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
156	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
157	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
162	C₂×D₄×C₁₃	—	2	128	no	—
163	C₂×D₄×C₁₃	—	2	128	no	—
164	C₂×D₄×C₁₃	—	2	64	no	—
165	C₂×D₄×C₁₃	—	2	64	no	—
166	C₂×D₄×C₁₃	—	2	16	no	—
167	C₂×D₄×C₁₃	—	2	16	no	—
168	C₂×D₄×C₁₃	—	2	8	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	—	2	8	no	—
171	C₂×D₄×C₁₃	—	2	8	no	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	2	8	no	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	8	no	—
177	C₂×D₄×C₁₃	—	2	8	no	—
178	C₂×D₄×C₁₃	—	2	16	no	—
179	C₂×D₄×C₁₃	—	2	16	no	—
180	C₂×D₄×C₁₃	—	2	16	no	—
181	C₂×D₄×C₁₃	—	4	8	no	—
182	C₂×D₄×C₁₃	—	4	16	no	—
183	C₂×D₄×C₁₃	—	4	32	no	—
184	C₂×D₄×C₁₃	—	4	16	no	—
185	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
186	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
187	C₂²×C₄×C₁₃	—	2	32	no	—
188	C₂²×C₄×C₁₃	—	2	8	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	2	16	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	2	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	—	2	8	no	—
196	C₂²×C₄×C₁₃	—	4	4	no	—
197	C₂²×C₄×C₁₃	—	4	8	no	—
198	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	complemented
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
201	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
202	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
203	C₁₃×C₄⋊C₄	—	2	16	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	2	8	no	—
206	C₁₃×C₂²⋊C₄	—	2	8	no	—
207	C₁₃×C₂²⋊C₄	—	2	8	no	—
208	C₁₃×C₂²⋊C₄	—	2	4	no	—
209	C₁₃×C₂²⋊C₄	—	2	8	no	—
210	C₁₃×C₂²⋊C₄	—	2	16	no	—
211	C₁₃×C₂²⋊C₄	—	2	16	no	—
212	C₁₃×C₂²⋊C₄	—	2	16	no	—
213	C₁₃×C₂²⋊C₄	—	4	8	no	—
214	C₁₃×C₂²⋊C₄	—	4	16	no	—
215	C₂⁴×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#534	C₂×C₁₃	1	2	yes	complemented
217	C₂²×#120	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2849	C₂×C₁₃	1	2	yes	complemented
219	#2846	C₂×C₁₃	1	2	yes	complemented
220	#2613	C₂×C₁₃	1	4	yes	complemented
221	#2410	C₂×C₁₃	1	8	yes	complemented
222	#2405	C₂×C₁₃	1	4	yes	complemented
223	#2403	C₂×C₁₃	1	4	yes	complemented
224	#2308	C₂×C₁₃	1	2	yes	complemented
225	C₂×#379	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	32	no	—
227	C₂³×C₁₃	—	2	8	no	—
228	C₂³×C₁₃	—	2	16	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	2	32	no	—
235	C₂³×C₁₃	—	2	16	no	—
236	C₂³×C₁₃	—	2	16	no	—
237	C₂³×C₁₃	—	2	8	no	—
238	C₂³×C₁₃	—	2	16	no	—
239	C₂³×C₁₃	—	2	16	no	—
240	C₂³×C₁₃	—	2	16	no	—
241	C₂³×C₁₃	—	2	4	no	—
242	C₂³×C₁₃	—	2	4	no	—
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	4	no	—
245	C₂³×C₁₃	—	2	16	no	—
246	C₂³×C₁₃	—	2	4	no	—
247	C₂³×C₁₃	—	2	4	no	—
248	C₂³×C₁₃	—	2	2	no	—
249	C₂³×C₁₃	—	2	8	no	—
250	C₂³×C₁₃	—	4	8	no	—
251	C₂³×C₁₃	—	4	8	no	—
252	C₂³×C₁₃	—	4	8	no	—
253	C₂³×C₁₃	—	4	8	no	—
254	C₂³×C₁₃	—	4	16	no	—
255	C₂³×C₁₃	—	4	16	no	—
256	C₂³×C₁₃	—	4	32	no	—
257	C₂³×C₁₃	—	4	32	no	—
258	C₂³×C₁₃	—	4	64	no	—
259	C₂³×C₁₃	—	4	128	no	—
260	C₂³×C₁₃	—	4	128	no	—
261	C₂³×C₁₃	—	4	16	no	—
262	C₂³×C₁₃	—	4	16	no	—
263	C₂³×C₁₃	—	4	16	no	—
264	C₂³×C₁₃	—	4	16	no	—
265	C₂³×C₁₃	—	4	8	no	—
266	C₂³×C₁₃	—	4	16	no	—
267	C₂³×C₁₃	—	4	4	no	—
268	C₂³×C₁₃	—	8	8	no	—
269	C₂³×C₁₃	#120	1	16	yes	complemented
270	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
271	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
272	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
274	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
275	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
276	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
277	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
278	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
279	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
280	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
281	D₄×C₁₃	—	2	64	no	—
282	D₄×C₁₃	—	2	32	no	—
283	D₄×C₁₃	—	2	32	no	—
284	D₄×C₁₃	—	4	16	no	—
285	D₄×C₁₃	—	4	8	no	—
286	D₄×C₁₃	—	4	8	no	—
287	D₄×C₁₃	—	4	16	no	—
288	D₄×C₁₃	—	8	16	no	—
289	C₂×C₄×C₁₃	—	2	32	no	—
290	C₂×C₄×C₁₃	—	2	16	no	—
291	C₂×C₄×C₁₃	—	2	4	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	8	no	—
294	C₂×C₄×C₁₃	—	2	2	no	—
295	C₂×C₄×C₁₃	—	2	4	no	—
296	C₂×C₄×C₁₃	—	2	4	no	—
297	C₂×C₄×C₁₃	—	2	16	no	—
298	C₂×C₄×C₁₃	—	2	8	no	—
299	C₂×C₄×C₁₃	—	4	8	no	—
300	C₂×C₄×C₁₃	—	4	4	no	—
301	C₂×C₄×C₁₃	—	8	8	no	—
302	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
303	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
304	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic, complemented
305	C₂³×D₄	—	2	8	no	—
306	C₂³×D₄	—	2	16	no	—
307	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
308	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
309	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
310	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
311	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
313	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
314	#534	—	2	16	no	—
315	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
316	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
317	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
318	C₂×#120	—	2	8	no	—
319	C₂×#120	C₂²×C₁₃	1	2	yes	—
320	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
321	C₂×#120	C₂²×C₁₃	1	2	yes	complemented
322	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
323	C₂×#120	C₂²×C₁₃	1	8	yes	complemented
324	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
325	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
326	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
327	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
328	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
329	#394	C₂²×C₁₃	1	16	yes	complemented
330	#392	C₂²×C₁₃	1	16	yes	complemented
331	#386	C₂²×C₁₃	1	8	yes	complemented
332	#386	C₂²×C₁₃	1	8	yes	complemented
333	#386	C₂²×C₁₃	1	8	yes	complemented
334	#385	C₂²×C₁₃	1	8	yes	complemented
335	#381	C₂²×C₁₃	1	4	yes	complemented
336	#379	C₂²×C₁₃	1	2	yes	complemented
337	#379	C₂²×C₁₃	1	4	yes	complemented
338	#379	C₂²×C₁₃	1	8	yes	complemented
339	#379	C₂²×C₁₃	1	2	yes	complemented
340	#379	C₂²×C₁₃	1	4	yes	complemented
341	C₂²×C₁₃	—	2	32	no	—
342	C₂²×C₁₃	—	2	4	no	—
343	C₂²×C₁₃	—	2	4	no	—
344	C₂²×C₁₃	—	2	4	no	—
345	C₂²×C₁₃	—	2	4	no	—
346	C₂²×C₁₃	—	2	4	no	—
347	C₂²×C₁₃	—	2	8	no	—
348	C₂²×C₁₃	—	2	8	no	—
349	C₂²×C₁₃	—	2	16	no	—
350	C₂²×C₁₃	—	2	8	no	—
351	C₂²×C₁₃	—	2	4	no	—
352	C₂²×C₁₃	—	2	8	no	—
353	C₂²×C₁₃	—	2	4	no	—
354	C₂²×C₁₃	—	2	4	no	—
355	C₂²×C₁₃	—	2	16	no	—
356	C₂²×C₁₃	—	4	16	no	—
357	C₂²×C₁₃	—	4	32	no	—
358	C₂²×C₁₃	—	4	32	no	—
359	C₂²×C₁₃	—	4	16	no	—
360	C₂²×C₁₃	—	4	32	no	—
361	C₂²×C₁₃	—	4	64	no	—
362	C₂²×C₁₃	—	4	8	no	—
363	C₂²×C₁₃	—	4	8	no	—
364	C₂²×C₁₃	—	4	8	no	—
365	C₂²×C₁₃	—	4	2	no	—
366	C₂²×C₁₃	—	4	4	no	—
367	C₂²×C₁₃	—	4	8	no	—
368	C₂²×C₁₃	—	8	8	no	—
369	C₂²×C₁₃	C₂×#120	1	4	yes	—
370	C₂²×C₁₃	C₂×#120	1	4	yes	—
371	C₂²×C₁₃	C₂×#120	1	4	yes	—
372	C₂²×C₁₃	#534	1	8	yes	complemented
373	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
374	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
375	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
376	C₄×C₁₃	—	2	8	no	—
377	C₄×C₁₃	—	4	2	no	—
378	C₄×C₁₃	—	4	4	no	—
379	C₄×C₁₃	—	4	8	no	—
380	C₂⁵	—	2	8	no	—
381	C₂⁵	—	2	4	no	—
382	C₂⁵	—	2	8	no	—
383	C₂⁵	—	4	8	no	—
384	C₂⁵	—	4	8	no	—
385	C₂⁵	D₄×C₁₃	1	8	yes	complemented
386	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
387	C₂⁵	C₂³×C₁₃	1	4	yes	—
388	C₂⁵	C₂³×C₁₃	1	2	yes	—
389	C₂⁵	C₂³×C₁₃	1	2	yes	—
390	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
391	C₂⁵	C₂³×C₁₃	1	2	yes	—
392	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
393	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic, complemented
394	C₂²×D₄	—	2	128	no	—
395	C₂²×D₄	—	2	16	no	—
396	C₂²×D₄	—	2	8	no	—
397	C₂²×D₄	—	2	8	no	—
398	C₂²×D₄	—	2	16	no	—
399	C₂²×D₄	—	2	8	no	—
400	C₂²×D₄	—	2	8	no	—
401	C₂²×D₄	—	2	32	no	—
402	C₂²×D₄	—	2	32	no	—
403	C₂²×D₄	—	2	8	no	—
404	C₂²×D₄	—	2	4	no	—
405	C₂²×D₄	—	2	8	no	—
406	C₂²×D₄	—	2	8	no	—
407	C₂²×D₄	—	4	8	no	—
408	C₂²×D₄	D₄×C₁₃	1	16	yes	complemented
409	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
410	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
411	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
412	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
413	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
414	C₂²×D₄	C₂³×C₁₃	1	2	yes	complemented
415	C₂²×D₄	C₂³×C₁₃	1	8	yes	complemented
416	C₂²×D₄	C₂³×C₁₃	1	4	yes	complemented
417	C₂³×C₄	—	2	4	no	—
418	C₂³×C₄	—	2	8	no	—
419	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
421	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic, complemented
422	C₂³×C₄	C₂³×C₁₃	1	4	yes	complemented
423	C₂³×C₄	C₂³×C₁₃	1	2	yes	complemented
424	#123	—	2	16	no	—
425	#123	—	2	16	no	—
426	#121	—	2	32	no	—
427	#120	—	2	8	no	—
428	#120	—	2	16	no	—
429	#120	—	2	8	no	—
430	#120	—	2	16	no	—
431	#120	—	2	16	no	—
432	#120	—	4	16	no	—
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	complemented
434	C₂×C₂²⋊C₄	—	2	8	no	—
435	C₂×C₂²⋊C₄	—	2	4	no	—
436	C₂×C₂²⋊C₄	—	2	8	no	—
437	C₂×C₂²⋊C₄	—	4	8	no	—
438	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	complemented
443	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
444	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	complemented
445	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
446	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
447	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	complemented
448	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
449	#95	C₂³×C₁₃	1	16	yes	complemented
450	C₂×C₁₃	—	2	4	no	—
451	C₂×C₁₃	—	2	8	no	—
452	C₂×C₁₃	—	2	4	no	—
453	C₂×C₁₃	—	2	4	no	—
454	C₂×C₁₃	—	4	4	no	—
455	C₂×C₁₃	—	4	8	no	—
456	C₂×C₁₃	—	8	2	no	—
457	C₂×C₁₃	C₂²×#120	1	1	yes	characteristic
458	C₂×C₁₃	C₂×#534	1	2	yes	—
459	C₂×C₁₃	#3484	1	4	yes	—
460	C₂⁴	—	2	4	no	—
461	C₂⁴	—	2	8	no	—
462	C₂⁴	—	2	32	no	—
463	C₂⁴	—	2	32	no	—
464	C₂⁴	—	2	16	no	—
465	C₂⁴	—	2	8	no	—
466	C₂⁴	—	2	8	no	—
467	C₂⁴	—	2	8	no	—
468	C₂⁴	—	2	4	no	—
469	C₂⁴	—	2	4	no	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	2	8	no	—
472	C₂⁴	—	2	8	no	—
473	C₂⁴	—	2	2	no	—
474	C₂⁴	—	2	16	no	—
475	C₂⁴	—	2	4	no	—
476	C₂⁴	—	4	32	no	—
477	C₂⁴	—	4	4	no	—
478	C₂⁴	—	4	4	no	—
479	C₂⁴	—	4	4	no	—
480	C₂⁴	—	4	4	no	—
481	C₂⁴	—	4	8	no	—
482	C₂⁴	—	4	8	no	—
483	C₂⁴	—	4	4	no	—
484	C₂⁴	—	4	64	no	—
485	C₂⁴	—	4	64	no	—
486	C₂⁴	—	4	32	no	—
487	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
488	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
489	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
490	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
491	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
492	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
493	C₂⁴	C₂×D₄×C₁₃	1	8	yes	complemented
494	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
495	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
496	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
497	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
501	C₂×D₄	—	2	128	no	—
502	C₂×D₄	—	2	128	no	—
503	C₂×D₄	—	2	64	no	—
504	C₂×D₄	—	2	64	no	—
505	C₂×D₄	—	2	16	no	—
506	C₂×D₄	—	2	16	no	—
507	C₂×D₄	—	2	8	no	—
508	C₂×D₄	—	2	8	no	—
509	C₂×D₄	—	2	8	no	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	8	no	—
513	C₂×D₄	—	2	8	no	—
514	C₂×D₄	—	2	4	no	—
515	C₂×D₄	—	2	8	no	—
516	C₂×D₄	—	2	8	no	—
517	C₂×D₄	—	2	16	no	—
518	C₂×D₄	—	2	16	no	—
519	C₂×D₄	—	2	16	no	—
520	C₂×D₄	—	4	8	no	—
521	C₂×D₄	—	4	16	no	—
522	C₂×D₄	—	4	32	no	—
523	C₂×D₄	—	4	16	no	—
524	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
525	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	complemented
526	C₂²×C₄	—	2	32	no	—
527	C₂²×C₄	—	2	8	no	—
528	C₂²×C₄	—	2	4	no	—
529	C₂²×C₄	—	2	4	no	—
530	C₂²×C₄	—	2	16	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	8	no	—
535	C₂²×C₄	—	4	4	no	—
536	C₂²×C₄	—	4	8	no	—
537	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	complemented
538	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
540	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
542	C₄⋊C₄	—	2	16	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	8	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	8	no	—
549	C₂²⋊C₄	—	2	16	no	—
550	C₂²⋊C₄	—	2	16	no	—
551	C₂²⋊C₄	—	2	16	no	—
552	C₂²⋊C₄	—	4	8	no	—
553	C₂²⋊C₄	—	4	16	no	—
554	C₁₃	#34980	1	1	yes	characteristic, direct product factor, Sylow
555	C₂³	—	2	32	no	—
556	C₂³	—	2	8	no	—
557	C₂³	—	2	16	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	4	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	32	no	—
564	C₂³	—	2	16	no	—
565	C₂³	—	2	16	no	—
566	C₂³	—	2	8	no	—
567	C₂³	—	2	16	no	—
568	C₂³	—	2	16	no	—
569	C₂³	—	2	16	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	2	4	no	—
574	C₂³	—	2	16	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	8	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	8	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	8	no	—
583	C₂³	—	4	16	no	—
584	C₂³	—	4	16	no	—
585	C₂³	—	4	32	no	—
586	C₂³	—	4	32	no	—
587	C₂³	—	4	64	no	—
588	C₂³	—	4	128	no	—
589	C₂³	—	4	128	no	—
590	C₂³	—	4	16	no	—
591	C₂³	—	4	16	no	—
592	C₂³	—	4	16	no	—
593	C₂³	—	4	16	no	—
594	C₂³	—	4	8	no	—
595	C₂³	—	4	16	no	—
596	C₂³	—	4	4	no	—
597	C₂³	—	8	8	no	—
598	C₂³	C₁₃×#120	1	16	yes	complemented
599	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
600	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
601	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
602	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
603	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
604	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
605	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
606	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
607	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
608	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
609	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
610	D₄	—	2	64	no	—
611	D₄	—	2	32	no	—
612	D₄	—	2	32	no	—
613	D₄	—	4	16	no	—
614	D₄	—	4	8	no	—
615	D₄	—	4	8	no	—
616	D₄	—	4	16	no	—
617	D₄	—	8	16	no	—
618	C₂×C₄	—	2	32	no	—
619	C₂×C₄	—	2	16	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	16	no	—
627	C₂×C₄	—	2	8	no	—
628	C₂×C₄	—	4	8	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	—	8	8	no	—
631	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
632	C₂²	—	2	32	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	4	no	—
638	C₂²	—	2	8	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	2	16	no	—
641	C₂²	—	2	8	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	8	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	16	no	—
647	C₂²	—	4	16	no	—
648	C₂²	—	4	32	no	—
649	C₂²	—	4	32	no	—
650	C₂²	—	4	16	no	—
651	C₂²	—	4	32	no	—
652	C₂²	—	4	64	no	—
653	C₂²	—	4	8	no	—
654	C₂²	—	4	8	no	—
655	C₂²	—	4	8	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	4	4	no	—
658	C₂²	—	4	8	no	—
659	C₂²	—	8	8	no	—
660	C₂²	C₂×C₁₃×#120	1	4	yes	—
661	C₂²	C₂×C₁₃×#120	1	4	yes	—
662	C₂²	C₂×C₁₃×#120	1	4	yes	—
663	C₂²	C₁₃×#534	1	8	yes	complemented
664	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
665	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
666	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
667	C₄	—	2	8	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	8	no	—
671	C₂	—	2	4	no	—
672	C₂	—	2	8	no	—
673	C₂	—	2	4	no	—
674	C₂	—	2	4	no	—
675	C₂	—	4	4	no	—
676	C₂	—	4	8	no	—
677	C₂	—	8	2	no	—
678	C₂	C₂²×C₁₃×#120	1	1	yes	characteristic
679	C₂	C₂×C₁₃×#534	1	2	yes	—
680	C₂	C₁₃×#3484	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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. C₂⁴×D₄×C₁₃	C₂	semidirect
2. C₂×C₁₃×#534	C₂	semidirect
3. C₂²×C₁₃×#120	C₂	semidirect
4. C₁₃×#2849	C₂	semidirect
5. C₁₃×#2846	C₂	semidirect
6. C₁₃×#2613	C₂	semidirect
7. C₁₃×#2410	C₂	semidirect
8. C₁₃×#2405	C₂	semidirect
9. C₁₃×#2403	C₂	semidirect
10. C₁₃×#2308	C₂	semidirect
11. C₂×C₁₃×#379	C₂	semidirect
13. C₂⁶×C₁₃	C₂²	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂³×D₄×C₁₃	C₂²	semidirect
20. C₂³×D₄×C₁₃	C₂²	semidirect
21. C₂³×D₄×C₁₃	C₂²	semidirect
22. C₂⁴×C₄×C₁₃	C₂²	semidirect
24. C₂×C₁₃×#123	C₂²	semidirect
25. C₂×C₁₃×#123	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
29. C₂×C₁₃×#120	C₂²	semidirect
30. C₂×C₁₃×#120	C₂²	semidirect
31. C₂×C₁₃×#120	C₂²	semidirect
32. C₂×C₁₃×#120	C₂²	semidirect
33. C₂×C₁₃×#120	C₂²	semidirect
34. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
35. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
36. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
37. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
38. C₁₃×#394	C₂²	semidirect
39. C₁₃×#392	C₂²	semidirect
40. C₁₃×#386	C₂²	semidirect
41. C₁₃×#386	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#385	C₂²	semidirect
44. C₁₃×#381	C₂²	semidirect
45. C₁₃×#379	C₂²	semidirect
46. C₁₃×#379	C₂²	semidirect
47. C₁₃×#379	C₂²	semidirect
48. C₁₃×#379	C₂²	semidirect
49. C₁₃×#379	C₂²	semidirect
55. C₂⁵×C₁₃	D₄	semidirect
63. C₂⁵×C₁₃	C₂³	semidirect
78. C₂²×D₄×C₁₃	D₄	semidirect
84. C₂²×D₄×C₁₃	C₂³	semidirect
85. C₂²×D₄×C₁₃	C₂³	semidirect
86. C₂²×D₄×C₁₃	C₂³	semidirect
91. C₂³×C₄×C₁₃	C₂³	semidirect
92. C₂³×C₄×C₁₃	C₂³	semidirect
93. C₂³×C₄×C₁₃	C₂³	semidirect
103. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
112. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
113. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
114. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
115. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
116. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
117. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
118. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
119. C₁₃×#95	C₂³	semidirect
120. #34980	C₁₃	direct (N × H)
154. C₂⁴×C₁₃	C₂×D₄	semidirect
186. C₂×D₄×C₁₃	C₂×D₄	semidirect
198. C₂²×C₄×C₁₃	C₂×D₄	semidirect
215. C₂⁴×D₄	C₂×C₁₃	semidirect
216. C₂×#534	C₂×C₁₃	semidirect
217. C₂²×#120	C₂×C₁₃	semidirect
218. #2849	C₂×C₁₃	semidirect
219. #2846	C₂×C₁₃	semidirect
220. #2613	C₂×C₁₃	semidirect
221. #2410	C₂×C₁₃	semidirect
222. #2405	C₂×C₁₃	semidirect
223. #2403	C₂×C₁₃	semidirect
224. #2308	C₂×C₁₃	semidirect
225. C₂×#379	C₂×C₁₃	semidirect
269. C₂³×C₁₃	#120	semidirect
304. C₂⁶	C₂²×C₁₃	semidirect
309. C₂³×D₄	C₂²×C₁₃	semidirect
310. C₂³×D₄	C₂²×C₁₃	semidirect
311. C₂³×D₄	C₂²×C₁₃	semidirect
312. C₂³×D₄	C₂²×C₁₃	semidirect
313. C₂⁴×C₄	C₂²×C₁₃	semidirect
315. C₂×#123	C₂²×C₁₃	semidirect
316. C₂×#123	C₂²×C₁₃	semidirect
317. C₂×#121	C₂²×C₁₃	semidirect
320. C₂×#120	C₂²×C₁₃	semidirect
321. C₂×#120	C₂²×C₁₃	semidirect
322. C₂×#120	C₂²×C₁₃	semidirect
323. C₂×#120	C₂²×C₁₃	semidirect
324. C₂×#120	C₂²×C₁₃	semidirect
325. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
326. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
327. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
328. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
329. #394	C₂²×C₁₃	semidirect
330. #392	C₂²×C₁₃	semidirect
331. #386	C₂²×C₁₃	semidirect
332. #386	C₂²×C₁₃	semidirect
333. #386	C₂²×C₁₃	semidirect
334. #385	C₂²×C₁₃	semidirect
335. #381	C₂²×C₁₃	semidirect
336. #379	C₂²×C₁₃	semidirect
337. #379	C₂²×C₁₃	semidirect
338. #379	C₂²×C₁₃	semidirect
339. #379	C₂²×C₁₃	semidirect
340. #379	C₂²×C₁₃	semidirect
372. C₂²×C₁₃	#534	semidirect
385. C₂⁵	D₄×C₁₃	semidirect
393. C₂⁵	C₂³×C₁₃	semidirect
408. C₂²×D₄	D₄×C₁₃	semidirect
414. C₂²×D₄	C₂³×C₁₃	semidirect
415. C₂²×D₄	C₂³×C₁₃	semidirect
416. C₂²×D₄	C₂³×C₁₃	semidirect
421. C₂³×C₄	C₂³×C₁₃	semidirect
422. C₂³×C₄	C₂³×C₁₃	semidirect
423. C₂³×C₄	C₂³×C₁₃	semidirect
433. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
442. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
443. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
444. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
445. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
446. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
447. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
448. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
449. #95	C₂³×C₁₃	semidirect
493. C₂⁴	C₂×D₄×C₁₃	semidirect
525. C₂×D₄	C₂×D₄×C₁₃	semidirect
537. C₂²×C₄	C₂×D₄×C₁₃	semidirect
554. C₁₃	#34980	direct (N × H)
598. C₂³	C₁₃×#120	semidirect
663. C₂²	C₁₃×#534	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₃	2
C₂×C₁₃×#534	2
C₂²×C₁₃×#120	2
C₁₃×#2849	2
C₁₃×#2846	2
C₁₃×#2613	2
C₁₃×#2410	2
C₁₃×#2405	2
C₁₃×#2403	2
C₁₃×#2308	2
C₂×C₁₃×#379	2
#34980	13

Subgroups — C13×#34980 #15721319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34980 #15721319