Subgroups — C₁₃×#35076 #15721415

Order 3328.

3418 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2854	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2847	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2635	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2591	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2539	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2487	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2414	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2408	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2405	C₂	1	2	yes	maximal, complemented
12	C₁₃×#2403	C₂	1	2	yes	maximal, complemented
13	C₁₃×#2321	C₂	1	4	yes	maximal, complemented
14	C₁₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#123	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#121	—	2	8	no	—
22	C₂×C₁₃×#121	C₂²	1	2	yes	—
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#120	C₂²	1	4	yes	—
28	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
29	C₂×C₄×D₄×C₁₃	—	2	8	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
33	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
35	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#400	C₂²	1	4	yes	complemented
42	C₁₃×#399	C₂²	1	4	yes	complemented
43	C₁₃×#394	C₂²	1	4	yes	complemented
44	C₁₃×#394	C₂²	1	8	yes	complemented
45	C₁₃×#392	C₂²	1	4	yes	complemented
46	C₁₃×#392	C₂²	1	8	yes	complemented
47	C₁₃×#390	C₂²	1	8	yes	complemented
48	C₁₃×#390	C₂²	1	4	yes	complemented
49	C₁₃×#389	C₂²	1	4	yes	complemented
50	C₁₃×#388	C₂²	1	8	yes	complemented
51	C₁₃×#388	C₂²	1	8	yes	complemented
52	C₁₃×#386	C₂²	1	4	yes	—
53	C₁₃×#386	C₂²	1	8	yes	complemented
54	C₁₃×#386	C₂²	1	4	yes	complemented
55	C₁₃×#386	C₂²	1	4	yes	complemented
56	C₁₃×#385	C₂²	1	4	yes	complemented
57	C₁₃×#381	C₂²	1	2	yes	complemented
58	C₁₃×#380	C₂²	1	2	yes	complemented
59	C₁₃×#380	C₂²	1	2	yes	complemented
60	C₁₃×#380	C₂²	1	4	yes	complemented
61	C₁₃×#379	C₂²	1	2	yes	—
62	C₁₃×#379	C₂²	1	4	yes	complemented
63	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
64	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
65	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
66	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
67	C₂⁵×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	—	2	4	no	—
69	C₂²×D₄×C₁₃	—	2	8	no	—
70	C₂²×D₄×C₁₃	—	2	8	no	—
71	C₂²×D₄×C₁₃	—	2	4	no	—
72	C₂²×D₄×C₁₃	—	4	4	no	—
73	C₂²×D₄×C₁₃	—	4	8	no	—
74	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
81	C₂³×C₄×C₁₃	—	2	4	no	—
82	C₂³×C₄×C₁₃	—	4	4	no	—
83	C₂³×C₄×C₁₃	—	4	4	no	—
84	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
85	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
94	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
97	C₁₃×#123	—	4	8	no	—
98	C₁₃×#121	—	2	8	no	—
99	C₁₃×#121	—	2	8	no	—
100	C₁₃×#121	—	2	8	no	—
101	C₁₃×#121	—	2	8	no	—
102	C₁₃×#121	—	4	8	no	—
103	C₁₃×#120	—	2	16	no	—
104	C₁₃×#120	—	4	8	no	—
105	C₄×D₄×C₁₃	—	2	8	no	—
106	C₄×D₄×C₁₃	—	2	8	no	—
107	C₄×D₄×C₁₃	—	2	8	no	—
108	C₄×D₄×C₁₃	—	2	8	no	—
109	C₁₃×#117	—	4	4	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
129	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
130	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
131	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
132	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
133	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
134	C₂×C₄²×C₁₃	—	2	4	no	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
138	C₁₃×#95	C₂³	1	4	yes	—
139	C₁₃×#95	C₂³	1	4	yes	—
140	C₁₃×#95	C₂³	1	8	yes	—
141	C₁₃×#95	C₂³	1	8	yes	—
142	#35076	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
143	C₂⁴×C₁₃	—	2	2	no	—
144	C₂⁴×C₁₃	—	2	4	no	—
145	C₂⁴×C₁₃	—	2	4	no	—
146	C₂⁴×C₁₃	—	2	4	no	—
147	C₂⁴×C₁₃	—	2	4	no	—
148	C₂⁴×C₁₃	—	2	4	no	—
149	C₂⁴×C₁₃	—	2	8	no	—
150	C₂⁴×C₁₃	—	4	2	no	—
151	C₂⁴×C₁₃	—	4	2	no	—
152	C₂⁴×C₁₃	—	4	4	no	—
153	C₂⁴×C₁₃	—	4	4	no	—
154	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
155	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
156	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×D₄×C₁₃	—	2	32	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	4	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	8	no	—
166	C₂×D₄×C₁₃	—	2	8	no	—
167	C₂×D₄×C₁₃	—	2	8	no	—
168	C₂×D₄×C₁₃	—	2	8	no	—
169	C₂×D₄×C₁₃	—	2	16	no	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	4	no	—
172	C₂×D₄×C₁₃	—	2	4	no	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	4	4	no	—
175	C₂×D₄×C₁₃	—	4	4	no	—
176	C₂×D₄×C₁₃	—	4	4	no	—
177	C₂×D₄×C₁₃	—	4	16	no	—
178	C₂×D₄×C₁₃	—	4	8	no	—
179	C₂×D₄×C₁₃	—	4	8	no	—
180	C₂×D₄×C₁₃	—	4	32	no	—
181	C₂×D₄×C₁₃	#41	1	8	yes	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	2	2	no	—
188	C₂²×C₄×C₁₃	—	2	2	no	—
189	C₂²×C₄×C₁₃	—	2	4	no	—
190	C₂²×C₄×C₁₃	—	2	4	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	8	no	—
194	C₂²×C₄×C₁₃	—	4	16	no	—
195	C₂²×C₄×C₁₃	—	4	2	no	—
196	C₂²×C₄×C₁₃	—	4	2	no	—
197	C₂²×C₄×C₁₃	—	4	2	no	—
198	C₂²×C₄×C₁₃	—	4	4	no	—
199	C₂²×C₄×C₁₃	—	4	2	no	—
200	C₂²×C₄×C₁₃	—	4	4	no	—
201	C₂²×C₄×C₁₃	—	4	16	no	—
202	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
203	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
206	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×C₄⋊C₄	—	2	4	no	—
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	2	4	no	—
220	C₁₃×C₄⋊C₄	—	2	4	no	—
221	C₁₃×C₄⋊C₄	—	2	8	no	—
222	C₁₃×C₄⋊C₄	—	4	8	no	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	2	4	no	—
225	C₁₃×C₂²⋊C₄	—	2	8	no	—
226	C₁₃×C₂²⋊C₄	—	2	8	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	—	2	4	no	—
229	C₁₃×C₂²⋊C₄	—	2	8	no	—
230	C₁₃×C₂²⋊C₄	—	2	8	no	—
231	C₁₃×C₂²⋊C₄	—	2	16	no	—
232	C₁₃×C₂²⋊C₄	—	4	4	no	—
233	C₁₃×C₂²⋊C₄	—	4	8	no	—
234	C₁₃×C₂²⋊C₄	—	4	8	no	—
235	C₁₃×C₂²⋊C₄	—	4	8	no	—
236	C₄²×C₁₃	—	2	4	no	—
237	C₄²×C₁₃	—	2	4	no	—
238	C₄²×C₁₃	—	4	4	no	—
239	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
240	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2854	C₂×C₁₃	1	2	yes	complemented
242	#2847	C₂×C₁₃	1	2	yes	complemented
243	#2635	C₂×C₁₃	1	4	yes	complemented
244	#2591	C₂×C₁₃	1	2	yes	complemented
245	#2539	C₂×C₁₃	1	2	yes	complemented
246	#2487	C₂×C₁₃	1	2	yes	complemented
247	#2414	C₂×C₁₃	1	4	yes	complemented
248	#2408	C₂×C₁₃	1	2	yes	complemented
249	#2405	C₂×C₁₃	1	2	yes	complemented
250	#2403	C₂×C₁₃	1	2	yes	complemented
251	#2321	C₂×C₁₃	1	4	yes	complemented
252	#2280	C₂×C₁₃	1	1	yes	characteristic, complemented
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	2	2	no	—
255	C₂³×C₁₃	—	2	2	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	2	8	no	—
258	C₂³×C₁₃	—	2	8	no	—
259	C₂³×C₁₃	—	2	8	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	—	2	4	no	—
265	C₂³×C₁₃	—	2	4	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	4	no	—
268	C₂³×C₁₃	—	2	8	no	—
269	C₂³×C₁₃	—	2	4	no	—
270	C₂³×C₁₃	—	2	8	no	—
271	C₂³×C₁₃	—	2	4	no	—
272	C₂³×C₁₃	—	4	4	no	—
273	C₂³×C₁₃	—	4	16	no	—
274	C₂³×C₁₃	—	4	16	no	—
275	C₂³×C₁₃	—	4	4	no	—
276	C₂³×C₁₃	—	4	8	no	—
277	C₂³×C₁₃	—	4	8	no	—
278	C₂³×C₁₃	—	4	4	no	—
279	C₂³×C₁₃	—	4	8	no	—
280	C₂³×C₁₃	—	8	16	no	—
281	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
283	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂³×C₁₃	C₂×#41	1	4	yes	—
285	C₂³×C₁₃	C₂×#41	1	4	yes	—
286	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
287	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
288	D₄×C₁₃	—	2	16	no	—
289	D₄×C₁₃	—	2	16	no	—
290	D₄×C₁₃	—	4	8	no	—
291	D₄×C₁₃	—	4	16	no	—
292	D₄×C₁₃	—	4	16	no	—
293	D₄×C₁₃	—	4	8	no	—
294	D₄×C₁₃	—	8	16	no	—
295	C₂×C₄×C₁₃	—	2	8	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	2	no	—
298	C₂×C₄×C₁₃	—	2	2	no	—
299	C₂×C₄×C₁₃	—	2	2	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	8	no	—
302	C₂×C₄×C₁₃	—	2	8	no	—
303	C₂×C₄×C₁₃	—	2	8	no	—
304	C₂×C₄×C₁₃	—	2	2	no	—
305	C₂×C₄×C₁₃	—	2	2	no	—
306	C₂×C₄×C₁₃	—	2	4	no	—
307	C₂×C₄×C₁₃	—	2	8	no	—
308	C₂×C₄×C₁₃	—	2	8	no	—
309	C₂×C₄×C₁₃	—	2	8	no	—
310	C₂×C₄×C₁₃	—	2	4	no	—
311	C₂×C₄×C₁₃	—	2	4	no	—
312	C₂×C₄×C₁₃	—	2	4	no	—
313	C₂×C₄×C₁₃	—	2	4	no	—
314	C₂×C₄×C₁₃	—	4	4	no	—
315	C₂×C₄×C₁₃	—	4	4	no	—
316	C₂×C₄×C₁₃	—	4	4	no	—
317	C₂×C₄×C₁₃	—	4	8	no	—
318	C₂×C₄×C₁₃	—	4	4	no	—
319	C₂×C₄×C₁₃	—	4	8	no	—
320	C₂×C₄×C₁₃	—	4	4	no	—
321	C₂×C₄×C₁₃	—	4	8	no	—
322	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
327	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
328	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
330	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
331	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
333	C₂×#123	C₂²×C₁₃	1	4	yes	complemented
334	C₂×#121	—	2	8	no	—
335	C₂×#121	C₂²×C₁₃	1	2	yes	—
336	C₂×#121	C₂²×C₁₃	1	2	yes	—
337	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
338	C₂×#121	C₂²×C₁₃	1	2	yes	complemented
339	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
340	C₂×#120	C₂²×C₁₃	1	4	yes	—
341	C₂×#120	C₂²×C₁₃	1	4	yes	complemented
342	C₂×C₄×D₄	—	2	8	no	—
343	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
344	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
345	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
346	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
347	C₂×#117	C₂²×C₁₃	1	2	yes	complemented
348	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
349	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
350	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
352	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
354	#400	C₂²×C₁₃	1	4	yes	complemented
355	#399	C₂²×C₁₃	1	4	yes	complemented
356	#394	C₂²×C₁₃	1	4	yes	complemented
357	#394	C₂²×C₁₃	1	8	yes	complemented
358	#392	C₂²×C₁₃	1	8	yes	complemented
359	#392	C₂²×C₁₃	1	4	yes	complemented
360	#390	C₂²×C₁₃	1	8	yes	complemented
361	#390	C₂²×C₁₃	1	4	yes	complemented
362	#389	C₂²×C₁₃	1	4	yes	complemented
363	#388	C₂²×C₁₃	1	8	yes	complemented
364	#388	C₂²×C₁₃	1	8	yes	complemented
365	#386	C₂²×C₁₃	1	4	yes	—
366	#386	C₂²×C₁₃	1	8	yes	complemented
367	#386	C₂²×C₁₃	1	4	yes	complemented
368	#386	C₂²×C₁₃	1	4	yes	complemented
369	#385	C₂²×C₁₃	1	4	yes	complemented
370	#381	C₂²×C₁₃	1	2	yes	complemented
371	#380	C₂²×C₁₃	1	2	yes	complemented
372	#380	C₂²×C₁₃	1	4	yes	complemented
373	#380	C₂²×C₁₃	1	2	yes	complemented
374	#379	C₂²×C₁₃	1	2	yes	—
375	#379	C₂²×C₁₃	1	4	yes	complemented
376	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
377	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	complemented
378	C₂²×C₁₃	—	2	2	no	—
379	C₂²×C₁₃	—	2	2	no	—
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	8	no	—
383	C₂²×C₁₃	—	2	8	no	—
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	2	2	no	—
387	C₂²×C₁₃	—	2	2	no	—
388	C₂²×C₁₃	—	2	8	no	—
389	C₂²×C₁₃	—	4	16	no	—
390	C₂²×C₁₃	—	4	16	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	—	4	2	no	—
393	C₂²×C₁₃	—	4	4	no	—
394	C₂²×C₁₃	—	4	4	no	—
395	C₂²×C₁₃	—	4	4	no	—
396	C₂²×C₁₃	—	4	4	no	—
397	C₂²×C₁₃	—	4	4	no	—
398	C₂²×C₁₃	—	4	8	no	—
399	C₂²×C₁₃	—	4	8	no	—
400	C₂²×C₁₃	—	8	16	no	—
401	C₂²×C₁₃	#525	1	4	yes	—
402	C₂²×C₁₃	#535	1	4	yes	—
403	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
404	C₂²×C₁₃	C₂²×#41	1	2	yes	—
405	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
406	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
407	C₄×C₁₃	—	2	4	no	—
408	C₄×C₁₃	—	2	2	no	—
409	C₄×C₁₃	—	2	2	no	—
410	C₄×C₁₃	—	2	2	no	—
411	C₄×C₁₃	—	4	2	no	—
412	C₄×C₁₃	—	4	2	no	—
413	C₄×C₁₃	—	4	4	no	—
414	C₄×C₁₃	—	4	8	no	—
415	C₄×C₁₃	#534	1	4	yes	—
416	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
417	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
418	C₂⁵	C₂³×C₁₃	1	2	yes	—
419	C₂²×D₄	—	2	4	no	—
420	C₂²×D₄	—	2	8	no	—
421	C₂²×D₄	—	2	8	no	—
422	C₂²×D₄	—	2	4	no	—
423	C₂²×D₄	—	4	4	no	—
424	C₂²×D₄	—	4	8	no	—
425	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
426	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
427	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
428	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
429	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
430	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
431	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
432	C₂³×C₄	—	2	4	no	—
433	C₂³×C₄	—	4	4	no	—
434	C₂³×C₄	—	4	4	no	—
435	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
436	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
439	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
443	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
444	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
445	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
448	#123	—	4	8	no	—
449	#121	—	2	8	no	—
450	#121	—	2	8	no	—
451	#121	—	2	8	no	—
452	#121	—	2	8	no	—
453	#121	—	4	8	no	—
454	#120	—	2	16	no	—
455	#120	—	4	8	no	—
456	C₄×D₄	—	2	8	no	—
457	C₄×D₄	—	2	8	no	—
458	C₄×D₄	—	2	8	no	—
459	C₄×D₄	—	2	8	no	—
460	#117	—	4	4	no	—
461	C₂×C₄⋊C₄	—	2	4	no	—
462	C₂×C₄⋊C₄	—	2	4	no	—
463	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
469	C₂×C₂²⋊C₄	—	2	4	no	—
470	C₂×C₂²⋊C₄	—	2	4	no	—
471	C₂×C₂²⋊C₄	—	2	8	no	—
472	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
477	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
478	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
485	C₂×C₄²	—	2	4	no	—
486	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
487	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
488	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
489	#95	C₂³×C₁₃	1	4	yes	—
490	#95	C₂³×C₁₃	1	4	yes	—
491	#95	C₂³×C₁₃	1	8	yes	—
492	#95	C₂³×C₁₃	1	8	yes	—
493	C₂×C₁₃	—	2	4	no	—
494	C₂×C₁₃	—	2	4	no	—
495	C₂×C₁₃	—	4	2	no	—
496	C₂×C₁₃	—	4	4	no	—
497	C₂×C₁₃	—	8	4	no	—
498	C₂×C₁₃	C₂×#525	1	1	yes	characteristic
499	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
500	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
501	C₂×C₁₃	#3519	1	4	yes	—
502	C₂⁴	—	2	2	no	—
503	C₂⁴	—	2	4	no	—
504	C₂⁴	—	2	4	no	—
505	C₂⁴	—	2	4	no	—
506	C₂⁴	—	2	4	no	—
507	C₂⁴	—	2	4	no	—
508	C₂⁴	—	2	8	no	—
509	C₂⁴	—	4	2	no	—
510	C₂⁴	—	4	2	no	—
511	C₂⁴	—	4	4	no	—
512	C₂⁴	—	4	4	no	—
513	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
514	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
515	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
516	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
517	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
518	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
519	C₂×D₄	—	2	32	no	—
520	C₂×D₄	—	2	4	no	—
521	C₂×D₄	—	2	4	no	—
522	C₂×D₄	—	2	4	no	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	8	no	—
528	C₂×D₄	—	2	16	no	—
529	C₂×D₄	—	2	4	no	—
530	C₂×D₄	—	2	4	no	—
531	C₂×D₄	—	2	4	no	—
532	C₂×D₄	—	2	8	no	—
533	C₂×D₄	—	4	4	no	—
534	C₂×D₄	—	4	4	no	—
535	C₂×D₄	—	4	4	no	—
536	C₂×D₄	—	4	16	no	—
537	C₂×D₄	—	4	8	no	—
538	C₂×D₄	—	4	8	no	—
539	C₂×D₄	—	4	32	no	—
540	C₂×D₄	C₁₃×#41	1	8	yes	—
541	C₂²×C₄	—	2	2	no	—
542	C₂²×C₄	—	2	4	no	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	4	no	—
545	C₂²×C₄	—	2	4	no	—
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	4	no	—
549	C₂²×C₄	—	2	4	no	—
550	C₂²×C₄	—	2	4	no	—
551	C₂²×C₄	—	2	4	no	—
552	C₂²×C₄	—	2	8	no	—
553	C₂²×C₄	—	4	16	no	—
554	C₂²×C₄	—	4	2	no	—
555	C₂²×C₄	—	4	2	no	—
556	C₂²×C₄	—	4	2	no	—
557	C₂²×C₄	—	4	4	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	4	16	no	—
561	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
562	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
563	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
564	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
565	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
566	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
567	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
568	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
569	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
570	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
571	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
573	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
574	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
576	C₄⋊C₄	—	2	4	no	—
577	C₄⋊C₄	—	2	4	no	—
578	C₄⋊C₄	—	2	4	no	—
579	C₄⋊C₄	—	2	4	no	—
580	C₄⋊C₄	—	2	8	no	—
581	C₄⋊C₄	—	4	8	no	—
582	C₂²⋊C₄	—	2	4	no	—
583	C₂²⋊C₄	—	2	4	no	—
584	C₂²⋊C₄	—	2	8	no	—
585	C₂²⋊C₄	—	2	8	no	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	4	no	—
588	C₂²⋊C₄	—	2	8	no	—
589	C₂²⋊C₄	—	2	8	no	—
590	C₂²⋊C₄	—	2	16	no	—
591	C₂²⋊C₄	—	4	4	no	—
592	C₂²⋊C₄	—	4	8	no	—
593	C₂²⋊C₄	—	4	8	no	—
594	C₂²⋊C₄	—	4	8	no	—
595	C₄²	—	2	4	no	—
596	C₄²	—	2	4	no	—
597	C₄²	—	4	4	no	—
598	C₁₃	#35076	1	1	yes	characteristic, direct product factor, Sylow
599	C₂³	—	2	2	no	—
600	C₂³	—	2	2	no	—
601	C₂³	—	2	2	no	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	8	no	—
604	C₂³	—	2	8	no	—
605	C₂³	—	2	8	no	—
606	C₂³	—	2	2	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	4	no	—
611	C₂³	—	2	4	no	—
612	C₂³	—	2	2	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	8	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	8	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	4	4	no	—
619	C₂³	—	4	16	no	—
620	C₂³	—	4	16	no	—
621	C₂³	—	4	4	no	—
622	C₂³	—	4	8	no	—
623	C₂³	—	4	8	no	—
624	C₂³	—	4	4	no	—
625	C₂³	—	4	8	no	—
626	C₂³	—	8	16	no	—
627	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
628	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
629	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
630	C₂³	C₂×C₁₃×#41	1	4	yes	—
631	C₂³	C₂×C₁₃×#41	1	4	yes	—
632	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
633	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
634	D₄	—	2	16	no	—
635	D₄	—	2	16	no	—
636	D₄	—	4	8	no	—
637	D₄	—	4	16	no	—
638	D₄	—	4	16	no	—
639	D₄	—	4	8	no	—
640	D₄	—	8	16	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	8	no	—
648	C₂×C₄	—	2	8	no	—
649	C₂×C₄	—	2	8	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	8	no	—
655	C₂×C₄	—	2	8	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	2	4	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	8	no	—
664	C₂×C₄	—	4	4	no	—
665	C₂×C₄	—	4	8	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	8	no	—
668	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
669	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
670	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
671	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
672	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
673	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
674	C₂²	—	2	8	no	—
675	C₂²	—	2	8	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	2	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	2	8	no	—
681	C₂²	—	2	2	no	—
682	C₂²	—	2	4	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	4	16	no	—
686	C₂²	—	4	16	no	—
687	C₂²	—	4	4	no	—
688	C₂²	—	4	4	no	—
689	C₂²	—	4	2	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	8	no	—
693	C₂²	—	4	4	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	8	16	no	—
697	C₂²	C₁₃×#525	1	4	yes	—
698	C₂²	C₁₃×#535	1	4	yes	—
699	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
700	C₂²	C₂²×C₁₃×#41	1	2	yes	—
701	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
702	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
703	C₄	—	2	4	no	—
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	4	8	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	4	no	—
711	C₄	C₁₃×#534	1	4	yes	—
712	C₂	—	2	4	no	—
713	C₂	—	2	4	no	—
714	C₂	—	4	4	no	—
715	C₂	—	4	2	no	—
716	C₂	—	8	4	no	—
717	C₂	C₂×C₁₃×#525	1	1	yes	characteristic
718	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
719	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
720	C₂	C₁₃×#3519	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. C₂²×C₁₃×#121	C₂	semidirect
2. C₂²×C₄×D₄×C₁₃	C₂	semidirect
3. C₁₃×#2854	C₂	semidirect
4. C₁₃×#2847	C₂	semidirect
5. C₁₃×#2635	C₂	semidirect
6. C₁₃×#2591	C₂	semidirect
7. C₁₃×#2539	C₂	semidirect
8. C₁₃×#2487	C₂	semidirect
9. C₁₃×#2414	C₂	semidirect
10. C₁₃×#2408	C₂	semidirect
11. C₁₃×#2405	C₂	semidirect
12. C₁₃×#2403	C₂	semidirect
13. C₁₃×#2321	C₂	semidirect
14. C₁₃×#2280	C₂	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂⁴×C₄×C₁₃	C₂²	semidirect
20. C₂×C₁₃×#123	C₂²	semidirect
24. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
28. C₂×C₁₃×#120	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₂×C₄×D₄×C₁₃	C₂²	semidirect
34. C₂×C₁₃×#117	C₂²	semidirect
35. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
36. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
38. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
39. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
40. C₂²×C₄²×C₁₃	C₂²	semidirect
41. C₁₃×#400	C₂²	semidirect
42. C₁₃×#399	C₂²	semidirect
43. C₁₃×#394	C₂²	semidirect
44. C₁₃×#394	C₂²	semidirect
45. C₁₃×#392	C₂²	semidirect
46. C₁₃×#392	C₂²	semidirect
47. C₁₃×#390	C₂²	semidirect
48. C₁₃×#390	C₂²	semidirect
49. C₁₃×#389	C₂²	semidirect
50. C₁₃×#388	C₂²	semidirect
51. C₁₃×#388	C₂²	semidirect
53. C₁₃×#386	C₂²	semidirect
54. C₁₃×#386	C₂²	semidirect
55. C₁₃×#386	C₂²	semidirect
56. C₁₃×#385	C₂²	semidirect
57. C₁₃×#381	C₂²	semidirect
58. C₁₃×#380	C₂²	semidirect
59. C₁₃×#380	C₂²	semidirect
60. C₁₃×#380	C₂²	semidirect
62. C₁₃×#379	C₂²	semidirect
63. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
64. C₄×C₁₃×C₂²⋊C₄	C₂²	semidirect
84. C₂³×C₄×C₁₃	D₄	semidirect
142. #35076	C₁₃	direct (N × H)
239. C₂²×#121	C₂×C₁₃	semidirect
240. C₂²×C₄×D₄	C₂×C₁₃	semidirect
241. #2854	C₂×C₁₃	semidirect
242. #2847	C₂×C₁₃	semidirect
243. #2635	C₂×C₁₃	semidirect
244. #2591	C₂×C₁₃	semidirect
245. #2539	C₂×C₁₃	semidirect
246. #2487	C₂×C₁₃	semidirect
247. #2414	C₂×C₁₃	semidirect
248. #2408	C₂×C₁₃	semidirect
249. #2405	C₂×C₁₃	semidirect
250. #2403	C₂×C₁₃	semidirect
251. #2321	C₂×C₁₃	semidirect
252. #2280	C₂×C₁₃	semidirect
330. C₂³×D₄	C₂²×C₁₃	semidirect
332. C₂⁴×C₄	C₂²×C₁₃	semidirect
333. C₂×#123	C₂²×C₁₃	semidirect
337. C₂×#121	C₂²×C₁₃	semidirect
338. C₂×#121	C₂²×C₁₃	semidirect
339. C₂×#121	C₂²×C₁₃	semidirect
341. C₂×#120	C₂²×C₁₃	semidirect
345. C₂×C₄×D₄	C₂²×C₁₃	semidirect
346. C₂×C₄×D₄	C₂²×C₁₃	semidirect
347. C₂×#117	C₂²×C₁₃	semidirect
348. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
349. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
351. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
352. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
353. C₂²×C₄²	C₂²×C₁₃	semidirect
354. #400	C₂²×C₁₃	semidirect
355. #399	C₂²×C₁₃	semidirect
356. #394	C₂²×C₁₃	semidirect
357. #394	C₂²×C₁₃	semidirect
358. #392	C₂²×C₁₃	semidirect
359. #392	C₂²×C₁₃	semidirect
360. #390	C₂²×C₁₃	semidirect
361. #390	C₂²×C₁₃	semidirect
362. #389	C₂²×C₁₃	semidirect
363. #388	C₂²×C₁₃	semidirect
364. #388	C₂²×C₁₃	semidirect
366. #386	C₂²×C₁₃	semidirect
367. #386	C₂²×C₁₃	semidirect
368. #386	C₂²×C₁₃	semidirect
369. #385	C₂²×C₁₃	semidirect
370. #381	C₂²×C₁₃	semidirect
371. #380	C₂²×C₁₃	semidirect
372. #380	C₂²×C₁₃	semidirect
373. #380	C₂²×C₁₃	semidirect
375. #379	C₂²×C₁₃	semidirect
376. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
377. C₄×C₂²⋊C₄	C₂²×C₁₃	semidirect
435. C₂³×C₄	D₄×C₁₃	semidirect
598. C₁₃	#35076	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×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2854	2
C₁₃×#2847	2
C₁₃×#2635	2
C₁₃×#2591	2
C₁₃×#2539	2
C₁₃×#2487	2
C₁₃×#2414	2
C₁₃×#2408	2
C₁₃×#2405	2
C₁₃×#2403	2
C₁₃×#2321	2
C₁₃×#2280	2
#35076	13

Subgroups — C13×#35076 #15721415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#35076 #15721415