Subgroups — C₁₃×#3535 #13112593

Order 1664.

1038 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#563	C₂	1	2	yes	maximal, complemented
2	C₁₃×#562	C₂	1	2	yes	maximal, complemented
3	C₁₃×#554	C₂	1	2	yes	maximal, complemented
4	C₁₃×#552	C₂	1	2	yes	maximal, complemented
5	C₁₃×#551	C₂	1	2	yes	maximal, complemented
6	C₁₃×#551	C₂	1	2	yes	maximal, complemented
7	C₁₃×#547	C₂	1	2	yes	maximal, complemented
8	C₁₃×#546	C₂	1	2	yes	maximal, complemented
9	C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#542	C₂	1	2	yes	maximal, complemented
12	C₁₃×#539	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#539	C₂	1	2	yes	maximal, complemented
14	C₁₃×#539	C₂	1	2	yes	maximal, complemented
15	C₁₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₃×#536	C₂	1	2	yes	maximal, complemented
17	C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#41	C₂²	1	2	yes	—
21	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
22	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
27	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
28	C₁₃×#126	C₂²	1	2	yes	complemented
29	C₁₃×#126	C₂²	1	2	yes	complemented
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#126	C₂²	1	2	yes	complemented
32	C₁₃×#126	C₂²	1	2	yes	complemented
33	C₁₃×#126	C₂²	1	2	yes	complemented
34	C₁₃×#125	C₂²	1	2	yes	complemented
35	C₁₃×#125	C₂²	1	2	yes	complemented
36	C₁₃×#125	C₂²	1	2	yes	complemented
37	C₁₃×#125	C₂²	1	2	yes	complemented
38	C₁₃×#125	C₂²	1	2	yes	complemented
39	C₁₃×#124	C₂²	1	2	yes	—
40	C₁₃×#124	C₂²	1	2	yes	complemented
41	C₁₃×#124	C₂²	1	2	yes	complemented
42	C₁₃×#124	C₂²	1	2	yes	complemented
43	C₁₃×#123	C₂²	1	2	yes	—
44	C₁₃×#123	C₂²	1	2	yes	—
45	C₁₃×#123	C₂²	1	2	yes	—
46	C₁₃×#123	C₂²	1	2	yes	—
47	C₁₃×#123	C₂²	1	2	yes	—
48	C₁₃×#123	C₂²	1	2	yes	—
49	C₁₃×#123	C₂²	1	2	yes	—
50	C₁₃×#123	C₂²	1	2	yes	complemented
51	C₁₃×#123	C₂²	1	2	yes	complemented
52	C₁₃×#123	C₂²	1	2	yes	complemented
53	C₁₃×#123	C₂²	1	2	yes	complemented
54	C₁₃×#123	C₂²	1	2	yes	complemented
55	C₁₃×#123	C₂²	1	2	yes	complemented
56	C₁₃×#123	C₂²	1	2	yes	complemented
57	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
60	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
61	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
62	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
63	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
67	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
70	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
71	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
72	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
73	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₁₃×#121	C₂²	1	1	yes	characteristic
78	C₁₃×#121	C₂²	1	2	yes	—
79	C₁₃×#121	C₂²	1	2	yes	—
80	C₁₃×#121	C₂²	1	2	yes	—
81	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
82	C₁₃×#121	C₂²	1	2	yes	complemented
83	C₁₃×#120	C₂²	1	2	yes	—
84	C₁₃×#120	C₂²	1	2	yes	—
85	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
86	C₄×D₄×C₁₃	C₂²	1	2	yes	—
87	C₄×D₄×C₁₃	C₂²	1	2	yes	—
88	C₄×D₄×C₁₃	C₂²	1	2	yes	—
89	C₄×D₄×C₁₃	C₂²	1	2	yes	—
90	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
91	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
92	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
93	C₁₃×#117	C₂²	1	2	yes	—
94	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
95	C₁₃×#117	C₂²	1	2	yes	complemented
96	C₁₃×#117	C₂²	1	2	yes	complemented
97	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
101	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
102	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
109	C₁₃×#41	—	4	4	no	—
110	C₁₃×#41	—	4	2	no	—
111	C₂×Q₈×C₁₃	—	4	2	no	—
112	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
113	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
115	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
117	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂×D₄×C₁₃	C₂³	1	2	yes	—
121	C₂×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂×D₄×C₁₃	C₂³	1	2	yes	—
123	C₂×D₄×C₁₃	C₂³	1	2	yes	—
124	C₂×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	—	4	2	no	—
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
150	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
151	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₄²×C₁₃	C₂³	1	2	yes	—
195	C₄²×C₁₃	C₂³	1	2	yes	—
196	C₄²×C₁₃	C₂³	1	2	yes	—
197	C₄²×C₁₃	C₂³	1	2	yes	—
198	C₄²×C₁₃	C₂³	1	2	yes	—
199	#3535	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	2	2	no	—
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	—	4	1	no	—
206	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₁₃	C₂⁴	1	2	yes	—
208	C₂³×C₁₃	C₂⁴	1	2	yes	—
209	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
211	Q₈×C₁₃	—	4	1	no	—
212	Q₈×C₁₃	—	4	2	no	—
213	Q₈×C₁₃	—	4	1	no	—
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	4	1	no	—
216	Q₈×C₁₃	—	4	2	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	4	2	no	—
223	D₄×C₁₃	—	4	1	no	—
224	D₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	#563	C₂×C₁₃	1	2	yes	complemented
256	#562	C₂×C₁₃	1	2	yes	complemented
257	#554	C₂×C₁₃	1	2	yes	complemented
258	#552	C₂×C₁₃	1	2	yes	complemented
259	#551	C₂×C₁₃	1	2	yes	complemented
260	#551	C₂×C₁₃	1	2	yes	complemented
261	#547	C₂×C₁₃	1	2	yes	complemented
262	#546	C₂×C₁₃	1	2	yes	complemented
263	#544	C₂×C₁₃	1	1	yes	characteristic, complemented
264	#543	C₂×C₁₃	1	1	yes	characteristic, complemented
265	#542	C₂×C₁₃	1	2	yes	complemented
266	#539	C₂×C₁₃	1	1	yes	characteristic, complemented
267	#539	C₂×C₁₃	1	2	yes	complemented
268	#539	C₂×C₁₃	1	2	yes	complemented
269	#538	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#536	C₂×C₁₃	1	2	yes	complemented
271	#525	C₂×C₁₃	1	1	yes	characteristic, complemented
272	C₂×#123	C₂×C₁₃	1	1	yes	characteristic, complemented
273	C₂×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	1	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	2	1	no	—
287	C₂²×C₁₃	—	4	4	no	—
288	C₂²×C₁₃	—	8	2	no	—
289	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
290	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
291	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
292	C₄×C₁₃	—	2	1	no	—
293	C₄×C₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₂×#41	C₂²×C₁₃	1	2	yes	—
307	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
309	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
311	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
312	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
313	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
314	#126	C₂²×C₁₃	1	2	yes	complemented
315	#126	C₂²×C₁₃	1	2	yes	complemented
316	#126	C₂²×C₁₃	1	2	yes	complemented
317	#126	C₂²×C₁₃	1	2	yes	complemented
318	#126	C₂²×C₁₃	1	2	yes	complemented
319	#126	C₂²×C₁₃	1	2	yes	complemented
320	#125	C₂²×C₁₃	1	2	yes	complemented
321	#125	C₂²×C₁₃	1	2	yes	complemented
322	#125	C₂²×C₁₃	1	2	yes	complemented
323	#125	C₂²×C₁₃	1	2	yes	complemented
324	#125	C₂²×C₁₃	1	2	yes	complemented
325	#124	C₂²×C₁₃	1	2	yes	—
326	#124	C₂²×C₁₃	1	2	yes	complemented
327	#124	C₂²×C₁₃	1	2	yes	complemented
328	#124	C₂²×C₁₃	1	2	yes	complemented
329	#123	C₂²×C₁₃	1	2	yes	—
330	#123	C₂²×C₁₃	1	2	yes	—
331	#123	C₂²×C₁₃	1	2	yes	—
332	#123	C₂²×C₁₃	1	2	yes	—
333	#123	C₂²×C₁₃	1	2	yes	—
334	#123	C₂²×C₁₃	1	2	yes	—
335	#123	C₂²×C₁₃	1	2	yes	—
336	#123	C₂²×C₁₃	1	2	yes	complemented
337	#123	C₂²×C₁₃	1	2	yes	complemented
338	#123	C₂²×C₁₃	1	2	yes	complemented
339	#123	C₂²×C₁₃	1	2	yes	complemented
340	#123	C₂²×C₁₃	1	2	yes	complemented
341	#123	C₂²×C₁₃	1	2	yes	complemented
342	#123	C₂²×C₁₃	1	2	yes	complemented
343	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
344	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
345	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
346	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
348	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
349	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
350	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
351	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
352	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
354	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
355	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
356	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
357	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
358	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
359	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
360	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
361	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
362	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
363	#121	C₂²×C₁₃	1	1	yes	characteristic
364	#121	C₂²×C₁₃	1	2	yes	—
365	#121	C₂²×C₁₃	1	2	yes	—
366	#121	C₂²×C₁₃	1	2	yes	—
367	#121	C₂²×C₁₃	1	1	yes	characteristic, complemented
368	#121	C₂²×C₁₃	1	2	yes	complemented
369	#120	C₂²×C₁₃	1	2	yes	—
370	#120	C₂²×C₁₃	1	2	yes	—
371	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
372	C₄×D₄	C₂²×C₁₃	1	2	yes	—
373	C₄×D₄	C₂²×C₁₃	1	2	yes	—
374	C₄×D₄	C₂²×C₁₃	1	2	yes	—
375	C₄×D₄	C₂²×C₁₃	1	2	yes	—
376	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
377	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
378	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
379	#117	C₂²×C₁₃	1	2	yes	—
380	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
381	#117	C₂²×C₁₃	1	2	yes	complemented
382	#117	C₂²×C₁₃	1	2	yes	complemented
383	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
386	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
387	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
388	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
390	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
393	C₂×C₁₃	—	2	2	no	—
394	C₂×C₁₃	—	2	2	no	—
395	C₂×C₁₃	—	4	2	no	—
396	C₂×C₁₃	—	4	1	no	—
397	C₂×C₁₃	—	4	2	no	—
398	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
399	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
400	C₂×C₁₃	#585	1	1	yes	characteristic
401	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
402	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
403	#41	—	4	4	no	—
404	#41	—	4	2	no	—
405	C₂×Q₈	—	4	2	no	—
406	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
407	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
409	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
411	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	C₂³×C₁₃	1	2	yes	—
414	C₂×D₄	C₂³×C₁₃	1	2	yes	—
415	C₂×D₄	C₂³×C₁₃	1	2	yes	—
416	C₂×D₄	C₂³×C₁₃	1	2	yes	—
417	C₂×D₄	C₂³×C₁₃	1	2	yes	—
418	C₂×D₄	C₂³×C₁₃	1	2	yes	—
419	C₂×D₄	C₂³×C₁₃	1	2	yes	—
420	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
430	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
431	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
435	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
436	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
438	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
441	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
442	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
444	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
447	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
450	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
452	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
453	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
456	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
457	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
458	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
459	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
461	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
462	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
463	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
464	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
465	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
467	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
468	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
469	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
470	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
471	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
472	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
473	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
474	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
475	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
476	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
477	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
478	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
480	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
481	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
485	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
486	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
488	C₄²	C₂³×C₁₃	1	2	yes	—
489	C₄²	C₂³×C₁₃	1	2	yes	—
490	C₄²	C₂³×C₁₃	1	2	yes	—
491	C₄²	C₂³×C₁₃	1	2	yes	—
492	C₄²	C₂³×C₁₃	1	2	yes	—
493	C₁₃	#3535	1	1	yes	characteristic, direct product factor, Sylow
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
501	C₂³	C₂⁴×C₁₃	1	2	yes	—
502	C₂³	C₂⁴×C₁₃	1	2	yes	—
503	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
504	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	2	4	no	—
513	D₄	—	2	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
536	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
537	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
538	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
539	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
540	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
541	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
542	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
543	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
544	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
545	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
546	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
547	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	1	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	8	2	no	—
564	C₂²	C₁₃×H(5,𝔽₂)	1	2	yes	—
565	C₂²	C₁₃×2₋¹⁺⁴	1	2	yes	—
566	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	2	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₂	—	2	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
587	C₂	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
588	C₂	C₁₃×#585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₃×#563	C₂	semidirect
2. C₁₃×#562	C₂	semidirect
3. C₁₃×#554	C₂	semidirect
4. C₁₃×#552	C₂	semidirect
5. C₁₃×#551	C₂	semidirect
6. C₁₃×#551	C₂	semidirect
7. C₁₃×#547	C₂	semidirect
8. C₁₃×#546	C₂	semidirect
9. C₁₃×#544	C₂	semidirect
10. C₁₃×#543	C₂	semidirect
11. C₁₃×#542	C₂	semidirect
12. C₁₃×#539	C₂	semidirect
13. C₁₃×#539	C₂	semidirect
14. C₁₃×#539	C₂	semidirect
15. C₁₃×#538	C₂	semidirect
16. C₁₃×#536	C₂	semidirect
17. C₁₃×#525	C₂	semidirect
18. C₂×C₁₃×#123	C₂	semidirect
19. C₂×C₁₃×C₂²⋊Q₈	C₂	semidirect
21. C₂×C₁₃×#41	C₂²	semidirect
22. C₂²×Q₈×C₁₃	C₂²	semidirect
25. C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×C₄⋊Q₈	C₂²	semidirect
27. C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₁₃×#126	C₂²	semidirect
29. C₁₃×#126	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#126	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#126	C₂²	semidirect
34. C₁₃×#125	C₂²	semidirect
35. C₁₃×#125	C₂²	semidirect
36. C₁₃×#125	C₂²	semidirect
37. C₁₃×#125	C₂²	semidirect
38. C₁₃×#125	C₂²	semidirect
40. C₁₃×#124	C₂²	semidirect
41. C₁₃×#124	C₂²	semidirect
42. C₁₃×#124	C₂²	semidirect
50. C₁₃×#123	C₂²	semidirect
51. C₁₃×#123	C₂²	semidirect
52. C₁₃×#123	C₂²	semidirect
53. C₁₃×#123	C₂²	semidirect
54. C₁₃×#123	C₂²	semidirect
55. C₁₃×#123	C₂²	semidirect
56. C₁₃×#123	C₂²	semidirect
63. C₁₃×C₂²⋊Q₈	C₂²	semidirect
64. C₁₃×C₂²⋊Q₈	C₂²	semidirect
65. C₁₃×C₂²⋊Q₈	C₂²	semidirect
66. C₁₃×C₂²⋊Q₈	C₂²	semidirect
67. C₁₃×C₂²⋊Q₈	C₂²	semidirect
68. C₁₃×C₂²⋊Q₈	C₂²	semidirect
69. C₁₃×C₂²⋊Q₈	C₂²	semidirect
70. C₁₃×C₂²⋊Q₈	C₂²	semidirect
71. C₁₃×C₂²⋊Q₈	C₂²	semidirect
72. C₁₃×C₂²⋊Q₈	C₂²	semidirect
73. C₁₃×C₂²⋊Q₈	C₂²	semidirect
74. C₁₃×C₂²⋊Q₈	C₂²	semidirect
75. C₁₃×C₂²⋊Q₈	C₂²	semidirect
76. C₁₃×C₂²⋊Q₈	C₂²	semidirect
81. C₁₃×#121	C₂²	semidirect
82. C₁₃×#121	C₂²	semidirect
85. C₄×Q₈×C₁₃	C₂²	semidirect
90. C₄×D₄×C₁₃	C₂²	semidirect
91. C₄×D₄×C₁₃	C₂²	semidirect
92. C₄×D₄×C₁₃	C₂²	semidirect
94. C₁₃×#117	C₂²	semidirect
95. C₁₃×#117	C₂²	semidirect
96. C₁₃×#117	C₂²	semidirect
99. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
100. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
101. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
199. #3535	C₁₃	direct (N × H)
255. #563	C₂×C₁₃	semidirect
256. #562	C₂×C₁₃	semidirect
257. #554	C₂×C₁₃	semidirect
258. #552	C₂×C₁₃	semidirect
259. #551	C₂×C₁₃	semidirect
260. #551	C₂×C₁₃	semidirect
261. #547	C₂×C₁₃	semidirect
262. #546	C₂×C₁₃	semidirect
263. #544	C₂×C₁₃	semidirect
264. #543	C₂×C₁₃	semidirect
265. #542	C₂×C₁₃	semidirect
266. #539	C₂×C₁₃	semidirect
267. #539	C₂×C₁₃	semidirect
268. #539	C₂×C₁₃	semidirect
269. #538	C₂×C₁₃	semidirect
270. #536	C₂×C₁₃	semidirect
271. #525	C₂×C₁₃	semidirect
272. C₂×#123	C₂×C₁₃	semidirect
273. C₂×C₂²⋊Q₈	C₂×C₁₃	semidirect
307. C₂×#41	C₂²×C₁₃	semidirect
308. C₂²×Q₈	C₂²×C₁₃	semidirect
311. C₄⋊Q₈	C₂²×C₁₃	semidirect
312. C₄⋊Q₈	C₂²×C₁₃	semidirect
313. C₄⋊Q₈	C₂²×C₁₃	semidirect
314. #126	C₂²×C₁₃	semidirect
315. #126	C₂²×C₁₃	semidirect
316. #126	C₂²×C₁₃	semidirect
317. #126	C₂²×C₁₃	semidirect
318. #126	C₂²×C₁₃	semidirect
319. #126	C₂²×C₁₃	semidirect
320. #125	C₂²×C₁₃	semidirect
321. #125	C₂²×C₁₃	semidirect
322. #125	C₂²×C₁₃	semidirect
323. #125	C₂²×C₁₃	semidirect
324. #125	C₂²×C₁₃	semidirect
326. #124	C₂²×C₁₃	semidirect
327. #124	C₂²×C₁₃	semidirect
328. #124	C₂²×C₁₃	semidirect
336. #123	C₂²×C₁₃	semidirect
337. #123	C₂²×C₁₃	semidirect
338. #123	C₂²×C₁₃	semidirect
339. #123	C₂²×C₁₃	semidirect
340. #123	C₂²×C₁₃	semidirect
341. #123	C₂²×C₁₃	semidirect
342. #123	C₂²×C₁₃	semidirect
349. C₂²⋊Q₈	C₂²×C₁₃	semidirect
350. C₂²⋊Q₈	C₂²×C₁₃	semidirect
351. C₂²⋊Q₈	C₂²×C₁₃	semidirect
352. C₂²⋊Q₈	C₂²×C₁₃	semidirect
353. C₂²⋊Q₈	C₂²×C₁₃	semidirect
354. C₂²⋊Q₈	C₂²×C₁₃	semidirect
355. C₂²⋊Q₈	C₂²×C₁₃	semidirect
356. C₂²⋊Q₈	C₂²×C₁₃	semidirect
357. C₂²⋊Q₈	C₂²×C₁₃	semidirect
358. C₂²⋊Q₈	C₂²×C₁₃	semidirect
359. C₂²⋊Q₈	C₂²×C₁₃	semidirect
360. C₂²⋊Q₈	C₂²×C₁₃	semidirect
361. C₂²⋊Q₈	C₂²×C₁₃	semidirect
362. C₂²⋊Q₈	C₂²×C₁₃	semidirect
367. #121	C₂²×C₁₃	semidirect
368. #121	C₂²×C₁₃	semidirect
371. C₄×Q₈	C₂²×C₁₃	semidirect
376. C₄×D₄	C₂²×C₁₃	semidirect
377. C₄×D₄	C₂²×C₁₃	semidirect
378. C₄×D₄	C₂²×C₁₃	semidirect
380. #117	C₂²×C₁₃	semidirect
381. #117	C₂²×C₁₃	semidirect
382. #117	C₂²×C₁₃	semidirect
385. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
386. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
387. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
493. C₁₃	#3535	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#563	2
C₁₃×#562	2
C₁₃×#554	2
C₁₃×#552	2
C₁₃×#551	2
C₁₃×#547	2
C₁₃×#546	2
C₁₃×#544	2
C₁₃×#543	2
C₁₃×#542	2
C₁₃×#539	2
C₁₃×#538	2
C₁₃×#536	2
C₁₃×#525	2
C₂×C₁₃×#123	2
C₂×C₁₃×C₂²⋊Q₈	2
#3535	13

Subgroups — C13×#3535 #13112593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3535 #13112593