Subgroups — C₁₃×#3521 #13112579

Order 1664.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#553	C₂	1	2	yes	maximal, complemented
6	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#552	C₂	1	2	yes	maximal, complemented
8	C₁₃×#551	C₂	1	2	yes	maximal, complemented
9	C₁₃×#551	C₂	1	2	yes	maximal, complemented
10	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#539	C₂	1	2	yes	maximal, complemented
16	C₁₃×#538	C₂	1	2	yes	maximal, complemented
17	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#529	C₂	1	2	yes	maximal, complemented
19	C₁₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#126	C₂	1	2	yes	maximal, complemented
21	C₁₃×#520	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
26	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#126	C₂²	1	1	yes	characteristic
30	C₁₃×#126	C₂²	1	2	yes	—
31	C₁₃×#126	C₂²	1	2	yes	—
32	C₁₃×#126	C₂²	1	2	yes	—
33	C₁₃×#126	C₂²	1	2	yes	—
34	C₁₃×#126	C₂²	1	2	yes	complemented
35	C₁₃×#126	C₂²	1	2	yes	complemented
36	C₁₃×#126	C₂²	1	2	yes	complemented
37	C₁₃×#126	C₂²	1	2	yes	complemented
38	C₁₃×#126	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#126	C₂²	1	2	yes	complemented
40	C₁₃×#126	C₂²	1	2	yes	complemented
41	C₁₃×#125	C₂²	1	2	yes	complemented
42	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
43	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
44	C₁₃×#125	C₂²	1	2	yes	complemented
45	C₁₃×#125	C₂²	1	2	yes	complemented
46	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
47	C₁₃×#124	C₂²	1	1	yes	characteristic
48	C₁₃×#124	C₂²	1	1	yes	characteristic
49	C₁₃×#124	C₂²	1	2	yes	—
50	C₁₃×#124	C₂²	1	1	yes	characteristic
51	C₁₃×#124	C₂²	1	2	yes	complemented
52	C₁₃×#123	C₂²	1	2	yes	—
53	C₁₃×#123	C₂²	1	1	yes	characteristic
54	C₁₃×#123	C₂²	1	2	yes	—
55	C₁₃×#123	C₂²	1	2	yes	—
56	C₁₃×#123	C₂²	1	2	yes	complemented
57	C₁₃×#123	C₂²	1	2	yes	complemented
58	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
59	C₁₃×#123	C₂²	1	2	yes	complemented
60	C₁₃×#123	C₂²	1	2	yes	complemented
61	C₁₃×#123	C₂²	1	2	yes	complemented
62	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
63	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
66	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	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	1	yes	characteristic, complemented
71	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
72	C₁₃×#121	C₂²	1	1	yes	characteristic
73	C₁₃×#121	C₂²	1	1	yes	characteristic
74	C₁₃×#121	C₂²	1	2	yes	—
75	C₁₃×#121	C₂²	1	2	yes	—
76	C₁₃×#121	C₂²	1	1	yes	characteristic
77	C₁₃×#121	C₂²	1	2	yes	complemented
78	C₁₃×#121	C₂²	1	2	yes	complemented
79	C₁₃×#120	C₂²	1	2	yes	—
80	C₁₃×#120	C₂²	1	2	yes	—
81	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
85	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
86	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
87	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
88	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
89	C₄×D₄×C₁₃	C₂²	1	2	yes	—
90	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
91	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
92	C₄×D₄×C₁₃	C₂²	1	2	yes	—
93	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
94	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
95	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
96	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
97	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
98	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
99	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
100	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
101	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
103	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
104	C₁₃×#117	C₂²	1	1	yes	characteristic
105	C₁₃×#117	C₂²	1	1	yes	characteristic
106	C₁₃×#117	C₂²	1	2	yes	complemented
107	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
108	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
109	C₁₃×#117	C₂²	1	2	yes	complemented
110	C₁₃×#117	C₂²	1	2	yes	complemented
111	C₁₃×#117	C₂²	1	2	yes	complemented
112	C₁₃×#117	C₂²	1	2	yes	complemented
113	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
114	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
115	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
116	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
117	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
118	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
120	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
123	C₂⁴×C₁₃	C₂³	1	2	yes	—
124	C₁₃×#41	—	2	4	no	—
125	C₁₃×#41	—	2	4	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	C₂³	1	2	yes	—
132	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₃	C₂³	1	2	yes	—
134	C₂×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂×D₄×C₁₃	C₂³	1	2	yes	—
138	C₂×D₄×C₁₃	C₂³	1	2	yes	—
139	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
155	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
182	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
186	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
188	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
189	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
195	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
201	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
204	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
206	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
210	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
213	C₄²×C₁₃	C₂³	1	1	yes	characteristic
214	C₄²×C₁₃	C₂³	1	1	yes	characteristic
215	C₄²×C₁₃	C₂³	1	1	yes	characteristic
216	C₄²×C₁₃	C₂³	1	2	yes	—
217	C₄²×C₁₃	C₂³	1	2	yes	—
218	C₄²×C₁₃	C₂³	1	1	yes	characteristic
219	C₄²×C₁₃	C₂³	1	2	yes	—
220	C₄²×C₁₃	C₂³	1	2	yes	—
221	C₄²×C₁₃	C₂³	1	1	yes	characteristic
222	C₄²×C₁₃	C₂³	1	2	yes	—
223	C₄²×C₁₃	C₂³	1	2	yes	—
224	C₄²×C₁₃	C₂³	1	1	yes	characteristic
225	#3521	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	4	2	no	—
228	C₂³×C₁₃	—	4	2	no	—
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	2	yes	—
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₁₃	C₂⁴	1	2	yes	—
234	Q₈×C₁₃	—	2	2	no	—
235	Q₈×C₁₃	—	2	2	no	—
236	Q₈×C₁₃	—	4	1	no	—
237	Q₈×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	2	4	no	—
239	D₄×C₁₃	—	2	4	no	—
240	D₄×C₁₃	—	2	4	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	D₄×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	4	1	no	—
247	D₄×C₁₃	#41	1	4	yes	—
248	C₂×C₄×C₁₃	—	2	4	no	—
249	C₂×C₄×C₁₃	—	2	4	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	2	no	—
256	C₂×C₄×C₁₃	—	4	2	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	2	no	—
262	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
267	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
269	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
270	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
272	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
274	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
278	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
280	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#556	C₂×C₁₃	1	1	yes	characteristic, complemented
282	#554	C₂×C₁₃	1	1	yes	characteristic, complemented
283	#553	C₂×C₁₃	1	1	yes	characteristic, complemented
284	#553	C₂×C₁₃	1	2	yes	complemented
285	#552	C₂×C₁₃	1	1	yes	characteristic, complemented
286	#552	C₂×C₁₃	1	2	yes	complemented
287	#551	C₂×C₁₃	1	2	yes	complemented
288	#551	C₂×C₁₃	1	2	yes	complemented
289	#547	C₂×C₁₃	1	1	yes	characteristic, complemented
290	#546	C₂×C₁₃	1	1	yes	characteristic, complemented
291	#546	C₂×C₁₃	1	1	yes	characteristic, complemented
292	#542	C₂×C₁₃	1	1	yes	characteristic, complemented
293	#541	C₂×C₁₃	1	1	yes	characteristic, complemented
294	#539	C₂×C₁₃	1	2	yes	complemented
295	#538	C₂×C₁₃	1	2	yes	complemented
296	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
297	#529	C₂×C₁₃	1	2	yes	complemented
298	#529	C₂×C₁₃	1	1	yes	characteristic, complemented
299	C₂×#126	C₂×C₁₃	1	2	yes	complemented
300	#520	C₂×C₁₃	1	1	yes	characteristic, complemented
301	#518	C₂×C₁₃	1	1	yes	characteristic, complemented
302	C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	2	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	8	4	no	—
318	C₂²×C₁₃	C₂×#41	1	4	yes	—
319	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	C₂×#41	1	2	yes	—
338	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
340	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
341	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
342	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
343	#126	C₂²×C₁₃	1	1	yes	characteristic
344	#126	C₂²×C₁₃	1	2	yes	—
345	#126	C₂²×C₁₃	1	2	yes	—
346	#126	C₂²×C₁₃	1	2	yes	—
347	#126	C₂²×C₁₃	1	2	yes	—
348	#126	C₂²×C₁₃	1	2	yes	complemented
349	#126	C₂²×C₁₃	1	2	yes	complemented
350	#126	C₂²×C₁₃	1	2	yes	complemented
351	#126	C₂²×C₁₃	1	2	yes	complemented
352	#126	C₂²×C₁₃	1	1	yes	characteristic, complemented
353	#126	C₂²×C₁₃	1	2	yes	complemented
354	#126	C₂²×C₁₃	1	2	yes	complemented
355	#125	C₂²×C₁₃	1	2	yes	complemented
356	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
357	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
358	#125	C₂²×C₁₃	1	2	yes	complemented
359	#125	C₂²×C₁₃	1	2	yes	complemented
360	#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
361	#124	C₂²×C₁₃	1	1	yes	characteristic
362	#124	C₂²×C₁₃	1	1	yes	characteristic
363	#124	C₂²×C₁₃	1	2	yes	—
364	#124	C₂²×C₁₃	1	1	yes	characteristic
365	#124	C₂²×C₁₃	1	2	yes	complemented
366	#123	C₂²×C₁₃	1	2	yes	—
367	#123	C₂²×C₁₃	1	1	yes	characteristic
368	#123	C₂²×C₁₃	1	2	yes	—
369	#123	C₂²×C₁₃	1	2	yes	—
370	#123	C₂²×C₁₃	1	2	yes	complemented
371	#123	C₂²×C₁₃	1	2	yes	complemented
372	#123	C₂²×C₁₃	1	1	yes	characteristic, complemented
373	#123	C₂²×C₁₃	1	2	yes	complemented
374	#123	C₂²×C₁₃	1	2	yes	complemented
375	#123	C₂²×C₁₃	1	2	yes	complemented
376	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
377	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
378	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
379	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
380	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
381	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
382	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
383	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
384	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
385	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
386	#121	C₂²×C₁₃	1	1	yes	characteristic
387	#121	C₂²×C₁₃	1	1	yes	characteristic
388	#121	C₂²×C₁₃	1	2	yes	—
389	#121	C₂²×C₁₃	1	2	yes	—
390	#121	C₂²×C₁₃	1	1	yes	characteristic
391	#121	C₂²×C₁₃	1	2	yes	complemented
392	#121	C₂²×C₁₃	1	2	yes	complemented
393	#120	C₂²×C₁₃	1	2	yes	—
394	#120	C₂²×C₁₃	1	2	yes	—
395	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
396	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
397	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
398	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
399	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
400	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
401	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
402	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
403	C₄×D₄	C₂²×C₁₃	1	2	yes	—
404	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
405	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
406	C₄×D₄	C₂²×C₁₃	1	2	yes	—
407	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
408	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
409	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
410	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
411	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
412	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
413	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
414	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
415	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
416	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
417	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
418	#117	C₂²×C₁₃	1	1	yes	characteristic
419	#117	C₂²×C₁₃	1	1	yes	characteristic
420	#117	C₂²×C₁₃	1	2	yes	complemented
421	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
422	#117	C₂²×C₁₃	1	1	yes	characteristic, complemented
423	#117	C₂²×C₁₃	1	2	yes	complemented
424	#117	C₂²×C₁₃	1	2	yes	complemented
425	#117	C₂²×C₁₃	1	2	yes	complemented
426	#117	C₂²×C₁₃	1	2	yes	complemented
427	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
428	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
429	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
430	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
431	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
435	C₂×C₄²	C₂²×C₁₃	1	2	yes	complemented
436	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic, complemented
437	C₂×C₁₃	—	2	4	no	—
438	C₂×C₁₃	—	4	1	no	—
439	C₂×C₁₃	—	4	1	no	—
440	C₂×C₁₃	—	4	2	no	—
441	C₂×C₁₃	—	4	1	no	—
442	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
443	C₂×C₁₃	#585	1	1	yes	characteristic
444	C₂×C₁₃	#585	1	1	yes	characteristic
445	C₂⁴	C₂³×C₁₃	1	2	yes	—
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	C₂³×C₁₃	1	2	yes	—
454	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×D₄	C₂³×C₁₃	1	2	yes	—
456	C₂×D₄	C₂³×C₁₃	1	2	yes	—
457	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×D₄	C₂³×C₁₃	1	2	yes	—
460	C₂×D₄	C₂³×C₁₃	1	2	yes	—
461	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
462	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
466	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
470	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
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	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
479	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
483	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
484	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
486	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
487	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
488	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
489	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
490	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
491	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
498	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
499	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
500	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
501	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
502	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
504	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
505	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
506	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
507	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
508	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
509	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
510	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
511	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
512	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
513	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
514	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
515	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
516	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
517	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
518	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
519	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
520	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
521	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
522	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
523	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
524	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
525	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
526	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
527	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
528	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
529	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
530	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
532	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
533	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
534	C₂²⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
535	C₄²	C₂³×C₁₃	1	1	yes	characteristic
536	C₄²	C₂³×C₁₃	1	1	yes	characteristic
537	C₄²	C₂³×C₁₃	1	1	yes	characteristic
538	C₄²	C₂³×C₁₃	1	2	yes	—
539	C₄²	C₂³×C₁₃	1	2	yes	—
540	C₄²	C₂³×C₁₃	1	1	yes	characteristic
541	C₄²	C₂³×C₁₃	1	2	yes	—
542	C₄²	C₂³×C₁₃	1	2	yes	—
543	C₄²	C₂³×C₁₃	1	1	yes	characteristic
544	C₄²	C₂³×C₁₃	1	2	yes	—
545	C₄²	C₂³×C₁₃	1	2	yes	—
546	C₄²	C₂³×C₁₃	1	1	yes	characteristic
547	C₁₃	#3521	1	1	yes	characteristic, direct product factor, Sylow
548	C₂³	—	2	4	no	—
549	C₂³	—	4	2	no	—
550	C₂³	—	4	2	no	—
551	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
552	C₂³	C₂⁴×C₁₃	1	2	yes	—
553	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
554	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
555	C₂³	C₂⁴×C₁₃	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	4	2	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	1	no	—
569	D₄	C₁₃×#41	1	4	yes	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	2	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
589	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
591	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
592	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
594	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
596	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
600	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	1	no	—
610	C₂²	—	2	1	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	8	4	no	—
617	C₂²	C₂×C₁₃×#41	1	4	yes	—
618	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	C₂×C₁₃×#41	1	2	yes	—
637	C₂	—	2	4	no	—
638	C₂	—	4	1	no	—
639	C₂	—	4	2	no	—
640	C₂	—	4	1	no	—
641	C₂	—	4	1	no	—
642	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
643	C₂	C₁₃×#585	1	1	yes	characteristic
644	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×#556	C₂	semidirect
2. C₁₃×#556	C₂	semidirect
3. C₁₃×#554	C₂	semidirect
4. C₁₃×#553	C₂	semidirect
5. C₁₃×#553	C₂	semidirect
6. C₁₃×#552	C₂	semidirect
7. C₁₃×#552	C₂	semidirect
8. C₁₃×#551	C₂	semidirect
9. C₁₃×#551	C₂	semidirect
10. C₁₃×#547	C₂	semidirect
11. C₁₃×#546	C₂	semidirect
12. C₁₃×#546	C₂	semidirect
13. C₁₃×#542	C₂	semidirect
14. C₁₃×#541	C₂	semidirect
15. C₁₃×#539	C₂	semidirect
16. C₁₃×#538	C₂	semidirect
17. C₁₃×#529	C₂	semidirect
18. C₁₃×#529	C₂	semidirect
19. C₁₃×#529	C₂	semidirect
20. C₂×C₁₃×#126	C₂	semidirect
21. C₁₃×#520	C₂	semidirect
22. C₁₃×#518	C₂	semidirect
23. C₄×C₁₃×#41	C₂	semidirect
27. C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×#126	C₂²	semidirect
35. C₁₃×#126	C₂²	semidirect
36. C₁₃×#126	C₂²	semidirect
37. C₁₃×#126	C₂²	semidirect
38. C₁₃×#126	C₂²	semidirect
39. C₁₃×#126	C₂²	semidirect
40. C₁₃×#126	C₂²	semidirect
41. C₁₃×#125	C₂²	semidirect
42. C₁₃×#125	C₂²	semidirect
43. C₁₃×#125	C₂²	semidirect
44. C₁₃×#125	C₂²	semidirect
45. C₁₃×#125	C₂²	semidirect
46. C₁₃×#125	C₂²	semidirect
51. C₁₃×#124	C₂²	semidirect
56. C₁₃×#123	C₂²	semidirect
57. C₁₃×#123	C₂²	semidirect
58. C₁₃×#123	C₂²	semidirect
59. C₁₃×#123	C₂²	semidirect
60. C₁₃×#123	C₂²	semidirect
61. C₁₃×#123	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
77. C₁₃×#121	C₂²	semidirect
78. C₁₃×#121	C₂²	semidirect
81. C₄×Q₈×C₁₃	C₂²	semidirect
82. C₄×Q₈×C₁₃	C₂²	semidirect
83. C₄×Q₈×C₁₃	C₂²	semidirect
84. C₄×Q₈×C₁₃	C₂²	semidirect
85. C₄×Q₈×C₁₃	C₂²	semidirect
86. C₄×Q₈×C₁₃	C₂²	semidirect
97. C₄×D₄×C₁₃	C₂²	semidirect
98. C₄×D₄×C₁₃	C₂²	semidirect
99. C₄×D₄×C₁₃	C₂²	semidirect
100. C₄×D₄×C₁₃	C₂²	semidirect
101. C₄×D₄×C₁₃	C₂²	semidirect
102. C₄×D₄×C₁₃	C₂²	semidirect
103. C₄×D₄×C₁₃	C₂²	semidirect
106. C₁₃×#117	C₂²	semidirect
107. C₁₃×#117	C₂²	semidirect
108. C₁₃×#117	C₂²	semidirect
109. C₁₃×#117	C₂²	semidirect
110. C₁₃×#117	C₂²	semidirect
111. C₁₃×#117	C₂²	semidirect
112. C₁₃×#117	C₂²	semidirect
113. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
114. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
115. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
116. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
121. C₂×C₄²×C₁₃	C₂²	semidirect
122. C₂×C₄²×C₁₃	C₂²	semidirect
225. #3521	C₁₃	direct (N × H)
280. #556	C₂×C₁₃	semidirect
281. #556	C₂×C₁₃	semidirect
282. #554	C₂×C₁₃	semidirect
283. #553	C₂×C₁₃	semidirect
284. #553	C₂×C₁₃	semidirect
285. #552	C₂×C₁₃	semidirect
286. #552	C₂×C₁₃	semidirect
287. #551	C₂×C₁₃	semidirect
288. #551	C₂×C₁₃	semidirect
289. #547	C₂×C₁₃	semidirect
290. #546	C₂×C₁₃	semidirect
291. #546	C₂×C₁₃	semidirect
292. #542	C₂×C₁₃	semidirect
293. #541	C₂×C₁₃	semidirect
294. #539	C₂×C₁₃	semidirect
295. #538	C₂×C₁₃	semidirect
296. #529	C₂×C₁₃	semidirect
297. #529	C₂×C₁₃	semidirect
298. #529	C₂×C₁₃	semidirect
299. C₂×#126	C₂×C₁₃	semidirect
300. #520	C₂×C₁₃	semidirect
301. #518	C₂×C₁₃	semidirect
302. C₄×#41	C₂×C₁₃	semidirect
341. C₄⋊Q₈	C₂²×C₁₃	semidirect
342. C₄⋊Q₈	C₂²×C₁₃	semidirect
348. #126	C₂²×C₁₃	semidirect
349. #126	C₂²×C₁₃	semidirect
350. #126	C₂²×C₁₃	semidirect
351. #126	C₂²×C₁₃	semidirect
352. #126	C₂²×C₁₃	semidirect
353. #126	C₂²×C₁₃	semidirect
354. #126	C₂²×C₁₃	semidirect
355. #125	C₂²×C₁₃	semidirect
356. #125	C₂²×C₁₃	semidirect
357. #125	C₂²×C₁₃	semidirect
358. #125	C₂²×C₁₃	semidirect
359. #125	C₂²×C₁₃	semidirect
360. #125	C₂²×C₁₃	semidirect
365. #124	C₂²×C₁₃	semidirect
370. #123	C₂²×C₁₃	semidirect
371. #123	C₂²×C₁₃	semidirect
372. #123	C₂²×C₁₃	semidirect
373. #123	C₂²×C₁₃	semidirect
374. #123	C₂²×C₁₃	semidirect
375. #123	C₂²×C₁₃	semidirect
378. C₂²⋊Q₈	C₂²×C₁₃	semidirect
379. C₂²⋊Q₈	C₂²×C₁₃	semidirect
380. C₂²⋊Q₈	C₂²×C₁₃	semidirect
381. C₂²⋊Q₈	C₂²×C₁₃	semidirect
382. C₂²⋊Q₈	C₂²×C₁₃	semidirect
383. C₂²⋊Q₈	C₂²×C₁₃	semidirect
384. C₂²⋊Q₈	C₂²×C₁₃	semidirect
385. C₂²⋊Q₈	C₂²×C₁₃	semidirect
391. #121	C₂²×C₁₃	semidirect
392. #121	C₂²×C₁₃	semidirect
395. C₄×Q₈	C₂²×C₁₃	semidirect
396. C₄×Q₈	C₂²×C₁₃	semidirect
397. C₄×Q₈	C₂²×C₁₃	semidirect
398. C₄×Q₈	C₂²×C₁₃	semidirect
399. C₄×Q₈	C₂²×C₁₃	semidirect
400. C₄×Q₈	C₂²×C₁₃	semidirect
411. C₄×D₄	C₂²×C₁₃	semidirect
412. C₄×D₄	C₂²×C₁₃	semidirect
413. C₄×D₄	C₂²×C₁₃	semidirect
414. C₄×D₄	C₂²×C₁₃	semidirect
415. C₄×D₄	C₂²×C₁₃	semidirect
416. C₄×D₄	C₂²×C₁₃	semidirect
417. C₄×D₄	C₂²×C₁₃	semidirect
420. #117	C₂²×C₁₃	semidirect
421. #117	C₂²×C₁₃	semidirect
422. #117	C₂²×C₁₃	semidirect
423. #117	C₂²×C₁₃	semidirect
424. #117	C₂²×C₁₃	semidirect
425. #117	C₂²×C₁₃	semidirect
426. #117	C₂²×C₁₃	semidirect
427. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
428. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
429. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
430. C₂×C₄⋊C₄	C₂²×C₁₃	semidirect
435. C₂×C₄²	C₂²×C₁₃	semidirect
436. C₂×C₄²	C₂²×C₁₃	semidirect
547. C₁₃	#3521	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×#556	2
C₁₃×#554	2
C₁₃×#553	2
C₁₃×#552	2
C₁₃×#551	2
C₁₃×#547	2
C₁₃×#546	2
C₁₃×#542	2
C₁₃×#541	2
C₁₃×#539	2
C₁₃×#538	2
C₁₃×#529	2
C₂×C₁₃×#126	2
C₁₃×#520	2
C₁₃×#518	2
C₄×C₁₃×#41	2
#3521	13

Subgroups — C13×#3521 #13112579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3521 #13112579