Subgroups — C₁₃×#62905 #15749244

Order 3328.

7326 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3560	C₂	1	12	yes	maximal, complemented
2	C₁₃×#3559	C₂	1	6	yes	maximal, complemented
3	C₁₃×#3537	C₂	1	6	yes	maximal, complemented
4	C₁₃×#3534	C₂	1	12	yes	maximal, complemented
5	C₁₃×#3519	C₂	1	6	yes	maximal, complemented
6	C₁₃×#3496	C₂	1	6	yes	maximal, complemented
7	C₁₃×#3496	C₂	1	3	yes	maximal, complemented
8	C₁₃×#3494	C₂	1	6	yes	maximal, complemented
9	C₂×C₁₃×#553	C₂	1	3	yes	maximal, complemented
10	C₁₃×#3459	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3459	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	6	yes	complemented
13	C₁₃×#563	C₂²	1	12	yes	complemented
14	C₁₃×#562	C₂²	1	12	yes	complemented
15	C₁₃×#560	C₂²	1	24	yes	complemented
16	C₁₃×#555	C₂²	1	6	yes	complemented
17	C₁₃×#554	C₂²	1	6	yes	complemented
18	C₁₃×#553	C₂²	1	12	yes	complemented
19	C₁₃×#553	C₂²	1	12	yes	complemented
20	C₁₃×#553	C₂²	1	24	yes	complemented
21	C₁₃×#553	C₂²	1	12	yes	complemented
22	C₁₃×#553	C₂²	1	12	yes	complemented
23	C₁₃×#551	C₂²	1	24	yes	complemented
24	C₁₃×#550	C₂²	1	2	yes	complemented
25	C₁₃×#547	C₂²	1	24	yes	complemented
26	C₁₃×#547	C₂²	1	12	yes	complemented
27	C₁₃×#546	C₂²	1	12	yes	complemented
28	C₁₃×#546	C₂²	1	24	yes	complemented
29	C₁₃×#546	C₂²	1	24	yes	complemented
30	C₁₃×#546	C₂²	1	24	yes	complemented
31	D₄²×C₁₃	C₂²	1	6	yes	complemented
32	D₄²×C₁₃	C₂²	1	12	yes	complemented
33	D₄²×C₁₃	C₂²	1	24	yes	complemented
34	C₁₃×#544	C₂²	1	6	yes	complemented
35	C₁₃×#543	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#542	C₂²	1	12	yes	complemented
37	C₁₃×#540	C₂²	1	12	yes	complemented
38	C₁₃×#540	C₂²	1	12	yes	complemented
39	C₁₃×#539	C₂²	1	24	yes	complemented
40	C₁₃×#539	C₂²	1	12	yes	complemented
41	C₁₃×#539	C₂²	1	6	yes	complemented
42	C₁₃×#538	C₂²	1	24	yes	complemented
43	C₁₃×#538	C₂²	1	6	yes	complemented
44	C₁₃×#538	C₂²	1	12	yes	complemented
45	C₁₃×#538	C₂²	1	12	yes	complemented
46	C₁₃×#537	C₂²	1	12	yes	complemented
47	C₁₃×#537	C₂²	1	6	yes	complemented
48	C₁₃×#535	C₂²	1	6	yes	complemented
49	C₁₃×#534	C₂²	1	12	yes	complemented
50	C₁₃×#534	C₂²	1	6	yes	complemented
51	C₁₃×#534	C₂²	1	12	yes	complemented
52	C₁₃×#534	C₂²	1	3	yes	complemented
53	C₁₃×#534	C₂²	1	6	yes	complemented
54	C₁₃×#532	C₂²	1	6	yes	complemented
55	C₁₃×#532	C₂²	1	12	yes	complemented
56	C₁₃×#529	C₂²	1	6	yes	complemented
57	C₁₃×#529	C₂²	1	12	yes	complemented
58	C₂×C₁₃×#126	C₂²	1	6	yes	complemented
59	C₂×C₁₃×#125	C₂²	1	3	yes	complemented
60	C₁₃×#525	C₂²	1	12	yes	complemented
61	C₁₃×#525	C₂²	1	6	yes	complemented
62	C₂×C₁₃×#123	C₂²	1	6	yes	complemented
63	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
64	C₂×C₁₃×#121	C₂²	1	3	yes	complemented
65	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
66	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
67	C₂×C₁₃×#121	C₂²	1	3	yes	complemented
68	C₁₃×#520	C₂²	1	2	yes	complemented
69	C₁₃×#518	C₂²	1	6	yes	complemented
70	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
71	C₂×C₄×D₄×C₁₃	C₂²	1	6	yes	complemented
72	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
73	C₂×C₁₃×#117	C₂²	1	3	yes	complemented
74	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
75	C₁₃×H(5,𝔽₂)	—	4	24	no	—
76	C₂×C₁₃×#41	C₂³	1	2	yes	—
77	C₂×C₁₃×#41	C₂³	1	12	yes	—
78	C₂×C₁₃×#41	C₂³	1	24	yes	—
79	C₂×C₁₃×#41	C₂³	1	4	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
81	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
82	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
83	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
84	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
86	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
87	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
90	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
92	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
93	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
94	C₁₃×#127	C₂³	1	12	yes	—
95	C₁₃×#127	C₂³	1	6	yes	—
96	C₁₃×#126	C₂³	1	24	yes	—
97	C₁₃×#126	C₂³	1	24	yes	—
98	C₁₃×#126	C₂³	1	12	yes	—
99	C₁₃×#126	C₂³	1	24	yes	—
100	C₁₃×#125	C₂³	1	12	yes	—
101	C₁₃×#125	C₂³	1	12	yes	—
102	C₁₃×#125	C₂³	1	12	yes	—
103	C₁₃×#125	C₂³	1	6	yes	—
104	C₁₃×#124	C₂³	1	12	yes	—
105	C₁₃×#124	C₂³	1	6	yes	—
106	C₁₃×#124	C₂³	1	12	yes	—
107	C₁₃×#124	C₂³	1	24	yes	—
108	C₁₃×#123	C₂³	1	24	yes	—
109	C₁₃×#123	C₂³	1	24	yes	—
110	C₁₃×#123	C₂³	1	24	yes	—
111	C₁₃×#123	C₂³	1	12	yes	—
112	C₁₃×#123	C₂³	1	12	yes	—
113	C₁₃×#123	C₂³	1	24	yes	—
114	C₁₃×#123	C₂³	1	24	yes	—
115	C₁₃×#123	C₂³	1	24	yes	—
116	C₁₃×#123	C₂³	1	24	yes	—
117	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
118	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
119	C₁₃×C₂²⋊Q₈	C₂³	1	6	yes	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	12	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
123	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
124	C₁₃×#121	C₂³	1	6	yes	—
125	C₁₃×#121	C₂³	1	12	yes	—
126	C₁₃×#121	C₂³	1	24	yes	—
127	C₁₃×#121	C₂³	1	12	yes	—
128	C₁₃×#121	C₂³	1	12	yes	—
129	C₁₃×#121	C₂³	1	24	yes	—
130	C₁₃×#121	C₂³	1	12	yes	—
131	C₁₃×#121	C₂³	1	12	yes	—
132	C₁₃×#121	C₂³	1	12	yes	—
133	C₁₃×#121	C₂³	1	12	yes	—
134	C₁₃×#121	C₂³	1	12	yes	—
135	C₁₃×#121	C₂³	1	24	yes	—
136	C₁₃×#121	C₂³	1	12	yes	—
137	C₁₃×#121	C₂³	1	12	yes	—
138	C₁₃×#121	C₂³	1	6	yes	—
139	C₁₃×#121	C₂³	1	6	yes	—
140	C₁₃×#121	C₂³	1	12	yes	—
141	C₁₃×#121	C₂³	1	24	yes	—
142	C₁₃×#121	C₂³	1	24	yes	—
143	C₁₃×#121	C₂³	1	24	yes	—
144	C₁₃×#120	C₂³	1	12	yes	—
145	C₁₃×#120	C₂³	1	24	yes	—
146	C₁₃×#120	C₂³	1	24	yes	—
147	C₁₃×#120	C₂³	1	24	yes	—
148	C₁₃×#120	C₂³	1	24	yes	—
149	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
150	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
151	C₄×D₄×C₁₃	C₂³	1	6	yes	—
152	C₄×D₄×C₁₃	C₂³	1	12	yes	—
153	C₄×D₄×C₁₃	C₂³	1	24	yes	—
154	C₄×D₄×C₁₃	C₂³	1	12	yes	—
155	C₄×D₄×C₁₃	C₂³	1	24	yes	—
156	C₄×D₄×C₁₃	C₂³	1	12	yes	—
157	C₄×D₄×C₁₃	C₂³	1	6	yes	—
158	C₄×D₄×C₁₃	C₂³	1	12	yes	—
159	C₄×D₄×C₁₃	C₂³	1	12	yes	—
160	C₄×D₄×C₁₃	C₂³	1	12	yes	—
161	C₄×D₄×C₁₃	C₂³	1	12	yes	—
162	C₄×D₄×C₁₃	C₂³	1	6	yes	—
163	C₄×D₄×C₁₃	C₂³	1	24	yes	—
164	C₄×D₄×C₁₃	C₂³	1	12	yes	—
165	C₁₃×#117	C₂³	1	6	yes	—
166	C₁₃×#117	C₂³	1	6	yes	—
167	C₁₃×#117	C₂³	1	12	yes	—
168	C₁₃×#117	C₂³	1	6	yes	—
169	C₁₃×#117	C₂³	1	12	yes	—
170	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
171	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
172	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
173	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
174	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
175	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
176	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
177	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
178	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
179	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
180	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
181	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
182	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
183	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
184	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
185	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
186	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
187	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
188	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
189	#62905	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
191	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
192	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
193	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₁₃×#41	—	4	4	no	—
195	C₁₃×#41	—	4	24	no	—
196	C₁₃×#41	—	4	48	no	—
197	C₁₃×#41	—	8	4	no	—
198	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
199	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
200	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
201	C₂×D₄×C₁₃	—	2	24	no	—
202	C₂×D₄×C₁₃	—	2	12	no	—
203	C₂×D₄×C₁₃	—	4	6	no	—
204	C₂×D₄×C₁₃	—	4	12	no	—
205	C₂×D₄×C₁₃	—	4	48	no	—
206	C₂×D₄×C₁₃	—	4	24	no	—
207	C₂×D₄×C₁₃	—	8	6	no	—
208	C₂×D₄×C₁₃	—	8	12	no	—
209	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
210	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
211	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
212	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
213	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
214	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
215	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
216	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
217	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
218	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
219	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
220	C₂²×C₄×C₁₃	—	4	2	no	—
221	C₂²×C₄×C₁₃	—	4	6	no	—
222	C₂²×C₄×C₁₃	—	8	2	no	—
223	C₂²×C₄×C₁₃	—	8	6	no	—
224	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
225	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
226	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
227	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
228	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
229	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
230	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
231	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
232	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
233	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
234	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
235	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
236	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
237	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
238	C₁₃×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
239	C₁₃×C₄⋊C₄	C₂⁴	1	3	yes	—
240	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
241	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
242	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
243	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
244	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
245	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
246	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
247	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
248	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
249	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
250	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
251	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
252	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
253	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
254	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
255	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
256	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
257	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
258	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
259	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
260	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
261	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
262	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
263	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
264	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
265	C₄²×C₁₃	C₂⁴	1	12	yes	—
266	C₄²×C₁₃	C₂⁴	1	6	yes	—
267	C₄²×C₁₃	C₂⁴	1	12	yes	—
268	C₄²×C₁₃	C₂⁴	1	6	yes	—
269	#3560	C₂×C₁₃	1	12	yes	complemented
270	#3559	C₂×C₁₃	1	6	yes	complemented
271	#3537	C₂×C₁₃	1	6	yes	complemented
272	#3534	C₂×C₁₃	1	12	yes	complemented
273	#3519	C₂×C₁₃	1	6	yes	complemented
274	#3496	C₂×C₁₃	1	3	yes	complemented
275	#3496	C₂×C₁₃	1	6	yes	complemented
276	#3494	C₂×C₁₃	1	6	yes	complemented
277	C₂×#553	C₂×C₁₃	1	3	yes	complemented
278	#3459	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#3459	C₂×C₁₃	1	2	yes	complemented
280	C₂³×C₁₃	—	2	6	no	—
281	C₂³×C₁₃	—	2	12	no	—
282	C₂³×C₁₃	—	4	1	no	—
283	C₂³×C₁₃	—	4	1	no	—
284	C₂³×C₁₃	—	4	3	no	—
285	C₂³×C₁₃	—	4	6	no	—
286	C₂³×C₁₃	—	4	6	no	—
287	C₂³×C₁₃	—	4	3	no	—
288	C₂³×C₁₃	—	4	12	no	—
289	C₂³×C₁₃	—	4	12	no	—
290	C₂³×C₁₃	—	4	12	no	—
291	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
292	C₂³×C₁₃	C₂⁵	1	6	yes	—
293	C₂³×C₁₃	C₂⁵	1	12	yes	—
294	C₂³×C₁₃	C₂⁵	1	3	yes	—
295	Q₈×C₁₃	—	4	2	no	—
296	Q₈×C₁₃	—	4	12	no	—
297	Q₈×C₁₃	—	4	2	no	—
298	D₄×C₁₃	—	2	24	no	—
299	D₄×C₁₃	—	2	48	no	—
300	D₄×C₁₃	—	2	12	no	—
301	D₄×C₁₃	—	4	24	no	—
302	D₄×C₁₃	—	4	12	no	—
303	D₄×C₁₃	—	4	6	no	—
304	D₄×C₁₃	—	4	12	no	—
305	D₄×C₁₃	—	4	24	no	—
306	D₄×C₁₃	—	4	6	no	—
307	D₄×C₁₃	—	4	12	no	—
308	D₄×C₁₃	—	4	6	no	—
309	C₂×C₄×C₁₃	—	2	12	no	—
310	C₂×C₄×C₁₃	—	2	6	no	—
311	C₂×C₄×C₁₃	—	2	6	no	—
312	C₂×C₄×C₁₃	—	2	12	no	—
313	C₂×C₄×C₁₃	—	4	3	no	—
314	C₂×C₄×C₁₃	—	4	6	no	—
315	C₂×C₄×C₁₃	—	4	3	no	—
316	C₂×C₄×C₁₃	—	4	6	no	—
317	C₂×C₄×C₁₃	—	4	3	no	—
318	C₂×C₄×C₁₃	—	4	6	no	—
319	C₂×C₄×C₁₃	—	4	12	no	—
320	C₂×C₄×C₁₃	—	4	12	no	—
321	C₂×C₄×C₁₃	—	4	24	no	—
322	C₂×C₄×C₁₃	—	4	12	no	—
323	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
324	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
325	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
326	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
327	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
328	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
329	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
330	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
331	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	6	yes	complemented
332	#563	C₂²×C₁₃	1	12	yes	complemented
333	#562	C₂²×C₁₃	1	12	yes	complemented
334	#560	C₂²×C₁₃	1	24	yes	complemented
335	#555	C₂²×C₁₃	1	6	yes	complemented
336	#554	C₂²×C₁₃	1	6	yes	complemented
337	#553	C₂²×C₁₃	1	12	yes	complemented
338	#553	C₂²×C₁₃	1	24	yes	complemented
339	#553	C₂²×C₁₃	1	12	yes	complemented
340	#553	C₂²×C₁₃	1	12	yes	complemented
341	#553	C₂²×C₁₃	1	12	yes	complemented
342	#551	C₂²×C₁₃	1	24	yes	complemented
343	#550	C₂²×C₁₃	1	2	yes	complemented
344	#547	C₂²×C₁₃	1	12	yes	complemented
345	#547	C₂²×C₁₃	1	24	yes	complemented
346	#546	C₂²×C₁₃	1	24	yes	complemented
347	#546	C₂²×C₁₃	1	24	yes	complemented
348	#546	C₂²×C₁₃	1	24	yes	complemented
349	#546	C₂²×C₁₃	1	12	yes	complemented
350	D₄²	C₂²×C₁₃	1	12	yes	complemented
351	D₄²	C₂²×C₁₃	1	24	yes	complemented
352	D₄²	C₂²×C₁₃	1	6	yes	complemented
353	#544	C₂²×C₁₃	1	6	yes	complemented
354	#543	C₂²×C₁₃	1	1	yes	characteristic, complemented
355	#542	C₂²×C₁₃	1	12	yes	complemented
356	#540	C₂²×C₁₃	1	12	yes	complemented
357	#540	C₂²×C₁₃	1	12	yes	complemented
358	#539	C₂²×C₁₃	1	12	yes	complemented
359	#539	C₂²×C₁₃	1	6	yes	complemented
360	#539	C₂²×C₁₃	1	24	yes	complemented
361	#538	C₂²×C₁₃	1	6	yes	complemented
362	#538	C₂²×C₁₃	1	12	yes	complemented
363	#538	C₂²×C₁₃	1	24	yes	complemented
364	#538	C₂²×C₁₃	1	12	yes	complemented
365	#537	C₂²×C₁₃	1	12	yes	complemented
366	#537	C₂²×C₁₃	1	6	yes	complemented
367	#535	C₂²×C₁₃	1	6	yes	complemented
368	#534	C₂²×C₁₃	1	3	yes	complemented
369	#534	C₂²×C₁₃	1	6	yes	complemented
370	#534	C₂²×C₁₃	1	6	yes	complemented
371	#534	C₂²×C₁₃	1	12	yes	complemented
372	#534	C₂²×C₁₃	1	12	yes	complemented
373	#532	C₂²×C₁₃	1	12	yes	complemented
374	#532	C₂²×C₁₃	1	6	yes	complemented
375	#529	C₂²×C₁₃	1	12	yes	complemented
376	#529	C₂²×C₁₃	1	6	yes	complemented
377	C₂×#126	C₂²×C₁₃	1	6	yes	complemented
378	C₂×#125	C₂²×C₁₃	1	3	yes	complemented
379	#525	C₂²×C₁₃	1	6	yes	complemented
380	#525	C₂²×C₁₃	1	12	yes	complemented
381	C₂×#123	C₂²×C₁₃	1	6	yes	complemented
382	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
383	C₂×#121	C₂²×C₁₃	1	3	yes	complemented
384	C₂×#121	C₂²×C₁₃	1	3	yes	complemented
385	C₂×#121	C₂²×C₁₃	1	6	yes	complemented
386	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
387	#520	C₂²×C₁₃	1	2	yes	complemented
388	#518	C₂²×C₁₃	1	6	yes	complemented
389	C₂×C₄×D₄	C₂²×C₁₃	1	6	yes	complemented
390	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
391	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	complemented
392	C₂×#117	C₂²×C₁₃	1	3	yes	complemented
393	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
394	C₂²×C₁₃	—	2	3	no	—
395	C₂²×C₁₃	—	2	3	no	—
396	C₂²×C₁₃	—	2	6	no	—
397	C₂²×C₁₃	—	2	12	no	—
398	C₂²×C₁₃	—	2	6	no	—
399	C₂²×C₁₃	—	2	12	no	—
400	C₂²×C₁₃	—	2	12	no	—
401	C₂²×C₁₃	—	2	6	no	—
402	C₂²×C₁₃	—	4	4	no	—
403	C₂²×C₁₃	—	8	6	no	—
404	C₂²×C₁₃	—	8	12	no	—
405	C₂²×C₁₃	—	16	12	no	—
406	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
407	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
408	C₄×C₁₃	—	2	12	no	—
409	C₄×C₁₃	—	2	6	no	—
410	C₄×C₁₃	—	2	3	no	—
411	C₄×C₁₃	—	2	6	no	—
412	C₄×C₁₃	—	2	2	no	—
413	C₄×C₁₃	—	2	6	no	—
414	C₄×C₁₃	—	2	6	no	—
415	C₄×C₁₃	#585	1	2	yes	—
416	H(5,𝔽₂)	—	4	24	no	—
417	C₂×#41	C₂³×C₁₃	1	2	yes	—
418	C₂×#41	C₂³×C₁₃	1	24	yes	—
419	C₂×#41	C₂³×C₁₃	1	12	yes	—
420	C₂×#41	C₂³×C₁₃	1	4	yes	—
421	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
422	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
423	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
424	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
425	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
426	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
427	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
428	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
429	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
431	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
432	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
433	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
434	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
435	#127	C₂³×C₁₃	1	12	yes	—
436	#127	C₂³×C₁₃	1	6	yes	—
437	#126	C₂³×C₁₃	1	24	yes	—
438	#126	C₂³×C₁₃	1	24	yes	—
439	#126	C₂³×C₁₃	1	12	yes	—
440	#126	C₂³×C₁₃	1	24	yes	—
441	#125	C₂³×C₁₃	1	12	yes	—
442	#125	C₂³×C₁₃	1	12	yes	—
443	#125	C₂³×C₁₃	1	12	yes	—
444	#125	C₂³×C₁₃	1	6	yes	—
445	#124	C₂³×C₁₃	1	12	yes	—
446	#124	C₂³×C₁₃	1	6	yes	—
447	#124	C₂³×C₁₃	1	12	yes	—
448	#124	C₂³×C₁₃	1	24	yes	—
449	#123	C₂³×C₁₃	1	24	yes	—
450	#123	C₂³×C₁₃	1	24	yes	—
451	#123	C₂³×C₁₃	1	24	yes	—
452	#123	C₂³×C₁₃	1	12	yes	—
453	#123	C₂³×C₁₃	1	12	yes	—
454	#123	C₂³×C₁₃	1	24	yes	—
455	#123	C₂³×C₁₃	1	24	yes	—
456	#123	C₂³×C₁₃	1	24	yes	—
457	#123	C₂³×C₁₃	1	24	yes	—
458	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
459	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
460	C₂²⋊Q₈	C₂³×C₁₃	1	6	yes	—
461	C₂²⋊Q₈	C₂³×C₁₃	1	12	yes	—
462	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
463	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
464	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
465	#121	C₂³×C₁₃	1	6	yes	—
466	#121	C₂³×C₁₃	1	12	yes	—
467	#121	C₂³×C₁₃	1	24	yes	—
468	#121	C₂³×C₁₃	1	12	yes	—
469	#121	C₂³×C₁₃	1	12	yes	—
470	#121	C₂³×C₁₃	1	24	yes	—
471	#121	C₂³×C₁₃	1	12	yes	—
472	#121	C₂³×C₁₃	1	12	yes	—
473	#121	C₂³×C₁₃	1	12	yes	—
474	#121	C₂³×C₁₃	1	12	yes	—
475	#121	C₂³×C₁₃	1	12	yes	—
476	#121	C₂³×C₁₃	1	24	yes	—
477	#121	C₂³×C₁₃	1	12	yes	—
478	#121	C₂³×C₁₃	1	12	yes	—
479	#121	C₂³×C₁₃	1	6	yes	—
480	#121	C₂³×C₁₃	1	6	yes	—
481	#121	C₂³×C₁₃	1	12	yes	—
482	#121	C₂³×C₁₃	1	24	yes	—
483	#121	C₂³×C₁₃	1	24	yes	—
484	#121	C₂³×C₁₃	1	24	yes	—
485	#120	C₂³×C₁₃	1	12	yes	—
486	#120	C₂³×C₁₃	1	24	yes	—
487	#120	C₂³×C₁₃	1	24	yes	—
488	#120	C₂³×C₁₃	1	24	yes	—
489	#120	C₂³×C₁₃	1	24	yes	—
490	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
491	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
492	C₄×D₄	C₂³×C₁₃	1	6	yes	—
493	C₄×D₄	C₂³×C₁₃	1	12	yes	—
494	C₄×D₄	C₂³×C₁₃	1	24	yes	—
495	C₄×D₄	C₂³×C₁₃	1	12	yes	—
496	C₄×D₄	C₂³×C₁₃	1	24	yes	—
497	C₄×D₄	C₂³×C₁₃	1	12	yes	—
498	C₄×D₄	C₂³×C₁₃	1	6	yes	—
499	C₄×D₄	C₂³×C₁₃	1	12	yes	—
500	C₄×D₄	C₂³×C₁₃	1	12	yes	—
501	C₄×D₄	C₂³×C₁₃	1	12	yes	—
502	C₄×D₄	C₂³×C₁₃	1	12	yes	—
503	C₄×D₄	C₂³×C₁₃	1	6	yes	—
504	C₄×D₄	C₂³×C₁₃	1	24	yes	—
505	C₄×D₄	C₂³×C₁₃	1	12	yes	—
506	#117	C₂³×C₁₃	1	6	yes	—
507	#117	C₂³×C₁₃	1	6	yes	—
508	#117	C₂³×C₁₃	1	12	yes	—
509	#117	C₂³×C₁₃	1	6	yes	—
510	#117	C₂³×C₁₃	1	12	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
514	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
515	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
516	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
517	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
518	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
519	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₃	1	3	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₃	1	6	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
528	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
529	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
530	C₂×C₁₃	—	2	6	no	—
531	C₂×C₁₃	—	4	6	no	—
532	C₂×C₁₃	—	4	12	no	—
533	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
535	C₂×C₁₃	H(7,𝔽₂)	1	1	yes	characteristic
536	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
537	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
538	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
539	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
540	#41	—	4	4	no	—
541	#41	—	4	48	no	—
542	#41	—	4	24	no	—
543	#41	—	8	4	no	—
544	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
545	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
546	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
547	C₂×D₄	—	2	24	no	—
548	C₂×D₄	—	2	12	no	—
549	C₂×D₄	—	4	6	no	—
550	C₂×D₄	—	4	12	no	—
551	C₂×D₄	—	4	24	no	—
552	C₂×D₄	—	4	48	no	—
553	C₂×D₄	—	8	6	no	—
554	C₂×D₄	—	8	12	no	—
555	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
556	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
557	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
558	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
559	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
560	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
561	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
562	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
563	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
564	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
565	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
566	C₂²×C₄	—	4	2	no	—
567	C₂²×C₄	—	4	6	no	—
568	C₂²×C₄	—	8	2	no	—
569	C₂²×C₄	—	8	6	no	—
570	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
571	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
572	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
573	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
574	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
575	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
576	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
577	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
578	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
579	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
580	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
581	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
582	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
583	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
584	C₄⋊C₄	C₂⁴×C₁₃	1	1	yes	characteristic
585	C₄⋊C₄	C₂⁴×C₁₃	1	3	yes	—
586	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
587	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
588	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
589	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
590	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
591	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
592	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
593	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
594	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
595	C₄⋊C₄	C₂⁴×C₁₃	1	12	yes	—
596	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
597	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
598	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
599	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
600	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
601	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
602	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
603	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
604	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
605	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
606	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
607	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
608	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
609	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
610	C₂²⋊C₄	C₂⁴×C₁₃	1	12	yes	—
611	C₄²	C₂⁴×C₁₃	1	12	yes	—
612	C₄²	C₂⁴×C₁₃	1	6	yes	—
613	C₄²	C₂⁴×C₁₃	1	12	yes	—
614	C₄²	C₂⁴×C₁₃	1	6	yes	—
615	C₁₃	#62905	1	1	yes	characteristic, direct product factor, Sylow
616	C₂³	—	2	6	no	—
617	C₂³	—	2	12	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	3	no	—
621	C₂³	—	4	6	no	—
622	C₂³	—	4	6	no	—
623	C₂³	—	4	3	no	—
624	C₂³	—	4	12	no	—
625	C₂³	—	4	12	no	—
626	C₂³	—	4	12	no	—
627	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
628	C₂³	C₂⁵×C₁₃	1	6	yes	—
629	C₂³	C₂⁵×C₁₃	1	12	yes	—
630	C₂³	C₂⁵×C₁₃	1	3	yes	—
631	Q₈	—	4	12	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	4	2	no	—
634	D₄	—	2	24	no	—
635	D₄	—	2	48	no	—
636	D₄	—	2	12	no	—
637	D₄	—	4	24	no	—
638	D₄	—	4	12	no	—
639	D₄	—	4	6	no	—
640	D₄	—	4	12	no	—
641	D₄	—	4	24	no	—
642	D₄	—	4	6	no	—
643	D₄	—	4	12	no	—
644	D₄	—	4	6	no	—
645	C₂×C₄	—	2	12	no	—
646	C₂×C₄	—	2	6	no	—
647	C₂×C₄	—	2	6	no	—
648	C₂×C₄	—	2	12	no	—
649	C₂×C₄	—	4	3	no	—
650	C₂×C₄	—	4	6	no	—
651	C₂×C₄	—	4	3	no	—
652	C₂×C₄	—	4	6	no	—
653	C₂×C₄	—	4	3	no	—
654	C₂×C₄	—	4	6	no	—
655	C₂×C₄	—	4	12	no	—
656	C₂×C₄	—	4	12	no	—
657	C₂×C₄	—	4	24	no	—
658	C₂×C₄	—	4	12	no	—
659	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
660	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
661	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
662	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
663	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
664	C₂×C₄	C₂⁵×C₁₃	1	12	yes	—
665	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
666	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
667	C₂²	—	2	3	no	—
668	C₂²	—	2	3	no	—
669	C₂²	—	2	6	no	—
670	C₂²	—	2	12	no	—
671	C₂²	—	2	6	no	—
672	C₂²	—	2	12	no	—
673	C₂²	—	2	12	no	—
674	C₂²	—	2	6	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	8	6	no	—
677	C₂²	—	8	12	no	—
678	C₂²	—	16	12	no	—
679	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
680	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
681	C₄	—	2	12	no	—
682	C₄	—	2	6	no	—
683	C₄	—	2	3	no	—
684	C₄	—	2	6	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	6	no	—
687	C₄	—	2	6	no	—
688	C₄	C₁₃×#585	1	2	yes	—
689	C₂	—	2	6	no	—
690	C₂	—	4	6	no	—
691	C₂	—	4	12	no	—
692	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂	C₂×C₁₃×#585	1	1	yes	characteristic
694	C₂	C₁₃×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×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×#3560	C₂	semidirect
2. C₁₃×#3559	C₂	semidirect
3. C₁₃×#3537	C₂	semidirect
4. C₁₃×#3534	C₂	semidirect
5. C₁₃×#3519	C₂	semidirect
6. C₁₃×#3496	C₂	semidirect
7. C₁₃×#3496	C₂	semidirect
8. C₁₃×#3494	C₂	semidirect
9. C₂×C₁₃×#553	C₂	semidirect
10. C₁₃×#3459	C₂	semidirect
11. C₁₃×#3459	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
13. C₁₃×#563	C₂²	semidirect
14. C₁₃×#562	C₂²	semidirect
15. C₁₃×#560	C₂²	semidirect
16. C₁₃×#555	C₂²	semidirect
17. C₁₃×#554	C₂²	semidirect
18. C₁₃×#553	C₂²	semidirect
19. C₁₃×#553	C₂²	semidirect
20. C₁₃×#553	C₂²	semidirect
21. C₁₃×#553	C₂²	semidirect
22. C₁₃×#553	C₂²	semidirect
23. C₁₃×#551	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
26. C₁₃×#547	C₂²	semidirect
27. C₁₃×#546	C₂²	semidirect
28. C₁₃×#546	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
30. C₁₃×#546	C₂²	semidirect
31. D₄²×C₁₃	C₂²	semidirect
32. D₄²×C₁₃	C₂²	semidirect
33. D₄²×C₁₃	C₂²	semidirect
34. C₁₃×#544	C₂²	semidirect
35. C₁₃×#543	C₂²	semidirect
36. C₁₃×#542	C₂²	semidirect
37. C₁₃×#540	C₂²	semidirect
38. C₁₃×#540	C₂²	semidirect
39. C₁₃×#539	C₂²	semidirect
40. C₁₃×#539	C₂²	semidirect
41. C₁₃×#539	C₂²	semidirect
42. C₁₃×#538	C₂²	semidirect
43. C₁₃×#538	C₂²	semidirect
44. C₁₃×#538	C₂²	semidirect
45. C₁₃×#538	C₂²	semidirect
46. C₁₃×#537	C₂²	semidirect
47. C₁₃×#537	C₂²	semidirect
48. C₁₃×#535	C₂²	semidirect
49. C₁₃×#534	C₂²	semidirect
50. C₁₃×#534	C₂²	semidirect
51. C₁₃×#534	C₂²	semidirect
52. C₁₃×#534	C₂²	semidirect
53. C₁₃×#534	C₂²	semidirect
54. C₁₃×#532	C₂²	semidirect
55. C₁₃×#532	C₂²	semidirect
56. C₁₃×#529	C₂²	semidirect
57. C₁₃×#529	C₂²	semidirect
58. C₂×C₁₃×#126	C₂²	semidirect
59. C₂×C₁₃×#125	C₂²	semidirect
60. C₁₃×#525	C₂²	semidirect
61. C₁₃×#525	C₂²	semidirect
62. C₂×C₁₃×#123	C₂²	semidirect
63. C₂×C₁₃×#121	C₂²	semidirect
64. C₂×C₁₃×#121	C₂²	semidirect
65. C₂×C₁₃×#121	C₂²	semidirect
66. C₂×C₁₃×#121	C₂²	semidirect
67. C₂×C₁₃×#121	C₂²	semidirect
68. C₁₃×#520	C₂²	semidirect
69. C₁₃×#518	C₂²	semidirect
70. C₂×C₄×D₄×C₁₃	C₂²	semidirect
71. C₂×C₄×D₄×C₁₃	C₂²	semidirect
72. C₂×C₄×D₄×C₁₃	C₂²	semidirect
73. C₂×C₁₃×#117	C₂²	semidirect
74. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
189. #62905	C₁₃	direct (N × H)
269. #3560	C₂×C₁₃	semidirect
270. #3559	C₂×C₁₃	semidirect
271. #3537	C₂×C₁₃	semidirect
272. #3534	C₂×C₁₃	semidirect
273. #3519	C₂×C₁₃	semidirect
274. #3496	C₂×C₁₃	semidirect
275. #3496	C₂×C₁₃	semidirect
276. #3494	C₂×C₁₃	semidirect
277. C₂×#553	C₂×C₁₃	semidirect
278. #3459	C₂×C₁₃	semidirect
279. #3459	C₂×C₁₃	semidirect
331. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
332. #563	C₂²×C₁₃	semidirect
333. #562	C₂²×C₁₃	semidirect
334. #560	C₂²×C₁₃	semidirect
335. #555	C₂²×C₁₃	semidirect
336. #554	C₂²×C₁₃	semidirect
337. #553	C₂²×C₁₃	semidirect
338. #553	C₂²×C₁₃	semidirect
339. #553	C₂²×C₁₃	semidirect
340. #553	C₂²×C₁₃	semidirect
341. #553	C₂²×C₁₃	semidirect
342. #551	C₂²×C₁₃	semidirect
343. #550	C₂²×C₁₃	semidirect
344. #547	C₂²×C₁₃	semidirect
345. #547	C₂²×C₁₃	semidirect
346. #546	C₂²×C₁₃	semidirect
347. #546	C₂²×C₁₃	semidirect
348. #546	C₂²×C₁₃	semidirect
349. #546	C₂²×C₁₃	semidirect
350. D₄²	C₂²×C₁₃	semidirect
351. D₄²	C₂²×C₁₃	semidirect
352. D₄²	C₂²×C₁₃	semidirect
353. #544	C₂²×C₁₃	semidirect
354. #543	C₂²×C₁₃	semidirect
355. #542	C₂²×C₁₃	semidirect
356. #540	C₂²×C₁₃	semidirect
357. #540	C₂²×C₁₃	semidirect
358. #539	C₂²×C₁₃	semidirect
359. #539	C₂²×C₁₃	semidirect
360. #539	C₂²×C₁₃	semidirect
361. #538	C₂²×C₁₃	semidirect
362. #538	C₂²×C₁₃	semidirect
363. #538	C₂²×C₁₃	semidirect
364. #538	C₂²×C₁₃	semidirect
365. #537	C₂²×C₁₃	semidirect
366. #537	C₂²×C₁₃	semidirect
367. #535	C₂²×C₁₃	semidirect
368. #534	C₂²×C₁₃	semidirect
369. #534	C₂²×C₁₃	semidirect
370. #534	C₂²×C₁₃	semidirect
371. #534	C₂²×C₁₃	semidirect
372. #534	C₂²×C₁₃	semidirect
373. #532	C₂²×C₁₃	semidirect
374. #532	C₂²×C₁₃	semidirect
375. #529	C₂²×C₁₃	semidirect
376. #529	C₂²×C₁₃	semidirect
377. C₂×#126	C₂²×C₁₃	semidirect
378. C₂×#125	C₂²×C₁₃	semidirect
379. #525	C₂²×C₁₃	semidirect
380. #525	C₂²×C₁₃	semidirect
381. C₂×#123	C₂²×C₁₃	semidirect
382. C₂×#121	C₂²×C₁₃	semidirect
383. C₂×#121	C₂²×C₁₃	semidirect
384. C₂×#121	C₂²×C₁₃	semidirect
385. C₂×#121	C₂²×C₁₃	semidirect
386. C₂×#121	C₂²×C₁₃	semidirect
387. #520	C₂²×C₁₃	semidirect
388. #518	C₂²×C₁₃	semidirect
389. C₂×C₄×D₄	C₂²×C₁₃	semidirect
390. C₂×C₄×D₄	C₂²×C₁₃	semidirect
391. C₂×C₄×D₄	C₂²×C₁₃	semidirect
392. C₂×#117	C₂²×C₁₃	semidirect
393. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
615. C₁₃	#62905	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×#3560	2
C₁₃×#3559	2
C₁₃×#3537	2
C₁₃×#3534	2
C₁₃×#3519	2
C₁₃×#3496	2
C₁₃×#3494	2
C₂×C₁₃×#553	2
C₁₃×#3459	2
#62905	13

Subgroups — C13×#62905 #15749244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62905 #15749244