Subgroups — C₁₃×#62811 #15749150

Order 3328.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3489	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3488	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3487	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3486	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3485	C₂	1	6	yes	maximal, complemented
8	C₁₃×#3484	C₂	1	6	yes	maximal, complemented
9	D₄×C₁₃×#41	C₂	1	16	yes	maximal, complemented
10	C₁₃×#3449	C₂	1	6	yes	maximal, complemented
11	C₂×C₁₃×#525	C₂	1	6	yes	maximal, complemented
12	C₁₃×#3428	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#585	—	2	16	no	—
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
15	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	4	yes	complemented
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	6	yes	complemented
17	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂²×C₁₃×#41	—	2	16	no	—
19	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
21	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×#41	C₂²	1	3	yes	complemented
23	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
25	C₂²×C₁₃×#41	C₂²	1	6	yes	complemented
26	C₂²×C₁₃×#41	C₂²	1	8	yes	complemented
27	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂³×D₄×C₁₃	C₂²	1	3	yes	complemented
29	C₂⁴×C₄×C₁₃	C₂²	1	3	yes	complemented
30	C₁₃×#550	C₂²	1	16	yes	complemented
31	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
32	C₁₃×#548	C₂²	1	16	yes	complemented
33	C₁₃×#548	C₂²	1	16	yes	complemented
34	C₁₃×#547	C₂²	1	48	yes	complemented
35	C₁₃×#546	C₂²	1	48	yes	complemented
36	C₁₃×#546	C₂²	1	48	yes	complemented
37	D₄²×C₁₃	C₂²	1	48	yes	complemented
38	C₁₃×#537	C₂²	1	24	yes	complemented
39	C₁₃×#536	C₂²	1	12	yes	complemented
40	C₁₃×#536	C₂²	1	12	yes	complemented
41	C₁₃×#535	C₂²	1	12	yes	complemented
42	C₁₃×#535	C₂²	1	12	yes	complemented
43	C₁₃×#534	C₂²	1	24	yes	complemented
44	C₁₃×#532	C₂²	1	24	yes	complemented
45	C₁₃×#525	C₂²	1	4	yes	complemented
46	C₁₃×#525	C₂²	1	12	yes	complemented
47	C₁₃×#525	C₂²	1	12	yes	complemented
48	C₁₃×#525	C₂²	1	12	yes	complemented
49	C₁₃×#525	C₂²	1	24	yes	complemented
50	C₁₃×#525	C₂²	1	24	yes	complemented
51	C₁₃×#525	C₂²	1	24	yes	complemented
52	C₂×C₁₃×#123	C₂²	1	12	yes	complemented
53	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	complemented
54	C₂×C₁₃×#121	C₂²	1	12	yes	complemented
55	C₂×C₁₃×#120	C₂²	1	12	yes	complemented
56	C₁₃×#520	C₂²	1	8	yes	complemented
57	C₁₃×#519	C₂²	1	2	yes	complemented
58	C₁₃×#518	C₂²	1	6	yes	complemented
59	C₄×C₁₃×#41	C₂²	1	8	yes	complemented
60	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
61	C₂×C₁₃×#117	C₂²	1	6	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	3	yes	—
63	C₁₃×2₋¹⁺⁴	—	2	32	no	—
64	C₁₃×2₋¹⁺⁴	—	2	16	no	—
65	C₁₃×H(5,𝔽₂)	—	2	32	no	—
66	C₁₃×H(5,𝔽₂)	—	2	48	no	—
67	C₂×C₁₃×#41	—	2	64	no	—
68	C₂×C₁₃×#41	—	2	64	no	—
69	C₂×C₁₃×#41	—	2	64	no	—
70	C₂×C₁₃×#41	—	2	8	no	—
71	C₂×C₁₃×#41	—	2	24	no	—
72	C₂×C₁₃×#41	—	2	24	no	—
73	C₂×C₁₃×#41	—	2	48	no	—
74	C₂×C₁₃×#41	D₄	1	16	yes	complemented
75	C₂×C₁₃×#41	C₂³	1	4	yes	—
76	C₂×C₁₃×#41	C₂³	1	12	yes	—
77	C₂×C₁₃×#41	C₂³	1	12	yes	—
78	C₂×C₁₃×#41	C₂³	1	12	yes	—
79	C₂×C₁₃×#41	C₂³	1	24	yes	—
80	C₂×C₁₃×#41	C₂³	1	8	yes	—
81	C₂×C₁₃×#41	C₂³	1	4	yes	—
82	C₂×C₁₃×#41	C₂³	1	4	yes	—
83	C₂×C₁₃×#41	C₂³	1	12	yes	complemented
84	C₂×C₁₃×#41	C₂³	1	12	yes	complemented
85	C₂×C₁₃×#41	C₂³	1	24	yes	complemented
86	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
87	C₂²×Q₈×C₁₃	—	2	8	no	—
88	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
89	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
90	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₁₃	C₂³	1	6	yes	complemented
92	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
93	C₂²×D₄×C₁₃	—	2	24	no	—
94	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
95	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
96	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
97	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
98	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
99	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
100	C₂²×D₄×C₁₃	C₂³	1	6	yes	complemented
101	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
102	C₂³×C₄×C₁₃	—	2	24	no	—
103	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
104	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
105	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
106	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
108	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
109	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
110	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
111	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
112	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	complemented
113	C₁₃×#127	C₂³	1	24	yes	complemented
114	C₁₃×#124	C₂³	1	24	yes	complemented
115	C₁₃×#124	C₂³	1	24	yes	complemented
116	C₁₃×#123	C₂³	1	8	yes	—
117	C₁₃×#123	C₂³	1	24	yes	—
118	C₁₃×#123	C₂³	1	48	yes	complemented
119	C₁₃×#123	C₂³	1	48	yes	complemented
120	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
121	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	—
122	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	complemented
123	C₁₃×C₂²⋊Q₈	C₂³	1	24	yes	complemented
124	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
125	C₁₃×#121	C₂³	1	8	yes	—
126	C₁₃×#121	C₂³	1	24	yes	—
127	C₁₃×#121	C₂³	1	24	yes	complemented
128	C₁₃×#121	C₂³	1	24	yes	complemented
129	C₁₃×#121	C₂³	1	48	yes	complemented
130	C₁₃×#121	C₂³	1	96	yes	complemented
131	C₁₃×#120	C₂³	1	8	yes	—
132	C₁₃×#120	C₂³	1	24	yes	—
133	C₁₃×#120	C₂³	1	48	yes	—
134	C₁₃×#120	C₂³	1	48	yes	complemented
135	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
136	C₄×D₄×C₁₃	C₂³	1	16	yes	—
137	C₄×D₄×C₁₃	C₂³	1	48	yes	—
138	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
139	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
140	C₄×D₄×C₁₃	C₂³	1	48	yes	complemented
141	C₁₃×#117	C₂³	1	4	yes	—
142	C₁₃×#117	C₂³	1	12	yes	—
143	C₁₃×#117	C₂³	1	12	yes	complemented
144	C₁₃×#117	C₂³	1	12	yes	complemented
145	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
146	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
147	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
148	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
149	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	complemented
150	C₂×C₄²×C₁₃	C₂³	1	12	yes	complemented
151	#62811	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂⁴×C₁₃	—	2	12	no	—
153	C₂⁴×C₁₃	—	4	12	no	—
154	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
156	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
157	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
159	C₁₃×#41	—	2	32	no	—
160	C₁₃×#41	—	2	32	no	—
161	C₁₃×#41	—	2	96	no	—
162	C₁₃×#41	—	2	96	no	—
163	C₁₃×#41	—	2	16	no	—
164	C₁₃×#41	—	2	48	no	—
165	C₁₃×#41	—	2	48	no	—
166	C₁₃×#41	—	2	48	no	—
167	C₁₃×#41	—	2	48	no	—
168	C₁₃×#41	—	2	48	no	—
169	C₁₃×#41	C₂×D₄	1	32	yes	complemented
170	C₁₃×#41	C₂×D₄	1	32	yes	complemented
171	C₂×Q₈×C₁₃	—	2	32	no	—
172	C₂×Q₈×C₁₃	—	2	32	no	—
173	C₂×Q₈×C₁₃	—	2	12	no	—
174	C₂×Q₈×C₁₃	—	2	24	no	—
175	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
176	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
177	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
179	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
180	C₂×D₄×C₁₃	—	2	24	no	—
181	C₂×D₄×C₁₃	—	2	48	no	—
182	C₂×D₄×C₁₃	—	2	96	no	—
183	C₂×D₄×C₁₃	—	2	96	no	—
184	C₂×D₄×C₁₃	—	2	12	no	—
185	C₂×D₄×C₁₃	—	2	24	no	—
186	C₂×D₄×C₁₃	—	4	48	no	—
187	C₂×D₄×C₁₃	C₂×D₄	1	24	yes	complemented
188	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
189	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
190	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
191	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
192	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
193	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
194	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
195	C₂×D₄×C₁₃	C₂⁴	1	48	yes	—
196	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
197	C₂²×C₄×C₁₃	—	2	12	no	—
198	C₂²×C₄×C₁₃	—	2	4	no	—
199	C₂²×C₄×C₁₃	—	2	12	no	—
200	C₂²×C₄×C₁₃	—	2	12	no	—
201	C₂²×C₄×C₁₃	—	2	12	no	—
202	C₂²×C₄×C₁₃	—	2	48	no	—
203	C₂²×C₄×C₁₃	—	2	48	no	—
204	C₂²×C₄×C₁₃	—	2	48	no	—
205	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	complemented
206	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
208	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
209	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
210	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
211	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
213	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
215	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
217	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
218	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
219	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
220	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
221	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
222	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
224	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
225	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
226	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
227	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
228	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
229	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
230	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
231	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
232	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
233	C₄²×C₁₃	C₂⁴	1	24	yes	—
234	C₄²×C₁₃	C₂⁴	1	8	yes	—
235	C₂×#585	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#3489	C₂×C₁₃	1	8	yes	complemented
238	#3488	C₂×C₁₃	1	8	yes	complemented
239	#3487	C₂×C₁₃	1	2	yes	complemented
240	#3486	C₂×C₁₃	1	2	yes	complemented
241	#3485	C₂×C₁₃	1	6	yes	complemented
242	#3484	C₂×C₁₃	1	6	yes	complemented
243	D₄×#41	C₂×C₁₃	1	16	yes	complemented
244	#3449	C₂×C₁₃	1	6	yes	complemented
245	C₂×#525	C₂×C₁₃	1	6	yes	complemented
246	#3428	C₂×C₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	2	2	no	—
248	C₂³×C₁₃	—	2	4	no	—
249	C₂³×C₁₃	—	2	24	no	—
250	C₂³×C₁₃	—	2	6	no	—
251	C₂³×C₁₃	—	2	24	no	—
252	C₂³×C₁₃	—	2	24	no	—
253	C₂³×C₁₃	—	4	6	no	—
254	C₂³×C₁₃	—	4	12	no	—
255	C₂³×C₁₃	—	4	6	no	—
256	C₂³×C₁₃	—	4	24	no	—
257	C₂³×C₁₃	—	4	48	no	—
258	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
259	C₂³×C₁₃	C₂⁵	1	8	yes	—
260	C₂³×C₁₃	C₂⁵	1	6	yes	—
261	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
262	C₂³×C₁₃	C₂⁵	1	6	yes	—
263	C₂³×C₁₃	C₂⁵	1	2	yes	—
264	Q₈×C₁₃	—	2	8	no	—
265	Q₈×C₁₃	—	2	24	no	—
266	Q₈×C₁₃	—	2	24	no	—
267	Q₈×C₁₃	C₂²×D₄	1	16	yes	—
268	D₄×C₁₃	—	2	16	no	—
269	D₄×C₁₃	—	2	48	no	—
270	D₄×C₁₃	—	2	48	no	—
271	D₄×C₁₃	—	2	32	no	—
272	D₄×C₁₃	—	2	8	no	—
273	D₄×C₁₃	—	2	24	no	—
274	D₄×C₁₃	—	2	24	no	—
275	D₄×C₁₃	—	4	48	no	—
276	D₄×C₁₃	C₂²×D₄	1	48	yes	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	6	no	—
279	C₂×C₄×C₁₃	—	2	24	no	—
280	C₂×C₄×C₁₃	—	2	24	no	—
281	C₂×C₄×C₁₃	—	2	4	no	—
282	C₂×C₄×C₁₃	—	2	4	no	—
283	C₂×C₄×C₁₃	—	2	24	no	—
284	C₂×C₄×C₁₃	—	2	24	no	—
285	C₂×C₄×C₁₃	—	2	12	no	—
286	C₂×C₄×C₁₃	—	2	16	no	—
287	C₂×C₄×C₁₃	—	2	12	no	—
288	C₂×C₄×C₁₃	—	2	48	no	—
289	C₂×C₄×C₁₃	—	4	24	no	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
293	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
294	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
295	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
296	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
297	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
298	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
299	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
300	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
301	#585	—	2	16	no	—
302	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	complemented
303	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	4	yes	complemented
304	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	6	yes	complemented
305	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
306	C₂²×#41	—	2	16	no	—
307	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
308	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
309	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
310	C₂²×#41	C₂²×C₁₃	1	3	yes	complemented
311	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic, complemented
312	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
313	C₂²×#41	C₂²×C₁₃	1	6	yes	complemented
314	C₂²×#41	C₂²×C₁₃	1	8	yes	complemented
315	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
316	C₂³×D₄	C₂²×C₁₃	1	3	yes	complemented
317	C₂⁴×C₄	C₂²×C₁₃	1	3	yes	complemented
318	#550	C₂²×C₁₃	1	16	yes	complemented
319	D₄×Q₈	C₂²×C₁₃	1	16	yes	complemented
320	#548	C₂²×C₁₃	1	16	yes	complemented
321	#548	C₂²×C₁₃	1	16	yes	complemented
322	#547	C₂²×C₁₃	1	48	yes	complemented
323	#546	C₂²×C₁₃	1	48	yes	complemented
324	#546	C₂²×C₁₃	1	48	yes	complemented
325	D₄²	C₂²×C₁₃	1	48	yes	complemented
326	#537	C₂²×C₁₃	1	24	yes	complemented
327	#536	C₂²×C₁₃	1	12	yes	complemented
328	#536	C₂²×C₁₃	1	12	yes	complemented
329	#535	C₂²×C₁₃	1	12	yes	complemented
330	#535	C₂²×C₁₃	1	12	yes	complemented
331	#534	C₂²×C₁₃	1	24	yes	complemented
332	#532	C₂²×C₁₃	1	24	yes	complemented
333	#525	C₂²×C₁₃	1	4	yes	complemented
334	#525	C₂²×C₁₃	1	12	yes	complemented
335	#525	C₂²×C₁₃	1	12	yes	complemented
336	#525	C₂²×C₁₃	1	12	yes	complemented
337	#525	C₂²×C₁₃	1	24	yes	complemented
338	#525	C₂²×C₁₃	1	24	yes	complemented
339	#525	C₂²×C₁₃	1	24	yes	complemented
340	C₂×#123	C₂²×C₁₃	1	12	yes	complemented
341	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	complemented
342	C₂×#121	C₂²×C₁₃	1	12	yes	complemented
343	C₂×#120	C₂²×C₁₃	1	12	yes	complemented
344	#520	C₂²×C₁₃	1	8	yes	complemented
345	#519	C₂²×C₁₃	1	2	yes	complemented
346	#518	C₂²×C₁₃	1	6	yes	complemented
347	C₄×#41	C₂²×C₁₃	1	8	yes	complemented
348	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	complemented
349	C₂×#117	C₂²×C₁₃	1	6	yes	complemented
350	C₂²×C₁₃	—	2	8	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	12	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	2	2	no	—
355	C₂²×C₁₃	—	2	6	no	—
356	C₂²×C₁₃	—	2	8	no	—
357	C₂²×C₁₃	—	2	16	no	—
358	C₂²×C₁₃	—	2	12	no	—
359	C₂²×C₁₃	—	4	12	no	—
360	C₂²×C₁₃	—	4	48	no	—
361	C₂²×C₁₃	—	4	12	no	—
362	C₂²×C₁₃	—	8	24	no	—
363	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
364	C₂²×C₁₃	C₂³×D₄	1	12	yes	—
365	C₂²×C₁₃	#585	1	4	yes	complemented
366	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
367	C₄×C₁₃	—	2	2	no	—
368	C₄×C₁₃	—	2	6	no	—
369	C₄×C₁₃	—	2	8	no	—
370	C₄×C₁₃	—	2	16	no	—
371	C₄×C₁₃	C₂³×D₄	1	2	yes	—
372	C₄×C₁₃	C₂³×D₄	1	2	yes	—
373	C₄×C₁₃	C₂³×D₄	1	12	yes	—
374	C₂⁵	C₂³×C₁₃	1	3	yes	—
375	2₋¹⁺⁴	—	2	32	no	—
376	2₋¹⁺⁴	—	2	16	no	—
377	H(5,𝔽₂)	—	2	32	no	—
378	H(5,𝔽₂)	—	2	48	no	—
379	C₂×#41	—	2	64	no	—
380	C₂×#41	—	2	64	no	—
381	C₂×#41	—	2	64	no	—
382	C₂×#41	—	2	8	no	—
383	C₂×#41	—	2	24	no	—
384	C₂×#41	—	2	24	no	—
385	C₂×#41	—	2	48	no	—
386	C₂×#41	D₄×C₁₃	1	16	yes	complemented
387	C₂×#41	C₂³×C₁₃	1	4	yes	—
388	C₂×#41	C₂³×C₁₃	1	12	yes	—
389	C₂×#41	C₂³×C₁₃	1	12	yes	—
390	C₂×#41	C₂³×C₁₃	1	12	yes	—
391	C₂×#41	C₂³×C₁₃	1	24	yes	—
392	C₂×#41	C₂³×C₁₃	1	8	yes	—
393	C₂×#41	C₂³×C₁₃	1	4	yes	—
394	C₂×#41	C₂³×C₁₃	1	4	yes	—
395	C₂×#41	C₂³×C₁₃	1	12	yes	complemented
396	C₂×#41	C₂³×C₁₃	1	12	yes	complemented
397	C₂×#41	C₂³×C₁₃	1	24	yes	complemented
398	C₂×#41	C₂³×C₁₃	1	8	yes	complemented
399	C₂²×Q₈	—	2	8	no	—
400	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
401	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
402	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
403	C₂²×Q₈	C₂³×C₁₃	1	6	yes	complemented
404	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
405	C₂²×D₄	—	2	24	no	—
406	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
407	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
408	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
409	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
410	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
411	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
412	C₂²×D₄	C₂³×C₁₃	1	6	yes	complemented
413	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
414	C₂³×C₄	—	2	24	no	—
415	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
416	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
417	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
418	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
421	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
422	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
423	C₂³×C₄	C₂³×C₁₃	1	12	yes	complemented
424	C₄⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
425	#127	C₂³×C₁₃	1	24	yes	complemented
426	#124	C₂³×C₁₃	1	24	yes	complemented
427	#124	C₂³×C₁₃	1	24	yes	complemented
428	#123	C₂³×C₁₃	1	8	yes	—
429	#123	C₂³×C₁₃	1	24	yes	—
430	#123	C₂³×C₁₃	1	48	yes	complemented
431	#123	C₂³×C₁₃	1	48	yes	complemented
432	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
433	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	—
434	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
435	C₂²⋊Q₈	C₂³×C₁₃	1	24	yes	complemented
436	C₂²⋊Q₈	C₂³×C₁₃	1	48	yes	complemented
437	#121	C₂³×C₁₃	1	8	yes	—
438	#121	C₂³×C₁₃	1	24	yes	—
439	#121	C₂³×C₁₃	1	24	yes	complemented
440	#121	C₂³×C₁₃	1	24	yes	complemented
441	#121	C₂³×C₁₃	1	48	yes	complemented
442	#121	C₂³×C₁₃	1	96	yes	complemented
443	#120	C₂³×C₁₃	1	8	yes	—
444	#120	C₂³×C₁₃	1	24	yes	—
445	#120	C₂³×C₁₃	1	48	yes	—
446	#120	C₂³×C₁₃	1	48	yes	complemented
447	C₄×Q₈	C₂³×C₁₃	1	16	yes	complemented
448	C₄×D₄	C₂³×C₁₃	1	16	yes	—
449	C₄×D₄	C₂³×C₁₃	1	48	yes	—
450	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
451	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
452	C₄×D₄	C₂³×C₁₃	1	48	yes	complemented
453	#117	C₂³×C₁₃	1	4	yes	—
454	#117	C₂³×C₁₃	1	12	yes	—
455	#117	C₂³×C₁₃	1	12	yes	complemented
456	#117	C₂³×C₁₃	1	12	yes	complemented
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	complemented
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	complemented
462	C₂×C₄²	C₂³×C₁₃	1	12	yes	complemented
463	C₂×C₁₃	—	2	2	no	—
464	C₂×C₁₃	—	2	4	no	—
465	C₂×C₁₃	—	2	12	no	—
466	C₂×C₁₃	—	4	6	no	—
467	C₂×C₁₃	—	4	8	no	—
468	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
469	C₂×C₁₃	C₂×#585	1	2	yes	—
470	C₂⁴	—	2	12	no	—
471	C₂⁴	—	4	12	no	—
472	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
473	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
474	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
475	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
476	C₂⁴	C₂⁴×C₁₃	1	3	yes	—
477	#41	—	2	32	no	—
478	#41	—	2	32	no	—
479	#41	—	2	96	no	—
480	#41	—	2	96	no	—
481	#41	—	2	16	no	—
482	#41	—	2	48	no	—
483	#41	—	2	48	no	—
484	#41	—	2	48	no	—
485	#41	—	2	48	no	—
486	#41	—	2	48	no	—
487	#41	C₂×D₄×C₁₃	1	32	yes	complemented
488	#41	C₂×D₄×C₁₃	1	32	yes	complemented
489	C₂×Q₈	—	2	32	no	—
490	C₂×Q₈	—	2	32	no	—
491	C₂×Q₈	—	2	12	no	—
492	C₂×Q₈	—	2	24	no	—
493	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	complemented
494	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
495	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
496	C₂×Q₈	C₂⁴×C₁₃	1	12	yes	—
497	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
498	C₂×D₄	—	2	24	no	—
499	C₂×D₄	—	2	48	no	—
500	C₂×D₄	—	2	96	no	—
501	C₂×D₄	—	2	96	no	—
502	C₂×D₄	—	2	12	no	—
503	C₂×D₄	—	2	24	no	—
504	C₂×D₄	—	4	48	no	—
505	C₂×D₄	C₂×D₄×C₁₃	1	24	yes	complemented
506	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
507	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
508	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
509	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
510	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
511	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
512	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
513	C₂×D₄	C₂⁴×C₁₃	1	48	yes	—
514	C₂×D₄	C₂⁴×C₁₃	1	12	yes	—
515	C₂²×C₄	—	2	12	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	12	no	—
518	C₂²×C₄	—	2	12	no	—
519	C₂²×C₄	—	2	12	no	—
520	C₂²×C₄	—	2	48	no	—
521	C₂²×C₄	—	2	48	no	—
522	C₂²×C₄	—	2	48	no	—
523	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	complemented
524	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
529	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
531	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
534	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
536	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
537	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
538	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
539	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
541	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
542	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
543	C₄⋊C₄	C₂⁴×C₁₃	1	24	yes	—
544	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
545	C₂²⋊C₄	C₂⁴×C₁₃	1	8	yes	—
546	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
547	C₂²⋊C₄	C₂⁴×C₁₃	1	24	yes	—
548	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
549	C₂²⋊C₄	C₂⁴×C₁₃	1	16	yes	—
550	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
551	C₄²	C₂⁴×C₁₃	1	8	yes	—
552	C₄²	C₂⁴×C₁₃	1	24	yes	—
553	C₁₃	#62811	1	1	yes	characteristic, direct product factor, Sylow
554	C₂³	—	2	2	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	24	no	—
557	C₂³	—	2	6	no	—
558	C₂³	—	2	24	no	—
559	C₂³	—	2	24	no	—
560	C₂³	—	4	6	no	—
561	C₂³	—	4	12	no	—
562	C₂³	—	4	6	no	—
563	C₂³	—	4	24	no	—
564	C₂³	—	4	48	no	—
565	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
566	C₂³	C₂⁵×C₁₃	1	8	yes	—
567	C₂³	C₂⁵×C₁₃	1	6	yes	—
568	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
569	C₂³	C₂⁵×C₁₃	1	6	yes	—
570	C₂³	C₂⁵×C₁₃	1	2	yes	—
571	Q₈	—	2	8	no	—
572	Q₈	—	2	24	no	—
573	Q₈	—	2	24	no	—
574	Q₈	C₂²×D₄×C₁₃	1	16	yes	—
575	D₄	—	2	16	no	—
576	D₄	—	2	48	no	—
577	D₄	—	2	48	no	—
578	D₄	—	2	32	no	—
579	D₄	—	2	8	no	—
580	D₄	—	2	24	no	—
581	D₄	—	2	24	no	—
582	D₄	—	4	48	no	—
583	D₄	C₂²×D₄×C₁₃	1	48	yes	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	6	no	—
586	C₂×C₄	—	2	24	no	—
587	C₂×C₄	—	2	24	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	24	no	—
591	C₂×C₄	—	2	24	no	—
592	C₂×C₄	—	2	12	no	—
593	C₂×C₄	—	2	16	no	—
594	C₂×C₄	—	2	12	no	—
595	C₂×C₄	—	2	48	no	—
596	C₂×C₄	—	4	24	no	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
599	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
600	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
601	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
602	C₂×C₄	C₂⁵×C₁₃	1	2	yes	—
603	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
604	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
605	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
607	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
608	C₂²	—	2	8	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	12	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	6	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	16	no	—
616	C₂²	—	2	12	no	—
617	C₂²	—	4	12	no	—
618	C₂²	—	4	48	no	—
619	C₂²	—	4	12	no	—
620	C₂²	—	8	24	no	—
621	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
622	C₂²	C₂³×D₄×C₁₃	1	12	yes	—
623	C₂²	C₁₃×#585	1	4	yes	complemented
624	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
625	C₄	—	2	2	no	—
626	C₄	—	2	6	no	—
627	C₄	—	2	8	no	—
628	C₄	—	2	16	no	—
629	C₄	C₂³×D₄×C₁₃	1	2	yes	—
630	C₄	C₂³×D₄×C₁₃	1	2	yes	—
631	C₄	C₂³×D₄×C₁₃	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	4	no	—
634	C₂	—	2	12	no	—
635	C₂	—	4	6	no	—
636	C₂	—	4	8	no	—
637	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
638	C₂	C₂×C₁₃×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#585	C₂	semidirect
2. C₂³×C₁₃×#41	C₂	semidirect
3. C₁₃×#3489	C₂	semidirect
4. C₁₃×#3488	C₂	semidirect
5. C₁₃×#3487	C₂	semidirect
6. C₁₃×#3486	C₂	semidirect
7. C₁₃×#3485	C₂	semidirect
8. C₁₃×#3484	C₂	semidirect
9. D₄×C₁₃×#41	C₂	semidirect
10. C₁₃×#3449	C₂	semidirect
11. C₂×C₁₃×#525	C₂	semidirect
12. C₁₃×#3428	C₂	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₁₃×#41	C₂²	semidirect
21. C₂²×C₁₃×#41	C₂²	semidirect
22. C₂²×C₁₃×#41	C₂²	semidirect
23. C₂²×C₁₃×#41	C₂²	semidirect
24. C₂²×C₁₃×#41	C₂²	semidirect
25. C₂²×C₁₃×#41	C₂²	semidirect
26. C₂²×C₁₃×#41	C₂²	semidirect
27. C₂³×Q₈×C₁₃	C₂²	semidirect
28. C₂³×D₄×C₁₃	C₂²	semidirect
29. C₂⁴×C₄×C₁₃	C₂²	semidirect
30. C₁₃×#550	C₂²	semidirect
31. D₄×Q₈×C₁₃	C₂²	semidirect
32. C₁₃×#548	C₂²	semidirect
33. C₁₃×#548	C₂²	semidirect
34. C₁₃×#547	C₂²	semidirect
35. C₁₃×#546	C₂²	semidirect
36. C₁₃×#546	C₂²	semidirect
37. D₄²×C₁₃	C₂²	semidirect
38. C₁₃×#537	C₂²	semidirect
39. C₁₃×#536	C₂²	semidirect
40. C₁₃×#536	C₂²	semidirect
41. C₁₃×#535	C₂²	semidirect
42. C₁₃×#535	C₂²	semidirect
43. C₁₃×#534	C₂²	semidirect
44. C₁₃×#532	C₂²	semidirect
45. C₁₃×#525	C₂²	semidirect
46. C₁₃×#525	C₂²	semidirect
47. C₁₃×#525	C₂²	semidirect
48. C₁₃×#525	C₂²	semidirect
49. C₁₃×#525	C₂²	semidirect
50. C₁₃×#525	C₂²	semidirect
51. C₁₃×#525	C₂²	semidirect
52. C₂×C₁₃×#123	C₂²	semidirect
53. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₁₃×#121	C₂²	semidirect
55. C₂×C₁₃×#120	C₂²	semidirect
56. C₁₃×#520	C₂²	semidirect
57. C₁₃×#519	C₂²	semidirect
58. C₁₃×#518	C₂²	semidirect
59. C₄×C₁₃×#41	C₂²	semidirect
60. C₂×C₄×D₄×C₁₃	C₂²	semidirect
61. C₂×C₁₃×#117	C₂²	semidirect
74. C₂×C₁₃×#41	D₄	semidirect
83. C₂×C₁₃×#41	C₂³	semidirect
84. C₂×C₁₃×#41	C₂³	semidirect
85. C₂×C₁₃×#41	C₂³	semidirect
86. C₂×C₁₃×#41	C₂³	semidirect
91. C₂²×Q₈×C₁₃	C₂³	semidirect
92. C₂²×Q₈×C₁₃	C₂³	semidirect
100. C₂²×D₄×C₁₃	C₂³	semidirect
101. C₂²×D₄×C₁₃	C₂³	semidirect
111. C₂³×C₄×C₁₃	C₂³	semidirect
112. C₁₃×C₄⋊Q₈	C₂³	semidirect
113. C₁₃×#127	C₂³	semidirect
114. C₁₃×#124	C₂³	semidirect
115. C₁₃×#124	C₂³	semidirect
118. C₁₃×#123	C₂³	semidirect
119. C₁₃×#123	C₂³	semidirect
122. C₁₃×C₂²⋊Q₈	C₂³	semidirect
123. C₁₃×C₂²⋊Q₈	C₂³	semidirect
124. C₁₃×C₂²⋊Q₈	C₂³	semidirect
127. C₁₃×#121	C₂³	semidirect
128. C₁₃×#121	C₂³	semidirect
129. C₁₃×#121	C₂³	semidirect
130. C₁₃×#121	C₂³	semidirect
134. C₁₃×#120	C₂³	semidirect
135. C₄×Q₈×C₁₃	C₂³	semidirect
138. C₄×D₄×C₁₃	C₂³	semidirect
139. C₄×D₄×C₁₃	C₂³	semidirect
140. C₄×D₄×C₁₃	C₂³	semidirect
143. C₁₃×#117	C₂³	semidirect
144. C₁₃×#117	C₂³	semidirect
145. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
146. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
149. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
150. C₂×C₄²×C₁₃	C₂³	semidirect
151. #62811	C₁₃	direct (N × H)
169. C₁₃×#41	C₂×D₄	semidirect
170. C₁₃×#41	C₂×D₄	semidirect
175. C₂×Q₈×C₁₃	C₂×D₄	semidirect
187. C₂×D₄×C₁₃	C₂×D₄	semidirect
205. C₂²×C₄×C₁₃	C₂×D₄	semidirect
235. C₂×#585	C₂×C₁₃	semidirect
236. C₂³×#41	C₂×C₁₃	semidirect
237. #3489	C₂×C₁₃	semidirect
238. #3488	C₂×C₁₃	semidirect
239. #3487	C₂×C₁₃	semidirect
240. #3486	C₂×C₁₃	semidirect
241. #3485	C₂×C₁₃	semidirect
242. #3484	C₂×C₁₃	semidirect
243. D₄×#41	C₂×C₁₃	semidirect
244. #3449	C₂×C₁₃	semidirect
245. C₂×#525	C₂×C₁₃	semidirect
246. #3428	C₂×C₁₃	semidirect
302. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
303. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
304. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
305. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
308. C₂²×#41	C₂²×C₁₃	semidirect
309. C₂²×#41	C₂²×C₁₃	semidirect
310. C₂²×#41	C₂²×C₁₃	semidirect
311. C₂²×#41	C₂²×C₁₃	semidirect
312. C₂²×#41	C₂²×C₁₃	semidirect
313. C₂²×#41	C₂²×C₁₃	semidirect
314. C₂²×#41	C₂²×C₁₃	semidirect
315. C₂³×Q₈	C₂²×C₁₃	semidirect
316. C₂³×D₄	C₂²×C₁₃	semidirect
317. C₂⁴×C₄	C₂²×C₁₃	semidirect
318. #550	C₂²×C₁₃	semidirect
319. D₄×Q₈	C₂²×C₁₃	semidirect
320. #548	C₂²×C₁₃	semidirect
321. #548	C₂²×C₁₃	semidirect
322. #547	C₂²×C₁₃	semidirect
323. #546	C₂²×C₁₃	semidirect
324. #546	C₂²×C₁₃	semidirect
325. D₄²	C₂²×C₁₃	semidirect
326. #537	C₂²×C₁₃	semidirect
327. #536	C₂²×C₁₃	semidirect
328. #536	C₂²×C₁₃	semidirect
329. #535	C₂²×C₁₃	semidirect
330. #535	C₂²×C₁₃	semidirect
331. #534	C₂²×C₁₃	semidirect
332. #532	C₂²×C₁₃	semidirect
333. #525	C₂²×C₁₃	semidirect
334. #525	C₂²×C₁₃	semidirect
335. #525	C₂²×C₁₃	semidirect
336. #525	C₂²×C₁₃	semidirect
337. #525	C₂²×C₁₃	semidirect
338. #525	C₂²×C₁₃	semidirect
339. #525	C₂²×C₁₃	semidirect
340. C₂×#123	C₂²×C₁₃	semidirect
341. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
342. C₂×#121	C₂²×C₁₃	semidirect
343. C₂×#120	C₂²×C₁₃	semidirect
344. #520	C₂²×C₁₃	semidirect
345. #519	C₂²×C₁₃	semidirect
346. #518	C₂²×C₁₃	semidirect
347. C₄×#41	C₂²×C₁₃	semidirect
348. C₂×C₄×D₄	C₂²×C₁₃	semidirect
349. C₂×#117	C₂²×C₁₃	semidirect
365. C₂²×C₁₃	#585	semidirect
386. C₂×#41	D₄×C₁₃	semidirect
395. C₂×#41	C₂³×C₁₃	semidirect
396. C₂×#41	C₂³×C₁₃	semidirect
397. C₂×#41	C₂³×C₁₃	semidirect
398. C₂×#41	C₂³×C₁₃	semidirect
403. C₂²×Q₈	C₂³×C₁₃	semidirect
404. C₂²×Q₈	C₂³×C₁₃	semidirect
412. C₂²×D₄	C₂³×C₁₃	semidirect
413. C₂²×D₄	C₂³×C₁₃	semidirect
423. C₂³×C₄	C₂³×C₁₃	semidirect
424. C₄⋊Q₈	C₂³×C₁₃	semidirect
425. #127	C₂³×C₁₃	semidirect
426. #124	C₂³×C₁₃	semidirect
427. #124	C₂³×C₁₃	semidirect
430. #123	C₂³×C₁₃	semidirect
431. #123	C₂³×C₁₃	semidirect
434. C₂²⋊Q₈	C₂³×C₁₃	semidirect
435. C₂²⋊Q₈	C₂³×C₁₃	semidirect
436. C₂²⋊Q₈	C₂³×C₁₃	semidirect
439. #121	C₂³×C₁₃	semidirect
440. #121	C₂³×C₁₃	semidirect
441. #121	C₂³×C₁₃	semidirect
442. #121	C₂³×C₁₃	semidirect
446. #120	C₂³×C₁₃	semidirect
447. C₄×Q₈	C₂³×C₁₃	semidirect
450. C₄×D₄	C₂³×C₁₃	semidirect
451. C₄×D₄	C₂³×C₁₃	semidirect
452. C₄×D₄	C₂³×C₁₃	semidirect
455. #117	C₂³×C₁₃	semidirect
456. #117	C₂³×C₁₃	semidirect
457. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
458. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
461. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
462. C₂×C₄²	C₂³×C₁₃	semidirect
487. #41	C₂×D₄×C₁₃	semidirect
488. #41	C₂×D₄×C₁₃	semidirect
493. C₂×Q₈	C₂×D₄×C₁₃	semidirect
505. C₂×D₄	C₂×D₄×C₁₃	semidirect
523. C₂²×C₄	C₂×D₄×C₁₃	semidirect
553. C₁₃	#62811	direct (N × H)
623. C₂²	C₁₃×#585	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#585	2
C₂³×C₁₃×#41	2
C₁₃×#3489	2
C₁₃×#3488	2
C₁₃×#3487	2
C₁₃×#3486	2
C₁₃×#3485	2
C₁₃×#3484	2
D₄×C₁₃×#41	2
C₁₃×#3449	2
C₂×C₁₃×#525	2
C₁₃×#3428	2
#62811	13

Subgroups — C13×#62811 #15749150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#62811 #15749150