Subgroups — C₂²×C₁₃×#575 #15749422

Order 3328.

11294 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×#41	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#575	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₁₃×#137	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₃×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×#135	C₂	1	4	yes	maximal, complemented
6	C₂³×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₃×#41	—	2	2	no	—
8	C₂²×C₁₃×#41	—	2	24	no	—
9	C₂²×C₁₃×#41	—	2	2	no	—
10	C₂²×C₁₃×#41	C₂²	1	4	yes	—
11	C₂²×C₁₃×#41	C₂²	1	4	yes	complemented
12	C₂²×C₁₃×#41	C₂²	1	48	yes	complemented
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₁₃	—	2	2	no	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
16	C₂⁴×C₄×C₁₃	—	2	2	no	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#575	C₂²	1	256	yes	direct product factor
19	C₂×C₁₃×#137	C₂²	1	96	yes	complemented
20	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	96	yes	complemented
21	C₂×C₁₃×#135	C₂²	1	96	yes	complemented
22	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
24	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
25	C₂²×C₁₃×M₁₆	C₂²	1	4	yes	complemented
26	C₂²×C₁₃×M₁₆	C₂²	1	24	yes	complemented
27	C₂³×C₈×C₁₃	C₂²	1	2	yes	complemented
28	C₂⁵×C₁₃	—	2	2	no	—
29	C₂⁵×C₁₃	D₄	1	1	yes	characteristic
30	C₂×C₁₃×#41	—	2	24	no	—
31	C₂×C₁₃×#41	—	2	48	no	—
32	C₂×C₁₃×#41	—	2	48	no	—
33	C₂×C₁₃×#41	—	2	24	no	—
34	C₂×C₁₃×#41	—	2	192	no	—
35	C₂×C₁₃×#41	C₂³	1	48	yes	—
36	C₂×C₁₃×#41	C₂³	1	48	yes	complemented
37	C₂×C₁₃×#41	C₂³	1	128	yes	complemented
38	C₂²×Q₈×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	—	2	12	no	—
40	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
41	C₂²×Q₈×C₁₃	C₂³	1	24	yes	complemented
42	C₂²×D₄×C₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	—	2	48	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	12	no	—
47	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
48	C₂²×D₄×C₁₃	C₂³	1	24	yes	complemented
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₃	—	2	4	no	—
51	C₂³×C₄×C₁₃	—	2	48	no	—
52	C₂³×C₄×C₁₃	—	2	4	no	—
53	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	D₄	1	12	yes	—
55	C₂³×C₄×C₁₃	D₄	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#137	C₂³	1	256	yes	complemented
60	C₁₃×AGL(1,ℤ/8)	C₂³	1	256	yes	complemented
61	C₁₃×#135	C₂³	1	256	yes	complemented
62	C₂×C₁₃×Q₁₆	C₂³	1	48	yes	complemented
63	C₂×C₁₃×SD₁₆	C₂³	1	96	yes	complemented
64	C₂×C₁₃×D₈	C₂³	1	48	yes	complemented
65	C₂×C₁₃×M₁₆	C₂³	1	48	yes	complemented
66	C₂×C₁₃×M₁₆	C₂³	1	64	yes	complemented
67	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	24	yes	complemented
69	C₂²×#575	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂⁴×C₁₃	—	2	4	no	—
71	C₂⁴×C₁₃	—	2	24	no	—
72	C₂⁴×C₁₃	—	4	4	no	—
73	C₂⁴×C₁₃	—	4	16	no	—
74	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
75	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₁₃	C₂×D₄	1	12	yes	—
77	C₁₃×#41	—	2	96	no	—
78	C₁₃×#41	—	2	128	no	—
79	C₁₃×#41	—	2	128	no	—
80	C₁₃×#41	—	2	96	no	—
81	C₁₃×#41	C₂⁴	1	64	yes	—
82	C₁₃×#41	C₂⁴	1	64	yes	complemented
83	C₂×Q₈×C₁₃	—	2	12	no	—
84	C₂×Q₈×C₁₃	—	2	24	no	—
85	C₂×Q₈×C₁₃	—	2	48	no	—
86	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
87	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	complemented
88	C₂×D₄×C₁₃	—	2	48	no	—
89	C₂×D₄×C₁₃	—	2	48	no	—
90	C₂×D₄×C₁₃	—	2	128	no	—
91	C₂×D₄×C₁₃	—	2	12	no	—
92	C₂×D₄×C₁₃	—	2	24	no	—
93	C₂×D₄×C₁₃	—	2	48	no	—
94	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
95	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	24	no	—
98	C₂²×C₄×C₁₃	—	2	48	no	—
99	C₂²×C₄×C₁₃	—	2	48	no	—
100	C₂²×C₄×C₁₃	—	2	128	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	48	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
112	C₁₃×Q₁₆	C₂⁴	1	64	yes	complemented
113	C₁₃×SD₁₆	C₂⁴	1	128	yes	complemented
114	C₁₃×D₈	C₂⁴	1	64	yes	complemented
115	C₁₃×M₁₆	C₂⁴	1	64	yes	complemented
116	C₂×C₈×C₁₃	C₂⁴	1	24	yes	—
117	C₂×C₈×C₁₃	C₂⁴	1	32	yes	complemented
118	C₂³×#41	C₂×C₁₃	1	2	yes	complemented
119	C₂×#575	C₂×C₁₃	1	48	yes	direct product factor
120	C₂²×#137	C₂×C₁₃	1	4	yes	complemented
121	C₂²×AGL(1,ℤ/8)	C₂×C₁₃	1	4	yes	complemented
122	C₂²×#135	C₂×C₁₃	1	4	yes	complemented
123	C₂³×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂³×C₁₃	—	2	8	no	—
125	C₂³×C₁₃	—	2	4	no	—
126	C₂³×C₁₃	—	2	24	no	—
127	C₂³×C₁₃	—	2	32	no	—
128	C₂³×C₁₃	—	4	24	no	—
129	C₂³×C₁₃	—	4	96	no	—
130	C₂³×C₁₃	—	4	16	no	—
131	C₂³×C₁₃	C₂²×D₄	1	12	yes	—
132	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
133	C₂³×C₁₃	C₂²×D₄	1	16	yes	—
134	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₁₃	—	2	24	no	—
136	Q₈×C₁₃	—	2	32	no	—
137	Q₈×C₁₃	C₂⁵	1	16	yes	—
138	D₄×C₁₃	—	2	64	no	—
139	D₄×C₁₃	—	2	64	no	—
140	D₄×C₁₃	—	2	24	no	—
141	D₄×C₁₃	—	2	32	no	—
142	D₄×C₁₃	C₂⁵	1	16	yes	—
143	C₂×C₄×C₁₃	—	2	24	no	—
144	C₂×C₄×C₁₃	—	2	32	no	—
145	C₂×C₄×C₁₃	—	2	64	no	—
146	C₂×C₄×C₁₃	—	2	64	no	—
147	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
148	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	32	yes	—
150	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
151	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
152	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
153	C₂×C₄×C₁₃	C₂²×D₄	1	16	yes	—
154	C₂×C₄×C₁₃	C₂⁵	1	3	yes	—
155	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
156	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
157	C₈×C₁₃	C₂⁵	1	16	yes	—
158	C₂²×#41	—	2	2	no	—
159	C₂²×#41	—	2	2	no	—
160	C₂²×#41	—	2	24	no	—
161	C₂²×#41	C₂²×C₁₃	1	4	yes	—
162	C₂²×#41	C₂²×C₁₃	1	4	yes	complemented
163	C₂²×#41	C₂²×C₁₃	1	48	yes	complemented
164	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
165	C₂³×D₄	—	2	2	no	—
166	C₂³×D₄	C₂²×C₁₃	1	2	yes	complemented
167	C₂⁴×C₄	—	2	2	no	—
168	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
169	#575	C₂²×C₁₃	1	256	yes	direct product factor
170	C₂×#137	C₂²×C₁₃	1	96	yes	complemented
171	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	96	yes	complemented
172	C₂×#135	C₂²×C₁₃	1	96	yes	complemented
173	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
174	C₂²×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
175	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
176	C₂²×M₁₆	C₂²×C₁₃	1	4	yes	complemented
177	C₂²×M₁₆	C₂²×C₁₃	1	24	yes	complemented
178	C₂³×C₈	C₂²×C₁₃	1	2	yes	complemented
179	C₂²×C₁₃	—	2	24	no	—
180	C₂²×C₁₃	—	2	12	no	—
181	C₂²×C₁₃	—	2	16	no	—
182	C₂²×C₁₃	—	4	16	no	—
183	C₂²×C₁₃	—	4	64	no	—
184	C₂²×C₁₃	—	4	48	no	—
185	C₂²×C₁₃	#575	1	4	yes	direct product factor
186	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
187	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
188	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
189	C₄×C₁₃	—	2	16	no	—
190	C₄×C₁₃	C₂³×D₄	1	4	yes	—
191	C₄×C₁₃	C₂³×D₄	1	8	yes	—
192	C₄×C₁₃	C₂³×D₄	1	3	yes	—
193	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
194	C₂⁵	—	2	2	no	—
195	C₂⁵	D₄×C₁₃	1	1	yes	characteristic
196	C₂×#41	—	2	24	no	—
197	C₂×#41	—	2	48	no	—
198	C₂×#41	—	2	48	no	—
199	C₂×#41	—	2	24	no	—
200	C₂×#41	—	2	192	no	—
201	C₂×#41	C₂³×C₁₃	1	48	yes	—
202	C₂×#41	C₂³×C₁₃	1	48	yes	complemented
203	C₂×#41	C₂³×C₁₃	1	128	yes	complemented
204	C₂²×Q₈	—	2	2	no	—
205	C₂²×Q₈	—	2	12	no	—
206	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
207	C₂²×Q₈	C₂³×C₁₃	1	24	yes	complemented
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	—	2	4	no	—
210	C₂²×D₄	—	2	48	no	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	12	no	—
213	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
214	C₂²×D₄	C₂³×C₁₃	1	24	yes	complemented
215	C₂³×C₄	—	2	2	no	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	4	no	—
218	C₂³×C₄	—	2	48	no	—
219	C₂³×C₄	D₄×C₁₃	1	2	yes	—
220	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₁₃	1	12	yes	—
222	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
224	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
225	#137	C₂³×C₁₃	1	256	yes	complemented
226	AGL(1,ℤ/8)	C₂³×C₁₃	1	256	yes	complemented
227	#135	C₂³×C₁₃	1	256	yes	complemented
228	C₂×Q₁₆	C₂³×C₁₃	1	48	yes	complemented
229	C₂×SD₁₆	C₂³×C₁₃	1	96	yes	complemented
230	C₂×D₈	C₂³×C₁₃	1	48	yes	complemented
231	C₂×M₁₆	C₂³×C₁₃	1	48	yes	complemented
232	C₂×M₁₆	C₂³×C₁₃	1	64	yes	complemented
233	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
234	C₂²×C₈	C₂³×C₁₃	1	24	yes	complemented
235	C₂×C₁₃	—	2	8	no	—
236	C₂×C₁₃	—	2	4	no	—
237	C₂×C₁₃	—	4	16	no	—
238	C₂×C₁₃	C₂×#575	1	6	yes	direct product factor
239	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	24	no	—
242	C₂⁴	—	4	4	no	—
243	C₂⁴	—	4	16	no	—
244	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
245	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
246	C₂⁴	C₂×D₄×C₁₃	1	12	yes	—
247	#41	—	2	96	no	—
248	#41	—	2	128	no	—
249	#41	—	2	128	no	—
250	#41	—	2	96	no	—
251	#41	C₂⁴×C₁₃	1	64	yes	—
252	#41	C₂⁴×C₁₃	1	64	yes	complemented
253	C₂×Q₈	—	2	12	no	—
254	C₂×Q₈	—	2	24	no	—
255	C₂×Q₈	—	2	48	no	—
256	C₂×Q₈	C₂⁴×C₁₃	1	24	yes	—
257	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	complemented
258	C₂×D₄	—	2	48	no	—
259	C₂×D₄	—	2	48	no	—
260	C₂×D₄	—	2	128	no	—
261	C₂×D₄	—	2	12	no	—
262	C₂×D₄	—	2	24	no	—
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	C₂⁴×C₁₃	1	24	yes	—
265	C₂×D₄	C₂⁴×C₁₃	1	32	yes	complemented
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	24	no	—
268	C₂²×C₄	—	2	48	no	—
269	C₂²×C₄	—	2	48	no	—
270	C₂²×C₄	—	2	128	no	—
271	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃	1	48	yes	—
278	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
280	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
281	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
282	Q₁₆	C₂⁴×C₁₃	1	64	yes	complemented
283	SD₁₆	C₂⁴×C₁₃	1	128	yes	complemented
284	D₈	C₂⁴×C₁₃	1	64	yes	complemented
285	M₁₆	C₂⁴×C₁₃	1	64	yes	complemented
286	C₂×C₈	C₂⁴×C₁₃	1	24	yes	—
287	C₂×C₈	C₂⁴×C₁₃	1	32	yes	complemented
288	C₁₃	C₂²×#575	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	2	8	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	2	32	no	—
293	C₂³	—	4	24	no	—
294	C₂³	—	4	96	no	—
295	C₂³	—	4	16	no	—
296	C₂³	C₂²×D₄×C₁₃	1	12	yes	—
297	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
298	C₂³	C₂²×D₄×C₁₃	1	16	yes	—
299	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
300	Q₈	—	2	24	no	—
301	Q₈	—	2	32	no	—
302	Q₈	C₂⁵×C₁₃	1	16	yes	—
303	D₄	—	2	64	no	—
304	D₄	—	2	64	no	—
305	D₄	—	2	24	no	—
306	D₄	—	2	32	no	—
307	D₄	C₂⁵×C₁₃	1	16	yes	—
308	C₂×C₄	—	2	24	no	—
309	C₂×C₄	—	2	32	no	—
310	C₂×C₄	—	2	64	no	—
311	C₂×C₄	—	2	64	no	—
312	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
313	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
314	C₂×C₄	C₂²×D₄×C₁₃	1	32	yes	—
315	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
316	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
317	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
318	C₂×C₄	C₂²×D₄×C₁₃	1	16	yes	—
319	C₂×C₄	C₂⁵×C₁₃	1	3	yes	—
320	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
321	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
322	C₈	C₂⁵×C₁₃	1	16	yes	—
323	C₂²	—	2	24	no	—
324	C₂²	—	2	12	no	—
325	C₂²	—	2	16	no	—
326	C₂²	—	4	16	no	—
327	C₂²	—	4	64	no	—
328	C₂²	—	4	48	no	—
329	C₂²	C₁₃×#575	1	4	yes	direct product factor
330	C₂²	C₂³×D₄×C₁₃	1	8	yes	—
331	C₂²	C₂³×D₄×C₁₃	1	4	yes	—
332	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
333	C₄	—	2	16	no	—
334	C₄	C₂³×D₄×C₁₃	1	4	yes	—
335	C₄	C₂³×D₄×C₁₃	1	8	yes	—
336	C₄	C₂³×D₄×C₁₃	1	3	yes	—
337	C₄	C₂⁶×C₁₃	1	1	yes	characteristic
338	C₂	—	2	8	no	—
339	C₂	—	2	4	no	—
340	C₂	—	4	16	no	—
341	C₂	C₂×C₁₃×#575	1	6	yes	direct product factor
342	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₁₃
socle	C₂³×C₁₃	C₂²×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂⁴×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×#41	C₂	semidirect
2. C₂×C₁₃×#575	C₂	direct (N × H)
3. C₂²×C₁₃×#137	C₂	semidirect
4. C₂²×C₁₃×AGL(1,ℤ/8)	C₂	semidirect
5. C₂²×C₁₃×#135	C₂	semidirect
6. C₂³×C₁₃×M₁₆	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
12. C₂²×C₁₃×#41	C₂²	semidirect
13. C₂³×Q₈×C₁₃	C₂²	semidirect
15. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₁₃×#575	C₂²	direct (N × H)
19. C₂×C₁₃×#137	C₂²	semidirect
20. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂²×C₁₃×Q₁₆	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
24. C₂²×C₁₃×D₈	C₂²	semidirect
25. C₂²×C₁₃×M₁₆	C₂²	semidirect
26. C₂²×C₁₃×M₁₆	C₂²	semidirect
27. C₂³×C₈×C₁₃	C₂²	semidirect
36. C₂×C₁₃×#41	C₂³	semidirect
37. C₂×C₁₃×#41	C₂³	semidirect
41. C₂²×Q₈×C₁₃	C₂³	semidirect
48. C₂²×D₄×C₁₃	C₂³	semidirect
59. C₁₃×#137	C₂³	semidirect
60. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
61. C₁₃×#135	C₂³	semidirect
62. C₂×C₁₃×Q₁₆	C₂³	semidirect
63. C₂×C₁₃×SD₁₆	C₂³	semidirect
64. C₂×C₁₃×D₈	C₂³	semidirect
65. C₂×C₁₃×M₁₆	C₂³	semidirect
66. C₂×C₁₃×M₁₆	C₂³	semidirect
68. C₂²×C₈×C₁₃	C₂³	semidirect
69. C₂²×#575	C₁₃	direct (N × H)
82. C₁₃×#41	C₂⁴	semidirect
87. C₂×Q₈×C₁₃	C₂⁴	semidirect
95. C₂×D₄×C₁₃	C₂⁴	semidirect
112. C₁₃×Q₁₆	C₂⁴	semidirect
113. C₁₃×SD₁₆	C₂⁴	semidirect
114. C₁₃×D₈	C₂⁴	semidirect
115. C₁₃×M₁₆	C₂⁴	semidirect
117. C₂×C₈×C₁₃	C₂⁴	semidirect
118. C₂³×#41	C₂×C₁₃	semidirect
119. C₂×#575	C₂×C₁₃	direct (N × H)
120. C₂²×#137	C₂×C₁₃	semidirect
121. C₂²×AGL(1,ℤ/8)	C₂×C₁₃	semidirect
122. C₂²×#135	C₂×C₁₃	semidirect
123. C₂³×M₁₆	C₂×C₁₃	semidirect
162. C₂²×#41	C₂²×C₁₃	semidirect
163. C₂²×#41	C₂²×C₁₃	semidirect
164. C₂³×Q₈	C₂²×C₁₃	semidirect
166. C₂³×D₄	C₂²×C₁₃	semidirect
169. #575	C₂²×C₁₃	direct (N × H)
170. C₂×#137	C₂²×C₁₃	semidirect
171. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
172. C₂×#135	C₂²×C₁₃	semidirect
173. C₂²×Q₁₆	C₂²×C₁₃	semidirect
174. C₂²×SD₁₆	C₂²×C₁₃	semidirect
175. C₂²×D₈	C₂²×C₁₃	semidirect
176. C₂²×M₁₆	C₂²×C₁₃	semidirect
177. C₂²×M₁₆	C₂²×C₁₃	semidirect
178. C₂³×C₈	C₂²×C₁₃	semidirect
185. C₂²×C₁₃	#575	direct (N × H)
202. C₂×#41	C₂³×C₁₃	semidirect
203. C₂×#41	C₂³×C₁₃	semidirect
207. C₂²×Q₈	C₂³×C₁₃	semidirect
214. C₂²×D₄	C₂³×C₁₃	semidirect
225. #137	C₂³×C₁₃	semidirect
226. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
227. #135	C₂³×C₁₃	semidirect
228. C₂×Q₁₆	C₂³×C₁₃	semidirect
229. C₂×SD₁₆	C₂³×C₁₃	semidirect
230. C₂×D₈	C₂³×C₁₃	semidirect
231. C₂×M₁₆	C₂³×C₁₃	semidirect
232. C₂×M₁₆	C₂³×C₁₃	semidirect
234. C₂²×C₈	C₂³×C₁₃	semidirect
238. C₂×C₁₃	C₂×#575	direct (N × H)
252. #41	C₂⁴×C₁₃	semidirect
257. C₂×Q₈	C₂⁴×C₁₃	semidirect
265. C₂×D₄	C₂⁴×C₁₃	semidirect
282. Q₁₆	C₂⁴×C₁₃	semidirect
283. SD₁₆	C₂⁴×C₁₃	semidirect
284. D₈	C₂⁴×C₁₃	semidirect
285. M₁₆	C₂⁴×C₁₃	semidirect
287. C₂×C₈	C₂⁴×C₁₃	semidirect
288. C₁₃	C₂²×#575	direct (N × H)
329. C₂²	C₁₃×#575	direct (N × H)
341. C₂	C₂×C₁₃×#575	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×#41	2
C₂×C₁₃×#575	2
C₂²×C₁₃×#137	2
C₂²×C₁₃×AGL(1,ℤ/8)	2
C₂²×C₁₃×#135	2
C₂³×C₁₃×M₁₆	2
C₂²×#575	13

Subgroups — C22×C13×#575 #15749422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#575 #15749422