Subgroups — C₂²×C₁₃×#535 #15749013

Order 3328.

14414 conjugacy classes of subgroups.

The subgroup lattice has 348 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	1	yes	maximal, characteristic, complemented
2	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#535	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₁₃×#127	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#121	C₂	1	4	yes	maximal, complemented
7	C₂²×C₁₃×#120	C₂	1	4	yes	maximal, complemented
8	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₁₃×#41	—	2	16	no	—
11	C₂²×C₁₃×#41	C₂²	1	24	yes	complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₃	—	2	16	no	—
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
17	C₂³×D₄×C₁₃	C₂²	1	24	yes	complemented
18	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₃	C₂²	1	8	yes	complemented
20	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
22	C₁₃×#535	C₂²	1	256	yes	direct product factor
23	C₂×C₁₃×#127	C₂²	1	48	yes	complemented
24	C₂×C₁₃×#124	C₂²	1	48	yes	complemented
25	C₂×C₁₃×#121	C₂²	1	96	yes	complemented
26	C₂×C₁₃×#120	C₂²	1	96	yes	complemented
27	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
31	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
32	C₂⁵×C₁₃	—	2	16	no	—
33	C₂⁵×C₁₃	—	4	16	no	—
34	C₂⁵×C₁₃	C₂³	1	4	yes	—
35	C₂⁵×C₁₃	C₂³	1	2	yes	—
36	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
37	C₂⁵×C₁₃	C₂³	1	24	yes	—
38	C₂×C₁₃×#41	—	2	192	no	—
39	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
42	C₂²×D₄×C₁₃	—	2	16	no	—
43	C₂²×D₄×C₁₃	—	2	16	no	—
44	C₂²×D₄×C₁₃	—	2	16	no	—
45	C₂²×D₄×C₁₃	—	2	8	no	—
46	C₂²×D₄×C₁₃	—	2	192	no	—
47	C₂²×D₄×C₁₃	—	4	32	no	—
48	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
50	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
52	C₂²×D₄×C₁₃	C₂³	1	12	yes	complemented
53	C₂²×D₄×C₁₃	C₂³	1	96	yes	complemented
54	C₂³×C₄×C₁₃	—	2	16	no	—
55	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
56	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
61	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
62	C₁₃×#127	C₂³	1	128	yes	complemented
63	C₁₃×#124	C₂³	1	128	yes	complemented
64	C₁₃×#121	C₂³	1	256	yes	complemented
65	C₁₃×#120	C₂³	1	256	yes	complemented
66	C₁₃×#117	C₂³	1	64	yes	complemented
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	96	yes	complemented
70	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
71	C₂²×#535	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	2	8	no	—
73	C₂⁴×C₁₃	—	2	8	no	—
74	C₂⁴×C₁₃	—	2	96	no	—
75	C₂⁴×C₁₃	—	2	16	no	—
76	C₂⁴×C₁₃	—	2	16	no	—
77	C₂⁴×C₁₃	—	2	32	no	—
78	C₂⁴×C₁₃	—	4	96	no	—
79	C₂⁴×C₁₃	—	4	128	no	—
80	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
81	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
82	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
83	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
84	C₂⁴×C₁₃	C₂⁴	1	32	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₁₃×#41	—	2	256	no	—
87	C₂×Q₈×C₁₃	—	2	48	no	—
88	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
89	C₂×D₄×C₁₃	—	2	96	no	—
90	C₂×D₄×C₁₃	—	2	96	no	—
91	C₂×D₄×C₁₃	—	2	96	no	—
92	C₂×D₄×C₁₃	—	2	48	no	—
93	C₂×D₄×C₁₃	—	2	256	no	—
94	C₂×D₄×C₁₃	—	4	192	no	—
95	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
96	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
97	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
98	C₂×D₄×C₁₃	C₂⁴	1	16	yes	complemented
99	C₂×D₄×C₁₃	C₂⁴	1	128	yes	complemented
100	C₂²×C₄×C₁₃	—	2	8	no	—
101	C₂²×C₄×C₁₃	—	2	16	no	—
102	C₂²×C₄×C₁₃	—	2	96	no	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	complemented
106	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
107	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
108	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
112	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
113	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
114	C₁₃×C₂²⋊C₄	C₂⁴	1	128	yes	complemented
115	C₄²×C₁₃	C₂⁴	1	32	yes	complemented
116	C₂³×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₂⁴×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂×#535	C₂×C₁₃	1	48	yes	direct product factor
119	C₂²×#127	C₂×C₁₃	1	2	yes	complemented
120	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
121	C₂²×#121	C₂×C₁₃	1	4	yes	complemented
122	C₂²×#120	C₂×C₁₃	1	4	yes	complemented
123	C₂²×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂³×C₁₃	—	2	32	no	—
125	C₂³×C₁₃	—	2	24	no	—
126	C₂³×C₁₃	—	2	24	no	—
127	C₂³×C₁₃	—	2	64	no	—
128	C₂³×C₁₃	—	2	48	no	—
129	C₂³×C₁₃	—	2	48	no	—
130	C₂³×C₁₃	—	2	96	no	—
131	C₂³×C₁₃	—	4	64	no	—
132	C₂³×C₁₃	—	4	384	no	—
133	C₂³×C₁₃	—	4	32	no	—
134	C₂³×C₁₃	—	4	64	no	—
135	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
136	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
137	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
138	C₂³×C₁₃	C₂⁵	1	16	yes	—
139	C₂³×C₁₃	C₂⁵	1	8	yes	—
140	C₂³×C₁₃	C₂⁵	1	4	yes	—
141	C₂³×C₁₃	C₂⁵	1	3	yes	—
142	Q₈×C₁₃	—	2	32	no	—
143	D₄×C₁₃	—	2	64	no	—
144	D₄×C₁₃	—	2	64	no	—
145	D₄×C₁₃	—	2	64	no	—
146	D₄×C₁₃	—	2	32	no	—
147	D₄×C₁₃	—	4	128	no	—
148	C₂×C₄×C₁₃	—	2	24	no	—
149	C₂×C₄×C₁₃	—	2	48	no	—
150	C₂×C₄×C₁₃	—	2	64	no	—
151	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
152	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
153	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	complemented
154	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
155	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
156	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
157	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
158	C₂⁶	C₂²×C₁₃	1	2	yes	—
159	C₂²×#41	—	2	16	no	—
160	C₂²×#41	C₂²×C₁₃	1	24	yes	complemented
161	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×D₄	—	2	16	no	—
163	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
164	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
165	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
166	C₂³×D₄	C₂²×C₁₃	1	24	yes	complemented
167	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
168	C₂³×D₄	C₂²×C₁₃	1	8	yes	complemented
169	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
170	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	complemented
171	#535	C₂²×C₁₃	1	256	yes	direct product factor
172	C₂×#127	C₂²×C₁₃	1	48	yes	complemented
173	C₂×#124	C₂²×C₁₃	1	48	yes	complemented
174	C₂×#121	C₂²×C₁₃	1	96	yes	complemented
175	C₂×#120	C₂²×C₁₃	1	96	yes	complemented
176	C₂×#117	C₂²×C₁₃	1	24	yes	complemented
177	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	complemented
178	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
179	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
180	C₂²×C₄²	C₂²×C₁₃	1	2	yes	complemented
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	2	48	no	—
183	C₂²×C₁₃	—	2	8	no	—
184	C₂²×C₁₃	—	2	16	no	—
185	C₂²×C₁₃	—	2	16	no	—
186	C₂²×C₁₃	—	2	32	no	—
187	C₂²×C₁₃	—	4	128	no	—
188	C₂²×C₁₃	—	4	48	no	—
189	C₂²×C₁₃	—	4	96	no	—
190	C₂²×C₁₃	#535	1	16	yes	direct product factor
191	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
192	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
193	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
194	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
195	C₄×C₁₃	—	2	8	no	—
196	C₄×C₁₃	—	2	16	no	—
197	C₄×C₁₃	C₂³×D₄	1	8	yes	—
198	C₄×C₁₃	C₂³×D₄	1	8	yes	—
199	C₂⁵	—	2	16	no	—
200	C₂⁵	—	4	16	no	—
201	C₂⁵	C₂³×C₁₃	1	4	yes	—
202	C₂⁵	C₂³×C₁₃	1	2	yes	—
203	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
204	C₂⁵	C₂³×C₁₃	1	24	yes	—
205	C₂×#41	—	2	192	no	—
206	C₂×#41	C₂³×C₁₃	1	64	yes	complemented
207	C₂²×Q₈	—	2	8	no	—
208	C₂²×Q₈	C₂³×C₁₃	1	12	yes	complemented
209	C₂²×D₄	—	2	16	no	—
210	C₂²×D₄	—	2	16	no	—
211	C₂²×D₄	—	2	16	no	—
212	C₂²×D₄	—	2	8	no	—
213	C₂²×D₄	—	2	192	no	—
214	C₂²×D₄	—	4	32	no	—
215	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
216	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
217	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
218	C₂²×D₄	C₂³×C₁₃	1	64	yes	complemented
219	C₂²×D₄	C₂³×C₁₃	1	12	yes	complemented
220	C₂²×D₄	C₂³×C₁₃	1	96	yes	complemented
221	C₂³×C₄	—	2	16	no	—
222	C₂³×C₄	D₄×C₁₃	1	16	yes	complemented
223	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
224	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
225	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
228	C₂³×C₄	C₂³×C₁₃	1	24	yes	complemented
229	#127	C₂³×C₁₃	1	128	yes	complemented
230	#124	C₂³×C₁₃	1	128	yes	complemented
231	#121	C₂³×C₁₃	1	256	yes	complemented
232	#120	C₂³×C₁₃	1	256	yes	complemented
233	#117	C₂³×C₁₃	1	64	yes	complemented
234	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	complemented
235	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
236	C₂×C₂²⋊C₄	C₂³×C₁₃	1	96	yes	complemented
237	C₂×C₄²	C₂³×C₁₃	1	24	yes	complemented
238	C₂×C₁₃	—	2	8	no	—
239	C₂×C₁₃	—	4	8	no	—
240	C₂×C₁₃	—	4	16	no	—
241	C₂×C₁₃	C₂×#535	1	12	yes	direct product factor
242	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
243	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	8	no	—
246	C₂⁴	—	2	96	no	—
247	C₂⁴	—	2	16	no	—
248	C₂⁴	—	2	16	no	—
249	C₂⁴	—	2	32	no	—
250	C₂⁴	—	4	96	no	—
251	C₂⁴	—	4	128	no	—
252	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
253	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
254	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
255	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
256	C₂⁴	C₂⁴×C₁₃	1	32	yes	—
257	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
258	#41	—	2	256	no	—
259	C₂×Q₈	—	2	48	no	—
260	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	complemented
261	C₂×D₄	—	2	96	no	—
262	C₂×D₄	—	2	96	no	—
263	C₂×D₄	—	2	96	no	—
264	C₂×D₄	—	2	48	no	—
265	C₂×D₄	—	2	256	no	—
266	C₂×D₄	—	4	192	no	—
267	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
268	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
269	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
270	C₂×D₄	C₂⁴×C₁₃	1	16	yes	complemented
271	C₂×D₄	C₂⁴×C₁₃	1	128	yes	complemented
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	2	96	no	—
275	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
276	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
277	C₂²×C₄	C₂×D₄×C₁₃	1	96	yes	complemented
278	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
279	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
280	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
281	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
282	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
283	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	complemented
284	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	complemented
285	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
286	C₂²⋊C₄	C₂⁴×C₁₃	1	128	yes	complemented
287	C₄²	C₂⁴×C₁₃	1	32	yes	complemented
288	C₁₃	C₂²×#535	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	2	32	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	2	64	no	—
293	C₂³	—	2	48	no	—
294	C₂³	—	2	48	no	—
295	C₂³	—	2	96	no	—
296	C₂³	—	4	64	no	—
297	C₂³	—	4	384	no	—
298	C₂³	—	4	64	no	—
299	C₂³	—	4	32	no	—
300	C₂³	C₂²×D₄×C₁₃	1	24	yes	—
301	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
302	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
303	C₂³	C₂⁵×C₁₃	1	16	yes	—
304	C₂³	C₂⁵×C₁₃	1	8	yes	—
305	C₂³	C₂⁵×C₁₃	1	4	yes	—
306	C₂³	C₂⁵×C₁₃	1	3	yes	—
307	Q₈	—	2	32	no	—
308	D₄	—	2	64	no	—
309	D₄	—	2	64	no	—
310	D₄	—	2	64	no	—
311	D₄	—	2	32	no	—
312	D₄	—	4	128	no	—
313	C₂×C₄	—	2	24	no	—
314	C₂×C₄	—	2	48	no	—
315	C₂×C₄	—	2	64	no	—
316	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
317	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
318	C₂×C₄	C₂²×D₄×C₁₃	1	64	yes	complemented
319	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
320	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
321	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
322	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	48	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	2	16	no	—
327	C₂²	—	2	16	no	—
328	C₂²	—	2	32	no	—
329	C₂²	—	4	128	no	—
330	C₂²	—	4	48	no	—
331	C₂²	—	4	96	no	—
332	C₂²	C₁₃×#535	1	16	yes	direct product factor
333	C₂²	C₂³×D₄×C₁₃	1	8	yes	—
334	C₂²	C₂³×D₄×C₁₃	1	6	yes	—
335	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	12	yes	—
336	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
337	C₄	—	2	8	no	—
338	C₄	—	2	16	no	—
339	C₄	C₂³×D₄×C₁₃	1	8	yes	—
340	C₄	C₂³×D₄×C₁₃	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	16	no	—
343	C₂	—	4	8	no	—
344	C₂	C₂×C₁₃×#535	1	12	yes	direct product factor
345	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
346	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×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. C₂⁴×D₄×C₁₃	C₂	semidirect
3. C₂×C₁₃×#535	C₂	direct (N × H)
4. C₂²×C₁₃×#127	C₂	semidirect
5. C₂²×C₁₃×#124	C₂	semidirect
6. C₂²×C₁₃×#121	C₂	semidirect
7. C₂²×C₁₃×#120	C₂	semidirect
8. C₂²×C₁₃×#117	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
17. C₂³×D₄×C₁₃	C₂²	semidirect
18. C₂³×D₄×C₁₃	C₂²	semidirect
19. C₂³×D₄×C₁₃	C₂²	semidirect
21. C₂⁴×C₄×C₁₃	C₂²	semidirect
22. C₁₃×#535	C₂²	direct (N × H)
23. C₂×C₁₃×#127	C₂²	semidirect
24. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₁₃×#120	C₂²	semidirect
27. C₂×C₁₃×#117	C₂²	semidirect
28. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
31. C₂²×C₄²×C₁₃	C₂²	semidirect
39. C₂×C₁₃×#41	C₂³	semidirect
41. C₂²×Q₈×C₁₃	C₂³	semidirect
51. C₂²×D₄×C₁₃	C₂³	semidirect
52. C₂²×D₄×C₁₃	C₂³	semidirect
53. C₂²×D₄×C₁₃	C₂³	semidirect
55. C₂³×C₄×C₁₃	D₄	semidirect
61. C₂³×C₄×C₁₃	C₂³	semidirect
62. C₁₃×#127	C₂³	semidirect
63. C₁₃×#124	C₂³	semidirect
64. C₁₃×#121	C₂³	semidirect
65. C₁₃×#120	C₂³	semidirect
66. C₁₃×#117	C₂³	semidirect
67. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
69. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
70. C₂×C₄²×C₁₃	C₂³	semidirect
71. C₂²×#535	C₁₃	direct (N × H)
88. C₂×Q₈×C₁₃	C₂⁴	semidirect
98. C₂×D₄×C₁₃	C₂⁴	semidirect
99. C₂×D₄×C₁₃	C₂⁴	semidirect
105. C₂²×C₄×C₁₃	C₂×D₄	semidirect
111. C₂²×C₄×C₁₃	C₂⁴	semidirect
112. C₁₃×C₄⋊C₄	C₂⁴	semidirect
114. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
115. C₄²×C₁₃	C₂⁴	semidirect
116. C₂³×#41	C₂×C₁₃	semidirect
117. C₂⁴×D₄	C₂×C₁₃	semidirect
118. C₂×#535	C₂×C₁₃	direct (N × H)
119. C₂²×#127	C₂×C₁₃	semidirect
120. C₂²×#124	C₂×C₁₃	semidirect
121. C₂²×#121	C₂×C₁₃	semidirect
122. C₂²×#120	C₂×C₁₃	semidirect
123. C₂²×#117	C₂×C₁₃	semidirect
153. C₂×C₄×C₁₃	C₂²×D₄	semidirect
160. C₂²×#41	C₂²×C₁₃	semidirect
161. C₂³×Q₈	C₂²×C₁₃	semidirect
166. C₂³×D₄	C₂²×C₁₃	semidirect
167. C₂³×D₄	C₂²×C₁₃	semidirect
168. C₂³×D₄	C₂²×C₁₃	semidirect
170. C₂⁴×C₄	C₂²×C₁₃	semidirect
171. #535	C₂²×C₁₃	direct (N × H)
172. C₂×#127	C₂²×C₁₃	semidirect
173. C₂×#124	C₂²×C₁₃	semidirect
174. C₂×#121	C₂²×C₁₃	semidirect
175. C₂×#120	C₂²×C₁₃	semidirect
176. C₂×#117	C₂²×C₁₃	semidirect
177. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
179. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
180. C₂²×C₄²	C₂²×C₁₃	semidirect
190. C₂²×C₁₃	#535	direct (N × H)
206. C₂×#41	C₂³×C₁₃	semidirect
208. C₂²×Q₈	C₂³×C₁₃	semidirect
218. C₂²×D₄	C₂³×C₁₃	semidirect
219. C₂²×D₄	C₂³×C₁₃	semidirect
220. C₂²×D₄	C₂³×C₁₃	semidirect
222. C₂³×C₄	D₄×C₁₃	semidirect
228. C₂³×C₄	C₂³×C₁₃	semidirect
229. #127	C₂³×C₁₃	semidirect
230. #124	C₂³×C₁₃	semidirect
231. #121	C₂³×C₁₃	semidirect
232. #120	C₂³×C₁₃	semidirect
233. #117	C₂³×C₁₃	semidirect
234. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
236. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
237. C₂×C₄²	C₂³×C₁₃	semidirect
241. C₂×C₁₃	C₂×#535	direct (N × H)
260. C₂×Q₈	C₂⁴×C₁₃	semidirect
270. C₂×D₄	C₂⁴×C₁₃	semidirect
271. C₂×D₄	C₂⁴×C₁₃	semidirect
277. C₂²×C₄	C₂×D₄×C₁₃	semidirect
283. C₂²×C₄	C₂⁴×C₁₃	semidirect
284. C₄⋊C₄	C₂⁴×C₁₃	semidirect
286. C₂²⋊C₄	C₂⁴×C₁₃	semidirect
287. C₄²	C₂⁴×C₁₃	semidirect
288. C₁₃	C₂²×#535	direct (N × H)
318. C₂×C₄	C₂²×D₄×C₁₃	semidirect
332. C₂²	C₁₃×#535	direct (N × H)
344. C₂	C₂×C₁₃×#535	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
C₂⁴×D₄×C₁₃	2
C₂×C₁₃×#535	2
C₂²×C₁₃×#127	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#121	2
C₂²×C₁₃×#120	2
C₂²×C₁₃×#117	2
C₂²×#535	13

Subgroups — C22×C13×#535 #15749013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#535 #15749013