Subgroups — C₂²×C₁₃×#532 #15749005

Order 3328.

12878 conjugacy classes of subgroups.

The subgroup lattice has 300 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×#532	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₁₃×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#121	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄×D₄×C₁₃	C₂	1	4	yes	maximal, complemented
8	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	—	2	32	no	—
10	C₂²×C₁₃×#41	C₂²	1	48	yes	complemented
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
15	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	—
17	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#532	C₂²	1	256	yes	direct product factor
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
20	C₂×C₁₃×#127	C₂²	1	24	yes	complemented
21	C₂×C₁₃×#124	C₂²	1	48	yes	complemented
22	C₂×C₁₃×#121	C₂²	1	96	yes	complemented
23	C₂×C₄×D₄×C₁₃	C₂²	1	96	yes	complemented
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
26	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	24	yes	complemented
30	C₂⁵×C₁₃	C₂³	1	4	yes	—
31	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₁₃×#41	—	2	384	no	—
33	C₂×C₁₃×#41	C₂³	1	128	yes	complemented
34	C₂²×Q₈×C₁₃	—	2	16	no	—
35	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
36	C₂²×D₄×C₁₃	—	2	32	no	—
37	C₂²×D₄×C₁₃	—	2	16	no	—
38	C₂²×D₄×C₁₃	—	2	32	no	—
39	C₂²×D₄×C₁₃	C₂³	1	48	yes	—
40	C₂²×D₄×C₁₃	C₂³	1	48	yes	—
41	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
42	C₂³×C₄×C₁₃	—	2	32	no	—
43	C₂³×C₄×C₁₃	—	2	16	no	—
44	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	48	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
54	C₁₃×#127	C₂³	1	64	yes	complemented
55	C₁₃×#124	C₂³	1	128	yes	complemented
56	C₁₃×#121	C₂³	1	256	yes	complemented
57	C₄×D₄×C₁₃	C₂³	1	256	yes	complemented
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
59	C₂×C₁₃×C₂²⋊C₄	C₂³	1	96	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	64	yes	complemented
64	C₂²×#532	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂⁴×C₁₃	—	2	8	no	—
66	C₂⁴×C₁₃	—	2	16	no	—
67	C₂⁴×C₁₃	—	2	32	no	—
68	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
69	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
70	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
71	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
72	C₁₃×#41	—	2	512	no	—
73	C₂×Q₈×C₁₃	—	2	96	no	—
74	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
75	C₂×D₄×C₁₃	—	2	192	no	—
76	C₂×D₄×C₁₃	—	2	96	no	—
77	C₂×D₄×C₁₃	—	2	192	no	—
78	C₂×D₄×C₁₃	C₂⁴	1	64	yes	—
79	C₂×D₄×C₁₃	C₂⁴	1	64	yes	—
80	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
81	C₂²×C₄×C₁₃	—	2	16	no	—
82	C₂²×C₄×C₁₃	—	2	8	no	—
83	C₂²×C₄×C₁₃	—	2	192	no	—
84	C₂²×C₄×C₁₃	—	2	96	no	—
85	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	complemented
88	C₂²×C₄×C₁₃	#41	1	16	yes	complemented
89	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
90	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	64	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
97	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
98	C₁₃×C₂²⋊C₄	C₂⁴	1	128	yes	—
99	C₄²×C₁₃	C₂⁴	1	32	yes	—
100	C₄²×C₁₃	C₂⁴	1	16	yes	—
101	C₄²×C₁₃	C₂⁴	1	16	yes	—
102	C₂³×#41	C₂×C₁₃	1	2	yes	complemented
103	C₂×#532	C₂×C₁₃	1	48	yes	direct product factor
104	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
105	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic, complemented
106	C₂²×#124	C₂×C₁₃	1	2	yes	complemented
107	C₂²×#121	C₂×C₁₃	1	4	yes	complemented
108	C₂²×C₄×D₄	C₂×C₁₃	1	4	yes	complemented
109	C₂³×C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
110	C₂³×C₁₃	—	2	32	no	—
111	C₂³×C₁₃	—	2	24	no	—
112	C₂³×C₁₃	—	2	48	no	—
113	C₂³×C₁₃	—	2	96	no	—
114	C₂³×C₁₃	—	4	64	no	—
115	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
116	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
117	C₂³×C₁₃	C₂×#41	1	8	yes	—
118	C₂³×C₁₃	C₂⁵	1	16	yes	—
119	C₂³×C₁₃	C₂⁵	1	4	yes	—
120	C₂³×C₁₃	C₂⁵	1	3	yes	—
121	Q₈×C₁₃	—	2	64	no	—
122	D₄×C₁₃	—	2	128	no	—
123	D₄×C₁₃	—	2	64	no	—
124	D₄×C₁₃	—	2	128	no	—
125	C₂×C₄×C₁₃	—	2	48	no	—
126	C₂×C₄×C₁₃	—	2	24	no	—
127	C₂×C₄×C₁₃	—	2	128	no	—
128	C₂×C₄×C₁₃	—	2	64	no	—
129	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
130	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
131	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	complemented
132	C₂×C₄×C₁₃	C₂×#41	1	48	yes	complemented
133	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
134	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
135	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
136	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
137	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
138	C₂²×#41	—	2	32	no	—
139	C₂²×#41	C₂²×C₁₃	1	48	yes	complemented
140	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
141	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
142	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
143	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
144	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	—
145	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
146	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
147	#532	C₂²×C₁₃	1	256	yes	direct product factor
148	C₂×C₄⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
149	C₂×#127	C₂²×C₁₃	1	24	yes	complemented
150	C₂×#124	C₂²×C₁₃	1	48	yes	complemented
151	C₂×#121	C₂²×C₁₃	1	96	yes	complemented
152	C₂×C₄×D₄	C₂²×C₁₃	1	96	yes	complemented
153	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
154	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
155	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
156	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
157	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
158	C₂²×C₄²	C₂²×C₁₃	1	24	yes	complemented
159	C₂²×C₁₃	—	2	8	no	—
160	C₂²×C₁₃	—	2	48	no	—
161	C₂²×C₁₃	—	2	16	no	—
162	C₂²×C₁₃	—	2	32	no	—
163	C₂²×C₁₃	—	4	96	no	—
164	C₂²×C₁₃	#532	1	16	yes	direct product factor
165	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
166	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
167	C₂²×C₁₃	C₂²×#41	1	12	yes	—
168	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
169	C₄×C₁₃	—	2	16	no	—
170	C₄×C₁₃	—	2	8	no	—
171	C₄×C₁₃	C₂³×D₄	1	8	yes	—
172	C₄×C₁₃	C₂³×D₄	1	8	yes	—
173	C₄×C₁₃	C₂²×#41	1	16	yes	complemented
174	C₂⁵	C₂³×C₁₃	1	4	yes	—
175	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
176	C₂×#41	—	2	384	no	—
177	C₂×#41	C₂³×C₁₃	1	128	yes	complemented
178	C₂²×Q₈	—	2	16	no	—
179	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
180	C₂²×D₄	—	2	32	no	—
181	C₂²×D₄	—	2	16	no	—
182	C₂²×D₄	—	2	32	no	—
183	C₂²×D₄	C₂³×C₁₃	1	48	yes	—
184	C₂²×D₄	C₂³×C₁₃	1	48	yes	—
185	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
186	C₂³×C₄	—	2	32	no	—
187	C₂³×C₄	—	2	16	no	—
188	C₂³×C₄	D₄×C₁₃	1	16	yes	complemented
189	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
190	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
191	C₂³×C₄	C₂³×C₁₃	1	48	yes	—
192	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
193	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
194	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
195	C₂³×C₄	C₂³×C₁₃	1	12	yes	—
196	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
197	C₄⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
198	#127	C₂³×C₁₃	1	64	yes	complemented
199	#124	C₂³×C₁₃	1	128	yes	complemented
200	#121	C₂³×C₁₃	1	256	yes	complemented
201	C₄×D₄	C₂³×C₁₃	1	256	yes	complemented
202	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
203	C₂×C₂²⋊C₄	C₂³×C₁₃	1	96	yes	—
204	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
205	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
206	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
207	C₂×C₄²	C₂³×C₁₃	1	64	yes	complemented
208	C₂×C₁₃	—	2	8	no	—
209	C₂×C₁₃	—	4	16	no	—
210	C₂×C₁₃	C₂×#532	1	12	yes	direct product factor
211	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
212	C₂×C₁₃	C₂³×#41	1	2	yes	—
213	C₂⁴	—	2	8	no	—
214	C₂⁴	—	2	16	no	—
215	C₂⁴	—	2	32	no	—
216	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
217	C₂⁴	C₂⁴×C₁₃	1	24	yes	—
218	C₂⁴	C₂⁴×C₁₃	1	6	yes	—
219	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
220	#41	—	2	512	no	—
221	C₂×Q₈	—	2	96	no	—
222	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
223	C₂×D₄	—	2	192	no	—
224	C₂×D₄	—	2	96	no	—
225	C₂×D₄	—	2	192	no	—
226	C₂×D₄	C₂⁴×C₁₃	1	64	yes	—
227	C₂×D₄	C₂⁴×C₁₃	1	64	yes	—
228	C₂×D₄	C₂⁴×C₁₃	1	32	yes	—
229	C₂²×C₄	—	2	16	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	—	2	192	no	—
232	C₂²×C₄	—	2	96	no	—
233	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
234	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
235	C₂²×C₄	C₂×D₄×C₁₃	1	96	yes	complemented
236	C₂²×C₄	C₁₃×#41	1	16	yes	complemented
237	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
238	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
239	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
240	C₂²×C₄	C₂⁴×C₁₃	1	64	yes	—
241	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
242	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
243	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
244	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
245	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
246	C₂²⋊C₄	C₂⁴×C₁₃	1	128	yes	—
247	C₄²	C₂⁴×C₁₃	1	32	yes	—
248	C₄²	C₂⁴×C₁₃	1	16	yes	—
249	C₄²	C₂⁴×C₁₃	1	16	yes	—
250	C₁₃	C₂²×#532	1	1	yes	characteristic, direct product factor, Sylow
251	C₂³	—	2	32	no	—
252	C₂³	—	2	24	no	—
253	C₂³	—	2	48	no	—
254	C₂³	—	2	96	no	—
255	C₂³	—	4	64	no	—
256	C₂³	C₂²×D₄×C₁₃	1	24	yes	—
257	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
258	C₂³	C₂×C₁₃×#41	1	8	yes	—
259	C₂³	C₂⁵×C₁₃	1	16	yes	—
260	C₂³	C₂⁵×C₁₃	1	4	yes	—
261	C₂³	C₂⁵×C₁₃	1	3	yes	—
262	Q₈	—	2	64	no	—
263	D₄	—	2	128	no	—
264	D₄	—	2	64	no	—
265	D₄	—	2	128	no	—
266	C₂×C₄	—	2	48	no	—
267	C₂×C₄	—	2	24	no	—
268	C₂×C₄	—	2	128	no	—
269	C₂×C₄	—	2	64	no	—
270	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
271	C₂×C₄	C₂²×D₄×C₁₃	1	24	yes	—
272	C₂×C₄	C₂²×D₄×C₁₃	1	64	yes	complemented
273	C₂×C₄	C₂×C₁₃×#41	1	48	yes	complemented
274	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
275	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
276	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
277	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
278	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
279	C₂²	—	2	8	no	—
280	C₂²	—	2	48	no	—
281	C₂²	—	2	16	no	—
282	C₂²	—	2	32	no	—
283	C₂²	—	4	96	no	—
284	C₂²	C₁₃×#532	1	16	yes	direct product factor
285	C₂²	C₂³×D₄×C₁₃	1	8	yes	—
286	C₂²	C₂³×D₄×C₁₃	1	6	yes	—
287	C₂²	C₂²×C₁₃×#41	1	12	yes	—
288	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
289	C₄	—	2	16	no	—
290	C₄	—	2	8	no	—
291	C₄	C₂³×D₄×C₁₃	1	8	yes	—
292	C₄	C₂³×D₄×C₁₃	1	8	yes	—
293	C₄	C₂²×C₁₃×#41	1	16	yes	complemented
294	C₂	—	2	8	no	—
295	C₂	—	4	16	no	—
296	C₂	C₂×C₁₃×#532	1	12	yes	direct product factor
297	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic
298	C₂	C₂³×C₁₃×#41	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×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×#532	C₂	direct (N × H)
3. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
4. C₂²×C₁₃×#127	C₂	semidirect
5. C₂²×C₁₃×#124	C₂	semidirect
6. C₂²×C₁₃×#121	C₂	semidirect
7. C₂²×C₄×D₄×C₁₃	C₂	semidirect
8. C₂³×C₄²×C₁₃	C₂	semidirect
10. C₂²×C₁₃×#41	C₂²	semidirect
18. C₁₃×#532	C₂²	direct (N × H)
19. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
20. C₂×C₁₃×#127	C₂²	semidirect
21. C₂×C₁₃×#124	C₂²	semidirect
22. C₂×C₁₃×#121	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂²×C₄²×C₁₃	C₂²	semidirect
33. C₂×C₁₃×#41	C₂³	semidirect
44. C₂³×C₄×C₁₃	D₄	semidirect
53. C₁₃×C₄⋊Q₈	C₂³	semidirect
54. C₁₃×#127	C₂³	semidirect
55. C₁₃×#124	C₂³	semidirect
56. C₁₃×#121	C₂³	semidirect
57. C₄×D₄×C₁₃	C₂³	semidirect
63. C₂×C₄²×C₁₃	C₂³	semidirect
64. C₂²×#532	C₁₃	direct (N × H)
87. C₂²×C₄×C₁₃	C₂×D₄	semidirect
88. C₂²×C₄×C₁₃	#41	semidirect
102. C₂³×#41	C₂×C₁₃	semidirect
103. C₂×#532	C₂×C₁₃	direct (N × H)
104. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
105. C₂²×#127	C₂×C₁₃	semidirect
106. C₂²×#124	C₂×C₁₃	semidirect
107. C₂²×#121	C₂×C₁₃	semidirect
108. C₂²×C₄×D₄	C₂×C₁₃	semidirect
109. C₂³×C₄²	C₂×C₁₃	semidirect
131. C₂×C₄×C₁₃	C₂²×D₄	semidirect
132. C₂×C₄×C₁₃	C₂×#41	semidirect
139. C₂²×#41	C₂²×C₁₃	semidirect
147. #532	C₂²×C₁₃	direct (N × H)
148. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
149. C₂×#127	C₂²×C₁₃	semidirect
150. C₂×#124	C₂²×C₁₃	semidirect
151. C₂×#121	C₂²×C₁₃	semidirect
152. C₂×C₄×D₄	C₂²×C₁₃	semidirect
158. C₂²×C₄²	C₂²×C₁₃	semidirect
164. C₂²×C₁₃	#532	direct (N × H)
173. C₄×C₁₃	C₂²×#41	semidirect
177. C₂×#41	C₂³×C₁₃	semidirect
188. C₂³×C₄	D₄×C₁₃	semidirect
197. C₄⋊Q₈	C₂³×C₁₃	semidirect
198. #127	C₂³×C₁₃	semidirect
199. #124	C₂³×C₁₃	semidirect
200. #121	C₂³×C₁₃	semidirect
201. C₄×D₄	C₂³×C₁₃	semidirect
207. C₂×C₄²	C₂³×C₁₃	semidirect
210. C₂×C₁₃	C₂×#532	direct (N × H)
235. C₂²×C₄	C₂×D₄×C₁₃	semidirect
236. C₂²×C₄	C₁₃×#41	semidirect
250. C₁₃	C₂²×#532	direct (N × H)
272. C₂×C₄	C₂²×D₄×C₁₃	semidirect
273. C₂×C₄	C₂×C₁₃×#41	semidirect
284. C₂²	C₁₃×#532	direct (N × H)
293. C₄	C₂²×C₁₃×#41	semidirect
296. C₂	C₂×C₁₃×#532	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×#532	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#127	2
C₂²×C₁₃×#124	2
C₂²×C₁₃×#121	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₄²×C₁₃	2
C₂²×#532	13

Subgroups — C22×C13×#532 #15749005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#532 #15749005