Subgroups — C₂×C₁₃×#2308 #15720379

Order 3328.

8142 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2308	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#386	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₃×#381	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#379	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
8	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₁₃	—	2	16	no	—
10	C₂³×D₄×C₁₃	C₄	1	16	yes	complemented
11	C₂³×D₄×C₁₃	C₂²	1	4	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	8	yes	—
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×C₂²⋊C₄	—	2	16	no	—
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
17	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	16	yes	complemented
18	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
20	C₁₃×#386	C₂²	1	64	yes	complemented
21	C₁₃×#381	C₂²	1	16	yes	complemented
22	C₁₃×#379	C₂²	1	16	yes	complemented
23	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
24	C₂⁵×C₁₃	—	2	8	no	—
25	C₂⁵×C₁₃	—	4	8	no	—
26	C₂⁵×C₁₃	—	4	8	no	—
27	C₂⁵×C₁₃	C₂×C₄	1	8	yes	—
28	C₂⁵×C₁₃	C₂×C₄	1	8	yes	complemented
29	C₂⁵×C₁₃	D₄	1	16	yes	—
30	C₂⁵×C₁₃	C₂³	1	2	yes	—
31	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
32	C₂⁵×C₁₃	C₂³	1	2	yes	—
33	C₂⁵×C₁₃	C₂³	1	4	yes	—
34	C₂⁵×C₁₃	C₂³	1	4	yes	—
35	C₂²×D₄×C₁₃	—	2	128	no	—
36	C₂²×D₄×C₁₃	—	2	16	no	—
37	C₂²×D₄×C₁₃	—	2	16	no	—
38	C₂²×D₄×C₁₃	—	2	64	no	—
39	C₂²×D₄×C₁₃	C₂×C₄	1	32	yes	complemented
40	C₂²×D₄×C₁₃	C₂×C₄	1	64	yes	complemented
41	C₂²×D₄×C₁₃	C₂³	1	16	yes	—
42	C₂³×C₄×C₁₃	—	2	8	no	—
43	C₂³×C₄×C₁₃	—	2	16	no	—
44	C₂³×C₄×C₁₃	—	4	16	no	—
45	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	complemented
46	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
50	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	64	no	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
53	C₂×C₁₃×C₂²⋊C₄	—	4	16	no	—
54	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
56	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
57	C₁₃×#95	C₂³	1	32	yes	complemented
58	C₂×#2308	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁴×C₁₃	—	2	16	no	—
60	C₂⁴×C₁₃	—	2	8	no	—
61	C₂⁴×C₁₃	—	2	32	no	—
62	C₂⁴×C₁₃	—	2	8	no	—
63	C₂⁴×C₁₃	—	2	16	no	—
64	C₂⁴×C₁₃	—	2	16	no	—
65	C₂⁴×C₁₃	—	4	32	no	—
66	C₂⁴×C₁₃	—	4	32	no	—
67	C₂⁴×C₁₃	—	4	64	no	—
68	C₂⁴×C₁₃	—	4	16	no	—
69	C₂⁴×C₁₃	—	4	16	no	—
70	C₂⁴×C₁₃	—	4	64	no	—
71	C₂⁴×C₁₃	C₂²⋊C₄	1	64	yes	complemented
72	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
73	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
74	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
75	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
76	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	complemented
77	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
78	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
79	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
80	C₂⁴×C₁₃	C₂×D₄	1	32	yes	—
81	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
82	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
83	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
84	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
85	C₂×D₄×C₁₃	—	2	128	no	—
86	C₂×D₄×C₁₃	—	2	256	no	—
87	C₂×D₄×C₁₃	—	2	32	no	—
88	C₂×D₄×C₁₃	—	2	32	no	—
89	C₂×D₄×C₁₃	C₂²×C₄	1	64	yes	complemented
90	C₂²×C₄×C₁₃	—	2	32	no	—
91	C₂²×C₄×C₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₃	—	2	16	no	—
93	C₂²×C₄×C₁₃	—	2	16	no	—
94	C₂²×C₄×C₁₃	—	2	32	no	—
95	C₂²×C₄×C₁₃	—	2	32	no	—
96	C₂²×C₄×C₁₃	—	4	32	no	—
97	C₂²×C₄×C₁₃	—	4	64	no	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	complemented
100	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
102	C₁₃×C₂²⋊C₄	—	2	32	no	—
103	C₁₃×C₂²⋊C₄	—	2	32	no	—
104	C₁₃×C₂²⋊C₄	—	4	32	no	—
105	C₂⁴×D₄	C₂×C₁₃	1	1	yes	characteristic
106	C₂³×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
107	#2308	C₂×C₁₃	1	16	yes	direct product factor
108	C₂×#386	C₂×C₁₃	1	8	yes	complemented
109	C₂×#381	C₂×C₁₃	1	2	yes	complemented
110	C₂×#379	C₂×C₁₃	1	2	yes	complemented
111	C₂³×C₁₃	—	2	16	no	—
112	C₂³×C₁₃	—	2	32	no	—
113	C₂³×C₁₃	—	2	32	no	—
114	C₂³×C₁₃	—	2	32	no	—
115	C₂³×C₁₃	—	2	32	no	—
116	C₂³×C₁₃	—	2	16	no	—
117	C₂³×C₁₃	—	2	8	no	—
118	C₂³×C₁₃	—	2	16	no	—
119	C₂³×C₁₃	—	2	32	no	—
120	C₂³×C₁₃	—	2	32	no	—
121	C₂³×C₁₃	—	2	8	no	—
122	C₂³×C₁₃	—	2	16	no	—
123	C₂³×C₁₃	—	4	128	no	—
124	C₂³×C₁₃	—	4	32	no	—
125	C₂³×C₁₃	—	4	32	no	—
126	C₂³×C₁₃	—	4	64	no	—
127	C₂³×C₁₃	—	4	128	no	—
128	C₂³×C₁₃	—	4	64	no	—
129	C₂³×C₁₃	—	4	32	no	—
130	C₂³×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
131	C₂³×C₁₃	C₂×C₂²⋊C₄	1	32	yes	—
132	C₂³×C₁₃	C₂×C₂²⋊C₄	1	64	yes	complemented
133	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
134	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
135	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
136	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
137	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
138	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
139	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
140	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
141	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
142	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
143	D₄×C₁₃	—	2	128	no	—
144	C₂×C₄×C₁₃	—	2	16	no	—
145	C₂×C₄×C₁₃	—	2	32	no	—
146	C₂×C₄×C₁₃	—	2	8	no	—
147	C₂×C₄×C₁₃	—	2	16	no	—
148	C₂×C₄×C₁₃	—	2	32	no	—
149	C₂×C₄×C₁₃	—	4	64	no	—
150	C₂×C₄×C₁₃	—	4	32	no	—
151	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
152	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
153	C₂⁶	C₂²×C₁₃	1	1	yes	characteristic
154	C₂³×D₄	—	2	16	no	—
155	C₂³×D₄	C₄×C₁₃	1	16	yes	complemented
156	C₂³×D₄	C₂²×C₁₃	1	8	yes	—
157	C₂³×D₄	C₂²×C₁₃	1	4	yes	—
158	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
159	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	complemented
160	C₂²×C₂²⋊C₄	—	2	16	no	—
161	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
162	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	16	yes	complemented
163	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	complemented
164	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	complemented
165	#386	C₂²×C₁₃	1	64	yes	complemented
166	#381	C₂²×C₁₃	1	16	yes	complemented
167	#379	C₂²×C₁₃	1	16	yes	complemented
168	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
169	C₂²×C₁₃	—	2	32	no	—
170	C₂²×C₁₃	—	2	64	no	—
171	C₂²×C₁₃	—	2	8	no	—
172	C₂²×C₁₃	—	2	16	no	—
173	C₂²×C₁₃	—	2	16	no	—
174	C₂²×C₁₃	—	2	16	no	—
175	C₂²×C₁₃	—	2	16	no	—
176	C₂²×C₁₃	—	2	8	no	—
177	C₂²×C₁₃	—	2	16	no	—
178	C₂²×C₁₃	—	4	64	no	—
179	C₂²×C₁₃	—	4	64	no	—
180	C₂²×C₁₃	—	4	32	no	—
181	C₂²×C₁₃	—	4	16	no	—
182	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
183	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	16	yes	—
184	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
185	C₂²×C₁₃	#518	1	8	yes	—
186	C₂²×C₁₃	#534	1	16	yes	—
187	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
188	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
189	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
190	C₄×C₁₃	—	2	8	no	—
191	C₄×C₁₃	—	4	16	no	—
192	C₂⁵	—	2	8	no	—
193	C₂⁵	—	4	8	no	—
194	C₂⁵	—	4	8	no	—
195	C₂⁵	C₂×C₄×C₁₃	1	8	yes	—
196	C₂⁵	C₂×C₄×C₁₃	1	8	yes	complemented
197	C₂⁵	D₄×C₁₃	1	16	yes	—
198	C₂⁵	C₂³×C₁₃	1	2	yes	—
199	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
200	C₂⁵	C₂³×C₁₃	1	2	yes	—
201	C₂⁵	C₂³×C₁₃	1	4	yes	—
202	C₂⁵	C₂³×C₁₃	1	4	yes	—
203	C₂²×D₄	—	2	128	no	—
204	C₂²×D₄	—	2	16	no	—
205	C₂²×D₄	—	2	16	no	—
206	C₂²×D₄	—	2	64	no	—
207	C₂²×D₄	C₂×C₄×C₁₃	1	32	yes	complemented
208	C₂²×D₄	C₂×C₄×C₁₃	1	64	yes	complemented
209	C₂²×D₄	C₂³×C₁₃	1	16	yes	—
210	C₂³×C₄	—	2	8	no	—
211	C₂³×C₄	—	2	16	no	—
212	C₂³×C₄	—	4	16	no	—
213	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	complemented
214	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
215	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
216	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
217	C₂³×C₄	C₂³×C₁₃	1	16	yes	complemented
218	C₂×C₂²⋊C₄	—	2	16	no	—
219	C₂×C₂²⋊C₄	—	2	64	no	—
220	C₂×C₂²⋊C₄	—	2	16	no	—
221	C₂×C₂²⋊C₄	—	4	16	no	—
222	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	complemented
224	C₂×C₂²⋊C₄	C₂³×C₁₃	1	32	yes	complemented
225	#95	C₂³×C₁₃	1	32	yes	complemented
226	C₂×C₁₃	—	2	8	no	—
227	C₂×C₁₃	—	2	16	no	—
228	C₂×C₁₃	—	4	8	no	—
229	C₂×C₁₃	#2308	1	8	yes	direct product factor
230	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₁₃	C₂×#518	1	2	yes	—
232	C₂×C₁₃	C₂×#534	1	4	yes	—
233	C₂⁴	—	2	16	no	—
234	C₂⁴	—	2	8	no	—
235	C₂⁴	—	2	32	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	2	16	no	—
238	C₂⁴	—	2	16	no	—
239	C₂⁴	—	4	32	no	—
240	C₂⁴	—	4	32	no	—
241	C₂⁴	—	4	64	no	—
242	C₂⁴	—	4	16	no	—
243	C₂⁴	—	4	16	no	—
244	C₂⁴	—	4	64	no	—
245	C₂⁴	C₁₃×C₂²⋊C₄	1	64	yes	complemented
246	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
247	C₂⁴	C₂²×C₄×C₁₃	1	4	yes	—
248	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
249	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	—
250	C₂⁴	C₂²×C₄×C₁₃	1	16	yes	complemented
251	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
252	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
253	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
254	C₂⁴	C₂×D₄×C₁₃	1	32	yes	—
255	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
256	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
257	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
258	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
259	C₂×D₄	—	2	128	no	—
260	C₂×D₄	—	2	256	no	—
261	C₂×D₄	—	2	32	no	—
262	C₂×D₄	—	2	32	no	—
263	C₂×D₄	C₂²×C₄×C₁₃	1	64	yes	complemented
264	C₂²×C₄	—	2	32	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	16	no	—
267	C₂²×C₄	—	2	16	no	—
268	C₂²×C₄	—	2	32	no	—
269	C₂²×C₄	—	2	32	no	—
270	C₂²×C₄	—	4	32	no	—
271	C₂²×C₄	—	4	64	no	—
272	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
273	C₂²×C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
274	C₂²×C₄	C₂⁴×C₁₃	1	16	yes	—
275	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
276	C₂²⋊C₄	—	2	32	no	—
277	C₂²⋊C₄	—	2	32	no	—
278	C₂²⋊C₄	—	4	32	no	—
279	C₁₃	C₂×#2308	1	1	yes	characteristic, direct product factor, Sylow
280	C₂³	—	2	16	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	32	no	—
283	C₂³	—	2	32	no	—
284	C₂³	—	2	32	no	—
285	C₂³	—	2	16	no	—
286	C₂³	—	2	8	no	—
287	C₂³	—	2	16	no	—
288	C₂³	—	2	32	no	—
289	C₂³	—	2	32	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	16	no	—
292	C₂³	—	4	128	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	4	32	no	—
295	C₂³	—	4	64	no	—
296	C₂³	—	4	128	no	—
297	C₂³	—	4	64	no	—
298	C₂³	—	4	32	no	—
299	C₂³	C₂×C₁₃×C₂²⋊C₄	1	16	yes	—
300	C₂³	C₂×C₁₃×C₂²⋊C₄	1	32	yes	—
301	C₂³	C₂×C₁₃×C₂²⋊C₄	1	64	yes	complemented
302	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
303	C₂³	C₂³×C₄×C₁₃	1	4	yes	—
304	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
305	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
306	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
307	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
308	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
309	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
310	C₂³	C₁₃×H(5,𝔽₂)	1	8	yes	—
311	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
312	D₄	—	2	128	no	—
313	C₂×C₄	—	2	16	no	—
314	C₂×C₄	—	2	32	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	16	no	—
317	C₂×C₄	—	2	32	no	—
318	C₂×C₄	—	4	64	no	—
319	C₂×C₄	—	4	32	no	—
320	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
321	C₂²	—	2	32	no	—
322	C₂²	—	2	64	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	2	16	no	—
326	C₂²	—	2	16	no	—
327	C₂²	—	2	16	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	2	16	no	—
330	C₂²	—	4	64	no	—
331	C₂²	—	4	64	no	—
332	C₂²	—	4	32	no	—
333	C₂²	—	4	16	no	—
334	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	8	yes	—
335	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	16	yes	—
336	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	4	yes	—
337	C₂²	C₁₃×#518	1	8	yes	—
338	C₂²	C₁₃×#534	1	16	yes	—
339	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
340	C₂²	C₂³×D₄×C₁₃	1	2	yes	—
341	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	4	yes	—
342	C₄	—	2	8	no	—
343	C₄	—	4	16	no	—
344	C₂	—	2	8	no	—
345	C₂	—	2	16	no	—
346	C₂	—	4	8	no	—
347	C₂	C₁₃×#2308	1	8	yes	direct product factor
348	C₂	C₂³×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
349	C₂	C₂×C₁₃×#518	1	2	yes	—
350	C₂	C₂×C₁₃×#534	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁴×D₄×C₁₃	C₂
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
2. C₂³×C₁₃×C₂²⋊C₄	C₂	semidirect
3. C₁₃×#2308	C₂	direct (N × H)
4. C₂×C₁₃×#386	C₂	semidirect
5. C₂×C₁₃×#381	C₂	semidirect
6. C₂×C₁₃×#379	C₂	semidirect
10. C₂³×D₄×C₁₃	C₄	semidirect
14. C₂⁴×C₄×C₁₃	C₂²	semidirect
17. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
18. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
19. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
20. C₁₃×#386	C₂²	semidirect
21. C₁₃×#381	C₂²	semidirect
22. C₁₃×#379	C₂²	semidirect
23. C₂×C₁₃×#95	C₂²	semidirect
28. C₂⁵×C₁₃	C₂×C₄	semidirect
39. C₂²×D₄×C₁₃	C₂×C₄	semidirect
40. C₂²×D₄×C₁₃	C₂×C₄	semidirect
45. C₂³×C₄×C₁₃	C₂×C₄	semidirect
49. C₂³×C₄×C₁₃	C₂³	semidirect
55. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
56. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
57. C₁₃×#95	C₂³	semidirect
58. C₂×#2308	C₁₃	direct (N × H)
71. C₂⁴×C₁₃	C₂²⋊C₄	semidirect
76. C₂⁴×C₁₃	C₂²×C₄	semidirect
89. C₂×D₄×C₁₃	C₂²×C₄	semidirect
99. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
106. C₂³×C₂²⋊C₄	C₂×C₁₃	semidirect
107. #2308	C₂×C₁₃	direct (N × H)
108. C₂×#386	C₂×C₁₃	semidirect
109. C₂×#381	C₂×C₁₃	semidirect
110. C₂×#379	C₂×C₁₃	semidirect
132. C₂³×C₁₃	C₂×C₂²⋊C₄	semidirect
155. C₂³×D₄	C₄×C₁₃	semidirect
159. C₂⁴×C₄	C₂²×C₁₃	semidirect
162. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
163. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
164. C₂²×C₂²⋊C₄	C₂²×C₁₃	semidirect
165. #386	C₂²×C₁₃	semidirect
166. #381	C₂²×C₁₃	semidirect
167. #379	C₂²×C₁₃	semidirect
168. C₂×#95	C₂²×C₁₃	semidirect
196. C₂⁵	C₂×C₄×C₁₃	semidirect
207. C₂²×D₄	C₂×C₄×C₁₃	semidirect
208. C₂²×D₄	C₂×C₄×C₁₃	semidirect
213. C₂³×C₄	C₂×C₄×C₁₃	semidirect
217. C₂³×C₄	C₂³×C₁₃	semidirect
223. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
224. C₂×C₂²⋊C₄	C₂³×C₁₃	semidirect
225. #95	C₂³×C₁₃	semidirect
229. C₂×C₁₃	#2308	direct (N × H)
245. C₂⁴	C₁₃×C₂²⋊C₄	semidirect
250. C₂⁴	C₂²×C₄×C₁₃	semidirect
263. C₂×D₄	C₂²×C₄×C₁₃	semidirect
273. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
279. C₁₃	C₂×#2308	direct (N × H)
301. C₂³	C₂×C₁₃×C₂²⋊C₄	semidirect
347. C₂	C₁₃×#2308	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₁₃	2
C₂³×C₁₃×C₂²⋊C₄	2
C₁₃×#2308	2
C₂×C₁₃×#386	2
C₂×C₁₃×#381	2
C₂×C₁₃×#379	2
C₂×#2308	13

Subgroups — C2×C13×#2308 #15720379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2308 #15720379