Subgroups — C₂×C₁₃×#2217 #15719938

Order 3328.

754 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	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2217	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₁₃×#121	—	2	1	no	—
14	C₂×C₁₃×SD₃₂	—	2	4	no	—
15	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	complemented
16	C₂²×C₁₃×C₁₆	—	2	4	no	—
17	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	complemented
20	C₁₃×#467	—	2	2	no	—
21	C₁₃×#467	C₂²	1	4	yes	complemented
22	C₁₃×#466	—	2	2	no	—
23	C₁₃×#466	C₂²	1	4	yes	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	—	2	1	no	—
27	C₂×C₁₃×#102	—	2	1	no	—
28	C₁₃×#367	C₂²	1	4	yes	complemented
29	C₁₃×#358	C₂²	1	4	yes	complemented
30	C₁₃×#357	C₂²	1	4	yes	complemented
31	C₂²×Q₈×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	4	1	no	—
34	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₁₃×Q₁₆	—	2	2	no	—
36	C₂×C₁₃×Q₁₆	—	2	1	no	—
37	C₂×C₁₃×Q₁₆	—	2	2	no	—
38	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
39	C₂×C₁₃×D₈	—	2	2	no	—
40	C₂×C₁₃×D₈	—	2	1	no	—
41	C₂×C₁₃×D₈	—	2	2	no	—
42	C₂×C₁₃×D₈	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	—	2	2	no	—
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	D₄	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×C₂²⋊Q₈	—	2	4	no	—
50	C₁₃×C₂²⋊Q₈	—	4	2	no	—
51	C₁₃×#121	—	2	4	no	—
52	C₁₃×#121	—	4	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
58	C₁₃×SD₃₂	—	2	8	no	—
59	C₂×C₁₃×C₁₆	—	2	2	no	—
60	C₂×C₁₃×C₁₆	—	2	8	no	—
61	C₂×C₁₃×C₁₆	D₄	1	4	yes	complemented
62	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
64	C₁₃×#107	—	2	1	no	—
65	C₁₃×#107	—	2	1	no	—
66	C₁₃×#107	C₂³	1	2	yes	—
67	C₁₃×#107	C₂³	1	2	yes	—
68	C₁₃×#103	—	2	4	no	—
69	C₁₃×#102	—	2	4	no	—
70	C₂×#2217	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	—	4	1	no	—
72	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
73	C₂×Q₈×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	4	1	no	—
75	C₂×Q₈×C₁₃	—	4	2	no	—
76	C₂×Q₈×C₁₃	—	4	2	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	4	4	no	—
79	C₂×D₄×C₁₃	—	4	2	no	—
80	C₂×D₄×C₁₃	—	4	1	no	—
81	C₂×D₄×C₁₃	—	4	2	no	—
82	C₂×D₄×C₁₃	—	8	4	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	—	4	1	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	D₈	1	2	yes	—
89	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₁₃×Q₁₆	—	2	2	no	—
93	C₁₃×Q₁₆	—	2	2	no	—
94	C₁₃×Q₁₆	—	4	2	no	—
95	C₁₃×D₈	—	2	2	no	—
96	C₁₃×D₈	—	2	2	no	—
97	C₁₃×D₈	—	4	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₁₃	#41	1	2	yes	—
106	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	4	1	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₁₃×C₄⋊C₄	—	4	4	no	—
112	C₁₃×C₂²⋊C₄	—	4	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₁₃×C₁₆	—	2	2	no	—
115	C₁₃×C₁₆	C₂×D₄	1	4	yes	complemented
116	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₂³×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×#466	C₂×C₁₃	1	1	yes	characteristic
120	#2217	C₂×C₁₃	1	8	yes	direct product factor
121	C₂×#367	C₂×C₁₃	1	1	yes	characteristic, complemented
122	C₂×#358	C₂×C₁₃	1	1	yes	characteristic, complemented
123	C₂×#357	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂³×C₁₃	—	2	2	no	—
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	—	4	2	no	—
127	C₂³×C₁₃	—	8	2	no	—
128	C₂³×C₁₃	—	8	2	no	—
129	C₂³×C₁₃	—	8	2	no	—
130	C₂³×C₁₃	SD₃₂	1	4	yes	complemented
131	C₂³×C₁₃	C₂×D₈	1	2	yes	—
132	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
133	Q₈×C₁₃	—	4	2	no	—
134	Q₈×C₁₃	—	4	2	no	—
135	Q₈×C₁₃	—	8	2	no	—
136	D₄×C₁₃	—	4	2	no	—
137	D₄×C₁₃	—	4	2	no	—
138	D₄×C₁₃	—	8	8	no	—
139	D₄×C₁₃	—	8	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	8	2	no	—
148	C₂×C₄×C₁₃	—	8	2	no	—
149	C₂×C₄×C₁₃	—	8	2	no	—
150	C₂×C₄×C₁₃	#121	1	2	yes	—
151	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#135	1	2	yes	—
154	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₁₃	—	2	2	no	—
156	C₈×C₁₃	#121	1	2	yes	—
157	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
159	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
160	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
161	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
162	C₂×C₂²⋊Q₈	—	2	1	no	—
163	C₂×#121	—	2	1	no	—
164	C₂×SD₃₂	—	2	4	no	—
165	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	complemented
166	C₂²×C₁₆	—	2	4	no	—
167	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
168	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
169	C₂²×C₁₆	C₂²×C₁₃	1	4	yes	complemented
170	#467	—	2	2	no	—
171	#467	C₂²×C₁₃	1	4	yes	complemented
172	#466	—	2	2	no	—
173	#466	C₂²×C₁₃	1	4	yes	—
174	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×#103	—	2	1	no	—
177	C₂×#102	—	2	1	no	—
178	#367	C₂²×C₁₃	1	4	yes	complemented
179	#358	C₂²×C₁₃	1	4	yes	complemented
180	#357	C₂²×C₁₃	1	4	yes	complemented
181	C₂²×C₁₃	—	2	2	no	—
182	C₂²×C₁₃	—	2	8	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	8	2	no	—
185	C₂²×C₁₃	—	8	2	no	—
186	C₂²×C₁₃	—	8	2	no	—
187	C₂²×C₁₃	—	16	4	no	—
188	C₂²×C₁₃	#466	1	2	yes	—
189	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
190	C₂²×C₁₃	C₂×SD₃₂	1	4	yes	complemented
191	C₂²×C₁₃	#508	1	2	yes	—
192	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
193	C₄×C₁₃	—	2	2	no	—
194	C₄×C₁₃	—	8	2	no	—
195	C₄×C₁₃	—	8	2	no	—
196	C₄×C₁₃	—	8	2	no	—
197	C₄×C₁₃	#466	1	2	yes	—
198	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
199	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
200	C₂²×Q₈	—	2	1	no	—
201	C₂²×D₄	—	2	1	no	—
202	C₂²×D₄	—	4	1	no	—
203	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
204	C₂×Q₁₆	—	2	2	no	—
205	C₂×Q₁₆	—	2	1	no	—
206	C₂×Q₁₆	—	2	2	no	—
207	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
208	C₂×D₈	—	2	2	no	—
209	C₂×D₈	—	2	1	no	—
210	C₂×D₈	—	2	2	no	—
211	C₂×D₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
215	C₂²×C₈	D₄×C₁₃	1	2	yes	—
216	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
218	C₂²⋊Q₈	—	2	4	no	—
219	C₂²⋊Q₈	—	4	2	no	—
220	#121	—	2	4	no	—
221	#121	—	4	2	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	1	no	—
224	C₂×C₄⋊C₄	—	4	1	no	—
225	C₂×C₂²⋊C₄	—	4	1	no	—
226	C₂×C₂²⋊C₄	—	4	1	no	—
227	SD₃₂	—	2	8	no	—
228	C₂×C₁₆	—	2	2	no	—
229	C₂×C₁₆	—	2	8	no	—
230	C₂×C₁₆	D₄×C₁₃	1	4	yes	complemented
231	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
232	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
233	#107	—	2	1	no	—
234	#107	—	2	1	no	—
235	#107	C₂³×C₁₃	1	2	yes	—
236	#107	C₂³×C₁₃	1	2	yes	—
237	#103	—	2	4	no	—
238	#102	—	2	4	no	—
239	C₂×C₁₃	—	2	4	no	—
240	C₂×C₁₃	—	16	2	no	—
241	C₂×C₁₃	#2217	1	4	yes	direct product factor
242	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
243	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
244	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
245	C₂⁴	—	4	1	no	—
246	C₂⁴	C₁₃×D₈	1	1	yes	characteristic
247	C₂×Q₈	—	2	2	no	—
248	C₂×Q₈	—	4	1	no	—
249	C₂×Q₈	—	4	2	no	—
250	C₂×Q₈	—	4	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	4	4	no	—
253	C₂×D₄	—	4	2	no	—
254	C₂×D₄	—	4	1	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	—	8	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	4	1	no	—
260	C₂²×C₄	—	4	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
263	C₂²×C₄	C₁₃×D₈	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
266	Q₁₆	—	2	2	no	—
267	Q₁₆	—	2	2	no	—
268	Q₁₆	—	4	2	no	—
269	D₈	—	2	2	no	—
270	D₈	—	2	2	no	—
271	D₈	—	4	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
277	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
278	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
279	C₂×C₈	C₁₃×#41	1	2	yes	—
280	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
281	C₄⋊C₄	—	2	2	no	—
282	C₄⋊C₄	—	2	2	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₂²⋊C₄	—	4	4	no	—
287	C₂²⋊C₄	—	4	4	no	—
288	C₁₆	—	2	2	no	—
289	C₁₆	C₂×D₄×C₁₃	1	4	yes	complemented
290	C₁₃	C₂×#2217	1	1	yes	characteristic, direct product factor, Sylow
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	—	4	2	no	—
294	C₂³	—	8	2	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	C₁₃×SD₃₂	1	4	yes	complemented
298	C₂³	C₂×C₁₃×D₈	1	2	yes	—
299	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
300	Q₈	—	4	2	no	—
301	Q₈	—	4	2	no	—
302	Q₈	—	8	2	no	—
303	D₄	—	4	2	no	—
304	D₄	—	4	2	no	—
305	D₄	—	8	8	no	—
306	D₄	—	8	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	8	2	no	—
315	C₂×C₄	—	8	2	no	—
316	C₂×C₄	—	8	2	no	—
317	C₂×C₄	C₁₃×#121	1	2	yes	—
318	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
319	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
320	C₂×C₄	C₁₃×#135	1	2	yes	—
321	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
322	C₈	—	2	2	no	—
323	C₈	C₁₃×#121	1	2	yes	—
324	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
325	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	8	no	—
329	C₂²	—	8	2	no	—
330	C₂²	—	8	2	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	16	4	no	—
333	C₂²	C₁₃×#466	1	2	yes	—
334	C₂²	C₂×C₁₃×SD₃₂	1	2	yes	—
335	C₂²	C₂×C₁₃×SD₃₂	1	4	yes	complemented
336	C₂²	C₁₃×#508	1	2	yes	—
337	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
338	C₄	—	2	2	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	C₁₃×#466	1	2	yes	—
343	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
344	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
345	C₂	—	2	4	no	—
346	C₂	—	16	2	no	—
347	C₂	C₁₃×#2217	1	4	yes	direct product factor
348	C₂	C₂×C₁₃×#466	1	1	yes	characteristic
349	C₂	C₂²×C₁₃×SD₃₂	1	1	yes	characteristic
350	C₂	C₂×C₁₃×#508	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#466	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ C₂³×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×SD₃₂	C₂	semidirect
2. C₂³×C₁₃×C₁₆	C₂	semidirect
3. C₂×C₁₃×#467	C₂	semidirect
5. C₁₃×#2217	C₂	direct (N × H)
6. C₂×C₁₃×#367	C₂	semidirect
7. C₂×C₁₃×#358	C₂	semidirect
8. C₂×C₁₃×#357	C₂	semidirect
15. C₂×C₁₃×SD₃₂	C₂²	semidirect
19. C₂²×C₁₃×C₁₆	C₂²	semidirect
21. C₁₃×#467	C₂²	semidirect
28. C₁₃×#367	C₂²	semidirect
29. C₁₃×#358	C₂²	semidirect
30. C₁₃×#357	C₂²	semidirect
61. C₂×C₁₃×C₁₆	D₄	semidirect
70. C₂×#2217	C₁₃	direct (N × H)
115. C₁₃×C₁₆	C₂×D₄	semidirect
116. C₂²×SD₃₂	C₂×C₁₃	semidirect
117. C₂³×C₁₆	C₂×C₁₃	semidirect
118. C₂×#467	C₂×C₁₃	semidirect
120. #2217	C₂×C₁₃	direct (N × H)
121. C₂×#367	C₂×C₁₃	semidirect
122. C₂×#358	C₂×C₁₃	semidirect
123. C₂×#357	C₂×C₁₃	semidirect
130. C₂³×C₁₃	SD₃₂	semidirect
165. C₂×SD₃₂	C₂²×C₁₃	semidirect
169. C₂²×C₁₆	C₂²×C₁₃	semidirect
171. #467	C₂²×C₁₃	semidirect
178. #367	C₂²×C₁₃	semidirect
179. #358	C₂²×C₁₃	semidirect
180. #357	C₂²×C₁₃	semidirect
190. C₂²×C₁₃	C₂×SD₃₂	semidirect
230. C₂×C₁₆	D₄×C₁₃	semidirect
241. C₂×C₁₃	#2217	direct (N × H)
289. C₁₆	C₂×D₄×C₁₃	semidirect
290. C₁₃	C₂×#2217	direct (N × H)
297. C₂³	C₁₃×SD₃₂	semidirect
335. C₂²	C₂×C₁₃×SD₃₂	semidirect
347. C₂	C₁₃×#2217	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×SD₃₂	2
C₂³×C₁₃×C₁₆	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₁₃×#2217	2
C₂×C₁₃×#367	2
C₂×C₁₃×#358	2
C₂×C₁₃×#357	2
C₂×#2217	13

Subgroups — C2×C13×#2217 #15719938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2217 #15719938