Subgroups — C₂×C₁₃×#3358 #15747634

Order 3328.

2402 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3358	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#486	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#474	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₃×#459	C₂	1	3	yes	maximal, complemented
7	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×D₈	C₂	1	3	yes	maximal, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂³×Q₈×C₁₃	—	2	1	no	—
11	C₂²×C₁₃×D₈	C₂²	1	3	yes	—
12	C₁₃×#550	—	2	4	no	—
13	C₁₃×#550	C₂²	1	8	yes	complemented
14	D₄×Q₈×C₁₃	—	2	4	no	—
15	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
17	C₂×C₁₃×#127	C₂²	1	3	yes	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	3	no	—
19	C₂×C₁₃×#121	—	2	3	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
23	C₁₃×#486	C₂²	1	24	yes	complemented
24	C₁₃×#474	C₂²	1	24	yes	complemented
25	C₁₃×#459	C₂²	1	24	yes	complemented
26	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
27	C₄×C₁₃×D₈	C₂²	1	24	yes	complemented
28	C₂×C₁₃×#107	C₂²	1	3	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
30	C₂×C₁₃×#102	C₂²	1	6	yes	—
31	C₂×C₁₃×#102	C₂²	1	3	yes	—
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
34	C₂×C₁₃×#41	—	2	8	no	—
35	C₂×C₁₃×#41	—	4	8	no	—
36	C₂²×Q₈×C₁₃	—	2	8	no	—
37	C₂²×Q₈×C₁₃	—	2	3	no	—
38	C₂²×Q₈×C₁₃	—	4	8	no	—
39	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	—	2	3	no	—
41	C₂²×D₄×C₁₃	—	2	3	no	—
42	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	3	no	—
45	C₂³×C₄×C₁₃	—	2	3	no	—
46	C₂×C₁₃×D₈	—	2	12	no	—
47	C₂×C₁₃×D₈	C₂³	1	12	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
50	C₁₃×C₄⋊Q₈	—	2	6	no	—
51	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
52	C₁₃×#127	—	2	6	no	—
53	C₁₃×#127	C₂³	1	12	yes	—
54	C₁₃×C₂²⋊Q₈	—	2	24	no	—
55	C₁₃×#121	—	2	24	no	—
56	C₄×Q₈×C₁₃	D₄	1	4	yes	—
57	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
58	C₄×D₄×C₁₃	—	2	6	no	—
59	C₄×D₄×C₁₃	—	2	6	no	—
60	C₄×D₄×C₁₃	C₂³	1	12	yes	—
61	C₄×D₄×C₁₃	C₂³	1	12	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
63	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
68	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
69	C₁₃×#107	C₂³	1	12	yes	—
70	C₁₃×C₄⋊C₈	C₂³	1	12	yes	—
71	C₁₃×#102	C₂³	1	4	yes	—
72	C₁₃×#102	C₂³	1	12	yes	—
73	C₁₃×#102	C₂³	1	24	yes	—
74	C₄×C₈×C₁₃	C₂³	1	12	yes	—
75	C₂×#3358	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	1	no	—
77	C₂⁴×C₁₃	—	2	3	no	—
78	C₁₃×#41	—	4	32	no	—
79	C₂×Q₈×C₁₃	—	2	12	no	—
80	C₂×Q₈×C₁₃	—	4	32	no	—
81	C₂×Q₈×C₁₃	—	4	12	no	—
82	C₂×Q₈×C₁₃	D₈	1	8	yes	complemented
83	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
84	C₂×D₄×C₁₃	—	2	1	no	—
85	C₂×D₄×C₁₃	—	2	3	no	—
86	C₂×D₄×C₁₃	—	2	12	no	—
87	C₂×D₄×C₁₃	—	2	12	no	—
88	C₂×D₄×C₁₃	—	2	6	no	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	—	2	6	no	—
91	C₂×D₄×C₁₃	—	4	12	no	—
92	C₂×D₄×C₁₃	—	8	6	no	—
93	C₂×D₄×C₁₃	#41	1	4	yes	complemented
94	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
95	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₁₃	—	2	1	no	—
97	C₂²×C₄×C₁₃	—	2	3	no	—
98	C₂²×C₄×C₁₃	—	2	12	no	—
99	C₂²×C₄×C₁₃	—	2	12	no	—
100	C₂²×C₄×C₁₃	—	4	12	no	—
101	C₂²×C₄×C₁₃	—	4	12	no	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
105	C₁₃×D₈	—	2	24	no	—
106	C₂×C₈×C₁₃	—	2	6	no	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
109	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
110	C₁₃×C₄⋊C₄	—	2	12	no	—
111	C₁₃×C₄⋊C₄	—	2	1	no	—
112	C₁₃×C₄⋊C₄	—	2	3	no	—
113	C₁₃×C₄⋊C₄	C₂×D₄	1	12	yes	—
114	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
115	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
116	C₁₃×C₂²⋊C₄	—	2	12	no	—
117	C₁₃×C₂²⋊C₄	—	2	12	no	—
118	C₄²×C₁₃	C₂×D₄	1	6	yes	—
119	C₄²×C₁₃	C₂⁴	1	6	yes	—
120	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
121	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
122	#3358	C₂×C₁₃	1	16	yes	direct product factor
123	C₂×#486	C₂×C₁₃	1	3	yes	complemented
124	C₂×#474	C₂×C₁₃	1	3	yes	complemented
125	C₂×#459	C₂×C₁₃	1	3	yes	complemented
126	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
127	C₂×C₄×D₈	C₂×C₁₃	1	3	yes	complemented
128	C₂³×C₁₃	—	2	4	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	6	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	6	no	—
134	C₂³×C₁₃	—	4	6	no	—
135	C₂³×C₁₃	—	4	6	no	—
136	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₁₃	—	4	24	no	—
138	Q₈×C₁₃	C₂×D₈	1	16	yes	complemented
139	D₄×C₁₃	—	2	4	no	—
140	D₄×C₁₃	—	2	6	no	—
141	D₄×C₁₃	—	2	2	no	—
142	D₄×C₁₃	—	2	6	no	—
143	D₄×C₁₃	—	4	6	no	—
144	D₄×C₁₃	—	4	24	no	—
145	D₄×C₁₃	—	8	12	no	—
146	D₄×C₁₃	C₂×#41	1	4	yes	complemented
147	C₂×C₄×C₁₃	—	2	6	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	6	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	6	no	—
152	C₂×C₄×C₁₃	—	4	24	no	—
153	C₂×C₄×C₁₃	—	4	24	no	—
154	C₂×C₄×C₁₃	C₂×D₈	1	12	yes	—
155	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
156	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
158	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
160	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
161	C₈×C₁₃	—	2	6	no	—
162	C₈×C₁₃	—	2	2	no	—
163	C₂²×#41	—	2	1	no	—
164	C₂³×Q₈	—	2	1	no	—
165	C₂²×D₈	C₂²×C₁₃	1	3	yes	—
166	#550	—	2	4	no	—
167	#550	C₂²×C₁₃	1	8	yes	complemented
168	D₄×Q₈	—	2	4	no	—
169	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
170	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
171	C₂×#127	C₂²×C₁₃	1	3	yes	—
172	C₂×C₂²⋊Q₈	—	2	3	no	—
173	C₂×#121	—	2	3	no	—
174	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
176	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
177	#486	C₂²×C₁₃	1	24	yes	complemented
178	#474	C₂²×C₁₃	1	24	yes	complemented
179	#459	C₂²×C₁₃	1	24	yes	complemented
180	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
181	C₄×D₈	C₂²×C₁₃	1	24	yes	complemented
182	C₂×#107	C₂²×C₁₃	1	3	yes	—
183	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
184	C₂×#102	C₂²×C₁₃	1	3	yes	—
185	C₂×#102	C₂²×C₁₃	1	6	yes	—
186	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
187	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
188	C₂²×C₁₃	—	2	4	no	—
189	C₂²×C₁₃	—	4	8	no	—
190	C₂²×C₁₃	—	4	2	no	—
191	C₂²×C₁₃	—	4	2	no	—
192	C₂²×C₁₃	—	4	6	no	—
193	C₂²×C₁₃	—	4	6	no	—
194	C₂²×C₁₃	—	4	6	no	—
195	C₂²×C₁₃	—	8	12	no	—
196	C₂²×C₁₃	#548	1	2	yes	—
197	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
198	C₂²×C₁₃	#577	1	2	yes	—
199	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
200	C₄×C₁₃	—	2	6	no	—
201	C₄×C₁₃	—	4	2	no	—
202	C₄×C₁₃	—	4	6	no	—
203	C₄×C₁₃	#548	1	2	yes	—
204	C₄×C₁₃	C₂²×D₈	1	12	yes	—
205	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
206	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×#41	—	2	8	no	—
208	C₂×#41	—	4	8	no	—
209	C₂²×Q₈	—	2	8	no	—
210	C₂²×Q₈	—	2	3	no	—
211	C₂²×Q₈	—	4	8	no	—
212	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
213	C₂²×D₄	—	2	3	no	—
214	C₂²×D₄	—	2	3	no	—
215	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
216	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
217	C₂³×C₄	—	2	3	no	—
218	C₂³×C₄	—	2	3	no	—
219	C₂×D₈	—	2	12	no	—
220	C₂×D₈	C₂³×C₁₃	1	12	yes	—
221	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
222	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
223	C₄⋊Q₈	—	2	6	no	—
224	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
225	#127	—	2	6	no	—
226	#127	C₂³×C₁₃	1	12	yes	—
227	C₂²⋊Q₈	—	2	24	no	—
228	#121	—	2	24	no	—
229	C₄×Q₈	D₄×C₁₃	1	4	yes	—
230	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
231	C₄×D₄	—	2	6	no	—
232	C₄×D₄	—	2	6	no	—
233	C₄×D₄	C₂³×C₁₃	1	12	yes	—
234	C₄×D₄	C₂³×C₁₃	1	12	yes	—
235	C₂×C₄⋊C₄	—	2	3	no	—
236	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
239	C₂×C₂²⋊C₄	—	2	3	no	—
240	C₂×C₂²⋊C₄	—	2	3	no	—
241	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
242	#107	C₂³×C₁₃	1	12	yes	—
243	C₄⋊C₈	C₂³×C₁₃	1	12	yes	—
244	#102	C₂³×C₁₃	1	4	yes	—
245	#102	C₂³×C₁₃	1	12	yes	—
246	#102	C₂³×C₁₃	1	24	yes	—
247	C₄×C₈	C₂³×C₁₃	1	12	yes	—
248	C₂×C₁₃	—	4	4	no	—
249	C₂×C₁₃	—	8	6	no	—
250	C₂×C₁₃	#3358	1	4	yes	direct product factor
251	C₂×C₁₃	C₂×#548	1	1	yes	characteristic
252	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
253	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
254	C₂⁴	—	2	1	no	—
255	C₂⁴	—	2	3	no	—
256	#41	—	4	32	no	—
257	C₂×Q₈	—	2	12	no	—
258	C₂×Q₈	—	4	32	no	—
259	C₂×Q₈	—	4	12	no	—
260	C₂×Q₈	C₁₃×D₈	1	8	yes	complemented
261	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
262	C₂×D₄	—	2	1	no	—
263	C₂×D₄	—	2	3	no	—
264	C₂×D₄	—	2	12	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	6	no	—
269	C₂×D₄	—	4	12	no	—
270	C₂×D₄	—	8	6	no	—
271	C₂×D₄	C₁₃×#41	1	4	yes	complemented
272	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
273	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	3	no	—
276	C₂²×C₄	—	2	12	no	—
277	C₂²×C₄	—	2	12	no	—
278	C₂²×C₄	—	4	12	no	—
279	C₂²×C₄	—	4	12	no	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
282	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
283	D₈	—	2	24	no	—
284	C₂×C₈	—	2	6	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
287	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
288	C₄⋊C₄	—	2	12	no	—
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	3	no	—
291	C₄⋊C₄	C₂×D₄×C₁₃	1	12	yes	—
292	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
293	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
294	C₂²⋊C₄	—	2	12	no	—
295	C₂²⋊C₄	—	2	12	no	—
296	C₄²	C₂×D₄×C₁₃	1	6	yes	—
297	C₄²	C₂⁴×C₁₃	1	6	yes	—
298	C₁₃	C₂×#3358	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	6	no	—
302	C₂³	—	4	2	no	—
303	C₂³	—	4	2	no	—
304	C₂³	—	4	6	no	—
305	C₂³	—	4	6	no	—
306	C₂³	—	4	6	no	—
307	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
308	Q₈	—	4	24	no	—
309	Q₈	C₂×C₁₃×D₈	1	16	yes	complemented
310	D₄	—	2	4	no	—
311	D₄	—	2	6	no	—
312	D₄	—	2	2	no	—
313	D₄	—	2	6	no	—
314	D₄	—	4	6	no	—
315	D₄	—	4	24	no	—
316	D₄	—	8	12	no	—
317	D₄	C₂×C₁₃×#41	1	4	yes	complemented
318	C₂×C₄	—	2	6	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	6	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	6	no	—
323	C₂×C₄	—	4	24	no	—
324	C₂×C₄	—	4	24	no	—
325	C₂×C₄	C₂×C₁₃×D₈	1	12	yes	—
326	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
327	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
329	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
330	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
331	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
332	C₈	—	2	6	no	—
333	C₈	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	2	no	—
337	C₂²	—	4	8	no	—
338	C₂²	—	4	6	no	—
339	C₂²	—	4	6	no	—
340	C₂²	—	4	6	no	—
341	C₂²	—	8	12	no	—
342	C₂²	C₁₃×#548	1	2	yes	—
343	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
344	C₂²	C₁₃×#577	1	2	yes	—
345	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
346	C₄	—	2	6	no	—
347	C₄	—	4	2	no	—
348	C₄	—	4	6	no	—
349	C₄	C₁₃×#548	1	2	yes	—
350	C₄	C₂²×C₁₃×D₈	1	12	yes	—
351	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
352	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
353	C₂	—	4	4	no	—
354	C₂	—	8	6	no	—
355	C₂	C₁₃×#3358	1	4	yes	direct product factor
356	C₂	C₂×C₁₃×#548	1	1	yes	characteristic
357	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
358	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#550	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
3. C₁₃×#3358	C₂	direct (N × H)
4. C₂×C₁₃×#486	C₂	semidirect
5. C₂×C₁₃×#474	C₂	semidirect
6. C₂×C₁₃×#459	C₂	semidirect
7. C₂×C₈×Q₈×C₁₃	C₂	semidirect
8. C₂×C₄×C₁₃×D₈	C₂	semidirect
13. C₁₃×#550	C₂²	semidirect
15. D₄×Q₈×C₁₃	C₂²	semidirect
23. C₁₃×#486	C₂²	semidirect
24. C₁₃×#474	C₂²	semidirect
25. C₁₃×#459	C₂²	semidirect
26. C₈×Q₈×C₁₃	C₂²	semidirect
27. C₄×C₁₃×D₈	C₂²	semidirect
75. C₂×#3358	C₁₃	direct (N × H)
82. C₂×Q₈×C₁₃	D₈	semidirect
93. C₂×D₄×C₁₃	#41	semidirect
120. C₂×#550	C₂×C₁₃	semidirect
121. C₂×D₄×Q₈	C₂×C₁₃	semidirect
122. #3358	C₂×C₁₃	direct (N × H)
123. C₂×#486	C₂×C₁₃	semidirect
124. C₂×#474	C₂×C₁₃	semidirect
125. C₂×#459	C₂×C₁₃	semidirect
126. C₂×C₈×Q₈	C₂×C₁₃	semidirect
127. C₂×C₄×D₈	C₂×C₁₃	semidirect
138. Q₈×C₁₃	C₂×D₈	semidirect
146. D₄×C₁₃	C₂×#41	semidirect
167. #550	C₂²×C₁₃	semidirect
169. D₄×Q₈	C₂²×C₁₃	semidirect
177. #486	C₂²×C₁₃	semidirect
178. #474	C₂²×C₁₃	semidirect
179. #459	C₂²×C₁₃	semidirect
180. C₈×Q₈	C₂²×C₁₃	semidirect
181. C₄×D₈	C₂²×C₁₃	semidirect
250. C₂×C₁₃	#3358	direct (N × H)
260. C₂×Q₈	C₁₃×D₈	semidirect
271. C₂×D₄	C₁₃×#41	semidirect
298. C₁₃	C₂×#3358	direct (N × H)
309. Q₈	C₂×C₁₃×D₈	semidirect
317. D₄	C₂×C₁₃×#41	semidirect
355. C₂	C₁₃×#3358	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#550	2
C₂×D₄×Q₈×C₁₃	2
C₁₃×#3358	2
C₂×C₁₃×#486	2
C₂×C₁₃×#474	2
C₂×C₁₃×#459	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×D₈	2
C₂×#3358	13

Subgroups — C2×C13×#3358 #15747634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3358 #15747634