Subgroups — C₂×C₁₃×#3389 #15747702

Order 3328.

1898 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3389	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#501	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#442	C₂	1	2	yes	maximal
10	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
12	C₁₃×#554	—	2	8	no	—
13	C₁₃×#554	C₂²	1	16	yes	complemented
14	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₃×#125	C₂²	1	2	yes	—
16	C₂×C₁₃×#125	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₁₃×#501	C₂²	1	16	yes	complemented
26	C₁₃×#499	C₂²	1	8	yes	complemented
27	C₁₃×#478	C₂²	1	16	yes	complemented
28	C₁₃×#478	C₂²	1	16	yes	complemented
29	C₁₃×#474	C₂²	1	16	yes	complemented
30	C₁₃×#446	C₂²	1	8	yes	complemented
31	C₁₃×#442	C₂²	1	16	yes	—
32	C₄×C₁₃×D₈	C₂²	1	8	yes	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	C₂²	1	2	yes	—
35	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#106	C₂²	1	2	yes	—
38	C₂×C₁₃×#106	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	2	yes	—
42	C₂×C₁₃×#102	C₂²	1	2	yes	—
43	C₂×C₁₃×#102	C₂²	1	2	yes	—
44	C₂×C₁₃×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂³×C₄×C₁₃	—	2	2	no	—
52	C₂×C₁₃×D₈	Q₈	1	8	yes	complemented
53	C₂×C₁₃×D₈	C₂³	1	4	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×C₄⋊Q₈	—	2	4	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
59	C₁₃×#125	—	2	4	no	—
60	C₁₃×#125	—	2	4	no	—
61	C₁₃×#125	C₂³	1	8	yes	—
62	C₁₃×#125	C₂³	1	8	yes	—
63	C₁₃×C₂²⋊Q₈	—	2	16	no	—
64	C₁₃×C₂²⋊Q₈	—	2	16	no	—
65	C₁₃×C₂²⋊Q₈	—	2	16	no	—
66	C₄×Q₈×C₁₃	D₄	1	4	yes	—
67	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
68	C₄×D₄×C₁₃	—	2	4	no	—
69	C₄×D₄×C₁₃	—	2	4	no	—
70	C₄×D₄×C₁₃	—	2	4	no	—
71	C₄×D₄×C₁₃	C₂³	1	8	yes	—
72	C₄×D₄×C₁₃	C₂³	1	8	yes	—
73	C₄×D₄×C₁₃	C₂³	1	8	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₁₃×#107	C₂³	1	4	yes	—
91	C₁₃×#107	C₂³	1	4	yes	—
92	C₁₃×#107	C₂³	1	8	yes	—
93	C₁₃×#107	C₂³	1	4	yes	—
94	C₁₃×#106	C₂³	1	8	yes	—
95	C₁₃×#106	C₂³	1	8	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
98	C₁₃×#102	C₂³	1	8	yes	—
99	C₁₃×#102	C₂³	1	8	yes	—
100	C₁₃×#102	C₂³	1	8	yes	—
101	C₁₃×#97	C₂³	1	8	yes	—
102	C₄×C₈×C₁₃	C₂³	1	4	yes	—
103	C₂×#3389	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	8	no	—
106	C₂×Q₈×C₁₃	—	4	2	no	—
107	C₂×Q₈×C₁₃	—	8	4	no	—
108	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	2	4	no	—
111	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	—
112	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	8	no	—
119	C₂²×C₄×C₁₃	—	4	8	no	—
120	C₂²×C₄×C₁₃	—	8	4	no	—
121	C₂²×C₄×C₁₃	—	8	4	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×D₈	C₂×Q₈	1	16	yes	complemented
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	4	no	—
130	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
131	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
132	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
133	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
134	C₁₃×C₄⋊C₄	—	2	8	no	—
135	C₁₃×C₄⋊C₄	—	2	8	no	—
136	C₁₃×C₄⋊C₄	—	2	8	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	2	8	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	2	2	no	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
144	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
145	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
146	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
147	C₁₃×C₂²⋊C₄	—	2	8	no	—
148	C₁₃×C₂²⋊C₄	—	2	8	no	—
149	C₁₃×C₂²⋊C₄	—	2	8	no	—
150	C₄²×C₁₃	C₂×D₄	1	2	yes	—
151	C₄²×C₁₃	C₂×D₄	1	4	yes	—
152	C₄²×C₁₃	C₂⁴	1	2	yes	—
153	C₄²×C₁₃	C₂⁴	1	4	yes	—
154	C₂×#554	C₂×C₁₃	1	2	yes	complemented
155	#3389	C₂×C₁₃	1	16	yes	direct product factor
156	C₂×#501	C₂×C₁₃	1	2	yes	complemented
157	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
158	C₂×#478	C₂×C₁₃	1	2	yes	complemented
159	C₂×#478	C₂×C₁₃	1	2	yes	complemented
160	C₂×#474	C₂×C₁₃	1	2	yes	complemented
161	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂×#442	C₂×C₁₃	1	2	yes	—
163	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
164	C₂³×C₁₃	—	2	8	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	4	4	no	—
167	C₂³×C₁₃	—	4	4	no	—
168	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₃	—	4	4	no	—
170	Q₈×C₁₃	—	8	8	no	—
171	D₄×C₁₃	—	2	8	no	—
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	C₂²×Q₈	1	8	yes	—
174	C₂×C₄×C₁₃	—	2	4	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	4	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	4	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	4	16	no	—
182	C₂×C₄×C₁₃	—	4	4	no	—
183	C₂×C₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	4	4	no	—
185	C₂×C₄×C₁₃	—	8	8	no	—
186	C₂×C₄×C₁₃	—	8	8	no	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
193	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
194	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
195	C₈×C₁₃	—	2	2	no	—
196	C₈×C₁₃	—	2	4	no	—
197	C₈×C₁₃	C₂²×Q₈	1	4	yes	—
198	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
199	#554	—	2	8	no	—
200	#554	C₂²×C₁₃	1	16	yes	complemented
201	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
202	C₂×#125	C₂²×C₁₃	1	2	yes	—
203	C₂×#125	C₂²×C₁₃	1	2	yes	—
204	C₂×C₂²⋊Q₈	—	2	2	no	—
205	C₂×C₂²⋊Q₈	—	2	2	no	—
206	C₂×C₂²⋊Q₈	—	2	2	no	—
207	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
209	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₄⋊C₄	—	2	2	no	—
212	#501	C₂²×C₁₃	1	16	yes	complemented
213	#499	C₂²×C₁₃	1	8	yes	complemented
214	#478	C₂²×C₁₃	1	16	yes	complemented
215	#478	C₂²×C₁₃	1	16	yes	complemented
216	#474	C₂²×C₁₃	1	16	yes	complemented
217	#446	C₂²×C₁₃	1	8	yes	complemented
218	#442	C₂²×C₁₃	1	16	yes	—
219	C₄×D₈	C₂²×C₁₃	1	8	yes	—
220	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×#107	C₂²×C₁₃	1	2	yes	—
222	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#106	C₂²×C₁₃	1	2	yes	—
225	C₂×#106	C₂²×C₁₃	1	2	yes	—
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
228	C₂×#102	C₂²×C₁₃	1	2	yes	—
229	C₂×#102	C₂²×C₁₃	1	2	yes	—
230	C₂×#102	C₂²×C₁₃	1	2	yes	—
231	C₂×#97	C₂²×C₁₃	1	2	yes	—
232	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×C₁₃	—	2	8	no	—
234	C₂²×C₁₃	—	4	16	no	—
235	C₂²×C₁₃	—	4	4	no	—
236	C₂²×C₁₃	—	4	4	no	—
237	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
238	C₂²×C₁₃	#575	1	2	yes	—
239	C₂²×C₁₃	#576	1	2	yes	—
240	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
241	C₄×C₁₃	—	2	4	no	—
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	2	2	no	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	4	4	no	—
246	C₄×C₁₃	—	4	4	no	—
247	C₄×C₁₃	—	4	4	no	—
248	C₄×C₁₃	D₄×Q₈	1	2	yes	—
249	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
250	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	C₂²×Q₈	—	2	2	no	—
252	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
253	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	2	2	no	—
257	C₂×D₈	Q₈×C₁₃	1	8	yes	complemented
258	C₂×D₈	C₂³×C₁₃	1	4	yes	—
259	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
261	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
262	C₄⋊Q₈	—	2	4	no	—
263	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
264	#125	—	2	4	no	—
265	#125	—	2	4	no	—
266	#125	C₂³×C₁₃	1	8	yes	—
267	#125	C₂³×C₁₃	1	8	yes	—
268	C₂²⋊Q₈	—	2	16	no	—
269	C₂²⋊Q₈	—	2	16	no	—
270	C₂²⋊Q₈	—	2	16	no	—
271	C₄×Q₈	D₄×C₁₃	1	4	yes	—
272	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	C₄×D₄	C₂³×C₁₃	1	8	yes	—
277	C₄×D₄	C₂³×C₁₃	1	8	yes	—
278	C₄×D₄	C₂³×C₁₃	1	8	yes	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	16	no	—
285	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
286	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
295	#107	C₂³×C₁₃	1	4	yes	—
296	#107	C₂³×C₁₃	1	4	yes	—
297	#107	C₂³×C₁₃	1	8	yes	—
298	#107	C₂³×C₁₃	1	4	yes	—
299	#106	C₂³×C₁₃	1	8	yes	—
300	#106	C₂³×C₁₃	1	8	yes	—
301	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
302	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
303	#102	C₂³×C₁₃	1	8	yes	—
304	#102	C₂³×C₁₃	1	8	yes	—
305	#102	C₂³×C₁₃	1	8	yes	—
306	#97	C₂³×C₁₃	1	8	yes	—
307	C₄×C₈	C₂³×C₁₃	1	4	yes	—
308	C₂×C₁₃	—	4	8	no	—
309	C₂×C₁₃	#3389	1	4	yes	direct product factor
310	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
312	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
313	C₂⁴	—	2	2	no	—
314	C₂×Q₈	—	2	8	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	8	4	no	—
317	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	4	no	—
320	C₂×D₄	C₂×Q₈×C₁₃	1	8	yes	—
321	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	4	8	no	—
329	C₂²×C₄	—	8	4	no	—
330	C₂²×C₄	—	8	4	no	—
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
336	D₈	C₂×Q₈×C₁₃	1	16	yes	complemented
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
340	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
341	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
342	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	8	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
352	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
353	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
354	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
355	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₄²	C₂×D₄×C₁₃	1	2	yes	—
360	C₄²	C₂×D₄×C₁₃	1	4	yes	—
361	C₄²	C₂⁴×C₁₃	1	2	yes	—
362	C₄²	C₂⁴×C₁₃	1	4	yes	—
363	C₁₃	C₂×#3389	1	1	yes	characteristic, direct product factor, Sylow
364	C₂³	—	2	8	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
369	Q₈	—	4	4	no	—
370	Q₈	—	8	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	4	no	—
373	D₄	C₂²×Q₈×C₁₃	1	8	yes	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	16	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	8	8	no	—
386	C₂×C₄	—	8	8	no	—
387	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
389	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
390	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
391	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
393	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
394	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	4	no	—
397	C₈	C₂²×Q₈×C₁₃	1	4	yes	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	16	no	—
402	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
403	C₂²	C₁₃×#575	1	2	yes	—
404	C₂²	C₁₃×#576	1	2	yes	—
405	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	D₄×Q₈×C₁₃	1	2	yes	—
414	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
415	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂	—	4	8	no	—
417	C₂	C₁₃×#3389	1	4	yes	direct product factor
418	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
419	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
420	C₂	C₂×C₁₃×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
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×#554	C₂	semidirect
2. C₁₃×#3389	C₂	direct (N × H)
3. C₂×C₁₃×#501	C₂	semidirect
4. C₂×C₁₃×#499	C₂	semidirect
5. C₂×C₁₃×#478	C₂	semidirect
6. C₂×C₁₃×#478	C₂	semidirect
7. C₂×C₁₃×#474	C₂	semidirect
8. C₂×C₁₃×#446	C₂	semidirect
13. C₁₃×#554	C₂²	semidirect
25. C₁₃×#501	C₂²	semidirect
26. C₁₃×#499	C₂²	semidirect
27. C₁₃×#478	C₂²	semidirect
28. C₁₃×#478	C₂²	semidirect
29. C₁₃×#474	C₂²	semidirect
30. C₁₃×#446	C₂²	semidirect
52. C₂×C₁₃×D₈	Q₈	semidirect
103. C₂×#3389	C₁₃	direct (N × H)
127. C₁₃×D₈	C₂×Q₈	semidirect
154. C₂×#554	C₂×C₁₃	semidirect
155. #3389	C₂×C₁₃	direct (N × H)
156. C₂×#501	C₂×C₁₃	semidirect
157. C₂×#499	C₂×C₁₃	semidirect
158. C₂×#478	C₂×C₁₃	semidirect
159. C₂×#478	C₂×C₁₃	semidirect
160. C₂×#474	C₂×C₁₃	semidirect
161. C₂×#446	C₂×C₁₃	semidirect
200. #554	C₂²×C₁₃	semidirect
212. #501	C₂²×C₁₃	semidirect
213. #499	C₂²×C₁₃	semidirect
214. #478	C₂²×C₁₃	semidirect
215. #478	C₂²×C₁₃	semidirect
216. #474	C₂²×C₁₃	semidirect
217. #446	C₂²×C₁₃	semidirect
257. C₂×D₈	Q₈×C₁₃	semidirect
309. C₂×C₁₃	#3389	direct (N × H)
336. D₈	C₂×Q₈×C₁₃	semidirect
363. C₁₃	C₂×#3389	direct (N × H)
417. C₂	C₁₃×#3389	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×#554	2
C₁₃×#3389	2
C₂×C₁₃×#501	2
C₂×C₁₃×#499	2
C₂×C₁₃×#478	2
C₂×C₁₃×#474	2
C₂×C₁₃×#446	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×D₈	2
C₂×#3389	13

Subgroups — C2×C13×#3389 #15747702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3389 #15747702