Subgroups — C₂×C₁₃×#3218 #15747125

Order 3328.

2146 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3218	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#491	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#461	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#451	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#448	C₂	1	2	yes	maximal
10	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	—	2	4	no	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	8	yes	complemented
20	C₁₃×#529	—	2	4	no	—
21	C₁₃×#529	C₂²	1	8	yes	—
22	C₂×C₁₃×#126	—	2	1	no	—
23	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#123	—	2	1	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#117	—	2	1	no	—
32	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
33	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#497	C₂²	1	16	yes	complemented
36	C₁₃×#491	C₂²	1	16	yes	complemented
37	C₁₃×#462	C₂²	1	16	yes	complemented
38	C₁₃×#461	C₂²	1	16	yes	complemented
39	C₁₃×#451	C₂²	1	16	yes	complemented
40	C₁₃×#448	C₂²	1	16	yes	—
41	C₁₃×#432	C₂²	1	8	yes	complemented
42	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#103	C₂²	1	4	yes	—
44	C₂×C₁₃×#103	C₂²	1	4	yes	—
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₂×C₁₃×#97	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	4	no	—
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	4	8	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	—	2	2	no	—
56	C₂³×C₄×C₁₃	—	2	1	no	—
57	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×Q₁₆	—	4	8	no	—
61	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
62	C₂×C₁₃×SD₁₆	—	4	8	no	—
63	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
65	C₁₃×C₄⋊Q₈	—	2	4	no	—
66	C₁₃×C₄⋊Q₈	—	2	4	no	—
67	C₁₃×C₄⋊Q₈	—	2	8	no	—
68	C₁₃×C₄⋊Q₈	—	2	8	no	—
69	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
70	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
71	C₁₃×#126	—	2	8	no	—
72	C₁₃×#125	—	2	2	no	—
73	C₁₃×#125	C₂³	1	4	yes	—
74	C₁₃×#124	—	2	2	no	—
75	C₁₃×#124	C₂³	1	4	yes	—
76	C₁₃×#123	—	2	8	no	—
77	C₁₃×C₂²⋊Q₈	—	2	2	no	—
78	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×#121	—	2	2	no	—
80	C₁₃×#121	C₂³	1	4	yes	—
81	C₄×Q₈×C₁₃	—	2	2	no	—
82	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
83	C₄×D₄×C₁₃	—	2	8	no	—
84	C₄×D₄×C₁₃	—	2	2	no	—
85	C₄×D₄×C₁₃	C₂³	1	4	yes	—
86	C₁₃×#117	—	2	8	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
93	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
94	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	D₄	1	4	yes	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
111	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
112	C₁₃×#103	C₂³	1	16	yes	—
113	C₁₃×#103	C₂³	1	16	yes	—
114	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
115	C₁₃×#97	C₂³	1	8	yes	—
116	C₂×#3218	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₃	—	2	1	no	—
118	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₁₃	—	2	1	no	—
120	C₂×Q₈×C₁₃	—	2	8	no	—
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	—	2	8	no	—
123	C₂×Q₈×C₁₃	—	2	4	no	—
124	C₂×Q₈×C₁₃	—	2	8	no	—
125	C₂×Q₈×C₁₃	—	4	16	no	—
126	C₂×Q₈×C₁₃	—	4	8	no	—
127	C₂×Q₈×C₁₃	—	4	16	no	—
128	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
129	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
130	C₂×D₄×C₁₃	—	2	4	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	4	no	—
133	C₂×D₄×C₁₃	—	4	4	no	—
134	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	—	2	4	no	—
136	C₂²×C₄×C₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₃	—	2	4	no	—
138	C₂²×C₄×C₁₃	—	2	8	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	—	2	4	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	4	8	no	—
145	C₂²×C₄×C₁₃	—	4	4	no	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
156	C₁₃×Q₁₆	—	4	16	no	—
157	C₁₃×SD₁₆	—	4	16	no	—
158	C₂×C₈×C₁₃	—	2	8	no	—
159	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₄⋊C₄	—	2	8	no	—
164	C₁₃×C₄⋊C₄	—	2	4	no	—
165	C₁₃×C₄⋊C₄	—	2	4	no	—
166	C₁₃×C₄⋊C₄	—	2	4	no	—
167	C₁₃×C₄⋊C₄	—	2	4	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
172	C₁₃×C₂²⋊C₄	—	2	4	no	—
173	C₁₃×C₂²⋊C₄	—	2	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	4	no	—
175	C₁₃×C₂²⋊C₄	—	2	4	no	—
176	C₁₃×C₂²⋊C₄	—	2	4	no	—
177	C₄²×C₁₃	—	2	4	no	—
178	C₄²×C₁₃	C₂×D₄	1	4	yes	—
179	C₄²×C₁₃	C₂×D₄	1	2	yes	—
180	C₄²×C₁₃	C₂×D₄	1	2	yes	—
181	C₄²×C₁₃	C₂×D₄	1	4	yes	—
182	C₄²×C₁₃	C₂⁴	1	2	yes	—
183	C₄²×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#529	C₂×C₁₃	1	1	yes	characteristic
186	#3218	C₂×C₁₃	1	16	yes	direct product factor
187	C₂×#497	C₂×C₁₃	1	2	yes	complemented
188	C₂×#491	C₂×C₁₃	1	2	yes	complemented
189	C₂×#462	C₂×C₁₃	1	2	yes	complemented
190	C₂×#461	C₂×C₁₃	1	2	yes	complemented
191	C₂×#451	C₂×C₁₃	1	2	yes	complemented
192	C₂×#448	C₂×C₁₃	1	2	yes	—
193	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	#137	1	4	yes	—
201	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
203	Q₈×C₁₃	—	2	8	no	—
204	Q₈×C₁₃	—	2	4	no	—
205	Q₈×C₁₃	—	2	8	no	—
206	Q₈×C₁₃	—	4	16	no	—
207	Q₈×C₁₃	—	4	2	no	—
208	Q₈×C₁₃	—	4	8	no	—
209	D₄×C₁₃	—	2	4	no	—
210	D₄×C₁₃	—	4	8	no	—
211	D₄×C₁₃	—	4	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	8	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	8	no	—
224	C₂×C₄×C₁₃	—	4	16	no	—
225	C₂×C₄×C₁₃	—	4	8	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	8	no	—
230	C₂×C₄×C₁₃	#137	1	4	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
239	C₈×C₁₃	—	2	8	no	—
240	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
241	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
242	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
243	C₂×C₄⋊Q₈	—	2	1	no	—
244	C₂×C₄⋊Q₈	—	2	1	no	—
245	C₂×C₄⋊Q₈	—	2	4	no	—
246	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
249	#529	—	2	4	no	—
250	#529	C₂²×C₁₃	1	8	yes	—
251	C₂×#126	—	2	1	no	—
252	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#123	—	2	1	no	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₄×D₄	—	2	1	no	—
259	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂×#117	—	2	1	no	—
261	C₂²×C₄⋊C₄	—	2	1	no	—
262	C₂²×C₄⋊C₄	—	2	1	no	—
263	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
264	#497	C₂²×C₁₃	1	16	yes	complemented
265	#491	C₂²×C₁₃	1	16	yes	complemented
266	#462	C₂²×C₁₃	1	16	yes	complemented
267	#461	C₂²×C₁₃	1	16	yes	complemented
268	#451	C₂²×C₁₃	1	16	yes	complemented
269	#448	C₂²×C₁₃	1	16	yes	—
270	#432	C₂²×C₁₃	1	8	yes	complemented
271	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
272	C₂×#103	C₂²×C₁₃	1	4	yes	—
273	C₂×#103	C₂²×C₁₃	1	4	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
275	C₂×#97	C₂²×C₁₃	1	2	yes	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	8	no	—
278	C₂²×C₁₃	—	2	2	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	8	4	no	—
283	C₂²×C₁₃	#535	1	2	yes	—
284	C₂²×C₁₃	C₂×#137	1	4	yes	—
285	C₂²×C₁₃	C₂×#137	1	2	yes	—
286	C₂²×C₁₃	C₂×#137	1	2	yes	—
287	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	4	8	no	—
293	C₄×C₁₃	—	4	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	#535	1	2	yes	—
297	C₄×C₁₃	C₂×#137	1	4	yes	—
298	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
299	C₂²×Q₈	—	2	2	no	—
300	C₂²×Q₈	—	2	4	no	—
301	C₂²×Q₈	—	4	8	no	—
302	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
304	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂³×C₄	—	2	2	no	—
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×Q₁₆	—	4	8	no	—
313	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
314	C₂×SD₁₆	—	4	8	no	—
315	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
316	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
317	C₄⋊Q₈	—	2	4	no	—
318	C₄⋊Q₈	—	2	4	no	—
319	C₄⋊Q₈	—	2	8	no	—
320	C₄⋊Q₈	—	2	8	no	—
321	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
322	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
323	#126	—	2	8	no	—
324	#125	—	2	2	no	—
325	#125	C₂³×C₁₃	1	4	yes	—
326	#124	—	2	2	no	—
327	#124	C₂³×C₁₃	1	4	yes	—
328	#123	—	2	8	no	—
329	C₂²⋊Q₈	—	2	2	no	—
330	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
331	#121	—	2	2	no	—
332	#121	C₂³×C₁₃	1	4	yes	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
335	C₄×D₄	—	2	8	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	C₂³×C₁₃	1	4	yes	—
338	#117	—	2	8	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	8	no	—
344	C₂×C₄⋊C₄	—	2	8	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	D₄×C₁₃	1	4	yes	—
360	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
363	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
364	#103	C₂³×C₁₃	1	16	yes	—
365	#103	C₂³×C₁₃	1	16	yes	—
366	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
367	#97	C₂³×C₁₃	1	8	yes	—
368	C₂×C₁₃	—	2	4	no	—
369	C₂×C₁₃	—	8	2	no	—
370	C₂×C₁₃	#3218	1	4	yes	direct product factor
371	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
372	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
373	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
374	C₂⁴	—	2	1	no	—
375	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	8	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	4	16	no	—
383	C₂×Q₈	—	4	8	no	—
384	C₂×Q₈	—	4	16	no	—
385	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
386	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
409	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
410	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
412	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
413	Q₁₆	—	4	16	no	—
414	SD₁₆	—	4	16	no	—
415	C₂×C₈	—	2	8	no	—
416	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
428	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₄²	—	2	4	no	—
435	C₄²	C₂×D₄×C₁₃	1	4	yes	—
436	C₄²	C₂×D₄×C₁₃	1	2	yes	—
437	C₄²	C₂×D₄×C₁₃	1	2	yes	—
438	C₄²	C₂×D₄×C₁₃	1	4	yes	—
439	C₄²	C₂⁴×C₁₃	1	2	yes	—
440	C₄²	C₂⁴×C₁₃	1	2	yes	—
441	C₁₃	C₂×#3218	1	1	yes	characteristic, direct product factor, Sylow
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	C₁₃×#137	1	4	yes	—
449	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
450	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	Q₈	—	2	8	no	—
452	Q₈	—	2	4	no	—
453	Q₈	—	2	8	no	—
454	Q₈	—	4	16	no	—
455	Q₈	—	4	8	no	—
456	Q₈	—	4	2	no	—
457	D₄	—	2	4	no	—
458	D₄	—	4	8	no	—
459	D₄	—	4	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	4	16	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	C₁₃×#137	1	4	yes	—
479	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
480	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
485	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
486	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
487	C₈	—	2	8	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	8	4	no	—
495	C₂²	C₁₃×#535	1	2	yes	—
496	C₂²	C₂×C₁₃×#137	1	4	yes	—
497	C₂²	C₂×C₁₃×#137	1	2	yes	—
498	C₂²	C₂×C₁₃×#137	1	2	yes	—
499	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	8	no	—
507	C₄	—	4	2	no	—
508	C₄	C₁₃×#535	1	2	yes	—
509	C₄	C₂×C₁₃×#137	1	4	yes	—
510	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
511	C₂	—	2	4	no	—
512	C₂	—	8	2	no	—
513	C₂	C₁₃×#3218	1	4	yes	direct product factor
514	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
515	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
516	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₁₃×#3218	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#491	C₂	semidirect
6. C₂×C₁₃×#462	C₂	semidirect
7. C₂×C₁₃×#461	C₂	semidirect
8. C₂×C₁₃×#451	C₂	semidirect
10. C₂×C₁₃×#432	C₂	semidirect
19. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
35. C₁₃×#497	C₂²	semidirect
36. C₁₃×#491	C₂²	semidirect
37. C₁₃×#462	C₂²	semidirect
38. C₁₃×#461	C₂²	semidirect
39. C₁₃×#451	C₂²	semidirect
41. C₁₃×#432	C₂²	semidirect
116. C₂×#3218	C₁₃	direct (N × H)
184. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
186. #3218	C₂×C₁₃	direct (N × H)
187. C₂×#497	C₂×C₁₃	semidirect
188. C₂×#491	C₂×C₁₃	semidirect
189. C₂×#462	C₂×C₁₃	semidirect
190. C₂×#461	C₂×C₁₃	semidirect
191. C₂×#451	C₂×C₁₃	semidirect
193. C₂×#432	C₂×C₁₃	semidirect
248. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
264. #497	C₂²×C₁₃	semidirect
265. #491	C₂²×C₁₃	semidirect
266. #462	C₂²×C₁₃	semidirect
267. #461	C₂²×C₁₃	semidirect
268. #451	C₂²×C₁₃	semidirect
270. #432	C₂²×C₁₃	semidirect
370. C₂×C₁₃	#3218	direct (N × H)
441. C₁₃	C₂×#3218	direct (N × H)
513. C₂	C₁₃×#3218	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×C₄⋊Q₈	2
C₂×C₁₃×#529	2
C₁₃×#3218	2
C₂×C₁₃×#497	2
C₂×C₁₃×#491	2
C₂×C₁₃×#462	2
C₂×C₁₃×#461	2
C₂×C₁₃×#451	2
C₂×C₁₃×#448	2
C₂×C₁₃×#432	2
C₂×#3218	13

Subgroups — C2×C13×#3218 #15747125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3218 #15747125