Subgroups — C₂×C₁₃×#3216 #15747127

Order 3328.

2166 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3216	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#497	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₃×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#452	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	2	yes	—
11	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
12	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
13	C₁₃×#533	—	2	4	no	—
14	C₁₃×#533	C₂²	1	8	yes	complemented
15	C₁₃×#532	—	2	4	no	—
16	C₁₃×#532	C₂²	1	8	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	—	2	1	no	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₃×#121	—	2	1	no	—
26	C₂×C₁₃×#121	—	2	1	no	—
27	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
28	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	—	2	1	no	—
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₁₃×#117	—	2	1	no	—
32	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#497	C₂²	1	16	yes	complemented
34	C₁₃×#489	C₂²	1	16	yes	complemented
35	C₁₃×#462	C₂²	1	16	yes	complemented
36	C₁₃×#460	C₂²	1	16	yes	complemented
37	C₁₃×#452	C₂²	1	32	yes	complemented
38	C₁₃×#432	C₂²	1	8	yes	complemented
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×#103	C₂²	1	4	yes	—
41	C₂×C₁₃×#102	C₂²	1	4	yes	—
42	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₁₃×#97	C₂²	1	2	yes	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	—	4	8	no	—
46	C₂×C₁₃×#41	C₂³	1	8	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	—	2	2	no	—
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×Q₁₆	—	4	8	no	—
59	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
60	C₂×C₁₃×SD₁₆	—	4	8	no	—
61	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
63	C₁₃×C₄⋊Q₈	—	2	2	no	—
64	C₁₃×C₄⋊Q₈	—	2	2	no	—
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
69	C₁₃×#127	—	2	2	no	—
70	C₁₃×#127	C₂³	1	4	yes	—
71	C₁₃×#125	—	2	8	no	—
72	C₁₃×#124	—	2	4	no	—
73	C₁₃×#124	C₂³	1	8	yes	—
74	C₁₃×C₂²⋊Q₈	—	2	8	no	—
75	C₁₃×C₂²⋊Q₈	—	2	4	no	—
76	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
77	C₁₃×#121	—	2	8	no	—
78	C₁₃×#121	—	2	8	no	—
79	C₄×Q₈×C₁₃	—	2	8	no	—
80	C₄×Q₈×C₁₃	—	2	4	no	—
81	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
82	C₄×D₄×C₁₃	—	2	8	no	—
83	C₄×D₄×C₁₃	—	2	8	no	—
84	C₁₃×#117	—	2	8	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	D₄	1	4	yes	—
100	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	16	yes	—
105	C₁₃×#102	C₂³	1	16	yes	—
106	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
107	C₁₃×#97	C₂³	1	8	yes	—
108	C₂×#3216	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₁₃×#41	—	4	16	no	—
112	C₁₃×#41	—	4	16	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	4	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	—	4	4	no	—
120	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
121	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
122	C₂×D₄×C₁₃	—	2	8	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	8	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	8	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×Q₁₆	—	4	16	no	—
150	C₁₃×SD₁₆	—	4	16	no	—
151	C₂×C₈×C₁₃	—	2	8	no	—
152	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	4	no	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	8	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₄²×C₁₃	—	2	8	no	—
166	C₄²×C₁₃	C₂×D₄	1	4	yes	—
167	C₄²×C₁₃	C₂×D₄	1	4	yes	—
168	C₄²×C₁₃	C₂×D₄	1	2	yes	—
169	C₄²×C₁₃	C₂×D₄	1	2	yes	—
170	C₄²×C₁₃	C₂⁴	1	2	yes	—
171	C₄²×C₁₃	C₂⁴	1	2	yes	—
172	C₂×#533	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#532	C₂×C₁₃	1	1	yes	characteristic
174	#3216	C₂×C₁₃	1	16	yes	direct product factor
175	C₂×#497	C₂×C₁₃	1	2	yes	complemented
176	C₂×#489	C₂×C₁₃	1	2	yes	complemented
177	C₂×#462	C₂×C₁₃	1	2	yes	complemented
178	C₂×#460	C₂×C₁₃	1	2	yes	complemented
179	C₂×#452	C₂×C₁₃	1	4	yes	complemented
180	C₂×#432	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂³×C₁₃	—	2	2	no	—
182	C₂³×C₁₃	—	2	2	no	—
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	4	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	—	4	4	no	—
187	C₂³×C₁₃	—	4	4	no	—
188	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
189	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₁₃	—	2	4	no	—
191	Q₈×C₁₃	—	2	4	no	—
192	Q₈×C₁₃	—	2	8	no	—
193	Q₈×C₁₃	—	4	8	no	—
194	Q₈×C₁₃	—	4	4	no	—
195	Q₈×C₁₃	—	4	4	no	—
196	D₄×C₁₃	—	2	8	no	—
197	D₄×C₁₃	—	4	8	no	—
198	D₄×C₁₃	—	4	16	no	—
199	D₄×C₁₃	—	4	4	no	—
200	D₄×C₁₃	—	4	8	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	4	4	no	—
212	C₂×C₄×C₁₃	—	4	16	no	—
213	C₂×C₄×C₁₃	—	4	4	no	—
214	C₂×C₄×C₁₃	—	4	4	no	—
215	C₂×C₄×C₁₃	—	4	4	no	—
216	C₂×C₄×C₁₃	#137	1	4	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
225	C₈×C₁₃	—	2	8	no	—
226	C₂²×#41	C₂²×C₁₃	1	2	yes	—
227	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
228	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
229	#533	—	2	4	no	—
230	#533	C₂²×C₁₃	1	8	yes	complemented
231	#532	—	2	4	no	—
232	#532	C₂²×C₁₃	1	8	yes	—
233	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#125	—	2	1	no	—
238	C₂×#124	C₂²×C₁₃	1	2	yes	—
239	C₂×C₂²⋊Q₈	—	2	1	no	—
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	C₂×#121	—	2	1	no	—
242	C₂×#121	—	2	1	no	—
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
245	C₂×C₄×D₄	—	2	1	no	—
246	C₂×C₄×D₄	—	2	1	no	—
247	C₂×#117	—	2	1	no	—
248	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
249	#497	C₂²×C₁₃	1	16	yes	complemented
250	#489	C₂²×C₁₃	1	16	yes	complemented
251	#462	C₂²×C₁₃	1	16	yes	complemented
252	#460	C₂²×C₁₃	1	16	yes	complemented
253	#452	C₂²×C₁₃	1	32	yes	complemented
254	#432	C₂²×C₁₃	1	8	yes	complemented
255	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
256	C₂×#103	C₂²×C₁₃	1	4	yes	—
257	C₂×#102	C₂²×C₁₃	1	4	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
259	C₂×#97	C₂²×C₁₃	1	2	yes	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	4	4	no	—
264	C₂²×C₁₃	—	4	4	no	—
265	C₂²×C₁₃	—	4	4	no	—
266	C₂²×C₁₃	—	4	4	no	—
267	C₂²×C₁₃	—	8	8	no	—
268	C₂²×C₁₃	#535	1	2	yes	—
269	C₂²×C₁₃	C₂×#137	1	2	yes	—
270	C₂²×C₁₃	#575	1	2	yes	—
271	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	4	4	no	—
277	C₄×C₁₃	—	4	4	no	—
278	C₄×C₁₃	—	4	4	no	—
279	C₄×C₁₃	#535	1	2	yes	—
280	C₄×C₁₃	C₂×#137	1	4	yes	—
281	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	4	8	no	—
284	C₂×#41	C₂³×C₁₃	1	8	yes	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
287	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
288	C₂²×D₄	—	2	2	no	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
292	C₂³×C₄	—	2	2	no	—
293	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×Q₁₆	—	4	8	no	—
297	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
298	C₂×SD₁₆	—	4	8	no	—
299	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
300	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
305	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
306	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
307	#127	—	2	2	no	—
308	#127	C₂³×C₁₃	1	4	yes	—
309	#125	—	2	8	no	—
310	#124	—	2	4	no	—
311	#124	C₂³×C₁₃	1	8	yes	—
312	C₂²⋊Q₈	—	2	8	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
315	#121	—	2	8	no	—
316	#121	—	2	8	no	—
317	C₄×Q₈	—	2	8	no	—
318	C₄×Q₈	—	2	4	no	—
319	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
320	C₄×D₄	—	2	8	no	—
321	C₄×D₄	—	2	8	no	—
322	#117	—	2	8	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	D₄×C₁₃	1	4	yes	—
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
341	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
342	#103	C₂³×C₁₃	1	16	yes	—
343	#102	C₂³×C₁₃	1	16	yes	—
344	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
345	#97	C₂³×C₁₃	1	8	yes	—
346	C₂×C₁₃	—	4	2	no	—
347	C₂×C₁₃	—	8	4	no	—
348	C₂×C₁₃	#3216	1	4	yes	direct product factor
349	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
350	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
351	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
352	C₂⁴	—	2	2	no	—
353	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
354	#41	—	4	16	no	—
355	#41	—	4	16	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	—	2	8	no	—
362	C₂×Q₈	—	4	4	no	—
363	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
364	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	8	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	8	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
392	Q₁₆	—	4	16	no	—
393	SD₁₆	—	4	16	no	—
394	C₂×C₈	—	2	8	no	—
395	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₄²	—	2	8	no	—
409	C₄²	C₂×D₄×C₁₃	1	4	yes	—
410	C₄²	C₂×D₄×C₁₃	1	4	yes	—
411	C₄²	C₂×D₄×C₁₃	1	2	yes	—
412	C₄²	C₂×D₄×C₁₃	1	2	yes	—
413	C₄²	C₂⁴×C₁₃	1	2	yes	—
414	C₄²	C₂⁴×C₁₃	1	2	yes	—
415	C₁₃	C₂×#3216	1	1	yes	characteristic, direct product factor, Sylow
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	4	no	—
422	C₂³	—	4	4	no	—
423	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
424	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	2	8	no	—
428	Q₈	—	4	8	no	—
429	Q₈	—	4	4	no	—
430	Q₈	—	4	4	no	—
431	D₄	—	2	8	no	—
432	D₄	—	4	8	no	—
433	D₄	—	4	16	no	—
434	D₄	—	4	4	no	—
435	D₄	—	4	8	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	16	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	C₁₃×#137	1	4	yes	—
452	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
458	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
459	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
460	C₈	—	2	8	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	8	8	no	—
469	C₂²	C₁₃×#535	1	2	yes	—
470	C₂²	C₂×C₁₃×#137	1	2	yes	—
471	C₂²	C₁₃×#575	1	2	yes	—
472	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	4	no	—
479	C₄	—	4	4	no	—
480	C₄	C₁₃×#535	1	2	yes	—
481	C₄	C₂×C₁₃×#137	1	4	yes	—
482	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
483	C₂	—	4	2	no	—
484	C₂	—	8	4	no	—
485	C₂	C₁₃×#3216	1	4	yes	direct product factor
486	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
487	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
488	C₂	C₂×C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#532	C₂
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. C₂×C₁₃×#533	C₂	semidirect
3. C₁₃×#3216	C₂	direct (N × H)
4. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#489	C₂	semidirect
6. C₂×C₁₃×#462	C₂	semidirect
7. C₂×C₁₃×#460	C₂	semidirect
8. C₂×C₁₃×#452	C₂	semidirect
9. C₂×C₁₃×#432	C₂	semidirect
14. C₁₃×#533	C₂²	semidirect
33. C₁₃×#497	C₂²	semidirect
34. C₁₃×#489	C₂²	semidirect
35. C₁₃×#462	C₂²	semidirect
36. C₁₃×#460	C₂²	semidirect
37. C₁₃×#452	C₂²	semidirect
38. C₁₃×#432	C₂²	semidirect
108. C₂×#3216	C₁₃	direct (N × H)
172. C₂×#533	C₂×C₁₃	semidirect
174. #3216	C₂×C₁₃	direct (N × H)
175. C₂×#497	C₂×C₁₃	semidirect
176. C₂×#489	C₂×C₁₃	semidirect
177. C₂×#462	C₂×C₁₃	semidirect
178. C₂×#460	C₂×C₁₃	semidirect
179. C₂×#452	C₂×C₁₃	semidirect
180. C₂×#432	C₂×C₁₃	semidirect
230. #533	C₂²×C₁₃	semidirect
249. #497	C₂²×C₁₃	semidirect
250. #489	C₂²×C₁₃	semidirect
251. #462	C₂²×C₁₃	semidirect
252. #460	C₂²×C₁₃	semidirect
253. #452	C₂²×C₁₃	semidirect
254. #432	C₂²×C₁₃	semidirect
348. C₂×C₁₃	#3216	direct (N × H)
415. C₁₃	C₂×#3216	direct (N × H)
485. C₂	C₁₃×#3216	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×#533	2
C₂×C₁₃×#532	2
C₁₃×#3216	2
C₂×C₁₃×#497	2
C₂×C₁₃×#489	2
C₂×C₁₃×#462	2
C₂×C₁₃×#460	2
C₂×C₁₃×#452	2
C₂×C₁₃×#432	2
C₂×#3216	13

Subgroups — C2×C13×#3216 #15747127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3216 #15747127