Subgroups — C₂×C₁₃×#3331 #15747490

Order 3328.

2158 conjugacy classes of subgroups.

The subgroup lattice has 560 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	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3331	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#483	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#470	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#417	C₂	1	2	yes	maximal, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	C₂²	1	8	yes	complemented
19	C₁₃×#547	—	2	4	no	—
20	C₁₃×#547	C₂²	1	8	yes	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#125	—	2	1	no	—
24	C₂×C₁₃×#123	—	2	2	no	—
25	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₁₃×#121	—	2	1	no	—
29	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₁₃	—	2	1	no	—
31	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
34	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#487	C₂²	1	8	yes	complemented
36	C₁₃×#483	C₂²	1	16	yes	complemented
37	C₁₃×#476	C₂²	1	8	yes	complemented
38	C₁₃×#470	C₂²	1	16	yes	complemented
39	C₁₃×#462	C₂²	1	8	yes	complemented
40	C₁₃×#452	C₂²	1	16	yes	complemented
41	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
42	C₁₃×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₃×#106	C₂²	1	2	yes	—
44	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#417	C₂²	1	16	yes	complemented
47	C₂×C₁₃×#103	C₂²	1	2	yes	—
48	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#102	C₂²	1	2	yes	—
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#41	—	2	4	no	—
56	C₂×C₁₃×#41	—	2	8	no	—
57	C₂×C₁₃×#41	—	4	4	no	—
58	C₂×C₁₃×#41	C₂³	1	8	yes	—
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	—	2	2	no	—
63	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	—	2	2	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	—	2	2	no	—
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂×C₁₃×Q₁₆	—	4	4	no	—
70	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×SD₁₆	—	2	4	no	—
72	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
73	C₂×C₁₃×M₁₆	—	4	4	no	—
74	C₂×C₁₃×M₁₆	C₂³	1	8	yes	—
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	2	2	no	—
80	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₁₃×#125	—	2	8	no	—
83	C₁₃×#123	—	2	16	no	—
84	C₁₃×C₂²⋊Q₈	—	2	4	no	—
85	C₁₃×C₂²⋊Q₈	—	2	4	no	—
86	C₁₃×C₂²⋊Q₈	—	2	16	no	—
87	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₁₃×#121	—	2	8	no	—
90	C₄×Q₈×C₁₃	—	2	2	no	—
91	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
92	C₄×D₄×C₁₃	—	2	8	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	D₄	1	4	yes	—
95	C₄×D₄×C₁₃	C₂³	1	4	yes	—
96	C₄×D₄×C₁₃	C₂³	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
111	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₁₃	—	2	1	no	—
116	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
117	C₁₃×#106	C₂³	1	4	yes	—
118	C₁₃×#106	C₂³	1	8	yes	—
119	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
120	C₁₃×#103	C₂³	1	8	yes	—
121	C₁₃×#103	C₂³	1	8	yes	—
122	C₁₃×#103	C₂³	1	4	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	4	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₄×C₈×C₁₃	C₂³	1	4	yes	—
128	C₂×#3331	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
129	C₂⁴×C₁₃	—	2	1	no	—
130	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
131	C₁₃×#41	—	2	16	no	—
132	C₁₃×#41	—	4	8	no	—
133	C₁₃×#41	—	4	16	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	2	no	—
138	C₂×Q₈×C₁₃	—	2	4	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	8	2	no	—
142	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
143	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
144	C₂×D₄×C₁₃	—	2	8	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	4	8	no	—
149	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
150	C₂×D₄×C₁₃	#41	1	4	yes	—
151	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	—	2	4	no	—
153	C₂²×C₄×C₁₃	—	2	4	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	4	8	no	—
163	C₂²×C₄×C₁₃	—	4	4	no	—
164	C₂²×C₄×C₁₃	—	8	4	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₁₃×Q₁₆	—	4	8	no	—
172	C₁₃×SD₁₆	—	2	8	no	—
173	C₁₃×M₁₆	—	4	8	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	2	2	no	—
176	C₂×C₈×C₁₃	—	2	4	no	—
177	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
178	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
179	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	2	8	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	4	no	—
186	C₁₃×C₄⋊C₄	—	2	4	no	—
187	C₁₃×C₄⋊C₄	—	2	8	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
191	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	8	no	—
196	C₁₃×C₂²⋊C₄	—	2	4	no	—
197	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
198	C₄²×C₁₃	—	2	4	no	—
199	C₄²×C₁₃	C₂×D₄	1	2	yes	—
200	C₄²×C₁₃	C₂⁴	1	2	yes	—
201	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₂×#547	C₂×C₁₃	1	1	yes	characteristic
203	#3331	C₂×C₁₃	1	16	yes	direct product factor
204	C₂×#487	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#483	C₂×C₁₃	1	2	yes	complemented
206	C₂×#476	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#470	C₂×C₁₃	1	2	yes	complemented
208	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#452	C₂×C₁₃	1	2	yes	complemented
210	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#436	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂×#417	C₂×C₁₃	1	2	yes	complemented
213	C₂³×C₁₃	—	2	4	no	—
214	C₂³×C₁₃	—	2	4	no	—
215	C₂³×C₁₃	—	2	4	no	—
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	2	2	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
221	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
222	Q₈×C₁₃	—	2	2	no	—
223	Q₈×C₁₃	—	2	4	no	—
224	Q₈×C₁₃	—	2	2	no	—
225	Q₈×C₁₃	—	2	4	no	—
226	Q₈×C₁₃	—	4	2	no	—
227	Q₈×C₁₃	—	4	4	no	—
228	Q₈×C₁₃	—	8	4	no	—
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	8	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	4	16	no	—
233	D₄×C₁₃	C₂×#41	1	4	yes	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	—	2	8	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	4	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	4	16	no	—
245	C₂×C₄×C₁₃	—	4	4	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	4	8	no	—
251	C₂×C₄×C₁₃	—	8	8	no	—
252	C₂×C₄×C₁₃	#137	1	4	yes	—
253	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
258	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
259	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
260	C₈×C₁₃	—	2	2	no	—
261	C₈×C₁₃	—	2	2	no	—
262	C₈×C₁₃	—	2	4	no	—
263	C₂²×#41	C₂²×C₁₃	1	2	yes	—
264	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
265	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
267	#554	—	2	4	no	—
268	#554	C₂²×C₁₃	1	8	yes	complemented
269	#547	—	2	4	no	—
270	#547	C₂²×C₁₃	1	8	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#125	—	2	1	no	—
274	C₂×#123	—	2	2	no	—
275	C₂×C₂²⋊Q₈	—	2	2	no	—
276	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
277	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
278	C₂×#121	—	2	1	no	—
279	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	—	2	1	no	—
284	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
285	#487	C₂²×C₁₃	1	8	yes	complemented
286	#483	C₂²×C₁₃	1	16	yes	complemented
287	#476	C₂²×C₁₃	1	8	yes	complemented
288	#470	C₂²×C₁₃	1	16	yes	complemented
289	#462	C₂²×C₁₃	1	8	yes	complemented
290	#452	C₂²×C₁₃	1	16	yes	complemented
291	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
292	#436	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#106	C₂²×C₁₃	1	2	yes	—
295	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
296	#417	C₂²×C₁₃	1	16	yes	complemented
297	C₂×#103	C₂²×C₁₃	1	2	yes	—
298	C₂×#103	C₂²×C₁₃	1	2	yes	—
299	C₂×#103	C₂²×C₁₃	1	2	yes	—
300	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#102	C₂²×C₁₃	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
304	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	2	4	no	—
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	4	no	—
309	C₂²×C₁₃	—	4	8	no	—
310	C₂²×C₁₃	—	4	8	no	—
311	C₂²×C₁₃	—	4	2	no	—
312	C₂²×C₁₃	—	4	2	no	—
313	C₂²×C₁₃	#546	1	2	yes	—
314	C₂²×C₁₃	C₂×#137	1	2	yes	—
315	C₂²×C₁₃	#577	1	2	yes	—
316	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
317	C₄×C₁₃	—	2	4	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	4	4	no	—
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	—	4	2	no	—
322	C₄×C₁₃	—	4	2	no	—
323	C₄×C₁₃	—	4	4	no	—
324	C₄×C₁₃	#546	1	2	yes	—
325	C₄×C₁₃	C₂×#137	1	4	yes	—
326	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
327	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
328	C₂×#41	—	2	4	no	—
329	C₂×#41	—	2	8	no	—
330	C₂×#41	—	4	4	no	—
331	C₂×#41	C₂³×C₁₃	1	8	yes	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
334	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
335	C₂²×D₄	—	2	2	no	—
336	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂³×C₄	—	2	2	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	—	2	2	no	—
341	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
342	C₂×Q₁₆	—	4	4	no	—
343	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
346	C₂×M₁₆	—	4	4	no	—
347	C₂×M₁₆	C₂³×C₁₃	1	8	yes	—
348	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
350	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
354	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
355	#125	—	2	8	no	—
356	#123	—	2	16	no	—
357	C₂²⋊Q₈	—	2	4	no	—
358	C₂²⋊Q₈	—	2	4	no	—
359	C₂²⋊Q₈	—	2	16	no	—
360	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
361	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
362	#121	—	2	8	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
365	C₄×D₄	—	2	8	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	D₄×C₁₃	1	4	yes	—
368	C₄×D₄	C₂³×C₁₃	1	4	yes	—
369	C₄×D₄	C₂³×C₁₃	1	4	yes	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	4	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	8	no	—
379	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	#106	C₂³×C₁₃	1	4	yes	—
391	#106	C₂³×C₁₃	1	8	yes	—
392	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
393	#103	C₂³×C₁₃	1	8	yes	—
394	#103	C₂³×C₁₃	1	8	yes	—
395	#103	C₂³×C₁₃	1	4	yes	—
396	#103	C₂³×C₁₃	1	8	yes	—
397	#102	C₂³×C₁₃	1	4	yes	—
398	#102	C₂³×C₁₃	1	8	yes	—
399	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
400	C₄×C₈	C₂³×C₁₃	1	4	yes	—
401	C₂×C₁₃	—	4	4	no	—
402	C₂×C₁₃	—	4	4	no	—
403	C₂×C₁₃	#3331	1	4	yes	direct product factor
404	C₂×C₁₃	C₂×#546	1	1	yes	characteristic
405	C₂×C₁₃	C₂²×#137	1	1	yes	characteristic
406	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
407	C₂⁴	—	2	1	no	—
408	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
409	#41	—	2	16	no	—
410	#41	—	4	8	no	—
411	#41	—	4	16	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	—	8	2	no	—
420	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
421	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	4	8	no	—
427	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
428	C₂×D₄	C₁₃×#41	1	4	yes	—
429	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	8	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	8	no	—
440	C₂²×C₄	—	4	8	no	—
441	C₂²×C₄	—	4	4	no	—
442	C₂²×C₄	—	8	4	no	—
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	Q₁₆	—	4	8	no	—
450	SD₁₆	—	2	8	no	—
451	M₁₆	—	4	8	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	4	no	—
455	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
456	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
457	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
470	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
471	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
476	C₄²	—	2	4	no	—
477	C₄²	C₂×D₄×C₁₃	1	2	yes	—
478	C₄²	C₂⁴×C₁₃	1	2	yes	—
479	C₁₃	C₂×#3331	1	1	yes	characteristic, direct product factor, Sylow
480	C₂³	—	2	4	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
488	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
489	Q₈	—	2	2	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	2	2	no	—
492	Q₈	—	2	4	no	—
493	Q₈	—	4	4	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	8	4	no	—
496	D₄	—	2	4	no	—
497	D₄	—	2	8	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	16	no	—
500	D₄	C₂×C₁₃×#41	1	4	yes	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	4	16	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	8	8	no	—
519	C₂×C₄	C₁₃×#137	1	4	yes	—
520	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
521	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
524	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
525	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
527	C₈	—	2	2	no	—
528	C₈	—	2	2	no	—
529	C₈	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	8	no	—
537	C₂²	—	4	8	no	—
538	C₂²	C₁₃×#546	1	2	yes	—
539	C₂²	C₂×C₁₃×#137	1	2	yes	—
540	C₂²	C₁₃×#577	1	2	yes	—
541	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	2	no	—
549	C₄	C₁₃×#546	1	2	yes	—
550	C₄	C₂×C₁₃×#137	1	4	yes	—
551	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
552	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂	—	4	4	no	—
554	C₂	—	4	4	no	—
555	C₂	C₁₃×#3331	1	4	yes	direct product factor
556	C₂	C₂×C₁₃×#546	1	1	yes	characteristic
557	C₂	C₂²×C₁₃×#137	1	1	yes	characteristic
558	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#547	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
3. C₁₃×#3331	C₂	direct (N × H)
4. C₂×C₁₃×#487	C₂	semidirect
5. C₂×C₁₃×#483	C₂	semidirect
6. C₂×C₁₃×#476	C₂	semidirect
7. C₂×C₁₃×#470	C₂	semidirect
8. C₂×C₁₃×#462	C₂	semidirect
9. C₂×C₁₃×#452	C₂	semidirect
10. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
11. C₂×C₁₃×#436	C₂	semidirect
12. C₂×C₁₃×#417	C₂	semidirect
18. C₁₃×#554	C₂²	semidirect
35. C₁₃×#487	C₂²	semidirect
36. C₁₃×#483	C₂²	semidirect
37. C₁₃×#476	C₂²	semidirect
38. C₁₃×#470	C₂²	semidirect
39. C₁₃×#462	C₂²	semidirect
40. C₁₃×#452	C₂²	semidirect
41. C₄×C₁₃×SD₁₆	C₂²	semidirect
42. C₁₃×#436	C₂²	semidirect
46. C₁₃×#417	C₂²	semidirect
128. C₂×#3331	C₁₃	direct (N × H)
201. C₂×#554	C₂×C₁₃	semidirect
203. #3331	C₂×C₁₃	direct (N × H)
204. C₂×#487	C₂×C₁₃	semidirect
205. C₂×#483	C₂×C₁₃	semidirect
206. C₂×#476	C₂×C₁₃	semidirect
207. C₂×#470	C₂×C₁₃	semidirect
208. C₂×#462	C₂×C₁₃	semidirect
209. C₂×#452	C₂×C₁₃	semidirect
210. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
211. C₂×#436	C₂×C₁₃	semidirect
212. C₂×#417	C₂×C₁₃	semidirect
268. #554	C₂²×C₁₃	semidirect
285. #487	C₂²×C₁₃	semidirect
286. #483	C₂²×C₁₃	semidirect
287. #476	C₂²×C₁₃	semidirect
288. #470	C₂²×C₁₃	semidirect
289. #462	C₂²×C₁₃	semidirect
290. #452	C₂²×C₁₃	semidirect
291. C₄×SD₁₆	C₂²×C₁₃	semidirect
292. #436	C₂²×C₁₃	semidirect
296. #417	C₂²×C₁₃	semidirect
403. C₂×C₁₃	#3331	direct (N × H)
479. C₁₃	C₂×#3331	direct (N × H)
555. C₂	C₁₃×#3331	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
C₂×C₁₃×#547	2
C₁₃×#3331	2
C₂×C₁₃×#487	2
C₂×C₁₃×#483	2
C₂×C₁₃×#476	2
C₂×C₁₃×#470	2
C₂×C₁₃×#462	2
C₂×C₁₃×#452	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₁₃×#436	2
C₂×C₁₃×#417	2
C₂×#3331	13

Subgroups — C2×C13×#3331 #15747490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3331 #15747490