Subgroups — C₂×C₁₃×#3285 #15747384

Order 3328.

2794 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#548	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3285	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	—	2	8	no	—
16	C₂×C₁₃×#135	C₂²	1	8	yes	complemented
17	C₂²×C₁₃×Q₁₆	—	2	8	no	—
18	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
22	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
23	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
24	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#548	—	2	8	no	—
28	C₁₃×#548	C₂²	1	16	yes	complemented
29	C₂×C₁₃×#124	—	2	2	no	—
30	C₂×C₁₃×#124	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₁₃×#121	—	2	2	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₃	—	2	2	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#495	C₂²	1	8	yes	complemented
39	C₁₃×#467	C₂²	1	8	yes	complemented
40	C₁₃×#466	C₂²	1	8	yes	complemented
41	C₁₃×#464	C₂²	1	16	yes	complemented
42	C₁₃×#452	C₂²	1	16	yes	complemented
43	C₁₃×#448	C₂²	1	16	yes	complemented
44	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
45	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
46	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₁₃×#103	C₂²	1	2	yes	—
49	C₂×C₁₃×#103	C₂²	1	2	yes	—
50	C₂×C₁₃×#102	C₂²	1	2	yes	—
51	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#41	—	2	4	no	—
55	C₂×C₁₃×#41	—	2	8	no	—
56	C₂×C₁₃×#41	—	4	4	no	—
57	C₂×C₁₃×#41	C₂³	1	8	yes	—
58	C₂²×Q₈×C₁₃	—	2	2	no	—
59	C₂²×Q₈×C₁₃	—	2	4	no	—
60	C₂²×Q₈×C₁₃	—	2	8	no	—
61	C₂²×Q₈×C₁₃	—	4	4	no	—
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×Q₈×C₁₃	C₂³	1	8	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	—	2	2	no	—
70	C₂³×C₄×C₁₃	—	2	2	no	—
71	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#135	—	2	32	no	—
74	C₂×C₁₃×Q₁₆	—	2	8	no	—
75	C₂×C₁₃×Q₁₆	—	2	32	no	—
76	C₂×C₁₃×Q₁₆	—	2	4	no	—
77	C₂×C₁₃×Q₁₆	D₄	1	8	yes	complemented
78	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
79	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
80	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
81	C₂×C₁₃×SD₁₆	—	2	8	no	—
82	C₂×C₁₃×SD₁₆	—	4	4	no	—
83	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×D₈	—	2	4	no	—
86	C₂×C₁₃×D₈	C₂³	1	4	yes	—
87	C₂²×C₈×C₁₃	—	2	4	no	—
88	C₂²×C₈×C₁₃	—	2	4	no	—
89	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
93	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₁₃×#124	—	2	16	no	—
96	C₁₃×#124	—	2	4	no	—
97	C₁₃×#124	C₂³	1	8	yes	—
98	C₁₃×C₂²⋊Q₈	—	2	4	no	—
99	C₁₃×C₂²⋊Q₈	—	2	16	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
101	C₁₃×#121	—	2	16	no	—
102	C₁₃×#121	—	2	4	no	—
103	C₁₃×#121	C₂³	1	8	yes	—
104	C₄×Q₈×C₁₃	—	2	4	no	—
105	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
106	C₄×D₄×C₁₃	—	2	16	no	—
107	C₄×D₄×C₁₃	D₄	1	4	yes	—
108	C₄×D₄×C₁₃	C₂³	1	4	yes	—
109	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	—	2	2	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₁₃×#107	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#103	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
127	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
128	C₄×C₈×C₁₃	C₂³	1	4	yes	—
129	C₂×#3285	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	—	2	2	no	—
131	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₁₃×#41	—	2	16	no	—
134	C₁₃×#41	—	4	8	no	—
135	C₁₃×#41	—	4	16	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	2	8	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	4	no	—
140	C₂×Q₈×C₁₃	—	2	16	no	—
141	C₂×Q₈×C₁₃	—	2	4	no	—
142	C₂×Q₈×C₁₃	—	2	4	no	—
143	C₂×Q₈×C₁₃	—	4	8	no	—
144	C₂×Q₈×C₁₃	—	4	8	no	—
145	C₂×Q₈×C₁₃	—	4	16	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
147	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	2	8	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	2	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	4	8	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	8	no	—
165	C₂²×C₄×C₁₃	—	2	2	no	—
166	C₂²×C₄×C₁₃	—	2	2	no	—
167	C₂²×C₄×C₁₃	—	2	8	no	—
168	C₂²×C₄×C₁₃	—	4	8	no	—
169	C₂²×C₄×C₁₃	—	4	8	no	—
170	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₁₃×Q₁₆	—	2	16	no	—
180	C₁₃×Q₁₆	—	2	8	no	—
181	C₁₃×Q₁₆	C₂×D₄	1	16	yes	complemented
182	C₁₃×SD₁₆	—	2	16	no	—
183	C₁₃×SD₁₆	—	4	8	no	—
184	C₁₃×D₈	—	2	8	no	—
185	C₂×C₈×C₁₃	—	2	2	no	—
186	C₂×C₈×C₁₃	—	2	2	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	—	2	8	no	—
189	C₂×C₈×C₁₃	—	2	8	no	—
190	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
191	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
192	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
193	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
194	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
195	C₁₃×C₄⋊C₄	—	2	8	no	—
196	C₁₃×C₄⋊C₄	—	2	8	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₁₃×C₂²⋊C₄	—	2	8	no	—
201	C₁₃×C₂²⋊C₄	—	2	8	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
205	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
206	C₄²×C₁₃	—	2	8	no	—
207	C₄²×C₁₃	C₂×D₄	1	2	yes	—
208	C₄²×C₁₃	C₂⁴	1	2	yes	—
209	C₂²×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂×#548	C₂×C₁₃	1	2	yes	complemented
212	#3285	C₂×C₁₃	1	16	yes	direct product factor
213	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
215	C₂×#466	C₂×C₁₃	1	1	yes	characteristic, complemented
216	C₂×#464	C₂×C₁₃	1	2	yes	complemented
217	C₂×#452	C₂×C₁₃	1	2	yes	complemented
218	C₂×#448	C₂×C₁₃	1	2	yes	complemented
219	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
220	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂³×C₁₃	—	2	2	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	2	2	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	4	4	no	—
228	C₂³×C₁₃	—	4	4	no	—
229	C₂³×C₁₃	—	4	4	no	—
230	C₂³×C₁₃	#135	1	4	yes	complemented
231	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
232	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	8	no	—
235	Q₈×C₁₃	—	2	4	no	—
236	Q₈×C₁₃	—	2	4	no	—
237	Q₈×C₁₃	—	2	4	no	—
238	Q₈×C₁₃	—	4	16	no	—
239	Q₈×C₁₃	—	4	4	no	—
240	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
241	D₄×C₁₃	—	2	8	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	4	no	—
244	D₄×C₁₃	—	4	16	no	—
245	D₄×C₁₃	—	4	16	no	—
246	D₄×C₁₃	—	4	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	8	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	4	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	4	16	no	—
262	C₂×C₄×C₁₃	—	4	16	no	—
263	C₂×C₄×C₁₃	—	4	4	no	—
264	C₂×C₄×C₁₃	—	4	4	no	—
265	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
272	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
273	C₈×C₁₃	—	2	2	no	—
274	C₈×C₁₃	—	2	2	no	—
275	C₈×C₁₃	—	2	2	no	—
276	C₈×C₁₃	C₂²×D₄	1	4	yes	—
277	C₂²×#41	C₂²×C₁₃	1	2	yes	—
278	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
279	C₂×#135	—	2	8	no	—
280	C₂×#135	C₂²×C₁₃	1	8	yes	complemented
281	C₂²×Q₁₆	—	2	8	no	—
282	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
283	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
284	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
285	C₂²×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
286	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
287	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
288	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
291	#548	—	2	8	no	—
292	#548	C₂²×C₁₃	1	16	yes	complemented
293	C₂×#124	—	2	2	no	—
294	C₂×#124	C₂²×C₁₃	1	2	yes	—
295	C₂×C₂²⋊Q₈	—	2	2	no	—
296	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
297	C₂×#121	—	2	2	no	—
298	C₂×#121	C₂²×C₁₃	1	2	yes	—
299	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
300	C₂×C₄×D₄	—	2	2	no	—
301	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
302	#495	C₂²×C₁₃	1	8	yes	complemented
303	#467	C₂²×C₁₃	1	8	yes	complemented
304	#466	C₂²×C₁₃	1	8	yes	complemented
305	#464	C₂²×C₁₃	1	16	yes	complemented
306	#452	C₂²×C₁₃	1	16	yes	complemented
307	#448	C₂²×C₁₃	1	16	yes	complemented
308	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
309	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
310	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#103	C₂²×C₁₃	1	2	yes	—
313	C₂×#103	C₂²×C₁₃	1	2	yes	—
314	C₂×#102	C₂²×C₁₃	1	2	yes	—
315	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	8	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	2	no	—
323	C₂²×C₁₃	—	2	2	no	—
324	C₂²×C₁₃	—	4	4	no	—
325	C₂²×C₁₃	—	4	4	no	—
326	C₂²×C₁₃	—	4	4	no	—
327	C₂²×C₁₃	—	4	4	no	—
328	C₂²×C₁₃	—	8	8	no	—
329	C₂²×C₁₃	D₄²	1	2	yes	—
330	C₂²×C₁₃	C₂×#135	1	2	yes	—
331	C₂²×C₁₃	C₂×#135	1	4	yes	complemented
332	C₂²×C₁₃	#578	1	2	yes	—
333	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	8	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	4	no	—
340	C₄×C₁₃	—	4	4	no	—
341	C₄×C₁₃	D₄²	1	2	yes	—
342	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×#41	—	2	4	no	—
345	C₂×#41	—	2	8	no	—
346	C₂×#41	—	4	4	no	—
347	C₂×#41	C₂³×C₁₃	1	8	yes	—
348	C₂²×Q₈	—	2	2	no	—
349	C₂²×Q₈	—	2	4	no	—
350	C₂²×Q₈	—	2	8	no	—
351	C₂²×Q₈	—	4	4	no	—
352	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
353	C₂²×Q₈	C₂³×C₁₃	1	8	yes	—
354	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
359	C₂³×C₄	—	2	2	no	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
363	#135	—	2	32	no	—
364	C₂×Q₁₆	—	2	8	no	—
365	C₂×Q₁₆	—	2	32	no	—
366	C₂×Q₁₆	—	2	4	no	—
367	C₂×Q₁₆	D₄×C₁₃	1	8	yes	complemented
368	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
369	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
370	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
371	C₂×SD₁₆	—	2	8	no	—
372	C₂×SD₁₆	—	4	4	no	—
373	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
374	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
375	C₂×D₈	—	2	4	no	—
376	C₂×D₈	C₂³×C₁₃	1	4	yes	—
377	C₂²×C₈	—	2	4	no	—
378	C₂²×C₈	—	2	4	no	—
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
382	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
383	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
385	#124	—	2	16	no	—
386	#124	—	2	4	no	—
387	#124	C₂³×C₁₃	1	8	yes	—
388	C₂²⋊Q₈	—	2	4	no	—
389	C₂²⋊Q₈	—	2	16	no	—
390	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
391	#121	—	2	16	no	—
392	#121	—	2	4	no	—
393	#121	C₂³×C₁₃	1	8	yes	—
394	C₄×Q₈	—	2	4	no	—
395	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
396	C₄×D₄	—	2	16	no	—
397	C₄×D₄	D₄×C₁₃	1	4	yes	—
398	C₄×D₄	C₂³×C₁₃	1	4	yes	—
399	C₂×C₄⋊C₄	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	2	no	—
401	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	—	2	2	no	—
405	C₂×C₂²⋊C₄	—	2	2	no	—
406	C₂×C₂²⋊C₄	—	2	2	no	—
407	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
411	#107	C₂³×C₁₃	1	4	yes	—
412	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
413	#103	C₂³×C₁₃	1	8	yes	—
414	#103	C₂³×C₁₃	1	8	yes	—
415	#102	C₂³×C₁₃	1	8	yes	—
416	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
417	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
418	C₄×C₈	C₂³×C₁₃	1	4	yes	—
419	C₂×C₁₃	—	2	4	no	—
420	C₂×C₁₃	—	4	2	no	—
421	C₂×C₁₃	—	8	4	no	—
422	C₂×C₁₃	#3285	1	4	yes	direct product factor
423	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
424	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
425	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
426	C₂⁴	—	2	2	no	—
427	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
429	#41	—	2	16	no	—
430	#41	—	4	8	no	—
431	#41	—	4	16	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	8	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	4	no	—
436	C₂×Q₈	—	2	16	no	—
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	4	8	no	—
440	C₂×Q₈	—	4	8	no	—
441	C₂×Q₈	—	4	16	no	—
442	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
443	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
444	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	8	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	4	8	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
454	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	8	no	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	—	4	8	no	—
465	C₂²×C₄	—	4	8	no	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
475	Q₁₆	—	2	16	no	—
476	Q₁₆	—	2	8	no	—
477	Q₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
478	SD₁₆	—	2	16	no	—
479	SD₁₆	—	4	8	no	—
480	D₈	—	2	8	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	8	no	—
485	C₂×C₈	—	2	8	no	—
486	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
487	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
488	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
489	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
490	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
491	C₄⋊C₄	—	2	8	no	—
492	C₄⋊C₄	—	2	8	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
496	C₂²⋊C₄	—	2	8	no	—
497	C₂²⋊C₄	—	2	8	no	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
501	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
502	C₄²	—	2	8	no	—
503	C₄²	C₂×D₄×C₁₃	1	2	yes	—
504	C₄²	C₂⁴×C₁₃	1	2	yes	—
505	C₁₃	C₂×#3285	1	1	yes	characteristic, direct product factor, Sylow
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	4	no	—
514	C₂³	—	4	4	no	—
515	C₂³	C₁₃×#135	1	4	yes	complemented
516	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
517	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
518	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
519	Q₈	—	2	8	no	—
520	Q₈	—	2	4	no	—
521	Q₈	—	2	4	no	—
522	Q₈	—	2	4	no	—
523	Q₈	—	4	16	no	—
524	Q₈	—	4	4	no	—
525	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
526	D₄	—	2	8	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	4	no	—
529	D₄	—	4	16	no	—
530	D₄	—	4	16	no	—
531	D₄	—	4	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	4	16	no	—
547	C₂×C₄	—	4	16	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
556	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
557	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₈	—	2	2	no	—
561	C₈	C₂²×D₄×C₁₃	1	4	yes	—
562	C₂²	—	2	8	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	8	8	no	—
573	C₂²	D₄²×C₁₃	1	2	yes	—
574	C₂²	C₂×C₁₃×#135	1	2	yes	—
575	C₂²	C₂×C₁₃×#135	1	4	yes	complemented
576	C₂²	C₁₃×#578	1	2	yes	—
577	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	4	no	—
585	C₄	D₄²×C₁₃	1	2	yes	—
586	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
587	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂	—	2	4	no	—
589	C₂	—	4	2	no	—
590	C₂	—	8	4	no	—
591	C₂	C₁₃×#3285	1	4	yes	direct product factor
592	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
593	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
594	C₂	C₂×C₁₃×#578	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#135	C₂	semidirect
2. C₂³×C₁₃×Q₁₆	C₂	semidirect
3. C₂×C₁₃×#548	C₂	semidirect
4. C₁₃×#3285	C₂	direct (N × H)
5. C₂×C₁₃×#495	C₂	semidirect
6. C₂×C₁₃×#467	C₂	semidirect
7. C₂×C₁₃×#466	C₂	semidirect
8. C₂×C₁₃×#464	C₂	semidirect
9. C₂×C₁₃×#452	C₂	semidirect
10. C₂×C₁₃×#448	C₂	semidirect
11. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
12. C₂×C₈×D₄×C₁₃	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
21. C₂²×C₁₃×Q₁₆	C₂²	semidirect
28. C₁₃×#548	C₂²	semidirect
38. C₁₃×#495	C₂²	semidirect
39. C₁₃×#467	C₂²	semidirect
40. C₁₃×#466	C₂²	semidirect
41. C₁₃×#464	C₂²	semidirect
42. C₁₃×#452	C₂²	semidirect
43. C₁₃×#448	C₂²	semidirect
44. C₄×C₁₃×Q₁₆	C₂²	semidirect
45. C₈×D₄×C₁₃	C₂²	semidirect
77. C₂×C₁₃×Q₁₆	D₄	semidirect
129. C₂×#3285	C₁₃	direct (N × H)
181. C₁₃×Q₁₆	C₂×D₄	semidirect
209. C₂²×#135	C₂×C₁₃	semidirect
210. C₂³×Q₁₆	C₂×C₁₃	semidirect
211. C₂×#548	C₂×C₁₃	semidirect
212. #3285	C₂×C₁₃	direct (N × H)
213. C₂×#495	C₂×C₁₃	semidirect
214. C₂×#467	C₂×C₁₃	semidirect
215. C₂×#466	C₂×C₁₃	semidirect
216. C₂×#464	C₂×C₁₃	semidirect
217. C₂×#452	C₂×C₁₃	semidirect
218. C₂×#448	C₂×C₁₃	semidirect
219. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
220. C₂×C₈×D₄	C₂×C₁₃	semidirect
230. C₂³×C₁₃	#135	semidirect
280. C₂×#135	C₂²×C₁₃	semidirect
285. C₂²×Q₁₆	C₂²×C₁₃	semidirect
292. #548	C₂²×C₁₃	semidirect
302. #495	C₂²×C₁₃	semidirect
303. #467	C₂²×C₁₃	semidirect
304. #466	C₂²×C₁₃	semidirect
305. #464	C₂²×C₁₃	semidirect
306. #452	C₂²×C₁₃	semidirect
307. #448	C₂²×C₁₃	semidirect
308. C₄×Q₁₆	C₂²×C₁₃	semidirect
309. C₈×D₄	C₂²×C₁₃	semidirect
331. C₂²×C₁₃	C₂×#135	semidirect
367. C₂×Q₁₆	D₄×C₁₃	semidirect
422. C₂×C₁₃	#3285	direct (N × H)
477. Q₁₆	C₂×D₄×C₁₃	semidirect
505. C₁₃	C₂×#3285	direct (N × H)
515. C₂³	C₁₃×#135	semidirect
575. C₂²	C₂×C₁₃×#135	semidirect
591. C₂	C₁₃×#3285	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×#135	2
C₂³×C₁₃×Q₁₆	2
C₂×C₁₃×#548	2
C₁₃×#3285	2
C₂×C₁₃×#495	2
C₂×C₁₃×#467	2
C₂×C₁₃×#466	2
C₂×C₁₃×#464	2
C₂×C₁₃×#452	2
C₂×C₁₃×#448	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂×#3285	13

Subgroups — C2×C13×#3285 #15747384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3285 #15747384