Subgroups — C₂×C₁₃×#3284 #15747383

Order 3328.

2858 conjugacy classes of subgroups.

The subgroup lattice has 620 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	2	yes	maximal, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3284	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#449	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×SD₁₆	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	C₂²×C₁₃×#41	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	—	2	16	no	—
16	C₂×C₁₃×#135	C₂²	1	16	yes	complemented
17	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
20	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
22	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#550	—	2	4	no	—
24	C₁₃×#550	C₂²	1	8	yes	complemented
25	C₁₃×#547	—	2	4	no	—
26	C₁₃×#547	C₂²	1	8	yes	complemented
27	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#127	—	2	1	no	—
29	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#123	—	2	2	no	—
31	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	—	2	1	no	—
33	C₂×C₁₃×#121	—	2	2	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₁₃	—	2	1	no	—
37	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
40	C₁₃×#492	C₂²	1	8	yes	complemented
41	C₁₃×#465	C₂²	1	16	yes	complemented
42	C₁₃×#462	C₂²	1	8	yes	complemented
43	C₁₃×#459	C₂²	1	8	yes	complemented
44	C₁₃×#452	C₂²	1	16	yes	complemented
45	C₁₃×#449	C₂²	1	16	yes	complemented
46	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
47	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#103	C₂²	1	2	yes	—
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	2	yes	—
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
55	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#41	—	2	4	no	—
57	C₂×C₁₃×#41	—	2	4	no	—
58	C₂×C₁₃×#41	—	2	8	no	—
59	C₂×C₁₃×#41	—	2	8	no	—
60	C₂×C₁₃×#41	—	4	4	no	—
61	C₂×C₁₃×#41	—	4	4	no	—
62	C₂×C₁₃×#41	C₂³	1	8	yes	—
63	C₂×C₁₃×#41	C₂³	1	8	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	—	2	2	no	—
69	C₂²×D₄×C₁₃	—	2	1	no	—
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₃	—	2	1	no	—
75	C₂³×C₄×C₁₃	—	2	2	no	—
76	C₂³×C₄×C₁₃	—	2	2	no	—
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₁₃×#135	—	2	64	no	—
79	C₂×C₁₃×Q₁₆	—	2	8	no	—
80	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×SD₁₆	—	2	8	no	—
82	C₂×C₁₃×SD₁₆	—	4	4	no	—
83	C₂×C₁₃×SD₁₆	D₄	1	8	yes	complemented
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
86	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×D₈	—	2	8	no	—
88	C₂×C₁₃×D₈	C₂³	1	8	yes	—
89	C₂²×C₈×C₁₃	—	2	8	no	—
90	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
92	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
93	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
94	C₁₃×C₄⋊Q₈	—	2	2	no	—
95	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
96	C₁₃×#127	—	2	8	no	—
97	C₁₃×#127	—	2	2	no	—
98	C₁₃×#127	C₂³	1	4	yes	—
99	C₁₃×#123	—	2	16	no	—
100	C₁₃×C₂²⋊Q₈	—	2	4	no	—
101	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#121	—	2	4	no	—
104	C₁₃×#121	—	2	16	no	—
105	C₁₃×#121	C₂³	1	8	yes	—
106	C₄×Q₈×C₁₃	—	2	2	no	—
107	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
108	C₄×D₄×C₁₃	—	2	8	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	D₄	1	4	yes	—
111	C₄×D₄×C₁₃	C₂³	1	4	yes	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
114	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
118	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
125	C₂×C₄²×C₁₃	—	2	1	no	—
126	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
127	C₁₃×#106	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
129	C₁₃×#103	C₂³	1	4	yes	—
130	C₁₃×#103	C₂³	1	8	yes	—
131	C₁₃×#102	C₂³	1	4	yes	—
132	C₁₃×#102	C₂³	1	8	yes	—
133	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
134	C₄×C₈×C₁₃	C₂³	1	4	yes	—
135	C₂×#3284	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁴×C₁₃	—	2	1	no	—
137	C₂⁴×C₁₃	—	2	2	no	—
138	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
139	C₁₃×#41	—	2	16	no	—
140	C₁₃×#41	—	2	16	no	—
141	C₁₃×#41	—	4	8	no	—
142	C₁₃×#41	—	4	8	no	—
143	C₁₃×#41	—	4	16	no	—
144	C₁₃×#41	—	4	16	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	—	2	2	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	4	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
151	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
152	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
153	C₂×D₄×C₁₃	—	2	8	no	—
154	C₂×D₄×C₁₃	—	2	8	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	2	4	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	4	no	—
159	C₂×D₄×C₁₃	—	2	4	no	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	4	8	no	—
165	C₂×D₄×C₁₃	—	4	8	no	—
166	C₂×D₄×C₁₃	—	4	4	no	—
167	C₂×D₄×C₁₃	—	8	2	no	—
168	C₂×D₄×C₁₃	—	8	4	no	—
169	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
170	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
171	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
172	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	1	no	—
177	C₂²×C₄×C₁₃	—	2	1	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	8	no	—
181	C₂²×C₄×C₁₃	—	2	8	no	—
182	C₂²×C₄×C₁₃	—	4	8	no	—
183	C₂²×C₄×C₁₃	—	4	8	no	—
184	C₂²×C₄×C₁₃	—	4	4	no	—
185	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×Q₁₆	—	2	16	no	—
192	C₁₃×SD₁₆	—	2	16	no	—
193	C₁₃×SD₁₆	—	4	8	no	—
194	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
195	C₁₃×D₈	—	2	16	no	—
196	C₂×C₈×C₁₃	—	2	4	no	—
197	C₂×C₈×C₁₃	—	2	2	no	—
198	C₂×C₈×C₁₃	—	2	16	no	—
199	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
200	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
201	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
202	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	8	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	4	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
212	C₁₃×C₂²⋊C₄	—	2	8	no	—
213	C₁₃×C₂²⋊C₄	—	2	8	no	—
214	C₁₃×C₂²⋊C₄	—	2	4	no	—
215	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	C₂×D₄	1	2	yes	—
218	C₄²×C₁₃	C₂⁴	1	2	yes	—
219	C₂²×#135	C₂×C₁₃	1	2	yes	complemented
220	C₂×#550	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×#547	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#3284	C₂×C₁₃	1	16	yes	direct product factor
223	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#465	C₂×C₁₃	1	2	yes	complemented
225	C₂×#462	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
227	C₂×#452	C₂×C₁₃	1	2	yes	complemented
228	C₂×#449	C₂×C₁₃	1	2	yes	complemented
229	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	2	4	no	—
234	C₂³×C₁₃	—	2	4	no	—
235	C₂³×C₁₃	—	2	2	no	—
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	—	4	2	no	—
238	C₂³×C₁₃	—	4	2	no	—
239	C₂³×C₁₃	—	4	4	no	—
240	C₂³×C₁₃	—	4	4	no	—
241	C₂³×C₁₃	—	4	4	no	—
242	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
243	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₁₃	—	2	4	no	—
245	Q₈×C₁₃	—	2	2	no	—
246	Q₈×C₁₃	—	2	4	no	—
247	Q₈×C₁₃	—	2	4	no	—
248	Q₈×C₁₃	—	4	4	no	—
249	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
250	D₄×C₁₃	—	2	4	no	—
251	D₄×C₁₃	—	2	8	no	—
252	D₄×C₁₃	—	2	4	no	—
253	D₄×C₁₃	—	2	2	no	—
254	D₄×C₁₃	—	2	4	no	—
255	D₄×C₁₃	—	4	16	no	—
256	D₄×C₁₃	—	4	16	no	—
257	D₄×C₁₃	—	4	4	no	—
258	D₄×C₁₃	—	4	8	no	—
259	D₄×C₁₃	—	8	4	no	—
260	D₄×C₁₃	—	8	8	no	—
261	D₄×C₁₃	C₂²×D₄	1	4	yes	—
262	C₂×C₄×C₁₃	—	2	4	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	8	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	4	16	no	—
273	C₂×C₄×C₁₃	—	4	16	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	8	no	—
278	C₂×C₄×C₁₃	#135	1	4	yes	complemented
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
285	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
286	C₈×C₁₃	—	2	4	no	—
287	C₈×C₁₃	—	2	2	no	—
288	C₈×C₁₃	C₂²×D₄	1	4	yes	—
289	C₂²×#41	C₂²×C₁₃	1	2	yes	—
290	C₂²×#41	C₂²×C₁₃	1	2	yes	—
291	C₂×#135	—	2	16	no	—
292	C₂×#135	C₂²×C₁₃	1	16	yes	complemented
293	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
294	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
295	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
296	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
298	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
299	#550	—	2	4	no	—
300	#550	C₂²×C₁₃	1	8	yes	complemented
301	#547	—	2	4	no	—
302	#547	C₂²×C₁₃	1	8	yes	complemented
303	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#127	—	2	1	no	—
305	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#123	—	2	2	no	—
307	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
308	C₂×#121	—	2	1	no	—
309	C₂×#121	—	2	2	no	—
310	C₂×#121	C₂²×C₁₃	1	2	yes	—
311	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×C₄×D₄	—	2	1	no	—
313	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
315	C₂²×C₄⋊C₄	—	2	1	no	—
316	#492	C₂²×C₁₃	1	8	yes	complemented
317	#465	C₂²×C₁₃	1	16	yes	complemented
318	#462	C₂²×C₁₃	1	8	yes	complemented
319	#459	C₂²×C₁₃	1	8	yes	complemented
320	#452	C₂²×C₁₃	1	16	yes	complemented
321	#449	C₂²×C₁₃	1	16	yes	complemented
322	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
323	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
324	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#103	C₂²×C₁₃	1	2	yes	—
328	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#102	C₂²×C₁₃	1	2	yes	—
330	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
331	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂²×C₁₃	—	2	4	no	—
333	C₂²×C₁₃	—	2	4	no	—
334	C₂²×C₁₃	—	2	4	no	—
335	C₂²×C₁₃	—	2	4	no	—
336	C₂²×C₁₃	—	4	8	no	—
337	C₂²×C₁₃	—	4	8	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	—	4	2	no	—
340	C₂²×C₁₃	—	4	4	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	4	no	—
343	C₂²×C₁₃	—	8	8	no	—
344	C₂²×C₁₃	D₄²	1	2	yes	—
345	C₂²×C₁₃	C₂×#135	1	2	yes	—
346	C₂²×C₁₃	#577	1	2	yes	—
347	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
348	C₄×C₁₃	—	2	4	no	—
349	C₄×C₁₃	—	2	4	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	4	4	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	2	no	—
354	C₄×C₁₃	D₄²	1	2	yes	—
355	C₄×C₁₃	C₂×#135	1	4	yes	complemented
356	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂×#41	—	2	4	no	—
359	C₂×#41	—	2	4	no	—
360	C₂×#41	—	2	8	no	—
361	C₂×#41	—	2	8	no	—
362	C₂×#41	—	4	4	no	—
363	C₂×#41	—	4	4	no	—
364	C₂×#41	C₂³×C₁₃	1	8	yes	—
365	C₂×#41	C₂³×C₁₃	1	8	yes	—
366	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
367	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	—	2	2	no	—
370	C₂²×D₄	—	2	2	no	—
371	C₂²×D₄	—	2	1	no	—
372	C₂²×D₄	—	2	1	no	—
373	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
375	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	—	2	2	no	—
378	C₂³×C₄	—	2	2	no	—
379	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
380	#135	—	2	64	no	—
381	C₂×Q₁₆	—	2	8	no	—
382	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
383	C₂×SD₁₆	—	2	8	no	—
384	C₂×SD₁₆	—	4	4	no	—
385	C₂×SD₁₆	D₄×C₁₃	1	8	yes	complemented
386	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
387	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
388	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
389	C₂×D₈	—	2	8	no	—
390	C₂×D₈	C₂³×C₁₃	1	8	yes	—
391	C₂²×C₈	—	2	8	no	—
392	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
393	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
394	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
396	C₄⋊Q₈	—	2	2	no	—
397	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
398	#127	—	2	8	no	—
399	#127	—	2	2	no	—
400	#127	C₂³×C₁₃	1	4	yes	—
401	#123	—	2	16	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
404	#121	—	2	8	no	—
405	#121	—	2	4	no	—
406	#121	—	2	16	no	—
407	#121	C₂³×C₁₃	1	8	yes	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
410	C₄×D₄	—	2	8	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	D₄×C₁₃	1	4	yes	—
413	C₄×D₄	C₂³×C₁₃	1	4	yes	—
414	C₄×D₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	2	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	8	no	—
420	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
429	#106	C₂³×C₁₃	1	4	yes	—
430	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
431	#103	C₂³×C₁₃	1	4	yes	—
432	#103	C₂³×C₁₃	1	8	yes	—
433	#102	C₂³×C₁₃	1	4	yes	—
434	#102	C₂³×C₁₃	1	8	yes	—
435	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
436	C₄×C₈	C₂³×C₁₃	1	4	yes	—
437	C₂×C₁₃	—	4	4	no	—
438	C₂×C₁₃	—	4	4	no	—
439	C₂×C₁₃	—	8	4	no	—
440	C₂×C₁₃	#3284	1	4	yes	direct product factor
441	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
442	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
443	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
444	C₂⁴	—	2	1	no	—
445	C₂⁴	—	2	2	no	—
446	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
447	#41	—	2	16	no	—
448	#41	—	2	16	no	—
449	#41	—	4	8	no	—
450	#41	—	4	8	no	—
451	#41	—	4	16	no	—
452	#41	—	4	16	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	4	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
459	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
460	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	8	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	4	8	no	—
473	C₂×D₄	—	4	8	no	—
474	C₂×D₄	—	4	4	no	—
475	C₂×D₄	—	8	2	no	—
476	C₂×D₄	—	8	4	no	—
477	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
478	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
479	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
480	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	8	no	—
489	C₂²×C₄	—	2	8	no	—
490	C₂²×C₄	—	4	8	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
496	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
498	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
499	Q₁₆	—	2	16	no	—
500	SD₁₆	—	2	16	no	—
501	SD₁₆	—	4	8	no	—
502	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
503	D₈	—	2	16	no	—
504	C₂×C₈	—	2	4	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	16	no	—
507	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
508	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
509	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
510	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	8	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	4	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
518	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
519	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²⋊C₄	—	2	8	no	—
521	C₂²⋊C₄	—	2	8	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
524	C₄²	—	2	4	no	—
525	C₄²	C₂×D₄×C₁₃	1	2	yes	—
526	C₄²	C₂⁴×C₁₃	1	2	yes	—
527	C₁₃	C₂×#3284	1	1	yes	characteristic, direct product factor, Sylow
528	C₂³	—	2	4	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	4	2	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	4	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
540	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
541	Q₈	—	2	4	no	—
542	Q₈	—	2	2	no	—
543	Q₈	—	2	4	no	—
544	Q₈	—	2	4	no	—
545	Q₈	—	4	4	no	—
546	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
547	D₄	—	2	4	no	—
548	D₄	—	2	8	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	4	no	—
552	D₄	—	4	16	no	—
553	D₄	—	4	16	no	—
554	D₄	—	4	4	no	—
555	D₄	—	4	8	no	—
556	D₄	—	8	4	no	—
557	D₄	—	8	8	no	—
558	D₄	C₂²×D₄×C₁₃	1	4	yes	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	8	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	4	16	no	—
570	C₂×C₄	—	4	16	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	C₁₃×#135	1	4	yes	complemented
576	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
577	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
580	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
581	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
582	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	—	2	2	no	—
585	C₈	C₂²×D₄×C₁₃	1	4	yes	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	4	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	2	4	no	—
590	C₂²	—	4	8	no	—
591	C₂²	—	4	8	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	2	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	8	8	no	—
598	C₂²	D₄²×C₁₃	1	2	yes	—
599	C₂²	C₂×C₁₃×#135	1	2	yes	—
600	C₂²	C₁₃×#577	1	2	yes	—
601	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	4	no	—
604	C₄	—	2	4	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	4	no	—
608	C₄	D₄²×C₁₃	1	2	yes	—
609	C₄	C₂×C₁₃×#135	1	4	yes	complemented
610	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
611	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂	—	4	4	no	—
613	C₂	—	4	4	no	—
614	C₂	—	8	4	no	—
615	C₂	C₁₃×#3284	1	4	yes	direct product factor
616	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
617	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
618	C₂	C₂×C₁₃×#577	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. C₂×C₁₃×#550	C₂	semidirect
3. C₂×C₁₃×#547	C₂	semidirect
4. C₁₃×#3284	C₂	direct (N × H)
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#465	C₂	semidirect
7. C₂×C₁₃×#462	C₂	semidirect
8. C₂×C₁₃×#459	C₂	semidirect
9. C₂×C₁₃×#452	C₂	semidirect
10. C₂×C₁₃×#449	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₈×D₄×C₁₃	C₂	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
26. C₁₃×#547	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#465	C₂²	semidirect
42. C₁₃×#462	C₂²	semidirect
43. C₁₃×#459	C₂²	semidirect
44. C₁₃×#452	C₂²	semidirect
45. C₁₃×#449	C₂²	semidirect
46. C₄×C₁₃×SD₁₆	C₂²	semidirect
47. C₈×D₄×C₁₃	C₂²	semidirect
83. C₂×C₁₃×SD₁₆	D₄	semidirect
135. C₂×#3284	C₁₃	direct (N × H)
194. C₁₃×SD₁₆	C₂×D₄	semidirect
219. C₂²×#135	C₂×C₁₃	semidirect
220. C₂×#550	C₂×C₁₃	semidirect
221. C₂×#547	C₂×C₁₃	semidirect
222. #3284	C₂×C₁₃	direct (N × H)
223. C₂×#492	C₂×C₁₃	semidirect
224. C₂×#465	C₂×C₁₃	semidirect
225. C₂×#462	C₂×C₁₃	semidirect
226. C₂×#459	C₂×C₁₃	semidirect
227. C₂×#452	C₂×C₁₃	semidirect
228. C₂×#449	C₂×C₁₃	semidirect
229. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
230. C₂×C₈×D₄	C₂×C₁₃	semidirect
278. C₂×C₄×C₁₃	#135	semidirect
292. C₂×#135	C₂²×C₁₃	semidirect
300. #550	C₂²×C₁₃	semidirect
302. #547	C₂²×C₁₃	semidirect
316. #492	C₂²×C₁₃	semidirect
317. #465	C₂²×C₁₃	semidirect
318. #462	C₂²×C₁₃	semidirect
319. #459	C₂²×C₁₃	semidirect
320. #452	C₂²×C₁₃	semidirect
321. #449	C₂²×C₁₃	semidirect
322. C₄×SD₁₆	C₂²×C₁₃	semidirect
323. C₈×D₄	C₂²×C₁₃	semidirect
355. C₄×C₁₃	C₂×#135	semidirect
385. C₂×SD₁₆	D₄×C₁₃	semidirect
440. C₂×C₁₃	#3284	direct (N × H)
502. SD₁₆	C₂×D₄×C₁₃	semidirect
527. C₁₃	C₂×#3284	direct (N × H)
575. C₂×C₄	C₁₃×#135	semidirect
609. C₄	C₂×C₁₃×#135	semidirect
615. C₂	C₁₃×#3284	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
C₂×C₁₃×#550	2
C₂×C₁₃×#547	2
C₁₃×#3284	2
C₂×C₁₃×#492	2
C₂×C₁₃×#465	2
C₂×C₁₃×#462	2
C₂×C₁₃×#459	2
C₂×C₁₃×#452	2
C₂×C₁₃×#449	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂×#3284	13

Subgroups — C2×C13×#3284 #15747383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3284 #15747383