Subgroups — C₂×C₁₃×#3403 #15747739

Order 3328.

2066 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#559	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3403	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#496	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#463	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
17	C₁₃×#559	—	2	8	no	—
18	C₁₃×#559	C₂²	1	16	yes	complemented
19	C₂×C₁₃×#127	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	—	2	2	no	—
21	C₂×C₁₃×#124	C₂²	1	2	yes	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#123	—	2	2	no	—
24	C₂×C₁₃×#123	—	2	2	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	—	2	2	no	—
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
30	C₁₃×#496	C₂²	1	16	yes	complemented
31	C₁₃×#495	C₂²	1	8	yes	complemented
32	C₁₃×#464	C₂²	1	16	yes	complemented
33	C₁₃×#463	C₂²	1	16	yes	complemented
34	C₁₃×#459	C₂²	1	16	yes	complemented
35	C₁₃×#446	C₂²	1	8	yes	complemented
36	C₁₃×#440	C₂²	1	16	yes	complemented
37	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
38	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	C₂²	1	2	yes	—
42	C₂×C₁₃×#102	C₂²	1	2	yes	—
43	C₂×C₁₃×#102	C₂²	1	2	yes	—
44	C₂×C₁₃×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	—	2	2	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	—	2	2	no	—
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	4	2	no	—
55	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
56	C₂×C₁₃×SD₁₆	—	2	8	no	—
57	C₂×C₁₃×SD₁₆	—	4	4	no	—
58	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
59	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
60	C₂×C₁₃×D₈	—	2	4	no	—
61	C₂×C₁₃×D₈	—	4	4	no	—
62	C₂×C₁₃×D₈	—	4	2	no	—
63	C₂×C₁₃×D₈	C₂³	1	4	yes	—
64	C₂×C₁₃×D₈	C₂³	1	4	yes	—
65	C₂×C₁₃×D₈	C₂³	1	8	yes	—
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₁₃×#127	—	2	4	no	—
70	C₁₃×#127	C₂³	1	8	yes	—
71	C₁₃×#124	—	2	16	no	—
72	C₁₃×#124	—	2	4	no	—
73	C₁₃×#124	—	2	4	no	—
74	C₁₃×#124	C₂³	1	8	yes	—
75	C₁₃×#124	C₂³	1	8	yes	—
76	C₁₃×#123	—	2	16	no	—
77	C₁₃×#123	—	2	16	no	—
78	C₄×Q₈×C₁₃	—	2	4	no	—
79	C₄×Q₈×C₁₃	D₄	1	4	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
81	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
82	C₄×D₄×C₁₃	—	2	16	no	—
83	C₄×D₄×C₁₃	—	2	4	no	—
84	C₄×D₄×C₁₃	—	2	4	no	—
85	C₄×D₄×C₁₃	C₂³	1	8	yes	—
86	C₄×D₄×C₁₃	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
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×C₁₃×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₄²×C₁₃	—	2	2	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#107	C₂³	1	4	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
103	C₁₃×#103	C₂³	1	8	yes	—
104	C₁₃×#102	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#97	C₂³	1	8	yes	—
107	C₄×C₈×C₁₃	C₂³	1	4	yes	—
108	C₂×#3403	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	4	2	no	—
115	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
116	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	8	no	—
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	—	2	4	no	—
124	C₂×D₄×C₁₃	—	2	4	no	—
125	C₂×D₄×C₁₃	—	4	8	no	—
126	C₂×D₄×C₁₃	—	8	4	no	—
127	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	8	no	—
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	8	4	no	—
134	C₂²×C₄×C₁₃	—	8	4	no	—
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₁₃×Q₁₆	—	4	4	no	—
141	C₁₃×SD₁₆	—	2	16	no	—
142	C₁₃×SD₁₆	—	4	8	no	—
143	C₁₃×D₈	—	2	8	no	—
144	C₁₃×D₈	—	4	8	no	—
145	C₁₃×D₈	—	4	4	no	—
146	C₂×C₈×C₁₃	—	2	4	no	—
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	#41	1	4	yes	—
149	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
150	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
151	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
155	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
156	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₁₃×C₂²⋊C₄	—	2	8	no	—
160	C₁₃×C₂²⋊C₄	—	2	8	no	—
161	C₁₃×C₂²⋊C₄	—	2	8	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₄²×C₁₃	—	2	8	no	—
164	C₄²×C₁₃	C₂×D₄	1	2	yes	—
165	C₄²×C₁₃	C₂×D₄	1	4	yes	—
166	C₄²×C₁₃	C₂⁴	1	2	yes	—
167	C₄²×C₁₃	C₂⁴	1	4	yes	—
168	C₂×#559	C₂×C₁₃	1	2	yes	complemented
169	#3403	C₂×C₁₃	1	16	yes	direct product factor
170	C₂×#496	C₂×C₁₃	1	2	yes	complemented
171	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂×#464	C₂×C₁₃	1	2	yes	complemented
173	C₂×#463	C₂×C₁₃	1	2	yes	complemented
174	C₂×#459	C₂×C₁₃	1	2	yes	complemented
175	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×#440	C₂×C₁₃	1	2	yes	complemented
177	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂³×C₁₃	—	2	4	no	—
179	C₂³×C₁₃	—	2	4	no	—
180	C₂³×C₁₃	—	4	4	no	—
181	C₂³×C₁₃	—	4	4	no	—
182	C₂³×C₁₃	—	4	4	no	—
183	C₂³×C₁₃	—	4	4	no	—
184	C₂³×C₁₃	—	4	4	no	—
185	C₂³×C₁₃	—	4	4	no	—
186	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₁₃	—	2	4	no	—
188	Q₈×C₁₃	—	2	4	no	—
189	Q₈×C₁₃	—	4	4	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	D₄×C₁₃	—	2	4	no	—
192	D₄×C₁₃	—	2	4	no	—
193	D₄×C₁₃	—	2	4	no	—
194	D₄×C₁₃	—	2	4	no	—
195	D₄×C₁₃	—	4	16	no	—
196	D₄×C₁₃	—	4	4	no	—
197	D₄×C₁₃	—	4	4	no	—
198	D₄×C₁₃	—	8	8	no	—
199	C₂×C₄×C₁₃	—	2	4	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	8	8	no	—
208	C₂×C₄×C₁₃	—	8	8	no	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
210	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
215	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
216	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
217	C₈×C₁₃	—	2	4	no	—
218	C₈×C₁₃	—	2	2	no	—
219	C₈×C₁₃	C₂×#41	1	4	yes	—
220	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
222	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
223	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
224	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
226	#559	—	2	8	no	—
227	#559	C₂²×C₁₃	1	16	yes	complemented
228	C₂×#127	C₂²×C₁₃	1	2	yes	—
229	C₂×#124	—	2	2	no	—
230	C₂×#124	C₂²×C₁₃	1	2	yes	—
231	C₂×#124	C₂²×C₁₃	1	2	yes	—
232	C₂×#123	—	2	2	no	—
233	C₂×#123	—	2	2	no	—
234	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
235	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄×D₄	—	2	2	no	—
237	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
239	#496	C₂²×C₁₃	1	16	yes	complemented
240	#495	C₂²×C₁₃	1	8	yes	complemented
241	#464	C₂²×C₁₃	1	16	yes	complemented
242	#463	C₂²×C₁₃	1	16	yes	complemented
243	#459	C₂²×C₁₃	1	16	yes	complemented
244	#446	C₂²×C₁₃	1	8	yes	complemented
245	#440	C₂²×C₁₃	1	16	yes	complemented
246	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
247	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#103	C₂²×C₁₃	1	2	yes	—
251	C₂×#102	C₂²×C₁₃	1	2	yes	—
252	C₂×#102	C₂²×C₁₃	1	2	yes	—
253	C₂×#97	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₁₃	—	4	4	no	—
256	C₂²×C₁₃	—	4	4	no	—
257	C₂²×C₁₃	—	4	4	no	—
258	C₂²×C₁₃	—	4	4	no	—
259	C₂²×C₁₃	—	4	4	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	—	8	8	no	—
262	C₂²×C₁₃	—	8	8	no	—
263	C₂²×C₁₃	#550	1	2	yes	—
264	C₂²×C₁₃	#575	1	2	yes	—
265	C₂²×C₁₃	#576	1	2	yes	—
266	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	4	no	—
271	C₄×C₁₃	—	4	4	no	—
272	C₄×C₁₃	—	4	4	no	—
273	C₄×C₁₃	#550	1	2	yes	—
274	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
275	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
276	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
277	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
281	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂×Q₁₆	—	4	2	no	—
285	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
286	C₂×SD₁₆	—	2	8	no	—
287	C₂×SD₁₆	—	4	4	no	—
288	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
289	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
290	C₂×D₈	—	2	4	no	—
291	C₂×D₈	—	4	4	no	—
292	C₂×D₈	—	4	2	no	—
293	C₂×D₈	C₂³×C₁₃	1	4	yes	—
294	C₂×D₈	C₂³×C₁₃	1	4	yes	—
295	C₂×D₈	C₂³×C₁₃	1	8	yes	—
296	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
299	#127	—	2	4	no	—
300	#127	C₂³×C₁₃	1	8	yes	—
301	#124	—	2	16	no	—
302	#124	—	2	4	no	—
303	#124	—	2	4	no	—
304	#124	C₂³×C₁₃	1	8	yes	—
305	#124	C₂³×C₁₃	1	8	yes	—
306	#123	—	2	16	no	—
307	#123	—	2	16	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	D₄×C₁₃	1	4	yes	—
310	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
311	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
312	C₄×D₄	—	2	16	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	C₂³×C₁₃	1	8	yes	—
316	C₄×D₄	C₂³×C₁₃	1	8	yes	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
319	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
330	#107	C₂³×C₁₃	1	4	yes	—
331	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
332	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
333	#103	C₂³×C₁₃	1	8	yes	—
334	#102	C₂³×C₁₃	1	8	yes	—
335	#102	C₂³×C₁₃	1	8	yes	—
336	#97	C₂³×C₁₃	1	8	yes	—
337	C₄×C₈	C₂³×C₁₃	1	4	yes	—
338	C₂×C₁₃	—	8	4	no	—
339	C₂×C₁₃	—	8	4	no	—
340	C₂×C₁₃	#3403	1	4	yes	direct product factor
341	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
342	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
343	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
344	C₂⁴	—	2	2	no	—
345	C₂⁴	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	4	2	no	—
350	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
351	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	8	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	4	8	no	—
361	C₂×D₄	—	8	4	no	—
362	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
363	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	8	4	no	—
369	C₂²×C₄	—	8	4	no	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
375	Q₁₆	—	4	4	no	—
376	SD₁₆	—	2	16	no	—
377	SD₁₆	—	4	8	no	—
378	D₈	—	2	8	no	—
379	D₈	—	4	8	no	—
380	D₈	—	4	4	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	C₁₃×#41	1	4	yes	—
384	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
385	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
386	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
390	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
391	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₄²	—	2	8	no	—
399	C₄²	C₂×D₄×C₁₃	1	2	yes	—
400	C₄²	C₂×D₄×C₁₃	1	4	yes	—
401	C₄²	C₂⁴×C₁₃	1	2	yes	—
402	C₄²	C₂⁴×C₁₃	1	4	yes	—
403	C₁₃	C₂×#3403	1	1	yes	characteristic, direct product factor, Sylow
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	4	no	—
411	C₂³	—	4	4	no	—
412	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	4	no	—
416	Q₈	—	4	4	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	4	16	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	4	no	—
424	D₄	—	8	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	—	8	8	no	—
435	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
439	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
441	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
442	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
443	C₈	—	2	4	no	—
444	C₈	—	2	2	no	—
445	C₈	C₂×C₁₃×#41	1	4	yes	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	8	8	no	—
453	C₂²	—	8	8	no	—
454	C₂²	C₁₃×#550	1	2	yes	—
455	C₂²	C₁₃×#575	1	2	yes	—
456	C₂²	C₁₃×#576	1	2	yes	—
457	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
458	C₄	—	2	4	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	4	no	—
464	C₄	C₁₃×#550	1	2	yes	—
465	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
466	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂	—	8	4	no	—
468	C₂	—	8	4	no	—
469	C₂	C₁₃×#3403	1	4	yes	direct product factor
470	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
471	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
472	C₂	C₂×C₁₃×#576	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×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#559	C₂	semidirect
2. C₁₃×#3403	C₂	direct (N × H)
3. C₂×C₁₃×#496	C₂	semidirect
4. C₂×C₁₃×#495	C₂	semidirect
5. C₂×C₁₃×#464	C₂	semidirect
6. C₂×C₁₃×#463	C₂	semidirect
7. C₂×C₁₃×#459	C₂	semidirect
8. C₂×C₁₃×#446	C₂	semidirect
9. C₂×C₁₃×#440	C₂	semidirect
10. C₂×C₄×C₁₃×D₈	C₂	semidirect
18. C₁₃×#559	C₂²	semidirect
30. C₁₃×#496	C₂²	semidirect
31. C₁₃×#495	C₂²	semidirect
32. C₁₃×#464	C₂²	semidirect
33. C₁₃×#463	C₂²	semidirect
34. C₁₃×#459	C₂²	semidirect
35. C₁₃×#446	C₂²	semidirect
36. C₁₃×#440	C₂²	semidirect
37. C₄×C₁₃×D₈	C₂²	semidirect
108. C₂×#3403	C₁₃	direct (N × H)
168. C₂×#559	C₂×C₁₃	semidirect
169. #3403	C₂×C₁₃	direct (N × H)
170. C₂×#496	C₂×C₁₃	semidirect
171. C₂×#495	C₂×C₁₃	semidirect
172. C₂×#464	C₂×C₁₃	semidirect
173. C₂×#463	C₂×C₁₃	semidirect
174. C₂×#459	C₂×C₁₃	semidirect
175. C₂×#446	C₂×C₁₃	semidirect
176. C₂×#440	C₂×C₁₃	semidirect
177. C₂×C₄×D₈	C₂×C₁₃	semidirect
227. #559	C₂²×C₁₃	semidirect
239. #496	C₂²×C₁₃	semidirect
240. #495	C₂²×C₁₃	semidirect
241. #464	C₂²×C₁₃	semidirect
242. #463	C₂²×C₁₃	semidirect
243. #459	C₂²×C₁₃	semidirect
244. #446	C₂²×C₁₃	semidirect
245. #440	C₂²×C₁₃	semidirect
246. C₄×D₈	C₂²×C₁₃	semidirect
340. C₂×C₁₃	#3403	direct (N × H)
403. C₁₃	C₂×#3403	direct (N × H)
469. C₂	C₁₃×#3403	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×#559	2
C₁₃×#3403	2
C₂×C₁₃×#496	2
C₂×C₁₃×#495	2
C₂×C₁₃×#464	2
C₂×C₁₃×#463	2
C₂×C₁₃×#459	2
C₂×C₁₃×#446	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×D₈	2
C₂×#3403	13

Subgroups — C2×C13×#3403 #15747739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3403 #15747739