Subgroups — C₂×D₄×C₁₃×D₈ #15747378

Order 3328.

3710 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
2	C₂×D₄²×C₁₃	C₂	1	2	yes	maximal, complemented
3	D₄×C₁₃×D₈	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#447	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	—	2	2	no	—
11	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
12	C₂²×C₁₃×D₈	—	2	16	no	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×D₈	C₂²	1	2	yes	complemented
17	C₂²×C₁₃×D₈	C₂²	1	16	yes	complemented
18	C₂³×C₈×C₁₃	C₂²	1	2	yes	complemented
19	D₄²×C₁₃	—	2	8	no	—
20	D₄²×C₁₃	C₂²	1	16	yes	complemented
21	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#121	—	2	2	no	—
23	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#120	—	2	4	no	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
27	C₁₃×#493	C₂²	1	8	yes	complemented
28	C₁₃×#466	C₂²	1	16	yes	complemented
29	C₁₃×#459	C₂²	1	16	yes	complemented
30	C₁₃×#447	C₂²	1	32	yes	complemented
31	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
32	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
36	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₂⁵×C₁₃	—	2	4	no	—
40	C₂²×D₄×C₁₃	—	2	16	no	—
41	C₂²×D₄×C₁₃	—	2	4	no	—
42	C₂²×D₄×C₁₃	—	2	16	no	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	2	8	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	4	8	no	—
48	C₂²×D₄×C₁₃	—	4	16	no	—
49	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂×C₁₃×D₈	—	2	16	no	—
56	C₂×C₁₃×D₈	—	2	64	no	—
57	C₂×C₁₃×D₈	—	2	8	no	—
58	C₂×C₁₃×D₈	—	4	4	no	—
59	C₂×C₁₃×D₈	D₄	1	8	yes	direct product factor
60	C₂×C₁₃×D₈	C₂³	1	4	yes	—
61	C₂×C₁₃×D₈	C₂³	1	16	yes	complemented
62	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
63	C₂×C₁₃×D₈	C₂³	1	8	yes	complemented
64	C₂²×C₈×C₁₃	—	2	8	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	8	yes	complemented
69	C₁₃×#127	—	2	4	no	—
70	C₁₃×#127	C₂³	1	8	yes	complemented
71	C₁₃×#121	—	2	8	no	—
72	C₁₃×#121	—	2	16	no	—
73	C₁₃×#121	C₂³	1	16	yes	complemented
74	C₁₃×#120	—	2	32	no	—
75	C₄×D₄×C₁₃	—	2	4	no	—
76	C₄×D₄×C₁₃	D₄	1	4	yes	—
77	C₄×D₄×C₁₃	C₂³	1	4	yes	—
78	C₄×D₄×C₁₃	C₂³	1	8	yes	complemented
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₁₃×#107	C₂³	1	4	yes	complemented
86	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
87	C₁₃×#102	C₂³	1	8	yes	complemented
88	C₁₃×#102	C₂³	1	16	yes	complemented
89	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
90	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
91	C₂×D₄×D₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	16	no	—
95	C₂⁴×C₁₃	—	4	16	no	—
96	C₂⁴×C₁₃	—	4	16	no	—
97	C₂⁴×C₁₃	—	8	8	no	—
98	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
99	C₂×D₄×C₁₃	—	2	32	no	—
100	C₂×D₄×C₁₃	—	2	16	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	8	no	—
103	C₂×D₄×C₁₃	—	2	16	no	—
104	C₂×D₄×C₁₃	—	2	4	no	—
105	C₂×D₄×C₁₃	—	2	8	no	—
106	C₂×D₄×C₁₃	—	2	8	no	—
107	C₂×D₄×C₁₃	—	2	4	no	—
108	C₂×D₄×C₁₃	—	2	8	no	—
109	C₂×D₄×C₁₃	—	4	16	no	—
110	C₂×D₄×C₁₃	—	4	32	no	—
111	C₂×D₄×C₁₃	—	4	16	no	—
112	C₂×D₄×C₁₃	—	4	16	no	—
113	C₂×D₄×C₁₃	—	4	64	no	—
114	C₂×D₄×C₁₃	—	4	8	no	—
115	C₂×D₄×C₁₃	—	8	4	no	—
116	C₂×D₄×C₁₃	D₈	1	8	yes	direct product factor
117	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
118	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	complemented
119	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
120	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₃	—	2	4	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	4	8	no	—
126	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₁₃×D₈	—	2	32	no	—
133	C₁₃×D₈	—	2	16	no	—
134	C₁₃×D₈	—	4	8	no	—
135	C₁₃×D₈	C₂×D₄	1	16	yes	direct product factor
136	C₂×C₈×C₁₃	—	2	4	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	16	no	—
139	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
140	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
142	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
143	C₁₃×C₄⋊C₄	—	2	2	no	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
145	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
146	C₁₃×C₂²⋊C₄	—	2	8	no	—
147	C₁₃×C₂²⋊C₄	—	2	16	no	—
148	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
149	C₄²×C₁₃	C₂×D₄	1	2	yes	—
150	C₄²×C₁₃	C₂⁴	1	2	yes	—
151	C₂³×D₈	C₂×C₁₃	1	2	yes	complemented
152	C₂×D₄²	C₂×C₁₃	1	2	yes	complemented
153	D₄×D₈	C₂×C₁₃	1	16	yes	direct product factor
154	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
155	C₂×#466	C₂×C₁₃	1	2	yes	complemented
156	C₂×#459	C₂×C₁₃	1	2	yes	complemented
157	C₂×#447	C₂×C₁₃	1	4	yes	complemented
158	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
160	C₂³×C₁₃	—	2	4	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	—	2	8	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	—	2	8	no	—
165	C₂³×C₁₃	—	4	32	no	—
166	C₂³×C₁₃	—	4	4	no	—
167	C₂³×C₁₃	—	4	4	no	—
168	C₂³×C₁₃	—	4	8	no	—
169	C₂³×C₁₃	—	4	8	no	—
170	C₂³×C₁₃	—	4	32	no	—
171	C₂³×C₁₃	—	4	8	no	—
172	C₂³×C₁₃	—	8	16	no	—
173	C₂³×C₁₃	—	8	64	no	—
174	C₂³×C₁₃	C₂×D₈	1	8	yes	complemented
175	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
176	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
177	D₄×C₁₃	—	2	8	no	—
178	D₄×C₁₃	—	2	8	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	8	no	—
181	D₄×C₁₃	—	4	32	no	—
182	D₄×C₁₃	—	4	32	no	—
183	D₄×C₁₃	—	4	8	no	—
184	D₄×C₁₃	—	4	16	no	—
185	D₄×C₁₃	—	8	8	no	—
186	D₄×C₁₃	C₂×D₈	1	16	yes	direct product factor
187	D₄×C₁₃	C₂²×D₄	1	8	yes	complemented
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	—	4	16	no	—
196	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	complemented
197	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₈×C₁₃	—	2	4	no	—
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	C₂²×D₄	1	4	yes	complemented
207	C₂³×D₄	—	2	2	no	—
208	C₂³×D₄	C₂²×C₁₃	1	4	yes	complemented
209	C₂²×D₈	—	2	16	no	—
210	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
212	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
213	C₂²×D₈	C₂²×C₁₃	1	2	yes	complemented
214	C₂²×D₈	C₂²×C₁₃	1	16	yes	complemented
215	C₂³×C₈	C₂²×C₁₃	1	2	yes	complemented
216	D₄²	—	2	8	no	—
217	D₄²	C₂²×C₁₃	1	16	yes	complemented
218	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
219	C₂×#121	—	2	2	no	—
220	C₂×#121	C₂²×C₁₃	1	4	yes	complemented
221	C₂×#120	—	2	4	no	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
224	#493	C₂²×C₁₃	1	8	yes	complemented
225	#466	C₂²×C₁₃	1	16	yes	complemented
226	#459	C₂²×C₁₃	1	16	yes	complemented
227	#447	C₂²×C₁₃	1	32	yes	complemented
228	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
229	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
230	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
232	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
233	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
235	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	2	16	no	—
238	C₂²×C₁₃	—	2	4	no	—
239	C₂²×C₁₃	—	2	8	no	—
240	C₂²×C₁₃	—	4	16	no	—
241	C₂²×C₁₃	—	4	4	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	4	8	no	—
244	C₂²×C₁₃	—	4	8	no	—
245	C₂²×C₁₃	—	4	8	no	—
246	C₂²×C₁₃	—	8	64	no	—
247	C₂²×C₁₃	—	8	16	no	—
248	C₂²×C₁₃	D₄²	1	2	yes	—
249	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
250	C₂²×C₁₃	C₂²×D₈	1	8	yes	complemented
251	C₂²×C₁₃	#576	1	2	yes	—
252	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
253	C₄×C₁₃	—	2	4	no	—
254	C₄×C₁₃	—	2	2	no	—
255	C₄×C₁₃	—	4	4	no	—
256	C₄×C₁₃	D₄²	1	2	yes	—
257	C₄×C₁₃	C₂²×D₈	1	4	yes	complemented
258	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
259	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
260	C₂⁵	—	2	4	no	—
261	C₂²×D₄	—	2	16	no	—
262	C₂²×D₄	—	2	4	no	—
263	C₂²×D₄	—	2	16	no	—
264	C₂²×D₄	—	2	4	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	8	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	4	8	no	—
269	C₂²×D₄	—	4	16	no	—
270	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
271	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
272	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	16	yes	complemented
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
276	C₂×D₈	—	2	16	no	—
277	C₂×D₈	—	2	64	no	—
278	C₂×D₈	—	2	8	no	—
279	C₂×D₈	—	4	4	no	—
280	C₂×D₈	D₄×C₁₃	1	8	yes	direct product factor
281	C₂×D₈	C₂³×C₁₃	1	4	yes	—
282	C₂×D₈	C₂³×C₁₃	1	16	yes	complemented
283	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
284	C₂×D₈	C₂³×C₁₃	1	8	yes	complemented
285	C₂²×C₈	—	2	8	no	—
286	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₃	1	8	yes	complemented
290	#127	—	2	4	no	—
291	#127	C₂³×C₁₃	1	8	yes	complemented
292	#121	—	2	8	no	—
293	#121	—	2	16	no	—
294	#121	C₂³×C₁₃	1	16	yes	complemented
295	#120	—	2	32	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	D₄×C₁₃	1	4	yes	—
298	C₄×D₄	C₂³×C₁₃	1	4	yes	—
299	C₄×D₄	C₂³×C₁₃	1	8	yes	complemented
300	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
305	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
306	#107	C₂³×C₁₃	1	4	yes	complemented
307	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
308	#102	C₂³×C₁₃	1	8	yes	complemented
309	#102	C₂³×C₁₃	1	16	yes	complemented
310	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
311	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
312	C₂×C₁₃	—	2	8	no	—
313	C₂×C₁₃	—	4	8	no	—
314	C₂×C₁₃	—	8	8	no	—
315	C₂×C₁₃	D₄×D₈	1	4	yes	direct product factor
316	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
317	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	16	no	—
322	C₂⁴	—	4	16	no	—
323	C₂⁴	—	4	16	no	—
324	C₂⁴	—	8	8	no	—
325	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
326	C₂×D₄	—	2	32	no	—
327	C₂×D₄	—	2	16	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	8	no	—
330	C₂×D₄	—	2	16	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	8	no	—
336	C₂×D₄	—	4	16	no	—
337	C₂×D₄	—	4	32	no	—
338	C₂×D₄	—	4	16	no	—
339	C₂×D₄	—	4	16	no	—
340	C₂×D₄	—	4	64	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	8	4	no	—
343	C₂×D₄	C₁₃×D₈	1	8	yes	direct product factor
344	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
345	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	complemented
346	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
347	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	4	8	no	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
356	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	D₈	—	2	32	no	—
360	D₈	—	2	16	no	—
361	D₈	—	4	8	no	—
362	D₈	C₂×D₄×C₁₃	1	16	yes	direct product factor
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	16	no	—
366	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
367	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
368	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
369	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
372	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
376	C₄²	C₂×D₄×C₁₃	1	2	yes	—
377	C₄²	C₂⁴×C₁₃	1	2	yes	—
378	C₁₃	C₂×D₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	8	no	—
384	C₂³	—	4	32	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	8	no	—
389	C₂³	—	4	32	no	—
390	C₂³	—	4	8	no	—
391	C₂³	—	8	16	no	—
392	C₂³	—	8	64	no	—
393	C₂³	C₂×C₁₃×D₈	1	8	yes	complemented
394	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
395	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
396	D₄	—	2	8	no	—
397	D₄	—	2	8	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	8	no	—
400	D₄	—	4	32	no	—
401	D₄	—	4	32	no	—
402	D₄	—	4	8	no	—
403	D₄	—	4	16	no	—
404	D₄	—	8	8	no	—
405	D₄	C₂×C₁₃×D₈	1	16	yes	direct product factor
406	D₄	C₂²×D₄×C₁₃	1	8	yes	complemented
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	complemented
416	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
421	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	2	no	—
425	C₈	C₂²×D₄×C₁₃	1	4	yes	complemented
426	C₂²	—	2	16	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	4	16	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	8	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	8	64	no	—
437	C₂²	—	8	16	no	—
438	C₂²	D₄²×C₁₃	1	2	yes	—
439	C₂²	C₂²×C₁₃×D₈	1	2	yes	—
440	C₂²	C₂²×C₁₃×D₈	1	8	yes	complemented
441	C₂²	C₁₃×#576	1	2	yes	—
442	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	4	no	—
446	C₄	D₄²×C₁₃	1	2	yes	—
447	C₄	C₂²×C₁₃×D₈	1	4	yes	complemented
448	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
449	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂	—	2	8	no	—
451	C₂	—	4	8	no	—
452	C₂	—	8	8	no	—
453	C₂	D₄×C₁₃×D₈	1	4	yes	direct product factor
454	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
455	C₂	C₂³×C₁₃×D₈	1	1	yes	characteristic
456	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×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×D₈	C₂	semidirect
2. C₂×D₄²×C₁₃	C₂	semidirect
3. D₄×C₁₃×D₈	C₂	direct (N × H)
4. C₂×C₁₃×#493	C₂	semidirect
5. C₂×C₁₃×#466	C₂	semidirect
6. C₂×C₁₃×#459	C₂	semidirect
7. C₂×C₁₃×#447	C₂	semidirect
8. C₂×C₄×C₁₃×D₈	C₂	semidirect
9. C₂×C₈×D₄×C₁₃	C₂	semidirect
11. C₂³×D₄×C₁₃	C₂²	semidirect
14. C₂²×C₁₃×D₈	C₂²	semidirect
15. C₂²×C₁₃×D₈	C₂²	semidirect
16. C₂²×C₁₃×D₈	C₂²	semidirect
17. C₂²×C₁₃×D₈	C₂²	semidirect
18. C₂³×C₈×C₁₃	C₂²	semidirect
20. D₄²×C₁₃	C₂²	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
23. C₂×C₁₃×#121	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
27. C₁₃×#493	C₂²	semidirect
28. C₁₃×#466	C₂²	semidirect
29. C₁₃×#459	C₂²	semidirect
30. C₁₃×#447	C₂²	semidirect
31. C₄×C₁₃×D₈	C₂²	semidirect
32. C₈×D₄×C₁₃	C₂²	semidirect
33. C₂×C₁₃×#107	C₂²	semidirect
34. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
35. C₂×C₁₃×#102	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
37. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
38. C₂×C₄×C₈×C₁₃	C₂²	semidirect
52. C₂²×D₄×C₁₃	C₂³	semidirect
59. C₂×C₁₃×D₈	D₄	direct (N × H)
61. C₂×C₁₃×D₈	C₂³	semidirect
62. C₂×C₁₃×D₈	C₂³	semidirect
63. C₂×C₁₃×D₈	C₂³	semidirect
68. C₂²×C₈×C₁₃	C₂³	semidirect
70. C₁₃×#127	C₂³	semidirect
73. C₁₃×#121	C₂³	semidirect
78. C₄×D₄×C₁₃	C₂³	semidirect
85. C₁₃×#107	C₂³	semidirect
86. C₁₃×C₄⋊C₈	C₂³	semidirect
87. C₁₃×#102	C₂³	semidirect
88. C₁₃×#102	C₂³	semidirect
89. C₁₃×C₂²⋊C₈	C₂³	semidirect
90. C₄×C₈×C₁₃	C₂³	semidirect
91. C₂×D₄×D₈	C₁₃	direct (N × H)
116. C₂×D₄×C₁₃	D₈	direct (N × H)
118. C₂×D₄×C₁₃	C₂×D₄	semidirect
135. C₁₃×D₈	C₂×D₄	direct (N × H)
139. C₂×C₈×C₁₃	C₂×D₄	semidirect
151. C₂³×D₈	C₂×C₁₃	semidirect
152. C₂×D₄²	C₂×C₁₃	semidirect
153. D₄×D₈	C₂×C₁₃	direct (N × H)
154. C₂×#493	C₂×C₁₃	semidirect
155. C₂×#466	C₂×C₁₃	semidirect
156. C₂×#459	C₂×C₁₃	semidirect
157. C₂×#447	C₂×C₁₃	semidirect
158. C₂×C₄×D₈	C₂×C₁₃	semidirect
159. C₂×C₈×D₄	C₂×C₁₃	semidirect
174. C₂³×C₁₃	C₂×D₈	semidirect
186. D₄×C₁₃	C₂×D₈	direct (N × H)
187. D₄×C₁₃	C₂²×D₄	semidirect
196. C₂×C₄×C₁₃	C₂×D₈	semidirect
206. C₈×C₁₃	C₂²×D₄	semidirect
208. C₂³×D₄	C₂²×C₁₃	semidirect
211. C₂²×D₈	C₂²×C₁₃	semidirect
212. C₂²×D₈	C₂²×C₁₃	semidirect
213. C₂²×D₈	C₂²×C₁₃	semidirect
214. C₂²×D₈	C₂²×C₁₃	semidirect
215. C₂³×C₈	C₂²×C₁₃	semidirect
217. D₄²	C₂²×C₁₃	semidirect
218. C₂×#127	C₂²×C₁₃	semidirect
220. C₂×#121	C₂²×C₁₃	semidirect
223. C₂×C₄×D₄	C₂²×C₁₃	semidirect
224. #493	C₂²×C₁₃	semidirect
225. #466	C₂²×C₁₃	semidirect
226. #459	C₂²×C₁₃	semidirect
227. #447	C₂²×C₁₃	semidirect
228. C₄×D₈	C₂²×C₁₃	semidirect
229. C₈×D₄	C₂²×C₁₃	semidirect
230. C₂×#107	C₂²×C₁₃	semidirect
231. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
232. C₂×#102	C₂²×C₁₃	semidirect
233. C₂×#102	C₂²×C₁₃	semidirect
234. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
235. C₂×C₄×C₈	C₂²×C₁₃	semidirect
250. C₂²×C₁₃	C₂²×D₈	semidirect
257. C₄×C₁₃	C₂²×D₈	semidirect
273. C₂²×D₄	C₂³×C₁₃	semidirect
280. C₂×D₈	D₄×C₁₃	direct (N × H)
282. C₂×D₈	C₂³×C₁₃	semidirect
283. C₂×D₈	C₂³×C₁₃	semidirect
284. C₂×D₈	C₂³×C₁₃	semidirect
289. C₂²×C₈	C₂³×C₁₃	semidirect
291. #127	C₂³×C₁₃	semidirect
294. #121	C₂³×C₁₃	semidirect
299. C₄×D₄	C₂³×C₁₃	semidirect
306. #107	C₂³×C₁₃	semidirect
307. C₄⋊C₈	C₂³×C₁₃	semidirect
308. #102	C₂³×C₁₃	semidirect
309. #102	C₂³×C₁₃	semidirect
310. C₂²⋊C₈	C₂³×C₁₃	semidirect
311. C₄×C₈	C₂³×C₁₃	semidirect
315. C₂×C₁₃	D₄×D₈	direct (N × H)
343. C₂×D₄	C₁₃×D₈	direct (N × H)
345. C₂×D₄	C₂×D₄×C₁₃	semidirect
362. D₈	C₂×D₄×C₁₃	direct (N × H)
366. C₂×C₈	C₂×D₄×C₁₃	semidirect
378. C₁₃	C₂×D₄×D₈	direct (N × H)
393. C₂³	C₂×C₁₃×D₈	semidirect
405. D₄	C₂×C₁₃×D₈	direct (N × H)
406. D₄	C₂²×D₄×C₁₃	semidirect
415. C₂×C₄	C₂×C₁₃×D₈	semidirect
425. C₈	C₂²×D₄×C₁₃	semidirect
440. C₂²	C₂²×C₁₃×D₈	semidirect
447. C₄	C₂²×C₁₃×D₈	semidirect
453. C₂	D₄×C₁₃×D₈	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₃×D₈	2
C₂×D₄²×C₁₃	2
D₄×C₁₃×D₈	2
C₂×C₁₃×#493	2
C₂×C₁₃×#466	2
C₂×C₁₃×#459	2
C₂×C₁₃×#447	2
C₂×C₄×C₁₃×D₈	2
C₂×C₈×D₄×C₁₃	2
C₂×D₄×D₈	13

Subgroups — C2×D4×C13×D8 #15747378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₁₃×D₈ #15747378