Subgroups — C₂×D₄×Q₈×D₁₃ #16769831

Order 3328.

11798 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂×Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×Dic₂₆	C₂	1	3	yes	maximal, complemented
4	C₂×#11719432	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
6	C₂×#11719337	C₂	1	6	yes	maximal, complemented
7	D₄×Q₈×D₁₃	C₂	1	32	yes	maximal, direct product factor
8	C₂×D₁₃×C₄⋊Q₈	C₂	1	3	yes	maximal, complemented
9	C₂×D₁₃×C₂²⋊Q₈	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×D₁₃	C₂	1	3	yes	maximal
12	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
14	C₂²×Q₈×D₁₃	—	2	32	no	—
15	C₂²×Q₈×D₁₃	C₂²	1	6	yes	—
16	C₂²×Q₈×D₁₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×D₁₃	C₂²	1	6	yes	complemented
18	C₂²×Q₈×D₁₃	C₂²	1	2	yes	complemented
19	C₂²×Q₈×D₁₃	C₂²	1	32	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₁₃	C₂²	1	6	yes	—
22	C₂³×Dic₂₆	C₂²	1	6	yes	complemented
23	D₄×Q₈×C₁₃	C₂²	1	16	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
25	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	6	yes	complemented
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
28	Q₈×C₂²⋊D₁₃	C₂²	1	32	yes	complemented
29	C₂×#88200	C₂²	1	6	yes	complemented
30	C₂×Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#88198	C₂²	1	6	yes	complemented
32	C₂×D₄×Dic₁₃	C₂²	1	3	yes	—
33	C₂×C₄×C₂²⋊D₁₃	C₂²	1	6	yes	—
34	C₂×#88178	C₂²	1	6	yes	complemented
35	#11719432	C₂²	1	48	yes	complemented
36	D₁₃×C₄⋊Q₈	C₂²	1	48	yes	complemented
37	#11719337	C₂²	1	96	yes	complemented
38	D₁₃×C₂²⋊Q₈	C₂²	1	96	yes	complemented
39	Q₈×D₅₂	C₂²	1	16	yes	complemented
40	C₄×Q₈×D₁₃	C₂²	1	16	yes	complemented
41	C₄×D₄×D₁₃	C₂²	1	48	yes	—
42	D₄×Dic₂₆	C₂²	1	48	yes	complemented
43	C₂×#88151	C₂²	1	6	yes	complemented
44	C₂×#88150	C₂²	1	12	yes	complemented
45	C₂×#88147	C₂²	1	3	yes	—
46	C₂×C₄⋊C₄×D₁₃	C₂²	1	3	yes	—
47	C₂×C₄⋊C₄×D₁₃	C₂²	1	3	yes	—
48	C₂×C₄⋊C₄×D₁₃	C₂²	1	6	yes	—
49	C₂×#88142	C₂²	1	6	yes	complemented
50	C₂×#88142	C₂²	1	6	yes	complemented
51	C₂×#88141	C₂²	1	3	yes	complemented
52	C₂×#88135	C₂²	1	6	yes	—
53	C₂×C₂²⋊C₄×D₁₃	C₂²	1	6	yes	—
54	C₂×#88132	C₂²	1	12	yes	complemented
55	C₂×C₄×D₅₂	C₂²	1	3	yes	—
56	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
57	C₂×#88123	C₂²	1	3	yes	complemented
58	C₂×C₄×Dic₂₆	C₂²	1	3	yes	complemented
59	C₂⁴×D₁₃	C₂³	1	2	yes	—
60	C₂²×Q₈×C₁₃	—	2	16	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	16	yes	complemented
64	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
66	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
67	C₂³×Dic₁₃	C₂³	1	6	yes	—
68	C₂×Q₈×D₁₃	—	2	16	no	—
69	C₂×Q₈×D₁₃	—	2	256	no	—
70	C₂×Q₈×D₁₃	—	2	48	no	—
71	C₂×Q₈×D₁₃	—	2	48	no	—
72	C₂×Q₈×D₁₃	D₄	1	16	yes	direct product factor
73	C₂×Q₈×D₁₃	C₂³	1	48	yes	—
74	C₂×Q₈×D₁₃	C₂³	1	8	yes	—
75	C₂×Q₈×D₁₃	C₂³	1	48	yes	complemented
76	C₂×Q₈×D₁₃	C₂³	1	16	yes	complemented
77	C₂×D₄×D₁₃	Q₈	1	16	yes	direct product factor
78	C₂×D₄×D₁₃	C₂³	1	8	yes	—
79	C₂²×D₅₂	C₂³	1	1	yes	characteristic
80	C₂²×C₄×D₁₃	—	2	48	no	—
81	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
82	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
83	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
84	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
85	C₂²×C₄×D₁₃	C₂³	1	48	yes	—
86	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
87	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Dic₂₆	—	2	48	no	—
89	C₂²×Dic₂₆	C₂³	1	6	yes	—
90	C₂²×Dic₂₆	C₂³	1	12	yes	—
91	C₂²×Dic₂₆	C₂³	1	3	yes	—
92	C₂²×Dic₂₆	C₂³	1	48	yes	complemented
93	C₁₃×C₄⋊Q₈	C₂³	1	24	yes	complemented
94	C₁₃×C₂²⋊Q₈	C₂³	1	48	yes	complemented
95	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
96	C₄×D₄×C₁₃	C₂³	1	24	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
102	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
103	#88200	C₂³	1	48	yes	complemented
104	Q₈×Dic₁₃	C₂³	1	8	yes	complemented
105	#88198	C₂³	1	48	yes	complemented
106	D₄×Dic₁₃	C₂³	1	24	yes	—
107	C₄×C₂²⋊D₁₃	C₂³	1	48	yes	—
108	C₂×#6103	C₂³	1	6	yes	—
109	C₂×#6103	C₂³	1	6	yes	—
110	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
111	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
112	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
113	#88178	C₂³	1	48	yes	complemented
114	C₂×#6101	C₂³	1	6	yes	—
115	C₂×#6101	C₂³	1	12	yes	—
116	C₂×#6101	C₂³	1	6	yes	—
117	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
118	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
119	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
120	#88151	C₂³	1	48	yes	complemented
121	#88150	C₂³	1	96	yes	complemented
122	#88147	C₂³	1	24	yes	—
123	C₄⋊C₄×D₁₃	C₂³	1	24	yes	—
124	C₄⋊C₄×D₁₃	C₂³	1	48	yes	—
125	C₄⋊C₄×D₁₃	C₂³	1	24	yes	—
126	#88142	C₂³	1	48	yes	complemented
127	#88142	C₂³	1	48	yes	complemented
128	#88141	C₂³	1	24	yes	complemented
129	#88135	C₂³	1	48	yes	—
130	C₂²⋊C₄×D₁₃	C₂³	1	48	yes	—
131	#88132	C₂³	1	96	yes	complemented
132	C₄×D₅₂	C₂³	1	24	yes	—
133	C₄²×D₁₃	C₂³	1	24	yes	—
134	#88123	C₂³	1	24	yes	complemented
135	C₄×Dic₂₆	C₂³	1	24	yes	complemented
136	C₂²×D₄×Q₈	—	13	1	no	maximal, Sylow
137	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
138	C₂³×D₁₃	—	2	8	no	—
139	C₂³×D₁₃	—	2	8	no	—
140	C₂³×D₁₃	C₂×Q₈	1	16	yes	complemented
141	C₂³×D₁₃	C₂⁴	1	8	yes	—
142	C₂³×D₁₃	C₂⁴	1	2	yes	—
143	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
144	C₂×Q₈×C₁₃	—	2	64	no	—
145	C₂×Q₈×C₁₃	—	2	24	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
147	C₂×Q₈×C₁₃	C₂⁴	1	24	yes	—
148	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
149	C₂×D₄×C₁₃	C₂×Q₈	1	8	yes	complemented
150	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	—	2	24	no	—
152	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₂×C₂²⋊D₁₃	C₂×Q₈	1	16	yes	complemented
158	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
159	C₂²×Dic₁₃	—	2	24	no	—
160	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
161	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
162	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
163	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
164	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
165	Q₈×D₁₃	—	2	64	no	—
166	Q₈×D₁₃	—	2	192	no	—
167	Q₈×D₁₃	—	2	192	no	—
168	Q₈×D₁₃	C₂×D₄	1	64	yes	direct product factor
169	D₄×D₁₃	C₂×Q₈	1	64	yes	direct product factor
170	C₂×D₅₂	C₂×Q₈	1	8	yes	complemented
171	C₂×D₅₂	C₂⁴	1	4	yes	—
172	C₂×C₄×D₁₃	—	2	24	no	—
173	C₂×C₄×D₁₃	—	2	12	no	—
174	C₂×C₄×D₁₃	—	2	24	no	—
175	C₂×C₄×D₁₃	—	2	24	no	—
176	C₂×C₄×D₁₃	—	2	192	no	—
177	C₂×C₄×D₁₃	C₂×D₄	1	24	yes	—
178	C₂×C₄×D₁₃	C₂×Q₈	1	8	yes	complemented
179	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
180	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
181	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
182	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
183	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
184	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
185	C₂×Dic₂₆	—	2	24	no	—
186	C₂×Dic₂₆	—	2	48	no	—
187	C₂×Dic₂₆	—	2	192	no	—
188	C₂×Dic₂₆	C₂×D₄	1	24	yes	complemented
189	C₂×Dic₂₆	C₂⁴	1	24	yes	—
190	C₂×Dic₂₆	C₂⁴	1	48	yes	—
191	C₂×Dic₂₆	C₂⁴	1	12	yes	—
192	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
193	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
194	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	—
195	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
196	C₄²×C₁₃	C₂⁴	1	12	yes	—
197	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
198	#6103	C₂⁴	1	24	yes	—
199	#6103	C₂⁴	1	24	yes	—
200	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
201	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
202	C₄⋊Dic₁₃	C₂⁴	1	24	yes	—
203	#6101	C₂⁴	1	24	yes	—
204	#6101	C₂⁴	1	48	yes	—
205	#6101	C₂⁴	1	24	yes	—
206	C₄×Dic₁₃	C₂⁴	1	12	yes	—
207	C₄×Dic₁₃	C₂⁴	1	12	yes	—
208	C₄×Dic₁₃	C₂⁴	1	12	yes	—
209	C₂⁴×Q₈	—	13	2	no	—
210	C₂×D₄×Q₈	—	13	2	no	—
211	C₂×D₄×Q₈	—	13	32	no	—
212	C₂×D₄×Q₈	—	13	3	no	—
213	C₂×D₄×Q₈	—	13	6	no	—
214	C₂×D₄×Q₈	—	13	1	no	—
215	C₂×D₄×Q₈	—	13	3	no	—
216	C₂×D₄×Q₈	D₁₃	1	1	yes	characteristic, direct product factor
217	C₂²×C₄⋊Q₈	—	13	3	no	—
218	C₂²×C₂²⋊Q₈	—	13	6	no	—
219	C₂²×C₄×Q₈	—	13	1	no	—
220	C₂²×C₄×D₄	—	13	3	no	—
221	C₂³×C₁₃	—	2	4	no	—
222	C₂³×C₁₃	—	2	4	no	—
223	C₂³×C₁₃	C₂²×Q₈	1	8	yes	complemented
224	C₂³×C₁₃	C₂⁵	1	4	yes	—
225	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
226	C₂²×D₁₃	—	2	4	no	—
227	C₂²×D₁₃	—	2	4	no	—
228	C₂²×D₁₃	—	2	64	no	—
229	C₂²×D₁₃	—	2	16	no	—
230	C₂²×D₁₃	—	2	16	no	—
231	C₂²×D₁₃	C₂²×D₄	1	4	yes	—
232	C₂²×D₁₃	C₂²×Q₈	1	4	yes	—
233	C₂²×D₁₃	C₂²×Q₈	1	32	yes	complemented
234	C₂²×D₁₃	C₂²×Q₈	1	8	yes	complemented
235	C₂²×D₁₃	2₋¹⁺⁴	1	4	yes	—
236	C₂²×D₁₃	C₂⁵	1	4	yes	—
237	C₂²×D₁₃	C₂⁵	1	2	yes	—
238	Q₈×C₁₃	—	2	48	no	—
239	Q₈×C₁₃	C₂²×D₄	1	16	yes	complemented
240	D₄×C₁₃	C₂²×Q₈	1	16	yes	complemented
241	C₂×C₄×C₁₃	—	2	12	no	—
242	C₂×C₄×C₁₃	—	2	6	no	—
243	C₂×C₄×C₁₃	—	2	48	no	—
244	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
245	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	complemented
246	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
247	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
248	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
249	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
250	C₂²⋊D₁₃	C₂²×Q₈	1	32	yes	complemented
251	C₂×Dic₁₃	—	2	12	no	—
252	C₂×Dic₁₃	—	2	6	no	—
253	C₂×Dic₁₃	—	2	48	no	—
254	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
255	C₂×Dic₁₃	C₂²×Q₈	1	4	yes	complemented
256	C₂×Dic₁₃	C₂⁵	1	6	yes	—
257	C₂×Dic₁₃	C₂⁵	1	12	yes	—
258	C₂×Dic₁₃	C₂⁵	1	6	yes	—
259	C₂×Dic₁₃	C₂⁵	1	2	yes	—
260	D₅₂	C₂²×Q₈	1	16	yes	complemented
261	C₄×D₁₃	—	2	48	no	—
262	C₄×D₁₃	—	2	24	no	—
263	C₄×D₁₃	—	2	48	no	—
264	C₄×D₁₃	—	2	48	no	—
265	C₄×D₁₃	C₂²×D₄	1	48	yes	—
266	C₄×D₁₃	C₂²×Q₈	1	16	yes	complemented
267	Dic₂₆	—	2	48	no	—
268	Dic₂₆	—	2	96	no	—
269	Dic₂₆	C₂²×D₄	1	48	yes	complemented
270	C₂³×Q₈	—	13	1	no	—
271	C₂³×Q₈	—	13	6	no	—
272	C₂³×Q₈	—	13	6	no	—
273	C₂³×Q₈	—	13	2	no	—
274	C₂³×Q₈	—	13	32	no	—
275	C₂³×Q₈	—	13	6	no	—
276	C₂³×Q₈	—	26	32	no	—
277	C₂³×Q₈	C₂×D₁₃	1	2	yes	complemented
278	C₂³×D₄	—	13	1	no	—
279	C₂⁴×C₄	—	13	6	no	—
280	D₄×Q₈	—	13	32	no	—
281	D₄×Q₈	—	13	48	no	—
282	D₄×Q₈	—	13	96	no	—
283	D₄×Q₈	—	13	16	no	—
284	D₄×Q₈	—	13	48	no	—
285	D₄×Q₈	C₂×D₁₃	1	16	yes	direct product factor
286	C₂×C₄⋊Q₈	—	13	6	no	—
287	C₂×C₄⋊Q₈	—	13	48	no	—
288	C₂×C₄⋊Q₈	—	13	6	no	—
289	C₂×C₄⋊Q₈	—	13	6	no	—
290	C₂×C₄⋊Q₈	—	13	3	no	—
291	C₂×C₄⋊Q₈	C₂×D₁₃	1	3	yes	complemented
292	C₂×C₂²⋊Q₈	—	13	6	no	—
293	C₂×C₂²⋊Q₈	—	13	6	no	—
294	C₂×C₂²⋊Q₈	—	13	96	no	—
295	C₂×C₂²⋊Q₈	—	13	12	no	—
296	C₂×C₂²⋊Q₈	—	13	6	no	—
297	C₂×C₂²⋊Q₈	—	13	12	no	—
298	C₂×C₂²⋊Q₈	C₂×D₁₃	1	6	yes	complemented
299	C₂×C₄×Q₈	—	13	1	no	—
300	C₂×C₄×Q₈	—	13	16	no	—
301	C₂×C₄×Q₈	—	13	3	no	—
302	C₂×C₄×Q₈	—	13	3	no	—
303	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
304	C₂×C₄×D₄	—	13	3	no	—
305	C₂×C₄×D₄	—	13	6	no	—
306	C₂×C₄×D₄	—	13	48	no	—
307	C₂×C₄×D₄	—	13	3	no	—
308	C₂×C₄×D₄	—	13	6	no	—
309	C₂×C₄×D₄	—	13	3	no	—
310	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	—
311	C₂²×C₄⋊C₄	—	13	3	no	—
312	C₂²×C₄⋊C₄	—	13	3	no	—
313	C₂²×C₄⋊C₄	—	13	6	no	—
314	C₂²×C₂²⋊C₄	—	13	6	no	—
315	C₂²×C₄²	—	13	3	no	—
316	C₂²×C₁₃	—	2	4	no	—
317	C₂²×C₁₃	—	2	4	no	—
318	C₂²×C₁₃	—	2	16	no	—
319	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
320	C₂²×C₁₃	C₂³×Q₈	1	2	yes	—
321	C₂²×C₁₃	C₂³×Q₈	1	8	yes	complemented
322	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
323	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
324	C₂×D₁₃	—	2	4	no	—
325	C₂×D₁₃	—	2	4	no	—
326	C₂×D₁₃	—	2	16	no	—
327	C₂×D₁₃	—	2	64	no	—
328	C₂×D₁₃	D₄×Q₈	1	16	yes	direct product factor
329	C₂×D₁₃	C₂³×D₄	1	4	yes	—
330	C₂×D₁₃	C₂³×Q₈	1	4	yes	—
331	C₂×D₁₃	C₂³×Q₈	1	8	yes	complemented
332	C₂×D₁₃	C₂×2₋¹⁺⁴	1	4	yes	—
333	C₄×C₁₃	—	2	12	no	—
334	C₄×C₁₃	—	2	6	no	—
335	C₄×C₁₃	C₂³×D₄	1	12	yes	—
336	C₄×C₁₃	C₂³×Q₈	1	4	yes	complemented
337	Dic₁₃	—	2	12	no	—
338	Dic₁₃	—	2	6	no	—
339	Dic₁₃	C₂³×D₄	1	12	yes	—
340	Dic₁₃	C₂³×Q₈	1	4	yes	complemented
341	C₂⁵	—	13	2	no	—
342	C₂²×Q₈	—	2	16	no	—
343	C₂²×Q₈	—	13	16	no	—
344	C₂²×Q₈	—	13	8	no	—
345	C₂²×Q₈	—	13	48	no	—
346	C₂²×Q₈	—	13	48	no	—
347	C₂²×Q₈	—	13	16	no	—
348	C₂²×Q₈	—	13	3	no	—
349	C₂²×Q₈	—	13	12	no	—
350	C₂²×Q₈	—	13	6	no	—
351	C₂²×Q₈	—	13	48	no	—
352	C₂²×Q₈	—	26	48	no	—
353	C₂²×Q₈	—	26	48	no	—
354	C₂²×Q₈	—	26	256	no	—
355	C₂²×Q₈	—	26	48	no	—
356	C₂²×Q₈	—	26	16	no	—
357	C₂²×Q₈	C₂²×D₁₃	1	6	yes	—
358	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
359	C₂²×Q₈	C₂²×D₁₃	1	16	yes	complemented
360	C₂²×D₄	—	13	2	no	—
361	C₂²×D₄	—	13	16	no	—
362	C₂²×D₄	—	13	8	no	—
363	C₂²×D₄	—	13	1	no	—
364	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
365	C₂³×C₄	—	13	1	no	—
366	C₂³×C₄	—	13	3	no	—
367	C₂³×C₄	—	13	6	no	—
368	C₂³×C₄	—	13	3	no	—
369	C₂³×C₄	—	13	6	no	—
370	C₂³×C₄	—	13	6	no	—
371	C₂³×C₄	—	13	48	no	—
372	C₂³×C₄	—	13	6	no	—
373	C₂³×C₄	—	26	48	no	—
374	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
375	C₄⋊Q₈	—	13	48	no	—
376	C₄⋊Q₈	—	13	48	no	—
377	C₄⋊Q₈	—	13	48	no	—
378	C₄⋊Q₈	—	13	24	no	—
379	C₄⋊Q₈	C₂²×D₁₃	1	24	yes	complemented
380	C₂²⋊Q₈	—	13	48	no	—
381	C₂²⋊Q₈	—	13	48	no	—
382	C₂²⋊Q₈	—	13	96	no	—
383	C₂²⋊Q₈	—	13	48	no	—
384	C₂²⋊Q₈	—	13	96	no	—
385	C₂²⋊Q₈	C₂²×D₁₃	1	48	yes	complemented
386	C₄×Q₈	—	13	8	no	—
387	C₄×Q₈	—	13	24	no	—
388	C₄×Q₈	—	13	24	no	—
389	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
390	C₄×D₄	—	13	24	no	—
391	C₄×D₄	—	13	48	no	—
392	C₄×D₄	—	13	24	no	—
393	C₄×D₄	—	13	48	no	—
394	C₄×D₄	—	13	24	no	—
395	C₄×D₄	C₂²×D₁₃	1	24	yes	—
396	C₂×C₄⋊C₄	—	13	6	no	—
397	C₂×C₄⋊C₄	—	13	3	no	—
398	C₂×C₄⋊C₄	—	13	6	no	—
399	C₂×C₄⋊C₄	—	13	3	no	—
400	C₂×C₄⋊C₄	—	13	12	no	—
401	C₂×C₄⋊C₄	—	13	6	no	—
402	C₂×C₄⋊C₄	—	13	24	no	—
403	C₂×C₄⋊C₄	—	13	24	no	—
404	C₂×C₄⋊C₄	—	13	48	no	—
405	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
406	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
407	C₂×C₄⋊C₄	C₂²×D₁₃	1	6	yes	—
408	C₂×C₂²⋊C₄	—	13	6	no	—
409	C₂×C₂²⋊C₄	—	13	6	no	—
410	C₂×C₂²⋊C₄	—	13	6	no	—
411	C₂×C₂²⋊C₄	—	13	48	no	—
412	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
413	C₂×C₄²	—	13	3	no	—
414	C₂×C₄²	—	13	3	no	—
415	C₂×C₄²	—	13	3	no	—
416	C₂×C₄²	—	13	24	no	—
417	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
418	C₂×C₁₃	—	2	8	no	—
419	C₂×C₁₃	C₂×D₄×Q₈	1	4	yes	complemented
420	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
421	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
422	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
423	D₁₃	—	2	8	no	—
424	D₁₃	C₂×D₄×Q₈	1	8	yes	direct product factor
425	C₂⁴	—	13	1	no	—
426	C₂⁴	—	13	16	no	—
427	C₂⁴	—	13	8	no	—
428	C₂⁴	—	13	2	no	—
429	C₂⁴	—	26	8	no	—
430	C₂⁴	—	26	8	no	—
431	C₂⁴	C₂³×D₁₃	1	2	yes	—
432	C₂×Q₈	—	2	64	no	—
433	C₂×Q₈	—	2	24	no	—
434	C₂×Q₈	—	13	64	no	—
435	C₂×Q₈	—	13	24	no	—
436	C₂×Q₈	—	13	12	no	—
437	C₂×Q₈	—	13	48	no	—
438	C₂×Q₈	—	13	24	no	—
439	C₂×Q₈	—	26	48	no	—
440	C₂×Q₈	—	26	192	no	—
441	C₂×Q₈	—	26	192	no	—
442	C₂×Q₈	—	26	192	no	—
443	C₂×Q₈	—	26	64	no	—
444	C₂×Q₈	—	26	24	no	—
445	C₂×Q₈	D₄×D₁₃	1	8	yes	direct product factor
446	C₂×Q₈	C₂³×D₁₃	1	24	yes	—
447	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
448	C₂×D₄	—	13	16	no	—
449	C₂×D₄	—	13	8	no	—
450	C₂×D₄	—	13	64	no	—
451	C₂×D₄	—	13	8	no	—
452	C₂×D₄	—	13	4	no	—
453	C₂×D₄	Q₈×D₁₃	1	8	yes	direct product factor
454	C₂×D₄	C₂³×D₁₃	1	4	yes	—
455	C₂²×C₄	—	2	24	no	—
456	C₂²×C₄	—	13	1	no	—
457	C₂²×C₄	—	13	3	no	—
458	C₂²×C₄	—	13	24	no	—
459	C₂²×C₄	—	13	8	no	—
460	C₂²×C₄	—	13	4	no	—
461	C₂²×C₄	—	13	12	no	—
462	C₂²×C₄	—	13	24	no	—
463	C₂²×C₄	—	13	3	no	—
464	C₂²×C₄	—	13	6	no	—
465	C₂²×C₄	—	13	12	no	—
466	C₂²×C₄	—	13	24	no	—
467	C₂²×C₄	—	13	24	no	—
468	C₂²×C₄	—	13	24	no	—
469	C₂²×C₄	—	26	24	no	—
470	C₂²×C₄	—	26	192	no	—
471	C₂²×C₄	—	26	24	no	—
472	C₂²×C₄	—	26	12	no	—
473	C₂²×C₄	—	26	24	no	—
474	C₂²×C₄	—	26	24	no	—
475	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
476	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
477	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
478	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
479	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
480	C₄⋊C₄	—	13	24	no	—
481	C₄⋊C₄	—	13	12	no	—
482	C₄⋊C₄	—	13	24	no	—
483	C₄⋊C₄	—	13	12	no	—
484	C₄⋊C₄	—	13	48	no	—
485	C₄⋊C₄	—	13	24	no	—
486	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
487	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
488	C₄⋊C₄	C₂³×D₁₃	1	24	yes	—
489	C₂²⋊C₄	—	13	24	no	—
490	C₂²⋊C₄	—	13	24	no	—
491	C₂²⋊C₄	—	13	24	no	—
492	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
493	C₄²	—	13	12	no	—
494	C₄²	—	13	12	no	—
495	C₄²	—	13	12	no	—
496	C₄²	C₂³×D₁₃	1	12	yes	—
497	C₁₃	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	13	4	no	—
501	C₂³	—	13	4	no	—
502	C₂³	—	13	4	no	—
503	C₂³	—	13	2	no	—
504	C₂³	—	13	8	no	—
505	C₂³	—	13	32	no	—
506	C₂³	—	13	4	no	—
507	C₂³	—	26	16	no	—
508	C₂³	—	26	64	no	—
509	C₂³	—	26	16	no	—
510	C₂³	—	26	4	no	—
511	C₂³	—	26	4	no	—
512	C₂³	C₂×Q₈×D₁₃	1	8	yes	complemented
513	C₂³	C₂⁴×D₁₃	1	4	yes	—
514	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
515	Q₈	—	2	48	no	—
516	Q₈	—	13	48	no	—
517	Q₈	—	26	96	no	—
518	Q₈	—	26	48	no	—
519	Q₈	C₂×D₄×D₁₃	1	16	yes	direct product factor
520	D₄	—	13	32	no	—
521	D₄	—	13	16	no	—
522	D₄	C₂×Q₈×D₁₃	1	16	yes	direct product factor
523	C₂×C₄	—	2	12	no	—
524	C₂×C₄	—	2	6	no	—
525	C₂×C₄	—	2	48	no	—
526	C₂×C₄	—	13	12	no	—
527	C₂×C₄	—	13	4	no	—
528	C₂×C₄	—	13	2	no	—
529	C₂×C₄	—	13	6	no	—
530	C₂×C₄	—	13	48	no	—
531	C₂×C₄	—	13	16	no	—
532	C₂×C₄	—	13	6	no	—
533	C₂×C₄	—	13	12	no	—
534	C₂×C₄	—	26	48	no	—
535	C₂×C₄	—	26	24	no	—
536	C₂×C₄	—	26	48	no	—
537	C₂×C₄	—	26	48	no	—
538	C₂×C₄	—	26	12	no	—
539	C₂×C₄	—	26	6	no	—
540	C₂×C₄	—	26	48	no	—
541	C₂×C₄	C₂×D₄×D₁₃	1	12	yes	—
542	C₂×C₄	C₂×Q₈×D₁₃	1	4	yes	complemented
543	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
544	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
545	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
546	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
547	C₂²	—	2	16	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	4	no	—
550	C₂²	—	13	16	no	—
551	C₂²	—	13	4	no	—
552	C₂²	—	13	4	no	—
553	C₂²	—	13	4	no	—
554	C₂²	—	13	8	no	—
555	C₂²	—	26	64	no	—
556	C₂²	—	26	16	no	—
557	C₂²	—	26	4	no	—
558	C₂²	—	26	4	no	—
559	C₂²	C₂²×D₄×D₁₃	1	2	yes	—
560	C₂²	C₂²×Q₈×D₁₃	1	2	yes	—
561	C₂²	C₂²×Q₈×D₁₃	1	8	yes	complemented
562	C₂²	D₁₃×2₋¹⁺⁴	1	2	yes	—
563	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
564	C₄	—	2	12	no	—
565	C₄	—	2	6	no	—
566	C₄	—	13	12	no	—
567	C₄	—	13	4	no	—
568	C₄	—	26	12	no	—
569	C₄	—	26	6	no	—
570	C₄	C₂²×D₄×D₁₃	1	12	yes	—
571	C₄	C₂²×Q₈×D₁₃	1	4	yes	complemented
572	C₂	—	2	8	no	—
573	C₂	—	13	8	no	—
574	C₂	—	26	8	no	—
575	C₂	D₄×Q₈×D₁₃	1	4	yes	direct product factor
576	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
577	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
578	C₂	C₂×D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×D₄×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×D₁₃	C₂²
hypercenter	C₂×D₄×Q₈	D₁₃
hypocenter	C₁₃	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₁₃	C₂	semidirect
2. C₂×Q₈×D₅₂	C₂	semidirect
3. C₂×D₄×Dic₂₆	C₂	semidirect
4. C₂×#11719432	C₂	semidirect
5. C₂×Q₈×C₂²⋊D₁₃	C₂	semidirect
6. C₂×#11719337	C₂	semidirect
7. D₄×Q₈×D₁₃	C₂	direct (N × H)
8. C₂×D₁₃×C₄⋊Q₈	C₂	semidirect
9. C₂×D₁₃×C₂²⋊Q₈	C₂	semidirect
10. C₂×C₄×Q₈×D₁₃	C₂	semidirect
12. C₂×D₄×Q₈×C₁₃	C₂	semidirect
13. C₂³×Q₈×C₁₃	C₂²	semidirect
17. C₂²×Q₈×D₁₃	C₂²	semidirect
18. C₂²×Q₈×D₁₃	C₂²	semidirect
19. C₂²×Q₈×D₁₃	C₂²	semidirect
22. C₂³×Dic₂₆	C₂²	semidirect
23. D₄×Q₈×C₁₃	C₂²	semidirect
24. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. Q₈×C₂²⋊D₁₃	C₂²	semidirect
29. C₂×#88200	C₂²	semidirect
30. C₂×Q₈×Dic₁₃	C₂²	semidirect
31. C₂×#88198	C₂²	semidirect
34. C₂×#88178	C₂²	semidirect
35. #11719432	C₂²	semidirect
36. D₁₃×C₄⋊Q₈	C₂²	semidirect
37. #11719337	C₂²	semidirect
38. D₁₃×C₂²⋊Q₈	C₂²	semidirect
39. Q₈×D₅₂	C₂²	semidirect
40. C₄×Q₈×D₁₃	C₂²	semidirect
42. D₄×Dic₂₆	C₂²	semidirect
43. C₂×#88151	C₂²	semidirect
44. C₂×#88150	C₂²	semidirect
49. C₂×#88142	C₂²	semidirect
50. C₂×#88142	C₂²	semidirect
51. C₂×#88141	C₂²	semidirect
54. C₂×#88132	C₂²	semidirect
57. C₂×#88123	C₂²	semidirect
58. C₂×C₄×Dic₂₆	C₂²	semidirect
63. C₂²×Q₈×C₁₃	C₂³	semidirect
72. C₂×Q₈×D₁₃	D₄	direct (N × H)
75. C₂×Q₈×D₁₃	C₂³	semidirect
76. C₂×Q₈×D₁₃	C₂³	semidirect
77. C₂×D₄×D₁₃	Q₈	direct (N × H)
92. C₂²×Dic₂₆	C₂³	semidirect
93. C₁₃×C₄⋊Q₈	C₂³	semidirect
94. C₁₃×C₂²⋊Q₈	C₂³	semidirect
95. C₄×Q₈×C₁₃	C₂³	semidirect
103. #88200	C₂³	semidirect
104. Q₈×Dic₁₃	C₂³	semidirect
105. #88198	C₂³	semidirect
113. #88178	C₂³	semidirect
120. #88151	C₂³	semidirect
121. #88150	C₂³	semidirect
126. #88142	C₂³	semidirect
127. #88142	C₂³	semidirect
128. #88141	C₂³	semidirect
131. #88132	C₂³	semidirect
134. #88123	C₂³	semidirect
135. C₄×Dic₂₆	C₂³	semidirect
140. C₂³×D₁₃	C₂×Q₈	semidirect
146. C₂×Q₈×C₁₃	C₂×D₄	semidirect
149. C₂×D₄×C₁₃	C₂×Q₈	semidirect
157. C₂×C₂²⋊D₁₃	C₂×Q₈	semidirect
168. Q₈×D₁₃	C₂×D₄	direct (N × H)
169. D₄×D₁₃	C₂×Q₈	direct (N × H)
170. C₂×D₅₂	C₂×Q₈	semidirect
178. C₂×C₄×D₁₃	C₂×Q₈	semidirect
188. C₂×Dic₂₆	C₂×D₄	semidirect
216. C₂×D₄×Q₈	D₁₃	direct (N × H)
223. C₂³×C₁₃	C₂²×Q₈	semidirect
233. C₂²×D₁₃	C₂²×Q₈	semidirect
234. C₂²×D₁₃	C₂²×Q₈	semidirect
239. Q₈×C₁₃	C₂²×D₄	semidirect
240. D₄×C₁₃	C₂²×Q₈	semidirect
245. C₂×C₄×C₁₃	C₂²×Q₈	semidirect
250. C₂²⋊D₁₃	C₂²×Q₈	semidirect
255. C₂×Dic₁₃	C₂²×Q₈	semidirect
260. D₅₂	C₂²×Q₈	semidirect
266. C₄×D₁₃	C₂²×Q₈	semidirect
269. Dic₂₆	C₂²×D₄	semidirect
277. C₂³×Q₈	C₂×D₁₃	semidirect
285. D₄×Q₈	C₂×D₁₃	direct (N × H)
291. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
298. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
303. C₂×C₄×Q₈	C₂×D₁₃	semidirect
321. C₂²×C₁₃	C₂³×Q₈	semidirect
328. C₂×D₁₃	D₄×Q₈	direct (N × H)
331. C₂×D₁₃	C₂³×Q₈	semidirect
336. C₄×C₁₃	C₂³×Q₈	semidirect
340. Dic₁₃	C₂³×Q₈	semidirect
359. C₂²×Q₈	C₂²×D₁₃	semidirect
379. C₄⋊Q₈	C₂²×D₁₃	semidirect
385. C₂²⋊Q₈	C₂²×D₁₃	semidirect
389. C₄×Q₈	C₂²×D₁₃	semidirect
419. C₂×C₁₃	C₂×D₄×Q₈	semidirect
424. D₁₃	C₂×D₄×Q₈	direct (N × H)
445. C₂×Q₈	D₄×D₁₃	direct (N × H)
453. C₂×D₄	Q₈×D₁₃	direct (N × H)
497. C₁₃	C₂²×D₄×Q₈	semidirect
512. C₂³	C₂×Q₈×D₁₃	semidirect
519. Q₈	C₂×D₄×D₁₃	direct (N × H)
522. D₄	C₂×Q₈×D₁₃	direct (N × H)
542. C₂×C₄	C₂×Q₈×D₁₃	semidirect
561. C₂²	C₂²×Q₈×D₁₃	semidirect
571. C₄	C₂²×Q₈×D₁₃	semidirect
575. C₂	D₄×Q₈×D₁₃	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×Q₈×D₁₃	2
C₂×Q₈×D₅₂	2
C₂×D₄×Dic₂₆	2
C₂×#11719432	2
C₂×Q₈×C₂²⋊D₁₃	2
C₂×#11719337	2
D₄×Q₈×D₁₃	2
C₂×D₁₃×C₄⋊Q₈	2
C₂×D₁₃×C₂²⋊Q₈	2
C₂×C₄×Q₈×D₁₃	2
C₂×C₄×D₄×D₁₃	2
C₂×D₄×Q₈×C₁₃	2
C₂²×D₄×Q₈	13

Subgroups — C2×D4×Q8×D13 #16769831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×Q₈×D₁₃ #16769831