Subgroups — Q₈×C₁₃×#135 #15747696

Order 3328.

1786 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₃×#41	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3383	C₂	1	3	yes	maximal, complemented
3	Q₈×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3381	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3380	C₂	1	3	yes	maximal, complemented
6	Q₈×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
7	Q₈×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3160	C₂	1	3	yes	maximal, complemented
9	C₁₃×#3076	C₂	1	6	yes	maximal, complemented
10	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	3	yes	maximal
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	Q₈²×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#557	C₂²	1	6	yes	—
15	C₁₃×#554	—	2	6	no	—
16	C₁₃×#554	C₂²	1	6	yes	—
17	D₄×Q₈×C₁₃	—	2	2	no	—
18	D₄×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₁₃×#533	—	2	6	no	—
20	C₁₃×#533	C₂²	1	6	yes	—
21	C₄×C₁₃×#41	C₂²	1	6	yes	—
22	C₂×C₄×Q₈×C₁₃	—	2	2	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#500	C₂²	1	3	yes	—
25	C₁₃×#500	C₂²	1	3	yes	—
26	C₁₃×#499	C₂²	1	6	yes	—
27	C₁₃×#499	C₂²	1	6	yes	—
28	C₁₃×#498	C₂²	1	6	yes	—
29	C₁₃×#479	C₂²	1	12	yes	—
30	C₁₃×#478	C₂²	1	12	yes	—
31	C₁₃×#477	C₂²	1	6	yes	—
32	C₁₃×#476	C₂²	1	6	yes	—
33	C₁₃×#475	C₂²	1	6	yes	—
34	C₁₃×#474	C₂²	1	6	yes	—
35	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
38	C₈×Q₈×C₁₃	C₂²	1	3	yes	—
39	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
40	C₄×C₁₃×Q₁₆	C₂²	1	3	yes	—
41	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
42	C₄×C₁₃×SD₁₆	C₂²	1	6	yes	—
43	C₄×C₁₃×D₈	C₂²	1	3	yes	—
44	C₄×C₁₃×D₈	C₂²	1	3	yes	—
45	C₁₃×#427	C₂²	1	6	yes	—
46	C₁₃×#427	C₂²	1	3	yes	—
47	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
48	C₁₃×#416	C₂²	1	6	yes	—
49	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
50	C₂×C₁₃×#41	C₂³	1	2	yes	—
51	C₂²×Q₈×C₁₃	—	2	2	no	—
52	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
53	C₁₃×#135	Q₈	1	8	yes	direct product factor
54	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊Q₈	—	2	6	no	—
60	C₁₃×C₄⋊Q₈	—	2	6	no	—
61	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
63	C₁₃×#125	—	2	12	no	—
64	C₁₃×#125	C₂³	1	12	yes	—
65	C₁₃×C₂²⋊Q₈	—	2	6	no	—
66	C₁₃×C₂²⋊Q₈	—	2	6	no	—
67	C₁₃×C₂²⋊Q₈	—	2	6	no	—
68	C₁₃×C₂²⋊Q₈	—	2	6	no	—
69	C₁₃×C₂²⋊Q₈	—	2	12	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	6	no	—
72	C₄×Q₈×C₁₃	—	2	6	no	—
73	C₄×Q₈×C₁₃	—	2	6	no	—
74	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₃	D₄	1	3	yes	—
76	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
77	C₄×Q₈×C₁₃	C₂³	1	6	yes	—
78	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₄×Q₈×C₁₃	C₂³	1	3	yes	—
80	C₄×D₄×C₁₃	—	2	6	no	—
81	C₄×D₄×C₁₃	—	2	6	no	—
82	C₄×D₄×C₁₃	C₂³	1	6	yes	—
83	C₄×D₄×C₁₃	C₂³	1	6	yes	—
84	C₁₃×#117	—	2	6	no	—
85	C₁₃×#117	C₂³	1	6	yes	—
86	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
87	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
88	C₂×C₄²×C₁₃	—	2	6	no	—
89	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
90	C₁₃×#107	C₂³	1	3	yes	—
91	C₁₃×#107	C₂³	1	3	yes	—
92	C₁₃×#107	C₂³	1	6	yes	—
93	C₁₃×#107	C₂³	1	6	yes	—
94	C₁₃×#106	C₂³	1	6	yes	—
95	C₁₃×#106	C₂³	1	12	yes	—
96	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
97	C₁₃×C₄⋊C₈	C₂³	1	3	yes	—
98	C₁₃×C₄⋊C₈	C₂³	1	6	yes	—
99	C₁₃×#103	C₂³	1	6	yes	—
100	C₁₃×#103	C₂³	1	6	yes	—
101	C₁₃×#102	C₂³	1	6	yes	—
102	C₁₃×#102	C₂³	1	6	yes	—
103	C₄×C₈×C₁₃	C₂³	1	3	yes	—
104	C₄×C₈×C₁₃	C₂³	1	3	yes	—
105	C₄×C₈×C₁₃	C₂³	1	3	yes	—
106	C₄×C₈×C₁₃	C₂³	1	3	yes	—
107	Q₈×#135	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	C₂×Q₈	1	8	yes	complemented
110	C₂×Q₈×C₁₃	—	2	4	no	—
111	C₂×Q₈×C₁₃	—	2	6	no	—
112	C₂×Q₈×C₁₃	—	2	6	no	—
113	C₂×Q₈×C₁₃	—	4	8	no	—
114	C₂×Q₈×C₁₃	C₂×D₄	1	3	yes	—
115	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	6	no	—
121	C₂²×C₄×C₁₃	—	2	6	no	—
122	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×Q₁₆	C₂×Q₈	1	4	yes	complemented
126	C₁₃×SD₁₆	C₂×Q₈	1	8	yes	complemented
127	C₁₃×D₈	C₂×Q₈	1	4	yes	complemented
128	C₂×C₈×C₁₃	—	2	6	no	—
129	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
130	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
131	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
132	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	—	2	12	no	—
135	C₁₃×C₄⋊C₄	—	2	6	no	—
136	C₁₃×C₄⋊C₄	—	2	6	no	—
137	C₁₃×C₄⋊C₄	—	2	6	no	—
138	C₁₃×C₄⋊C₄	—	2	6	no	—
139	C₁₃×C₄⋊C₄	—	2	12	no	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
142	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
144	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
145	C₁₃×C₂²⋊C₄	—	2	6	no	—
146	C₁₃×C₂²⋊C₄	—	2	6	no	—
147	C₁₃×C₂²⋊C₄	—	2	6	no	—
148	C₄²×C₁₃	—	2	6	no	—
149	C₄²×C₁₃	—	2	6	no	—
150	C₄²×C₁₃	—	2	6	no	—
151	C₄²×C₁₃	C₂×D₄	1	3	yes	—
152	C₄²×C₁₃	C₂×D₄	1	3	yes	—
153	C₄²×C₁₃	C₂⁴	1	3	yes	—
154	C₄²×C₁₃	C₂⁴	1	3	yes	—
155	Q₈×#41	C₂×C₁₃	1	2	yes	complemented
156	#3383	C₂×C₁₃	1	3	yes	complemented
157	Q₈×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
158	#3381	C₂×C₁₃	1	6	yes	complemented
159	#3380	C₂×C₁₃	1	3	yes	complemented
160	Q₈×SD₁₆	C₂×C₁₃	1	2	yes	complemented
161	Q₈×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#3160	C₂×C₁₃	1	3	yes	complemented
163	#3076	C₂×C₁₃	1	6	yes	complemented
164	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
165	C₄×#135	C₂×C₁₃	1	3	yes	—
166	C₂³×C₁₃	—	2	2	no	—
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	6	no	—
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	4	12	no	—
171	Q₈×C₁₃	—	8	6	no	—
172	Q₈×C₁₃	#135	1	4	yes	direct product factor
173	Q₈×C₁₃	C₂²×Q₈	1	4	yes	—
174	D₄×C₁₃	—	2	8	no	—
175	D₄×C₁₃	—	2	2	no	—
176	D₄×C₁₃	C₂²×Q₈	1	4	yes	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	6	no	—
180	C₂×C₄×C₁₃	—	2	6	no	—
181	C₂×C₄×C₁₃	—	2	6	no	—
182	C₂×C₄×C₁₃	—	4	3	no	—
183	C₂×C₄×C₁₃	—	4	12	no	—
184	C₂×C₄×C₁₃	—	8	6	no	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
189	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
191	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
192	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
193	C₈×C₁₃	—	2	3	no	—
194	C₈×C₁₃	—	2	3	no	—
195	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
196	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
197	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
198	Q₈²	C₂²×C₁₃	1	2	yes	—
199	#557	C₂²×C₁₃	1	6	yes	—
200	#554	—	2	6	no	—
201	#554	C₂²×C₁₃	1	6	yes	—
202	D₄×Q₈	—	2	2	no	—
203	D₄×Q₈	C₂²×C₁₃	1	2	yes	—
204	#533	—	2	6	no	—
205	#533	C₂²×C₁₃	1	6	yes	—
206	C₄×#41	C₂²×C₁₃	1	6	yes	—
207	C₂×C₄×Q₈	—	2	2	no	—
208	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	#500	C₂²×C₁₃	1	3	yes	—
210	#500	C₂²×C₁₃	1	3	yes	—
211	#499	C₂²×C₁₃	1	6	yes	—
212	#499	C₂²×C₁₃	1	6	yes	—
213	#498	C₂²×C₁₃	1	6	yes	—
214	#479	C₂²×C₁₃	1	12	yes	—
215	#478	C₂²×C₁₃	1	12	yes	—
216	#477	C₂²×C₁₃	1	6	yes	—
217	#476	C₂²×C₁₃	1	6	yes	—
218	#475	C₂²×C₁₃	1	6	yes	—
219	#474	C₂²×C₁₃	1	6	yes	—
220	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
222	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
223	C₈×Q₈	C₂²×C₁₃	1	3	yes	—
224	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
225	C₄×Q₁₆	C₂²×C₁₃	1	3	yes	—
226	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
227	C₄×SD₁₆	C₂²×C₁₃	1	6	yes	—
228	C₄×D₈	C₂²×C₁₃	1	3	yes	—
229	C₄×D₈	C₂²×C₁₃	1	3	yes	—
230	#427	C₂²×C₁₃	1	6	yes	—
231	#427	C₂²×C₁₃	1	3	yes	—
232	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
233	#416	C₂²×C₁₃	1	6	yes	—
234	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	4	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
241	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
242	C₄×C₁₃	—	2	3	no	—
243	C₄×C₁₃	—	2	3	no	—
244	C₄×C₁₃	—	2	4	no	—
245	C₄×C₁₃	—	2	3	no	—
246	C₄×C₁₃	—	4	6	no	—
247	C₄×C₁₃	—	4	6	no	—
248	C₄×C₁₃	D₄×Q₈	1	2	yes	—
249	C₄×C₁₃	C₂×#135	1	6	yes	—
250	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
251	C₄×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
252	C₂×#41	C₂³×C₁₃	1	2	yes	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
255	#135	Q₈×C₁₃	1	8	yes	direct product factor
256	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
258	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
260	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	6	no	—
262	C₄⋊Q₈	—	2	6	no	—
263	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
264	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
265	#125	—	2	12	no	—
266	#125	C₂³×C₁₃	1	12	yes	—
267	C₂²⋊Q₈	—	2	6	no	—
268	C₂²⋊Q₈	—	2	6	no	—
269	C₂²⋊Q₈	—	2	6	no	—
270	C₂²⋊Q₈	—	2	6	no	—
271	C₂²⋊Q₈	—	2	12	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	6	no	—
274	C₄×Q₈	—	2	6	no	—
275	C₄×Q₈	—	2	6	no	—
276	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
277	C₄×Q₈	D₄×C₁₃	1	3	yes	—
278	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
279	C₄×Q₈	C₂³×C₁₃	1	6	yes	—
280	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₄×Q₈	C₂³×C₁₃	1	3	yes	—
282	C₄×D₄	—	2	6	no	—
283	C₄×D₄	—	2	6	no	—
284	C₄×D₄	C₂³×C₁₃	1	6	yes	—
285	C₄×D₄	C₂³×C₁₃	1	6	yes	—
286	#117	—	2	6	no	—
287	#117	C₂³×C₁₃	1	6	yes	—
288	C₂×C₄⋊C₄	—	2	6	no	—
289	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
290	C₂×C₄²	—	2	6	no	—
291	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
292	#107	C₂³×C₁₃	1	3	yes	—
293	#107	C₂³×C₁₃	1	3	yes	—
294	#107	C₂³×C₁₃	1	6	yes	—
295	#107	C₂³×C₁₃	1	6	yes	—
296	#106	C₂³×C₁₃	1	6	yes	—
297	#106	C₂³×C₁₃	1	12	yes	—
298	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
299	C₄⋊C₈	C₂³×C₁₃	1	3	yes	—
300	C₄⋊C₈	C₂³×C₁₃	1	6	yes	—
301	#103	C₂³×C₁₃	1	6	yes	—
302	#103	C₂³×C₁₃	1	6	yes	—
303	#102	C₂³×C₁₃	1	6	yes	—
304	#102	C₂³×C₁₃	1	6	yes	—
305	C₄×C₈	C₂³×C₁₃	1	3	yes	—
306	C₄×C₈	C₂³×C₁₃	1	3	yes	—
307	C₄×C₈	C₂³×C₁₃	1	3	yes	—
308	C₄×C₈	C₂³×C₁₃	1	3	yes	—
309	C₂×C₁₃	—	2	2	no	—
310	C₂×C₁₃	—	4	4	no	—
311	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
312	C₂×C₁₃	C₂²×#135	1	1	yes	characteristic
313	C₂×C₁₃	#3584	1	1	yes	characteristic
314	#41	—	2	4	no	—
315	#41	C₂×Q₈×C₁₃	1	8	yes	complemented
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	6	no	—
318	C₂×Q₈	—	2	6	no	—
319	C₂×Q₈	—	4	8	no	—
320	C₂×Q₈	C₂×D₄×C₁₃	1	3	yes	—
321	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
322	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	6	no	—
327	C₂²×C₄	—	2	6	no	—
328	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
329	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
330	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
331	Q₁₆	C₂×Q₈×C₁₃	1	4	yes	complemented
332	SD₁₆	C₂×Q₈×C₁₃	1	8	yes	complemented
333	D₈	C₂×Q₈×C₁₃	1	4	yes	complemented
334	C₂×C₈	—	2	6	no	—
335	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	complemented
336	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
337	C₂×C₈	C₂⁴×C₁₃	1	3	yes	—
338	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
339	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
340	C₄⋊C₄	—	2	12	no	—
341	C₄⋊C₄	—	2	6	no	—
342	C₄⋊C₄	—	2	6	no	—
343	C₄⋊C₄	—	2	6	no	—
344	C₄⋊C₄	—	2	6	no	—
345	C₄⋊C₄	—	2	12	no	—
346	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
347	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
348	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
349	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
350	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
351	C₂²⋊C₄	—	2	6	no	—
352	C₂²⋊C₄	—	2	6	no	—
353	C₂²⋊C₄	—	2	6	no	—
354	C₄²	—	2	6	no	—
355	C₄²	—	2	6	no	—
356	C₄²	—	2	6	no	—
357	C₄²	C₂×D₄×C₁₃	1	3	yes	—
358	C₄²	C₂×D₄×C₁₃	1	3	yes	—
359	C₄²	C₂⁴×C₁₃	1	3	yes	—
360	C₄²	C₂⁴×C₁₃	1	3	yes	—
361	C₁₃	Q₈×#135	1	1	yes	characteristic, direct product factor, Sylow
362	C₂³	—	2	2	no	—
363	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
364	Q₈	—	2	6	no	—
365	Q₈	—	2	2	no	—
366	Q₈	—	4	12	no	—
367	Q₈	—	8	6	no	—
368	Q₈	C₁₃×#135	1	4	yes	direct product factor
369	Q₈	C₂²×Q₈×C₁₃	1	4	yes	—
370	D₄	—	2	8	no	—
371	D₄	—	2	2	no	—
372	D₄	C₂²×Q₈×C₁₃	1	4	yes	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	2	6	no	—
378	C₂×C₄	—	4	3	no	—
379	C₂×C₄	—	4	12	no	—
380	C₂×C₄	—	8	6	no	—
381	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
382	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
383	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
384	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
386	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
387	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
388	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
389	C₈	—	2	3	no	—
390	C₈	—	2	3	no	—
391	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
392	C₈	C₂²×Q₈×C₁₃	1	2	yes	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
399	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
400	C₄	—	2	3	no	—
401	C₄	—	2	3	no	—
402	C₄	—	2	3	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	6	no	—
405	C₄	—	4	6	no	—
406	C₄	D₄×Q₈×C₁₃	1	2	yes	—
407	C₄	C₂×C₁₃×#135	1	6	yes	—
408	C₄	C₂³×Q₈×C₁₃	1	1	yes	characteristic
409	C₄	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	4	4	no	—
412	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
413	C₂	C₂²×C₁₃×#135	1	1	yes	characteristic
414	C₂	C₁₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
socle	C₂²×C₁₃	C₂³×D₄
prime radical	C₂×C₁₃×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×C₁₃×#41	C₂	semidirect
2. C₁₃×#3383	C₂	semidirect
3. Q₈×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#3381	C₂	semidirect
5. C₁₃×#3380	C₂	semidirect
6. Q₈×C₁₃×SD₁₆	C₂	semidirect
7. Q₈×C₁₃×D₈	C₂	semidirect
8. C₁₃×#3160	C₂	semidirect
9. C₁₃×#3076	C₂	semidirect
10. C₂×C₈×Q₈×C₁₃	C₂	semidirect
53. C₁₃×#135	Q₈	direct (N × H)
107. Q₈×#135	C₁₃	direct (N × H)
109. C₁₃×#41	C₂×Q₈	semidirect
125. C₁₃×Q₁₆	C₂×Q₈	semidirect
126. C₁₃×SD₁₆	C₂×Q₈	semidirect
127. C₁₃×D₈	C₂×Q₈	semidirect
129. C₂×C₈×C₁₃	C₂×Q₈	semidirect
155. Q₈×#41	C₂×C₁₃	semidirect
156. #3383	C₂×C₁₃	semidirect
157. Q₈×Q₁₆	C₂×C₁₃	semidirect
158. #3381	C₂×C₁₃	semidirect
159. #3380	C₂×C₁₃	semidirect
160. Q₈×SD₁₆	C₂×C₁₃	semidirect
161. Q₈×D₈	C₂×C₁₃	semidirect
162. #3160	C₂×C₁₃	semidirect
163. #3076	C₂×C₁₃	semidirect
164. C₂×C₈×Q₈	C₂×C₁₃	semidirect
172. Q₈×C₁₃	#135	direct (N × H)
255. #135	Q₈×C₁₃	direct (N × H)
315. #41	C₂×Q₈×C₁₃	semidirect
331. Q₁₆	C₂×Q₈×C₁₃	semidirect
332. SD₁₆	C₂×Q₈×C₁₃	semidirect
333. D₈	C₂×Q₈×C₁₃	semidirect
335. C₂×C₈	C₂×Q₈×C₁₃	semidirect
361. C₁₃	Q₈×#135	direct (N × H)
368. Q₈	C₁₃×#135	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₃×#41	2
C₁₃×#3383	2
Q₈×C₁₃×Q₁₆	2
C₁₃×#3381	2
C₁₃×#3380	2
Q₈×C₁₃×SD₁₆	2
Q₈×C₁₃×D₈	2
C₁₃×#3160	2
C₁₃×#3076	2
C₂×C₈×Q₈×C₁₃	2
C₄×C₁₃×#135	2
Q₈×#135	13

Subgroups — Q8×C13×#135 #15747696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₃×#135 #15747696