Subgroups — C₂×C₄×C₁₃×C₂²⋊Q₈ #15720369

Order 3328.

3854 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³×C₄×C₁₃	C₂³
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
4. C₄×C₁₃×C₂²⋊Q₈	C₂	direct (N × H)
5. C₂×C₁₃×#391	C₂	semidirect
6. C₂×C₁₃×#389	C₂	semidirect
7. C₂×C₁₃×#387	C₂	semidirect
10. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
11. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
17. C₂×C₁₃×C₂²⋊Q₈	C₄	direct (N × H)
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#391	C₂²	semidirect
38. C₁₃×#389	C₂²	semidirect
39. C₁₃×#387	C₂²	semidirect
42. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
43. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
53. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
63. C₂³×C₄×C₁₃	Q₈	semidirect
77. C₁₃×C₂²⋊Q₈	C₂×C₄	direct (N × H)
83. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
84. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
113. C₂×C₄×C₂²⋊Q₈	C₁₃	direct (N × H)
126. C₂×Q₈×C₁₃	C₂²×C₄	semidirect
165. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
183. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
184. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
194. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
196. C₄×C₂²⋊Q₈	C₂×C₁₃	direct (N × H)
197. C₂×#391	C₂×C₁₃	semidirect
198. C₂×#389	C₂×C₁₃	semidirect
199. C₂×#387	C₂×C₁₃	semidirect
202. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
203. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
215. C₂³×C₁₃	C₄×Q₈	semidirect
258. C₂×C₄×C₁₃	C₂²⋊Q₈	direct (N × H)
275. C₂×C₂²⋊Q₈	C₄×C₁₃	direct (N × H)
278. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
295. #391	C₂²×C₁₃	semidirect
296. #389	C₂²×C₁₃	semidirect
297. #387	C₂²×C₁₃	semidirect
300. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
301. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
317. C₂²×C₁₃	C₂×C₄×Q₈	semidirect
339. C₄×C₁₃	C₂×C₂²⋊Q₈	direct (N × H)
343. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
353. C₂³×C₄	Q₈×C₁₃	semidirect
367. C₂²⋊Q₈	C₂×C₄×C₁₃	direct (N × H)
373. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
374. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
404. C₂×C₁₃	C₄×C₂²⋊Q₈	direct (N × H)
424. C₂×Q₈	C₂²×C₄×C₁₃	semidirect
463. C₂²×C₄	C₂×Q₈×C₁₃	semidirect
481. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
482. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
491. C₁₃	C₂×C₄×C₂²⋊Q₈	direct (N × H)
502. C₂³	C₄×Q₈×C₁₃	semidirect
545. C₂×C₄	C₁₃×C₂²⋊Q₈	direct (N × H)
567. C₂²	C₂×C₄×Q₈×C₁₃	semidirect
589. C₄	C₂×C₁₃×C₂²⋊Q₈	direct (N × H)
591. C₂	C₄×C₁₃×C₂²⋊Q₈	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×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₃	2
C₂³×C₄²×C₁₃	2
C₄×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#391	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₁₃×#385	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×C₄×C₂²⋊Q₈	13

Subgroups — C2×C4×C13×C22⋊Q8 #15720369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₃×C₂²⋊Q₈ #15720369