Subgroups — C₂²×C₁₃×#554 #15749041

Order 3328.

8454 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₃×#125	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal
8	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	—
15	C₁₃×#554	C₂²	1	256	yes	direct product factor
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	24	yes	complemented
17	C₂×C₁₃×#125	C₂²	1	48	yes	complemented
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	96	yes	complemented
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	48	yes	complemented
20	C₂×C₄×Q₈×C₁₃	C₂²	1	24	yes	complemented
21	C₂×C₄×D₄×C₁₃	C₂²	1	48	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	48	yes	complemented
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
34	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
35	C₂⁵×C₁₃	C₂³	1	2	yes	—
36	C₂²×Q₈×C₁₃	—	2	8	no	—
37	C₂²×Q₈×C₁₃	—	4	8	no	—
38	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
39	C₂²×Q₈×C₁₃	C₂³	1	24	yes	—
40	C₂²×D₄×C₁₃	Q₈	1	16	yes	complemented
41	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
42	C₂³×C₄×C₁₃	—	2	16	no	—
43	C₂³×C₄×C₁₃	—	4	16	no	—
44	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	48	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂³	1	64	yes	complemented
54	C₁₃×#125	C₂³	1	128	yes	complemented
55	C₁₃×C₂²⋊Q₈	C₂³	1	256	yes	complemented
56	C₁₃×C₂²⋊Q₈	C₂³	1	128	yes	complemented
57	C₄×Q₈×C₁₃	C₂³	1	64	yes	complemented
58	C₄×D₄×C₁₃	C₂³	1	128	yes	—
59	C₄×D₄×C₁₃	C₂³	1	64	yes	—
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	128	yes	complemented
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
70	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
71	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
72	C₂²×#554	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	—	2	8	no	—
74	C₂⁴×C₁₃	—	2	8	no	—
75	C₂⁴×C₁₃	C₂×Q₈	1	16	yes	—
76	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
77	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
78	C₂×Q₈×C₁₃	—	2	48	no	—
79	C₂×Q₈×C₁₃	—	4	48	no	—
80	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
81	C₂×Q₈×C₁₃	C₂⁴	1	32	yes	—
82	C₂×D₄×C₁₃	C₂×Q₈	1	96	yes	complemented
83	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
84	C₂²×C₄×C₁₃	—	2	8	no	—
85	C₂²×C₄×C₁₃	—	2	8	no	—
86	C₂²×C₄×C₁₃	—	2	8	no	—
87	C₂²×C₄×C₁₃	—	2	16	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	96	no	—
90	C₂²×C₄×C₁₃	—	4	96	no	—
91	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
92	C₂²×C₄×C₁₃	#41	1	8	yes	—
93	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	64	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
102	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
103	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
104	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
105	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
106	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
107	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
108	C₁₃×C₄⋊C₄	C₂⁴	1	64	yes	—
109	C₁₃×C₂²⋊C₄	C₂⁴	1	64	yes	—
110	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
111	C₄²×C₁₃	C₂⁴	1	32	yes	—
112	C₄²×C₁₃	C₂⁴	1	16	yes	—
113	C₂×#554	C₂×C₁₃	1	48	yes	direct product factor
114	C₂²×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
115	C₂²×#125	C₂×C₁₃	1	2	yes	complemented
116	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	4	yes	complemented
117	C₂²×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
118	C₂²×C₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
120	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	—
121	C₂³×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
122	C₂³×C₁₃	—	2	64	no	—
123	C₂³×C₁₃	—	2	24	no	—
124	C₂³×C₁₃	—	2	24	no	—
125	C₂³×C₁₃	C₂²×Q₈	1	48	yes	—
126	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
127	C₂³×C₁₃	C₂×#41	1	4	yes	—
128	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
129	C₂³×C₁₃	C₂⁵	1	8	yes	—
130	C₂³×C₁₃	C₂⁵	1	3	yes	—
131	Q₈×C₁₃	—	2	32	no	—
132	Q₈×C₁₃	—	4	32	no	—
133	D₄×C₁₃	C₂²×Q₈	1	64	yes	complemented
134	C₂×C₄×C₁₃	—	2	24	no	—
135	C₂×C₄×C₁₃	—	2	24	no	—
136	C₂×C₄×C₁₃	—	2	24	no	—
137	C₂×C₄×C₁₃	—	2	48	no	—
138	C₂×C₄×C₁₃	—	2	12	no	—
139	C₂×C₄×C₁₃	—	2	64	no	—
140	C₂×C₄×C₁₃	—	4	64	no	—
141	C₂×C₄×C₁₃	C₂²×Q₈	1	24	yes	—
142	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
143	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
144	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
145	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
146	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
147	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
149	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
150	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
151	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
152	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
153	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
154	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	—
155	#554	C₂²×C₁₃	1	256	yes	direct product factor
156	C₂×C₄⋊Q₈	C₂²×C₁₃	1	24	yes	complemented
157	C₂×#125	C₂²×C₁₃	1	48	yes	complemented
158	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	96	yes	complemented
159	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	48	yes	complemented
160	C₂×C₄×Q₈	C₂²×C₁₃	1	24	yes	complemented
161	C₂×C₄×D₄	C₂²×C₁₃	1	48	yes	—
162	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	—
163	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
164	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
165	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
167	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
169	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
170	C₂²×C₄⋊C₄	C₂²×C₁₃	1	48	yes	complemented
171	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
172	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
173	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
174	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
175	C₂²×C₁₃	—	2	8	no	—
176	C₂²×C₁₃	—	2	8	no	—
177	C₂²×C₁₃	—	2	96	no	—
178	C₂²×C₁₃	#554	1	16	yes	direct product factor
179	C₂²×C₁₃	C₂³×Q₈	1	16	yes	—
180	C₂²×C₁₃	C₂³×Q₈	1	6	yes	—
181	C₂²×C₁₃	C₂²×#41	1	6	yes	—
182	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
183	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
184	C₄×C₁₃	—	2	8	no	—
185	C₄×C₁₃	—	2	8	no	—
186	C₄×C₁₃	—	2	8	no	—
187	C₄×C₁₃	—	2	16	no	—
188	C₄×C₁₃	—	2	4	no	—
189	C₄×C₁₃	C₂³×Q₈	1	8	yes	—
190	C₄×C₁₃	C₂²×#41	1	8	yes	—
191	C₂⁵	C₂³×C₁₃	1	2	yes	—
192	C₂²×Q₈	—	2	8	no	—
193	C₂²×Q₈	—	4	8	no	—
194	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
195	C₂²×Q₈	C₂³×C₁₃	1	24	yes	—
196	C₂²×D₄	Q₈×C₁₃	1	16	yes	complemented
197	C₂²×D₄	C₂³×C₁₃	1	12	yes	—
198	C₂³×C₄	—	2	16	no	—
199	C₂³×C₄	—	4	16	no	—
200	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
201	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
203	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
204	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	24	yes	—
206	C₂³×C₄	C₂³×C₁₃	1	48	yes	—
207	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
209	C₄⋊Q₈	C₂³×C₁₃	1	64	yes	complemented
210	#125	C₂³×C₁₃	1	128	yes	complemented
211	C₂²⋊Q₈	C₂³×C₁₃	1	256	yes	complemented
212	C₂²⋊Q₈	C₂³×C₁₃	1	128	yes	complemented
213	C₄×Q₈	C₂³×C₁₃	1	64	yes	complemented
214	C₄×D₄	C₂³×C₁₃	1	128	yes	—
215	C₄×D₄	C₂³×C₁₃	1	64	yes	—
216	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
217	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
218	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
219	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
222	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
223	C₂×C₄⋊C₄	C₂³×C₁₃	1	128	yes	complemented
224	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₁₃	1	24	yes	—
226	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
227	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
228	C₂×C₁₃	—	2	16	no	—
229	C₂×C₁₃	C₂×#554	1	12	yes	direct product factor
230	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
231	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
232	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
233	C₂⁴	—	2	8	no	—
234	C₂⁴	—	2	8	no	—
235	C₂⁴	C₂×Q₈×C₁₃	1	16	yes	—
236	C₂⁴	C₂⁴×C₁₃	1	12	yes	—
237	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
238	C₂×Q₈	—	2	48	no	—
239	C₂×Q₈	—	4	48	no	—
240	C₂×Q₈	C₂⁴×C₁₃	1	16	yes	—
241	C₂×Q₈	C₂⁴×C₁₃	1	32	yes	—
242	C₂×D₄	C₂×Q₈×C₁₃	1	96	yes	complemented
243	C₂×D₄	C₂⁴×C₁₃	1	16	yes	—
244	C₂²×C₄	—	2	8	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	16	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	96	no	—
250	C₂²×C₄	—	4	96	no	—
251	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
252	C₂²×C₄	C₁₃×#41	1	8	yes	—
253	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
254	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
255	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
256	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
257	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
258	C₂²×C₄	C₂⁴×C₁₃	1	32	yes	—
259	C₂²×C₄	C₂⁴×C₁₃	1	64	yes	—
260	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
261	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
262	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
263	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
264	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
265	C₄⋊C₄	C₂⁴×C₁₃	1	16	yes	—
266	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
267	C₄⋊C₄	C₂⁴×C₁₃	1	32	yes	—
268	C₄⋊C₄	C₂⁴×C₁₃	1	64	yes	—
269	C₂²⋊C₄	C₂⁴×C₁₃	1	64	yes	—
270	C₂²⋊C₄	C₂⁴×C₁₃	1	32	yes	—
271	C₄²	C₂⁴×C₁₃	1	32	yes	—
272	C₄²	C₂⁴×C₁₃	1	16	yes	—
273	C₁₃	C₂²×#554	1	1	yes	characteristic, direct product factor, Sylow
274	C₂³	—	2	64	no	—
275	C₂³	—	2	24	no	—
276	C₂³	—	2	24	no	—
277	C₂³	C₂²×Q₈×C₁₃	1	48	yes	—
278	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
279	C₂³	C₂×C₁₃×#41	1	4	yes	—
280	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
281	C₂³	C₂⁵×C₁₃	1	8	yes	—
282	C₂³	C₂⁵×C₁₃	1	3	yes	—
283	Q₈	—	2	32	no	—
284	Q₈	—	4	32	no	—
285	D₄	C₂²×Q₈×C₁₃	1	64	yes	complemented
286	C₂×C₄	—	2	24	no	—
287	C₂×C₄	—	2	24	no	—
288	C₂×C₄	—	2	24	no	—
289	C₂×C₄	—	2	48	no	—
290	C₂×C₄	—	2	12	no	—
291	C₂×C₄	—	2	64	no	—
292	C₂×C₄	—	4	64	no	—
293	C₂×C₄	C₂²×Q₈×C₁₃	1	24	yes	—
294	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
295	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
296	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
297	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
298	C₂×C₄	C₂⁵×C₁₃	1	8	yes	—
299	C₂×C₄	C₂⁵×C₁₃	1	16	yes	—
300	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
301	C₂×C₄	C₂⁵×C₁₃	1	4	yes	—
302	C₂²	—	2	8	no	—
303	C₂²	—	2	8	no	—
304	C₂²	—	2	96	no	—
305	C₂²	C₁₃×#554	1	16	yes	direct product factor
306	C₂²	C₂³×Q₈×C₁₃	1	16	yes	—
307	C₂²	C₂³×Q₈×C₁₃	1	6	yes	—
308	C₂²	C₂²×C₁₃×#41	1	6	yes	—
309	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	6	yes	—
310	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
311	C₄	—	2	8	no	—
312	C₄	—	2	8	no	—
313	C₄	—	2	8	no	—
314	C₄	—	2	16	no	—
315	C₄	—	2	4	no	—
316	C₄	C₂³×Q₈×C₁₃	1	8	yes	—
317	C₄	C₂²×C₁₃×#41	1	8	yes	—
318	C₂	—	2	16	no	—
319	C₂	C₂×C₁₃×#554	1	12	yes	direct product factor
320	C₂	C₂⁴×Q₈×C₁₃	1	1	yes	characteristic
321	C₂	C₂³×C₁₃×#41	1	1	yes	characteristic
322	C₂	C₂²×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	direct (N × H)
2. C₂²×C₁₃×C₄⋊Q₈	C₂	semidirect
3. C₂²×C₁₃×#125	C₂	semidirect
4. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
5. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₄×Q₈×C₁₃	C₂	semidirect
9. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
15. C₁₃×#554	C₂²	direct (N × H)
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₁₃×#125	C₂²	semidirect
18. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
19. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
40. C₂²×D₄×C₁₃	Q₈	semidirect
53. C₁₃×C₄⋊Q₈	C₂³	semidirect
54. C₁₃×#125	C₂³	semidirect
55. C₁₃×C₂²⋊Q₈	C₂³	semidirect
56. C₁₃×C₂²⋊Q₈	C₂³	semidirect
57. C₄×Q₈×C₁₃	C₂³	semidirect
67. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
72. C₂²×#554	C₁₃	direct (N × H)
82. C₂×D₄×C₁₃	C₂×Q₈	semidirect
113. C₂×#554	C₂×C₁₃	direct (N × H)
114. C₂²×C₄⋊Q₈	C₂×C₁₃	semidirect
115. C₂²×#125	C₂×C₁₃	semidirect
116. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
117. C₂²×C₂²⋊Q₈	C₂×C₁₃	semidirect
118. C₂²×C₄×Q₈	C₂×C₁₃	semidirect
121. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
133. D₄×C₁₃	C₂²×Q₈	semidirect
155. #554	C₂²×C₁₃	direct (N × H)
156. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
157. C₂×#125	C₂²×C₁₃	semidirect
158. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
159. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
160. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
170. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
178. C₂²×C₁₃	#554	direct (N × H)
196. C₂²×D₄	Q₈×C₁₃	semidirect
209. C₄⋊Q₈	C₂³×C₁₃	semidirect
210. #125	C₂³×C₁₃	semidirect
211. C₂²⋊Q₈	C₂³×C₁₃	semidirect
212. C₂²⋊Q₈	C₂³×C₁₃	semidirect
213. C₄×Q₈	C₂³×C₁₃	semidirect
223. C₂×C₄⋊C₄	C₂³×C₁₃	semidirect
229. C₂×C₁₃	C₂×#554	direct (N × H)
242. C₂×D₄	C₂×Q₈×C₁₃	semidirect
273. C₁₃	C₂²×#554	direct (N × H)
285. D₄	C₂²×Q₈×C₁₃	semidirect
305. C₂²	C₁₃×#554	direct (N × H)
319. C₂	C₂×C₁₃×#554	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×#554	2
C₂²×C₁₃×C₄⋊Q₈	2
C₂²×C₁₃×#125	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×C₄×Q₈×C₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
C₂²×#554	13

Subgroups — C22×C13×#554 #15749041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×#554 #15749041