Subgroups — C₂²×C₄×#6129 #16769491

Order 3328.

12878 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6129	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6129	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
7	C₂²×#88135	C₂	1	2	yes	maximal, complemented
8	C₂²×#88146	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#88131	C₂	1	2	yes	maximal, complemented
10	C₂³×C₄×Dic₁₃	C₂	1	2	yes	maximal, complemented
11	C₂²×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
16	C₂⁴×Dic₁₃	C₂²	1	2	yes	—
17	C₂⁴×Dic₁₃	C₂²	1	2	yes	—
18	C₂²×#6129	C₄	1	32	yes	direct product factor
19	C₂²×#6129	C₂²	1	24	yes	—
20	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
22	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
23	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
29	C₂×D₄×Dic₁₃	C₂²	1	24	yes	complemented
30	C₂×C₄×C₂²⋊D₁₃	C₂²	1	48	yes	complemented
31	C₂²×#6103	C₂²	1	2	yes	—
32	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
33	C₂²×#6101	C₂²	1	2	yes	—
34	C₂²×#6101	C₂²	1	2	yes	—
35	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
39	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
40	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
41	C₂²×C₄×Dic₁₃	C₂²	1	48	yes	complemented
42	C₄×#6129	C₂²	1	256	yes	direct product factor
43	C₂×#88146	C₂²	1	24	yes	complemented
44	C₂×#88141	C₂²	1	24	yes	complemented
45	C₂×#88135	C₂²	1	48	yes	complemented
46	C₂×#88131	C₂²	1	48	yes	complemented
47	C₂×C₄²×D₁₃	C₂²	1	24	yes	complemented
48	C₂×C₄×Dic₂₆	C₂²	1	24	yes	complemented
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
52	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
53	C₂³×C₄×C₁₃	—	2	16	no	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₂²⋊D₁₃	C₂×C₄	1	32	yes	complemented
60	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
61	C₂³×Dic₁₃	—	2	16	no	—
62	C₂³×Dic₁₃	C₂×C₄	1	32	yes	complemented
63	C₂³×Dic₁₃	C₂³	1	24	yes	—
64	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
65	C₂³×Dic₁₃	C₂³	1	2	yes	—
66	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
67	C₂³×Dic₁₃	C₂³	1	2	yes	—
68	C₂³×Dic₁₃	C₂³	1	24	yes	—
69	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
70	C₂×#6129	C₂×C₄	1	384	yes	direct product factor
71	C₂×#6129	C₂³	1	64	yes	—
72	C₂²×C₄×D₁₃	—	2	8	no	—
73	C₂²×C₄×D₁₃	—	2	8	no	—
74	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	complemented
75	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
76	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
77	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
78	C₂²×Dic₂₆	C₂×C₄	1	16	yes	complemented
79	C₂²×Dic₂₆	C₂³	1	12	yes	—
80	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
83	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
84	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
85	D₄×Dic₁₃	C₂³	1	64	yes	complemented
86	C₄×C₂²⋊D₁₃	C₂³	1	128	yes	complemented
87	C₂×#6103	C₂³	1	24	yes	—
88	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
89	C₂×#6101	C₂³	1	24	yes	—
90	C₂×#6101	C₂³	1	24	yes	—
91	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
92	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
93	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
94	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
95	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
96	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
97	C₂×C₄×Dic₁₃	C₂³	1	128	yes	complemented
98	#88146	C₂³	1	64	yes	complemented
99	#88141	C₂³	1	64	yes	complemented
100	#88135	C₂³	1	128	yes	complemented
101	#88131	C₂³	1	128	yes	complemented
102	C₄²×D₁₃	C₂³	1	64	yes	complemented
103	C₄×Dic₂₆	C₂³	1	64	yes	complemented
104	C₂²×C₄×#41	—	13	1	no	maximal, Sylow
105	C₂⁴×C₁₃	—	2	8	no	—
106	C₂⁴×C₁₃	—	2	8	no	—
107	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
108	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂³×D₁₃	—	2	4	no	—
111	C₂³×D₁₃	—	2	4	no	—
112	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
113	C₂³×D₁₃	C₂⁴	1	6	yes	—
114	C₂×D₄×C₁₃	C₂²×C₄	1	96	yes	complemented
115	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	96	no	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
120	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
121	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
126	C₂×C₂²⋊D₁₃	C₂²×C₄	1	192	yes	complemented
127	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
128	C₂²×Dic₁₃	—	2	4	no	—
129	C₂²×Dic₁₃	—	2	8	no	—
130	C₂²×Dic₁₃	—	2	96	no	—
131	C₂²×Dic₁₃	C₂²×C₄	1	16	yes	—
132	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
133	C₂²×Dic₁₃	C₂²×C₄	1	192	yes	complemented
134	C₂²×Dic₁₃	#41	1	8	yes	complemented
135	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
136	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
137	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
138	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
139	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
140	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
141	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
142	#6129	C₂²×C₄	1	512	yes	direct product factor
143	C₂×C₄×D₁₃	—	2	48	no	—
144	C₂×C₄×D₁₃	—	2	48	no	—
145	C₂×C₄×D₁₃	C₂²×C₄	1	96	yes	complemented
146	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
147	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
148	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
149	C₂×Dic₂₆	C₂²×C₄	1	96	yes	complemented
150	C₂×Dic₂₆	C₂⁴	1	16	yes	—
151	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
152	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
153	C₄²×C₁₃	C₂⁴	1	16	yes	—
154	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
155	#6103	C₂⁴	1	32	yes	—
156	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
157	#6101	C₂⁴	1	32	yes	—
158	#6101	C₂⁴	1	32	yes	—
159	C₄×Dic₁₃	C₂⁴	1	32	yes	—
160	C₄×Dic₁₃	C₂⁴	1	16	yes	—
161	C₄×Dic₁₃	C₂⁴	1	16	yes	—
162	C₄×Dic₁₃	C₂⁴	1	16	yes	—
163	C₄×Dic₁₃	C₂⁴	1	32	yes	—
164	C₄×Dic₁₃	C₂⁴	1	32	yes	—
165	C₂³×#41	—	13	1	no	—
166	C₂×C₄×#41	—	13	48	no	—
167	C₂²×C₄×Q₈	—	13	1	no	—
168	C₂²×C₄×Q₈	—	13	1	no	—
169	C₂²×C₄×D₄	—	13	1	no	—
170	C₂²×C₄×D₄	—	13	2	no	—
171	C₂²×C₄×D₄	—	13	2	no	—
172	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
173	C₂²×#117	—	13	1	no	—
174	C₂²×#117	—	13	2	no	—
175	C₂³×C₄²	—	13	1	no	—
176	C₂³×C₄²	—	13	2	no	—
177	C₂³×C₁₃	—	2	64	no	—
178	C₂³×C₁₃	—	2	24	no	—
179	C₂³×C₁₃	—	2	24	no	—
180	C₂³×C₁₃	C₂³×C₄	1	48	yes	—
181	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
182	C₂³×C₁₃	C₂×#41	1	4	yes	—
183	C₂³×C₁₃	C₂×#41	1	4	yes	—
184	C₂³×C₁₃	C₂⁵	1	8	yes	—
185	C₂³×C₁₃	C₂⁵	1	3	yes	—
186	C₂²×D₁₃	—	2	32	no	—
187	C₂²×D₁₃	—	2	12	no	—
188	C₂²×D₁₃	—	2	12	no	—
189	C₂²×D₁₃	C₂³×C₄	1	24	yes	—
190	C₂²×D₁₃	C₂⁵	1	4	yes	—
191	D₄×C₁₃	C₂³×C₄	1	64	yes	complemented
192	C₂×C₄×C₁₃	—	2	12	no	—
193	C₂×C₄×C₁₃	—	2	24	no	—
194	C₂×C₄×C₁₃	—	2	64	no	—
195	C₂×C₄×C₁₃	C₂³×C₄	1	24	yes	—
196	C₂×C₄×C₁₃	C₂×#41	1	24	yes	complemented
197	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
198	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
199	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
200	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
201	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
202	C₂×Dic₁₃	—	2	12	no	—
203	C₂×Dic₁₃	—	2	24	no	—
204	C₂×Dic₁₃	—	2	64	no	—
205	C₂×Dic₁₃	C₂³×C₄	1	48	yes	—
206	C₂×Dic₁₃	C₂³×C₄	1	24	yes	—
207	C₂×Dic₁₃	C₂³×C₄	1	128	yes	complemented
208	C₂×Dic₁₃	C₂×#41	1	24	yes	complemented
209	C₂×Dic₁₃	C₂⁵	1	4	yes	—
210	C₂×Dic₁₃	C₂⁵	1	8	yes	—
211	C₂×Dic₁₃	C₂⁵	1	4	yes	—
212	C₂×Dic₁₃	C₂⁵	1	8	yes	—
213	C₂×Dic₁₃	C₂⁵	1	4	yes	—
214	C₄×D₁₃	—	2	32	no	—
215	C₄×D₁₃	—	2	32	no	—
216	C₄×D₁₃	C₂³×C₄	1	64	yes	complemented
217	Dic₂₆	C₂³×C₄	1	64	yes	complemented
218	C₂²×#41	—	13	32	no	—
219	C₂²×#41	—	13	24	no	—
220	C₂³×Q₈	—	13	1	no	—
221	C₂³×D₄	—	13	2	no	—
222	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
223	C₂⁴×C₄	—	13	2	no	—
224	C₂⁴×C₄	—	13	1	no	—
225	C₂⁴×C₄	—	13	2	no	—
226	C₂⁴×C₄	—	13	1	no	—
227	C₂⁴×C₄	—	13	1	no	—
228	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
229	C₄×#41	—	13	256	no	—
230	C₂×C₄×Q₈	—	13	24	no	—
231	C₂×C₄×Q₈	—	13	24	no	—
232	C₂×C₄×D₄	—	13	24	no	—
233	C₂×C₄×D₄	—	13	48	no	—
234	C₂×C₄×D₄	—	13	48	no	—
235	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	complemented
236	C₂×#117	—	13	24	no	—
237	C₂×#117	—	13	48	no	—
238	C₂²×C₄⋊C₄	—	13	2	no	—
239	C₂²×C₄⋊C₄	—	13	2	no	—
240	C₂²×C₄⋊C₄	—	13	1	no	—
241	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	—	13	2	no	—
243	C₂²×C₂²⋊C₄	—	13	2	no	—
244	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
245	C₂²×C₄²	—	13	2	no	—
246	C₂²×C₄²	—	13	1	no	—
247	C₂²×C₄²	—	13	2	no	—
248	C₂²×C₄²	—	13	1	no	—
249	C₂²×C₄²	—	13	48	no	—
250	C₂²×C₄²	—	13	1	no	—
251	C₂²×C₄²	—	13	2	no	—
252	C₂²×C₄²	—	13	24	no	—
253	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
254	C₂²×C₁₃	—	2	8	no	—
255	C₂²×C₁₃	—	2	8	no	—
256	C₂²×C₁₃	—	2	96	no	—
257	C₂²×C₁₃	C₄×#41	1	16	yes	complemented
258	C₂²×C₁₃	C₂⁴×C₄	1	16	yes	—
259	C₂²×C₁₃	C₂⁴×C₄	1	6	yes	—
260	C₂²×C₁₃	C₂²×#41	1	6	yes	—
261	C₂²×C₁₃	C₂²×#41	1	6	yes	—
262	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
263	C₂×D₁₃	—	2	4	no	—
264	C₂×D₁₃	—	2	4	no	—
265	C₂×D₁₃	—	2	48	no	—
266	C₂×D₁₃	C₂⁴×C₄	1	8	yes	—
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	2	8	no	—
269	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
270	C₄×C₁₃	C₂²×#41	1	8	yes	complemented
271	Dic₁₃	—	2	4	no	—
272	Dic₁₃	—	2	8	no	—
273	Dic₁₃	C₂⁴×C₄	1	16	yes	—
274	Dic₁₃	C₂⁴×C₄	1	8	yes	—
275	Dic₁₃	C₂²×#41	1	8	yes	complemented
276	C₂⁵	—	13	1	no	—
277	C₂⁵	C₂²×D₁₃	1	2	yes	—
278	C₂×#41	—	13	384	no	—
279	C₂×#41	—	13	64	no	—
280	C₂²×Q₈	—	13	16	no	—
281	C₂²×Q₈	—	13	12	no	—
282	C₂²×D₄	—	13	32	no	—
283	C₂²×D₄	—	13	24	no	—
284	C₂²×D₄	C₄×D₁₃	1	16	yes	complemented
285	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
286	C₂³×C₄	—	2	16	no	—
287	C₂³×C₄	—	13	32	no	—
288	C₂³×C₄	—	13	2	no	—
289	C₂³×C₄	—	13	24	no	—
290	C₂³×C₄	—	13	1	no	—
291	C₂³×C₄	—	13	1	no	—
292	C₂³×C₄	—	13	16	no	—
293	C₂³×C₄	—	13	12	no	—
294	C₂³×C₄	—	13	1	no	—
295	C₂³×C₄	—	13	2	no	—
296	C₂³×C₄	—	13	24	no	—
297	C₂³×C₄	—	13	12	no	—
298	C₂³×C₄	—	13	12	no	—
299	C₂³×C₄	—	26	8	no	—
300	C₂³×C₄	—	26	16	no	—
301	C₂³×C₄	—	26	8	no	—
302	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
303	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂²×D₁₃	1	24	yes	—
305	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
307	C₄×Q₈	—	13	64	no	—
308	C₄×Q₈	—	13	64	no	—
309	C₄×D₄	—	13	64	no	—
310	C₄×D₄	—	13	128	no	—
311	C₄×D₄	—	13	128	no	—
312	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
313	#117	—	13	64	no	—
314	#117	—	13	128	no	—
315	C₂×C₄⋊C₄	—	13	24	no	—
316	C₂×C₄⋊C₄	—	13	24	no	—
317	C₂×C₄⋊C₄	—	13	12	no	—
318	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	—
319	C₂×C₂²⋊C₄	—	13	24	no	—
320	C₂×C₂²⋊C₄	—	13	24	no	—
321	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
322	C₂×C₄²	—	13	24	no	—
323	C₂×C₄²	—	13	12	no	—
324	C₂×C₄²	—	13	24	no	—
325	C₂×C₄²	—	13	12	no	—
326	C₂×C₄²	—	13	24	no	—
327	C₂×C₄²	—	13	128	no	—
328	C₂×C₄²	—	13	12	no	—
329	C₂×C₄²	—	13	64	no	—
330	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
331	C₂×C₁₃	—	2	16	no	—
332	C₂×C₁₃	C₂×C₄×#41	1	12	yes	complemented
333	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
334	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
335	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
336	D₁₃	—	2	8	no	—
337	C₂⁴	—	2	8	no	—
338	C₂⁴	—	2	8	no	—
339	C₂⁴	—	13	8	no	—
340	C₂⁴	—	13	6	no	—
341	C₂⁴	—	26	4	no	—
342	C₂⁴	—	26	4	no	—
343	C₂⁴	C₂×C₄×D₁₃	1	16	yes	—
344	C₂⁴	C₂³×D₁₃	1	12	yes	—
345	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
346	#41	—	13	512	no	—
347	C₂×Q₈	—	13	96	no	—
348	C₂×Q₈	—	13	16	no	—
349	C₂×D₄	—	13	192	no	—
350	C₂×D₄	—	13	32	no	—
351	C₂×D₄	C₂×C₄×D₁₃	1	96	yes	complemented
352	C₂×D₄	C₂³×D₁₃	1	16	yes	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	96	no	—
356	C₂²×C₄	—	13	8	no	—
357	C₂²×C₄	—	13	16	no	—
358	C₂²×C₄	—	13	192	no	—
359	C₂²×C₄	—	13	8	no	—
360	C₂²×C₄	—	13	6	no	—
361	C₂²×C₄	—	13	6	no	—
362	C₂²×C₄	—	13	12	no	—
363	C₂²×C₄	—	13	32	no	—
364	C₂²×C₄	—	13	96	no	—
365	C₂²×C₄	—	13	16	no	—
366	C₂²×C₄	—	13	6	no	—
367	C₂²×C₄	—	13	12	no	—
368	C₂²×C₄	—	13	32	no	—
369	C₂²×C₄	—	13	16	no	—
370	C₂²×C₄	—	13	16	no	—
371	C₂²×C₄	—	26	48	no	—
372	C₂²×C₄	—	26	96	no	—
373	C₂²×C₄	—	26	4	no	—
374	C₂²×C₄	—	26	8	no	—
375	C₂²×C₄	—	26	48	no	—
376	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
377	C₂²×C₄	#6129	1	8	yes	direct product factor
378	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
379	C₂²×C₄	C₂³×D₁₃	1	32	yes	—
380	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
381	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
382	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
383	C₄⋊C₄	—	13	32	no	—
384	C₄⋊C₄	—	13	32	no	—
385	C₄⋊C₄	—	13	16	no	—
386	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
387	C₂²⋊C₄	—	13	32	no	—
388	C₂²⋊C₄	—	13	32	no	—
389	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
390	C₄²	—	13	16	no	—
391	C₄²	—	13	32	no	—
392	C₄²	—	13	16	no	—
393	C₄²	—	13	32	no	—
394	C₄²	—	13	16	no	—
395	C₄²	—	13	32	no	—
396	C₄²	C₂³×D₁₃	1	16	yes	—
397	C₁₃	C₂²×C₄×#41	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	2	64	no	—
399	C₂³	—	2	24	no	—
400	C₂³	—	2	24	no	—
401	C₂³	—	13	24	no	—
402	C₂³	—	13	4	no	—
403	C₂³	—	26	32	no	—
404	C₂³	—	26	12	no	—
405	C₂³	—	26	12	no	—
406	C₂³	C₂²×C₄×D₁₃	1	48	yes	—
407	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
408	C₂³	C₂×#6129	1	4	yes	—
409	C₂³	#41×D₁₃	1	4	yes	—
410	C₂³	C₂⁴×D₁₃	1	8	yes	—
411	C₂³	C₂⁴×D₁₃	1	3	yes	—
412	Q₈	—	13	64	no	—
413	D₄	—	13	128	no	—
414	D₄	C₂²×C₄×D₁₃	1	64	yes	complemented
415	C₂×C₄	—	2	24	no	—
416	C₂×C₄	—	2	12	no	—
417	C₂×C₄	—	2	64	no	—
418	C₂×C₄	—	13	24	no	—
419	C₂×C₄	—	13	48	no	—
420	C₂×C₄	—	13	128	no	—
421	C₂×C₄	—	13	24	no	—
422	C₂×C₄	—	13	4	no	—
423	C₂×C₄	—	13	4	no	—
424	C₂×C₄	—	13	8	no	—
425	C₂×C₄	—	13	64	no	—
426	C₂×C₄	—	13	8	no	—
427	C₂×C₄	—	13	4	no	—
428	C₂×C₄	—	26	32	no	—
429	C₂×C₄	—	26	64	no	—
430	C₂×C₄	—	26	12	no	—
431	C₂×C₄	—	26	24	no	—
432	C₂×C₄	—	26	32	no	—
433	C₂×C₄	C₂²×C₄×D₁₃	1	24	yes	—
434	C₂×C₄	C₂×#6129	1	24	yes	direct product factor
435	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
436	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
437	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
438	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
439	C₂²	—	2	96	no	—
440	C₂²	—	2	8	no	—
441	C₂²	—	2	8	no	—
442	C₂²	—	13	8	no	—
443	C₂²	—	26	48	no	—
444	C₂²	—	26	4	no	—
445	C₂²	—	26	4	no	—
446	C₂²	C₄×#6129	1	16	yes	direct product factor
447	C₂²	C₂³×C₄×D₁₃	1	16	yes	—
448	C₂²	C₂³×C₄×D₁₃	1	6	yes	—
449	C₂²	C₂²×#6129	1	6	yes	—
450	C₂²	C₂×#41×D₁₃	1	6	yes	—
451	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	2	8	no	—
454	C₄	—	13	8	no	—
455	C₄	—	13	16	no	—
456	C₄	—	13	8	no	—
457	C₄	—	26	8	no	—
458	C₄	—	26	4	no	—
459	C₄	C₂³×C₄×D₁₃	1	8	yes	—
460	C₄	C₂²×#6129	1	8	yes	direct product factor
461	C₂	—	2	16	no	—
462	C₂	—	26	8	no	—
463	C₂	C₂×C₄×#6129	1	12	yes	direct product factor
464	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
465	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
466	C₂	C₂³×#6129	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×#6129	C₂
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×C₄×#41
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#6129	C₂	direct (N × H)
3. C₂²×C₄×Dic₂₆	C₂	semidirect
4. C₂²×#88141	C₂	semidirect
5. C₂²×D₄×Dic₁₃	C₂	semidirect
6. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
7. C₂²×#88135	C₂	semidirect
8. C₂²×#88146	C₂	semidirect
9. C₂²×#88131	C₂	semidirect
10. C₂³×C₄×Dic₁₃	C₂	semidirect
11. C₂²×C₄²×D₁₃	C₂	semidirect
12. C₂²×C₄×D₄×C₁₃	C₂	semidirect
18. C₂²×#6129	C₄	direct (N × H)
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. C₂×D₄×Dic₁₃	C₂²	semidirect
30. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
41. C₂²×C₄×Dic₁₃	C₂²	semidirect
42. C₄×#6129	C₂²	direct (N × H)
43. C₂×#88146	C₂²	semidirect
44. C₂×#88141	C₂²	semidirect
45. C₂×#88135	C₂²	semidirect
46. C₂×#88131	C₂²	semidirect
47. C₂×C₄²×D₁₃	C₂²	semidirect
48. C₂×C₄×Dic₂₆	C₂²	semidirect
51. C₂²×D₄×C₁₃	C₂×C₄	semidirect
59. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
62. C₂³×Dic₁₃	C₂×C₄	semidirect
70. C₂×#6129	C₂×C₄	direct (N × H)
74. C₂²×C₄×D₁₃	C₂×C₄	semidirect
78. C₂²×Dic₂₆	C₂×C₄	semidirect
80. C₄×D₄×C₁₃	C₂³	semidirect
85. D₄×Dic₁₃	C₂³	semidirect
86. C₄×C₂²⋊D₁₃	C₂³	semidirect
97. C₂×C₄×Dic₁₃	C₂³	semidirect
98. #88146	C₂³	semidirect
99. #88141	C₂³	semidirect
100. #88135	C₂³	semidirect
101. #88131	C₂³	semidirect
102. C₄²×D₁₃	C₂³	semidirect
103. C₄×Dic₂₆	C₂³	semidirect
114. C₂×D₄×C₁₃	C₂²×C₄	semidirect
120. C₂²×C₄×C₁₃	#41	semidirect
126. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
133. C₂²×Dic₁₃	C₂²×C₄	semidirect
134. C₂²×Dic₁₃	#41	semidirect
142. #6129	C₂²×C₄	direct (N × H)
145. C₂×C₄×D₁₃	C₂²×C₄	semidirect
149. C₂×Dic₂₆	C₂²×C₄	semidirect
172. C₂²×C₄×D₄	D₁₃	semidirect
191. D₄×C₁₃	C₂³×C₄	semidirect
196. C₂×C₄×C₁₃	C₂×#41	semidirect
201. C₂²⋊D₁₃	C₂³×C₄	semidirect
207. C₂×Dic₁₃	C₂³×C₄	semidirect
208. C₂×Dic₁₃	C₂×#41	semidirect
216. C₄×D₁₃	C₂³×C₄	semidirect
217. Dic₂₆	C₂³×C₄	semidirect
235. C₂×C₄×D₄	C₂×D₁₃	semidirect
257. C₂²×C₁₃	C₄×#41	semidirect
270. C₄×C₁₃	C₂²×#41	semidirect
275. Dic₁₃	C₂²×#41	semidirect
284. C₂²×D₄	C₄×D₁₃	semidirect
312. C₄×D₄	C₂²×D₁₃	semidirect
332. C₂×C₁₃	C₂×C₄×#41	semidirect
351. C₂×D₄	C₂×C₄×D₁₃	semidirect
377. C₂²×C₄	#6129	direct (N × H)
397. C₁₃	C₂²×C₄×#41	semidirect
414. D₄	C₂²×C₄×D₁₃	semidirect
434. C₂×C₄	C₂×#6129	direct (N × H)
446. C₂²	C₄×#6129	direct (N × H)
460. C₄	C₂²×#6129	direct (N × H)
463. C₂	C₂×C₄×#6129	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×#6129	2
C₂×C₄×#6129	2
C₂²×C₄×Dic₂₆	2
C₂²×#88141	2
C₂²×D₄×Dic₁₃	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88135	2
C₂²×#88146	2
C₂²×#88131	2
C₂³×C₄×Dic₁₃	2
C₂²×C₄²×D₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂²×C₄×#41	13

Subgroups — C22×C4×#6129 #16769491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#6129 #16769491