Subgroups — C₂²×#11719364 #16769899

Order 3328.

9526 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719364	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88133	C₂	1	2	yes	maximal, complemented
3	C₂²×#88190	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88137	C₂	1	2	yes	maximal, complemented
5	C₂²×#88150	C₂	1	2	yes	maximal, complemented
6	C₂²×#88191	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
8	C₂²×#88146	C₂	1	2	yes	maximal, complemented
9	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
15	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
16	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
17	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₁₃×#123	C₂²	1	24	yes	complemented
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
25	C₂×#88191	C₂²	1	24	yes	—
26	C₂×#88190	C₂²	1	24	yes	complemented
27	C₂×C₄×C₂²⋊D₁₃	C₂²	1	48	yes	complemented
28	C₂²×#6103	C₂²	1	2	yes	—
29	C₂²×#6103	C₂²	1	2	yes	—
30	C₂²×#6103	C₂²	1	2	yes	—
31	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
32	C₂²×#6101	C₂²	1	2	yes	complemented
33	C₂²×#6101	C₂²	1	2	yes	complemented
34	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	complemented
36	#11719364	C₂²	1	256	yes	direct product factor
37	C₂×#88150	C₂²	1	48	yes	complemented
38	C₂×#88146	C₂²	1	48	yes	complemented
39	C₂×#88137	C₂²	1	48	yes	complemented
40	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	complemented
41	C₂×#88133	C₂²	1	48	yes	complemented
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
44	C₂⁴×D₁₃	—	2	16	no	—
45	C₂⁴×D₁₃	—	4	4	no	—
46	C₂⁴×D₁₃	C₂³	1	12	yes	—
47	C₂⁴×D₁₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₃	—	4	4	no	—
49	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
50	C₂³×C₄×C₁₃	—	4	4	no	—
51	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	12	yes	complemented
55	C₂²×C₂²⋊D₁₃	—	2	16	no	—
56	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
57	C₂³×Dic₁₃	C₂³	1	2	yes	—
58	C₂³×Dic₁₃	C₂³	1	2	yes	—
59	C₂³×Dic₁₃	C₂³	1	2	yes	—
60	C₂²×C₄×D₁₃	—	2	16	no	—
61	C₂²×C₄×D₁₃	—	4	8	no	—
62	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
63	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
64	C₂²×Dic₂₆	—	4	4	no	—
65	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
66	C₁₃×#123	C₂³	1	64	yes	complemented
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	complemented
70	C₂×C₂²⋊Dic₁₃	C₂³	1	12	yes	—
71	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
72	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	complemented
73	#88191	C₂³	1	64	yes	—
74	#88190	C₂³	1	64	yes	complemented
75	C₄×C₂²⋊D₁₃	C₂³	1	128	yes	complemented
76	C₂×#6103	C₂³	1	24	yes	—
77	C₂×#6103	C₂³	1	24	yes	—
78	C₂×#6103	C₂³	1	24	yes	—
79	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
80	C₂×#6101	C₂³	1	24	yes	complemented
81	C₂×#6101	C₂³	1	24	yes	complemented
82	C₂×C₄×Dic₁₃	C₂³	1	24	yes	complemented
83	C₂×C₄×Dic₁₃	C₂³	1	12	yes	complemented
84	#88150	C₂³	1	128	yes	complemented
85	#88146	C₂³	1	128	yes	complemented
86	#88137	C₂³	1	128	yes	complemented
87	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	complemented
88	#88133	C₂³	1	128	yes	complemented
89	C₂²×#551	—	13	1	no	maximal, Sylow
90	C₂⁴×C₁₃	—	2	8	no	—
91	C₂⁴×C₁₃	—	2	8	no	—
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
95	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
96	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₂³×D₁₃	—	2	8	no	—
98	C₂³×D₁₃	—	2	8	no	—
99	C₂³×D₁₃	—	2	96	no	—
100	C₂³×D₁₃	—	4	24	no	—
101	C₂³×D₁₃	—	4	64	no	—
102	C₂³×D₁₃	#41	1	16	yes	—
103	C₂³×D₁₃	C₂⁴	1	16	yes	—
104	C₂³×D₁₃	C₂⁴	1	12	yes	—
105	C₂×D₄×C₁₃	—	4	24	no	—
106	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
107	C₂²×C₄×C₁₃	—	2	8	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	4	24	no	—
111	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
113	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
115	C₂×C₂²⋊D₁₃	—	2	96	no	—
116	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
117	C₂²×Dic₁₃	—	2	8	no	—
118	C₂²×Dic₁₃	—	2	8	no	—
119	C₂²×Dic₁₃	—	2	8	no	—
120	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
121	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
122	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
123	C₂×C₄×D₁₃	—	2	96	no	—
124	C₂×C₄×D₁₃	—	4	48	no	—
125	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
126	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
127	C₂×Dic₂₆	—	4	24	no	—
128	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
129	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
130	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
131	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
132	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
133	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
134	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
135	#6103	C₂⁴	1	32	yes	—
136	#6103	C₂⁴	1	32	yes	—
137	#6103	C₂⁴	1	32	yes	—
138	C₄⋊Dic₁₃	C₂⁴	1	32	yes	complemented
139	#6101	C₂⁴	1	32	yes	complemented
140	#6101	C₂⁴	1	32	yes	complemented
141	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
142	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
143	C₂×#551	—	13	48	no	—
144	C₂²×#126	—	13	2	no	—
145	C₂²×#124	—	13	1	no	—
146	C₂²×#123	—	13	2	no	—
147	C₂²×#123	D₁₃	1	1	yes	characteristic, complemented
148	C₂²×C₂²⋊Q₈	—	13	2	no	—
149	C₂²×#120	—	13	1	no	—
150	C₂²×C₄×D₄	—	13	2	no	—
151	C₂²×#117	—	13	2	no	—
152	C₂³×C₂²⋊C₄	—	13	2	no	—
153	C₂³×C₁₃	—	2	24	no	—
154	C₂³×C₁₃	—	2	24	no	—
155	C₂³×C₁₃	—	2	12	no	—
156	C₂³×C₁₃	—	2	12	no	—
157	C₂³×C₁₃	—	4	16	no	—
158	C₂³×C₁₃	—	4	16	no	—
159	C₂³×C₁₃	C₂×#41	1	8	yes	—
160	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
161	C₂³×C₁₃	C₂⁵	1	4	yes	—
162	C₂³×C₁₃	C₂⁵	1	4	yes	—
163	C₂³×C₁₃	C₂⁵	1	3	yes	—
164	C₂²×D₁₃	—	2	64	no	—
165	C₂²×D₁₃	—	2	24	no	—
166	C₂²×D₁₃	—	2	24	no	—
167	C₂²×D₁₃	—	2	64	no	—
168	C₂²×D₁₃	—	4	16	no	—
169	C₂²×D₁₃	—	4	192	no	—
170	C₂²×D₁₃	C₂×#41	1	48	yes	—
171	C₂²×D₁₃	C₂⁵	1	8	yes	—
172	D₄×C₁₃	—	4	16	no	—
173	C₂×C₄×C₁₃	—	2	24	no	—
174	C₂×C₄×C₁₃	—	2	12	no	—
175	C₂×C₄×C₁₃	—	2	24	no	—
176	C₂×C₄×C₁₃	—	4	16	no	—
177	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
178	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
179	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
180	C₂²⋊D₁₃	—	2	64	no	—
181	C₂×Dic₁₃	—	2	24	no	—
182	C₂×Dic₁₃	—	2	24	no	—
183	C₂×Dic₁₃	—	2	24	no	—
184	C₂×Dic₁₃	C₂⁵	1	8	yes	—
185	C₂×Dic₁₃	C₂⁵	1	8	yes	—
186	C₂×Dic₁₃	C₂⁵	1	8	yes	—
187	C₄×D₁₃	—	2	64	no	—
188	C₄×D₁₃	—	4	32	no	—
189	Dic₂₆	—	4	16	no	—
190	C₂⁶	—	13	1	no	—
191	C₂³×Q₈	—	13	1	no	—
192	C₂³×D₄	—	13	2	no	—
193	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
194	C₂⁴×C₄	—	13	2	no	—
195	C₂⁴×C₄	—	13	2	no	—
196	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
197	#551	—	13	256	no	—
198	C₂×#126	—	13	48	no	—
199	C₂×#124	—	13	24	no	—
200	C₂×#123	—	13	48	no	—
201	C₂×#123	C₂×D₁₃	1	24	yes	complemented
202	C₂×C₂²⋊Q₈	—	13	48	no	—
203	C₂×#120	—	13	24	no	—
204	C₂×C₄×D₄	—	13	48	no	—
205	C₂×#117	—	13	48	no	—
206	C₂²×C₄⋊C₄	—	13	2	no	—
207	C₂²×C₄⋊C₄	—	13	2	no	—
208	C₂²×C₄⋊C₄	—	13	2	no	—
209	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
210	C₂²×C₂²⋊C₄	—	13	2	no	—
211	C₂²×C₂²⋊C₄	—	13	2	no	—
212	C₂²×C₂²⋊C₄	—	13	1	no	—
213	C₂²×C₂²⋊C₄	—	13	2	no	—
214	C₂²×C₂²⋊C₄	—	13	2	no	—
215	C₂²×C₂²⋊C₄	—	13	2	no	—
216	C₂²×C₂²⋊C₄	—	13	48	no	—
217	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
218	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
219	C₂²×C₄²	—	13	1	no	—
220	C₂²×C₄²	—	13	2	no	—
221	C₂²×C₁₃	—	2	8	no	—
222	C₂²×C₁₃	—	2	8	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	2	4	no	—
225	C₂²×C₁₃	—	4	24	no	—
226	C₂²×C₁₃	—	4	24	no	—
227	C₂²×C₁₃	#551	1	16	yes	complemented
228	C₂²×C₁₃	C₂²×#41	1	12	yes	—
229	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
230	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
231	C₂×D₁₃	—	2	8	no	—
232	C₂×D₁₃	—	2	8	no	—
233	C₂×D₁₃	—	2	96	no	—
234	C₂×D₁₃	—	4	64	no	—
235	C₂×D₁₃	C₂²×#41	1	16	yes	—
236	C₄×C₁₃	—	2	8	no	—
237	C₄×C₁₃	—	2	4	no	—
238	C₄×C₁₃	—	2	8	no	—
239	Dic₁₃	—	2	8	no	—
240	Dic₁₃	—	2	8	no	—
241	Dic₁₃	—	2	8	no	—
242	C₂⁵	—	13	2	no	—
243	C₂⁵	—	13	12	no	—
244	C₂⁵	—	26	16	no	—
245	C₂⁵	—	52	4	no	—
246	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
247	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
248	C₂²×Q₈	—	13	12	no	—
249	C₂²×Q₈	—	52	4	no	—
250	C₂²×D₄	—	4	4	no	—
251	C₂²×D₄	—	13	24	no	—
252	C₂²×D₄	—	26	16	no	—
253	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
254	C₂³×C₄	—	4	4	no	—
255	C₂³×C₄	—	13	2	no	—
256	C₂³×C₄	—	13	2	no	—
257	C₂³×C₄	—	13	2	no	—
258	C₂³×C₄	—	13	24	no	—
259	C₂³×C₄	—	13	24	no	—
260	C₂³×C₄	—	26	16	no	—
261	C₂³×C₄	—	52	8	no	—
262	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
263	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
264	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
265	C₂³×C₄	C₂²×D₁₃	1	12	yes	complemented
266	#126	—	13	128	no	—
267	#124	—	13	64	no	—
268	#123	—	13	128	no	—
269	#123	C₂²×D₁₃	1	64	yes	complemented
270	C₂²⋊Q₈	—	13	128	no	—
271	#120	—	13	64	no	—
272	C₄×D₄	—	13	128	no	—
273	#117	—	13	128	no	—
274	C₂×C₄⋊C₄	—	13	24	no	—
275	C₂×C₄⋊C₄	—	13	24	no	—
276	C₂×C₄⋊C₄	—	13	24	no	—
277	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
278	C₂×C₂²⋊C₄	—	13	24	no	—
279	C₂×C₂²⋊C₄	—	13	24	no	—
280	C₂×C₂²⋊C₄	—	13	12	no	—
281	C₂×C₂²⋊C₄	—	13	24	no	—
282	C₂×C₂²⋊C₄	—	13	24	no	—
283	C₂×C₂²⋊C₄	—	13	24	no	—
284	C₂×C₂²⋊C₄	—	13	128	no	—
285	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
286	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	complemented
287	C₂×C₄²	—	13	12	no	—
288	C₂×C₄²	—	13	24	no	—
289	C₂×C₁₃	—	4	4	no	—
290	C₂×C₁₃	—	4	4	no	—
291	C₂×C₁₃	C₂×#551	1	12	yes	complemented
292	C₂×C₁₃	C₂³×#41	1	2	yes	—
293	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
294	D₁₃	—	2	16	no	—
295	C₂⁴	—	2	4	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	2	8	no	—
299	C₂⁴	—	13	16	no	—
300	C₂⁴	—	13	12	no	—
301	C₂⁴	—	13	16	no	—
302	C₂⁴	—	26	96	no	—
303	C₂⁴	—	26	8	no	—
304	C₂⁴	—	26	8	no	—
305	C₂⁴	—	52	24	no	—
306	C₂⁴	—	52	64	no	—
307	C₂⁴	C₂³×D₁₃	1	6	yes	—
308	C₂⁴	C₂³×D₁₃	1	6	yes	—
309	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
310	C₂×Q₈	—	13	16	no	—
311	C₂×Q₈	—	52	24	no	—
312	C₂×D₄	—	4	24	no	—
313	C₂×D₄	—	13	32	no	—
314	C₂×D₄	—	26	96	no	—
315	C₂×D₄	C₂³×D₁₃	1	16	yes	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	4	24	no	—
320	C₂²×C₄	—	13	12	no	—
321	C₂²×C₄	—	13	12	no	—
322	C₂²×C₄	—	13	12	no	—
323	C₂²×C₄	—	13	32	no	—
324	C₂²×C₄	—	13	32	no	—
325	C₂²×C₄	—	26	96	no	—
326	C₂²×C₄	—	26	8	no	—
327	C₂²×C₄	—	26	8	no	—
328	C₂²×C₄	—	26	8	no	—
329	C₂²×C₄	—	52	48	no	—
330	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
331	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
332	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
333	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
334	C₄⋊C₄	—	13	32	no	—
335	C₄⋊C₄	—	13	32	no	—
336	C₄⋊C₄	—	13	32	no	—
337	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
338	C₂²⋊C₄	—	13	32	no	—
339	C₂²⋊C₄	—	13	32	no	—
340	C₂²⋊C₄	—	13	16	no	—
341	C₂²⋊C₄	—	13	32	no	—
342	C₂²⋊C₄	—	13	32	no	—
343	C₂²⋊C₄	—	13	32	no	—
344	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
345	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
346	C₄²	—	13	16	no	—
347	C₄²	—	13	32	no	—
348	C₁₃	C₂²×#551	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	2	12	no	—
350	C₂³	—	2	12	no	—
351	C₂³	—	2	24	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	4	16	no	—
354	C₂³	—	4	16	no	—
355	C₂³	—	13	48	no	—
356	C₂³	—	13	8	no	—
357	C₂³	—	26	64	no	—
358	C₂³	—	26	64	no	—
359	C₂³	—	26	24	no	—
360	C₂³	—	26	24	no	—
361	C₂³	—	52	16	no	—
362	C₂³	—	52	192	no	—
363	C₂³	#88251	1	4	yes	—
364	C₂³	#41×D₁₃	1	8	yes	—
365	C₂³	C₂⁴×D₁₃	1	4	yes	—
366	C₂³	C₂⁴×D₁₃	1	4	yes	—
367	C₂³	C₂⁴×D₁₃	1	3	yes	—
368	Q₈	—	52	16	no	—
369	D₄	—	4	16	no	—
370	D₄	—	26	64	no	—
371	C₂×C₄	—	2	24	no	—
372	C₂×C₄	—	2	12	no	—
373	C₂×C₄	—	2	24	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	—	13	8	no	—
376	C₂×C₄	—	13	8	no	—
377	C₂×C₄	—	13	8	no	—
378	C₂×C₄	—	26	64	no	—
379	C₂×C₄	—	26	24	no	—
380	C₂×C₄	—	26	24	no	—
381	C₂×C₄	—	26	24	no	—
382	C₂×C₄	—	52	32	no	—
383	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
384	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
385	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
386	C₂²	—	2	8	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	24	no	—
391	C₂²	—	4	24	no	—
392	C₂²	—	13	16	no	—
393	C₂²	—	26	96	no	—
394	C₂²	—	26	8	no	—
395	C₂²	—	26	8	no	—
396	C₂²	—	52	64	no	—
397	C₂²	#11719364	1	16	yes	direct product factor
398	C₂²	C₂×#88251	1	6	yes	—
399	C₂²	C₂×#41×D₁₃	1	12	yes	—
400	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	8	no	—
403	C₄	—	2	4	no	—
404	C₄	—	26	8	no	—
405	C₄	—	26	8	no	—
406	C₄	—	26	8	no	—
407	C₂	—	4	4	no	—
408	C₂	—	4	4	no	—
409	C₂	—	26	16	no	—
410	C₂	C₂×#11719364	1	12	yes	direct product factor
411	C₂	C₂²×#41×D₁₃	1	2	yes	—
412	C₂	C₂²×#88251	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#123	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂²×#88191	C₂
hypercenter	C₂²×#123	D₁₃
hypocenter	C₁₃	C₂²×#551
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#123

Complements

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

N	H ≅ G/N	type
1. C₂×#11719364	C₂	direct (N × H)
2. C₂²×#88133	C₂	semidirect
3. C₂²×#88190	C₂	semidirect
4. C₂²×#88137	C₂	semidirect
5. C₂²×#88150	C₂	semidirect
7. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
8. C₂²×#88146	C₂	semidirect
9. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
10. C₂²×C₁₃×#123	C₂	semidirect
13. C₂⁴×C₄×C₁₃	C₂²	semidirect
17. C₂³×Dic₂₆	C₂²	semidirect
18. C₂×C₁₃×#123	C₂²	semidirect
19. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
21. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
24. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
26. C₂×#88190	C₂²	semidirect
27. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
31. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
32. C₂²×#6101	C₂²	semidirect
33. C₂²×#6101	C₂²	semidirect
34. C₂²×C₄×Dic₁₃	C₂²	semidirect
35. C₂²×C₄×Dic₁₃	C₂²	semidirect
36. #11719364	C₂²	direct (N × H)
37. C₂×#88150	C₂²	semidirect
38. C₂×#88146	C₂²	semidirect
39. C₂×#88137	C₂²	semidirect
40. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
41. C₂×#88133	C₂²	semidirect
54. C₂³×C₄×C₁₃	C₂³	semidirect
65. C₂²×Dic₂₆	C₂³	semidirect
66. C₁₃×#123	C₂³	semidirect
67. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
69. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
72. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
74. #88190	C₂³	semidirect
75. C₄×C₂²⋊D₁₃	C₂³	semidirect
79. C₂×C₄⋊Dic₁₃	C₂³	semidirect
80. C₂×#6101	C₂³	semidirect
81. C₂×#6101	C₂³	semidirect
82. C₂×C₄×Dic₁₃	C₂³	semidirect
83. C₂×C₄×Dic₁₃	C₂³	semidirect
84. #88150	C₂³	semidirect
85. #88146	C₂³	semidirect
86. #88137	C₂³	semidirect
87. C₂²⋊C₄×D₁₃	C₂³	semidirect
88. #88133	C₂³	semidirect
114. C₂²×C₄×C₁₃	C₂⁴	semidirect
128. C₂×Dic₂₆	C₂⁴	semidirect
129. C₁₃×C₄⋊C₄	C₂⁴	semidirect
131. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
134. C₂²⋊Dic₁₃	C₂⁴	semidirect
138. C₄⋊Dic₁₃	C₂⁴	semidirect
139. #6101	C₂⁴	semidirect
140. #6101	C₂⁴	semidirect
141. C₄×Dic₁₃	C₂⁴	semidirect
142. C₄×Dic₁₃	C₂⁴	semidirect
147. C₂²×#123	D₁₃	semidirect
196. C₂⁴×C₄	C₂×D₁₃	semidirect
201. C₂×#123	C₂×D₁₃	semidirect
209. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
218. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
227. C₂²×C₁₃	#551	semidirect
265. C₂³×C₄	C₂²×D₁₃	semidirect
269. #123	C₂²×D₁₃	semidirect
277. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
286. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
291. C₂×C₁₃	C₂×#551	semidirect
333. C₂²×C₄	C₂³×D₁₃	semidirect
337. C₄⋊C₄	C₂³×D₁₃	semidirect
345. C₂²⋊C₄	C₂³×D₁₃	semidirect
348. C₁₃	C₂²×#551	semidirect
397. C₂²	#11719364	direct (N × H)
410. C₂	C₂×#11719364	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×#11719364	2
C₂²×#88133	2
C₂²×#88190	2
C₂²×#88137	2
C₂²×#88150	2
C₂²×#88191	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88146	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×#123	2
C₂²×#551	13

Subgroups — C22×#11719364 #16769899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719364 #16769899