Subgroups — C₂×#23777275 #35196628

Order 20224.

8622 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777275	C₂	1	32	yes	maximal, direct product factor
2	C₂×#19099295	C₂	1	4	yes	maximal, complemented
3	C₂×#19099233	C₂	1	4	yes	maximal, complemented
4	C₂×#19099200	C₂	1	8	yes	maximal, complemented
5	C₂×#19099166	C₂	1	4	yes	maximal, complemented
6	C₂×#19099127	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19099116	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#19099108	C₂	1	4	yes	maximal, complemented
9	C₂²×#14579157	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19099038	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#19099037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#535×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#11929623	C₂²	1	8	yes	complemented
15	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	—
17	#19099295	C₂²	1	64	yes	complemented
18	#19099233	C₂²	1	64	yes	complemented
19	#19099200	C₂²	1	128	yes	complemented
20	#19099166	C₂²	1	64	yes	complemented
21	#19099127	C₂²	1	16	yes	complemented
22	#19099116	C₂²	1	16	yes	complemented
23	#19099108	C₂²	1	64	yes	complemented
24	C₂×#14579160	C₂²	1	2	yes	complemented
25	C₂×#14579157	C₂²	1	4	yes	—
26	C₂×#14579157	C₂²	1	2	yes	—
27	C₂×#14579157	C₂²	1	2	yes	—
28	C₂×#14579157	C₂²	1	16	yes	complemented
29	C₂×#14579157	C₂²	1	2	yes	complemented
30	C₂×#14579152	C₂²	1	2	yes	complemented
31	C₂×#14579150	C₂²	1	2	yes	complemented
32	C₂×#14579147	C₂²	1	8	yes	complemented
33	C₂×#14579145	C₂²	1	8	yes	complemented
34	C₂×#14579143	C₂²	1	8	yes	complemented
35	C₂×#14579138	C₂²	1	4	yes	—
36	C₂×#14579135	C₂²	1	4	yes	complemented
37	C₂×#14579133	C₂²	1	8	yes	complemented
38	C₂×#14579133	C₂²	1	8	yes	complemented
39	C₂×#14579132	C₂²	1	8	yes	complemented
40	C₂×#14579129	C₂²	1	4	yes	—
41	#19099038	C₂²	1	16	yes	complemented
42	#19099037	C₂²	1	16	yes	complemented
43	#41×Dic₇₉	C₂²	1	16	yes	complemented
44	C₂×Q₈×Dic₇₉	C₂²	1	2	yes	complemented
45	C₂×C₄×Dic₁₅₈	C₂²	1	4	yes	complemented
46	C₂×C₄×D₃₁₆	C₂²	1	4	yes	complemented
47	C₂×D₄×Dic₇₉	C₂²	1	4	yes	—
48	C₂×D₄×Dic₇₉	C₂²	1	2	yes	complemented
49	C₂×D₄×Dic₇₉	C₂²	1	4	yes	complemented
50	C₂×D₄×Dic₇₉	C₂²	1	4	yes	complemented
51	C₂×#14579123	C₂²	1	4	yes	complemented
52	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	8	yes	complemented
53	C₂×#14579120	C₂²	1	1	yes	characteristic
54	C₂×#14579120	C₂²	1	1	yes	characteristic
55	C₂×#14579120	C₂²	1	2	yes	complemented
56	C₂²×C₂²⋊Dic₇₉	C₂²	1	4	yes	—
57	C₂×C₂²⋊C₄×D₇₉	C₂²	1	4	yes	—
58	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
59	C₂²×C₄×Dic₇₉	C₂²	1	2	yes	complemented
60	C₂²×#41×C₇₉	C₂²	1	1	yes	characteristic
61	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
62	#535×C₇₉	C₂²	1	16	yes	complemented
63	C₂×#127×C₇₉	C₂²	1	2	yes	complemented
64	C₂×#124×C₇₉	C₂²	1	2	yes	complemented
65	C₂×#121×C₇₉	C₂²	1	4	yes	complemented
66	C₂×#120×C₇₉	C₂²	1	4	yes	—
67	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
68	C₂⁴×D₇₉	C₂³	1	2	yes	—
69	C₂×#11929623	—	4	32	no	—
70	C₂×#11929623	C₂³	1	64	yes	complemented
71	C₂²×Dic₁₅₈	C₂³	1	4	yes	—
72	C₂²×D₃₁₆	—	2	8	no	—
73	C₂²×D₃₁₆	C₂³	1	2	yes	—
74	C₂²×D₃₁₆	C₂³	1	2	yes	—
75	C₂²×D₃₁₆	C₂³	1	8	yes	—
76	C₂²×C₂²⋊D₇₉	—	4	16	no	—
77	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
78	C₂²×C₂²⋊D₇₉	C₂³	1	32	yes	—
79	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
80	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
81	C₂³×Dic₇₉	C₂³	1	2	yes	—
82	C₂³×Dic₇₉	C₂³	1	4	yes	—
83	C₂³×Dic₇₉	C₂³	1	8	yes	—
84	C₂²×C₄×D₇₉	C₂³	1	8	yes	—
85	#14579160	C₂³	1	16	yes	complemented
86	#14579157	C₂³	1	16	yes	—
87	#14579157	C₂³	1	32	yes	—
88	#14579157	C₂³	1	16	yes	—
89	#14579157	C₂³	1	16	yes	complemented
90	#14579152	C₂³	1	16	yes	complemented
91	#14579150	C₂³	1	16	yes	complemented
92	#14579147	C₂³	1	64	yes	complemented
93	#14579145	C₂³	1	64	yes	complemented
94	#14579143	C₂³	1	64	yes	complemented
95	#14579138	C₂³	1	32	yes	—
96	#14579135	C₂³	1	32	yes	complemented
97	#14579133	C₂³	1	64	yes	complemented
98	#14579133	C₂³	1	64	yes	complemented
99	#14579132	C₂³	1	64	yes	complemented
100	#14579129	C₂³	1	32	yes	—
101	Q₈×Dic₇₉	C₂³	1	16	yes	complemented
102	C₄×Dic₁₅₈	C₂³	1	32	yes	complemented
103	C₄×D₃₁₆	C₂³	1	32	yes	complemented
104	D₄×Dic₇₉	C₂³	1	32	yes	—
105	D₄×Dic₇₉	C₂³	1	32	yes	complemented
106	D₄×Dic₇₉	C₂³	1	16	yes	complemented
107	D₄×Dic₇₉	C₂³	1	32	yes	complemented
108	#14579123	C₂³	1	32	yes	complemented
109	(C₂²⋊D₇₉)⋊C₄	C₂³	1	64	yes	complemented
110	#14579120	C₂³	1	8	yes	—
111	#14579120	C₂³	1	8	yes	—
112	#14579120	C₂³	1	16	yes	complemented
113	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
114	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
115	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
116	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
117	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
118	C₂×Dic₇₉⋊C₄	C₂³	1	4	yes	—
119	C₂×C₂²⋊Dic₇₉	C₂³	1	32	yes	—
120	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊Dic₇₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
123	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
124	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
125	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	8	yes	—
126	C₂²⋊C₄×D₇₉	C₂³	1	32	yes	—
127	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
128	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
129	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
130	C₂×C₄×Dic₇₉	C₂³	1	8	yes	—
131	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
132	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
133	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
134	C₂×C₄×Dic₇₉	C₂³	1	16	yes	complemented
135	C₂⁵×C₇₉	C₂³	1	2	yes	—
136	C₂×#41×C₇₉	—	2	8	no	—
137	C₂×#41×C₇₉	C₂³	1	8	yes	—
138	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
139	C₂²×D₄×C₇₉	—	2	8	no	—
140	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
141	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
142	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
143	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
144	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
145	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
146	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
147	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
148	#127×C₇₉	C₂³	1	16	yes	complemented
149	#124×C₇₉	C₂³	1	16	yes	complemented
150	#121×C₇₉	C₂³	1	32	yes	complemented
151	#120×C₇₉	C₂³	1	32	yes	—
152	#117×C₇₉	C₂³	1	8	yes	—
153	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
156	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
157	C₂³×D₇₉	—	2	8	no	—
158	C₂³×D₇₉	—	4	8	no	—
159	C₂³×D₇₉	C₂⁴	1	4	yes	—
160	C₂³×D₇₉	C₂⁴	1	8	yes	—
161	#11929623	—	4	128	no	—
162	C₂×Dic₁₅₈	—	2	16	no	—
163	C₂×Dic₁₅₈	C₂⁴	1	16	yes	—
164	C₂×D₃₁₆	—	2	8	no	—
165	C₂×D₃₁₆	—	2	8	no	—
166	C₂×D₃₁₆	—	2	32	no	—
167	C₂×D₃₁₆	C₂⁴	1	8	yes	—
168	C₂×D₃₁₆	C₂⁴	1	8	yes	—
169	C₂×C₂²⋊D₇₉	—	2	32	no	—
170	C₂×C₂²⋊D₇₉	—	4	64	no	—
171	C₂×C₂²⋊D₇₉	—	4	16	no	—
172	C₂×C₂²⋊D₇₉	—	4	16	no	—
173	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
174	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
175	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
176	C₂²×Dic₇₉	—	2	16	no	—
177	C₂²×Dic₇₉	—	2	8	no	—
178	C₂²×Dic₇₉	—	4	16	no	—
179	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
180	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
181	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
182	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
183	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
184	C₂²×Dic₇₉	C₂⁴	1	32	yes	—
185	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
186	C₂×C₄×D₇₉	—	4	16	no	—
187	C₂×C₄×D₇₉	C₂⁴	1	32	yes	—
188	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
189	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
190	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
191	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
192	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
193	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
194	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
195	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
196	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	—
197	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
198	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
199	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
200	C₄×Dic₇₉	C₂⁴	1	4	yes	—
201	C₄×Dic₇₉	C₂⁴	1	4	yes	—
202	C₄×Dic₇₉	C₂⁴	1	8	yes	—
203	C₄×Dic₇₉	C₂⁴	1	8	yes	—
204	C₄×Dic₇₉	C₂⁴	1	16	yes	—
205	C₄×Dic₇₉	C₂⁴	1	8	yes	—
206	C₂⁴×C₇₉	—	2	8	no	—
207	C₂⁴×C₇₉	—	4	8	no	—
208	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
209	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
210	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
211	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
212	#41×C₇₉	—	2	32	no	—
213	C₂×Q₈×C₇₉	—	2	4	no	—
214	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
215	C₂×D₄×C₇₉	—	2	8	no	—
216	C₂×D₄×C₇₉	—	2	8	no	—
217	C₂×D₄×C₇₉	—	2	8	no	—
218	C₂×D₄×C₇₉	—	2	4	no	—
219	C₂×D₄×C₇₉	—	2	32	no	—
220	C₂×D₄×C₇₉	—	4	16	no	—
221	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
222	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
223	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
224	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
225	C₂×D₄×C₇₉	C₂⁴	1	32	yes	—
226	C₂²×C₄×C₇₉	—	2	8	no	—
227	C₂²×C₄×C₇₉	#41	1	8	yes	complemented
228	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
229	C₂²×C₄×C₇₉	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
231	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
233	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
235	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
236	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	—
237	C₄²×C₇₉	C₂⁴	1	8	yes	—
238	C₂³×C₇₉	—	2	4	no	—
239	C₂³×C₇₉	—	2	4	no	—
240	C₂³×C₇₉	—	2	8	no	—
241	C₂³×C₇₉	—	2	8	no	—
242	C₂³×C₇₉	—	2	16	no	—
243	C₂³×C₇₉	—	2	16	no	—
244	C₂³×C₇₉	—	4	16	no	—
245	C₂³×C₇₉	—	8	16	no	—
246	C₂³×C₇₉	C₂×#41	1	4	yes	—
247	C₂³×C₇₉	C₂⁵	1	8	yes	—
248	C₂³×C₇₉	C₂⁵	1	4	yes	—
249	C₂³×C₇₉	C₂⁵	1	2	yes	—
250	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
251	C₂²×D₇₉	—	2	8	no	—
252	C₂²×D₇₉	—	2	16	no	—
253	C₂²×D₇₉	—	2	16	no	—
254	C₂²×D₇₉	—	4	16	no	—
255	C₂²×D₇₉	—	8	16	no	—
256	C₂²×D₇₉	C₂⁵	1	8	yes	—
257	Q₈×C₇₉	—	2	8	no	—
258	D₄×C₇₉	—	2	16	no	—
259	D₄×C₇₉	—	2	16	no	—
260	D₄×C₇₉	—	2	16	no	—
261	D₄×C₇₉	—	2	8	no	—
262	D₄×C₇₉	—	4	32	no	—
263	C₂×C₄×C₇₉	—	2	4	no	—
264	C₂×C₄×C₇₉	—	2	8	no	—
265	C₂×C₄×C₇₉	—	2	16	no	—
266	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
267	C₂×C₄×C₇₉	C₂×#41	1	4	yes	—
268	C₂×C₄×C₇₉	C₂×#41	1	16	yes	complemented
269	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
270	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
271	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
272	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
273	C₂²⋊D₇₉	—	2	64	no	—
274	C₂²⋊D₇₉	—	4	32	no	—
275	C₂²⋊D₇₉	—	4	32	no	—
276	C₂×Dic₇₉	—	2	8	no	—
277	C₂×Dic₇₉	—	2	4	no	—
278	C₂×Dic₇₉	—	2	8	no	—
279	C₂×Dic₇₉	—	2	16	no	—
280	C₂×Dic₇₉	—	2	32	no	—
281	C₂×Dic₇₉	—	4	32	no	—
282	C₂×Dic₇₉	H(5,𝔽₂)	1	8	yes	—
283	C₂×Dic₇₉	C₂⁵	1	8	yes	—
284	C₂×Dic₇₉	C₂⁵	1	4	yes	—
285	C₂×Dic₇₉	C₂⁵	1	8	yes	—
286	C₂×Dic₇₉	C₂⁵	1	4	yes	—
287	D₃₁₆	—	2	16	no	—
288	D₃₁₆	—	2	16	no	—
289	C₄×D₇₉	—	4	32	no	—
290	Dic₁₅₈	—	2	32	no	—
291	C₂²×C₇₉	—	2	4	no	—
292	C₂²×C₇₉	—	2	8	no	—
293	C₂²×C₇₉	—	2	4	no	—
294	C₂²×C₇₉	—	2	8	no	—
295	C₂²×C₇₉	—	2	16	no	—
296	C₂²×C₇₉	—	2	8	no	—
297	C₂²×C₇₉	—	4	8	no	—
298	C₂²×C₇₉	—	4	16	no	—
299	C₂²×C₇₉	—	8	16	no	—
300	C₂²×C₇₉	C₂²×#41	1	4	yes	—
301	C₂²×C₇₉	C₂²×#41	1	2	yes	—
302	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
303	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
304	C₂×D₇₉	—	2	8	no	—
305	C₂×D₇₉	—	2	16	no	—
306	C₂×D₇₉	—	4	16	no	—
307	C₂×D₇₉	—	8	16	no	—
308	C₄×C₇₉	—	2	4	no	—
309	C₄×C₇₉	—	2	8	no	—
310	C₄×C₇₉	C₂²×#41	1	4	yes	—
311	C₄×C₇₉	C₂²×#41	1	4	yes	—
312	Dic₇₉	—	2	4	no	—
313	Dic₇₉	—	2	8	no	—
314	Dic₇₉	—	2	8	no	—
315	Dic₇₉	C₂×H(5,𝔽₂)	1	8	yes	—
316	C₂×#3508	—	79	1	no	maximal, Sylow
317	C₂×C₇₉	—	2	4	no	—
318	C₂×C₇₉	—	4	4	no	—
319	C₂×C₇₉	—	4	8	no	—
320	C₂×C₇₉	#3508	1	4	yes	complemented
321	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
322	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
323	D₇₉	—	4	8	no	—
324	#3508	—	79	32	no	—
325	C₂×#559	—	79	4	no	—
326	C₂×#550	—	79	4	no	—
327	C₂×#546	—	79	8	no	—
328	C₂×#540	—	79	4	no	—
329	C₂×#535	—	79	1	no	—
330	C₂×#535	D₇₉	1	1	yes	characteristic, complemented
331	C₂×#533	—	79	1	no	—
332	C₂×#532	—	79	4	no	—
333	C₂²×#127	—	79	1	no	—
334	C₂×#518	—	79	1	no	—
335	C₂×#518	—	79	1	no	—
336	C₂×C₄×#41	—	79	1	no	—
337	C₇₉	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
338	C₂²×#41	—	79	8	no	—
339	C₂²×#41	C₂×D₇₉	1	1	yes	characteristic
340	C₂³×D₄	—	79	4	no	—
341	C₂³×D₄	—	79	1	no	—
342	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
343	#559	—	79	64	no	—
344	#550	—	79	64	no	—
345	#546	—	79	128	no	—
346	#540	—	79	64	no	—
347	#535	—	79	16	no	—
348	#535	C₂×D₇₉	1	16	yes	complemented
349	#533	—	79	16	no	—
350	#532	—	79	64	no	—
351	C₂×C₄⋊Q₈	—	79	2	no	—
352	C₂×#127	—	79	2	no	—
353	C₂×#127	—	79	2	no	—
354	C₂×#127	—	79	4	no	—
355	C₂×#127	—	79	16	no	—
356	C₂×#127	—	79	2	no	—
357	C₂×#127	C₂×D₇₉	1	2	yes	complemented
358	C₂×#125	—	79	2	no	—
359	C₂×#124	—	79	2	no	—
360	C₂×#124	—	79	8	no	—
361	C₂×#124	C₂×D₇₉	1	2	yes	complemented
362	C₂×#123	—	79	8	no	—
363	C₂×#123	—	79	8	no	—
364	C₂×C₂²⋊Q₈	—	79	4	no	—
365	C₂×#121	—	79	8	no	—
366	C₂×#121	—	79	8	no	—
367	C₂×#121	—	79	8	no	—
368	C₂×#121	—	79	4	no	—
369	C₂×#121	C₂×D₇₉	1	4	yes	complemented
370	C₂×#120	—	79	4	no	—
371	C₂×#120	C₂×D₇₉	1	4	yes	—
372	#518	—	79	16	no	—
373	#518	—	79	16	no	—
374	C₄×#41	—	79	16	no	—
375	C₂×C₄×Q₈	—	79	2	no	—
376	C₂×C₄×Q₈	—	79	4	no	—
377	C₂×C₄×D₄	—	79	4	no	—
378	C₂×C₄×D₄	—	79	2	no	—
379	C₂×C₄×D₄	—	79	4	no	—
380	C₂×C₄×D₄	—	79	4	no	—
381	C₂×C₄×D₄	—	79	4	no	—
382	C₂×C₄×D₄	—	79	8	no	—
383	C₂×C₄×D₄	—	79	4	no	—
384	C₂×#117	—	79	1	no	—
385	C₂×#117	—	79	2	no	—
386	C₂×#117	—	79	1	no	—
387	C₂×#117	C₂×D₇₉	1	1	yes	characteristic
388	C₂²×C₂²⋊C₄	—	79	4	no	—
389	C₂²×C₂²⋊C₄	—	79	4	no	—
390	C₂²×C₄²	—	79	1	no	—
391	C₂²×C₄²	—	79	2	no	—
392	C₂⁵	—	79	2	no	—
393	C₂⁵	C₂²×D₇₉	1	2	yes	—
394	C₂×#41	—	2	8	no	—
395	C₂×#41	—	316	32	no	—
396	C₂×#41	—	79	64	no	—
397	C₂×#41	C₂²×D₇₉	1	8	yes	—
398	C₂²×Q₈	—	79	4	no	—
399	C₂²×Q₈	C₂²×D₇₉	1	1	yes	characteristic
400	C₂²×D₄	—	2	8	no	—
401	C₂²×D₄	—	316	16	no	—
402	C₂²×D₄	—	79	8	no	—
403	C₂²×D₄	—	79	8	no	—
404	C₂²×D₄	—	79	32	no	—
405	C₂²×D₄	—	79	8	no	—
406	C₂²×D₄	—	79	2	no	—
407	C₂²×D₄	—	79	2	no	—
408	C₂²×D₄	—	79	8	no	—
409	C₂²×D₄	—	158	8	no	—
410	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
411	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
412	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
413	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
414	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
415	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
416	C₂³×C₄	—	79	8	no	—
417	C₂³×C₄	—	79	8	no	—
418	C₂³×C₄	—	79	4	no	—
419	C₂³×C₄	—	79	2	no	—
420	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
421	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
422	C₄⋊Q₈	—	79	16	no	—
423	#127	—	79	16	no	—
424	#127	—	79	16	no	—
425	#127	—	79	32	no	—
426	#127	—	79	16	no	—
427	#127	C₂²×D₇₉	1	16	yes	complemented
428	#125	—	79	16	no	—
429	#124	—	79	16	no	—
430	#124	—	79	64	no	—
431	#124	C₂²×D₇₉	1	16	yes	complemented
432	#123	—	79	64	no	—
433	#123	—	79	64	no	—
434	C₂²⋊Q₈	—	79	32	no	—
435	#121	—	79	64	no	—
436	#121	—	79	64	no	—
437	#121	—	79	64	no	—
438	#121	—	79	32	no	—
439	#121	C₂²×D₇₉	1	32	yes	complemented
440	#120	—	79	32	no	—
441	#120	C₂²×D₇₉	1	32	yes	—
442	C₄×Q₈	—	79	16	no	—
443	C₄×Q₈	—	79	32	no	—
444	C₄×D₄	—	79	32	no	—
445	C₄×D₄	—	79	16	no	—
446	C₄×D₄	—	79	32	no	—
447	C₄×D₄	—	79	32	no	—
448	C₄×D₄	—	79	32	no	—
449	C₄×D₄	—	79	64	no	—
450	C₄×D₄	—	79	32	no	—
451	#117	—	79	8	no	—
452	#117	—	79	16	no	—
453	#117	—	79	8	no	—
454	#117	C₂²×D₇₉	1	8	yes	—
455	C₂×C₄⋊C₄	—	79	2	no	—
456	C₂×C₄⋊C₄	—	79	2	no	—
457	C₂×C₄⋊C₄	—	79	4	no	—
458	C₂×C₄⋊C₄	—	79	4	no	—
459	C₂×C₄⋊C₄	—	79	4	no	—
460	C₂×C₄⋊C₄	—	79	4	no	—
461	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
462	C₂×C₂²⋊C₄	—	79	2	no	—
463	C₂×C₂²⋊C₄	—	79	2	no	—
464	C₂×C₂²⋊C₄	—	79	8	no	—
465	C₂×C₂²⋊C₄	—	79	32	no	—
466	C₂×C₂²⋊C₄	—	79	4	no	—
467	C₂×C₂²⋊C₄	—	79	8	no	—
468	C₂×C₂²⋊C₄	—	79	8	no	—
469	C₂×C₂²⋊C₄	—	79	32	no	—
470	C₂×C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
472	C₂×C₄²	—	79	2	no	—
473	C₂×C₄²	—	79	1	no	—
474	C₂×C₄²	—	79	2	no	—
475	C₂×C₄²	—	79	4	no	—
476	C₂×C₄²	—	79	2	no	—
477	C₂×C₄²	—	79	8	no	—
478	C₂×C₄²	—	79	16	no	—
479	C₂×C₄²	—	79	1	no	—
480	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
481	C₂⁴	—	2	8	no	—
482	C₂⁴	—	4	8	no	—
483	C₂⁴	—	316	8	no	—
484	C₂⁴	—	79	8	no	—
485	C₂⁴	—	79	4	no	—
486	C₂⁴	—	158	8	no	—
487	C₂⁴	C₂³×D₇₉	1	4	yes	—
488	C₂⁴	C₂³×D₇₉	1	2	yes	—
489	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
490	C₂⁴	C₂³×D₇₉	1	8	yes	—
491	#41	—	2	32	no	—
492	#41	—	316	128	no	—
493	C₂×Q₈	—	2	4	no	—
494	C₂×Q₈	—	79	16	no	—
495	C₂×Q₈	—	158	16	no	—
496	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	2	8	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	2	32	no	—
502	C₂×D₄	—	4	16	no	—
503	C₂×D₄	—	316	16	no	—
504	C₂×D₄	—	316	16	no	—
505	C₂×D₄	—	316	64	no	—
506	C₂×D₄	—	79	32	no	—
507	C₂×D₄	—	79	32	no	—
508	C₂×D₄	—	79	32	no	—
509	C₂×D₄	—	79	8	no	—
510	C₂×D₄	—	79	8	no	—
511	C₂×D₄	—	158	32	no	—
512	C₂×D₄	—	158	8	no	—
513	C₂×D₄	—	158	8	no	—
514	C₂×D₄	—	158	32	no	—
515	C₂×D₄	C₂³×D₇₉	1	8	yes	—
516	C₂×D₄	C₂³×D₇₉	1	8	yes	—
517	C₂×D₄	C₂³×D₇₉	1	8	yes	—
518	C₂×D₄	C₂³×D₇₉	1	4	yes	—
519	C₂×D₄	C₂³×D₇₉	1	32	yes	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	316	16	no	—
522	C₂²×C₄	—	316	16	no	—
523	C₂²×C₄	—	79	32	no	—
524	C₂²×C₄	—	79	32	no	—
525	C₂²×C₄	—	79	2	no	—
526	C₂²×C₄	—	79	16	no	—
527	C₂²×C₄	—	79	8	no	—
528	C₂²×C₄	—	79	4	no	—
529	C₂²×C₄	—	79	2	no	—
530	C₂²×C₄	—	79	4	no	—
531	C₂²×C₄	—	158	8	no	—
532	C₂²×C₄	—	158	16	no	—
533	C₂²×C₄	#11929623	1	8	yes	complemented
534	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
535	C₂²×C₄	C₂³×D₇₉	1	2	yes	—
536	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
537	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
538	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
539	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
540	C₄⋊C₄	—	79	16	no	—
541	C₄⋊C₄	—	79	16	no	—
542	C₄⋊C₄	—	79	8	no	—
543	C₄⋊C₄	—	79	8	no	—
544	C₄⋊C₄	—	79	16	no	—
545	C₄⋊C₄	—	79	16	no	—
546	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
547	C₂²⋊C₄	—	79	8	no	—
548	C₂²⋊C₄	—	79	8	no	—
549	C₂²⋊C₄	—	79	32	no	—
550	C₂²⋊C₄	—	79	16	no	—
551	C₂²⋊C₄	—	79	32	no	—
552	C₂²⋊C₄	—	79	32	no	—
553	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
554	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	—
555	C₄²	—	79	4	no	—
556	C₄²	—	79	8	no	—
557	C₄²	—	79	4	no	—
558	C₄²	—	79	16	no	—
559	C₄²	—	79	8	no	—
560	C₄²	—	79	8	no	—
561	C₄²	C₂³×D₇₉	1	8	yes	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	16	no	—
564	C₂³	—	2	8	no	—
565	C₂³	—	2	4	no	—
566	C₂³	—	2	8	no	—
567	C₂³	—	2	16	no	—
568	C₂³	—	4	16	no	—
569	C₂³	—	8	16	no	—
570	C₂³	—	316	16	no	—
571	C₂³	—	79	8	no	—
572	C₂³	—	632	16	no	—
573	C₂³	—	158	16	no	—
574	C₂³	—	158	8	no	—
575	C₂³	—	158	16	no	—
576	C₂³	C₂×#11929623	1	4	yes	—
577	C₂³	C₂⁴×D₇₉	1	8	yes	—
578	C₂³	C₂⁴×D₇₉	1	4	yes	—
579	C₂³	C₂⁴×D₇₉	1	2	yes	—
580	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
581	Q₈	—	2	8	no	—
582	Q₈	—	158	32	no	—
583	D₄	—	2	16	no	—
584	D₄	—	2	16	no	—
585	D₄	—	2	16	no	—
586	D₄	—	2	8	no	—
587	D₄	—	4	32	no	—
588	D₄	—	316	32	no	—
589	D₄	—	316	32	no	—
590	D₄	—	158	64	no	—
591	D₄	—	158	16	no	—
592	D₄	—	158	16	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	16	no	—
596	C₂×C₄	—	316	32	no	—
597	C₂×C₄	—	316	32	no	—
598	C₂×C₄	—	79	8	no	—
599	C₂×C₄	—	79	4	no	—
600	C₂×C₄	—	79	8	no	—
601	C₂×C₄	—	79	4	no	—
602	C₂×C₄	—	79	8	no	—
603	C₂×C₄	—	158	16	no	—
604	C₂×C₄	—	158	32	no	—
605	C₂×C₄	—	158	8	no	—
606	C₂×C₄	—	158	8	no	—
607	C₂×C₄	—	158	4	no	—
608	C₂×C₄	C₂×#11929623	1	4	yes	—
609	C₂×C₄	C₂×#11929623	1	4	yes	—
610	C₂×C₄	C₂×#11929623	1	16	yes	complemented
611	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
612	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
613	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
614	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	8	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	8	no	—
619	C₂²	—	2	16	no	—
620	C₂²	—	2	8	no	—
621	C₂²	—	4	16	no	—
622	C₂²	—	4	8	no	—
623	C₂²	—	8	16	no	—
624	C₂²	—	316	16	no	—
625	C₂²	—	632	16	no	—
626	C₂²	—	158	8	no	—
627	C₂²	—	158	16	no	—
628	C₂²	C₂²×#11929623	1	4	yes	—
629	C₂²	C₂²×#11929623	1	2	yes	—
630	C₂²	H(5,𝔽₂)×D₇₉	1	4	yes	—
631	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	8	no	—
634	C₄	—	79	8	no	—
635	C₄	—	158	8	no	—
636	C₄	—	158	8	no	—
637	C₄	—	158	4	no	—
638	C₄	C₂²×#11929623	1	4	yes	—
639	C₄	C₂²×#11929623	1	4	yes	—
640	C₂	—	2	4	no	—
641	C₂	—	4	8	no	—
642	C₂	—	4	4	no	—
643	C₂	—	316	8	no	—
644	C₂	#23777275	1	4	yes	direct product factor
645	C₂	C₂³×#11929623	1	1	yes	characteristic
646	C₂	C₂×H(5,𝔽₂)×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#535×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#535	D₇₉
hypocenter	C₇₉	C₂×#3508
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#535

Complements

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

N	H ≅ G/N	type
1. #23777275	C₂	direct (N × H)
2. C₂×#19099295	C₂	semidirect
3. C₂×#19099233	C₂	semidirect
4. C₂×#19099200	C₂	semidirect
5. C₂×#19099166	C₂	semidirect
6. C₂×#19099127	C₂	semidirect
7. C₂×#19099116	C₂	semidirect
8. C₂×#19099108	C₂	semidirect
9. C₂²×#14579157	C₂	semidirect
10. C₂×#19099038	C₂	semidirect
11. C₂×#19099037	C₂	semidirect
12. C₂×#41×Dic₇₉	C₂	semidirect
13. C₂×#535×C₇₉	C₂	semidirect
14. C₂²×#11929623	C₂²	semidirect
17. #19099295	C₂²	semidirect
18. #19099233	C₂²	semidirect
19. #19099200	C₂²	semidirect
20. #19099166	C₂²	semidirect
21. #19099127	C₂²	semidirect
22. #19099116	C₂²	semidirect
23. #19099108	C₂²	semidirect
24. C₂×#14579160	C₂²	semidirect
28. C₂×#14579157	C₂²	semidirect
29. C₂×#14579157	C₂²	semidirect
30. C₂×#14579152	C₂²	semidirect
31. C₂×#14579150	C₂²	semidirect
32. C₂×#14579147	C₂²	semidirect
33. C₂×#14579145	C₂²	semidirect
34. C₂×#14579143	C₂²	semidirect
36. C₂×#14579135	C₂²	semidirect
37. C₂×#14579133	C₂²	semidirect
38. C₂×#14579133	C₂²	semidirect
39. C₂×#14579132	C₂²	semidirect
41. #19099038	C₂²	semidirect
42. #19099037	C₂²	semidirect
43. #41×Dic₇₉	C₂²	semidirect
44. C₂×Q₈×Dic₇₉	C₂²	semidirect
45. C₂×C₄×Dic₁₅₈	C₂²	semidirect
46. C₂×C₄×D₃₁₆	C₂²	semidirect
48. C₂×D₄×Dic₇₉	C₂²	semidirect
49. C₂×D₄×Dic₇₉	C₂²	semidirect
50. C₂×D₄×Dic₇₉	C₂²	semidirect
51. C₂×#14579123	C₂²	semidirect
52. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
55. C₂×#14579120	C₂²	semidirect
59. C₂²×C₄×Dic₇₉	C₂²	semidirect
62. #535×C₇₉	C₂²	semidirect
63. C₂×#127×C₇₉	C₂²	semidirect
64. C₂×#124×C₇₉	C₂²	semidirect
65. C₂×#121×C₇₉	C₂²	semidirect
70. C₂×#11929623	C₂³	semidirect
85. #14579160	C₂³	semidirect
89. #14579157	C₂³	semidirect
90. #14579152	C₂³	semidirect
91. #14579150	C₂³	semidirect
92. #14579147	C₂³	semidirect
93. #14579145	C₂³	semidirect
94. #14579143	C₂³	semidirect
96. #14579135	C₂³	semidirect
97. #14579133	C₂³	semidirect
98. #14579133	C₂³	semidirect
99. #14579132	C₂³	semidirect
101. Q₈×Dic₇₉	C₂³	semidirect
102. C₄×Dic₁₅₈	C₂³	semidirect
103. C₄×D₃₁₆	C₂³	semidirect
105. D₄×Dic₇₉	C₂³	semidirect
106. D₄×Dic₇₉	C₂³	semidirect
107. D₄×Dic₇₉	C₂³	semidirect
108. #14579123	C₂³	semidirect
109. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
112. #14579120	C₂³	semidirect
134. C₂×C₄×Dic₇₉	C₂³	semidirect
148. #127×C₇₉	C₂³	semidirect
149. #124×C₇₉	C₂³	semidirect
150. #121×C₇₉	C₂³	semidirect
227. C₂²×C₄×C₇₉	#41	semidirect
268. C₂×C₄×C₇₉	C₂×#41	semidirect
320. C₂×C₇₉	#3508	semidirect
330. C₂×#535	D₇₉	semidirect
337. C₇₉	C₂×#3508	semidirect
348. #535	C₂×D₇₉	semidirect
357. C₂×#127	C₂×D₇₉	semidirect
361. C₂×#124	C₂×D₇₉	semidirect
369. C₂×#121	C₂×D₇₉	semidirect
427. #127	C₂²×D₇₉	semidirect
431. #124	C₂²×D₇₉	semidirect
439. #121	C₂²×D₇₉	semidirect
533. C₂²×C₄	#11929623	semidirect
610. C₂×C₄	C₂×#11929623	semidirect
644. C₂	#23777275	direct (N × H)

Maximal subgroups

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

subgroup	index
#23777275	2
C₂×#19099295	2
C₂×#19099233	2
C₂×#19099200	2
C₂×#19099166	2
C₂×#19099127	2
C₂×#19099116	2
C₂×#19099108	2
C₂²×#14579157	2
C₂×#19099038	2
C₂×#19099037	2
C₂×#41×Dic₇₉	2
C₂×#535×C₇₉	2
C₂×#3508	79

Subgroups — C2×#23777275 #35196628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#23777275 #35196628