Subgroups — #35196887

Order 20224.

9494 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777555	C₂	1	24	yes	maximal, complemented
2	#23777089	C₂	1	6	yes	maximal, complemented
3	#23777087	C₂	1	12	yes	maximal, complemented
4	#23777035	C₂	1	6	yes	maximal, complemented
5	#23777029	C₂	1	12	yes	maximal, complemented
6	C₂²×#14579130	C₂	1	2	yes	maximal, complemented
7	C₂²×#120×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14579206	C₂²	1	6	yes	complemented
9	C₂³×C₂²⋊D₇₉	C₂²	1	6	yes	complemented
10	#19099306	C₂²	1	8	yes	complemented
11	#19099302	C₂²	1	24	yes	complemented
12	#19099244	C₂²	1	24	yes	complemented
13	#19099239	C₂²	1	48	yes	complemented
14	#19099207	C₂²	1	48	yes	complemented
15	#19099203	C₂²	1	48	yes	complemented
16	#19099200	C₂²	1	48	yes	complemented
17	D₄×C₂²⋊D₇₉	C₂²	1	48	yes	complemented
18	#19099195	C₂²	1	24	yes	complemented
19	#19099189	C₂²	1	6	yes	complemented
20	#19099151	C₂²	1	24	yes	complemented
21	#19099148	C₂²	1	48	yes	complemented
22	#19099130	C₂²	1	12	yes	complemented
23	#19099128	C₂²	1	24	yes	complemented
24	#19099125	C₂²	1	6	yes	complemented
25	#19099123	C₂²	1	24	yes	complemented
26	#19099122	C₂²	1	12	yes	complemented
27	#19099122	C₂²	1	12	yes	complemented
28	#19099074	C₂²	1	12	yes	complemented
29	#19099069	C₂²	1	24	yes	complemented
30	C₂×#14579130	C₂²	1	12	yes	complemented
31	C₂×#14579130	C₂²	1	12	yes	complemented
32	C₂×#14579130	C₂²	1	24	yes	complemented
33	C₂×#14579130	C₂²	1	4	yes	complemented
34	#120×D₇₉	C₂²	1	8	yes	complemented
35	#19099038	C₂²	1	6	yes	complemented
36	#19099036	C₂²	1	12	yes	complemented
37	C₂²×C₂²⋊Dic₇₉	C₂²	1	6	yes	complemented
38	C₂⁶×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	C₂³×D₄×C₇₉	C₂²	1	3	yes	complemented
40	C₂×#120×C₇₉	C₂²	1	12	yes	complemented
41	C₂×#120×C₇₉	C₂²	1	12	yes	complemented
42	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	3	yes	complemented
43	C₂⁴×D₇₉	C₂³	1	2	yes	complemented
44	#14579206	—	4	24	no	—
45	C₂×#11929624	C₂³	1	12	yes	complemented
46	C₂×#11929623	C₂³	1	24	yes	complemented
47	C₂²×C₂²⋊D₇₉	—	4	24	no	—
48	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
49	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
50	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
51	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	complemented
52	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	complemented
53	C₂×D₄×D₇₉	C₂³	1	24	yes	complemented
54	C₂³×Dic₇₉	C₂³	1	6	yes	complemented
55	#14579157	C₂³	1	24	yes	complemented
56	#14579154	C₂³	1	48	yes	complemented
57	#14579148	C₂³	1	24	yes	complemented
58	#14579147	C₂³	1	48	yes	complemented
59	#14579145	C₂³	1	24	yes	complemented
60	#14579144	C₂³	1	24	yes	complemented
61	#14579143	C₂³	1	48	yes	complemented
62	#14579142	C₂³	1	24	yes	complemented
63	#14579142	C₂³	1	24	yes	complemented
64	#14579140	C₂³	1	24	yes	complemented
65	#14579138	C₂³	1	48	yes	complemented
66	#14579135	C₂³	1	24	yes	complemented
67	#14579134	C₂³	1	48	yes	complemented
68	#14579133	C₂³	1	48	yes	complemented
69	#14579133	C₂³	1	48	yes	complemented
70	#14579132	C₂³	1	48	yes	complemented
71	#14579131	C₂³	1	24	yes	complemented
72	#14579130	C₂³	1	48	yes	—
73	#14579130	C₂³	1	24	yes	complemented
74	#14579130	C₂³	1	24	yes	complemented
75	#14579130	C₂³	1	16	yes	complemented
76	#14579130	C₂³	1	8	yes	complemented
77	#14579130	C₂³	1	8	yes	complemented
78	#14579130	C₂³	1	24	yes	complemented
79	#14579129	C₂³	1	24	yes	complemented
80	#14579129	C₂³	1	24	yes	complemented
81	D₄×Dic₇₉	C₂³	1	48	yes	complemented
82	C₄×C₂²⋊D₇₉	C₂³	1	48	yes	complemented
83	(C₂²⋊D₇₉)⋊C₄	C₂³	1	48	yes	complemented
84	#14579120	C₂³	1	12	yes	complemented
85	#14579117	C₂³	1	24	yes	complemented
86	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	—
87	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	complemented
88	C₂×C₂²⋊Dic₇₉	C₂³	1	24	yes	complemented
89	C₂×C₂²⋊Dic₇₉	C₂³	1	24	yes	complemented
90	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	complemented
91	C₂²⋊C₄×D₇₉	C₂³	1	24	yes	complemented
92	C₂⁵×C₇₉	—	4	12	no	—
93	C₂⁵×C₇₉	C₂³	1	3	yes	—
94	C₂⁵×C₇₉	C₂³	1	6	yes	—
95	C₂⁵×C₇₉	C₂³	1	6	yes	—
96	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic, complemented
97	C₂²×D₄×C₇₉	—	4	12	no	—
98	C₂²×D₄×C₇₉	C₂³	1	6	yes	—
99	C₂²×D₄×C₇₉	C₂³	1	24	yes	complemented
100	C₂²×D₄×C₇₉	C₂³	1	6	yes	complemented
101	C₂³×C₄×C₇₉	C₂³	1	3	yes	complemented
102	#120×C₇₉	C₂³	1	24	yes	—
103	#120×C₇₉	C₂³	1	24	yes	complemented
104	#120×C₇₉	C₂³	1	8	yes	complemented
105	#120×C₇₉	C₂³	1	8	yes	complemented
106	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
107	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	complemented
108	C₂×C₂²⋊C₄×C₇₉	C₂³	1	24	yes	complemented
109	C₂³×D₇₉	—	4	12	no	—
110	C₂³×D₇₉	C₂⁴	1	12	yes	—
111	C₂³×D₇₉	C₂⁴	1	4	yes	complemented
112	#11929624	—	4	24	no	—
113	#11929623	—	4	48	no	—
114	C₂×Dic₁₅₈	C₂⁴	1	12	yes	complemented
115	C₂×D₃₁₆	C₂⁴	1	12	yes	complemented
116	C₂×C₂²⋊D₇₉	—	2	48	no	—
117	C₂×C₂²⋊D₇₉	—	4	24	no	—
118	C₂×C₂²⋊D₇₉	—	4	48	no	—
119	C₂×C₂²⋊D₇₉	—	4	48	no	—
120	C₂×C₂²⋊D₇₉	—	4	24	no	—
121	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	—
122	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	—
123	C₂×C₂²⋊D₇₉	C₂⁴	1	48	yes	—
124	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	complemented
125	D₄×D₇₉	—	4	48	no	—
126	C₂²×Dic₇₉	—	4	12	no	—
127	C₂²×Dic₇₉	C₂⁴	1	12	yes	—
128	C₂²×Dic₇₉	C₂⁴	1	24	yes	—
129	C₂²×Dic₇₉	C₂⁴	1	12	yes	complemented
130	C₂×C₄×D₇₉	C₂⁴	1	24	yes	complemented
131	C₄⋊Dic₇₉	C₂⁴	1	24	yes	complemented
132	Dic₇₉⋊C₄	C₂⁴	1	48	yes	complemented
133	C₂²⋊Dic₇₉	C₂⁴	1	24	yes	—
134	C₂²⋊Dic₇₉	C₂⁴	1	24	yes	—
135	C₂²⋊Dic₇₉	C₂⁴	1	48	yes	—
136	C₂²⋊Dic₇₉	C₂⁴	1	24	yes	complemented
137	(C₂×D₇₉)⋊C₄	C₂⁴	1	48	yes	complemented
138	C₄×Dic₇₉	C₂⁴	1	24	yes	complemented
139	C₂⁴×C₇₉	—	2	12	no	—
140	C₂⁴×C₇₉	—	2	24	no	—
141	C₂⁴×C₇₉	—	4	24	no	—
142	C₂⁴×C₇₉	—	4	12	no	—
143	C₂⁴×C₇₉	—	4	12	no	—
144	C₂⁴×C₇₉	—	4	24	no	—
145	C₂⁴×C₇₉	—	4	6	no	—
146	C₂⁴×C₇₉	—	4	64	no	—
147	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
148	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
150	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
151	C₂⁴×C₇₉	C₂⁴	1	3	yes	—
152	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
153	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
154	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
155	C₂⁴×C₇₉	C₂⁴	1	3	yes	—
156	C₂×D₄×C₇₉	—	2	24	no	—
157	C₂×D₄×C₇₉	—	4	12	no	—
158	C₂×D₄×C₇₉	—	4	48	no	—
159	C₂×D₄×C₇₉	C₂⁴	1	24	yes	—
160	C₂×D₄×C₇₉	C₂⁴	1	24	yes	—
161	C₂²×C₄×C₇₉	—	4	6	no	—
162	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
163	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
164	C₂²⋊C₄×C₇₉	C₂⁴	1	24	yes	—
165	C₂²⋊C₄×C₇₉	C₂⁴	1	24	yes	—
166	C₂³×C₇₉	—	2	12	no	—
167	C₂³×C₇₉	—	2	6	no	—
168	C₂³×C₇₉	—	2	24	no	—
169	C₂³×C₇₉	—	2	24	no	—
170	C₂³×C₇₉	—	2	12	no	—
171	C₂³×C₇₉	—	2	24	no	—
172	C₂³×C₇₉	—	2	6	no	—
173	C₂³×C₇₉	—	2	12	no	—
174	C₂³×C₇₉	—	4	6	no	—
175	C₂³×C₇₉	—	4	12	no	—
176	C₂³×C₇₉	—	4	6	no	—
177	C₂³×C₇₉	—	4	6	no	—
178	C₂³×C₇₉	—	4	12	no	—
179	C₂³×C₇₉	—	4	6	no	—
180	C₂³×C₇₉	—	4	12	no	—
181	C₂³×C₇₉	—	4	96	no	—
182	C₂³×C₇₉	—	4	48	no	—
183	C₂³×C₇₉	—	4	96	no	—
184	C₂³×C₇₉	—	8	8	no	—
185	C₂³×C₇₉	H(5,𝔽₂)	1	12	yes	complemented
186	C₂³×C₇₉	C₂⁵	1	6	yes	—
187	C₂³×C₇₉	C₂⁵	1	4	yes	—
188	C₂³×C₇₉	C₂⁵	1	3	yes	—
189	C₂³×C₇₉	C₂⁵	1	6	yes	—
190	C₂²×D₇₉	—	2	24	no	—
191	C₂²×D₇₉	—	4	24	no	—
192	C₂²×D₇₉	—	4	12	no	—
193	C₂²×D₇₉	—	8	16	no	—
194	C₂²×D₇₉	C₂⁵	1	8	yes	—
195	D₄×C₇₉	—	2	48	no	—
196	D₄×C₇₉	—	4	24	no	—
197	C₂×C₄×C₇₉	—	2	12	no	—
198	C₂×C₄×C₇₉	—	4	12	no	—
199	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
200	C₂²⋊D₇₉	—	2	48	no	—
201	C₂²⋊D₇₉	—	2	48	no	—
202	C₂²⋊D₇₉	—	4	24	no	—
203	C₂²⋊D₇₉	—	4	48	no	—
204	C₂×Dic₇₉	—	2	24	no	—
205	C₂×Dic₇₉	—	4	24	no	—
206	C₂×Dic₇₉	—	4	12	no	—
207	C₂×Dic₇₉	C₂⁵	1	24	yes	—
208	D₃₁₆	—	4	12	no	—
209	C₄×D₇₉	—	4	24	no	—
210	Dic₁₅₈	—	4	12	no	—
211	C₂²×C₇₉	—	2	16	no	—
212	C₂²×C₇₉	—	2	8	no	—
213	C₂²×C₇₉	—	2	6	no	—
214	C₂²×C₇₉	—	2	12	no	—
215	C₂²×C₇₉	—	2	12	no	—
216	C₂²×C₇₉	—	2	12	no	—
217	C₂²×C₇₉	—	2	6	no	—
218	C₂²×C₇₉	—	4	12	no	—
219	C₂²×C₇₉	—	4	24	no	—
220	C₂²×C₇₉	—	4	48	no	—
221	C₂²×C₇₉	—	4	24	no	—
222	C₂²×C₇₉	—	4	12	no	—
223	C₂²×C₇₉	—	4	8	no	—
224	C₂²×C₇₉	—	8	12	no	—
225	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
226	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	12	yes	—
227	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
228	C₂×D₇₉	—	2	24	no	—
229	C₂×D₇₉	—	8	24	no	—
230	C₂×D₇₉	—	16	4	no	—
231	C₄×C₇₉	—	2	12	no	—
232	Dic₇₉	—	2	24	no	—
233	#62817	—	79	1	no	maximal, Sylow
234	C₂×C₇₉	—	2	12	no	—
235	C₂×C₇₉	—	2	6	no	—
236	C₂×C₇₉	—	4	4	no	—
237	C₂×C₇₉	—	4	6	no	—
238	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	3	yes	—
239	D₇₉	—	4	8	no	—
240	#3532	—	79	24	no	—
241	#3490	—	79	12	no	—
242	#3490	—	79	6	no	—
243	#3484	—	79	6	no	—
244	#3484	—	79	12	no	—
245	C₂²×#120	—	79	2	no	—
246	C₂²×#120	D₇₉	1	1	yes	characteristic, complemented
247	C₇₉	#62817	1	1	yes	characteristic, complemented, Sylow
248	C₂⁶	C₂×D₇₉	1	1	yes	characteristic, complemented
249	C₂×H(5,𝔽₂)	—	79	6	no	—
250	C₂³×D₄	—	79	6	no	—
251	C₂³×D₄	C₂×D₇₉	1	3	yes	complemented
252	H(3,𝔽₄)	—	79	8	no	—
253	#560	—	79	24	no	—
254	#551	—	79	24	no	—
255	#551	—	79	48	no	—
256	#546	—	79	48	no	—
257	#546	—	79	48	no	—
258	#546	—	79	48	no	—
259	D₄²	—	79	48	no	—
260	D₄²	—	79	24	no	—
261	#543	—	79	6	no	—
262	#538	—	79	48	no	—
263	#538	—	79	24	no	—
264	#535	—	79	12	no	—
265	#535	—	79	24	no	—
266	#534	—	79	12	no	—
267	#534	—	79	12	no	—
268	#534	—	79	24	no	—
269	#534	—	79	6	no	—
270	#525	—	79	12	no	—
271	#525	—	79	24	no	—
272	C₂×#120	—	79	12	no	—
273	C₂×#120	—	79	12	no	—
274	C₂×#120	—	79	24	no	—
275	C₂×#120	—	79	4	no	—
276	C₂×#120	—	79	8	no	—
277	C₂×#120	C₂×D₇₉	1	12	yes	complemented
278	C₂×#120	C₂×D₇₉	1	12	yes	complemented
279	#518	—	79	6	no	—
280	#518	—	79	12	no	—
281	C₂²×C₂²⋊C₄	—	79	6	no	—
282	C₂²×C₂²⋊C₄	C₂×D₇₉	1	3	yes	complemented
283	C₂⁵	—	4	12	no	—
284	C₂⁵	—	79	2	no	—
285	C₂⁵	C₂²×D₇₉	1	6	yes	—
286	C₂⁵	C₂²×D₇₉	1	3	yes	—
287	C₂⁵	C₂²×D₇₉	1	6	yes	—
288	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic, complemented
289	H(5,𝔽₂)	—	316	24	no	—
290	C₂×#41	—	79	24	no	—
291	C₂×#41	—	79	12	no	—
292	C₂²×D₄	—	4	12	no	—
293	C₂²×D₄	—	316	24	no	—
294	C₂²×D₄	—	79	12	no	—
295	C₂²×D₄	—	79	24	no	—
296	C₂²×D₄	—	79	24	no	—
297	C₂²×D₄	—	79	12	no	—
298	C₂²×D₄	—	79	24	no	—
299	C₂²×D₄	—	79	12	no	—
300	C₂²×D₄	C₂²×D₇₉	1	6	yes	—
301	C₂²×D₄	C₂²×D₇₉	1	6	yes	complemented
302	C₂²×D₄	C₂²×D₇₉	1	24	yes	complemented
303	C₂³×C₄	—	79	6	no	—
304	C₂³×C₄	C₂²×D₇₉	1	3	yes	complemented
305	#127	—	79	24	no	—
306	#126	—	79	48	no	—
307	#124	—	79	24	no	—
308	#124	—	79	48	no	—
309	#123	—	79	24	no	—
310	#123	—	79	24	no	—
311	#123	—	79	24	no	—
312	#123	—	79	24	no	—
313	#123	—	79	48	no	—
314	C₂²⋊Q₈	—	79	24	no	—
315	C₂²⋊Q₈	—	79	48	no	—
316	#121	—	79	48	no	—
317	#121	—	79	48	no	—
318	#121	—	79	48	no	—
319	#121	—	79	24	no	—
320	#121	—	79	48	no	—
321	#120	—	79	8	no	—
322	#120	—	79	8	no	—
323	#120	—	79	24	no	—
324	#120	—	79	24	no	—
325	#120	—	79	48	no	—
326	#120	—	79	16	no	—
327	#120	—	79	24	no	—
328	#120	—	79	24	no	—
329	#120	—	79	24	no	—
330	#120	—	79	24	no	—
331	#120	C₂²×D₇₉	1	24	yes	—
332	#120	C₂²×D₇₉	1	8	yes	complemented
333	#120	C₂²×D₇₉	1	24	yes	complemented
334	#120	C₂²×D₇₉	1	8	yes	complemented
335	C₄×D₄	—	79	48	no	—
336	C₄×D₄	—	79	48	no	—
337	C₄×D₄	—	79	48	no	—
338	#117	—	79	12	no	—
339	#117	—	79	24	no	—
340	C₂×C₂²⋊C₄	—	79	12	no	—
341	C₂×C₂²⋊C₄	—	79	12	no	—
342	C₂×C₂²⋊C₄	—	79	24	no	—
343	C₂×C₂²⋊C₄	—	79	24	no	—
344	C₂×C₂²⋊C₄	—	79	12	no	—
345	C₂×C₂²⋊C₄	—	79	24	no	—
346	C₂×C₂²⋊C₄	C₂²×D₇₉	1	6	yes	—
347	C₂×C₂²⋊C₄	C₂²×D₇₉	1	6	yes	complemented
348	C₂×C₂²⋊C₄	C₂²×D₇₉	1	24	yes	complemented
349	C₂⁴	—	2	12	no	—
350	C₂⁴	—	2	24	no	—
351	C₂⁴	—	4	12	no	—
352	C₂⁴	—	4	24	no	—
353	C₂⁴	—	4	24	no	—
354	C₂⁴	—	4	12	no	—
355	C₂⁴	—	4	6	no	—
356	C₂⁴	—	4	64	no	—
357	C₂⁴	—	316	12	no	—
358	C₂⁴	—	79	4	no	—
359	C₂⁴	—	79	12	no	—
360	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
361	C₂⁴	C₂³×D₇₉	1	2	yes	—
362	C₂⁴	C₂³×D₇₉	1	6	yes	—
363	C₂⁴	C₂³×D₇₉	1	12	yes	—
364	C₂⁴	C₂³×D₇₉	1	6	yes	—
365	C₂⁴	C₂³×D₇₉	1	6	yes	—
366	C₂⁴	C₂³×D₇₉	1	3	yes	—
367	C₂⁴	C₂³×D₇₉	1	2	yes	—
368	C₂⁴	C₂³×D₇₉	1	3	yes	—
369	#41	—	316	24	no	—
370	#41	—	316	48	no	—
371	C₂×Q₈	—	79	12	no	—
372	C₂×D₄	—	2	24	no	—
373	C₂×D₄	—	4	12	no	—
374	C₂×D₄	—	4	48	no	—
375	C₂×D₄	—	316	48	no	—
376	C₂×D₄	—	316	48	no	—
377	C₂×D₄	—	316	48	no	—
378	C₂×D₄	—	316	24	no	—
379	C₂×D₄	—	316	24	no	—
380	C₂×D₄	—	79	48	no	—
381	C₂×D₄	—	79	24	no	—
382	C₂×D₄	—	79	24	no	—
383	C₂×D₄	—	79	24	no	—
384	C₂×D₄	—	79	12	no	—
385	C₂×D₄	—	158	48	no	—
386	C₂×D₄	C₂³×D₇₉	1	24	yes	—
387	C₂×D₄	C₂³×D₇₉	1	24	yes	—
388	C₂²×C₄	—	4	6	no	—
389	C₂²×C₄	—	316	12	no	—
390	C₂²×C₄	—	79	24	no	—
391	C₂²×C₄	—	79	12	no	—
392	C₂²×C₄	—	79	24	no	—
393	C₂²×C₄	—	79	12	no	—
394	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
395	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
396	C₄⋊C₄	—	79	48	no	—
397	C₄⋊C₄	—	79	24	no	—
398	C₂²⋊C₄	—	79	24	no	—
399	C₂²⋊C₄	—	79	24	no	—
400	C₂²⋊C₄	—	79	48	no	—
401	C₂²⋊C₄	—	79	24	no	—
402	C₂²⋊C₄	—	79	48	no	—
403	C₂²⋊C₄	C₂³×D₇₉	1	24	yes	—
404	C₂²⋊C₄	C₂³×D₇₉	1	24	yes	—
405	C₄²	—	79	24	no	—
406	C₂³	—	2	6	no	—
407	C₂³	—	2	12	no	—
408	C₂³	—	2	24	no	—
409	C₂³	—	2	6	no	—
410	C₂³	—	2	24	no	—
411	C₂³	—	2	24	no	—
412	C₂³	—	2	12	no	—
413	C₂³	—	2	12	no	—
414	C₂³	—	4	6	no	—
415	C₂³	—	4	12	no	—
416	C₂³	—	4	6	no	—
417	C₂³	—	4	6	no	—
418	C₂³	—	4	12	no	—
419	C₂³	—	4	6	no	—
420	C₂³	—	4	12	no	—
421	C₂³	—	4	48	no	—
422	C₂³	—	4	96	no	—
423	C₂³	—	4	96	no	—
424	C₂³	—	8	8	no	—
425	C₂³	—	316	24	no	—
426	C₂³	—	316	12	no	—
427	C₂³	—	79	8	no	—
428	C₂³	—	632	16	no	—
429	C₂³	—	158	24	no	—
430	C₂³	#14579206	1	12	yes	complemented
431	C₂³	C₂⁴×D₇₉	1	6	yes	—
432	C₂³	C₂⁴×D₇₉	1	4	yes	—
433	C₂³	C₂⁴×D₇₉	1	3	yes	—
434	C₂³	C₂⁴×D₇₉	1	6	yes	—
435	Q₈	—	316	12	no	—
436	D₄	—	2	48	no	—
437	D₄	—	4	24	no	—
438	D₄	—	316	12	no	—
439	D₄	—	316	48	no	—
440	D₄	—	316	24	no	—
441	D₄	—	158	48	no	—
442	D₄	—	158	48	no	—
443	C₂×C₄	—	2	12	no	—
444	C₂×C₄	—	4	12	no	—
445	C₂×C₄	—	316	24	no	—
446	C₂×C₄	—	316	24	no	—
447	C₂×C₄	—	316	12	no	—
448	C₂×C₄	—	79	24	no	—
449	C₂×C₄	—	158	24	no	—
450	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	16	no	—
453	C₂²	—	2	6	no	—
454	C₂²	—	2	12	no	—
455	C₂²	—	2	12	no	—
456	C₂²	—	2	6	no	—
457	C₂²	—	2	12	no	—
458	C₂²	—	4	12	no	—
459	C₂²	—	4	48	no	—
460	C₂²	—	4	24	no	—
461	C₂²	—	4	12	no	—
462	C₂²	—	4	24	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	8	12	no	—
465	C₂²	—	632	24	no	—
466	C₂²	—	158	24	no	—
467	C₂²	—	1264	4	no	—
468	C₂²	C₂×#14579206	1	6	yes	—
469	C₂²	C₂×#14579206	1	12	yes	—
470	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
471	C₄	—	2	12	no	—
472	C₄	—	158	24	no	—
473	C₂	—	2	6	no	—
474	C₂	—	2	12	no	—
475	C₂	—	4	6	no	—
476	C₂	—	4	4	no	—
477	C₂	—	316	8	no	—
478	C₂	C₂²×#14579206	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₂²×#120×C₇₉	C₂
hypercenter	C₂²×#120	D₇₉
hypocenter	C₇₉	#62817
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. #23777555	C₂	semidirect
2. #23777089	C₂	semidirect
3. #23777087	C₂	semidirect
4. #23777035	C₂	semidirect
5. #23777029	C₂	semidirect
6. C₂²×#14579130	C₂	semidirect
7. C₂²×#120×C₇₉	C₂	semidirect
8. C₂×#14579206	C₂²	semidirect
9. C₂³×C₂²⋊D₇₉	C₂²	semidirect
10. #19099306	C₂²	semidirect
11. #19099302	C₂²	semidirect
12. #19099244	C₂²	semidirect
13. #19099239	C₂²	semidirect
14. #19099207	C₂²	semidirect
15. #19099203	C₂²	semidirect
16. #19099200	C₂²	semidirect
17. D₄×C₂²⋊D₇₉	C₂²	semidirect
18. #19099195	C₂²	semidirect
19. #19099189	C₂²	semidirect
20. #19099151	C₂²	semidirect
21. #19099148	C₂²	semidirect
22. #19099130	C₂²	semidirect
23. #19099128	C₂²	semidirect
24. #19099125	C₂²	semidirect
25. #19099123	C₂²	semidirect
26. #19099122	C₂²	semidirect
27. #19099122	C₂²	semidirect
28. #19099074	C₂²	semidirect
29. #19099069	C₂²	semidirect
30. C₂×#14579130	C₂²	semidirect
31. C₂×#14579130	C₂²	semidirect
32. C₂×#14579130	C₂²	semidirect
33. C₂×#14579130	C₂²	semidirect
34. #120×D₇₉	C₂²	semidirect
35. #19099038	C₂²	semidirect
36. #19099036	C₂²	semidirect
37. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
38. C₂⁶×C₇₉	C₂²	semidirect
39. C₂³×D₄×C₇₉	C₂²	semidirect
40. C₂×#120×C₇₉	C₂²	semidirect
41. C₂×#120×C₇₉	C₂²	semidirect
42. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
43. C₂⁴×D₇₉	C₂³	semidirect
45. C₂×#11929624	C₂³	semidirect
46. C₂×#11929623	C₂³	semidirect
49. C₂²×C₂²⋊D₇₉	C₂³	semidirect
50. C₂²×C₂²⋊D₇₉	C₂³	semidirect
51. C₂²×C₂²⋊D₇₉	C₂³	semidirect
52. C₂²×C₂²⋊D₇₉	C₂³	semidirect
53. C₂×D₄×D₇₉	C₂³	semidirect
54. C₂³×Dic₇₉	C₂³	semidirect
55. #14579157	C₂³	semidirect
56. #14579154	C₂³	semidirect
57. #14579148	C₂³	semidirect
58. #14579147	C₂³	semidirect
59. #14579145	C₂³	semidirect
60. #14579144	C₂³	semidirect
61. #14579143	C₂³	semidirect
62. #14579142	C₂³	semidirect
63. #14579142	C₂³	semidirect
64. #14579140	C₂³	semidirect
65. #14579138	C₂³	semidirect
66. #14579135	C₂³	semidirect
67. #14579134	C₂³	semidirect
68. #14579133	C₂³	semidirect
69. #14579133	C₂³	semidirect
70. #14579132	C₂³	semidirect
71. #14579131	C₂³	semidirect
73. #14579130	C₂³	semidirect
74. #14579130	C₂³	semidirect
75. #14579130	C₂³	semidirect
76. #14579130	C₂³	semidirect
77. #14579130	C₂³	semidirect
78. #14579130	C₂³	semidirect
79. #14579129	C₂³	semidirect
80. #14579129	C₂³	semidirect
81. D₄×Dic₇₉	C₂³	semidirect
82. C₄×C₂²⋊D₇₉	C₂³	semidirect
83. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
84. #14579120	C₂³	semidirect
85. #14579117	C₂³	semidirect
87. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
88. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
89. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
90. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
91. C₂²⋊C₄×D₇₉	C₂³	semidirect
96. C₂⁵×C₇₉	C₂³	semidirect
99. C₂²×D₄×C₇₉	C₂³	semidirect
100. C₂²×D₄×C₇₉	C₂³	semidirect
101. C₂³×C₄×C₇₉	C₂³	semidirect
103. #120×C₇₉	C₂³	semidirect
104. #120×C₇₉	C₂³	semidirect
105. #120×C₇₉	C₂³	semidirect
107. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
108. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
111. C₂³×D₇₉	C₂⁴	semidirect
114. C₂×Dic₁₅₈	C₂⁴	semidirect
115. C₂×D₃₁₆	C₂⁴	semidirect
124. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
129. C₂²×Dic₇₉	C₂⁴	semidirect
130. C₂×C₄×D₇₉	C₂⁴	semidirect
131. C₄⋊Dic₇₉	C₂⁴	semidirect
132. Dic₇₉⋊C₄	C₂⁴	semidirect
136. C₂²⋊Dic₇₉	C₂⁴	semidirect
137. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
138. C₄×Dic₇₉	C₂⁴	semidirect
185. C₂³×C₇₉	H(5,𝔽₂)	semidirect
246. C₂²×#120	D₇₉	semidirect
247. C₇₉	#62817	semidirect
248. C₂⁶	C₂×D₇₉	semidirect
251. C₂³×D₄	C₂×D₇₉	semidirect
277. C₂×#120	C₂×D₇₉	semidirect
278. C₂×#120	C₂×D₇₉	semidirect
282. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
288. C₂⁵	C₂²×D₇₉	semidirect
301. C₂²×D₄	C₂²×D₇₉	semidirect
302. C₂²×D₄	C₂²×D₇₉	semidirect
304. C₂³×C₄	C₂²×D₇₉	semidirect
332. #120	C₂²×D₇₉	semidirect
333. #120	C₂²×D₇₉	semidirect
334. #120	C₂²×D₇₉	semidirect
347. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
348. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
430. C₂³	#14579206	semidirect

Maximal subgroups

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

subgroup	index
#23777555	2
#23777089	2
#23777087	2
#23777035	2
#23777029	2
C₂²×#14579130	2
C₂²×#120×C₇₉	2
#62817	79