Subgroups — C₇₉×#24514 #34136203

Order 20224.

896 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#451×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#433×C₇₉	C₂	1	1	yes	maximal, characteristic
3	C₇₉×#2625	C₂	1	1	yes	maximal, characteristic
4	C₇₉×#2310	C₂	1	1	yes	maximal, characteristic
5	C₇₉×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₉×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₉×#2056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#1971	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₉×#1933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₉×#1873	C₂	1	1	yes	maximal, characteristic
14	C₇₉×#1854	C₂	1	1	yes	maximal, characteristic
15	C₇₉×#1787	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₇₉	C₂²	1	1	yes	characteristic
22	#451×C₇₉	—	2	4	no	—
23	#433×C₇₉	—	2	4	no	—
24	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
34	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
40	#400×C₇₉	—	2	1	no	—
41	#398×C₇₉	—	2	1	no	—
42	#397×C₇₉	—	2	1	no	—
43	#397×C₇₉	—	2	1	no	—
44	#391×C₇₉	—	2	1	no	—
45	#391×C₇₉	—	2	1	no	—
46	#391×C₇₉	C₂²	1	1	yes	characteristic
47	#391×C₇₉	C₂²	1	1	yes	characteristic
48	#391×C₇₉	C₂²	1	1	yes	characteristic
49	#391×C₇₉	C₂²	1	1	yes	characteristic
50	#391×C₇₉	C₂²	1	1	yes	characteristic
51	#391×C₇₉	C₂²	1	1	yes	characteristic
52	#389×C₇₉	C₂²	1	1	yes	characteristic
53	#389×C₇₉	C₂²	1	1	yes	characteristic
54	#381×C₇₉	—	2	1	no	—
55	#381×C₇₉	—	2	1	no	—
56	#380×C₇₉	C₂²	1	1	yes	characteristic
57	#340×C₇₉	C₂²	1	1	yes	characteristic
58	#340×C₇₉	C₂²	1	1	yes	characteristic
59	#340×C₇₉	C₂²	1	1	yes	characteristic
60	#340×C₇₉	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₇₉	—	2	2	no	—
62	C₂²×Q₈×C₇₉	—	2	2	no	—
63	C₂²×Q₈×C₇₉	—	2	1	no	—
64	C₂²×Q₈×C₇₉	—	2	2	no	—
65	C₂²×Q₈×C₇₉	—	2	2	no	—
66	C₂²×Q₈×C₇₉	—	4	1	no	—
67	C₂²×Q₈×C₇₉	—	4	1	no	—
68	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₇₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₇₉	—	2	1	no	—
72	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
73	C₂×Q₁₆×C₇₉	—	2	2	no	—
74	C₂×Q₁₆×C₇₉	—	2	2	no	—
75	C₂×Q₁₆×C₇₉	—	2	2	no	—
76	C₂×Q₁₆×C₇₉	—	2	2	no	—
77	C₂×Q₁₆×C₇₉	—	4	1	no	—
78	C₂×Q₁₆×C₇₉	—	4	1	no	—
79	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₂²⋊Q₈×C₇₉	—	2	2	no	—
84	C₂²⋊Q₈×C₇₉	—	2	2	no	—
85	#117×C₇₉	—	2	2	no	—
86	#117×C₇₉	—	2	2	no	—
87	#117×C₇₉	—	4	1	no	—
88	#117×C₇₉	—	4	1	no	—
89	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₇₉	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₉	—	2	1	no	—
105	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
107	#107×C₇₉	—	4	1	no	—
108	#106×C₇₉	—	4	1	no	—
109	C₄⋊C₈×C₇₉	—	2	2	no	—
110	C₄⋊C₈×C₇₉	—	2	2	no	—
111	#103×C₇₉	—	2	2	no	—
112	#103×C₇₉	—	2	2	no	—
113	#103×C₇₉	—	2	2	no	—
114	#103×C₇₉	—	2	2	no	—
115	#103×C₇₉	—	4	1	no	—
116	#103×C₇₉	—	4	1	no	—
117	#103×C₇₉	—	4	1	no	—
118	#103×C₇₉	—	4	1	no	—
119	C₂²⋊C₈×C₇₉	—	2	2	no	—
120	C₂²⋊C₈×C₇₉	D₄	1	4	yes	—
121	#97×C₇₉	—	2	2	no	—
122	C₄×C₈×C₇₉	—	2	2	no	—
123	#95×C₇₉	—	2	1	no	—
124	#95×C₇₉	—	2	1	no	—
125	#95×C₇₉	—	2	1	no	—
126	#95×C₇₉	—	2	1	no	—
127	#95×C₇₉	—	2	1	no	—
128	#95×C₇₉	—	2	1	no	—
129	#95×C₇₉	—	2	1	no	—
130	#95×C₇₉	—	2	1	no	—
131	#95×C₇₉	—	2	1	no	—
132	#95×C₇₉	—	2	1	no	—
133	#95×C₇₉	—	2	1	no	—
134	#95×C₇₉	—	2	1	no	—
135	#95×C₇₉	—	2	1	no	—
136	#95×C₇₉	—	2	1	no	—
137	#95×C₇₉	—	2	1	no	—
138	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₇₉	—	2	4	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×Q₈×C₇₉	—	2	1	no	—
142	C₂×Q₈×C₇₉	—	2	1	no	—
143	C₂×Q₈×C₇₉	—	2	1	no	—
144	C₂×Q₈×C₇₉	—	2	1	no	—
145	C₂×Q₈×C₇₉	—	2	1	no	—
146	C₂×Q₈×C₇₉	—	2	1	no	—
147	C₂×Q₈×C₇₉	—	2	1	no	—
148	C₂×Q₈×C₇₉	—	2	1	no	—
149	C₂×Q₈×C₇₉	—	2	1	no	—
150	C₂×Q₈×C₇₉	—	2	1	no	—
151	C₂×Q₈×C₇₉	—	2	1	no	—
152	C₂×Q₈×C₇₉	—	2	1	no	—
153	C₂×Q₈×C₇₉	—	2	1	no	—
154	C₂×Q₈×C₇₉	—	2	1	no	—
155	C₂×Q₈×C₇₉	—	2	1	no	—
156	C₂×Q₈×C₇₉	—	4	4	no	—
157	C₂×Q₈×C₇₉	—	4	4	no	—
158	C₂×Q₈×C₇₉	—	4	4	no	—
159	C₂×Q₈×C₇₉	—	4	4	no	—
160	C₂×Q₈×C₇₉	—	4	2	no	—
161	C₂×Q₈×C₇₉	—	4	2	no	—
162	C₂×Q₈×C₇₉	#41	1	2	yes	—
163	C₂×Q₈×C₇₉	#41	1	2	yes	—
164	C₂²×C₄×C₇₉	—	2	1	no	—
165	C₂²×C₄×C₇₉	—	2	1	no	—
166	C₂²×C₄×C₇₉	—	2	1	no	—
167	C₂²×C₄×C₇₉	—	2	1	no	—
168	C₂²×C₄×C₇₉	—	2	4	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	—	2	1	no	—
174	C₂²×C₄×C₇₉	—	2	1	no	—
175	C₂²×C₄×C₇₉	—	2	1	no	—
176	C₂²×C₄×C₇₉	—	2	1	no	—
177	C₂²×C₄×C₇₉	—	4	2	no	—
178	C₂²×C₄×C₇₉	—	4	2	no	—
179	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₇₉	#41	1	2	yes	—
186	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₇₉	—	4	4	no	—
188	Q₁₆×C₇₉	—	4	4	no	—
189	C₂×C₈×C₇₉	—	2	1	no	—
190	C₂×C₈×C₇₉	—	2	1	no	—
191	C₂×C₈×C₇₉	—	2	1	no	—
192	C₂×C₈×C₇₉	—	2	1	no	—
193	C₂×C₈×C₇₉	—	2	1	no	—
194	C₂×C₈×C₇₉	—	2	1	no	—
195	C₂×C₈×C₇₉	—	2	1	no	—
196	C₂×C₈×C₇₉	—	2	1	no	—
197	C₂×C₈×C₇₉	—	2	1	no	—
198	C₂×C₈×C₇₉	—	2	1	no	—
199	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
200	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
201	C₄⋊C₄×C₇₉	—	2	2	no	—
202	C₄⋊C₄×C₇₉	—	2	2	no	—
203	C₄⋊C₄×C₇₉	—	2	1	no	—
204	C₄⋊C₄×C₇₉	—	2	1	no	—
205	C₄⋊C₄×C₇₉	—	2	1	no	—
206	C₄⋊C₄×C₇₉	—	2	1	no	—
207	C₄⋊C₄×C₇₉	—	2	1	no	—
208	C₄⋊C₄×C₇₉	—	2	1	no	—
209	C₄⋊C₄×C₇₉	—	2	1	no	—
210	C₄⋊C₄×C₇₉	—	2	1	no	—
211	C₄⋊C₄×C₇₉	—	2	1	no	—
212	C₄⋊C₄×C₇₉	—	2	1	no	—
213	C₄⋊C₄×C₇₉	—	4	2	no	—
214	C₄⋊C₄×C₇₉	—	8	1	no	—
215	C₄⋊C₄×C₇₉	—	8	1	no	—
216	C₂²⋊C₄×C₇₉	—	2	2	no	—
217	C₂²⋊C₄×C₇₉	—	2	2	no	—
218	C₂²⋊C₄×C₇₉	—	4	2	no	—
219	C₂²⋊C₄×C₇₉	—	4	2	no	—
220	C₂²⋊C₄×C₇₉	—	8	1	no	—
221	C₄²×C₇₉	—	2	1	no	—
222	C₄²×C₇₉	—	2	1	no	—
223	C₄²×C₇₉	—	2	1	no	—
224	C₄²×C₇₉	—	2	1	no	—
225	C₄²×C₇₉	—	4	2	no	—
226	C₂³×C₇₉	—	2	1	no	—
227	C₂³×C₇₉	—	2	1	no	—
228	C₂³×C₇₉	—	2	1	no	—
229	C₂³×C₇₉	—	2	1	no	—
230	C₂³×C₇₉	—	2	1	no	—
231	C₂³×C₇₉	—	2	1	no	—
232	C₂³×C₇₉	#121	1	2	yes	—
233	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₇₉	—	2	2	no	—
235	Q₈×C₇₉	—	2	2	no	—
236	Q₈×C₇₉	—	2	2	no	—
237	Q₈×C₇₉	—	2	2	no	—
238	Q₈×C₇₉	—	4	8	no	—
239	Q₈×C₇₉	—	4	1	no	—
240	Q₈×C₇₉	—	4	1	no	—
241	Q₈×C₇₉	—	4	1	no	—
242	Q₈×C₇₉	—	4	1	no	—
243	Q₈×C₇₉	—	4	1	no	—
244	Q₈×C₇₉	—	4	1	no	—
245	Q₈×C₇₉	—	4	1	no	—
246	Q₈×C₇₉	—	4	1	no	—
247	C₂×C₄×C₇₉	—	2	1	no	—
248	C₂×C₄×C₇₉	—	2	1	no	—
249	C₂×C₄×C₇₉	—	2	2	no	—
250	C₂×C₄×C₇₉	—	2	2	no	—
251	C₂×C₄×C₇₉	—	2	2	no	—
252	C₂×C₄×C₇₉	—	2	2	no	—
253	C₂×C₄×C₇₉	—	2	1	no	—
254	C₂×C₄×C₇₉	—	2	1	no	—
255	C₂×C₄×C₇₉	—	2	1	no	—
256	C₂×C₄×C₇₉	—	2	1	no	—
257	C₂×C₄×C₇₉	—	2	2	no	—
258	C₂×C₄×C₇₉	—	2	2	no	—
259	C₂×C₄×C₇₉	—	2	1	no	—
260	C₂×C₄×C₇₉	—	2	1	no	—
261	C₂×C₄×C₇₉	—	2	1	no	—
262	C₂×C₄×C₇₉	—	2	1	no	—
263	C₂×C₄×C₇₉	—	2	1	no	—
264	C₂×C₄×C₇₉	—	2	1	no	—
265	C₂×C₄×C₇₉	—	2	1	no	—
266	C₂×C₄×C₇₉	—	2	1	no	—
267	C₂×C₄×C₇₉	—	4	8	no	—
268	C₂×C₄×C₇₉	—	4	1	no	—
269	C₂×C₄×C₇₉	—	4	1	no	—
270	C₂×C₄×C₇₉	—	4	1	no	—
271	C₂×C₄×C₇₉	—	4	1	no	—
272	C₂×C₄×C₇₉	—	4	1	no	—
273	C₂×C₄×C₇₉	—	4	1	no	—
274	C₂×C₄×C₇₉	—	4	1	no	—
275	C₂×C₄×C₇₉	—	4	1	no	—
276	C₂×C₄×C₇₉	—	4	1	no	—
277	C₂×C₄×C₇₉	—	4	1	no	—
278	C₂×C₄×C₇₉	—	4	1	no	—
279	C₂×C₄×C₇₉	—	4	1	no	—
280	C₂×C₄×C₇₉	—	4	1	no	—
281	C₂×C₄×C₇₉	—	4	1	no	—
282	C₂×C₄×C₇₉	—	4	1	no	—
283	C₂×C₄×C₇₉	—	4	1	no	—
284	C₂×C₄×C₇₉	—	4	1	no	—
285	C₂×C₄×C₇₉	—	4	1	no	—
286	C₂×C₄×C₇₉	—	4	1	no	—
287	C₂×C₄×C₇₉	—	4	1	no	—
288	C₂×C₄×C₇₉	—	4	1	no	—
289	C₂×C₄×C₇₉	—	4	1	no	—
290	C₂×C₄×C₇₉	#121	1	2	yes	—
291	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
297	C₈×C₇₉	—	2	2	no	—
298	C₈×C₇₉	—	2	2	no	—
299	C₈×C₇₉	—	4	1	no	—
300	C₈×C₇₉	—	4	1	no	—
301	C₂²×C₇₉	—	2	2	no	—
302	C₂²×C₇₉	—	2	2	no	—
303	C₂²×C₇₉	—	2	2	no	—
304	C₂²×C₇₉	—	4	1	no	—
305	C₂²×C₇₉	—	4	1	no	—
306	C₂²×C₇₉	—	4	1	no	—
307	C₂²×C₇₉	—	4	1	no	—
308	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
309	C₂²×C₇₉	#525	1	1	yes	characteristic
310	C₂²×C₇₉	#535	1	1	yes	characteristic
311	C₂²×C₇₉	#577	1	1	yes	characteristic
312	C₂²×C₇₉	#578	1	1	yes	characteristic
313	C₂²×C₇₉	#578	1	1	yes	characteristic
314	C₂²×C₇₉	#578	1	1	yes	characteristic
315	C₄×C₇₉	—	2	2	no	—
316	C₄×C₇₉	—	4	2	no	—
317	C₄×C₇₉	—	4	2	no	—
318	C₄×C₇₉	—	4	1	no	—
319	C₄×C₇₉	—	4	1	no	—
320	C₄×C₇₉	—	4	1	no	—
321	C₄×C₇₉	—	4	1	no	—
322	C₄×C₇₉	—	8	1	no	—
323	C₄×C₇₉	—	8	1	no	—
324	C₄×C₇₉	—	8	1	no	—
325	C₄×C₇₉	—	8	1	no	—
326	C₄×C₇₉	—	8	1	no	—
327	C₄×C₇₉	—	8	1	no	—
328	C₄×C₇₉	#546	1	1	yes	characteristic
329	C₄×C₇₉	#546	1	1	yes	characteristic
330	C₄×C₇₉	#551	1	1	yes	characteristic
331	C₄×C₇₉	#551	1	1	yes	characteristic
332	#24514	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂×C₇₉	—	4	2	no	—
334	C₂×C₇₉	#2411	1	1	yes	characteristic
335	C₂×C₇₉	#3059	1	1	yes	characteristic
336	C₂×C₇₉	#3063	1	1	yes	characteristic
337	C₂×C₇₉	#3121	1	1	yes	characteristic
338	C₂×C₇₉	#3127	1	1	yes	characteristic
339	C₂×C₇₉	#3223	1	1	yes	characteristic
340	C₂×C₇₉	#3225	1	1	yes	characteristic
341	C₂×#451	C₂×C₇₉	1	1	yes	characteristic
342	C₂×#433	C₂×C₇₉	1	1	yes	characteristic
343	#2625	C₂×C₇₉	1	1	yes	characteristic
344	#2310	C₂×C₇₉	1	1	yes	characteristic
345	#2068	C₂×C₇₉	1	1	yes	characteristic, complemented
346	#2066	C₂×C₇₉	1	1	yes	characteristic, complemented
347	#2056	C₂×C₇₉	1	1	yes	characteristic, complemented
348	#2056	C₂×C₇₉	1	1	yes	characteristic, complemented
349	#1971	C₂×C₇₉	1	1	yes	characteristic, complemented
350	#1969	C₂×C₇₉	1	1	yes	characteristic, complemented
351	#1935	C₂×C₇₉	1	1	yes	characteristic, complemented
352	#1933	C₂×C₇₉	1	1	yes	characteristic, complemented
353	#1873	C₂×C₇₉	1	1	yes	characteristic
354	#1854	C₂×C₇₉	1	1	yes	characteristic
355	#1787	C₂×C₇₉	1	1	yes	characteristic
356	C₇₉	#24514	1	1	yes	characteristic, direct product factor, Sylow
357	C₂³×Q₈	C₂²×C₇₉	1	1	yes	characteristic
358	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
359	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic
360	C₂×C₂²⋊Q₈	C₂²×C₇₉	1	1	yes	characteristic
361	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
362	C₂×#117	C₂²×C₇₉	1	1	yes	characteristic
363	#451	—	2	4	no	—
364	#433	—	2	4	no	—
365	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic
366	C₂×#106	C₂²×C₇₉	1	1	yes	characteristic
367	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
368	C₂×C₄⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
369	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
370	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
371	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
374	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
375	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
376	C₂×#103	C₂²×C₇₉	1	1	yes	characteristic
377	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
378	C₂×C₂²⋊C₈	C₂²×C₇₉	1	1	yes	characteristic
379	C₂×#97	C₂²×C₇₉	1	1	yes	characteristic
380	C₂×C₄×C₈	C₂²×C₇₉	1	1	yes	characteristic
381	#400	—	2	1	no	—
382	#398	—	2	1	no	—
383	#397	—	2	1	no	—
384	#397	—	2	1	no	—
385	#391	—	2	1	no	—
386	#391	—	2	1	no	—
387	#391	C₂²×C₇₉	1	1	yes	characteristic
388	#391	C₂²×C₇₉	1	1	yes	characteristic
389	#391	C₂²×C₇₉	1	1	yes	characteristic
390	#391	C₂²×C₇₉	1	1	yes	characteristic
391	#391	C₂²×C₇₉	1	1	yes	characteristic
392	#391	C₂²×C₇₉	1	1	yes	characteristic
393	#389	C₂²×C₇₉	1	1	yes	characteristic
394	#389	C₂²×C₇₉	1	1	yes	characteristic
395	#381	—	2	1	no	—
396	#381	—	2	1	no	—
397	#380	C₂²×C₇₉	1	1	yes	characteristic
398	#340	C₂²×C₇₉	1	1	yes	characteristic
399	#340	C₂²×C₇₉	1	1	yes	characteristic
400	#340	C₂²×C₇₉	1	1	yes	characteristic
401	#340	C₂²×C₇₉	1	1	yes	characteristic
402	C₂²×Q₈	—	2	2	no	—
403	C₂²×Q₈	—	2	2	no	—
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	—	2	2	no	—
406	C₂²×Q₈	—	2	2	no	—
407	C₂²×Q₈	—	4	1	no	—
408	C₂²×Q₈	—	4	1	no	—
409	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
410	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₇₉	1	1	yes	characteristic
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	C₂³×C₇₉	1	1	yes	characteristic
414	C₂×Q₁₆	—	2	2	no	—
415	C₂×Q₁₆	—	2	2	no	—
416	C₂×Q₁₆	—	2	2	no	—
417	C₂×Q₁₆	—	2	2	no	—
418	C₂×Q₁₆	—	4	1	no	—
419	C₂×Q₁₆	—	4	1	no	—
420	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	2	no	—
426	#117	—	2	2	no	—
427	#117	—	2	2	no	—
428	#117	—	4	1	no	—
429	#117	—	4	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	D₄×C₇₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂³×C₇₉	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	D₄×C₇₉	1	1	yes	characteristic
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₇₉	1	1	yes	characteristic
448	#107	—	4	1	no	—
449	#106	—	4	1	no	—
450	C₄⋊C₈	—	2	2	no	—
451	C₄⋊C₈	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	—	2	2	no	—
454	#103	—	2	2	no	—
455	#103	—	2	2	no	—
456	#103	—	4	1	no	—
457	#103	—	4	1	no	—
458	#103	—	4	1	no	—
459	#103	—	4	1	no	—
460	C₂²⋊C₈	—	2	2	no	—
461	C₂²⋊C₈	D₄×C₇₉	1	4	yes	—
462	#97	—	2	2	no	—
463	C₄×C₈	—	2	2	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	—	2	1	no	—
475	#95	—	2	1	no	—
476	#95	—	2	1	no	—
477	#95	—	2	1	no	—
478	#95	—	2	1	no	—
479	C₂⁴	C₂×D₄×C₇₉	1	1	yes	characteristic
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	—	2	1	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	4	4	no	—
498	C₂×Q₈	—	4	4	no	—
499	C₂×Q₈	—	4	4	no	—
500	C₂×Q₈	—	4	4	no	—
501	C₂×Q₈	—	4	2	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	#41×C₇₉	1	2	yes	—
504	C₂×Q₈	#41×C₇₉	1	2	yes	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	2	1	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	2	no	—
520	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
521	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
522	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
523	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₇₉	1	2	yes	—
526	C₂²×C₄	#41×C₇₉	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₇₉	1	1	yes	characteristic
528	Q₁₆	—	4	4	no	—
529	Q₁₆	—	4	4	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
541	C₂×C₈	C₂×D₄×C₇₉	1	2	yes	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	—	2	1	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	1	no	—
551	C₄⋊C₄	—	2	1	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	4	2	no	—
555	C₄⋊C₄	—	8	1	no	—
556	C₄⋊C₄	—	8	1	no	—
557	C₂²⋊C₄	—	2	2	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	4	2	no	—
560	C₂²⋊C₄	—	4	2	no	—
561	C₂²⋊C₄	—	8	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	4	2	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	#121×C₇₉	1	2	yes	—
574	C₂³	C₂²×D₄×C₇₉	1	1	yes	characteristic
575	Q₈	—	2	2	no	—
576	Q₈	—	2	2	no	—
577	Q₈	—	2	2	no	—
578	Q₈	—	2	2	no	—
579	Q₈	—	4	8	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	Q₈	—	4	1	no	—
584	Q₈	—	4	1	no	—
585	Q₈	—	4	1	no	—
586	Q₈	—	4	1	no	—
587	Q₈	—	4	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	4	8	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	#121×C₇₉	1	2	yes	—
632	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
633	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
634	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
635	C₂×C₄	C₂×#41×C₇₉	1	1	yes	characteristic
636	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
637	C₂×C₄	H(5,𝔽₂)×C₇₉	1	1	yes	characteristic
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	4	1	no	—
641	C₈	—	4	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	C₂×#121×C₇₉	1	1	yes	characteristic
650	C₂²	#525×C₇₉	1	1	yes	characteristic
651	C₂²	#535×C₇₉	1	1	yes	characteristic
652	C₂²	#577×C₇₉	1	1	yes	characteristic
653	C₂²	#578×C₇₉	1	1	yes	characteristic
654	C₂²	#578×C₇₉	1	1	yes	characteristic
655	C₂²	#578×C₇₉	1	1	yes	characteristic
656	C₄	—	2	2	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	8	1	no	—
664	C₄	—	8	1	no	—
665	C₄	—	8	1	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	#546×C₇₉	1	1	yes	characteristic
670	C₄	#546×C₇₉	1	1	yes	characteristic
671	C₄	#551×C₇₉	1	1	yes	characteristic
672	C₄	#551×C₇₉	1	1	yes	characteristic
673	C₂	—	4	2	no	—
674	C₂	C₇₉×#2411	1	1	yes	characteristic
675	C₂	C₇₉×#3059	1	1	yes	characteristic
676	C₂	C₇₉×#3063	1	1	yes	characteristic
677	C₂	C₇₉×#3121	1	1	yes	characteristic
678	C₂	C₇₉×#3127	1	1	yes	characteristic
679	C₂	C₇₉×#3223	1	1	yes	characteristic
680	C₂	C₇₉×#3225	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₉
prime radical	C₂⁴×C₇₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×#117×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇₉×#2068	C₂	semidirect
6. C₇₉×#2066	C₂	semidirect
7. C₇₉×#2056	C₂	semidirect
8. C₇₉×#2056	C₂	semidirect
9. C₇₉×#1971	C₂	semidirect
10. C₇₉×#1969	C₂	semidirect
11. C₇₉×#1935	C₂	semidirect
12. C₇₉×#1933	C₂	semidirect
332. #24514	C₇₉	direct (N × H)
345. #2068	C₂×C₇₉	semidirect
346. #2066	C₂×C₇₉	semidirect
347. #2056	C₂×C₇₉	semidirect
348. #2056	C₂×C₇₉	semidirect
349. #1971	C₂×C₇₉	semidirect
350. #1969	C₂×C₇₉	semidirect
351. #1935	C₂×C₇₉	semidirect
352. #1933	C₂×C₇₉	semidirect
356. C₇₉	#24514	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×#451×C₇₉	2
C₂×#433×C₇₉	2
C₇₉×#2625	2
C₇₉×#2310	2
C₇₉×#2068	2
C₇₉×#2066	2
C₇₉×#2056	2
C₇₉×#1971	2
C₇₉×#1969	2
C₇₉×#1935	2
C₇₉×#1933	2
C₇₉×#1873	2
C₇₉×#1854	2
C₇₉×#1787	2
#24514	79

Subgroups — C79×#24514 #34136203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#24514 #34136203