Subgroups — C₇₉×#33520 #34145209

Order 20224.

1192 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₇₉	C₂	1	2	yes	maximal, complemented
3	C₂×#466×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₉×#2186	C₂	1	4	yes	maximal, complemented
5	C₇₉×#2185	C₂	1	2	yes	maximal, complemented
6	C₇₉×#2184	C₂	1	2	yes	maximal, complemented
7	C₇₉×#2139	C₂	1	2	yes	maximal, complemented
8	C₇₉×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₇₉	—	2	1	no	—
10	C₂×#135×C₇₉	—	2	8	no	—
11	C₂×#135×C₇₉	—	2	1	no	—
12	C₂×#135×C₇₉	—	2	1	no	—
13	C₂×#135×C₇₉	C₂²	1	2	yes	—
14	C₂×#135×C₇₉	C₂²	1	2	yes	complemented
15	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×SD₁₆×C₇₉	—	2	1	no	—
17	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×#121×C₇₉	—	2	1	no	—
21	#509×C₇₉	—	2	8	no	—
22	C₂×SD₃₂×C₇₉	C₂²	1	4	yes	complemented
23	C₂×D₁₆×C₇₉	C₂²	1	4	yes	complemented
24	C₂×M₃₂×C₇₉	C₂²	1	2	yes	complemented
25	#466×C₇₉	—	2	1	no	—
26	#466×C₇₉	—	2	1	no	—
27	#466×C₇₉	C₂²	1	2	yes	—
28	#466×C₇₉	C₂²	1	2	yes	complemented
29	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#102×C₇₉	—	2	1	no	—
31	#358×C₇₉	C₂²	1	4	yes	complemented
32	#357×C₇₉	C₂²	1	4	yes	complemented
33	C₂²⋊C₁₆×C₇₉	C₂²	1	2	yes	complemented
34	C₂²⋊C₁₆×C₇₉	C₂²	1	2	yes	complemented
35	C₂×#41×C₇₉	—	2	8	no	—
36	C₂×#41×C₇₉	—	2	2	no	—
37	C₂×#41×C₇₉	—	2	2	no	—
38	C₂×#41×C₇₉	—	4	4	no	—
39	C₂×#41×C₇₉	—	4	1	no	—
40	C₂×#41×C₇₉	—	4	1	no	—
41	C₂²×Q₈×C₇₉	—	2	1	no	—
42	C₂²×D₄×C₇₉	—	2	1	no	—
43	C₂²×D₄×C₇₉	—	2	1	no	—
44	C₂²×D₄×C₇₉	—	4	1	no	—
45	C₂²×D₄×C₇₉	—	4	1	no	—
46	C₂³×C₄×C₇₉	—	4	1	no	—
47	C₂³×C₄×C₇₉	D₄	1	1	yes	characteristic
48	#135×C₇₉	—	2	8	no	—
49	#135×C₇₉	—	2	8	no	—
50	#135×C₇₉	—	2	4	no	—
51	#135×C₇₉	—	2	4	no	—
52	#135×C₇₉	—	2	4	no	—
53	#135×C₇₉	D₄	1	8	yes	complemented
54	C₂×Q₁₆×C₇₉	—	2	4	no	—
55	C₂×Q₁₆×C₇₉	—	2	1	no	—
56	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
57	C₂×SD₁₆×C₇₉	—	2	8	no	—
58	C₂×SD₁₆×C₇₉	—	2	2	no	—
59	C₂×SD₁₆×C₇₉	—	2	2	no	—
60	C₂×D₈×C₇₉	—	2	4	no	—
61	C₂×D₈×C₇₉	—	2	1	no	—
62	C₂×D₈×C₇₉	—	2	4	no	—
63	C₂×D₈×C₇₉	—	2	1	no	—
64	C₂×D₈×C₇₉	C₂³	1	2	yes	—
65	C₂×D₈×C₇₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₇₉	—	2	4	no	—
67	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
73	#121×C₇₉	—	2	2	no	—
74	#121×C₇₉	—	2	2	no	—
75	#121×C₇₉	—	4	1	no	—
76	#121×C₇₉	—	4	1	no	—
77	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₇₉	—	4	1	no	—
79	SD₃₂×C₇₉	—	2	8	no	—
80	D₁₆×C₇₉	—	2	8	no	—
81	M₃₂×C₇₉	—	2	4	no	—
82	C₂×C₁₆×C₇₉	C₂³	1	4	yes	—
83	#107×C₇₉	—	2	1	no	—
84	#107×C₇₉	C₂³	1	2	yes	—
85	#102×C₇₉	—	2	2	no	—
86	#102×C₇₉	—	2	2	no	—
87	C₂⁴×C₇₉	—	4	1	no	—
88	C₂⁴×C₇₉	—	4	1	no	—
89	C₂⁴×C₇₉	D₈	1	1	yes	characteristic
90	#41×C₇₉	—	2	8	no	—
91	#41×C₇₉	—	2	8	no	—
92	#41×C₇₉	—	4	8	no	—
93	#41×C₇₉	—	4	4	no	—
94	#41×C₇₉	—	4	8	no	—
95	#41×C₇₉	—	4	4	no	—
96	C₂×Q₈×C₇₉	—	2	4	no	—
97	C₂×Q₈×C₇₉	—	2	2	no	—
98	C₂×Q₈×C₇₉	—	4	2	no	—
99	C₂×Q₈×C₇₉	—	4	1	no	—
100	C₂×D₄×C₇₉	—	2	4	no	—
101	C₂×D₄×C₇₉	—	2	2	no	—
102	C₂×D₄×C₇₉	—	2	2	no	—
103	C₂×D₄×C₇₉	—	4	2	no	—
104	C₂×D₄×C₇₉	—	4	8	no	—
105	C₂×D₄×C₇₉	—	4	2	no	—
106	C₂×D₄×C₇₉	—	4	2	no	—
107	C₂×D₄×C₇₉	—	4	2	no	—
108	C₂×D₄×C₇₉	—	4	2	no	—
109	C₂×D₄×C₇₉	—	4	2	no	—
110	C₂×D₄×C₇₉	—	4	1	no	—
111	C₂×D₄×C₇₉	—	4	1	no	—
112	C₂×D₄×C₇₉	—	4	2	no	—
113	C₂×D₄×C₇₉	—	8	4	no	—
114	C₂²×C₄×C₇₉	—	2	2	no	—
115	C₂²×C₄×C₇₉	—	2	2	no	—
116	C₂²×C₄×C₇₉	—	4	8	no	—
117	C₂²×C₄×C₇₉	—	4	1	no	—
118	C₂²×C₄×C₇₉	—	4	2	no	—
119	C₂²×C₄×C₇₉	—	4	2	no	—
120	C₂²×C₄×C₇₉	—	4	1	no	—
121	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	Q₁₆×C₇₉	—	2	4	no	—
128	Q₁₆×C₇₉	—	2	2	no	—
129	Q₁₆×C₇₉	C₂×D₄	1	4	yes	complemented
130	SD₁₆×C₇₉	—	2	8	no	—
131	SD₁₆×C₇₉	—	2	8	no	—
132	D₈×C₇₉	—	2	4	no	—
133	D₈×C₇₉	—	2	2	no	—
134	D₈×C₇₉	—	2	4	no	—
135	D₈×C₇₉	—	4	2	no	—
136	D₈×C₇₉	C₂×D₄	1	4	yes	complemented
137	C₂×C₈×C₇₉	—	2	2	no	—
138	C₂×C₈×C₇₉	—	2	2	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	2	no	—
142	C₂×C₈×C₇₉	C₂×D₄	1	4	yes	—
143	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₇₉	—	2	2	no	—
148	C₄⋊C₄×C₇₉	—	4	1	no	—
149	C₂²⋊C₄×C₇₉	—	4	2	no	—
150	C₂²⋊C₄×C₇₉	—	4	2	no	—
151	C₁₆×C₇₉	—	2	4	no	—
152	C₂³×C₇₉	—	2	2	no	—
153	C₂³×C₇₉	—	2	2	no	—
154	C₂³×C₇₉	—	4	1	no	—
155	C₂³×C₇₉	—	4	4	no	—
156	C₂³×C₇₉	—	4	2	no	—
157	C₂³×C₇₉	—	4	2	no	—
158	C₂³×C₇₉	—	8	2	no	—
159	C₂³×C₇₉	—	8	2	no	—
160	C₂³×C₇₉	—	8	2	no	—
161	C₂³×C₇₉	—	8	2	no	—
162	C₂³×C₇₉	—	8	2	no	—
163	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
164	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
165	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
166	Q₈×C₇₉	—	2	4	no	—
167	Q₈×C₇₉	—	4	4	no	—
168	Q₈×C₇₉	—	4	2	no	—
169	D₄×C₇₉	—	2	4	no	—
170	D₄×C₇₉	—	4	4	no	—
171	D₄×C₇₉	—	4	8	no	—
172	D₄×C₇₉	—	4	8	no	—
173	D₄×C₇₉	—	4	2	no	—
174	D₄×C₇₉	—	4	2	no	—
175	D₄×C₇₉	—	4	2	no	—
176	D₄×C₇₉	—	8	4	no	—
177	D₄×C₇₉	—	8	4	no	—
178	D₄×C₇₉	—	8	2	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	—	2	1	no	—
181	C₂×C₄×C₇₉	—	2	1	no	—
182	C₂×C₄×C₇₉	—	2	1	no	—
183	C₂×C₄×C₇₉	—	2	1	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	4	8	no	—
187	C₂×C₄×C₇₉	—	4	4	no	—
188	C₂×C₄×C₇₉	—	4	2	no	—
189	C₂×C₄×C₇₉	—	4	8	no	—
190	C₂×C₄×C₇₉	—	4	2	no	—
191	C₂×C₄×C₇₉	—	8	2	no	—
192	C₂×C₄×C₇₉	#120	1	2	yes	—
193	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₇₉	—	2	1	no	—
199	C₈×C₇₉	—	2	1	no	—
200	C₈×C₇₉	#120	1	2	yes	—
201	C₈×C₇₉	C₂²×D₄	1	2	yes	—
202	C₂²×C₇₉	—	2	1	no	—
203	C₂²×C₇₉	—	2	1	no	—
204	C₂²×C₇₉	—	2	1	no	—
205	C₂²×C₇₉	—	2	1	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	—	2	1	no	—
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	—	4	4	no	—
210	C₂²×C₇₉	—	4	4	no	—
211	C₂²×C₇₉	—	8	8	no	—
212	C₂²×C₇₉	—	8	2	no	—
213	C₂²×C₇₉	—	8	2	no	—
214	C₂²×C₇₉	—	8	2	no	—
215	C₂²×C₇₉	—	8	2	no	—
216	C₂²×C₇₉	—	8	2	no	—
217	C₂²×C₇₉	—	16	4	no	—
218	C₂²×C₇₉	#447	1	2	yes	—
219	C₂²×C₇₉	#509	1	2	yes	complemented
220	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
221	C₄×C₇₉	—	2	1	no	—
222	C₄×C₇₉	—	2	1	no	—
223	C₄×C₇₉	—	4	4	no	—
224	C₄×C₇₉	—	8	2	no	—
225	C₄×C₇₉	#447	1	2	yes	—
226	C₄×C₇₉	C₂×#120	1	1	yes	characteristic
227	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	#33520	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₇₉	—	2	2	no	—
230	C₂×C₇₉	—	2	2	no	—
231	C₂×C₇₉	—	4	1	no	—
232	C₂×C₇₉	—	8	4	no	—
233	C₂×C₇₉	—	16	2	no	—
234	C₂×C₇₉	C₂×#447	1	1	yes	characteristic
235	C₂×C₇₉	C₂×#509	1	1	yes	characteristic
236	C₂×C₇₉	#3414	1	1	yes	characteristic
237	C₂²×#135	C₂×C₇₉	1	1	yes	characteristic, complemented
238	C₂×#509	C₂×C₇₉	1	2	yes	complemented
239	C₂×#466	C₂×C₇₉	1	1	yes	characteristic, complemented
240	#2186	C₂×C₇₉	1	4	yes	complemented
241	#2185	C₂×C₇₉	1	2	yes	complemented
242	#2184	C₂×C₇₉	1	2	yes	complemented
243	#2139	C₂×C₇₉	1	2	yes	complemented
244	#2112	C₂×C₇₉	1	1	yes	characteristic, complemented
245	C₇₉	#33520	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×#41	—	2	1	no	—
247	C₂×#135	—	2	8	no	—
248	C₂×#135	—	2	1	no	—
249	C₂×#135	—	2	1	no	—
250	C₂×#135	C₂²×C₇₉	1	2	yes	—
251	C₂×#135	C₂²×C₇₉	1	2	yes	complemented
252	C₂²×Q₁₆	C₂²×C₇₉	1	1	yes	characteristic, complemented
253	C₂²×SD₁₆	—	2	1	no	—
254	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
255	C₂²×D₈	C₂²×C₇₉	1	1	yes	characteristic, complemented
256	C₂³×C₈	C₂²×C₇₉	1	1	yes	characteristic
257	C₂×#121	—	2	1	no	—
258	#509	—	2	8	no	—
259	C₂×SD₃₂	C₂²×C₇₉	1	4	yes	complemented
260	C₂×D₁₆	C₂²×C₇₉	1	4	yes	complemented
261	C₂×M₃₂	C₂²×C₇₉	1	2	yes	complemented
262	#466	—	2	1	no	—
263	#466	—	2	1	no	—
264	#466	C₂²×C₇₉	1	2	yes	—
265	#466	C₂²×C₇₉	1	2	yes	complemented
266	C₂×#107	C₂²×C₇₉	1	1	yes	characteristic, complemented
267	C₂×#102	—	2	1	no	—
268	#358	C₂²×C₇₉	1	4	yes	complemented
269	#357	C₂²×C₇₉	1	4	yes	complemented
270	C₂²⋊C₁₆	C₂²×C₇₉	1	2	yes	complemented
271	C₂²⋊C₁₆	C₂²×C₇₉	1	2	yes	complemented
272	C₂×#41	—	2	8	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	4	4	no	—
276	C₂×#41	—	4	1	no	—
277	C₂×#41	—	4	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	—	4	1	no	—
282	C₂²×D₄	—	4	1	no	—
283	C₂³×C₄	—	4	1	no	—
284	C₂³×C₄	D₄×C₇₉	1	1	yes	characteristic
285	#135	—	2	8	no	—
286	#135	—	2	8	no	—
287	#135	—	2	4	no	—
288	#135	—	2	4	no	—
289	#135	—	2	4	no	—
290	#135	D₄×C₇₉	1	8	yes	complemented
291	C₂×Q₁₆	—	2	4	no	—
292	C₂×Q₁₆	—	2	1	no	—
293	C₂×Q₁₆	C₂³×C₇₉	1	2	yes	—
294	C₂×SD₁₆	—	2	8	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×D₈	—	2	4	no	—
298	C₂×D₈	—	2	1	no	—
299	C₂×D₈	—	2	4	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	C₂³×C₇₉	1	2	yes	—
302	C₂×D₈	C₂³×C₇₉	1	2	yes	—
303	C₂²×C₈	—	2	4	no	—
304	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
305	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
306	C₂²×C₈	D₄×C₇₉	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₇₉	1	1	yes	characteristic
310	#121	—	2	2	no	—
311	#121	—	2	2	no	—
312	#121	—	4	1	no	—
313	#121	—	4	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	4	1	no	—
316	SD₃₂	—	2	8	no	—
317	D₁₆	—	2	8	no	—
318	M₃₂	—	2	4	no	—
319	C₂×C₁₆	C₂³×C₇₉	1	4	yes	—
320	#107	—	2	1	no	—
321	#107	C₂³×C₇₉	1	2	yes	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	C₂⁴	—	4	1	no	—
325	C₂⁴	—	4	1	no	—
326	C₂⁴	D₈×C₇₉	1	1	yes	characteristic
327	#41	—	2	8	no	—
328	#41	—	2	8	no	—
329	#41	—	4	8	no	—
330	#41	—	4	8	no	—
331	#41	—	4	4	no	—
332	#41	—	4	4	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	4	1	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	8	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	8	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	4	8	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	1	no	—
358	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
359	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
360	C₂²×C₄	D₈×C₇₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₇₉	1	1	yes	characteristic
364	Q₁₆	—	2	4	no	—
365	Q₁₆	—	2	2	no	—
366	Q₁₆	C₂×D₄×C₇₉	1	4	yes	complemented
367	SD₁₆	—	2	8	no	—
368	SD₁₆	—	2	8	no	—
369	D₈	—	2	4	no	—
370	D₈	—	2	2	no	—
371	D₈	—	2	4	no	—
372	D₈	—	4	2	no	—
373	D₈	C₂×D₄×C₇₉	1	4	yes	complemented
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
380	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
381	C₂×C₈	C₂×D₄×C₇₉	1	1	yes	characteristic
382	C₂×C₈	C₂×D₄×C₇₉	1	4	yes	—
383	C₂×C₈	C₂⁴×C₇₉	1	1	yes	characteristic
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₁₆	—	2	4	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	—	8	2	no	—
398	C₂³	—	8	2	no	—
399	C₂³	—	8	2	no	—
400	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
401	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
402	C₂³	C₂×D₈×C₇₉	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	4	4	no	—
405	Q₈	—	4	2	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	8	4	no	—
414	D₄	—	8	4	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	8	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	#120×C₇₉	1	2	yes	—
430	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
431	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
432	C₂×C₄	C₂×D₈×C₇₉	1	1	yes	characteristic
433	C₂×C₄	AGL(1,ℤ/8)×C₇₉	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₇₉	1	1	yes	characteristic
435	C₈	—	2	1	no	—
436	C₈	—	2	1	no	—
437	C₈	#120×C₇₉	1	2	yes	—
438	C₈	C₂²×D₄×C₇₉	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	8	8	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	16	4	no	—
455	C₂²	#447×C₇₉	1	2	yes	—
456	C₂²	#509×C₇₉	1	2	yes	complemented
457	C₂²	C₂²×D₈×C₇₉	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	4	no	—
461	C₄	—	8	2	no	—
462	C₄	#447×C₇₉	1	2	yes	—
463	C₄	C₂×#120×C₇₉	1	1	yes	characteristic
464	C₄	C₂×AGL(1,ℤ/8)×C₇₉	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	2	2	no	—
467	C₂	—	4	1	no	—
468	C₂	—	8	4	no	—
469	C₂	—	16	2	no	—
470	C₂	C₂×#447×C₇₉	1	1	yes	characteristic
471	C₂	C₂×#509×C₇₉	1	1	yes	characteristic
472	C₂	C₇₉×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ C₂³×C₈×C₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₇₉	C₂	semidirect
2. C₂×#509×C₇₉	C₂	semidirect
3. C₂×#466×C₇₉	C₂	semidirect
4. C₇₉×#2186	C₂	semidirect
5. C₇₉×#2185	C₂	semidirect
6. C₇₉×#2184	C₂	semidirect
7. C₇₉×#2139	C₂	semidirect
8. C₇₉×#2112	C₂	semidirect
14. C₂×#135×C₇₉	C₂²	semidirect
15. C₂²×Q₁₆×C₇₉	C₂²	semidirect
17. C₂²×D₈×C₇₉	C₂²	semidirect
18. C₂²×D₈×C₇₉	C₂²	semidirect
22. C₂×SD₃₂×C₇₉	C₂²	semidirect
23. C₂×D₁₆×C₇₉	C₂²	semidirect
24. C₂×M₃₂×C₇₉	C₂²	semidirect
28. #466×C₇₉	C₂²	semidirect
29. C₂×#107×C₇₉	C₂²	semidirect
31. #358×C₇₉	C₂²	semidirect
32. #357×C₇₉	C₂²	semidirect
33. C₂²⋊C₁₆×C₇₉	C₂²	semidirect
34. C₂²⋊C₁₆×C₇₉	C₂²	semidirect
53. #135×C₇₉	D₄	semidirect
129. Q₁₆×C₇₉	C₂×D₄	semidirect
136. D₈×C₇₉	C₂×D₄	semidirect
219. C₂²×C₇₉	#509	semidirect
228. #33520	C₇₉	direct (N × H)
237. C₂²×#135	C₂×C₇₉	semidirect
238. C₂×#509	C₂×C₇₉	semidirect
239. C₂×#466	C₂×C₇₉	semidirect
240. #2186	C₂×C₇₉	semidirect
241. #2185	C₂×C₇₉	semidirect
242. #2184	C₂×C₇₉	semidirect
243. #2139	C₂×C₇₉	semidirect
244. #2112	C₂×C₇₉	semidirect
245. C₇₉	#33520	direct (N × H)
251. C₂×#135	C₂²×C₇₉	semidirect
252. C₂²×Q₁₆	C₂²×C₇₉	semidirect
254. C₂²×D₈	C₂²×C₇₉	semidirect
255. C₂²×D₈	C₂²×C₇₉	semidirect
259. C₂×SD₃₂	C₂²×C₇₉	semidirect
260. C₂×D₁₆	C₂²×C₇₉	semidirect
261. C₂×M₃₂	C₂²×C₇₉	semidirect
265. #466	C₂²×C₇₉	semidirect
266. C₂×#107	C₂²×C₇₉	semidirect
268. #358	C₂²×C₇₉	semidirect
269. #357	C₂²×C₇₉	semidirect
270. C₂²⋊C₁₆	C₂²×C₇₉	semidirect
271. C₂²⋊C₁₆	C₂²×C₇₉	semidirect
290. #135	D₄×C₇₉	semidirect
366. Q₁₆	C₂×D₄×C₇₉	semidirect
373. D₈	C₂×D₄×C₇₉	semidirect
456. C₂²	#509×C₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₇₉	2
C₂×#509×C₇₉	2
C₂×#466×C₇₉	2
C₇₉×#2186	2
C₇₉×#2185	2
C₇₉×#2184	2
C₇₉×#2139	2
C₇₉×#2112	2
#33520	79

Subgroups — C79×#33520 #34145209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₉×#33520 #34145209