Subgroups — #34291839

Order 20224.

844 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098610	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098610	C₂	1	1	yes	maximal, characteristic
3	#430×D₇₉	C₂	1	2	yes	maximal
4	#23771816	C₂	1	1	yes	maximal, characteristic
5	#23764191	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764190	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764189	C₂	1	2	yes	maximal, complemented
8	#23764188	C₂	1	1	yes	maximal, characteristic, complemented
9	#23764187	C₂	1	2	yes	maximal, complemented
10	#344×D₇₉	C₂	1	2	yes	maximal
11	C₇₉×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11929607	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₇₉	C₂²	1	2	yes	—
14	C₂×M₁₆×D₇₉	C₂²	1	2	yes	—
15	C₂×M₁₆×D₇₉	C₂²	1	1	yes	characteristic
16	#117×D₇₉	C₂²	1	1	yes	characteristic
17	#19098612	C₂²	1	2	yes	—
18	#19098611	C₂²	1	2	yes	—
19	#19098611	C₂²	1	2	yes	—
20	#19098610	—	2	1	no	—
21	#19098610	—	2	1	no	—
22	#19098610	—	2	1	no	—
23	#19098610	—	2	1	no	—
24	#19098610	—	2	4	no	—
25	#19098610	C₄	1	8	yes	complemented
26	C₂×#14579097	C₂²	1	1	yes	characteristic
27	C₂×#14579097	C₂²	1	1	yes	characteristic
28	C₂×#14579096	C₂²	1	2	yes	—
29	C₂×#14579096	C₂²	1	2	yes	—
30	#108×D₇₉	—	2	4	no	—
31	#19098521	C₂²	1	1	yes	characteristic
32	#19098520	—	2	1	no	—
33	#19098519	C₂²	1	1	yes	characteristic
34	#19098518	C₂²	1	1	yes	characteristic
35	#19098517	—	2	1	no	—
36	#19098515	—	2	1	no	—
37	C₄×#11929607	—	2	1	no	—
38	#19098335	C₂²	1	2	yes	—
39	#19098334	C₂²	1	2	yes	—
40	#19098333	C₂²	1	2	yes	—
41	#430×C₇₉	C₂²	1	2	yes	—
42	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
44	#405×C₇₉	C₂²	1	1	yes	characteristic
45	#344×C₇₉	C₂²	1	2	yes	—
46	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
47	C₂×#11929608	C₂³	1	2	yes	—
48	C₂×#11929608	C₂³	1	2	yes	—
49	C₂×#11929608	C₂³	1	1	yes	characteristic
50	C₂×#11929607	—	2	1	no	—
51	C₂×#11929607	—	2	2	no	—
52	C₂×#11929607	—	2	2	no	—
53	C₂×#11929607	C₂×C₄	1	4	yes	—
54	C₂×#11929607	D₄	1	1	yes	characteristic
55	C₂×#11929607	D₄	1	1	yes	characteristic
56	C₂×#11929607	D₄	1	1	yes	characteristic
57	C₂×#11929607	D₄	1	1	yes	characteristic
58	C₂×#11929607	Q₈	1	4	yes	—
59	M₁₆×D₇₉	—	2	2	no	—
60	M₁₆×D₇₉	—	2	2	no	—
61	M₁₆×D₇₉	—	2	2	no	—
62	M₁₆×D₇₉	—	2	2	no	—
63	M₁₆×D₇₉	—	2	2	no	—
64	M₁₆×D₇₉	—	2	2	no	—
65	M₁₆×D₇₉	—	2	2	no	—
66	M₁₆×D₇₉	C₂×C₄	1	4	yes	—
67	M₁₆×D₇₉	C₂×C₄	1	4	yes	—
68	M₁₆×D₇₉	D₄	1	4	yes	—
69	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₇₉	—	2	1	no	—
71	C₂×C₈×D₇₉	—	2	2	no	—
72	C₂×C₈×D₇₉	—	2	2	no	—
73	#14579120	C₂³	1	1	yes	characteristic
74	#14579119	—	2	1	no	—
75	#14579118	—	2	1	no	—
76	#14579117	Q₈	1	2	yes	—
77	C₄⋊C₄×D₇₉	—	2	1	no	—
78	C₂²⋊C₄×D₇₉	Q₈	1	2	yes	—
79	C₄²×D₇₉	—	2	1	no	—
80	#14579097	—	2	1	no	—
81	#14579097	—	2	1	no	—
82	#14579097	—	2	4	no	—
83	#14579097	C₂×C₄	1	4	yes	complemented
84	#14579096	—	2	4	no	—
85	#14579096	—	2	4	no	—
86	#14579096	—	2	2	no	—
87	#14579096	—	2	2	no	—
88	#14579096	C₂×C₄	1	8	yes	complemented
89	#14579072	—	2	1	no	—
90	#14579071	—	2	1	no	—
91	#14579071	—	2	1	no	—
92	C₄×C₇₉⋊C₈	—	2	1	no	—
93	C₈×Dic₇₉	—	2	1	no	—
94	C₈×Dic₇₉	—	2	1	no	—
95	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
96	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
97	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
99	#117×C₇₉	C₂³	1	1	yes	characteristic
100	#108×C₇₉	—	2	4	no	—
101	#108×C₇₉	—	2	1	no	—
102	#108×C₇₉	—	2	1	no	—
103	#108×C₇₉	C₂×C₄	1	4	yes	complemented
104	#97×C₇₉	—	2	1	no	—
105	C₄×C₈×C₇₉	—	2	1	no	—
106	C₂³×D₇₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₇₉	—	2	2	no	—
109	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
113	C₂×C₄×D₇₉	C₂×Q₈	1	2	yes	—
114	C₂×C₄×D₇₉	#41	1	2	yes	—
115	C₂×C₄×D₇₉	#41	1	1	yes	characteristic
116	C₂×C₄×D₇₉	#41	1	1	yes	characteristic
117	#11929608	—	2	2	no	—
118	#11929608	—	2	2	no	—
119	#11929608	—	2	2	no	—
120	#11929608	—	2	1	no	—
121	#11929608	C₂²×C₄	1	4	yes	—
122	#11929608	C₂×D₄	1	2	yes	—
123	#11929607	—	2	4	no	—
124	#11929607	—	2	4	no	—
125	#11929607	—	2	4	no	—
126	#11929607	—	4	2	no	—
127	#11929607	—	4	2	no	—
128	#11929607	C₄⋊C₄	1	4	yes	—
129	#11929607	C₄⋊C₄	1	4	yes	—
130	#11929607	C₄⋊C₄	1	4	yes	—
131	#11929607	C₄⋊C₄	1	4	yes	—
132	C₂×C₇₉⋊C₈	—	2	1	no	—
133	C₂×C₇₉⋊C₈	—	2	2	no	—
134	C₂×C₇₉⋊C₈	—	2	2	no	—
135	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
139	C₈×D₇₉	—	2	4	no	—
140	C₈×D₇₉	—	2	4	no	—
141	C₈×D₇₉	—	2	4	no	—
142	C₈×D₇₉	—	4	2	no	—
143	C₈×D₇₉	—	4	2	no	—
144	C₄⋊Dic₇₉	—	2	1	no	—
145	Dic₇₉⋊C₄	—	2	2	no	—
146	C₂²⋊Dic₇₉	C₂×Q₈	1	2	yes	—
147	(C₂×D₇₉)⋊C₄	—	2	2	no	—
148	C₄×Dic₇₉	—	2	2	no	—
149	C₄×Dic₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₇₉	—	2	2	no	—
152	M₁₆×C₇₉	—	2	2	no	—
153	M₁₆×C₇₉	—	2	2	no	—
154	M₁₆×C₇₉	—	2	1	no	—
155	M₁₆×C₇₉	C₂²×C₄	1	4	yes	—
156	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₇₉	—	2	1	no	—
158	C₂×C₈×C₇₉	—	2	2	no	—
159	C₂×C₈×C₇₉	—	2	2	no	—
160	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
164	C₄⋊C₄×C₇₉	—	2	1	no	—
165	C₂²⋊C₄×C₇₉	C₂×Q₈	1	2	yes	—
166	C₄²×C₇₉	—	2	1	no	—
167	C₂³×C₇₉	C₂²×Q₈	1	1	yes	characteristic
168	C₂²×D₇₉	—	8	1	no	—
169	C₂²×D₇₉	C₄×Q₈	1	2	yes	—
170	C₂²×D₇₉	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂²×D₇₉	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂²×D₇₉	C₄⋊Q₈	1	2	yes	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
180	C₂×Dic₇₉	—	2	2	no	—
181	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
182	C₂×Dic₇₉	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×Dic₇₉	C₂²⋊Q₈	1	1	yes	characteristic
184	C₂×Dic₇₉	C₄⋊Q₈	1	2	yes	—
185	C₄×D₇₉	—	8	2	no	—
186	C₄×D₇₉	C₂×C₄⋊C₄	1	2	yes	—
187	C₄×D₇₉	C₂×C₄⋊C₄	1	2	yes	—
188	C₄×D₇₉	C₄×D₄	1	2	yes	—
189	C₄×D₇₉	C₄×D₄	1	2	yes	—
190	C₄×D₇₉	#121	1	2	yes	—
191	C₄×D₇₉	#121	1	2	yes	—
192	C₄×D₇₉	#125	1	2	yes	—
193	C₄×D₇₉	#125	1	2	yes	—
194	C₈×C₇₉	—	2	4	no	—
195	C₈×C₇₉	—	2	2	no	—
196	C₈×C₇₉	—	4	2	no	—
197	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
198	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
199	C₇₉⋊C₈	—	2	4	no	—
200	C₇₉⋊C₈	—	2	2	no	—
201	C₇₉⋊C₈	—	4	2	no	—
202	C₇₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
203	C₇₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
204	C₂²×C₇₉	—	4	1	no	—
205	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
206	C₂²×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
207	C₂²×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
208	C₂×D₇₉	—	4	2	no	—
209	C₂×D₇₉	—	4	1	no	—
210	C₂×D₇₉	—	4	1	no	—
211	C₂×D₇₉	—	4	2	no	—
212	C₂×D₇₉	#389	1	2	yes	—
213	C₂×D₇₉	#389	1	2	yes	—
214	C₄×C₇₉	—	4	2	no	—
215	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
218	C₄×C₇₉	C₂×#125	1	1	yes	characteristic
219	Dic₇₉	—	4	2	no	—
220	Dic₇₉	#389	1	2	yes	—
221	Dic₇₉	#389	1	2	yes	—
222	#21184	—	79	1	no	maximal, Sylow
223	C₂×C₇₉	—	2	1	no	—
224	C₂×C₇₉	—	2	1	no	—
225	C₂×C₇₉	—	2	1	no	—
226	C₂×C₇₉	C₂×#389	1	1	yes	characteristic
227	D₇₉	—	2	2	no	—
228	D₇₉	—	2	2	no	—
229	C₂×#430	—	79	1	no	—
230	C₂×#430	—	79	1	no	—
231	C₂×#430	—	79	2	no	—
232	#2873	—	79	1	no	—
233	#1953	—	79	2	no	—
234	#1953	—	79	1	no	—
235	#1953	—	79	1	no	—
236	#1953	—	79	1	no	—
237	#1953	—	79	2	no	—
238	#1953	D₇₉	1	1	yes	characteristic, complemented
239	C₂×#344	—	79	2	no	—
240	C₇₉	#21184	1	1	yes	characteristic, complemented, Sylow
241	C₂²×M₁₆	—	79	1	no	—
242	C₂²×M₁₆	—	79	1	no	—
243	C₂²×M₁₆	—	79	2	no	—
244	C₂²×M₁₆	—	79	2	no	—
245	C₂×#117	—	79	1	no	—
246	#430	—	79	8	no	—
247	#430	—	79	2	no	—
248	#430	—	79	2	no	—
249	#430	—	79	2	no	—
250	#430	—	158	4	no	—
251	#430	—	158	1	no	—
252	#430	—	158	1	no	—
253	#430	—	158	1	no	—
254	#430	—	158	1	no	—
255	#430	C₂×D₇₉	1	2	yes	—
256	C₂×#108	—	79	2	no	—
257	C₂×#108	—	79	1	no	—
258	C₂×#108	—	79	2	no	—
259	C₂×#108	—	79	1	no	—
260	C₂×#108	—	158	4	no	—
261	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
262	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
263	#405	—	79	1	no	—
264	#405	—	79	1	no	—
265	#405	—	79	1	no	—
266	#405	—	158	1	no	—
267	#405	—	158	1	no	—
268	#405	C₂×D₇₉	1	1	yes	characteristic
269	C₄×M₁₆	—	158	1	no	—
270	C₄×M₁₆	—	158	1	no	—
271	#344	—	79	2	no	—
272	#344	—	79	2	no	—
273	#344	—	79	2	no	—
274	#344	C₂×D₇₉	1	2	yes	—
275	C₂³×C₄	—	79	1	no	—
276	C₂×M₁₆	—	79	4	no	—
277	C₂×M₁₆	—	79	1	no	—
278	C₂×M₁₆	—	79	1	no	—
279	C₂×M₁₆	—	79	1	no	—
280	C₂×M₁₆	—	79	1	no	—
281	C₂×M₁₆	—	79	4	no	—
282	C₂×M₁₆	—	79	2	no	—
283	C₂×M₁₆	—	79	1	no	—
284	C₂×M₁₆	—	79	4	no	—
285	C₂×M₁₆	—	79	4	no	—
286	C₂×M₁₆	—	79	4	no	—
287	C₂×M₁₆	—	79	2	no	—
288	C₂×M₁₆	—	158	2	no	—
289	C₂×M₁₆	—	158	1	no	—
290	C₂×M₁₆	—	158	2	no	—
291	C₂×M₁₆	—	158	2	no	—
292	C₂×M₁₆	—	158	2	no	—
293	C₂×M₁₆	—	158	2	no	—
294	C₂×M₁₆	—	158	2	no	—
295	C₂×M₁₆	—	158	2	no	—
296	C₂×M₁₆	—	158	2	no	—
297	C₂×M₁₆	—	158	2	no	—
298	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
299	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
300	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
301	C₂²×C₈	—	79	1	no	—
302	C₂²×C₈	—	158	2	no	—
303	C₂²×C₈	—	158	1	no	—
304	C₂²×C₈	—	158	2	no	—
305	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
306	#117	—	79	1	no	—
307	#117	—	79	2	no	—
308	#117	—	158	1	no	—
309	#117	—	158	1	no	—
310	#117	C₂²×D₇₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	158	1	no	—
312	C₂×C₂²⋊C₄	—	79	2	no	—
313	C₂×C₄²	—	158	1	no	—
314	#108	—	2	4	no	—
315	#108	—	2	1	no	—
316	#108	—	2	1	no	—
317	#108	—	79	8	no	—
318	#108	—	79	4	no	—
319	#108	—	158	4	no	—
320	#108	—	158	2	no	—
321	#108	—	158	2	no	—
322	#108	—	158	4	no	—
323	#108	—	158	4	no	—
324	#108	—	158	1	no	—
325	#108	—	158	1	no	—
326	#108	C₄×D₇₉	1	4	yes	complemented
327	#97	—	2	1	no	—
328	#97	—	158	1	no	—
329	#97	—	158	1	no	—
330	#97	—	158	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	158	1	no	—
333	C₄×C₈	—	158	1	no	—
334	C₄×C₈	—	158	1	no	—
335	C₂⁴	—	79	1	no	—
336	C₂²×C₄	—	79	1	no	—
337	C₂²×C₄	—	79	2	no	—
338	C₂²×C₄	—	79	1	no	—
339	C₂²×C₄	—	79	1	no	—
340	C₂²×C₄	—	79	2	no	—
341	C₂²×C₄	—	79	2	no	—
342	C₂²×C₄	—	79	1	no	—
343	C₂²×C₄	—	79	1	no	—
344	C₂²×C₄	—	79	2	no	—
345	C₂²×C₄	—	158	2	no	—
346	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	1	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	316	2	no	—
352	M₁₆	—	316	2	no	—
353	M₁₆	—	79	4	no	—
354	M₁₆	—	79	4	no	—
355	M₁₆	—	79	4	no	—
356	M₁₆	—	79	4	no	—
357	M₁₆	—	79	4	no	—
358	M₁₆	—	79	2	no	—
359	M₁₆	—	158	4	no	—
360	M₁₆	—	158	4	no	—
361	M₁₆	—	158	4	no	—
362	M₁₆	—	158	2	no	—
363	M₁₆	—	158	2	no	—
364	M₁₆	—	158	2	no	—
365	M₁₆	—	158	1	no	—
366	M₁₆	C₂×C₄×D₇₉	1	4	yes	—
367	M₁₆	D₄×D₇₉	1	2	yes	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	316	2	no	—
372	C₂×C₈	—	316	2	no	—
373	C₂×C₈	—	79	2	no	—
374	C₂×C₈	—	79	2	no	—
375	C₂×C₈	—	79	1	no	—
376	C₂×C₈	—	79	1	no	—
377	C₂×C₈	—	158	4	no	—
378	C₂×C₈	—	158	4	no	—
379	C₂×C₈	—	158	4	no	—
380	C₂×C₈	—	158	2	no	—
381	C₂×C₈	—	158	1	no	—
382	C₂×C₈	—	158	2	no	—
383	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
384	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
385	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
386	C₂×C₈	Q₈×D₇₉	1	2	yes	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	158	2	no	—
389	C₄⋊C₄	—	158	1	no	—
390	C₂²⋊C₄	—	79	2	no	—
391	C₂²⋊C₄	—	158	2	no	—
392	C₂²⋊C₄	Q₈×D₇₉	1	2	yes	—
393	C₄²	—	2	1	no	—
394	C₄²	—	158	2	no	—
395	C₄²	—	158	1	no	—
396	C₂³	—	79	2	no	—
397	C₂³	—	79	1	no	—
398	C₂³	—	79	1	no	—
399	C₂³	—	79	2	no	—
400	C₂³	—	632	1	no	—
401	C₂³	C₂×Q₈×D₇₉	1	1	yes	characteristic
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	79	2	no	—
404	C₂×C₄	—	79	1	no	—
405	C₂×C₄	—	79	1	no	—
406	C₂×C₄	—	79	2	no	—
407	C₂×C₄	—	79	2	no	—
408	C₂×C₄	—	79	2	no	—
409	C₂×C₄	—	79	2	no	—
410	C₂×C₄	—	79	2	no	—
411	C₂×C₄	—	79	2	no	—
412	C₂×C₄	—	79	2	no	—
413	C₂×C₄	—	79	2	no	—
414	C₂×C₄	—	79	2	no	—
415	C₂×C₄	—	632	2	no	—
416	C₂×C₄	—	158	2	no	—
417	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
418	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
420	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
421	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
422	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	2	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	316	2	no	—
427	C₈	—	79	2	no	—
428	C₈	—	79	2	no	—
429	C₈	—	158	4	no	—
430	C₈	—	158	2	no	—
431	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
432	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
433	C₂²	—	4	1	no	—
434	C₂²	—	316	1	no	—
435	C₂²	—	316	1	no	—
436	C₂²	—	316	2	no	—
437	C₂²	—	316	2	no	—
438	C₂²	—	79	2	no	—
439	C₂²	—	79	2	no	—
440	C₂²	C₄×Q₈×D₇₉	1	1	yes	characteristic
441	C₂²	C₂²⋊Q₈×D₇₉	1	1	yes	characteristic
442	C₂²	C₄⋊Q₈×D₇₉	1	1	yes	characteristic
443	C₄	—	4	2	no	—
444	C₄	—	316	2	no	—
445	C₄	—	79	2	no	—
446	C₄	—	79	2	no	—
447	C₄	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
448	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
449	C₄	#121×D₇₉	1	1	yes	characteristic
450	C₄	#125×D₇₉	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	158	2	no	—
455	C₂	—	158	2	no	—
456	C₂	#389×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1953	C₂
socle	C₂×C₇₉	C₂×#389
prime radical	C₂³×D₇₉	C₂×Q₈
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1953	D₇₉
hypocenter	C₇₉	#21184
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
5. #23764191	C₂	semidirect
6. #23764190	C₂	semidirect
7. #23764189	C₂	semidirect
8. #23764188	C₂	semidirect
9. #23764187	C₂	semidirect
11. C₇₉×#1953	C₂	semidirect
25. #19098610	C₄	semidirect
83. #14579097	C₂×C₄	semidirect
88. #14579096	C₂×C₄	semidirect
103. #108×C₇₉	C₂×C₄	semidirect
238. #1953	D₇₉	semidirect
240. C₇₉	#21184	semidirect
326. #108	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098610	2
#430×D₇₉	2
#23771816	2
#23764191	2
#23764190	2
#23764189	2
#23764188	2
#23764187	2
#344×D₇₉	2
C₇₉×#1953	2
#21184	79