Subgroups — #34307965

Order 20224.

722 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#23772062	C₂	1	2	yes	maximal, complemented
3	#23764289	C₂	1	1	yes	maximal, characteristic
4	#23764051	C₂	1	2	yes	maximal, complemented
5	#23764045	C₂	1	2	yes	maximal, complemented
6	#23763570	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763418	C₂	1	2	yes	maximal, complemented
8	#23763282	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763279	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×Dic₇₉⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1974	C₂	1	1	yes	maximal, characteristic
12	#41×Dic₇₉	C₂²	1	2	yes	—
13	Q₁₆×Dic₇₉	C₄	1	1	yes	characteristic, complemented
14	Q₁₆×Dic₇₉	C₄	1	1	yes	characteristic, complemented
15	SD₁₆×Dic₇₉	C₄	1	2	yes	complemented
16	SD₁₆×Dic₇₉	C₄	1	2	yes	complemented
17	D₈×Dic₇₉	C₄	1	1	yes	characteristic, complemented
18	D₈×Dic₇₉	C₄	1	1	yes	characteristic, complemented
19	#19098621	—	2	2	no	—
20	#19098621	—	2	2	no	—
21	#19098617	—	2	2	no	—
22	#19098613	—	2	2	no	—
23	C₂×#14579097	C₂²	1	1	yes	characteristic
24	C₂×#14579096	C₂²	1	2	yes	—
25	#19098601	C₂²	1	1	yes	characteristic
26	#19098586	C₂²	1	2	yes	—
27	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#14579088	C₂²	1	2	yes	—
29	#19098559	C₂²	1	2	yes	—
30	#19098530	C₂²	1	2	yes	—
31	#19098521	C₂²	1	2	yes	—
32	#19098518	C₂²	1	2	yes	—
33	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
35	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
36	#19098324	C₂²	1	2	yes	—
37	#19098323	C₂²	1	2	yes	—
38	#19098318	C₂²	1	1	yes	characteristic
39	#19098317	C₂²	1	1	yes	characteristic
40	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#104×C₇₉	C₂²	1	2	yes	—
43	#408×C₇₉	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#11929608	C₂³	1	2	yes	—
46	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
48	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
49	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
50	D₄×Dic₇₉	—	2	2	no	—
51	D₄×Dic₇₉	—	2	2	no	—
52	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
53	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
54	#14579120	—	2	2	no	—
55	#14579120	C₂³	1	2	yes	—
56	C₂×Dic₇₉⋊C₄	—	2	1	no	—
57	C₂×C₄×Dic₇₉	—	2	2	no	—
58	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
60	#14579097	—	2	2	no	—
61	#14579096	—	4	2	no	—
62	#14579095	C₂×C₄	1	1	yes	characteristic
63	#14579095	C₂×C₄	1	1	yes	characteristic
64	#14579093	C₂×C₄	1	2	yes	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	Dic₇₉⋊C₈	—	2	2	no	—
67	Dic₇₉⋊C₈	D₄	1	1	yes	characteristic
68	Dic₇₉⋊C₈	D₄	1	1	yes	characteristic
69	Dic₇₉⋊C₈	D₄	1	1	yes	characteristic
70	Dic₇₉⋊C₈	D₄	1	1	yes	characteristic
71	#14579088	—	4	2	no	—
72	#14579085	C₂×C₄	1	2	yes	—
73	#14579085	C₂×C₄	1	2	yes	—
74	#14579082	C₂×C₄	1	2	yes	—
75	#14579082	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
78	#14579071	—	2	2	no	—
79	#14579071	—	2	2	no	—
80	C₈×Dic₇₉	—	2	2	no	—
81	C₈×Dic₇₉	—	2	2	no	—
82	C₈×Dic₇₉	—	2	2	no	—
83	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
87	C₇₉⋊#95	—	2	1	no	—
88	C₂×#41×C₇₉	C₂³	1	2	yes	—
89	#135×C₇₉	—	2	2	no	—
90	#135×C₇₉	—	2	2	no	—
91	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
93	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
94	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
95	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	#108×C₇₉	—	2	2	no	—
99	#104×C₇₉	—	4	2	no	—
100	C₂²⋊C₈×C₇₉	—	2	2	no	—
101	C₂²⋊C₈×C₇₉	—	2	2	no	—
102	C₄×C₈×C₇₉	—	2	2	no	—
103	C₂²×Dic₇₉	—	2	2	no	—
104	C₂²×Dic₇₉	—	2	2	no	—
105	C₂²×Dic₇₉	—	2	1	no	—
106	C₂²×Dic₇₉	#41	1	1	yes	characteristic
107	C₂²×Dic₇₉	#41	1	1	yes	characteristic
108	#11929608	—	2	2	no	—
109	#11929608	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	1	no	—
115	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₄⋊Dic₇₉	—	2	2	no	—
120	C₄⋊Dic₇₉	—	2	2	no	—
121	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
122	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
123	Dic₇₉⋊C₄	—	2	4	no	—
124	C₂²⋊Dic₇₉	—	2	2	no	—
125	C₂²⋊Dic₇₉	—	2	2	no	—
126	C₂²⋊Dic₇₉	—	2	2	no	—
127	C₄×Dic₇₉	—	2	2	no	—
128	C₄×Dic₇₉	—	2	2	no	—
129	C₄×Dic₇₉	—	2	2	no	—
130	C₄×Dic₇₉	—	2	1	no	—
131	C₄×Dic₇₉	—	2	1	no	—
132	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
136	#41×C₇₉	—	2	2	no	—
137	#41×C₇₉	—	2	2	no	—
138	#41×C₇₉	—	2	2	no	—
139	#41×C₇₉	—	2	2	no	—
140	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂×D₄×C₇₉	—	2	2	no	—
142	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	2	no	—
145	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₇₉	—	2	2	no	—
147	SD₁₆×C₇₉	—	2	4	no	—
148	D₈×C₇₉	—	2	2	no	—
149	M₁₆×C₇₉	—	2	2	no	—
150	M₁₆×C₇₉	—	2	2	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	1	no	—
153	C₂×C₈×C₇₉	—	2	1	no	—
154	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₉	#41	1	2	yes	—
159	C₂×C₈×C₇₉	#41	1	2	yes	—
160	C₄²×C₇₉	—	2	1	no	—
161	C₄²×C₇₉	—	2	1	no	—
162	C₂³×C₇₉	—	2	2	no	—
163	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
164	Q₈×C₇₉	—	2	2	no	—
165	Q₈×C₇₉	—	2	2	no	—
166	D₄×C₇₉	—	2	2	no	—
167	D₄×C₇₉	—	2	2	no	—
168	D₄×C₇₉	—	4	2	no	—
169	D₄×C₇₉	—	4	2	no	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	4	1	no	—
173	C₂×C₄×C₇₉	—	4	1	no	—
174	C₂×C₄×C₇₉	—	4	2	no	—
175	C₂×C₄×C₇₉	—	4	2	no	—
176	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂²×D₄	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×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×Dic₇₉	—	2	2	no	—
183	C₂×Dic₇₉	—	2	2	no	—
184	C₂×Dic₇₉	—	2	2	no	—
185	C₂×Dic₇₉	—	2	2	no	—
186	C₂×Dic₇₉	—	4	1	no	—
187	C₂×Dic₇₉	—	4	1	no	—
188	C₂×Dic₇₉	—	4	1	no	—
189	C₂×Dic₇₉	—	4	4	no	—
190	C₂×Dic₇₉	—	8	2	no	—
191	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
192	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
193	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
194	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
195	C₈×C₇₉	—	2	1	no	—
196	C₈×C₇₉	—	2	1	no	—
197	C₈×C₇₉	—	4	2	no	—
198	C₈×C₇₉	#117	1	2	yes	—
199	C₈×C₇₉	#117	1	2	yes	—
200	C₇₉⋊C₈	—	2	1	no	—
201	C₇₉⋊C₈	—	2	1	no	—
202	C₇₉⋊C₈	—	2	1	no	—
203	C₇₉⋊C₈	—	2	1	no	—
204	C₇₉⋊C₈	—	4	2	no	—
205	C₂²×C₇₉	—	2	1	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	—	4	2	no	—
208	C₂²×C₇₉	—	4	2	no	—
209	C₂²×C₇₉	—	4	2	no	—
210	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₇₉	#555	1	1	yes	characteristic
212	C₂²×C₇₉	#556	1	1	yes	characteristic
213	C₄×C₇₉	—	4	2	no	—
214	C₄×C₇₉	—	4	2	no	—
215	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
216	C₄×C₇₉	#520	1	1	yes	characteristic
217	C₄×C₇₉	#547	1	1	yes	characteristic
218	C₄×C₇₉	#550	1	1	yes	characteristic
219	Dic₇₉	—	2	1	no	—
220	Dic₇₉	—	2	1	no	—
221	Dic₇₉	—	2	1	no	—
222	Dic₇₉	—	4	2	no	—
223	Dic₇₉	—	4	2	no	—
224	Dic₇₉	—	4	2	no	—
225	Dic₇₉	#443	1	2	yes	—
226	#22802	—	79	1	no	maximal, Sylow
227	C₂×C₇₉	—	2	1	no	—
228	C₂×C₇₉	—	2	1	no	—
229	C₂×C₇₉	—	8	2	no	—
230	C₂×C₇₉	#2354	1	1	yes	characteristic
231	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
232	C₂×C₇₉	#2957	1	1	yes	characteristic
233	C₄×#135	—	79	1	no	—
234	#2925	—	79	2	no	—
235	#1974	—	79	1	no	—
236	#1974	D₇₉	1	1	yes	characteristic
237	#1929	—	79	2	no	—
238	#1929	—	79	2	no	—
239	#1848	—	79	1	no	—
240	#1806	—	79	2	no	—
241	#1772	—	79	1	no	—
242	#1772	—	79	1	no	—
243	C₈×C₄⋊C₄	—	79	1	no	—
244	C₇₉	#22802	1	1	yes	characteristic, complemented, Sylow
245	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
246	C₄×#41	—	79	2	no	—
247	C₄×Q₁₆	—	79	1	no	—
248	C₄×Q₁₆	—	79	1	no	—
249	C₄×SD₁₆	—	79	2	no	—
250	C₄×SD₁₆	—	79	2	no	—
251	C₄×D₈	—	79	1	no	—
252	C₄×D₈	—	79	1	no	—
253	#433	—	158	2	no	—
254	#433	—	158	2	no	—
255	#432	—	158	2	no	—
256	#431	—	158	2	no	—
257	C₂×#108	—	79	2	no	—
258	C₂×#108	—	79	1	no	—
259	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
260	#427	—	79	1	no	—
261	#423	—	79	2	no	—
262	C₂×C₄⋊C₈	—	79	1	no	—
263	C₂×#104	—	79	2	no	—
264	C₂×#104	C₂×D₇₉	1	2	yes	—
265	#416	—	79	2	no	—
266	#408	—	79	2	no	—
267	#408	C₂×D₇₉	1	2	yes	—
268	#405	—	79	2	no	—
269	#405	—	79	2	no	—
270	C₂×C₄×C₈	—	79	1	no	—
271	C₂×C₄×C₈	—	79	1	no	—
272	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	—	79	1	no	—
274	#339	—	79	2	no	—
275	#339	—	79	2	no	—
276	#336	—	79	1	no	—
277	#336	—	79	1	no	—
278	C₂×#41	C₂²×D₇₉	1	2	yes	—
279	#135	—	2	2	no	—
280	#135	—	2	2	no	—
281	C₂×Q₁₆	C₄×D₇₉	1	1	yes	characteristic
282	C₂×SD₁₆	C₄×D₇₉	1	2	yes	—
283	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic
284	C₂×M₁₆	—	79	2	no	—
285	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
286	C₂²×C₈	—	79	1	no	—
287	C₂²×C₈	—	79	1	no	—
288	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
290	C₄×Q₈	—	79	2	no	—
291	C₄×Q₈	—	79	2	no	—
292	C₄×D₄	—	79	2	no	—
293	C₄×D₄	—	79	2	no	—
294	C₄×D₄	—	158	2	no	—
295	C₄×D₄	—	158	2	no	—
296	#117	—	79	2	no	—
297	#117	—	158	2	no	—
298	C₂×C₄⋊C₄	—	158	1	no	—
299	C₂×C₄²	—	79	1	no	—
300	C₂×C₄²	—	79	1	no	—
301	C₂×C₄²	—	158	2	no	—
302	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
303	#108	—	2	2	no	—
304	#108	—	316	2	no	—
305	#108	—	158	2	no	—
306	#107	—	79	1	no	—
307	#107	—	79	1	no	—
308	#106	—	79	2	no	—
309	C₄⋊C₈	—	79	1	no	—
310	C₄⋊C₈	—	79	1	no	—
311	C₄⋊C₈	—	79	1	no	—
312	C₄⋊C₈	—	79	1	no	—
313	C₄⋊C₈	—	158	2	no	—
314	C₄⋊C₈	—	158	2	no	—
315	#104	—	4	2	no	—
316	#104	—	316	2	no	—
317	#103	—	79	2	no	—
318	#103	—	79	2	no	—
319	#102	—	79	2	no	—
320	#102	—	79	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	158	2	no	—
324	C₂²⋊C₈	—	158	2	no	—
325	#97	—	158	2	no	—
326	#97	—	158	2	no	—
327	C₄×C₈	—	2	2	no	—
328	C₄×C₈	—	79	1	no	—
329	C₄×C₈	—	79	1	no	—
330	C₄×C₈	—	79	1	no	—
331	C₄×C₈	—	79	1	no	—
332	C₄×C₈	—	158	2	no	—
333	C₄×C₈	—	158	2	no	—
334	C₄×C₈	—	158	2	no	—
335	#95	—	158	1	no	—
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	79	1	no	—
346	C₂²×C₄	—	79	1	no	—
347	C₂²×C₄	—	158	2	no	—
348	C₂²×C₄	—	158	1	no	—
349	C₂²×C₄	—	158	2	no	—
350	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
351	Q₁₆	—	2	2	no	—
352	SD₁₆	—	2	4	no	—
353	D₈	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	158	2	no	—
357	M₁₆	—	158	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	79	1	no	—
362	C₂×C₈	—	79	1	no	—
363	C₂×C₈	—	79	1	no	—
364	C₂×C₈	—	79	1	no	—
365	C₂×C₈	—	158	2	no	—
366	C₂×C₈	—	158	1	no	—
367	C₂×C₈	—	158	1	no	—
368	C₂×C₈	—	158	1	no	—
369	C₂×C₈	—	158	1	no	—
370	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
371	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
372	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
373	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
374	C₂×C₈	#11929623	1	2	yes	—
375	C₂×C₈	#11929623	1	2	yes	—
376	C₄⋊C₄	—	79	2	no	—
377	C₄⋊C₄	—	79	2	no	—
378	C₄⋊C₄	—	158	2	no	—
379	C₄⋊C₄	—	158	2	no	—
380	C₄⋊C₄	—	158	4	no	—
381	C₂²⋊C₄	—	158	2	no	—
382	C₂²⋊C₄	—	158	2	no	—
383	C₂²⋊C₄	—	158	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	79	1	no	—
387	C₄²	—	79	1	no	—
388	C₄²	—	79	1	no	—
389	C₄²	—	79	1	no	—
390	C₄²	—	158	2	no	—
391	C₄²	—	158	2	no	—
392	C₄²	—	158	1	no	—
393	C₄²	—	158	1	no	—
394	C₄²	—	158	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	#41×D₇₉	1	1	yes	characteristic
397	Q₈	—	2	2	no	—
398	Q₈	—	2	2	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	316	1	no	—
410	C₂×C₄	—	316	1	no	—
411	C₂×C₄	—	316	4	no	—
412	C₂×C₄	—	316	1	no	—
413	C₂×C₄	—	79	1	no	—
414	C₂×C₄	—	79	1	no	—
415	C₂×C₄	—	79	1	no	—
416	C₂×C₄	—	79	1	no	—
417	C₂×C₄	—	632	2	no	—
418	C₂×C₄	—	158	2	no	—
419	C₂×C₄	—	158	2	no	—
420	C₂×C₄	—	158	2	no	—
421	C₂×C₄	—	158	2	no	—
422	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
425	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
426	C₂×C₄	#14579206	1	1	yes	characteristic
427	C₂×C₄	#14579208	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	316	2	no	—
432	C₈	—	158	1	no	—
433	C₈	—	158	1	no	—
434	C₈	—	158	1	no	—
435	C₈	—	158	1	no	—
436	C₈	#14579117	1	2	yes	—
437	C₈	#14579117	1	2	yes	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
444	C₂²	#19099277	1	1	yes	characteristic
445	C₂²	#19099282	1	1	yes	characteristic
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	316	2	no	—
449	C₄	—	316	2	no	—
450	C₄	—	316	2	no	—
451	C₄	—	79	2	no	—
452	C₄	—	158	1	no	—
453	C₄	—	158	1	no	—
454	C₄	—	158	1	no	—
455	C₄	C₂×#14579117	1	1	yes	characteristic
456	C₄	#19099042	1	1	yes	characteristic
457	C₄	#19099213	1	1	yes	characteristic
458	C₄	#19099233	1	1	yes	characteristic
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	8	2	no	—
462	C₂	#23766348	1	1	yes	characteristic
463	C₂	#443×D₇₉	1	1	yes	characteristic
464	C₂	#23772312	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1974	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#135×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1974	D₇₉
hypocenter	C₇₉	#22802
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1974

Complements

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

N	H ≅ G/N	type
2. #23772062	C₂	semidirect
4. #23764051	C₂	semidirect
5. #23764045	C₂	semidirect
6. #23763570	C₂	semidirect
7. #23763418	C₂	semidirect
8. #23763282	C₂	semidirect
9. #23763279	C₂	semidirect
10. C₈×Dic₇₉⋊C₄	C₂	semidirect
13. Q₁₆×Dic₇₉	C₄	semidirect
14. Q₁₆×Dic₇₉	C₄	semidirect
15. SD₁₆×Dic₇₉	C₄	semidirect
16. SD₁₆×Dic₇₉	C₄	semidirect
17. D₈×Dic₇₉	C₄	semidirect
18. D₈×Dic₇₉	C₄	semidirect
244. C₇₉	#22802	semidirect

Maximal subgroups

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

subgroup	index
#135×Dic₇₉	2
#23772062	2
#23764289	2
#23764051	2
#23764045	2
#23763570	2
#23763418	2
#23763282	2
#23763279	2
C₈×Dic₇₉⋊C₄	2
C₇₉×#1974	2
#22802	79