Subgroups — #35197150

Order 20224.

8650 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777730	C₂	1	24	yes	maximal, complemented
2	#23777277	C₂	1	6	yes	maximal, complemented
3	#23777276	C₂	1	6	yes	maximal, complemented
4	#23777178	C₂	1	6	yes	maximal, complemented
5	#23777173	C₂	1	6	yes	maximal, complemented
6	#23777033	C₂	1	12	yes	maximal, complemented
7	#23776696	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#14579158	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14579207	C₂²	1	12	yes	complemented
11	C₂³×D₃₁₆	C₂²	1	6	yes	complemented
12	#19099304	C₂²	1	32	yes	complemented
13	#19099298	C₂²	1	24	yes	complemented
14	#19099235	C₂²	1	24	yes	complemented
15	#19099234	C₂²	1	24	yes	complemented
16	#19099209	C₂²	1	48	yes	complemented
17	#19099204	C₂²	1	48	yes	complemented
18	D₄×D₃₁₆	C₂²	1	48	yes	complemented
19	D₄×D₃₁₆	C₂²	1	24	yes	complemented
20	#19099197	C₂²	1	48	yes	complemented
21	#19099169	C₂²	1	24	yes	complemented
22	#19099168	C₂²	1	24	yes	complemented
23	#19099132	C₂²	1	12	yes	complemented
24	#19099132	C₂²	1	24	yes	complemented
25	#19099131	C₂²	1	24	yes	complemented
26	#19099127	C₂²	1	12	yes	complemented
27	#19099124	C₂²	1	48	yes	complemented
28	#19099120	C₂²	1	3	yes	complemented
29	#19099114	C₂²	1	12	yes	complemented
30	#19099113	C₂²	1	3	yes	complemented
31	#19099113	C₂²	1	12	yes	complemented
32	C₂×#14579158	C₂²	1	6	yes	complemented
33	C₂×#14579158	C₂²	1	6	yes	complemented
34	C₂×#14579158	C₂²	1	12	yes	complemented
35	C₂×#14579158	C₂²	1	4	yes	complemented
36	#127×D₇₉	C₂²	1	4	yes	complemented
37	#19099097	C₂²	1	12	yes	complemented
38	#19099074	C₂²	1	6	yes	complemented
39	#120×D₇₉	C₂²	1	16	yes	complemented
40	#19099037	C₂²	1	12	yes	complemented
41	C₄×#11929624	C₂²	1	6	yes	complemented
42	#533×C₇₉	C₂²	1	3	yes	complemented
43	#532×C₇₉	C₂²	1	3	yes	complemented
44	#529×C₇₉	C₂²	1	12	yes	complemented
45	#525×C₇₉	C₂²	1	6	yes	complemented
46	C₄×#41×C₇₉	C₂²	1	6	yes	complemented
47	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	C₂⁴×D₇₉	C₂³	1	4	yes	—
49	#14579207	—	4	48	no	—
50	C₂×#11929625	C₂³	1	24	yes	complemented
51	C₂×#11929624	C₂³	1	6	yes	—
52	C₂×#11929624	C₂³	1	24	yes	complemented
53	C₂²×D₃₁₆	—	4	24	no	—
54	C₂²×D₃₁₆	C₂³	1	12	yes	—
55	C₂²×D₃₁₆	C₂³	1	24	yes	—
56	C₂²×D₃₁₆	C₂³	1	24	yes	—
57	C₂²×D₃₁₆	C₂³	1	12	yes	—
58	C₂²×D₃₁₆	C₂³	1	24	yes	complemented
59	C₂×D₄×D₇₉	C₂³	1	48	yes	—
60	C₂×D₄×D₇₉	C₂³	1	24	yes	complemented
61	#14579161	C₂³	1	3	yes	complemented
62	#14579158	C₂³	1	12	yes	—
63	#14579158	C₂³	1	12	yes	—
64	#14579158	C₂³	1	24	yes	—
65	#14579158	C₂³	1	8	yes	—
66	#14579158	C₂³	1	4	yes	—
67	#14579158	C₂³	1	4	yes	—
68	#14579158	C₂³	1	24	yes	complemented
69	#14579158	C₂³	1	1	yes	characteristic, complemented
70	#14579157	C₂³	1	24	yes	complemented
71	#14579155	C₂³	1	8	yes	complemented
72	#14579153	C₂³	1	6	yes	complemented
73	#14579150	C₂³	1	24	yes	complemented
74	#14579149	C₂³	1	24	yes	complemented
75	#14579149	C₂³	1	6	yes	complemented
76	#14579146	C₂³	1	96	yes	complemented
77	#14579144	C₂³	1	12	yes	—
78	#14579140	C₂³	1	12	yes	—
79	#14579136	C₂³	1	48	yes	complemented
80	#14579136	C₂³	1	96	yes	complemented
81	#14579135	C₂³	1	12	yes	—
82	#14579135	C₂³	1	48	yes	complemented
83	#14579134	C₂³	1	96	yes	complemented
84	#14579131	C₂³	1	48	yes	—
85	#14579131	C₂³	1	96	yes	complemented
86	#14579130	C₂³	1	4	yes	—
87	#14579129	C₂³	1	48	yes	—
88	C₄×Dic₁₅₈	C₂³	1	12	yes	complemented
89	C₄×D₃₁₆	C₂³	1	48	yes	complemented
90	C₄×D₃₁₆	C₂³	1	12	yes	complemented
91	#14579123	C₂³	1	48	yes	complemented
92	C₄×C₂²⋊D₇₉	C₂³	1	24	yes	—
93	#14579120	C₂³	1	6	yes	—
94	#14579118	C₂³	1	12	yes	complemented
95	C₂²⋊C₄×D₇₉	C₂³	1	48	yes	—
96	C₄²×D₇₉	C₂³	1	4	yes	complemented
97	C₂×#41×C₇₉	C₂³	1	6	yes	—
98	C₂³×C₄×C₇₉	C₂³	1	3	yes	—
99	C₄⋊Q₈×C₇₉	C₂³	1	3	yes	complemented
100	#127×C₇₉	C₂³	1	1	yes	characteristic, complemented
101	#126×C₇₉	C₂³	1	8	yes	complemented
102	#125×C₇₉	C₂³	1	6	yes	complemented
103	#124×C₇₉	C₂³	1	6	yes	complemented
104	#123×C₇₉	C₂³	1	12	yes	—
105	C₂²⋊Q₈×C₇₉	C₂³	1	12	yes	—
106	#121×C₇₉	C₂³	1	12	yes	—
107	#120×C₇₉	C₂³	1	4	yes	—
108	C₄×Q₈×C₇₉	C₂³	1	12	yes	complemented
109	C₄×D₄×C₇₉	C₂³	1	24	yes	—
110	C₄×D₄×C₇₉	C₂³	1	12	yes	complemented
111	#117×C₇₉	C₂³	1	6	yes	—
112	#117×C₇₉	C₂³	1	12	yes	complemented
113	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
114	C₂×C₄²×C₇₉	C₂³	1	6	yes	—
115	C₂×C₄²×C₇₉	C₂³	1	3	yes	—
116	C₂×C₄²×C₇₉	C₂³	1	4	yes	complemented
117	C₂³×D₇₉	—	4	24	no	—
118	C₂³×D₇₉	C₂⁴	1	24	yes	—
119	C₂³×D₇₉	C₂⁴	1	16	yes	—
120	#11929625	—	4	48	no	—
121	#11929624	—	2	24	no	—
122	#11929624	—	4	48	no	—
123	C₂×Dic₁₅₈	C₂⁴	1	6	yes	—
124	C₂×D₃₁₆	—	2	48	no	—
125	C₂×D₃₁₆	—	4	24	no	—
126	C₂×D₃₁₆	—	4	48	no	—
127	C₂×D₃₁₆	—	4	48	no	—
128	C₂×D₃₁₆	—	4	48	no	—
129	C₂×D₃₁₆	C₂⁴	1	6	yes	—
130	C₂×D₃₁₆	C₂⁴	1	24	yes	—
131	C₂×D₃₁₆	C₂⁴	1	24	yes	—
132	C₂×D₃₁₆	C₂⁴	1	48	yes	—
133	C₂×D₃₁₆	C₂⁴	1	48	yes	—
134	C₂×C₂²⋊D₇₉	C₂⁴	1	12	yes	—
135	C₂×C₂²⋊D₇₉	C₂⁴	1	48	yes	—
136	D₄×D₇₉	—	4	96	no	—
137	D₄×D₇₉	—	4	48	no	—
138	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
139	C₂×C₄×D₇₉	C₂⁴	1	48	yes	—
140	C₄⋊Dic₇₉	C₂⁴	1	12	yes	—
141	Dic₇₉⋊C₄	C₂⁴	1	24	yes	—
142	C₂²⋊Dic₇₉	C₂⁴	1	12	yes	—
143	(C₂×D₇₉)⋊C₄	C₂⁴	1	96	yes	—
144	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	—
145	C₄×Dic₇₉	C₂⁴	1	12	yes	—
146	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
147	#41×C₇₉	—	2	24	no	—
148	C₂×Q₈×C₇₉	C₂⁴	1	6	yes	—
149	C₂×D₄×C₇₉	C₂⁴	1	12	yes	—
150	C₂×D₄×C₇₉	C₂⁴	1	6	yes	—
151	C₂²×C₄×C₇₉	—	2	12	no	—
152	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
153	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
154	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
155	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
157	C₄⋊C₄×C₇₉	C₂⁴	1	12	yes	—
158	C₄⋊C₄×C₇₉	C₂⁴	1	24	yes	—
159	C₂²⋊C₄×C₇₉	C₂⁴	1	12	yes	—
160	C₂²⋊C₄×C₇₉	C₂⁴	1	24	yes	—
161	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
162	C₄²×C₇₉	C₂⁴	1	3	yes	—
163	C₄²×C₇₉	C₂⁴	1	6	yes	—
164	C₄²×C₇₉	C₂⁴	1	3	yes	—
165	C₄²×C₇₉	C₂⁴	1	2	yes	—
166	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
167	C₄²×C₇₉	C₂⁴	1	12	yes	—
168	C₂³×C₇₉	—	2	6	no	—
169	C₂³×C₇₉	C₂⁵	1	4	yes	—
170	C₂³×C₇₉	C₂⁵	1	3	yes	—
171	C₂²×D₇₉	—	2	48	no	—
172	C₂²×D₇₉	—	4	48	no	—
173	C₂²×D₇₉	—	4	48	no	—
174	C₂²×D₇₉	—	8	32	no	—
175	C₂²×D₇₉	C₂⁵	1	4	yes	—
176	C₂²×D₇₉	C₂⁵	1	16	yes	—
177	Q₈×C₇₉	—	2	12	no	—
178	D₄×C₇₉	—	2	24	no	—
179	D₄×C₇₉	—	2	12	no	—
180	C₂×C₄×C₇₉	—	2	6	no	—
181	C₂×C₄×C₇₉	—	2	12	no	—
182	C₂×C₄×C₇₉	—	2	12	no	—
183	C₂×C₄×C₇₉	—	2	24	no	—
184	C₂×C₄×C₇₉	H(5,𝔽₂)	1	12	yes	complemented
185	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
186	C₂×C₄×C₇₉	C₂⁵	1	6	yes	—
187	C₂×C₄×C₇₉	C₂⁵	1	3	yes	—
188	C₂×C₄×C₇₉	C₂⁵	1	3	yes	—
189	C₂²⋊D₇₉	—	2	24	no	—
190	C₂²⋊D₇₉	—	4	48	no	—
191	C₂×Dic₇₉	C₂⁵	1	12	yes	—
192	D₃₁₆	—	2	48	no	—
193	D₃₁₆	—	2	48	no	—
194	D₃₁₆	—	2	12	no	—
195	D₃₁₆	—	4	48	no	—
196	D₃₁₆	—	4	48	no	—
197	C₄×D₇₉	—	2	24	no	—
198	C₄×D₇₉	—	4	48	no	—
199	Dic₁₅₈	—	2	12	no	—
200	C₂²×C₇₉	—	2	8	no	—
201	C₂²×C₇₉	—	2	6	no	—
202	C₂²×C₇₉	—	2	12	no	—
203	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
204	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
205	C₂×D₇₉	—	2	12	no	—
206	C₂×D₇₉	—	2	48	no	—
207	C₂×D₇₉	—	8	48	no	—
208	C₂×D₇₉	—	16	16	no	—
209	C₄×C₇₉	—	2	6	no	—
210	C₄×C₇₉	—	2	12	no	—
211	C₄×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
212	C₄×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
213	Dic₇₉	—	2	12	no	—
214	#62832	—	79	1	no	maximal, Sylow
215	C₂×C₇₉	—	2	6	no	—
216	C₂×C₇₉	—	4	4	no	—
217	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	3	yes	—
218	D₇₉	—	4	16	no	—
219	D₇₉	—	4	4	no	—
220	#3543	—	79	24	no	—
221	#3508	—	79	6	no	—
222	#3508	—	79	6	no	—
223	#3498	—	79	6	no	—
224	#3498	—	79	6	no	—
225	#3484	—	79	12	no	—
226	#3444	—	79	1	no	—
227	#3444	D₇₉	1	1	yes	characteristic, complemented
228	C₂²×#127	—	79	1	no	—
229	C₇₉	#62832	1	1	yes	characteristic, complemented, Sylow
230	C₂×H(5,𝔽₂)	—	79	12	no	—
231	C₂³×D₄	—	79	6	no	—
232	#560	—	79	32	no	—
233	#559	—	79	24	no	—
234	#550	—	79	24	no	—
235	#550	—	79	24	no	—
236	#546	—	79	48	no	—
237	#546	—	79	48	no	—
238	D₄²	—	79	48	no	—
239	D₄²	—	79	48	no	—
240	D₄²	—	79	24	no	—
241	#540	—	79	24	no	—
242	#540	—	79	24	no	—
243	#535	—	79	12	no	—
244	#535	—	79	24	no	—
245	#535	—	79	12	no	—
246	#535	—	79	24	no	—
247	#534	—	79	48	no	—
248	#533	—	79	3	no	—
249	#533	C₂×D₇₉	1	3	yes	complemented
250	#532	—	79	12	no	—
251	#532	—	79	3	no	—
252	#532	—	79	12	no	—
253	#532	C₂×D₇₉	1	3	yes	complemented
254	C₂×#127	—	79	4	no	—
255	C₂×#127	—	79	6	no	—
256	C₂×#127	—	79	6	no	—
257	C₂×#127	—	79	12	no	—
258	C₂×#127	—	79	4	no	—
259	#529	—	79	12	no	—
260	#529	C₂×D₇₉	1	12	yes	complemented
261	#525	—	79	6	no	—
262	#525	C₂×D₇₉	1	6	yes	complemented
263	C₂×#120	—	79	16	no	—
264	#518	—	79	12	no	—
265	C₄×#41	—	79	6	no	—
266	C₄×#41	C₂×D₇₉	1	6	yes	complemented
267	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
268	C₂⁵	—	79	4	no	—
269	H(5,𝔽₂)	—	316	48	no	—
270	C₂×#41	—	79	24	no	—
271	C₂×#41	—	79	24	no	—
272	C₂×#41	—	79	6	no	—
273	C₂×#41	C₂²×D₇₉	1	6	yes	—
274	C₂²×D₄	—	316	24	no	—
275	C₂²×D₄	—	79	48	no	—
276	C₂²×D₄	—	79	24	no	—
277	C₂²×D₄	—	79	12	no	—
278	C₂²×D₄	—	79	24	no	—
279	C₂²×D₄	—	79	24	no	—
280	C₂²×D₄	—	79	24	no	—
281	C₂²×D₄	—	79	12	no	—
282	C₂³×C₄	C₂²×D₇₉	1	3	yes	—
283	C₄⋊Q₈	—	79	3	no	—
284	C₄⋊Q₈	C₂²×D₇₉	1	3	yes	complemented
285	#127	—	79	24	no	—
286	#127	—	79	4	no	—
287	#127	—	79	4	no	—
288	#127	—	79	1	no	—
289	#127	—	79	12	no	—
290	#127	—	79	12	no	—
291	#127	—	79	24	no	—
292	#127	—	79	8	no	—
293	#127	—	79	24	no	—
294	#127	C₂²×D₇₉	1	1	yes	characteristic, complemented
295	#126	—	79	8	no	—
296	#126	C₂²×D₇₉	1	8	yes	complemented
297	#125	—	79	6	no	—
298	#125	C₂²×D₇₉	1	6	yes	complemented
299	#124	—	79	24	no	—
300	#124	—	79	6	no	—
301	#124	—	79	24	no	—
302	#124	C₂²×D₇₉	1	6	yes	complemented
303	#123	—	79	12	no	—
304	#123	—	79	96	no	—
305	#123	C₂²×D₇₉	1	12	yes	—
306	C₂²⋊Q₈	—	79	12	no	—
307	C₂²⋊Q₈	C₂²×D₇₉	1	12	yes	—
308	#121	—	79	12	no	—
309	#121	—	79	48	no	—
310	#121	—	79	48	no	—
311	#121	—	79	96	no	—
312	#121	—	79	96	no	—
313	#121	C₂²×D₇₉	1	12	yes	—
314	#120	—	79	4	no	—
315	#120	—	79	48	no	—
316	#120	—	79	48	no	—
317	#120	—	79	96	no	—
318	#120	C₂²×D₇₉	1	4	yes	—
319	C₄×Q₈	—	79	12	no	—
320	C₄×Q₈	C₂²×D₇₉	1	12	yes	complemented
321	C₄×D₄	—	79	24	no	—
322	C₄×D₄	—	79	48	no	—
323	C₄×D₄	—	79	12	no	—
324	C₄×D₄	—	79	48	no	—
325	C₄×D₄	C₂²×D₇₉	1	24	yes	—
326	C₄×D₄	C₂²×D₇₉	1	12	yes	complemented
327	#117	—	79	6	no	—
328	#117	—	79	12	no	—
329	#117	C₂²×D₇₉	1	6	yes	—
330	#117	C₂²×D₇₉	1	12	yes	complemented
331	C₂×C₂²⋊C₄	—	79	48	no	—
332	C₂×C₄²	—	79	4	no	—
333	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
334	C₂×C₄²	C₂²×D₇₉	1	3	yes	—
335	C₂×C₄²	C₂²×D₇₉	1	6	yes	—
336	C₂×C₄²	C₂²×D₇₉	1	4	yes	complemented
337	C₂⁴	—	316	24	no	—
338	C₂⁴	—	79	16	no	—
339	C₂⁴	—	79	24	no	—
340	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
341	#41	—	2	24	no	—
342	#41	—	316	48	no	—
343	#41	—	316	48	no	—
344	#41	—	158	24	no	—
345	C₂×Q₈	—	79	6	no	—
346	C₂×Q₈	C₂³×D₇₉	1	6	yes	—
347	C₂×D₄	—	316	24	no	—
348	C₂×D₄	—	316	48	no	—
349	C₂×D₄	—	316	48	no	—
350	C₂×D₄	—	316	48	no	—
351	C₂×D₄	—	316	96	no	—
352	C₂×D₄	—	316	48	no	—
353	C₂×D₄	—	79	48	no	—
354	C₂×D₄	—	79	12	no	—
355	C₂×D₄	—	79	48	no	—
356	C₂×D₄	—	79	48	no	—
357	C₂×D₄	—	79	24	no	—
358	C₂×D₄	—	79	6	no	—
359	C₂×D₄	—	79	24	no	—
360	C₂×D₄	—	158	48	no	—
361	C₂×D₄	C₂³×D₇₉	1	12	yes	—
362	C₂×D₄	C₂³×D₇₉	1	6	yes	—
363	C₂²×C₄	—	2	12	no	—
364	C₂²×C₄	—	79	48	no	—
365	C₂²×C₄	—	79	12	no	—
366	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
367	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
368	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
369	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
370	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
371	C₄⋊C₄	—	79	24	no	—
372	C₄⋊C₄	—	79	12	no	—
373	C₄⋊C₄	C₂³×D₇₉	1	12	yes	—
374	C₄⋊C₄	C₂³×D₇₉	1	24	yes	—
375	C₂²⋊C₄	—	79	12	no	—
376	C₂²⋊C₄	—	79	96	no	—
377	C₂²⋊C₄	—	79	24	no	—
378	C₂²⋊C₄	C₂³×D₇₉	1	12	yes	—
379	C₂²⋊C₄	C₂³×D₇₉	1	24	yes	—
380	C₄²	—	79	12	no	—
381	C₄²	C₂³×D₇₉	1	1	yes	characteristic
382	C₄²	C₂³×D₇₉	1	1	yes	characteristic
383	C₄²	C₂³×D₇₉	1	3	yes	—
384	C₄²	C₂³×D₇₉	1	3	yes	—
385	C₄²	C₂³×D₇₉	1	6	yes	—
386	C₄²	C₂³×D₇₉	1	2	yes	—
387	C₄²	C₂³×D₇₉	1	12	yes	—
388	C₂³	—	2	6	no	—
389	C₂³	—	316	48	no	—
390	C₂³	—	316	48	no	—
391	C₂³	—	79	16	no	—
392	C₂³	—	79	4	no	—
393	C₂³	—	632	32	no	—
394	C₂³	—	158	48	no	—
395	C₂³	C₂⁴×D₇₉	1	4	yes	—
396	C₂³	C₂⁴×D₇₉	1	3	yes	—
397	Q₈	—	2	12	no	—
398	Q₈	—	158	12	no	—
399	D₄	—	2	24	no	—
400	D₄	—	2	12	no	—
401	D₄	—	316	48	no	—
402	D₄	—	316	48	no	—
403	D₄	—	316	48	no	—
404	D₄	—	158	24	no	—
405	D₄	—	158	12	no	—
406	D₄	—	158	48	no	—
407	D₄	—	158	48	no	—
408	C₂×C₄	—	2	6	no	—
409	C₂×C₄	—	2	12	no	—
410	C₂×C₄	—	2	12	no	—
411	C₂×C₄	—	2	24	no	—
412	C₂×C₄	—	316	48	no	—
413	C₂×C₄	—	79	12	no	—
414	C₂×C₄	—	158	24	no	—
415	C₂×C₄	#14579207	1	12	yes	complemented
416	C₂×C₄	C₂⁴×D₇₉	1	6	yes	—
417	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
418	C₂×C₄	C₂⁴×D₇₉	1	3	yes	—
419	C₂×C₄	C₂⁴×D₇₉	1	3	yes	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	6	no	—
422	C₂²	—	2	12	no	—
423	C₂²	—	632	48	no	—
424	C₂²	—	158	48	no	—
425	C₂²	—	158	12	no	—
426	C₂²	—	1264	16	no	—
427	C₂²	C₂×#14579207	1	6	yes	—
428	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
429	C₄	—	2	6	no	—
430	C₄	—	2	12	no	—
431	C₄	—	158	12	no	—
432	C₄	C₂×#14579207	1	6	yes	—
433	C₄	C₂×#14579207	1	6	yes	—
434	C₂	—	2	6	no	—
435	C₂	—	4	4	no	—
436	C₂	—	316	16	no	—
437	C₂	—	316	4	no	—
438	C₂	C₂²×#14579207	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3444	C₂
hypercenter	#3444	D₇₉
hypocenter	C₇₉	#62832
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #23777730	C₂	semidirect
2. #23777277	C₂	semidirect
3. #23777276	C₂	semidirect
4. #23777178	C₂	semidirect
5. #23777173	C₂	semidirect
6. #23777033	C₂	semidirect
7. #23776696	C₂	semidirect
8. C₂²×#14579158	C₂	semidirect
9. C₇₉×#3444	C₂	semidirect
10. C₂×#14579207	C₂²	semidirect
11. C₂³×D₃₁₆	C₂²	semidirect
12. #19099304	C₂²	semidirect
13. #19099298	C₂²	semidirect
14. #19099235	C₂²	semidirect
15. #19099234	C₂²	semidirect
16. #19099209	C₂²	semidirect
17. #19099204	C₂²	semidirect
18. D₄×D₃₁₆	C₂²	semidirect
19. D₄×D₃₁₆	C₂²	semidirect
20. #19099197	C₂²	semidirect
21. #19099169	C₂²	semidirect
22. #19099168	C₂²	semidirect
23. #19099132	C₂²	semidirect
24. #19099132	C₂²	semidirect
25. #19099131	C₂²	semidirect
26. #19099127	C₂²	semidirect
27. #19099124	C₂²	semidirect
28. #19099120	C₂²	semidirect
29. #19099114	C₂²	semidirect
30. #19099113	C₂²	semidirect
31. #19099113	C₂²	semidirect
32. C₂×#14579158	C₂²	semidirect
33. C₂×#14579158	C₂²	semidirect
34. C₂×#14579158	C₂²	semidirect
35. C₂×#14579158	C₂²	semidirect
36. #127×D₇₉	C₂²	semidirect
37. #19099097	C₂²	semidirect
38. #19099074	C₂²	semidirect
39. #120×D₇₉	C₂²	semidirect
40. #19099037	C₂²	semidirect
41. C₄×#11929624	C₂²	semidirect
42. #533×C₇₉	C₂²	semidirect
43. #532×C₇₉	C₂²	semidirect
44. #529×C₇₉	C₂²	semidirect
45. #525×C₇₉	C₂²	semidirect
46. C₄×#41×C₇₉	C₂²	semidirect
47. C₂²×C₄²×C₇₉	C₂²	semidirect
50. C₂×#11929625	C₂³	semidirect
52. C₂×#11929624	C₂³	semidirect
58. C₂²×D₃₁₆	C₂³	semidirect
60. C₂×D₄×D₇₉	C₂³	semidirect
61. #14579161	C₂³	semidirect
68. #14579158	C₂³	semidirect
69. #14579158	C₂³	semidirect
70. #14579157	C₂³	semidirect
71. #14579155	C₂³	semidirect
72. #14579153	C₂³	semidirect
73. #14579150	C₂³	semidirect
74. #14579149	C₂³	semidirect
75. #14579149	C₂³	semidirect
76. #14579146	C₂³	semidirect
79. #14579136	C₂³	semidirect
80. #14579136	C₂³	semidirect
82. #14579135	C₂³	semidirect
83. #14579134	C₂³	semidirect
85. #14579131	C₂³	semidirect
88. C₄×Dic₁₅₈	C₂³	semidirect
89. C₄×D₃₁₆	C₂³	semidirect
90. C₄×D₃₁₆	C₂³	semidirect
91. #14579123	C₂³	semidirect
94. #14579118	C₂³	semidirect
96. C₄²×D₇₉	C₂³	semidirect
99. C₄⋊Q₈×C₇₉	C₂³	semidirect
100. #127×C₇₉	C₂³	semidirect
101. #126×C₇₉	C₂³	semidirect
102. #125×C₇₉	C₂³	semidirect
103. #124×C₇₉	C₂³	semidirect
108. C₄×Q₈×C₇₉	C₂³	semidirect
110. C₄×D₄×C₇₉	C₂³	semidirect
112. #117×C₇₉	C₂³	semidirect
116. C₂×C₄²×C₇₉	C₂³	semidirect
184. C₂×C₄×C₇₉	H(5,𝔽₂)	semidirect
227. #3444	D₇₉	semidirect
229. C₇₉	#62832	semidirect
249. #533	C₂×D₇₉	semidirect
253. #532	C₂×D₇₉	semidirect
260. #529	C₂×D₇₉	semidirect
262. #525	C₂×D₇₉	semidirect
266. C₄×#41	C₂×D₇₉	semidirect
267. C₂²×C₄²	C₂×D₇₉	semidirect
284. C₄⋊Q₈	C₂²×D₇₉	semidirect
294. #127	C₂²×D₇₉	semidirect
296. #126	C₂²×D₇₉	semidirect
298. #125	C₂²×D₇₉	semidirect
302. #124	C₂²×D₇₉	semidirect
320. C₄×Q₈	C₂²×D₇₉	semidirect
326. C₄×D₄	C₂²×D₇₉	semidirect
330. #117	C₂²×D₇₉	semidirect
336. C₂×C₄²	C₂²×D₇₉	semidirect
415. C₂×C₄	#14579207	semidirect

Maximal subgroups

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

subgroup	index
#23777730	2
#23777277	2
#23777276	2
#23777178	2
#23777173	2
#23777033	2
#23776696	2
C₂²×#14579158	2
C₇₉×#3444	2
#62832	79