Subgroups — C₇₃×#25569 #32934973

Order 18688.

1306 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#554×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#486×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#460×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2541	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2000	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1874	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
11	#554×C₇₃	—	2	4	no	—
12	#554×C₇₃	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#127×C₇₃	—	2	1	no	—
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#125×C₇₃	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₇₃	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
19	C₂×#121×C₇₃	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₃	—	2	1	no	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
24	#486×C₇₃	—	2	4	no	—
25	#460×C₇₃	—	2	4	no	—
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#103×C₇₃	C₂²	1	2	yes	—
28	C₂×#102×C₇₃	C₂²	1	4	yes	—
29	C₂×#102×C₇₃	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	—
31	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
32	#392×C₇₃	—	2	2	no	—
33	#390×C₇₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#340×C₇₃	C₂²	1	4	yes	—
36	#340×C₇₃	C₂²	1	2	yes	—
37	C₂²×Q₈×C₇₃	—	2	1	no	—
38	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₇₃	—	2	4	no	—
40	C₂²×D₄×C₇₃	—	2	1	no	—
41	C₂²×D₄×C₇₃	—	2	1	no	—
42	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₇₃	—	2	2	no	—
45	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
46	C₂×SD₁₆×C₇₃	—	2	4	no	—
47	C₂×SD₁₆×C₇₃	—	4	4	no	—
48	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₇₃	—	2	2	no	—
51	C₄⋊Q₈×C₇₃	D₄	1	4	yes	complemented
52	#127×C₇₃	—	2	2	no	—
53	#127×C₇₃	—	2	2	no	—
54	#127×C₇₃	—	4	4	no	—
55	#125×C₇₃	—	2	8	no	—
56	C₂²⋊Q₈×C₇₃	—	2	16	no	—
57	C₂²⋊Q₈×C₇₃	—	2	4	no	—
58	C₂²⋊Q₈×C₇₃	—	2	4	no	—
59	#121×C₇₃	—	2	8	no	—
60	#121×C₇₃	—	4	4	no	—
61	C₄×Q₈×C₇₃	—	2	2	no	—
62	C₄×Q₈×C₇₃	D₄	1	4	yes	complemented
63	C₄×D₄×C₇₃	—	2	8	no	—
64	C₄×D₄×C₇₃	—	2	2	no	—
65	C₄×D₄×C₇₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
72	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
79	C₂×C₄²×C₇₃	—	2	1	no	—
80	C₂×C₄²×C₇₃	—	2	1	no	—
81	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₇₃	—	2	2	no	—
83	#103×C₇₃	—	2	4	no	—
84	#102×C₇₃	—	2	4	no	—
85	#102×C₇₃	—	2	8	no	—
86	C₂²⋊C₈×C₇₃	—	4	4	no	—
87	C₄×C₈×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	1	no	—
89	C₂⁴×C₇₃	—	2	2	no	—
90	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₇₃	—	2	4	no	—
92	C₂×Q₈×C₇₃	—	2	1	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	8	2	no	—
96	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₇₃	—	2	2	no	—
98	C₂×D₄×C₇₃	—	2	2	no	—
99	C₂×D₄×C₇₃	—	2	2	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	4	no	—
102	C₂×D₄×C₇₃	—	2	4	no	—
103	C₂×D₄×C₇₃	—	4	8	no	—
104	C₂×D₄×C₇₃	—	4	8	no	—
105	C₂×D₄×C₇₃	—	4	2	no	—
106	C₂×D₄×C₇₃	—	4	2	no	—
107	C₂×D₄×C₇₃	—	4	2	no	—
108	C₂×D₄×C₇₃	—	4	2	no	—
109	C₂×D₄×C₇₃	—	8	2	no	—
110	C₂×D₄×C₇₃	—	8	4	no	—
111	C₂×D₄×C₇₃	SD₁₆	1	4	yes	complemented
112	C₂²×C₄×C₇₃	—	2	2	no	—
113	C₂²×C₄×C₇₃	—	2	1	no	—
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	8	no	—
117	C₂²×C₄×C₇₃	—	2	2	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	4	no	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	8	4	no	—
122	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
126	SD₁₆×C₇₃	—	4	8	no	—
127	C₂×C₈×C₇₃	—	2	2	no	—
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	4	no	—
132	C₄⋊C₄×C₇₃	—	2	8	no	—
133	C₄⋊C₄×C₇₃	—	2	8	no	—
134	C₄⋊C₄×C₇₃	—	2	4	no	—
135	C₄⋊C₄×C₇₃	—	2	4	no	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	2	1	no	—
138	C₄⋊C₄×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
142	C₄⋊C₄×C₇₃	#41	1	4	yes	—
143	C₂²⋊C₄×C₇₃	—	2	8	no	—
144	C₂²⋊C₄×C₇₃	—	2	4	no	—
145	C₂²⋊C₄×C₇₃	—	4	8	no	—
146	C₄²×C₇₃	—	2	4	no	—
147	C₄²×C₇₃	—	4	2	no	—
148	C₄²×C₇₃	C₂×D₄	1	2	yes	—
149	C₄²×C₇₃	C₂×D₄	1	2	yes	—
150	C₂³×C₇₃	—	2	2	no	—
151	C₂³×C₇₃	—	2	4	no	—
152	C₂³×C₇₃	—	2	2	no	—
153	C₂³×C₇₃	—	2	4	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	4	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	—	4	2	no	—
158	C₂³×C₇₃	—	4	4	no	—
159	C₂³×C₇₃	C₂×SD₁₆	1	4	yes	—
160	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₇₃	—	2	2	no	—
162	Q₈×C₇₃	—	2	2	no	—
163	Q₈×C₇₃	—	4	2	no	—
164	Q₈×C₇₃	—	8	4	no	—
165	D₄×C₇₃	—	2	8	no	—
166	D₄×C₇₃	—	4	2	no	—
167	D₄×C₇₃	—	4	2	no	—
168	D₄×C₇₃	—	4	4	no	—
169	D₄×C₇₃	—	8	4	no	—
170	D₄×C₇₃	—	8	16	no	—
171	D₄×C₇₃	—	8	4	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	4	no	—
177	C₂×C₄×C₇₃	—	2	4	no	—
178	C₂×C₄×C₇₃	—	2	4	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	4	4	no	—
183	C₂×C₄×C₇₃	—	4	2	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	2	no	—
186	C₂×C₄×C₇₃	—	4	4	no	—
187	C₂×C₄×C₇₃	—	8	8	no	—
188	C₂×C₄×C₇₃	#120	1	2	yes	—
189	C₂×C₄×C₇₃	#120	1	2	yes	—
190	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₇₃	#137	1	2	yes	—
192	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
195	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
196	C₈×C₇₃	—	4	2	no	—
197	C₈×C₇₃	—	4	2	no	—
198	C₂²×C₇₃	—	2	4	no	—
199	C₂²×C₇₃	—	2	8	no	—
200	C₂²×C₇₃	—	4	4	no	—
201	C₂²×C₇₃	—	4	2	no	—
202	C₂²×C₇₃	—	4	2	no	—
203	C₂²×C₇₃	—	8	4	no	—
204	C₂²×C₇₃	—	8	2	no	—
205	C₂²×C₇₃	—	8	2	no	—
206	C₂²×C₇₃	—	8	2	no	—
207	C₂²×C₇₃	—	8	4	no	—
208	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
209	C₂²×C₇₃	#546	1	2	yes	—
210	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
211	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
212	C₂²×C₇₃	#576	1	2	yes	—
213	C₄×C₇₃	—	2	2	no	—
214	C₄×C₇₃	—	4	2	no	—
215	C₄×C₇₃	—	4	2	no	—
216	C₄×C₇₃	—	4	2	no	—
217	C₄×C₇₃	—	4	4	no	—
218	C₄×C₇₃	—	4	4	no	—
219	C₄×C₇₃	#448	1	4	yes	—
220	C₄×C₇₃	#532	1	1	yes	characteristic
221	C₄×C₇₃	#535	1	1	yes	characteristic
222	C₄×C₇₃	#550	1	2	yes	—
223	#25569	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂×C₇₃	—	4	4	no	—
225	C₂×C₇₃	—	16	2	no	—
226	C₂×C₇₃	#2431	1	1	yes	characteristic
227	C₂×C₇₃	C₂×#448	1	1	yes	characteristic
228	C₂×C₇₃	#3008	1	1	yes	characteristic
229	C₂×C₇₃	#3295	1	2	yes	—
230	C₂×C₇₃	#3333	1	2	yes	—
231	C₂×#554	C₂×C₇₃	1	1	yes	characteristic, complemented
232	C₂×#486	C₂×C₇₃	1	1	yes	characteristic, complemented
233	C₂×#460	C₂×C₇₃	1	1	yes	characteristic, complemented
234	#2541	C₂×C₇₃	1	1	yes	characteristic
235	#2000	C₂×C₇₃	1	4	yes	complemented
236	#1987	C₂×C₇₃	1	1	yes	characteristic, complemented
237	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
238	#1874	C₂×C₇₃	1	4	yes	complemented
239	C₄×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
240	C₇₃	#25569	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
242	#554	—	2	4	no	—
243	#554	—	2	4	no	—
244	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
245	C₂×#127	—	2	1	no	—
246	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
247	C₂×#125	—	2	1	no	—
248	C₂×C₂²⋊Q₈	—	2	2	no	—
249	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
250	C₂×#121	C₂²×C₇₃	1	4	yes	—
251	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
252	C₂×C₄×D₄	—	2	1	no	—
253	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
255	#486	—	2	4	no	—
256	#460	—	2	4	no	—
257	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
258	C₂×#103	C₂²×C₇₃	1	2	yes	—
259	C₂×#102	C₂²×C₇₃	1	4	yes	—
260	C₂×#102	C₂²×C₇₃	1	2	yes	—
261	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	—
262	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
263	#392	—	2	2	no	—
264	#390	—	2	1	no	—
265	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
266	#340	C₂²×C₇₃	1	2	yes	—
267	#340	C₂²×C₇₃	1	4	yes	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
274	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×SD₁₆	—	4	4	no	—
279	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	D₄×C₇₃	1	4	yes	complemented
283	#127	—	2	2	no	—
284	#127	—	2	2	no	—
285	#127	—	4	4	no	—
286	#125	—	2	8	no	—
287	C₂²⋊Q₈	—	2	16	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	#121	—	2	8	no	—
291	#121	—	4	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	D₄×C₇₃	1	4	yes	complemented
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
313	C₄⋊C₈	—	2	2	no	—
314	#103	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	8	no	—
317	C₂²⋊C₈	—	4	4	no	—
318	C₄×C₈	—	2	2	no	—
319	#95	—	2	1	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	—	4	8	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	—	8	4	no	—
342	C₂×D₄	SD₁₆×C₇₃	1	4	yes	complemented
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	8	4	no	—
353	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
357	SD₁₆	—	4	8	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	4	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	8	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
372	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
373	C₄⋊C₄	#41×C₇₃	1	4	yes	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	8	no	—
377	C₄²	—	2	4	no	—
378	C₄²	—	4	2	no	—
379	C₄²	C₂×D₄×C₇₃	1	2	yes	—
380	C₄²	C₂×D₄×C₇₃	1	2	yes	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	4	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	4	no	—
390	C₂³	C₂×SD₁₆×C₇₃	1	4	yes	—
391	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	8	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	16	no	—
402	D₄	—	8	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	8	8	no	—
419	C₂×C₄	#120×C₇₃	1	2	yes	—
420	C₂×C₄	#120×C₇₃	1	2	yes	—
421	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
422	C₂×C₄	#137×C₇₃	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
426	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
427	C₈	—	4	2	no	—
428	C₈	—	4	2	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	8	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	—	8	2	no	—
436	C₂²	—	8	4	no	—
437	C₂²	—	8	4	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
440	C₂²	#546×C₇₃	1	2	yes	—
441	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
442	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
443	C₂²	#576×C₇₃	1	2	yes	—
444	C₄	—	2	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	#448×C₇₃	1	4	yes	—
451	C₄	#532×C₇₃	1	1	yes	characteristic
452	C₄	#535×C₇₃	1	1	yes	characteristic
453	C₄	#550×C₇₃	1	2	yes	—
454	C₂	—	4	4	no	—
455	C₂	—	16	2	no	—
456	C₂	C₇₃×#2431	1	1	yes	characteristic
457	C₂	C₂×#448×C₇₃	1	1	yes	characteristic
458	C₂	C₇₃×#3008	1	1	yes	characteristic
459	C₂	C₇₃×#3295	1	2	yes	—
460	C₂	C₇₃×#3333	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2541	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#554×C₇₃	C₂	semidirect
2. C₂×#486×C₇₃	C₂	semidirect
3. C₂×#460×C₇₃	C₂	semidirect
5. C₇₃×#2000	C₂	semidirect
6. C₇₃×#1987	C₂	semidirect
7. C₇₃×#1954	C₂	semidirect
8. C₇₃×#1874	C₂	semidirect
9. C₄×#103×C₇₃	C₂	semidirect
51. C₄⋊Q₈×C₇₃	D₄	semidirect
62. C₄×Q₈×C₇₃	D₄	semidirect
111. C₂×D₄×C₇₃	SD₁₆	semidirect
223. #25569	C₇₃	direct (N × H)
231. C₂×#554	C₂×C₇₃	semidirect
232. C₂×#486	C₂×C₇₃	semidirect
233. C₂×#460	C₂×C₇₃	semidirect
235. #2000	C₂×C₇₃	semidirect
236. #1987	C₂×C₇₃	semidirect
237. #1954	C₂×C₇₃	semidirect
238. #1874	C₂×C₇₃	semidirect
239. C₄×#103	C₂×C₇₃	semidirect
240. C₇₃	#25569	direct (N × H)
282. C₄⋊Q₈	D₄×C₇₃	semidirect
293. C₄×Q₈	D₄×C₇₃	semidirect
342. C₂×D₄	SD₁₆×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#554×C₇₃	2
C₂×#486×C₇₃	2
C₂×#460×C₇₃	2
C₇₃×#2541	2
C₇₃×#2000	2
C₇₃×#1987	2
C₇₃×#1954	2
C₇₃×#1874	2
C₄×#103×C₇₃	2
#25569	73

Subgroups — C73×#25569 #32934973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25569 #32934973