Subgroups — C₇₃×#10765 #32920169

Order 18688.

1254 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#520×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#413×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#410×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1736	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1733	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
8	#520×C₇₃	—	2	4	no	—
9	#520×C₇₃	—	2	4	no	—
10	C₂×C₄×Q₈×C₇₃	—	2	1	no	—
11	C₂×C₄×D₄×C₇₃	—	2	2	no	—
12	C₂×C₄×D₄×C₇₃	—	2	1	no	—
13	C₂×#117×C₇₃	C₄	1	2	yes	complemented
14	C₂×#117×C₇₃	C₂²	1	2	yes	—
15	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₃	C₄	1	2	yes	complemented
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	#413×C₇₃	—	2	2	no	—
19	#413×C₇₃	C₄	1	4	yes	complemented
20	C₂×#101×C₇₃	—	2	1	no	—
21	C₂×#100×C₇₃	—	2	1	no	—
22	#410×C₇₃	—	2	2	no	—
23	#410×C₇₃	C₄	1	4	yes	complemented
24	C₂×#99×C₇₃	—	2	2	no	—
25	#340×C₇₃	—	2	4	no	—
26	#339×C₇₃	—	2	4	no	—
27	C₂×#41×C₇₃	—	2	2	no	—
28	C₂×#41×C₇₃	—	2	2	no	—
29	C₂×#41×C₇₃	—	2	2	no	—
30	C₂×#41×C₇₃	—	2	2	no	—
31	C₂×#41×C₇₃	C₂×C₄	1	2	yes	—
32	C₂×#41×C₇₃	C₂×C₄	1	2	yes	—
33	C₂×#41×C₇₃	D₄	1	2	yes	—
34	C₂×#41×C₇₃	Q₈	1	2	yes	—
35	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₇₃	D₄	1	2	yes	—
37	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₇₃	—	2	2	no	—
39	C₂³×C₄×C₇₃	—	2	1	no	—
40	C₂³×C₄×C₇₃	C₂×C₄	1	2	yes	—
41	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₇₃	—	2	2	no	—
43	C₂×M₁₆×C₇₃	—	2	2	no	—
44	C₂×M₁₆×C₇₃	—	2	2	no	—
45	C₂×M₁₆×C₇₃	—	2	2	no	—
46	C₂×M₁₆×C₇₃	—	2	2	no	—
47	C₂×M₁₆×C₇₃	C₂×C₄	1	4	yes	complemented
48	C₂²×C₈×C₇₃	—	2	2	no	—
49	C₄×Q₈×C₇₃	—	2	8	no	—
50	C₄×D₄×C₇₃	—	2	16	no	—
51	C₄×D₄×C₇₃	—	2	8	no	—
52	#117×C₇₃	—	2	2	no	—
53	#117×C₇₃	—	2	4	no	—
54	#117×C₇₃	—	2	4	no	—
55	#117×C₇₃	—	2	2	no	—
56	#117×C₇₃	—	2	2	no	—
57	#117×C₇₃	—	2	2	no	—
58	#117×C₇₃	C₂×C₄	1	4	yes	complemented
59	#117×C₇₃	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₄²×C₇₃	—	2	2	no	—
74	C₂×C₄²×C₇₃	—	2	1	no	—
75	C₂×C₄²×C₇₃	—	2	2	no	—
76	#101×C₇₃	—	2	4	no	—
77	#100×C₇₃	—	2	4	no	—
78	#99×C₇₃	—	2	8	no	—
79	C₂⁴×C₇₃	C₂²⋊C₄	1	2	yes	—
80	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
81	#41×C₇₃	—	2	4	no	—
82	#41×C₇₃	—	2	4	no	—
83	#41×C₇₃	—	2	4	no	—
84	#41×C₇₃	—	2	4	no	—
85	#41×C₇₃	—	2	4	no	—
86	#41×C₇₃	—	2	4	no	—
87	#41×C₇₃	—	2	4	no	—
88	#41×C₇₃	—	2	4	no	—
89	C₂×Q₈×C₇₃	—	2	2	no	—
90	C₂×Q₈×C₇₃	—	2	2	no	—
91	C₂×Q₈×C₇₃	C₂²⋊C₄	1	2	yes	—
92	C₂×Q₈×C₇₃	C₄⋊C₄	1	2	yes	—
93	C₂×D₄×C₇₃	—	2	4	no	—
94	C₂×D₄×C₇₃	—	2	4	no	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	2	no	—
97	C₂×D₄×C₇₃	C₂²⋊C₄	1	4	yes	—
98	C₂×D₄×C₇₃	C₂²⋊C₄	1	2	yes	—
99	C₂×D₄×C₇₃	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₇₃	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
104	C₂²×C₄×C₇₃	—	2	2	no	—
105	C₂²×C₄×C₇₃	—	2	1	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	2	1	no	—
108	C₂²×C₄×C₇₃	—	2	8	no	—
109	C₂²×C₄×C₇₃	—	2	4	no	—
110	C₂²×C₄×C₇₃	—	4	2	no	—
111	C₂²×C₄×C₇₃	—	8	2	no	—
112	C₂²×C₄×C₇₃	—	8	4	no	—
113	C₂²×C₄×C₇₃	C₄²	1	4	yes	—
114	C₂²×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₇₃	C₄⋊C₄	1	4	yes	—
116	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	#41	1	2	yes	—
125	C₂²×C₄×C₇₃	#41	1	2	yes	—
126	M₁₆×C₇₃	—	2	4	no	—
127	M₁₆×C₇₃	—	2	4	no	—
128	M₁₆×C₇₃	—	4	2	no	—
129	M₁₆×C₇₃	—	4	2	no	—
130	C₂×C₈×C₇₃	—	2	4	no	—
131	C₂×C₈×C₇₃	—	4	2	no	—
132	C₂×C₈×C₇₃	—	4	2	no	—
133	C₄⋊C₄×C₇₃	—	2	8	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	2	1	no	—
136	C₄⋊C₄×C₇₃	—	2	1	no	—
137	C₄⋊C₄×C₇₃	—	2	4	no	—
138	C₄⋊C₄×C₇₃	—	2	4	no	—
139	C₄⋊C₄×C₇₃	—	4	2	no	—
140	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
141	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
142	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
143	C₂²⋊C₄×C₇₃	—	2	8	no	—
144	C₂²⋊C₄×C₇₃	—	2	4	no	—
145	C₂²⋊C₄×C₇₃	—	2	4	no	—
146	C₂²⋊C₄×C₇₃	—	4	2	no	—
147	C₄²×C₇₃	—	2	8	no	—
148	C₄²×C₇₃	—	2	4	no	—
149	C₄²×C₇₃	—	2	4	no	—
150	C₄²×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	2	2	no	—
152	C₂³×C₇₃	—	2	2	no	—
153	C₂³×C₇₃	—	4	1	no	—
154	C₂³×C₇₃	—	4	1	no	—
155	C₂³×C₇₃	—	4	2	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	#95	1	4	yes	—
158	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂³×C₇₃	#120	1	2	yes	—
162	C₂³×C₇₃	#123	1	2	yes	—
163	Q₈×C₇₃	—	2	4	no	—
164	Q₈×C₇₃	—	2	4	no	—
165	D₄×C₇₃	—	2	8	no	—
166	D₄×C₇₃	—	2	8	no	—
167	D₄×C₇₃	—	2	4	no	—
168	D₄×C₇₃	—	2	4	no	—
169	C₂×C₄×C₇₃	—	2	2	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	4	no	—
172	C₂×C₄×C₇₃	—	2	4	no	—
173	C₂×C₄×C₇₃	—	2	4	no	—
174	C₂×C₄×C₇₃	—	2	4	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	4	no	—
177	C₂×C₄×C₇₃	—	2	2	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	4	4	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	—	4	4	no	—
182	C₂×C₄×C₇₃	—	8	4	no	—
183	C₂×C₄×C₇₃	—	8	8	no	—
184	C₂×C₄×C₇₃	—	8	2	no	—
185	C₂×C₄×C₇₃	—	8	2	no	—
186	C₂×C₄×C₇₃	#95	1	4	yes	—
187	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
194	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
195	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₇₃	#120	1	2	yes	—
200	C₂×C₄×C₇₃	#121	1	2	yes	—
201	C₂×C₄×C₇₃	#121	1	2	yes	—
202	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
203	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
204	C₂×C₄×C₇₃	#123	1	2	yes	—
205	C₈×C₇₃	—	4	4	no	—
206	C₂²×C₇₃	—	2	1	no	—
207	C₂²×C₇₃	—	2	2	no	—
208	C₂²×C₇₃	—	2	1	no	—
209	C₂²×C₇₃	—	2	2	no	—
210	C₂²×C₇₃	—	2	4	no	—
211	C₂²×C₇₃	—	4	1	no	—
212	C₂²×C₇₃	—	4	1	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	4	4	no	—
215	C₂²×C₇₃	—	4	4	no	—
216	C₂²×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	4	2	no	—
218	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
219	C₂²×C₇₃	#379	1	1	yes	characteristic
220	C₂²×C₇₃	#381	1	1	yes	characteristic
221	C₂²×C₇₃	#385	1	2	yes	—
222	C₂²×C₇₃	#386	1	2	yes	—
223	C₄×C₇₃	—	2	4	no	—
224	C₄×C₇₃	—	4	4	no	—
225	C₄×C₇₃	—	4	2	no	—
226	C₄×C₇₃	—	4	2	no	—
227	C₄×C₇₃	—	8	4	no	—
228	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
230	C₄×C₇₃	#380	1	1	yes	characteristic
231	C₄×C₇₃	#380	1	1	yes	characteristic
232	C₄×C₇₃	#385	1	2	yes	—
233	C₄×C₇₃	#386	1	2	yes	—
234	#10765	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₇₃	—	2	2	no	—
236	C₂×C₇₃	—	2	1	no	—
237	C₂×C₇₃	—	2	1	no	—
238	C₂×C₇₃	—	2	2	no	—
239	C₂×C₇₃	—	4	4	no	—
240	C₂×C₇₃	C₂²⋊#95	1	1	yes	characteristic
241	C₂×C₇₃	#1795	1	1	yes	characteristic
242	C₂×C₇₃	#1796	1	1	yes	characteristic
243	C₂×#520	C₂×C₇₃	1	1	yes	characteristic
244	C₂×#413	C₂×C₇₃	1	1	yes	characteristic
245	C₂×#410	C₂×C₇₃	1	1	yes	characteristic
246	#1736	C₂×C₇₃	1	2	yes	complemented
247	#1733	C₂×C₇₃	1	2	yes	complemented
248	C₇₃	#10765	1	1	yes	characteristic, direct product factor, Sylow
249	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
251	#520	—	2	4	no	—
252	#520	—	2	4	no	—
253	C₂×C₄×Q₈	—	2	1	no	—
254	C₂×C₄×D₄	—	2	2	no	—
255	C₂×C₄×D₄	—	2	1	no	—
256	C₂×#117	C₄×C₇₃	1	2	yes	complemented
257	C₂×#117	C₂²×C₇₃	1	2	yes	—
258	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
259	C₂²×C₄⋊C₄	C₄×C₇₃	1	2	yes	complemented
260	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
261	#413	—	2	2	no	—
262	#413	C₄×C₇₃	1	4	yes	complemented
263	C₂×#101	—	2	1	no	—
264	C₂×#100	—	2	1	no	—
265	#410	—	2	2	no	—
266	#410	C₄×C₇₃	1	4	yes	complemented
267	C₂×#99	—	2	2	no	—
268	#340	—	2	4	no	—
269	#339	—	2	4	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	C₂×C₄×C₇₃	1	2	yes	—
275	C₂×#41	C₂×C₄×C₇₃	1	2	yes	—
276	C₂×#41	D₄×C₇₃	1	2	yes	—
277	C₂×#41	Q₈×C₇₃	1	2	yes	—
278	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
279	C₂²×D₄	D₄×C₇₃	1	2	yes	—
280	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
281	C₂³×C₄	—	2	2	no	—
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	C₂×C₄×C₇₃	1	2	yes	—
284	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	C₂×C₄×C₇₃	1	4	yes	complemented
291	C₂²×C₈	—	2	2	no	—
292	C₄×Q₈	—	2	8	no	—
293	C₄×D₄	—	2	16	no	—
294	C₄×D₄	—	2	8	no	—
295	#117	—	2	2	no	—
296	#117	—	2	4	no	—
297	#117	—	2	4	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	—	2	2	no	—
301	#117	C₂×C₄×C₇₃	1	4	yes	complemented
302	#117	D₄×C₇₃	1	4	yes	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	4	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
311	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	#101	—	2	4	no	—
320	#100	—	2	4	no	—
321	#99	—	2	8	no	—
322	C₂⁴	C₂²⋊C₄×C₇₃	1	2	yes	—
323	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
324	#41	—	2	4	no	—
325	#41	—	2	4	no	—
326	#41	—	2	4	no	—
327	#41	—	2	4	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²⋊C₄×C₇₃	1	2	yes	—
335	C₂×Q₈	C₄⋊C₄×C₇₃	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₂²⋊C₄×C₇₃	1	4	yes	—
341	C₂×D₄	C₂²⋊C₄×C₇₃	1	2	yes	—
342	C₂×D₄	C₄⋊C₄×C₇₃	1	4	yes	—
343	C₂×D₄	C₄⋊C₄×C₇₃	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	4	2	no	—
354	C₂²×C₄	—	8	2	no	—
355	C₂²×C₄	—	8	4	no	—
356	C₂²×C₄	C₄²×C₇₃	1	4	yes	—
357	C₂²×C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
358	C₂²×C₄	C₄⋊C₄×C₇₃	1	4	yes	—
359	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
361	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
366	C₂²×C₄	C₂×Q₈×C₇₃	1	1	yes	characteristic
367	C₂²×C₄	#41×C₇₃	1	2	yes	—
368	C₂²×C₄	#41×C₇₃	1	2	yes	—
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	4	no	—
371	M₁₆	—	4	2	no	—
372	M₁₆	—	4	2	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	4	2	no	—
375	C₂×C₈	—	4	2	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	4	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	4	yes	—
385	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	4	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₄²	—	2	8	no	—
391	C₄²	—	2	4	no	—
392	C₄²	—	2	4	no	—
393	C₄²	—	4	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	#95×C₇₃	1	4	yes	—
401	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
402	C₂³	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
403	C₂³	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
404	C₂³	#120×C₇₃	1	2	yes	—
405	C₂³	#123×C₇₃	1	2	yes	—
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	D₄	—	2	8	no	—
409	D₄	—	2	8	no	—
410	D₄	—	2	4	no	—
411	D₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	8	4	no	—
426	C₂×C₄	—	8	8	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	#95×C₇₃	1	4	yes	—
430	C₂×C₄	C₂×C₄²×C₇₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
432	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
435	C₂×C₄	C₂×C₄⋊C₄×C₇₃	1	1	yes	characteristic
436	C₂×C₄	#117×C₇₃	1	1	yes	characteristic
437	C₂×C₄	#117×C₇₃	1	1	yes	characteristic
438	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
439	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
440	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
442	C₂×C₄	#120×C₇₃	1	2	yes	—
443	C₂×C₄	#121×C₇₃	1	2	yes	—
444	C₂×C₄	#121×C₇₃	1	2	yes	—
445	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
446	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
447	C₂×C₄	#123×C₇₃	1	2	yes	—
448	C₈	—	4	4	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂×#95×C₇₃	1	1	yes	characteristic
462	C₂²	#379×C₇₃	1	1	yes	characteristic
463	C₂²	#381×C₇₃	1	1	yes	characteristic
464	C₂²	#385×C₇₃	1	2	yes	—
465	C₂²	#386×C₇₃	1	2	yes	—
466	C₄	—	2	4	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	8	4	no	—
471	C₄	C₄×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
472	C₄	C₄×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
473	C₄	#380×C₇₃	1	1	yes	characteristic
474	C₄	#380×C₇₃	1	1	yes	characteristic
475	C₄	#385×C₇₃	1	2	yes	—
476	C₄	#386×C₇₃	1	2	yes	—
477	C₂	—	2	2	no	—
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	2	2	no	—
481	C₂	—	4	4	no	—
482	C₂	C₇₃×C₂²⋊#95	1	1	yes	characteristic
483	C₂	C₇₃×#1795	1	1	yes	characteristic
484	C₂	C₇₃×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	#379
commutator	C₂×C₄	C₂×C₄²×C₇₃
Frattini, cosocle	C₂³×C₄	C₂³×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇₃×#1736	C₂	semidirect
5. C₇₃×#1733	C₂	semidirect
13. C₂×#117×C₇₃	C₄	semidirect
16. C₂²×C₄⋊C₄×C₇₃	C₄	semidirect
19. #413×C₇₃	C₄	semidirect
23. #410×C₇₃	C₄	semidirect
47. C₂×M₁₆×C₇₃	C₂×C₄	semidirect
58. #117×C₇₃	C₂×C₄	semidirect
234. #10765	C₇₃	direct (N × H)
246. #1736	C₂×C₇₃	semidirect
247. #1733	C₂×C₇₃	semidirect
248. C₇₃	#10765	direct (N × H)
256. C₂×#117	C₄×C₇₃	semidirect
259. C₂²×C₄⋊C₄	C₄×C₇₃	semidirect
262. #413	C₄×C₇₃	semidirect
266. #410	C₄×C₇₃	semidirect
290. C₂×M₁₆	C₂×C₄×C₇₃	semidirect
301. #117	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#520×C₇₃	2
C₂×#413×C₇₃	2
C₂×#410×C₇₃	2
C₇₃×#1736	2
C₇₃×#1733	2
#10765	73

Subgroups — C73×#10765 #32920169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#10765 #32920169