Subgroups — C₇₃×#25641 #32935045

Order 18688.

1172 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#497×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2014	C₂	1	2	yes	maximal
7	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1878	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
15	#559×C₇₃	—	2	4	no	—
16	#559×C₇₃	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#124×C₇₃	—	2	1	no	—
20	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#123×C₇₃	—	2	1	no	—
23	C₂×#123×C₇₃	—	2	1	no	—
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₇₃	—	2	1	no	—
27	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
29	#497×C₇₃	—	2	4	no	—
30	#461×C₇₃	—	2	4	no	—
31	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₃	C₂²	1	2	yes	—
33	C₂×#103×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#102×C₇₃	C₂²	1	2	yes	—
36	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
37	#400×C₇₃	—	2	1	no	—
38	#400×C₇₃	—	2	1	no	—
39	#391×C₇₃	—	2	1	no	—
40	#391×C₇₃	C₂²	1	2	yes	—
41	#391×C₇₃	C₂²	1	2	yes	—
42	#382×C₇₃	—	2	1	no	—
43	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#340×C₇₃	C₂²	1	2	yes	—
45	#336×C₇₃	C₂²	1	2	yes	—
46	#336×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	—	2	1	no	—
52	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	—	2	1	no	—
56	C₂×Q₁₆×C₇₃	—	2	4	no	—
57	C₂×Q₁₆×C₇₃	—	2	4	no	—
58	C₂×Q₁₆×C₇₃	—	4	2	no	—
59	C₂×SD₁₆×C₇₃	—	2	4	no	—
60	C₂×SD₁₆×C₇₃	—	2	4	no	—
61	C₂×SD₁₆×C₇₃	—	2	4	no	—
62	C₂×SD₁₆×C₇₃	—	4	2	no	—
63	C₂×SD₁₆×C₇₃	—	4	2	no	—
64	C₂×SD₁₆×C₇₃	—	4	2	no	—
65	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
66	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₇₃	—	2	2	no	—
68	C₄⋊Q₈×C₇₃	—	2	2	no	—
69	#127×C₇₃	—	2	2	no	—
70	#127×C₇₃	—	2	2	no	—
71	#124×C₇₃	—	2	8	no	—
72	#124×C₇₃	—	2	2	no	—
73	#124×C₇₃	—	2	2	no	—
74	#124×C₇₃	—	2	2	no	—
75	#124×C₇₃	D₄	1	4	yes	—
76	#123×C₇₃	—	2	8	no	—
77	#123×C₇₃	—	2	8	no	—
78	C₄×Q₈×C₇₃	—	2	2	no	—
79	C₄×Q₈×C₇₃	—	2	2	no	—
80	C₄×Q₈×C₇₃	—	2	2	no	—
81	C₄×Q₈×C₇₃	—	2	2	no	—
82	C₄×D₄×C₇₃	—	2	8	no	—
83	C₄×D₄×C₇₃	—	2	2	no	—
84	C₄×D₄×C₇₃	—	2	2	no	—
85	C₄×D₄×C₇₃	—	2	2	no	—
86	C₄×D₄×C₇₃	D₄	1	4	yes	—
87	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
101	C₂×C₄²×C₇₃	—	2	1	no	—
102	C₂×C₄²×C₇₃	—	2	1	no	—
103	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₇₃	—	2	2	no	—
107	#103×C₇₃	—	2	4	no	—
108	#103×C₇₃	—	4	2	no	—
109	#102×C₇₃	—	2	4	no	—
110	#102×C₇₃	—	4	2	no	—
111	#97×C₇₃	—	2	2	no	—
112	#95×C₇₃	—	2	1	no	—
113	#95×C₇₃	—	2	2	no	—
114	#95×C₇₃	—	2	2	no	—
115	#95×C₇₃	—	2	2	no	—
116	#95×C₇₃	—	2	2	no	—
117	C₂⁴×C₇₃	—	2	1	no	—
118	C₂⁴×C₇₃	—	2	1	no	—
119	C₂×Q₈×C₇₃	—	2	2	no	—
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	1	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	2	no	—
124	C₂×Q₈×C₇₃	—	2	2	no	—
125	C₂×Q₈×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	2	2	no	—
129	C₂×Q₈×C₇₃	—	2	2	no	—
130	C₂×Q₈×C₇₃	—	4	1	no	—
131	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₇₃	—	2	4	no	—
133	C₂×D₄×C₇₃	—	2	4	no	—
134	C₂×D₄×C₇₃	—	2	1	no	—
135	C₂×D₄×C₇₃	—	2	1	no	—
136	C₂×D₄×C₇₃	—	2	2	no	—
137	C₂×D₄×C₇₃	—	2	2	no	—
138	C₂×D₄×C₇₃	—	2	2	no	—
139	C₂×D₄×C₇₃	—	2	2	no	—
140	C₂×D₄×C₇₃	—	4	2	no	—
141	C₂×D₄×C₇₃	—	4	2	no	—
142	C₂×D₄×C₇₃	—	8	2	no	—
143	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₇₃	—	2	1	no	—
146	C₂²×C₄×C₇₃	—	2	1	no	—
147	C₂²×C₄×C₇₃	—	2	4	no	—
148	C₂²×C₄×C₇₃	—	2	4	no	—
149	C₂²×C₄×C₇₃	—	2	2	no	—
150	C₂²×C₄×C₇₃	—	2	2	no	—
151	C₂²×C₄×C₇₃	—	8	2	no	—
152	C₂²×C₄×C₇₃	—	8	2	no	—
153	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₇₃	—	4	8	no	—
161	SD₁₆×C₇₃	—	4	8	no	—
162	SD₁₆×C₇₃	—	4	8	no	—
163	C₂×C₈×C₇₃	—	2	2	no	—
164	C₂×C₈×C₇₃	—	2	2	no	—
165	C₂×C₈×C₇₃	—	2	2	no	—
166	C₂×C₈×C₇₃	—	2	2	no	—
167	C₂×C₈×C₇₃	—	2	2	no	—
168	C₂×C₈×C₇₃	#41	1	4	yes	—
169	C₄⋊C₄×C₇₃	—	2	4	no	—
170	C₄⋊C₄×C₇₃	—	2	2	no	—
171	C₄⋊C₄×C₇₃	—	2	2	no	—
172	C₄⋊C₄×C₇₃	—	2	2	no	—
173	C₄⋊C₄×C₇₃	—	2	1	no	—
174	C₄⋊C₄×C₇₃	—	2	2	no	—
175	C₄⋊C₄×C₇₃	—	2	2	no	—
176	C₄⋊C₄×C₇₃	—	4	2	no	—
177	C₄⋊C₄×C₇₃	—	4	2	no	—
178	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
179	C₂²⋊C₄×C₇₃	—	2	4	no	—
180	C₂²⋊C₄×C₇₃	—	2	4	no	—
181	C₂²⋊C₄×C₇₃	—	2	4	no	—
182	C₂²⋊C₄×C₇₃	—	2	4	no	—
183	C₂²⋊C₄×C₇₃	—	2	4	no	—
184	C₂²⋊C₄×C₇₃	—	2	4	no	—
185	C₄²×C₇₃	—	2	4	no	—
186	C₄²×C₇₃	—	2	1	no	—
187	C₄²×C₇₃	—	2	1	no	—
188	C₄²×C₇₃	—	2	1	no	—
189	C₄²×C₇₃	—	2	1	no	—
190	C₄²×C₇₃	—	4	2	no	—
191	C₄²×C₇₃	C₂×D₄	1	2	yes	—
192	C₄²×C₇₃	C₂×D₄	1	2	yes	—
193	C₂³×C₇₃	—	2	2	no	—
194	C₂³×C₇₃	—	2	2	no	—
195	C₂³×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	—	4	2	no	—
197	C₂³×C₇₃	—	4	1	no	—
198	C₂³×C₇₃	—	4	1	no	—
199	C₂³×C₇₃	—	4	1	no	—
200	C₂³×C₇₃	—	4	1	no	—
201	C₂³×C₇₃	—	4	2	no	—
202	C₂³×C₇₃	—	4	2	no	—
203	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₇₃	—	2	4	no	—
205	Q₈×C₇₃	—	4	4	no	—
206	Q₈×C₇₃	—	4	1	no	—
207	Q₈×C₇₃	—	4	1	no	—
208	Q₈×C₇₃	—	4	2	no	—
209	Q₈×C₇₃	—	4	2	no	—
210	Q₈×C₇₃	—	4	2	no	—
211	Q₈×C₇₃	—	4	2	no	—
212	D₄×C₇₃	—	2	2	no	—
213	D₄×C₇₃	—	2	2	no	—
214	D₄×C₇₃	—	2	4	no	—
215	D₄×C₇₃	—	4	8	no	—
216	D₄×C₇₃	—	4	1	no	—
217	D₄×C₇₃	—	4	1	no	—
218	D₄×C₇₃	—	4	2	no	—
219	D₄×C₇₃	—	8	4	no	—
220	C₂×C₄×C₇₃	—	2	1	no	—
221	C₂×C₄×C₇₃	—	2	1	no	—
222	C₂×C₄×C₇₃	—	2	1	no	—
223	C₂×C₄×C₇₃	—	2	1	no	—
224	C₂×C₄×C₇₃	—	2	2	no	—
225	C₂×C₄×C₇₃	—	2	2	no	—
226	C₂×C₄×C₇₃	—	2	1	no	—
227	C₂×C₄×C₇₃	—	2	1	no	—
228	C₂×C₄×C₇₃	—	2	2	no	—
229	C₂×C₄×C₇₃	—	2	1	no	—
230	C₂×C₄×C₇₃	—	2	1	no	—
231	C₂×C₄×C₇₃	—	2	1	no	—
232	C₂×C₄×C₇₃	—	2	2	no	—
233	C₂×C₄×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	4	2	no	—
235	C₂×C₄×C₇₃	—	4	2	no	—
236	C₂×C₄×C₇₃	—	4	2	no	—
237	C₂×C₄×C₇₃	—	4	2	no	—
238	C₂×C₄×C₇₃	—	4	2	no	—
239	C₂×C₄×C₇₃	—	4	2	no	—
240	C₂×C₄×C₇₃	—	4	2	no	—
241	C₂×C₄×C₇₃	—	4	2	no	—
242	C₂×C₄×C₇₃	—	8	4	no	—
243	C₂×C₄×C₇₃	—	8	4	no	—
244	C₂×C₄×C₇₃	#120	1	2	yes	—
245	C₂×C₄×C₇₃	#120	1	2	yes	—
246	C₂×C₄×C₇₃	#137	1	2	yes	—
247	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
250	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
251	C₈×C₇₃	—	2	4	no	—
252	C₈×C₇₃	—	4	2	no	—
253	C₂²×C₇₃	—	4	2	no	—
254	C₂²×C₇₃	—	4	2	no	—
255	C₂²×C₇₃	—	4	2	no	—
256	C₂²×C₇₃	—	4	2	no	—
257	C₂²×C₇₃	—	4	2	no	—
258	C₂²×C₇₃	—	4	2	no	—
259	C₂²×C₇₃	—	8	2	no	—
260	C₂²×C₇₃	—	8	2	no	—
261	C₂²×C₇₃	—	8	2	no	—
262	C₂²×C₇₃	—	8	2	no	—
263	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
264	C₂²×C₇₃	#550	1	2	yes	—
265	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
266	C₂²×C₇₃	#575	1	1	yes	characteristic
267	C₂²×C₇₃	#577	1	2	yes	—
268	C₄×C₇₃	—	2	2	no	—
269	C₄×C₇₃	—	2	2	no	—
270	C₄×C₇₃	—	2	2	no	—
271	C₄×C₇₃	—	4	2	no	—
272	C₄×C₇₃	—	4	1	no	—
273	C₄×C₇₃	—	4	1	no	—
274	C₄×C₇₃	—	4	1	no	—
275	C₄×C₇₃	—	4	2	no	—
276	C₄×C₇₃	—	8	2	no	—
277	C₄×C₇₃	—	8	2	no	—
278	C₄×C₇₃	#532	1	1	yes	characteristic
279	C₄×C₇₃	#535	1	1	yes	characteristic
280	C₄×C₇₃	#546	1	2	yes	—
281	#25641	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
282	C₂×C₇₃	—	8	2	no	—
283	C₂×C₇₃	—	8	2	no	—
284	C₂×C₇₃	#2431	1	1	yes	characteristic
285	C₂×C₇₃	#3007	1	1	yes	characteristic
286	C₂×C₇₃	#3009	1	1	yes	characteristic
287	C₂×C₇₃	#3400	1	2	yes	—
288	C₂×C₇₃	#3401	1	2	yes	—
289	C₂×#559	C₂×C₇₃	1	1	yes	characteristic
290	C₂×#497	C₂×C₇₃	1	1	yes	characteristic, complemented
291	C₂×#461	C₂×C₇₃	1	1	yes	characteristic, complemented
292	#2568	C₂×C₇₃	1	1	yes	characteristic, complemented
293	#2015	C₂×C₇₃	1	2	yes	complemented
294	#2014	C₂×C₇₃	1	2	yes	—
295	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#1983	C₂×C₇₃	1	1	yes	characteristic, complemented
297	#1878	C₂×C₇₃	1	2	yes	complemented
298	#1877	C₂×C₇₃	1	2	yes	complemented
299	#1762	C₂×C₇₃	1	1	yes	characteristic, complemented
300	C₇₃	#25641	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
302	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
303	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
304	#559	—	2	4	no	—
305	#559	—	2	4	no	—
306	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
308	C₂×#124	—	2	1	no	—
309	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
310	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
311	C₂×#123	—	2	1	no	—
312	C₂×#123	—	2	1	no	—
313	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
314	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
315	C₂×C₄×D₄	—	2	1	no	—
316	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
318	#497	—	2	4	no	—
319	#461	—	2	4	no	—
320	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
321	C₂×#103	C₂²×C₇₃	1	2	yes	—
322	C₂×#103	C₂²×C₇₃	1	2	yes	—
323	C₂×#102	C₂²×C₇₃	1	2	yes	—
324	C₂×#102	C₂²×C₇₃	1	2	yes	—
325	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
326	#400	—	2	1	no	—
327	#400	—	2	1	no	—
328	#391	—	2	1	no	—
329	#391	C₂²×C₇₃	1	2	yes	—
330	#391	C₂²×C₇₃	1	2	yes	—
331	#382	—	2	1	no	—
332	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
333	#340	C₂²×C₇₃	1	2	yes	—
334	#336	C₂²×C₇₃	1	2	yes	—
335	#336	C₂²×C₇₃	1	2	yes	—
336	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
337	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
338	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂×Q₁₆	—	2	4	no	—
346	C₂×Q₁₆	—	2	4	no	—
347	C₂×Q₁₆	—	4	2	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	4	2	no	—
352	C₂×SD₁₆	—	4	2	no	—
353	C₂×SD₁₆	—	4	2	no	—
354	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
355	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	—	2	2	no	—
358	#127	—	2	2	no	—
359	#127	—	2	2	no	—
360	#124	—	2	8	no	—
361	#124	—	2	2	no	—
362	#124	—	2	2	no	—
363	#124	—	2	2	no	—
364	#124	D₄×C₇₃	1	4	yes	—
365	#123	—	2	8	no	—
366	#123	—	2	8	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×D₄	—	2	8	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	D₄×C₇₃	1	4	yes	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
381	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
395	C₄⋊C₈	—	2	2	no	—
396	#103	—	2	4	no	—
397	#103	—	4	2	no	—
398	#102	—	2	4	no	—
399	#102	—	4	2	no	—
400	#97	—	2	2	no	—
401	#95	—	2	1	no	—
402	#95	—	2	2	no	—
403	#95	—	2	2	no	—
404	#95	—	2	2	no	—
405	#95	—	2	2	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	4	2	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	—	8	2	no	—
432	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
433	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	8	2	no	—
441	C₂²×C₄	—	8	2	no	—
442	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
449	Q₁₆	—	4	8	no	—
450	SD₁₆	—	4	8	no	—
451	SD₁₆	—	4	8	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	#41×C₇₃	1	4	yes	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₄²	—	2	4	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	4	2	no	—
480	C₄²	C₂×D₄×C₇₃	1	2	yes	—
481	C₄²	C₂×D₄×C₇₃	1	2	yes	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
493	Q₈	—	2	4	no	—
494	Q₈	—	4	4	no	—
495	Q₈	—	4	1	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	2	no	—
508	D₄	—	8	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	—	8	4	no	—
533	C₂×C₄	#120×C₇₃	1	2	yes	—
534	C₂×C₄	#120×C₇₃	1	2	yes	—
535	C₂×C₄	#137×C₇₃	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
539	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
540	C₈	—	2	4	no	—
541	C₈	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	8	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
553	C₂²	#550×C₇₃	1	2	yes	—
554	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
555	C₂²	#575×C₇₃	1	1	yes	characteristic
556	C₂²	#577×C₇₃	1	2	yes	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	8	2	no	—
566	C₄	—	8	2	no	—
567	C₄	#532×C₇₃	1	1	yes	characteristic
568	C₄	#535×C₇₃	1	1	yes	characteristic
569	C₄	#546×C₇₃	1	2	yes	—
570	C₂	—	8	2	no	—
571	C₂	—	8	2	no	—
572	C₂	C₇₃×#2431	1	1	yes	characteristic
573	C₂	C₇₃×#3007	1	1	yes	characteristic
574	C₂	C₇₃×#3009	1	1	yes	characteristic
575	C₂	C₇₃×#3400	1	2	yes	—
576	C₂	C₇₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#497×C₇₃	C₂	semidirect
3. C₂×#461×C₇₃	C₂	semidirect
4. C₇₃×#2568	C₂	semidirect
5. C₇₃×#2015	C₂	semidirect
7. C₇₃×#1985	C₂	semidirect
8. C₇₃×#1983	C₂	semidirect
9. C₇₃×#1878	C₂	semidirect
10. C₇₃×#1877	C₂	semidirect
11. C₇₃×#1762	C₂	semidirect
281. #25641	C₇₃	direct (N × H)
290. C₂×#497	C₂×C₇₃	semidirect
291. C₂×#461	C₂×C₇₃	semidirect
292. #2568	C₂×C₇₃	semidirect
293. #2015	C₂×C₇₃	semidirect
295. #1985	C₂×C₇₃	semidirect
296. #1983	C₂×C₇₃	semidirect
297. #1878	C₂×C₇₃	semidirect
298. #1877	C₂×C₇₃	semidirect
299. #1762	C₂×C₇₃	semidirect
300. C₇₃	#25641	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#559×C₇₃	2
C₂×#497×C₇₃	2
C₂×#461×C₇₃	2
C₇₃×#2568	2
C₇₃×#2015	2
C₇₃×#2014	2
C₇₃×#1985	2
C₇₃×#1983	2
C₇₃×#1878	2
C₇₃×#1877	2
C₇₃×#1762	2
#25641	73

Subgroups — C73×#25641 #32935045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25641 #32935045