Subgroups — C₇₃×#23738 #32933142

Order 18688.

1098 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#106×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#416×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2311	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#2097	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2096	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2094	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2092	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	#428×C₇₃	—	2	4	no	—
20	C₂×#107×C₇₃	C₂²	1	2	yes	—
21	C₂×#106×C₇₃	—	2	4	no	—
22	C₂×#106×C₇₃	C₂²	1	2	yes	—
23	C₂×#106×C₇₃	C₂²	1	2	yes	—
24	C₂×#106×C₇₃	C₂²	1	2	yes	—
25	#417×C₇₃	—	2	4	no	—
26	#416×C₇₃	—	2	4	no	—
27	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#103×C₇₃	C₂²	1	2	yes	—
29	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
33	#391×C₇₃	C₂²	1	2	yes	—
34	#390×C₇₃	C₂²	1	2	yes	—
35	#389×C₇₃	—	2	2	no	—
36	#386×C₇₃	—	2	2	no	—
37	#385×C₇₃	—	2	2	no	—
38	#384×C₇₃	C₂²	1	2	yes	—
39	#382×C₇₃	C₂²	1	2	yes	—
40	#380×C₇₃	—	2	2	no	—
41	#336×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂×#41×C₇₃	—	2	2	no	—
45	C₂×#41×C₇₃	—	2	2	no	—
46	C₂×#41×C₇₃	—	2	2	no	—
47	C₂×#41×C₇₃	—	2	2	no	—
48	C₂×#41×C₇₃	Q₈	1	4	yes	—
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	—	2	1	no	—
53	C₂³×C₄×C₇₃	—	2	1	no	—
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₇₃	—	2	2	no	—
57	C₂×M₁₆×C₇₃	—	2	2	no	—
58	C₂×M₁₆×C₇₃	D₄	1	4	yes	—
59	C₂²×C₈×C₇₃	—	2	2	no	—
60	C₂²×C₈×C₇₃	—	2	2	no	—
61	C₂²×C₈×C₇₃	D₄	1	4	yes	—
62	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
65	#117×C₇₃	—	2	2	no	—
66	#117×C₇₃	—	2	2	no	—
67	#117×C₇₃	—	2	2	no	—
68	#117×C₇₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
76	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
84	C₂×C₄²×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
86	#107×C₇₃	—	2	4	no	—
87	#106×C₇₃	—	2	4	no	—
88	#106×C₇₃	—	2	4	no	—
89	#106×C₇₃	—	2	4	no	—
90	#103×C₇₃	—	2	2	no	—
91	#103×C₇₃	—	2	2	no	—
92	#103×C₇₃	—	2	4	no	—
93	#102×C₇₃	—	2	2	no	—
94	#102×C₇₃	—	2	2	no	—
95	#102×C₇₃	—	2	4	no	—
96	#95×C₇₃	—	2	4	no	—
97	#95×C₇₃	—	2	4	no	—
98	C₂⁴×C₇₃	—	2	1	no	—
99	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
100	#41×C₇₃	—	2	8	no	—
101	#41×C₇₃	—	2	8	no	—
102	#41×C₇₃	—	4	4	no	—
103	#41×C₇₃	—	4	4	no	—
104	C₂×Q₈×C₇₃	—	2	1	no	—
105	C₂×Q₈×C₇₃	—	2	1	no	—
106	C₂×Q₈×C₇₃	—	2	1	no	—
107	C₂×Q₈×C₇₃	—	2	1	no	—
108	C₂×Q₈×C₇₃	—	2	1	no	—
109	C₂×Q₈×C₇₃	C₂×Q₈	1	2	yes	—
110	C₂×D₄×C₇₃	—	2	4	no	—
111	C₂×D₄×C₇₃	—	2	1	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	1	no	—
114	C₂×D₄×C₇₃	—	2	1	no	—
115	C₂×D₄×C₇₃	—	2	1	no	—
116	C₂×D₄×C₇₃	—	4	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₇₃	—	2	1	no	—
120	C₂²×C₄×C₇₃	—	2	4	no	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	2	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	1	no	—
125	C₂²×C₄×C₇₃	—	4	2	no	—
126	C₂²×C₄×C₇₃	—	4	2	no	—
127	C₂²×C₄×C₇₃	—	4	2	no	—
128	C₂²×C₄×C₇₃	—	4	2	no	—
129	C₂²×C₄×C₇₃	—	8	2	no	—
130	C₂²×C₄×C₇₃	—	8	2	no	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
136	C₂²×C₄×C₇₃	#41	1	2	yes	—
137	C₂²×C₄×C₇₃	#41	1	2	yes	—
138	C₂²×C₄×C₇₃	#41	1	2	yes	—
139	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₇₃	—	2	8	no	—
141	C₂×C₈×C₇₃	—	2	8	no	—
142	C₂×C₈×C₇₃	—	2	1	no	—
143	C₂×C₈×C₇₃	—	2	1	no	—
144	C₂×C₈×C₇₃	—	2	1	no	—
145	C₂×C₈×C₇₃	—	2	1	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₇₃	—	2	4	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	1	no	—
154	C₄⋊C₄×C₇₃	—	2	1	no	—
155	C₄⋊C₄×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	2	no	—
157	C₄⋊C₄×C₇₃	—	2	1	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	—	2	1	no	—
160	C₄⋊C₄×C₇₃	—	4	2	no	—
161	C₄⋊C₄×C₇₃	—	4	2	no	—
162	C₄⋊C₄×C₇₃	—	8	4	no	—
163	C₂²⋊C₄×C₇₃	—	2	4	no	—
164	C₂²⋊C₄×C₇₃	—	4	2	no	—
165	C₂²⋊C₄×C₇₃	—	8	4	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	2	2	no	—
168	C₄²×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	2	2	no	—
170	C₂³×C₇₃	—	2	2	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	—	4	1	no	—
173	C₂³×C₇₃	—	4	1	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₇₃	#123	1	2	yes	—
178	C₂³×C₇₃	#127	1	2	yes	—
179	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₇₃	—	2	2	no	—
181	Q₈×C₇₃	—	2	2	no	—
182	Q₈×C₇₃	—	4	1	no	—
183	Q₈×C₇₃	—	4	1	no	—
184	D₄×C₇₃	—	2	2	no	—
185	D₄×C₇₃	—	2	2	no	—
186	D₄×C₇₃	—	4	8	no	—
187	D₄×C₇₃	—	4	1	no	—
188	D₄×C₇₃	—	4	1	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	4	no	—
191	C₂×C₄×C₇₃	—	2	4	no	—
192	C₂×C₄×C₇₃	—	2	4	no	—
193	C₂×C₄×C₇₃	—	4	1	no	—
194	C₂×C₄×C₇₃	—	4	1	no	—
195	C₂×C₄×C₇₃	—	4	8	no	—
196	C₂×C₄×C₇₃	—	4	1	no	—
197	C₂×C₄×C₇₃	—	4	1	no	—
198	C₂×C₄×C₇₃	—	4	2	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	4	no	—
201	C₂×C₄×C₇₃	—	4	2	no	—
202	C₂×C₄×C₇₃	—	4	4	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	8	4	no	—
205	C₂×C₄×C₇₃	—	8	4	no	—
206	C₂×C₄×C₇₃	C₂²⋊Q₈	1	4	yes	—
207	C₂×C₄×C₇₃	C₂²⋊Q₈	1	4	yes	—
208	C₂×C₄×C₇₃	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₇₃	#123	1	4	yes	—
210	C₂×C₄×C₇₃	#123	1	4	yes	—
211	C₂×C₄×C₇₃	#123	1	2	yes	—
212	C₂×C₄×C₇₃	#127	1	2	yes	—
213	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
219	C₈×C₇₃	—	2	2	no	—
220	C₈×C₇₃	—	2	2	no	—
221	C₈×C₇₃	—	2	4	no	—
222	C₂²×C₇₃	—	2	4	no	—
223	C₂²×C₇₃	—	2	4	no	—
224	C₂²×C₇₃	—	2	2	no	—
225	C₂²×C₇₃	—	2	2	no	—
226	C₂²×C₇₃	—	4	4	no	—
227	C₂²×C₇₃	—	4	2	no	—
228	C₂²×C₇₃	—	8	2	no	—
229	C₂²×C₇₃	—	8	1	no	—
230	C₂²×C₇₃	—	8	1	no	—
231	C₂²×C₇₃	#399	1	4	yes	—
232	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
234	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
235	C₂²×C₇₃	#577	1	2	yes	—
236	C₂²×C₇₃	#577	1	2	yes	—
237	C₄×C₇₃	—	4	4	no	—
238	C₄×C₇₃	—	4	2	no	—
239	C₄×C₇₃	—	8	1	no	—
240	C₄×C₇₃	—	8	1	no	—
241	C₄×C₇₃	—	8	2	no	—
242	C₄×C₇₃	—	8	2	no	—
243	C₄×C₇₃	#399	1	4	yes	—
244	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
245	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
246	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
247	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
248	#23738	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
249	C₂×C₇₃	—	2	4	no	—
250	C₂×C₇₃	—	8	2	no	—
251	C₂×C₇₃	C₂×#399	1	1	yes	characteristic
252	C₂×C₇₃	#3084	1	2	yes	—
253	C₂×C₇₃	#3099	1	2	yes	—
254	C₂×C₇₃	#3154	1	1	yes	characteristic
255	C₂×C₇₃	#3154	1	1	yes	characteristic
256	C₂×#428	C₂×C₇₃	1	1	yes	characteristic, complemented
257	C₂²×#106	C₂×C₇₃	1	1	yes	characteristic, complemented
258	C₂×#417	C₂×C₇₃	1	1	yes	characteristic
259	C₂×#416	C₂×C₇₃	1	1	yes	characteristic
260	#2317	C₂×C₇₃	1	1	yes	characteristic, complemented
261	#2311	C₂×C₇₃	1	1	yes	characteristic
262	#2097	C₂×C₇₃	1	2	yes	complemented
263	#2096	C₂×C₇₃	1	2	yes	complemented
264	#2094	C₂×C₇₃	1	2	yes	complemented
265	#2092	C₂×C₇₃	1	2	yes	complemented
266	#1729	C₂×C₇₃	1	1	yes	characteristic, complemented
267	C₇₃	#23738	1	1	yes	characteristic, direct product factor, Sylow
268	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
269	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
271	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
275	#428	—	2	4	no	—
276	C₂×#107	C₂²×C₇₃	1	2	yes	—
277	C₂×#106	—	2	4	no	—
278	C₂×#106	C₂²×C₇₃	1	2	yes	—
279	C₂×#106	C₂²×C₇₃	1	2	yes	—
280	C₂×#106	C₂²×C₇₃	1	2	yes	—
281	#417	—	2	4	no	—
282	#416	—	2	4	no	—
283	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
284	C₂×#103	C₂²×C₇₃	1	2	yes	—
285	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×#102	C₂²×C₇₃	1	2	yes	—
288	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
289	#391	C₂²×C₇₃	1	2	yes	—
290	#390	C₂²×C₇₃	1	2	yes	—
291	#389	—	2	2	no	—
292	#386	—	2	2	no	—
293	#385	—	2	2	no	—
294	#384	C₂²×C₇₃	1	2	yes	—
295	#382	C₂²×C₇₃	1	2	yes	—
296	#380	—	2	2	no	—
297	#336	C₂²×C₇₃	1	2	yes	—
298	#336	C₂²×C₇₃	1	2	yes	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	—	2	2	no	—
304	C₂×#41	Q₈×C₇₃	1	4	yes	—
305	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	D₄×C₇₃	1	4	yes	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	D₄×C₇₃	1	4	yes	—
318	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
321	#117	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	—	2	2	no	—
324	#117	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	4	no	—
339	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
342	#107	—	2	4	no	—
343	#106	—	2	4	no	—
344	#106	—	2	4	no	—
345	#106	—	2	4	no	—
346	#103	—	2	2	no	—
347	#103	—	2	2	no	—
348	#103	—	2	4	no	—
349	#102	—	2	2	no	—
350	#102	—	2	2	no	—
351	#102	—	2	4	no	—
352	#95	—	2	4	no	—
353	#95	—	2	4	no	—
354	C₂⁴	—	2	1	no	—
355	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
356	#41	—	2	8	no	—
357	#41	—	2	8	no	—
358	#41	—	4	4	no	—
359	#41	—	4	4	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	C₂×Q₈×C₇₃	1	2	yes	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	C₂×Q₈×C₇₃	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	8	2	no	—
386	C₂²×C₄	—	8	2	no	—
387	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
388	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
391	C₂²×C₄	C₂×Q₈×C₇₃	1	2	yes	—
392	C₂²×C₄	#41×C₇₃	1	2	yes	—
393	C₂²×C₄	#41×C₇₃	1	2	yes	—
394	C₂²×C₄	#41×C₇₃	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
396	M₁₆	—	2	8	no	—
397	C₂×C₈	—	2	8	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
405	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
406	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	2	no	—
418	C₄⋊C₄	—	8	4	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₂²⋊C₄	—	8	4	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	4	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	C₂²⋊Q₈×C₇₃	1	2	yes	—
433	C₂³	#123×C₇₃	1	2	yes	—
434	C₂³	#127×C₇₃	1	2	yes	—
435	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	1	no	—
444	D₄	—	4	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	4	no	—
462	C₂×C₄	C₂²⋊Q₈×C₇₃	1	2	yes	—
463	C₂×C₄	C₂²⋊Q₈×C₇₃	1	4	yes	—
464	C₂×C₄	C₂²⋊Q₈×C₇₃	1	4	yes	—
465	C₂×C₄	#123×C₇₃	1	2	yes	—
466	C₂×C₄	#123×C₇₃	1	4	yes	—
467	C₂×C₄	#123×C₇₃	1	4	yes	—
468	C₂×C₄	#127×C₇₃	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
471	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
474	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	#399×C₇₃	1	4	yes	—
488	C₂²	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
489	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
490	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
491	C₂²	#577×C₇₃	1	2	yes	—
492	C₂²	#577×C₇₃	1	2	yes	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	2	no	—
496	C₄	—	8	2	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	#399×C₇₃	1	4	yes	—
500	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
501	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
502	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
503	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
504	C₂	—	2	4	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×#399×C₇₃	1	1	yes	characteristic
507	C₂	C₇₃×#3084	1	2	yes	—
508	C₂	C₇₃×#3099	1	2	yes	—
509	C₂	C₇₃×#3154	1	1	yes	characteristic
510	C₂	C₇₃×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#428×C₇₃	C₂	semidirect
2. C₂²×#106×C₇₃	C₂	semidirect
5. C₇₃×#2317	C₂	semidirect
7. C₇₃×#2097	C₂	semidirect
8. C₇₃×#2096	C₂	semidirect
9. C₇₃×#2094	C₂	semidirect
10. C₇₃×#2092	C₂	semidirect
11. C₇₃×#1729	C₂	semidirect
248. #23738	C₇₃	direct (N × H)
256. C₂×#428	C₂×C₇₃	semidirect
257. C₂²×#106	C₂×C₇₃	semidirect
260. #2317	C₂×C₇₃	semidirect
262. #2097	C₂×C₇₃	semidirect
263. #2096	C₂×C₇₃	semidirect
264. #2094	C₂×C₇₃	semidirect
265. #2092	C₂×C₇₃	semidirect
266. #1729	C₂×C₇₃	semidirect
267. C₇₃	#23738	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×#428×C₇₃	2
C₂²×#106×C₇₃	2
C₂×#417×C₇₃	2
C₂×#416×C₇₃	2
C₇₃×#2317	2
C₇₃×#2311	2
C₇₃×#2097	2
C₇₃×#2096	2
C₇₃×#2094	2
C₇₃×#2092	2
C₇₃×#1729	2
#23738	73

Subgroups — C73×#23738 #32933142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23738 #32933142