Subgroups — C₇₃×#60800 #32970204

Order 18688.

2134 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3218	C₂	1	8	yes	maximal, complemented
4	C₇₃×#3209	C₂	1	4	yes	maximal, complemented
5	C₇₃×#3206	C₂	1	4	yes	maximal, complemented
6	C₇₃×#3152	C₂	1	2	yes	maximal, complemented
7	C₇₃×#3139	C₂	1	2	yes	maximal, complemented
8	C₇₃×#3039	C₂	1	4	yes	maximal, complemented
9	C₇₃×#3004	C₂	1	4	yes	maximal, complemented
10	C₇₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×Q₈×C₇₃	C₂²	1	2	yes	—
12	C₂×#137×C₇₃	C₂²	1	8	yes	—
13	#533×C₇₃	C₂²	1	2	yes	—
14	#533×C₇₃	C₂²	1	1	yes	characteristic
15	#532×C₇₃	C₂²	1	1	yes	characteristic
16	#532×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₇₃	—	2	2	no	—
18	C₂×C₄⋊Q₈×C₇₃	—	2	2	no	—
19	C₂×C₄⋊Q₈×C₇₃	—	2	2	no	—
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
24	#529×C₇₃	—	2	2	no	—
25	#529×C₇₃	—	2	2	no	—
26	#529×C₇₃	C₂²	1	4	yes	—
27	#525×C₇₃	—	2	2	no	—
28	#525×C₇₃	C₂²	1	2	yes	—
29	C₄×#41×C₇₃	—	2	2	no	—
30	C₄×#41×C₇₃	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
33	#497×C₇₃	C₂²	1	8	yes	complemented
34	#494×C₇₃	C₂²	1	4	yes	complemented
35	#492×C₇₃	C₂²	1	4	yes	complemented
36	#491×C₇₃	C₂²	1	8	yes	complemented
37	#487×C₇₃	C₂²	1	8	yes	complemented
38	#462×C₇₃	C₂²	1	16	yes	complemented
39	#461×C₇₃	C₂²	1	16	yes	complemented
40	#451×C₇₃	C₂²	1	16	yes	—
41	#448×C₇₃	C₂²	1	16	yes	—
42	#432×C₇₃	C₂²	1	4	yes	—
43	#431×C₇₃	C₂²	1	4	yes	—
44	#423×C₇₃	C₂²	1	2	yes	—
45	#419×C₇₃	C₂²	1	8	yes	—
46	#407×C₇₃	C₂²	1	2	yes	—
47	C₄×M₁₆×C₇₃	C₂²	1	2	yes	—
48	C₂×#41×C₇₃	—	2	2	no	—
49	C₂×#41×C₇₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₇₃	—	2	4	no	—
51	C₂²×Q₈×C₇₃	—	2	2	no	—
52	C₂²×Q₈×C₇₃	—	4	8	no	—
53	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
54	C₂²×Q₈×C₇₃	C₂³	1	8	yes	—
55	C₂³×C₄×C₇₃	—	2	2	no	—
56	C₂³×C₄×C₇₃	D₄	1	2	yes	—
57	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
58	#137×C₇₃	—	4	16	no	—
59	C₂×Q₁₆×C₇₃	C₂³	1	16	yes	—
60	C₂×SD₁₆×C₇₃	C₂³	1	16	yes	—
61	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₇₃	—	2	2	no	—
63	C₄⋊Q₈×C₇₃	—	2	4	no	—
64	C₄⋊Q₈×C₇₃	—	2	2	no	—
65	C₄⋊Q₈×C₇₃	—	2	4	no	—
66	C₄⋊Q₈×C₇₃	—	2	4	no	—
67	C₄⋊Q₈×C₇₃	—	2	4	no	—
68	C₄⋊Q₈×C₇₃	—	2	4	no	—
69	C₄⋊Q₈×C₇₃	C₂³	1	8	yes	—
70	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
71	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
72	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
74	#127×C₇₃	C₂³	1	1	yes	characteristic
75	#126×C₇₃	—	2	4	no	—
76	#125×C₇₃	—	2	2	no	—
77	#125×C₇₃	C₂³	1	2	yes	—
78	#124×C₇₃	—	2	2	no	—
79	#124×C₇₃	C₂³	1	2	yes	—
80	#123×C₇₃	—	2	4	no	—
81	#123×C₇₃	—	2	2	no	—
82	C₂²⋊Q₈×C₇₃	—	2	2	no	—
83	C₂²⋊Q₈×C₇₃	—	2	2	no	—
84	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
85	#121×C₇₃	—	2	2	no	—
86	#121×C₇₃	—	2	2	no	—
87	#121×C₇₃	C₂³	1	4	yes	—
88	#120×C₇₃	—	2	2	no	—
89	C₄×Q₈×C₇₃	—	2	2	no	—
90	C₄×Q₈×C₇₃	—	2	2	no	—
91	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
92	C₄×D₄×C₇₃	—	2	4	no	—
93	C₄×D₄×C₇₃	—	2	4	no	—
94	C₄×D₄×C₇₃	—	2	4	no	—
95	C₄×D₄×C₇₃	—	2	2	no	—
96	C₄×D₄×C₇₃	—	2	2	no	—
97	C₄×D₄×C₇₃	C₂³	1	4	yes	—
98	#117×C₇₃	—	2	2	no	—
99	#117×C₇₃	—	2	4	no	—
100	#117×C₇₃	—	2	2	no	—
101	#117×C₇₃	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
103	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
104	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
105	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
106	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
107	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
108	C₂×C₄²×C₇₃	—	2	2	no	—
109	C₂×C₄²×C₇₃	D₄	1	2	yes	—
110	C₂×C₄²×C₇₃	D₄	1	2	yes	—
111	C₂×C₄²×C₇₃	D₄	1	2	yes	—
112	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
116	C₄⋊C₈×C₇₃	C₂³	1	8	yes	—
117	#103×C₇₃	C₂³	1	32	yes	—
118	C₂²⋊C₈×C₇₃	C₂³	1	8	yes	—
119	#97×C₇₃	C₂³	1	4	yes	—
120	C₄×C₈×C₇₃	C₂³	1	4	yes	—
121	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
122	#41×C₇₃	—	2	8	no	—
123	#41×C₇₃	—	4	8	no	—
124	C₂×Q₈×C₇₃	—	2	2	no	—
125	C₂×Q₈×C₇₃	—	2	8	no	—
126	C₂×Q₈×C₇₃	—	2	4	no	—
127	C₂×Q₈×C₇₃	—	2	16	no	—
128	C₂×Q₈×C₇₃	—	4	16	no	—
129	C₂×Q₈×C₇₃	—	4	8	no	—
130	C₂×Q₈×C₇₃	—	4	16	no	—
131	C₂×Q₈×C₇₃	C₂⁴	1	8	yes	—
132	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
133	C₂×D₄×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	4	no	—
135	C₂×D₄×C₇₃	—	2	2	no	—
136	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₇₃	—	2	8	no	—
138	C₂²×C₄×C₇₃	—	2	4	no	—
139	C₂²×C₄×C₇₃	—	2	8	no	—
140	C₂²×C₄×C₇₃	—	2	4	no	—
141	C₂²×C₄×C₇₃	—	2	2	no	—
142	C₂²×C₄×C₇₃	—	2	4	no	—
143	C₂²×C₄×C₇₃	—	4	8	no	—
144	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	Q₁₆×C₇₃	—	4	16	no	—
155	SD₁₆×C₇₃	—	4	16	no	—
156	M₁₆×C₇₃	—	2	8	no	—
157	C₂×C₈×C₇₃	C₂⁴	1	8	yes	—
158	C₄⋊C₄×C₇₃	—	2	8	no	—
159	C₄⋊C₄×C₇₃	—	2	8	no	—
160	C₄⋊C₄×C₇₃	—	2	8	no	—
161	C₄⋊C₄×C₇₃	—	2	8	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	2	4	no	—
165	C₄⋊C₄×C₇₃	—	2	4	no	—
166	C₄⋊C₄×C₇₃	—	2	4	no	—
167	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
168	C₂²⋊C₄×C₇₃	—	2	4	no	—
169	C₂²⋊C₄×C₇₃	—	2	2	no	—
170	C₂²⋊C₄×C₇₃	—	2	4	no	—
171	C₂²⋊C₄×C₇₃	—	2	4	no	—
172	C₂²⋊C₄×C₇₃	—	2	4	no	—
173	C₄²×C₇₃	—	2	4	no	—
174	C₄²×C₇₃	—	2	2	no	—
175	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₇₃	C₂×D₄	1	2	yes	—
177	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₇₃	C₂×D₄	1	2	yes	—
179	C₄²×C₇₃	C₂×D₄	1	2	yes	—
180	C₄²×C₇₃	C₂×D₄	1	2	yes	—
181	C₄²×C₇₃	C₂×D₄	1	2	yes	—
182	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
183	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
184	C₄²×C₇₃	C₂⁴	1	2	yes	—
185	C₂³×C₇₃	—	2	2	no	—
186	C₂³×C₇₃	—	2	4	no	—
187	C₂³×C₇₃	—	2	2	no	—
188	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
189	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
190	Q₈×C₇₃	—	2	16	no	—
191	Q₈×C₇₃	—	2	4	no	—
192	Q₈×C₇₃	—	4	16	no	—
193	Q₈×C₇₃	—	4	8	no	—
194	Q₈×C₇₃	—	4	4	no	—
195	D₄×C₇₃	—	2	4	no	—
196	D₄×C₇₃	—	4	4	no	—
197	D₄×C₇₃	—	4	8	no	—
198	D₄×C₇₃	—	4	4	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	4	no	—
201	C₂×C₄×C₇₃	—	2	4	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	4	no	—
204	C₂×C₄×C₇₃	—	2	4	no	—
205	C₂×C₄×C₇₃	—	2	4	no	—
206	C₂×C₄×C₇₃	—	2	4	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	4	no	—
209	C₂×C₄×C₇₃	—	2	8	no	—
210	C₂×C₄×C₇₃	—	4	16	no	—
211	C₂×C₄×C₇₃	—	4	8	no	—
212	C₂×C₄×C₇₃	—	4	4	no	—
213	C₂×C₄×C₇₃	—	4	8	no	—
214	C₂×C₄×C₇₃	#137	1	8	yes	complemented
215	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
222	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
223	C₈×C₇₃	—	2	8	no	—
224	C₂²×C₇₃	—	2	8	no	—
225	C₂²×C₇₃	—	2	2	no	—
226	C₂²×C₇₃	—	2	2	no	—
227	C₂²×C₇₃	—	2	2	no	—
228	C₂²×C₇₃	—	4	2	no	—
229	C₂²×C₇₃	—	4	4	no	—
230	C₂²×C₇₃	#535	1	2	yes	—
231	C₂²×C₇₃	C₂×#137	1	4	yes	—
232	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₇₃	—	2	2	no	—
234	C₄×C₇₃	—	2	2	no	—
235	C₄×C₇₃	—	2	2	no	—
236	C₄×C₇₃	—	4	8	no	—
237	C₄×C₇₃	—	4	2	no	—
238	C₄×C₇₃	—	4	4	no	—
239	C₄×C₇₃	#535	1	2	yes	—
240	C₄×C₇₃	C₂×#137	1	4	yes	—
241	C₄×C₇₃	C₂×#137	1	4	yes	—
242	C₄×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
243	#60800	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂×C₇₃	—	2	2	no	—
245	C₂×C₇₃	—	2	4	no	—
246	C₂×C₇₃	—	8	2	no	—
247	C₂×C₇₃	C₂×#535	1	1	yes	characteristic
248	C₂×C₇₃	C₂²×#137	1	2	yes	—
249	#3444	C₂×C₇₃	1	1	yes	characteristic
250	C₂²×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
251	#3218	C₂×C₇₃	1	8	yes	complemented
252	#3209	C₂×C₇₃	1	4	yes	complemented
253	#3206	C₂×C₇₃	1	4	yes	complemented
254	#3152	C₂×C₇₃	1	2	yes	complemented
255	#3139	C₂×C₇₃	1	2	yes	complemented
256	#3039	C₂×C₇₃	1	4	yes	complemented
257	#3004	C₂×C₇₃	1	4	yes	complemented
258	#2920	C₂×C₇₃	1	1	yes	characteristic, complemented
259	C₇₃	#60800	1	1	yes	characteristic, direct product factor, Sylow
260	C₂³×Q₈	C₂²×C₇₃	1	2	yes	—
261	C₂×#137	C₂²×C₇₃	1	8	yes	—
262	#533	C₂²×C₇₃	1	2	yes	—
263	#533	C₂²×C₇₃	1	1	yes	characteristic
264	#532	C₂²×C₇₃	1	1	yes	characteristic
265	#532	C₂²×C₇₃	1	2	yes	—
266	C₂×C₄⋊Q₈	—	2	2	no	—
267	C₂×C₄⋊Q₈	—	2	2	no	—
268	C₂×C₄⋊Q₈	—	2	2	no	—
269	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
270	C₂×C₄⋊Q₈	C₂²×C₇₃	1	4	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₇₃	1	4	yes	—
272	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
273	#529	—	2	2	no	—
274	#529	—	2	2	no	—
275	#529	C₂²×C₇₃	1	4	yes	—
276	#525	—	2	2	no	—
277	#525	C₂²×C₇₃	1	2	yes	—
278	C₄×#41	—	2	2	no	—
279	C₄×#41	C₂²×C₇₃	1	2	yes	—
280	C₂²×C₄⋊C₄	—	2	2	no	—
281	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
282	#497	C₂²×C₇₃	1	8	yes	complemented
283	#494	C₂²×C₇₃	1	4	yes	complemented
284	#492	C₂²×C₇₃	1	4	yes	complemented
285	#491	C₂²×C₇₃	1	8	yes	complemented
286	#487	C₂²×C₇₃	1	8	yes	complemented
287	#462	C₂²×C₇₃	1	16	yes	complemented
288	#461	C₂²×C₇₃	1	16	yes	complemented
289	#451	C₂²×C₇₃	1	16	yes	—
290	#448	C₂²×C₇₃	1	16	yes	—
291	#432	C₂²×C₇₃	1	4	yes	—
292	#431	C₂²×C₇₃	1	4	yes	—
293	#423	C₂²×C₇₃	1	2	yes	—
294	#419	C₂²×C₇₃	1	8	yes	—
295	#407	C₂²×C₇₃	1	2	yes	—
296	C₄×M₁₆	C₂²×C₇₃	1	2	yes	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	C₂³×C₇₃	1	2	yes	—
299	C₂²×Q₈	—	2	4	no	—
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	4	8	no	—
302	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
303	C₂²×Q₈	C₂³×C₇₃	1	8	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	D₄×C₇₃	1	2	yes	—
306	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
307	#137	—	4	16	no	—
308	C₂×Q₁₆	C₂³×C₇₃	1	16	yes	—
309	C₂×SD₁₆	C₂³×C₇₃	1	16	yes	—
310	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	4	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	4	no	—
317	C₄⋊Q₈	—	2	4	no	—
318	C₄⋊Q₈	C₂³×C₇₃	1	8	yes	—
319	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	—
320	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	—
321	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
323	#127	C₂³×C₇₃	1	1	yes	characteristic
324	#126	—	2	4	no	—
325	#125	—	2	2	no	—
326	#125	C₂³×C₇₃	1	2	yes	—
327	#124	—	2	2	no	—
328	#124	C₂³×C₇₃	1	2	yes	—
329	#123	—	2	4	no	—
330	#123	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	C₂³×C₇₃	1	4	yes	—
334	#121	—	2	2	no	—
335	#121	—	2	2	no	—
336	#121	C₂³×C₇₃	1	4	yes	—
337	#120	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×Q₈	—	2	2	no	—
340	C₄×Q₈	C₂³×C₇₃	1	4	yes	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	4	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	C₂³×C₇₃	1	4	yes	—
347	#117	—	2	2	no	—
348	#117	—	2	4	no	—
349	#117	—	2	2	no	—
350	#117	C₂³×C₇₃	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	—	2	4	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	4	no	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	D₄×C₇₃	1	2	yes	—
359	C₂×C₄²	D₄×C₇₃	1	2	yes	—
360	C₂×C₄²	D₄×C₇₃	1	2	yes	—
361	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
363	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
365	C₄⋊C₈	C₂³×C₇₃	1	8	yes	—
366	#103	C₂³×C₇₃	1	32	yes	—
367	C₂²⋊C₈	C₂³×C₇₃	1	8	yes	—
368	#97	C₂³×C₇₃	1	4	yes	—
369	C₄×C₈	C₂³×C₇₃	1	4	yes	—
370	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
371	#41	—	2	8	no	—
372	#41	—	4	8	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	16	no	—
377	C₂×Q₈	—	4	16	no	—
378	C₂×Q₈	—	4	8	no	—
379	C₂×Q₈	—	4	16	no	—
380	C₂×Q₈	C₂⁴×C₇₃	1	8	yes	—
381	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	4	8	no	—
393	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
397	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
398	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
400	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
403	Q₁₆	—	4	16	no	—
404	SD₁₆	—	4	16	no	—
405	M₁₆	—	2	8	no	—
406	C₂×C₈	C₂⁴×C₇₃	1	8	yes	—
407	C₄⋊C₄	—	2	8	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₄²	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₇₃	1	2	yes	—
426	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₇₃	1	2	yes	—
428	C₄²	C₂×D₄×C₇₃	1	2	yes	—
429	C₄²	C₂×D₄×C₇₃	1	2	yes	—
430	C₄²	C₂×D₄×C₇₃	1	2	yes	—
431	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
432	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
433	C₄²	C₂⁴×C₇₃	1	2	yes	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	2	no	—
437	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
438	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
439	Q₈	—	2	16	no	—
440	Q₈	—	2	4	no	—
441	Q₈	—	4	16	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	4	no	—
444	D₄	—	2	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	4	16	no	—
460	C₂×C₄	—	4	8	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	8	no	—
463	C₂×C₄	#137×C₇₃	1	8	yes	complemented
464	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
465	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
470	C₂×C₄	H(5,𝔽₂)×C₇₃	1	4	yes	—
471	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
472	C₈	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	2	no	—
479	C₂²	#535×C₇₃	1	2	yes	—
480	C₂²	C₂×#137×C₇₃	1	4	yes	—
481	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	8	no	—
487	C₄	—	4	2	no	—
488	C₄	#535×C₇₃	1	2	yes	—
489	C₄	C₂×#137×C₇₃	1	4	yes	—
490	C₄	C₂×#137×C₇₃	1	4	yes	—
491	C₄	C₂×H(5,𝔽₂)×C₇₃	1	2	yes	—
492	C₂	—	2	2	no	—
493	C₂	—	2	4	no	—
494	C₂	—	8	2	no	—
495	C₂	C₂×#535×C₇₃	1	1	yes	characteristic
496	C₂	C₂²×#137×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
prime radical	C₇₃×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊Q₈×C₇₃	C₂	semidirect
3. C₇₃×#3218	C₂	semidirect
4. C₇₃×#3209	C₂	semidirect
5. C₇₃×#3206	C₂	semidirect
6. C₇₃×#3152	C₂	semidirect
7. C₇₃×#3139	C₂	semidirect
8. C₇₃×#3039	C₂	semidirect
9. C₇₃×#3004	C₂	semidirect
10. C₇₃×#2920	C₂	semidirect
33. #497×C₇₃	C₂²	semidirect
34. #494×C₇₃	C₂²	semidirect
35. #492×C₇₃	C₂²	semidirect
36. #491×C₇₃	C₂²	semidirect
37. #487×C₇₃	C₂²	semidirect
38. #462×C₇₃	C₂²	semidirect
39. #461×C₇₃	C₂²	semidirect
214. C₂×C₄×C₇₃	#137	semidirect
243. #60800	C₇₃	direct (N × H)
250. C₂²×C₄⋊Q₈	C₂×C₇₃	semidirect
251. #3218	C₂×C₇₃	semidirect
252. #3209	C₂×C₇₃	semidirect
253. #3206	C₂×C₇₃	semidirect
254. #3152	C₂×C₇₃	semidirect
255. #3139	C₂×C₇₃	semidirect
256. #3039	C₂×C₇₃	semidirect
257. #3004	C₂×C₇₃	semidirect
258. #2920	C₂×C₇₃	semidirect
259. C₇₃	#60800	direct (N × H)
282. #497	C₂²×C₇₃	semidirect
283. #494	C₂²×C₇₃	semidirect
284. #492	C₂²×C₇₃	semidirect
285. #491	C₂²×C₇₃	semidirect
286. #487	C₂²×C₇₃	semidirect
287. #462	C₂²×C₇₃	semidirect
288. #461	C₂²×C₇₃	semidirect
463. C₂×C₄	#137×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3444	2
C₂²×C₄⋊Q₈×C₇₃	2
C₇₃×#3218	2
C₇₃×#3209	2
C₇₃×#3206	2
C₇₃×#3152	2
C₇₃×#3139	2
C₇₃×#3039	2
C₇₃×#3004	2
C₇₃×#2920	2
#60800	73

Subgroups — C73×#60800 #32970204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#60800 #32970204