Subgroups — C₆₇×#60585 #30739836

Order 17152.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3125	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3120	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3114	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3113	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3101	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#483×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3084	C₂	1	2	yes	maximal, complemented
12	C₆₇×#3046	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3002	C₂	1	1	yes	maximal, characteristic
15	C₆₇×#2952	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2947	C₂	1	2	yes	maximal, complemented
17	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#137×C₆₇	C₂²	1	2	yes	—
20	C₂×#135×C₆₇	C₂²	1	2	yes	—
21	#556×C₆₇	—	2	1	no	—
22	#554×C₆₇	—	2	1	no	—
23	#552×C₆₇	—	2	2	no	—
24	#552×C₆₇	—	2	1	no	—
25	#552×C₆₇	—	2	1	no	—
26	#551×C₆₇	—	2	2	no	—
27	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
28	#542×C₆₇	C₂²	1	2	yes	complemented
29	#541×C₆₇	C₂²	1	2	yes	complemented
30	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#533×C₆₇	C₂²	1	2	yes	—
32	#529×C₆₇	C₂²	1	2	yes	—
33	#525×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
35	#520×C₆₇	—	2	2	no	—
36	#520×C₆₇	—	2	1	no	—
37	#520×C₆₇	—	2	1	no	—
38	#520×C₆₇	C₂²	1	2	yes	—
39	#520×C₆₇	C₂²	1	4	yes	—
40	#520×C₆₇	C₂²	1	2	yes	—
41	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₆₇	—	2	2	no	—
45	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
46	C₂×#117×C₆₇	—	2	1	no	—
47	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₆₇	—	2	1	no	—
49	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
50	#484×C₆₇	C₂²	1	2	yes	complemented
51	#483×C₆₇	C₂²	1	2	yes	—
52	#483×C₆₇	C₂²	1	2	yes	—
53	#483×C₆₇	C₂²	1	2	yes	—
54	#483×C₆₇	C₂²	1	4	yes	complemented
55	#481×C₆₇	C₂²	1	2	yes	complemented
56	#480×C₆₇	C₂²	1	2	yes	—
57	#479×C₆₇	C₂²	1	4	yes	complemented
58	#478×C₆₇	C₂²	1	4	yes	complemented
59	#476×C₆₇	C₂²	1	4	yes	complemented
60	#475×C₆₇	C₂²	1	4	yes	complemented
61	#464×C₆₇	C₂²	1	4	yes	complemented
62	#463×C₆₇	C₂²	1	4	yes	complemented
63	#462×C₆₇	C₂²	1	4	yes	complemented
64	#461×C₆₇	C₂²	1	4	yes	complemented
65	#452×C₆₇	C₂²	1	2	yes	—
66	#452×C₆₇	C₂²	1	4	yes	—
67	#451×C₆₇	C₂²	1	2	yes	—
68	#451×C₆₇	C₂²	1	1	yes	characteristic
69	#450×C₆₇	C₂²	1	1	yes	characteristic
70	#450×C₆₇	C₂²	1	2	yes	—
71	#449×C₆₇	C₂²	1	2	yes	—
72	#448×C₆₇	C₂²	1	1	yes	characteristic
73	#447×C₆₇	C₂²	1	1	yes	characteristic
74	#442×C₆₇	C₂²	1	4	yes	complemented
75	#441×C₆₇	C₂²	1	4	yes	complemented
76	#441×C₆₇	C₂²	1	4	yes	complemented
77	#440×C₆₇	C₂²	1	4	yes	complemented
78	C₄×Q₁₆×C₆₇	C₂²	1	4	yes	complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
80	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
81	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
82	#433×C₆₇	C₂²	1	4	yes	complemented
83	#432×C₆₇	C₂²	1	2	yes	—
84	#431×C₆₇	C₂²	1	2	yes	—
85	#428×C₆₇	C₂²	1	2	yes	complemented
86	C₂×#106×C₆₇	C₂²	1	2	yes	complemented
87	#424×C₆₇	C₂²	1	2	yes	complemented
88	#417×C₆₇	C₂²	1	2	yes	—
89	#417×C₆₇	C₂²	1	2	yes	complemented
90	#416×C₆₇	C₂²	1	2	yes	—
91	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
92	#407×C₆₇	C₂²	1	1	yes	characteristic
93	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
94	#405×C₆₇	C₂²	1	2	yes	complemented
95	C₂×#41×C₆₇	—	2	8	no	—
96	C₂×#41×C₆₇	—	2	1	no	—
97	C₂×#41×C₆₇	—	2	1	no	—
98	C₂×#41×C₆₇	C₂³	1	2	yes	—
99	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
100	C₂×#41×C₆₇	C₂³	1	2	yes	—
101	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₆₇	—	2	1	no	—
104	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	—	2	1	no	—
106	C₂³×C₄×C₆₇	—	2	1	no	—
107	C₂³×C₄×C₆₇	—	2	2	no	—
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	#137×C₆₇	—	2	8	no	—
110	#135×C₆₇	—	2	8	no	—
111	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
112	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
115	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
116	C₂×D₈×C₆₇	C₂³	1	2	yes	—
117	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
118	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
119	C₄⋊Q₈×C₆₇	—	2	1	no	—
120	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
122	#126×C₆₇	—	2	2	no	—
123	#126×C₆₇	—	2	2	no	—
124	#126×C₆₇	—	2	2	no	—
125	#126×C₆₇	—	2	2	no	—
126	#125×C₆₇	—	2	2	no	—
127	#125×C₆₇	—	2	2	no	—
128	#125×C₆₇	—	2	1	no	—
129	#125×C₆₇	—	2	2	no	—
130	#125×C₆₇	C₂³	1	2	yes	—
131	#124×C₆₇	—	2	2	no	—
132	#124×C₆₇	C₂³	1	2	yes	—
133	#123×C₆₇	—	2	1	no	—
134	#123×C₆₇	—	2	2	no	—
135	#123×C₆₇	—	2	2	no	—
136	#123×C₆₇	—	2	2	no	—
137	C₂²⋊Q₈×C₆₇	—	2	1	no	—
138	C₂²⋊Q₈×C₆₇	—	2	1	no	—
139	C₂²⋊Q₈×C₆₇	—	2	2	no	—
140	C₂²⋊Q₈×C₆₇	—	2	1	no	—
141	C₂²⋊Q₈×C₆₇	—	2	1	no	—
142	C₂²⋊Q₈×C₆₇	—	2	2	no	—
143	C₂²⋊Q₈×C₆₇	—	2	2	no	—
144	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
145	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
147	C₂²⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
148	#121×C₆₇	C₂³	1	1	yes	characteristic
149	#121×C₆₇	C₂³	1	1	yes	characteristic
150	#120×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	—	2	2	no	—
154	C₄×Q₈×C₆₇	—	2	2	no	—
155	C₄×Q₈×C₆₇	—	2	2	no	—
156	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
157	C₄×Q₈×C₆₇	C₂³	1	4	yes	—
158	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
159	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
160	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	—	2	2	no	—
164	C₄×D₄×C₆₇	—	2	4	no	—
165	C₄×D₄×C₆₇	—	2	4	no	—
166	C₄×D₄×C₆₇	—	2	4	no	—
167	C₄×D₄×C₆₇	—	2	4	no	—
168	C₄×D₄×C₆₇	—	2	2	no	—
169	C₄×D₄×C₆₇	—	2	2	no	—
170	C₄×D₄×C₆₇	—	2	2	no	—
171	C₄×D₄×C₆₇	C₂³	1	4	yes	—
172	C₄×D₄×C₆₇	C₂³	1	4	yes	—
173	C₄×D₄×C₆₇	C₂³	1	2	yes	—
174	#117×C₆₇	—	2	2	no	—
175	#117×C₆₇	—	2	2	no	—
176	#117×C₆₇	—	2	4	no	—
177	#117×C₆₇	—	2	2	no	—
178	#117×C₆₇	—	2	1	no	—
179	#117×C₆₇	—	2	2	no	—
180	#117×C₆₇	—	2	2	no	—
181	#117×C₆₇	D₄	1	1	yes	characteristic
182	#117×C₆₇	D₄	1	2	yes	—
183	#117×C₆₇	D₄	1	1	yes	characteristic
184	#117×C₆₇	C₂³	1	1	yes	characteristic
185	#117×C₆₇	C₂³	1	1	yes	characteristic
186	#117×C₆₇	C₂³	1	1	yes	characteristic
187	#117×C₆₇	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
189	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
190	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
191	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
192	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
193	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
194	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
195	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
196	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
197	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
204	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
205	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
206	C₂×C₄²×C₆₇	—	2	2	no	—
207	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
208	#107×C₆₇	C₂³	1	4	yes	—
209	#106×C₆₇	C₂³	1	4	yes	—
210	#106×C₆₇	C₂³	1	4	yes	—
211	#106×C₆₇	C₂³	1	4	yes	—
212	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
213	C₄⋊C₈×C₆₇	C₂³	1	4	yes	—
214	#103×C₆₇	C₂³	1	2	yes	—
215	#103×C₆₇	C₂³	1	2	yes	—
216	#103×C₆₇	C₂³	1	4	yes	—
217	#103×C₆₇	C₂³	1	4	yes	—
218	#103×C₆₇	C₂³	1	4	yes	—
219	#103×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	2	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	2	yes	—
223	#102×C₆₇	C₂³	1	4	yes	—
224	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
225	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
226	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
227	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
229	#97×C₆₇	C₂³	1	4	yes	—
230	C₄×C₈×C₆₇	C₂³	1	4	yes	—
231	C₂⁴×C₆₇	—	2	1	no	—
232	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
233	#41×C₆₇	—	2	8	no	—
234	#41×C₆₇	—	2	8	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	4	no	—
238	#41×C₆₇	—	2	4	no	—
239	#41×C₆₇	#41	1	8	yes	—
240	C₂×Q₈×C₆₇	—	2	4	no	—
241	C₂×Q₈×C₆₇	—	2	1	no	—
242	C₂×Q₈×C₆₇	—	2	1	no	—
243	C₂×Q₈×C₆₇	—	2	2	no	—
244	C₂×Q₈×C₆₇	—	2	4	no	—
245	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
246	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
247	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
248	C₂×D₄×C₆₇	—	2	8	no	—
249	C₂×D₄×C₆₇	—	2	2	no	—
250	C₂×D₄×C₆₇	—	2	2	no	—
251	C₂×D₄×C₆₇	—	2	4	no	—
252	C₂×D₄×C₆₇	—	2	1	no	—
253	C₂×D₄×C₆₇	—	2	1	no	—
254	C₂×D₄×C₆₇	—	2	1	no	—
255	C₂×D₄×C₆₇	—	2	1	no	—
256	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
257	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	—	2	8	no	—
259	C₂²×C₄×C₆₇	—	2	1	no	—
260	C₂²×C₄×C₆₇	—	2	2	no	—
261	C₂²×C₄×C₆₇	—	2	2	no	—
262	C₂²×C₄×C₆₇	—	2	4	no	—
263	C₂²×C₄×C₆₇	—	2	2	no	—
264	C₂²×C₄×C₆₇	—	2	1	no	—
265	C₂²×C₄×C₆₇	—	2	1	no	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	1	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	2	no	—
272	C₂²×C₄×C₆₇	—	8	4	no	—
273	C₂²×C₄×C₆₇	—	8	2	no	—
274	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
282	Q₁₆×C₆₇	—	2	4	no	—
283	Q₁₆×C₆₇	—	2	8	no	—
284	SD₁₆×C₆₇	—	2	4	no	—
285	SD₁₆×C₆₇	—	2	4	no	—
286	SD₁₆×C₆₇	—	2	8	no	—
287	D₈×C₆₇	—	2	4	no	—
288	M₁₆×C₆₇	—	2	4	no	—
289	C₂×C₈×C₆₇	—	2	4	no	—
290	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
291	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
292	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
293	C₄⋊C₄×C₆₇	—	2	2	no	—
294	C₄⋊C₄×C₆₇	—	2	2	no	—
295	C₄⋊C₄×C₆₇	—	2	4	no	—
296	C₄⋊C₄×C₆₇	—	2	4	no	—
297	C₄⋊C₄×C₆₇	—	2	2	no	—
298	C₄⋊C₄×C₆₇	—	2	1	no	—
299	C₄⋊C₄×C₆₇	—	2	2	no	—
300	C₄⋊C₄×C₆₇	—	2	2	no	—
301	C₄⋊C₄×C₆₇	—	2	2	no	—
302	C₄⋊C₄×C₆₇	—	2	2	no	—
303	C₄⋊C₄×C₆₇	—	2	2	no	—
304	C₄⋊C₄×C₆₇	—	2	2	no	—
305	C₄⋊C₄×C₆₇	—	2	2	no	—
306	C₄⋊C₄×C₆₇	—	2	2	no	—
307	C₄⋊C₄×C₆₇	—	2	1	no	—
308	C₄⋊C₄×C₆₇	—	2	2	no	—
309	C₄⋊C₄×C₆₇	—	2	1	no	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
312	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
318	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
321	C₂²⋊C₄×C₆₇	—	2	2	no	—
322	C₂²⋊C₄×C₆₇	—	2	2	no	—
323	C₂²⋊C₄×C₆₇	—	2	1	no	—
324	C₂²⋊C₄×C₆₇	—	2	1	no	—
325	C₂²⋊C₄×C₆₇	—	2	1	no	—
326	C₂²⋊C₄×C₆₇	—	2	4	no	—
327	C₂²⋊C₄×C₆₇	—	2	4	no	—
328	C₂²⋊C₄×C₆₇	—	2	1	no	—
329	C₂²⋊C₄×C₆₇	—	2	2	no	—
330	C₂²⋊C₄×C₆₇	—	2	2	no	—
331	C₂²⋊C₄×C₆₇	—	2	1	no	—
332	C₂²⋊C₄×C₆₇	—	2	2	no	—
333	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
337	C₄²×C₆₇	—	2	4	no	—
338	C₄²×C₆₇	—	2	4	no	—
339	C₄²×C₆₇	—	2	2	no	—
340	C₄²×C₆₇	—	2	2	no	—
341	C₄²×C₆₇	—	2	2	no	—
342	C₄²×C₆₇	—	2	1	no	—
343	C₄²×C₆₇	C₂×D₄	1	2	yes	—
344	C₄²×C₆₇	C₂×D₄	1	2	yes	—
345	C₄²×C₆₇	C₂⁴	1	2	yes	—
346	C₄²×C₆₇	C₂⁴	1	2	yes	—
347	C₂³×C₆₇	—	2	4	no	—
348	C₂³×C₆₇	—	2	2	no	—
349	C₂³×C₆₇	—	2	2	no	—
350	C₂³×C₆₇	—	2	2	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	4	1	no	—
353	C₂³×C₆₇	—	4	2	no	—
354	C₂³×C₆₇	—	4	2	no	—
355	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
356	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
357	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₆₇	—	2	4	no	—
359	Q₈×C₆₇	—	2	2	no	—
360	Q₈×C₆₇	—	2	4	no	—
361	Q₈×C₆₇	—	2	2	no	—
362	Q₈×C₆₇	—	4	2	no	—
363	Q₈×C₆₇	—	8	2	no	—
364	Q₈×C₆₇	C₂×#41	1	4	yes	—
365	D₄×C₆₇	—	2	8	no	—
366	D₄×C₆₇	—	2	4	no	—
367	D₄×C₆₇	—	2	8	no	—
368	D₄×C₆₇	—	2	2	no	—
369	D₄×C₆₇	—	2	2	no	—
370	D₄×C₆₇	—	4	2	no	—
371	D₄×C₆₇	—	4	2	no	—
372	D₄×C₆₇	—	8	1	no	—
373	D₄×C₆₇	C₂×#41	1	4	yes	—
374	C₂×C₄×C₆₇	—	2	4	no	—
375	C₂×C₄×C₆₇	—	2	8	no	—
376	C₂×C₄×C₆₇	—	2	2	no	—
377	C₂×C₄×C₆₇	—	2	4	no	—
378	C₂×C₄×C₆₇	—	2	2	no	—
379	C₂×C₄×C₆₇	—	2	2	no	—
380	C₂×C₄×C₆₇	—	2	8	no	—
381	C₂×C₄×C₆₇	—	2	2	no	—
382	C₂×C₄×C₆₇	—	2	2	no	—
383	C₂×C₄×C₆₇	—	2	2	no	—
384	C₂×C₄×C₆₇	—	2	1	no	—
385	C₂×C₄×C₆₇	—	2	1	no	—
386	C₂×C₄×C₆₇	—	2	2	no	—
387	C₂×C₄×C₆₇	—	2	1	no	—
388	C₂×C₄×C₆₇	—	2	4	no	—
389	C₂×C₄×C₆₇	—	2	2	no	—
390	C₂×C₄×C₆₇	—	4	2	no	—
391	C₂×C₄×C₆₇	—	4	2	no	—
392	C₂×C₄×C₆₇	—	4	4	no	—
393	C₂×C₄×C₆₇	—	4	2	no	—
394	C₂×C₄×C₆₇	—	8	2	no	—
395	C₂×C₄×C₆₇	—	8	4	no	—
396	C₂×C₄×C₆₇	—	8	4	no	—
397	C₂×C₄×C₆₇	—	8	1	no	—
398	C₂×C₄×C₆₇	—	8	2	no	—
399	C₂×C₄×C₆₇	—	8	2	no	—
400	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
403	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
405	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
408	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
409	C₈×C₆₇	—	2	2	no	—
410	C₈×C₆₇	—	2	2	no	—
411	C₈×C₆₇	—	2	4	no	—
412	C₂²×C₆₇	—	2	1	no	—
413	C₂²×C₆₇	—	2	1	no	—
414	C₂²×C₆₇	—	2	1	no	—
415	C₂²×C₆₇	—	2	1	no	—
416	C₂²×C₆₇	—	2	1	no	—
417	C₂²×C₆₇	—	2	1	no	—
418	C₂²×C₆₇	—	2	4	no	—
419	C₂²×C₆₇	—	2	1	no	—
420	C₂²×C₆₇	—	4	4	no	—
421	C₂²×C₆₇	—	4	8	no	—
422	C₂²×C₆₇	—	4	2	no	—
423	C₂²×C₆₇	—	4	2	no	—
424	C₂²×C₆₇	—	4	1	no	—
425	C₂²×C₆₇	—	4	1	no	—
426	C₂²×C₆₇	—	4	1	no	—
427	C₂²×C₆₇	#525	1	2	yes	—
428	C₂²×C₆₇	#577	1	2	yes	—
429	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
430	C₄×C₆₇	—	2	2	no	—
431	C₄×C₆₇	—	2	2	no	—
432	C₄×C₆₇	—	2	1	no	—
433	C₄×C₆₇	—	2	4	no	—
434	C₄×C₆₇	—	2	1	no	—
435	C₄×C₆₇	—	2	2	no	—
436	C₄×C₆₇	—	2	2	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	1	no	—
439	C₄×C₆₇	—	4	1	no	—
440	C₄×C₆₇	—	4	2	no	—
441	C₄×C₆₇	—	4	4	no	—
442	C₄×C₆₇	—	4	1	no	—
443	C₄×C₆₇	#525	1	2	yes	—
444	C₄×C₆₇	C₂²×#41	1	2	yes	—
445	#60585	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
446	C₂×C₆₇	—	2	2	no	—
447	C₂×C₆₇	—	2	2	no	—
448	C₂×C₆₇	—	4	1	no	—
449	C₂×C₆₇	—	4	4	no	—
450	C₂×C₆₇	—	8	1	no	—
451	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
452	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
453	C₂×C₆₇	#3586	1	1	yes	characteristic
454	#3495	C₂×C₆₇	1	1	yes	characteristic, complemented
455	C₂×#520	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#3125	C₂×C₆₇	1	4	yes	complemented
457	#3120	C₂×C₆₇	1	4	yes	complemented
458	#3114	C₂×C₆₇	1	2	yes	complemented
459	#3113	C₂×C₆₇	1	2	yes	complemented
460	#3108	C₂×C₆₇	1	2	yes	complemented
461	#3101	C₂×C₆₇	1	2	yes	complemented
462	#3092	C₂×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#483	C₂×C₆₇	1	1	yes	characteristic, complemented
464	#3084	C₂×C₆₇	1	2	yes	complemented
465	#3046	C₂×C₆₇	1	2	yes	complemented
466	#3007	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3002	C₂×C₆₇	1	1	yes	characteristic
468	#2952	C₂×C₆₇	1	2	yes	complemented
469	#2947	C₂×C₆₇	1	2	yes	complemented
470	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
471	C₆₇	#60585	1	1	yes	characteristic, direct product factor, Sylow
472	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
473	C₂×#137	C₂²×C₆₇	1	2	yes	—
474	C₂×#135	C₂²×C₆₇	1	2	yes	—
475	#556	—	2	1	no	—
476	#554	—	2	1	no	—
477	#552	—	2	2	no	—
478	#552	—	2	1	no	—
479	#552	—	2	1	no	—
480	#551	—	2	2	no	—
481	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
482	#542	C₂²×C₆₇	1	2	yes	complemented
483	#541	C₂²×C₆₇	1	2	yes	complemented
484	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
485	#533	C₂²×C₆₇	1	2	yes	—
486	#529	C₂²×C₆₇	1	2	yes	—
487	#525	C₂²×C₆₇	1	1	yes	characteristic
488	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
489	#520	—	2	2	no	—
490	#520	—	2	1	no	—
491	#520	—	2	1	no	—
492	#520	C₂²×C₆₇	1	2	yes	—
493	#520	C₂²×C₆₇	1	4	yes	—
494	#520	C₂²×C₆₇	1	2	yes	—
495	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
496	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
497	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
498	C₂×C₄×D₄	—	2	2	no	—
499	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
500	C₂×#117	—	2	1	no	—
501	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
502	C₂²×C₄⋊C₄	—	2	1	no	—
503	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
504	#484	C₂²×C₆₇	1	2	yes	complemented
505	#483	C₂²×C₆₇	1	2	yes	—
506	#483	C₂²×C₆₇	1	2	yes	—
507	#483	C₂²×C₆₇	1	2	yes	—
508	#483	C₂²×C₆₇	1	4	yes	complemented
509	#481	C₂²×C₆₇	1	2	yes	complemented
510	#480	C₂²×C₆₇	1	2	yes	—
511	#479	C₂²×C₆₇	1	4	yes	complemented
512	#478	C₂²×C₆₇	1	4	yes	complemented
513	#476	C₂²×C₆₇	1	4	yes	complemented
514	#475	C₂²×C₆₇	1	4	yes	complemented
515	#464	C₂²×C₆₇	1	4	yes	complemented
516	#463	C₂²×C₆₇	1	4	yes	complemented
517	#462	C₂²×C₆₇	1	4	yes	complemented
518	#461	C₂²×C₆₇	1	4	yes	complemented
519	#452	C₂²×C₆₇	1	2	yes	—
520	#452	C₂²×C₆₇	1	4	yes	—
521	#451	C₂²×C₆₇	1	2	yes	—
522	#451	C₂²×C₆₇	1	1	yes	characteristic
523	#450	C₂²×C₆₇	1	1	yes	characteristic
524	#450	C₂²×C₆₇	1	2	yes	—
525	#449	C₂²×C₆₇	1	2	yes	—
526	#448	C₂²×C₆₇	1	1	yes	characteristic
527	#447	C₂²×C₆₇	1	1	yes	characteristic
528	#442	C₂²×C₆₇	1	4	yes	complemented
529	#441	C₂²×C₆₇	1	4	yes	complemented
530	#441	C₂²×C₆₇	1	4	yes	complemented
531	#440	C₂²×C₆₇	1	4	yes	complemented
532	C₄×Q₁₆	C₂²×C₆₇	1	4	yes	complemented
533	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
534	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
535	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
536	#433	C₂²×C₆₇	1	4	yes	complemented
537	#432	C₂²×C₆₇	1	2	yes	—
538	#431	C₂²×C₆₇	1	2	yes	—
539	#428	C₂²×C₆₇	1	2	yes	complemented
540	C₂×#106	C₂²×C₆₇	1	2	yes	complemented
541	#424	C₂²×C₆₇	1	2	yes	complemented
542	#417	C₂²×C₆₇	1	2	yes	—
543	#417	C₂²×C₆₇	1	2	yes	complemented
544	#416	C₂²×C₆₇	1	2	yes	—
545	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
546	#407	C₂²×C₆₇	1	1	yes	characteristic
547	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
548	#405	C₂²×C₆₇	1	2	yes	complemented
549	C₂×#41	—	2	8	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	1	no	—
552	C₂×#41	C₂³×C₆₇	1	2	yes	—
553	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
554	C₂×#41	C₂³×C₆₇	1	2	yes	—
555	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
556	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
559	C₂³×C₄	—	2	1	no	—
560	C₂³×C₄	—	2	1	no	—
561	C₂³×C₄	—	2	2	no	—
562	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
563	#137	—	2	8	no	—
564	#135	—	2	8	no	—
565	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
566	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
567	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
568	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
569	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
570	C₂×D₈	C₂³×C₆₇	1	2	yes	—
571	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
572	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
573	C₄⋊Q₈	—	2	1	no	—
574	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#126	—	2	2	no	—
580	#125	—	2	2	no	—
581	#125	—	2	2	no	—
582	#125	—	2	1	no	—
583	#125	—	2	2	no	—
584	#125	C₂³×C₆₇	1	2	yes	—
585	#124	—	2	2	no	—
586	#124	C₂³×C₆₇	1	2	yes	—
587	#123	—	2	1	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	C₂²⋊Q₈	—	2	1	no	—
592	C₂²⋊Q₈	—	2	1	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	1	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
599	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
601	C₂²⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
602	#121	C₂³×C₆₇	1	1	yes	characteristic
603	#121	C₂³×C₆₇	1	1	yes	characteristic
604	#120	—	2	1	no	—
605	C₄×Q₈	—	2	1	no	—
606	C₄×Q₈	—	2	1	no	—
607	C₄×Q₈	—	2	2	no	—
608	C₄×Q₈	—	2	2	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
611	C₄×Q₈	C₂³×C₆₇	1	4	yes	—
612	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
613	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
614	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	2	no	—
618	C₄×D₄	—	2	4	no	—
619	C₄×D₄	—	2	4	no	—
620	C₄×D₄	—	2	4	no	—
621	C₄×D₄	—	2	4	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	C₂³×C₆₇	1	4	yes	—
626	C₄×D₄	C₂³×C₆₇	1	4	yes	—
627	C₄×D₄	C₂³×C₆₇	1	2	yes	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	4	no	—
631	#117	—	2	2	no	—
632	#117	—	2	1	no	—
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	D₄×C₆₇	1	1	yes	characteristic
636	#117	D₄×C₆₇	1	2	yes	—
637	#117	D₄×C₆₇	1	1	yes	characteristic
638	#117	C₂³×C₆₇	1	1	yes	characteristic
639	#117	C₂³×C₆₇	1	1	yes	characteristic
640	#117	C₂³×C₆₇	1	1	yes	characteristic
641	#117	C₂³×C₆₇	1	2	yes	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	—	2	2	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	—	2	1	no	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	4	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
652	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
660	C₂×C₄²	—	2	2	no	—
661	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
662	#107	C₂³×C₆₇	1	4	yes	—
663	#106	C₂³×C₆₇	1	4	yes	—
664	#106	C₂³×C₆₇	1	4	yes	—
665	#106	C₂³×C₆₇	1	4	yes	—
666	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
667	C₄⋊C₈	C₂³×C₆₇	1	4	yes	—
668	#103	C₂³×C₆₇	1	4	yes	—
669	#103	C₂³×C₆₇	1	4	yes	—
670	#103	C₂³×C₆₇	1	2	yes	—
671	#103	C₂³×C₆₇	1	2	yes	—
672	#103	C₂³×C₆₇	1	4	yes	—
673	#103	C₂³×C₆₇	1	4	yes	—
674	#102	C₂³×C₆₇	1	2	yes	—
675	#102	C₂³×C₆₇	1	2	yes	—
676	#102	C₂³×C₆₇	1	4	yes	—
677	#102	C₂³×C₆₇	1	4	yes	—
678	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
679	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
680	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
681	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
682	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
683	#97	C₂³×C₆₇	1	4	yes	—
684	C₄×C₈	C₂³×C₆₇	1	4	yes	—
685	C₂⁴	—	2	1	no	—
686	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
687	#41	—	2	8	no	—
688	#41	—	2	8	no	—
689	#41	—	2	4	no	—
690	#41	—	2	4	no	—
691	#41	—	2	4	no	—
692	#41	—	2	4	no	—
693	#41	#41×C₆₇	1	8	yes	—
694	C₂×Q₈	—	2	4	no	—
695	C₂×Q₈	—	2	1	no	—
696	C₂×Q₈	—	2	1	no	—
697	C₂×Q₈	—	2	2	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
700	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
701	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
702	C₂×D₄	—	2	8	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
711	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
712	C₂²×C₄	—	2	8	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	8	4	no	—
727	C₂²×C₄	—	8	2	no	—
728	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
734	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
736	Q₁₆	—	2	4	no	—
737	Q₁₆	—	2	8	no	—
738	SD₁₆	—	2	4	no	—
739	SD₁₆	—	2	4	no	—
740	SD₁₆	—	2	8	no	—
741	D₈	—	2	4	no	—
742	M₁₆	—	2	4	no	—
743	C₂×C₈	—	2	4	no	—
744	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
745	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
746	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	2	4	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	2	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
766	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
767	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
770	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
772	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	1	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	1	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
789	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
790	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
791	C₄²	—	2	4	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	1	no	—
797	C₄²	C₂×D₄×C₆₇	1	2	yes	—
798	C₄²	C₂×D₄×C₆₇	1	2	yes	—
799	C₄²	C₂⁴×C₆₇	1	2	yes	—
800	C₄²	C₂⁴×C₆₇	1	2	yes	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
810	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
811	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
812	Q₈	—	2	4	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	2	4	no	—
815	Q₈	—	2	2	no	—
816	Q₈	—	4	2	no	—
817	Q₈	—	8	2	no	—
818	Q₈	C₂×#41×C₆₇	1	4	yes	—
819	D₄	—	2	8	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	8	no	—
822	D₄	—	2	2	no	—
823	D₄	—	2	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	4	2	no	—
826	D₄	—	8	1	no	—
827	D₄	C₂×#41×C₆₇	1	4	yes	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	8	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	8	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	2	no	—
853	C₂×C₄	—	8	1	no	—
854	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
855	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
856	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
861	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
862	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
863	C₈	—	2	2	no	—
864	C₈	—	2	2	no	—
865	C₈	—	2	4	no	—
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	8	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	#525×C₆₇	1	2	yes	—
882	C₂²	#577×C₆₇	1	2	yes	—
883	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	4	no	—
890	C₄	—	2	1	no	—
891	C₄	—	4	4	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	#525×C₆₇	1	2	yes	—
898	C₄	C₂²×#41×C₆₇	1	2	yes	—
899	C₂	—	2	2	no	—
900	C₂	—	2	2	no	—
901	C₂	—	4	1	no	—
902	C₂	—	4	4	no	—
903	C₂	—	8	1	no	—
904	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
905	C₂	C₂×#577×C₆₇	1	1	yes	characteristic
906	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3495	C₂	semidirect
2. C₂×#520×C₆₇	C₂	semidirect
3. C₆₇×#3125	C₂	semidirect
4. C₆₇×#3120	C₂	semidirect
5. C₆₇×#3114	C₂	semidirect
6. C₆₇×#3113	C₂	semidirect
7. C₆₇×#3108	C₂	semidirect
8. C₆₇×#3101	C₂	semidirect
9. C₆₇×#3092	C₂	semidirect
10. C₂×#483×C₆₇	C₂	semidirect
11. C₆₇×#3084	C₂	semidirect
12. C₆₇×#3046	C₂	semidirect
13. C₆₇×#3007	C₂	semidirect
15. C₆₇×#2952	C₂	semidirect
16. C₆₇×#2947	C₂	semidirect
17. C₆₇×#2924	C₂	semidirect
27. #544×C₆₇	C₂²	semidirect
28. #542×C₆₇	C₂²	semidirect
29. #541×C₆₇	C₂²	semidirect
30. #536×C₆₇	C₂²	semidirect
41. #520×C₆₇	C₂²	semidirect
42. #519×C₆₇	C₂²	semidirect
50. #484×C₆₇	C₂²	semidirect
54. #483×C₆₇	C₂²	semidirect
55. #481×C₆₇	C₂²	semidirect
57. #479×C₆₇	C₂²	semidirect
58. #478×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #464×C₆₇	C₂²	semidirect
62. #463×C₆₇	C₂²	semidirect
63. #462×C₆₇	C₂²	semidirect
64. #461×C₆₇	C₂²	semidirect
74. #442×C₆₇	C₂²	semidirect
75. #441×C₆₇	C₂²	semidirect
76. #441×C₆₇	C₂²	semidirect
77. #440×C₆₇	C₂²	semidirect
78. C₄×Q₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×SD₁₆×C₆₇	C₂²	semidirect
81. C₄×SD₁₆×C₆₇	C₂²	semidirect
82. #433×C₆₇	C₂²	semidirect
85. #428×C₆₇	C₂²	semidirect
86. C₂×#106×C₆₇	C₂²	semidirect
87. #424×C₆₇	C₂²	semidirect
89. #417×C₆₇	C₂²	semidirect
91. C₂×#103×C₆₇	C₂²	semidirect
94. #405×C₆₇	C₂²	semidirect
445. #60585	C₆₇	direct (N × H)
454. #3495	C₂×C₆₇	semidirect
455. C₂×#520	C₂×C₆₇	semidirect
456. #3125	C₂×C₆₇	semidirect
457. #3120	C₂×C₆₇	semidirect
458. #3114	C₂×C₆₇	semidirect
459. #3113	C₂×C₆₇	semidirect
460. #3108	C₂×C₆₇	semidirect
461. #3101	C₂×C₆₇	semidirect
462. #3092	C₂×C₆₇	semidirect
463. C₂×#483	C₂×C₆₇	semidirect
464. #3084	C₂×C₆₇	semidirect
465. #3046	C₂×C₆₇	semidirect
466. #3007	C₂×C₆₇	semidirect
468. #2952	C₂×C₆₇	semidirect
469. #2947	C₂×C₆₇	semidirect
470. #2924	C₂×C₆₇	semidirect
471. C₆₇	#60585	direct (N × H)
481. #544	C₂²×C₆₇	semidirect
482. #542	C₂²×C₆₇	semidirect
483. #541	C₂²×C₆₇	semidirect
484. #536	C₂²×C₆₇	semidirect
495. #520	C₂²×C₆₇	semidirect
496. #519	C₂²×C₆₇	semidirect
504. #484	C₂²×C₆₇	semidirect
508. #483	C₂²×C₆₇	semidirect
509. #481	C₂²×C₆₇	semidirect
511. #479	C₂²×C₆₇	semidirect
512. #478	C₂²×C₆₇	semidirect
513. #476	C₂²×C₆₇	semidirect
514. #475	C₂²×C₆₇	semidirect
515. #464	C₂²×C₆₇	semidirect
516. #463	C₂²×C₆₇	semidirect
517. #462	C₂²×C₆₇	semidirect
518. #461	C₂²×C₆₇	semidirect
528. #442	C₂²×C₆₇	semidirect
529. #441	C₂²×C₆₇	semidirect
530. #441	C₂²×C₆₇	semidirect
531. #440	C₂²×C₆₇	semidirect
532. C₄×Q₁₆	C₂²×C₆₇	semidirect
533. C₄×SD₁₆	C₂²×C₆₇	semidirect
534. C₄×SD₁₆	C₂²×C₆₇	semidirect
535. C₄×SD₁₆	C₂²×C₆₇	semidirect
536. #433	C₂²×C₆₇	semidirect
539. #428	C₂²×C₆₇	semidirect
540. C₂×#106	C₂²×C₆₇	semidirect
541. #424	C₂²×C₆₇	semidirect
543. #417	C₂²×C₆₇	semidirect
545. C₂×#103	C₂²×C₆₇	semidirect
548. #405	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3495	2
C₂×#520×C₆₇	2
C₆₇×#3125	2
C₆₇×#3120	2
C₆₇×#3114	2
C₆₇×#3113	2
C₆₇×#3108	2
C₆₇×#3101	2
C₆₇×#3092	2
C₂×#483×C₆₇	2
C₆₇×#3084	2
C₆₇×#3046	2
C₆₇×#3007	2
C₆₇×#3002	2
C₆₇×#2952	2
C₆₇×#2947	2
C₆₇×#2924	2
#60585	67

Subgroups — C67×#60585 #30739836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60585 #30739836