Subgroups — C₆₇×#60573 #30739824

Order 17152.

2004 conjugacy classes of subgroups.

The subgroup lattice has 1154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×2₋¹⁺⁴×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3127	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3121	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3108	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3107	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3104	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3102	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3082	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3044	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#3011	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×Q₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	#544×C₆₇	C₂²	1	1	yes	characteristic
30	#542×C₆₇	—	2	1	no	—
31	#542×C₆₇	C₂²	1	2	yes	—
32	#541×C₆₇	—	2	1	no	—
33	#541×C₆₇	C₂²	1	2	yes	—
34	#539×C₆₇	—	2	2	no	—
35	#537×C₆₇	C₂²	1	1	yes	characteristic
36	#536×C₆₇	C₂²	1	1	yes	characteristic
37	#536×C₆₇	C₂²	1	1	yes	characteristic
38	#533×C₆₇	—	2	1	no	—
39	#533×C₆₇	C₂²	1	2	yes	—
40	#529×C₆₇	—	2	2	no	—
41	#529×C₆₇	—	2	1	no	—
42	#529×C₆₇	C₂²	1	2	yes	—
43	#520×C₆₇	—	2	2	no	—
44	#520×C₆₇	—	2	1	no	—
45	#520×C₆₇	C₂²	1	1	yes	characteristic
46	#520×C₆₇	C₂²	1	2	yes	—
47	#520×C₆₇	C₂²	1	1	yes	characteristic
48	#519×C₆₇	—	2	1	no	—
49	#519×C₆₇	C₂²	1	1	yes	characteristic
50	#519×C₆₇	C₂²	1	2	yes	—
51	C₄×#41×C₆₇	—	2	2	no	—
52	C₄×#41×C₆₇	—	2	1	no	—
53	C₄×#41×C₆₇	C₂²	1	2	yes	—
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
56	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
58	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
59	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
60	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
61	#485×C₆₇	C₂²	1	2	yes	—
62	#485×C₆₇	C₂²	1	2	yes	—
63	#485×C₆₇	C₂²	1	2	yes	—
64	#484×C₆₇	C₂²	1	2	yes	—
65	#484×C₆₇	C₂²	1	2	yes	—
66	#483×C₆₇	C₂²	1	2	yes	—
67	#482×C₆₇	C₂²	1	2	yes	—
68	#480×C₆₇	C₂²	1	2	yes	—
69	#479×C₆₇	C₂²	1	2	yes	—
70	#479×C₆₇	C₂²	1	2	yes	—
71	#479×C₆₇	C₂²	1	2	yes	—
72	#478×C₆₇	C₂²	1	2	yes	—
73	#477×C₆₇	C₂²	1	2	yes	—
74	#477×C₆₇	C₂²	1	2	yes	—
75	#475×C₆₇	C₂²	1	2	yes	—
76	#474×C₆₇	C₂²	1	2	yes	—
77	#464×C₆₇	C₂²	1	2	yes	—
78	#464×C₆₇	C₂²	1	2	yes	—
79	#464×C₆₇	C₂²	1	2	yes	—
80	#463×C₆₇	C₂²	1	2	yes	—
81	#462×C₆₇	C₂²	1	2	yes	—
82	#462×C₆₇	C₂²	1	2	yes	—
83	#462×C₆₇	C₂²	1	2	yes	—
84	#461×C₆₇	C₂²	1	2	yes	—
85	#452×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	—
88	#451×C₆₇	C₂²	1	2	yes	—
89	#451×C₆₇	C₂²	1	2	yes	—
90	#451×C₆₇	C₂²	1	2	yes	—
91	#449×C₆₇	C₂²	1	2	yes	—
92	#448×C₆₇	C₂²	1	2	yes	—
93	#441×C₆₇	C₂²	1	2	yes	—
94	#441×C₆₇	C₂²	1	2	yes	—
95	#440×C₆₇	C₂²	1	2	yes	—
96	#440×C₆₇	C₂²	1	2	yes	—
97	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
98	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
99	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
100	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
101	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
102	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
103	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	—
104	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
105	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
106	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	—
107	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
108	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
109	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
112	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
113	#433×C₆₇	C₂²	1	2	yes	—
114	#433×C₆₇	C₂²	1	2	yes	—
115	#431×C₆₇	C₂²	1	2	yes	—
116	#431×C₆₇	C₂²	1	2	yes	—
117	#428×C₆₇	C₂²	1	1	yes	characteristic
118	#428×C₆₇	C₂²	1	1	yes	characteristic
119	#427×C₆₇	C₂²	1	1	yes	characteristic
120	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic
121	#424×C₆₇	C₂²	1	1	yes	characteristic
122	#424×C₆₇	C₂²	1	1	yes	characteristic
123	#419×C₆₇	C₂²	1	1	yes	characteristic
124	#419×C₆₇	C₂²	1	1	yes	characteristic
125	#417×C₆₇	C₂²	1	1	yes	characteristic
126	#417×C₆₇	C₂²	1	1	yes	characteristic
127	#416×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic
131	#408×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	2	4	no	—
137	C₂×#41×C₆₇	—	2	2	no	—
138	C₂×#41×C₆₇	—	2	1	no	—
139	C₂×#41×C₆₇	C₂³	1	2	yes	—
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×Q₈×C₆₇	—	2	1	no	—
144	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
145	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
147	#137×C₆₇	—	2	4	no	—
148	#137×C₆₇	—	2	4	no	—
149	#135×C₆₇	—	2	4	no	—
150	C₂×Q₁₆×C₆₇	—	2	4	no	—
151	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₆₇	—	2	1	no	—
166	C₄⋊Q₈×C₆₇	—	2	1	no	—
167	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
169	#126×C₆₇	—	2	2	no	—
170	#126×C₆₇	—	2	2	no	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#125×C₆₇	—	2	2	no	—
174	#125×C₆₇	—	2	1	no	—
175	#125×C₆₇	—	2	2	no	—
176	#125×C₆₇	—	2	2	no	—
177	#125×C₆₇	C₂³	1	2	yes	—
178	#124×C₆₇	—	2	1	no	—
179	#124×C₆₇	—	2	2	no	—
180	#124×C₆₇	C₂³	1	2	yes	—
181	#123×C₆₇	—	2	2	no	—
182	#123×C₆₇	—	2	2	no	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	C₂²⋊Q₈×C₆₇	—	2	1	no	—
186	C₂²⋊Q₈×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	1	no	—
189	C₂²⋊Q₈×C₆₇	—	2	2	no	—
190	C₂²⋊Q₈×C₆₇	—	2	2	no	—
191	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
192	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	#121×C₆₇	—	2	2	no	—
195	#121×C₆₇	—	2	1	no	—
196	#121×C₆₇	C₂³	1	2	yes	—
197	C₄×Q₈×C₆₇	—	2	1	no	—
198	C₄×Q₈×C₆₇	—	2	2	no	—
199	C₄×Q₈×C₆₇	—	2	1	no	—
200	C₄×Q₈×C₆₇	—	2	1	no	—
201	C₄×Q₈×C₆₇	—	2	2	no	—
202	C₄×Q₈×C₆₇	—	2	1	no	—
203	C₄×Q₈×C₆₇	—	2	2	no	—
204	C₄×Q₈×C₆₇	—	2	1	no	—
205	C₄×Q₈×C₆₇	—	2	2	no	—
206	C₄×Q₈×C₆₇	—	2	1	no	—
207	C₄×Q₈×C₆₇	—	2	1	no	—
208	C₄×Q₈×C₆₇	—	2	2	no	—
209	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
210	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
211	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
212	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
213	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
214	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
217	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
218	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
219	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	1	no	—
224	C₄×D₄×C₆₇	—	2	1	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	1	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	1	no	—
230	C₄×D₄×C₆₇	—	2	2	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	—	2	2	no	—
233	C₄×D₄×C₆₇	—	2	2	no	—
234	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
235	C₄×D₄×C₆₇	D₄	1	2	yes	—
236	C₄×D₄×C₆₇	D₄	1	2	yes	—
237	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
241	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	#117×C₆₇	—	2	2	no	—
244	#117×C₆₇	—	2	1	no	—
245	#117×C₆₇	—	2	2	no	—
246	#117×C₆₇	—	2	2	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	2	no	—
249	#117×C₆₇	—	2	1	no	—
250	#117×C₆₇	—	2	2	no	—
251	#117×C₆₇	—	2	1	no	—
252	#117×C₆₇	—	2	2	no	—
253	#117×C₆₇	C₂³	1	2	yes	—
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	1	yes	characteristic
257	#117×C₆₇	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
260	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
261	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
262	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
263	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
264	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₆₇	—	2	1	no	—
267	C₂×C₄²×C₆₇	—	2	2	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	—	2	1	no	—
270	C₂×C₄²×C₆₇	—	2	2	no	—
271	C₂×C₄²×C₆₇	—	2	1	no	—
272	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	2	yes	—
275	#107×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	1	yes	characteristic
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#106×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	2	yes	—
283	#106×C₆₇	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	1	yes	characteristic
299	#103×C₆₇	C₂³	1	2	yes	—
300	#103×C₆₇	C₂³	1	2	yes	—
301	#103×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	1	yes	characteristic
304	#102×C₆₇	C₂³	1	1	yes	characteristic
305	#102×C₆₇	C₂³	1	2	yes	—
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	#97×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	#41×C₆₇	—	2	16	no	—
319	#41×C₆₇	—	2	8	no	—
320	#41×C₆₇	—	2	4	no	—
321	#41×C₆₇	—	2	4	no	—
322	#41×C₆₇	—	2	2	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	#41	1	4	yes	—
328	C₂×Q₈×C₆₇	—	2	8	no	—
329	C₂×Q₈×C₆₇	—	2	4	no	—
330	C₂×Q₈×C₆₇	—	2	4	no	—
331	C₂×Q₈×C₆₇	—	2	2	no	—
332	C₂×Q₈×C₆₇	—	2	1	no	—
333	C₂×Q₈×C₆₇	—	2	1	no	—
334	C₂×Q₈×C₆₇	—	2	2	no	—
335	C₂×Q₈×C₆₇	—	2	2	no	—
336	C₂×Q₈×C₆₇	—	2	2	no	—
337	C₂×Q₈×C₆₇	—	2	2	no	—
338	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
339	C₂×Q₈×C₆₇	#41	1	4	yes	—
340	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
341	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
342	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
343	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
344	C₂×D₄×C₆₇	—	2	2	no	—
345	C₂×D₄×C₆₇	—	2	1	no	—
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
351	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₆₇	—	2	2	no	—
353	C₂²×C₄×C₆₇	—	2	1	no	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	2	no	—
358	C₂²×C₄×C₆₇	—	2	1	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	1	no	—
364	C₂²×C₄×C₆₇	—	2	2	no	—
365	C₂²×C₄×C₆₇	—	2	1	no	—
366	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
370	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
372	Q₁₆×C₆₇	—	2	4	no	—
373	Q₁₆×C₆₇	—	2	4	no	—
374	Q₁₆×C₆₇	—	2	2	no	—
375	Q₁₆×C₆₇	—	2	4	no	—
376	Q₁₆×C₆₇	—	2	4	no	—
377	SD₁₆×C₆₇	—	2	2	no	—
378	SD₁₆×C₆₇	—	2	4	no	—
379	SD₁₆×C₆₇	—	2	2	no	—
380	SD₁₆×C₆₇	—	2	4	no	—
381	D₈×C₆₇	—	2	2	no	—
382	M₁₆×C₆₇	—	2	2	no	—
383	M₁₆×C₆₇	—	2	2	no	—
384	C₂×C₈×C₆₇	—	2	2	no	—
385	C₂×C₈×C₆₇	—	2	2	no	—
386	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
389	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
390	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₄⋊C₄×C₆₇	—	2	2	no	—
393	C₄⋊C₄×C₆₇	—	2	2	no	—
394	C₄⋊C₄×C₆₇	—	2	2	no	—
395	C₄⋊C₄×C₆₇	—	2	2	no	—
396	C₄⋊C₄×C₆₇	—	2	1	no	—
397	C₄⋊C₄×C₆₇	—	2	2	no	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	1	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	2	no	—
407	C₄⋊C₄×C₆₇	—	2	2	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
423	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₇	—	2	2	no	—
425	C₂²⋊C₄×C₆₇	—	2	1	no	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	2	no	—
428	C₂²⋊C₄×C₆₇	—	2	1	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	1	no	—
432	C₂²⋊C₄×C₆₇	—	2	2	no	—
433	C₂²⋊C₄×C₆₇	—	2	1	no	—
434	C₂²⋊C₄×C₆₇	—	2	1	no	—
435	C₂²⋊C₄×C₆₇	—	2	2	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
441	C₄²×C₆₇	—	2	1	no	—
442	C₄²×C₆₇	—	2	2	no	—
443	C₄²×C₆₇	—	2	2	no	—
444	C₄²×C₆₇	—	2	2	no	—
445	C₄²×C₆₇	—	2	2	no	—
446	C₄²×C₆₇	—	2	2	no	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	—	2	1	no	—
449	C₄²×C₆₇	—	2	1	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	2	no	—
452	C₄²×C₆₇	—	2	1	no	—
453	C₄²×C₆₇	—	2	2	no	—
454	C₄²×C₆₇	—	2	1	no	—
455	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₆₇	C₂×D₄	1	2	yes	—
457	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₆₇	C₂×D₄	1	2	yes	—
459	C₄²×C₆₇	C₂⁴	1	2	yes	—
460	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
461	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
462	C₂³×C₆₇	—	2	1	no	—
463	C₂³×C₆₇	—	2	1	no	—
464	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
465	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₆₇	—	2	8	no	—
467	Q₈×C₆₇	—	2	2	no	—
468	Q₈×C₆₇	—	2	4	no	—
469	Q₈×C₆₇	—	2	1	no	—
470	Q₈×C₆₇	—	2	2	no	—
471	Q₈×C₆₇	—	2	2	no	—
472	Q₈×C₆₇	—	2	1	no	—
473	Q₈×C₆₇	—	2	2	no	—
474	Q₈×C₆₇	—	2	1	no	—
475	Q₈×C₆₇	—	4	2	no	—
476	Q₈×C₆₇	—	8	2	no	—
477	Q₈×C₆₇	C₂×#41	1	2	yes	—
478	Q₈×C₆₇	C₂×#41	1	4	yes	—
479	D₄×C₆₇	—	2	8	no	—
480	D₄×C₆₇	—	2	4	no	—
481	D₄×C₆₇	—	2	4	no	—
482	D₄×C₆₇	—	2	2	no	—
483	D₄×C₆₇	—	2	1	no	—
484	D₄×C₆₇	—	2	1	no	—
485	D₄×C₆₇	—	2	1	no	—
486	D₄×C₆₇	—	4	2	no	—
487	D₄×C₆₇	—	8	2	no	—
488	D₄×C₆₇	C₂×#41	1	2	yes	—
489	C₂×C₄×C₆₇	—	2	8	no	—
490	C₂×C₄×C₆₇	—	2	8	no	—
491	C₂×C₄×C₆₇	—	2	4	no	—
492	C₂×C₄×C₆₇	—	2	2	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	4	no	—
495	C₂×C₄×C₆₇	—	2	2	no	—
496	C₂×C₄×C₆₇	—	2	4	no	—
497	C₂×C₄×C₆₇	—	2	2	no	—
498	C₂×C₄×C₆₇	—	2	2	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	2	1	no	—
502	C₂×C₄×C₆₇	—	2	1	no	—
503	C₂×C₄×C₆₇	—	2	2	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	1	no	—
506	C₂×C₄×C₆₇	—	2	2	no	—
507	C₂×C₄×C₆₇	—	4	1	no	—
508	C₂×C₄×C₆₇	—	4	2	no	—
509	C₂×C₄×C₆₇	—	4	2	no	—
510	C₂×C₄×C₆₇	—	4	2	no	—
511	C₂×C₄×C₆₇	—	4	2	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	8	1	no	—
514	C₂×C₄×C₆₇	—	8	1	no	—
515	C₂×C₄×C₆₇	—	8	2	no	—
516	C₂×C₄×C₆₇	—	8	1	no	—
517	C₂×C₄×C₆₇	—	8	2	no	—
518	C₂×C₄×C₆₇	—	8	1	no	—
519	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
520	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
523	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
524	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
525	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
526	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
527	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
528	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
529	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	—	2	1	no	—
534	C₈×C₆₇	—	2	2	no	—
535	C₈×C₆₇	—	2	2	no	—
536	C₂²×C₆₇	—	2	1	no	—
537	C₂²×C₆₇	—	2	1	no	—
538	C₂²×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	2	no	—
540	C₂²×C₆₇	—	2	2	no	—
541	C₂²×C₆₇	—	2	2	no	—
542	C₂²×C₆₇	—	4	1	no	—
543	C₂²×C₆₇	—	4	1	no	—
544	C₂²×C₆₇	—	4	1	no	—
545	C₂²×C₆₇	—	4	1	no	—
546	C₂²×C₆₇	—	4	1	no	—
547	C₂²×C₆₇	#525	1	2	yes	—
548	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₆₇	—	2	1	no	—
550	C₄×C₆₇	—	2	1	no	—
551	C₄×C₆₇	—	2	2	no	—
552	C₄×C₆₇	—	2	4	no	—
553	C₄×C₆₇	—	2	2	no	—
554	C₄×C₆₇	—	2	2	no	—
555	C₄×C₆₇	—	2	1	no	—
556	C₄×C₆₇	—	2	2	no	—
557	C₄×C₆₇	—	4	1	no	—
558	C₄×C₆₇	—	4	2	no	—
559	C₄×C₆₇	—	4	2	no	—
560	C₄×C₆₇	—	4	1	no	—
561	C₄×C₆₇	—	4	1	no	—
562	C₄×C₆₇	—	4	2	no	—
563	C₄×C₆₇	—	4	1	no	—
564	C₄×C₆₇	—	4	1	no	—
565	C₄×C₆₇	#525	1	2	yes	—
566	C₄×C₆₇	#578	1	2	yes	—
567	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
568	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
569	#60573	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
570	C₂×C₆₇	—	2	2	no	—
571	C₂×C₆₇	—	4	2	no	—
572	C₂×C₆₇	—	4	2	no	—
573	C₂×C₆₇	—	8	1	no	—
574	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
575	C₂×C₆₇	C₂×#578	1	1	yes	characteristic
576	C₂×C₆₇	#3584	1	1	yes	characteristic
577	#3461	C₂×C₆₇	1	1	yes	characteristic, complemented
578	C₄×2₋¹⁺⁴	C₂×C₆₇	1	1	yes	characteristic, complemented
579	#3127	C₂×C₆₇	1	2	yes	complemented
580	#3124	C₂×C₆₇	1	2	yes	complemented
581	#3121	C₂×C₆₇	1	2	yes	complemented
582	#3120	C₂×C₆₇	1	2	yes	complemented
583	#3108	C₂×C₆₇	1	2	yes	complemented
584	#3107	C₂×C₆₇	1	2	yes	complemented
585	#3104	C₂×C₆₇	1	2	yes	complemented
586	#3102	C₂×C₆₇	1	2	yes	complemented
587	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
588	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
589	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
590	#3082	C₂×C₆₇	1	1	yes	characteristic, complemented
591	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
592	#3044	C₂×C₆₇	1	1	yes	characteristic, complemented
593	#3013	C₂×C₆₇	1	1	yes	characteristic
594	#3011	C₂×C₆₇	1	1	yes	characteristic, complemented
595	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
596	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
597	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
598	C₂×C₄×Q₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
599	#2922	C₂×C₆₇	1	1	yes	characteristic, complemented
600	C₆₇	#60573	1	1	yes	characteristic, direct product factor, Sylow
601	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
602	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
603	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
604	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
605	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
606	#544	C₂²×C₆₇	1	1	yes	characteristic
607	#542	—	2	1	no	—
608	#542	C₂²×C₆₇	1	2	yes	—
609	#541	—	2	1	no	—
610	#541	C₂²×C₆₇	1	2	yes	—
611	#539	—	2	2	no	—
612	#537	C₂²×C₆₇	1	1	yes	characteristic
613	#536	C₂²×C₆₇	1	1	yes	characteristic
614	#536	C₂²×C₆₇	1	1	yes	characteristic
615	#533	—	2	1	no	—
616	#533	C₂²×C₆₇	1	2	yes	—
617	#529	—	2	2	no	—
618	#529	—	2	1	no	—
619	#529	C₂²×C₆₇	1	2	yes	—
620	#520	—	2	2	no	—
621	#520	—	2	1	no	—
622	#520	C₂²×C₆₇	1	1	yes	characteristic
623	#520	C₂²×C₆₇	1	2	yes	—
624	#520	C₂²×C₆₇	1	1	yes	characteristic
625	#519	—	2	1	no	—
626	#519	C₂²×C₆₇	1	1	yes	characteristic
627	#519	C₂²×C₆₇	1	2	yes	—
628	C₄×#41	—	2	2	no	—
629	C₄×#41	—	2	1	no	—
630	C₄×#41	C₂²×C₆₇	1	2	yes	—
631	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
632	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
633	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
634	C₂×C₄×Q₈	—	2	1	no	—
635	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
636	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
637	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic
638	#485	C₂²×C₆₇	1	2	yes	—
639	#485	C₂²×C₆₇	1	2	yes	—
640	#485	C₂²×C₆₇	1	2	yes	—
641	#484	C₂²×C₆₇	1	2	yes	—
642	#484	C₂²×C₆₇	1	2	yes	—
643	#483	C₂²×C₆₇	1	2	yes	—
644	#482	C₂²×C₆₇	1	2	yes	—
645	#480	C₂²×C₆₇	1	2	yes	—
646	#479	C₂²×C₆₇	1	2	yes	—
647	#479	C₂²×C₆₇	1	2	yes	—
648	#479	C₂²×C₆₇	1	2	yes	—
649	#478	C₂²×C₆₇	1	2	yes	—
650	#477	C₂²×C₆₇	1	2	yes	—
651	#477	C₂²×C₆₇	1	2	yes	—
652	#475	C₂²×C₆₇	1	2	yes	—
653	#474	C₂²×C₆₇	1	2	yes	—
654	#464	C₂²×C₆₇	1	2	yes	—
655	#464	C₂²×C₆₇	1	2	yes	—
656	#464	C₂²×C₆₇	1	2	yes	—
657	#463	C₂²×C₆₇	1	2	yes	—
658	#462	C₂²×C₆₇	1	2	yes	—
659	#462	C₂²×C₆₇	1	2	yes	—
660	#462	C₂²×C₆₇	1	2	yes	—
661	#461	C₂²×C₆₇	1	2	yes	—
662	#452	C₂²×C₆₇	1	2	yes	—
663	#452	C₂²×C₆₇	1	2	yes	—
664	#452	C₂²×C₆₇	1	2	yes	—
665	#451	C₂²×C₆₇	1	2	yes	—
666	#451	C₂²×C₆₇	1	2	yes	—
667	#451	C₂²×C₆₇	1	2	yes	—
668	#449	C₂²×C₆₇	1	2	yes	—
669	#448	C₂²×C₆₇	1	2	yes	—
670	#441	C₂²×C₆₇	1	2	yes	—
671	#441	C₂²×C₆₇	1	2	yes	—
672	#440	C₂²×C₆₇	1	2	yes	—
673	#440	C₂²×C₆₇	1	2	yes	—
674	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
675	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
676	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
677	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
678	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
679	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
680	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	—
681	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
682	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
683	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	—
684	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
685	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
686	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
687	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
688	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
689	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
690	#433	C₂²×C₆₇	1	2	yes	—
691	#433	C₂²×C₆₇	1	2	yes	—
692	#431	C₂²×C₆₇	1	2	yes	—
693	#431	C₂²×C₆₇	1	2	yes	—
694	#428	C₂²×C₆₇	1	1	yes	characteristic
695	#428	C₂²×C₆₇	1	1	yes	characteristic
696	#427	C₂²×C₆₇	1	1	yes	characteristic
697	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic
698	#424	C₂²×C₆₇	1	1	yes	characteristic
699	#424	C₂²×C₆₇	1	1	yes	characteristic
700	#419	C₂²×C₆₇	1	1	yes	characteristic
701	#419	C₂²×C₆₇	1	1	yes	characteristic
702	#417	C₂²×C₆₇	1	1	yes	characteristic
703	#417	C₂²×C₆₇	1	1	yes	characteristic
704	#416	C₂²×C₆₇	1	1	yes	characteristic
705	#416	C₂²×C₆₇	1	1	yes	characteristic
706	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
707	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic
708	#408	C₂²×C₆₇	1	1	yes	characteristic
709	#408	C₂²×C₆₇	1	1	yes	characteristic
710	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
711	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
712	2₋¹⁺⁴	—	2	4	no	—
713	2₋¹⁺⁴	—	2	4	no	—
714	C₂×#41	—	2	2	no	—
715	C₂×#41	—	2	1	no	—
716	C₂×#41	C₂³×C₆₇	1	2	yes	—
717	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
718	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
719	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
720	C₂²×Q₈	—	2	1	no	—
721	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
722	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
723	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
724	#137	—	2	4	no	—
725	#137	—	2	4	no	—
726	#135	—	2	4	no	—
727	C₂×Q₁₆	—	2	4	no	—
728	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
732	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
737	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
740	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
741	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
742	C₄⋊Q₈	—	2	1	no	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
745	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
746	#126	—	2	2	no	—
747	#126	—	2	2	no	—
748	#126	—	2	2	no	—
749	#126	—	2	2	no	—
750	#125	—	2	2	no	—
751	#125	—	2	1	no	—
752	#125	—	2	2	no	—
753	#125	—	2	2	no	—
754	#125	C₂³×C₆₇	1	2	yes	—
755	#124	—	2	1	no	—
756	#124	—	2	2	no	—
757	#124	C₂³×C₆₇	1	2	yes	—
758	#123	—	2	2	no	—
759	#123	—	2	2	no	—
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	C₂²⋊Q₈	—	2	1	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	1	no	—
765	C₂²⋊Q₈	—	2	1	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
769	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
770	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
771	#121	—	2	2	no	—
772	#121	—	2	1	no	—
773	#121	C₂³×C₆₇	1	2	yes	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	2	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	1	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	—	2	1	no	—
782	C₄×Q₈	—	2	2	no	—
783	C₄×Q₈	—	2	1	no	—
784	C₄×Q₈	—	2	1	no	—
785	C₄×Q₈	—	2	2	no	—
786	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
787	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
788	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
789	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
790	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
791	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
792	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
793	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
794	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
795	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
796	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
797	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
798	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
799	C₄×D₄	—	2	2	no	—
800	C₄×D₄	—	2	1	no	—
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	2	no	—
811	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
812	C₄×D₄	D₄×C₆₇	1	2	yes	—
813	C₄×D₄	D₄×C₆₇	1	2	yes	—
814	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
815	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₇	1	2	yes	—
818	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
820	#117	—	2	2	no	—
821	#117	—	2	1	no	—
822	#117	—	2	2	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	2	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	1	no	—
829	#117	—	2	2	no	—
830	#117	C₂³×C₆₇	1	1	yes	characteristic
831	#117	C₂³×C₆₇	1	2	yes	—
832	#117	C₂³×C₆₇	1	1	yes	characteristic
833	#117	C₂³×C₆₇	1	1	yes	characteristic
834	#117	C₂³×C₆₇	1	2	yes	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	—	2	2	no	—
837	C₂×C₄⋊C₄	—	2	1	no	—
838	C₂×C₄⋊C₄	—	2	2	no	—
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
842	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
843	C₂×C₄²	—	2	1	no	—
844	C₂×C₄²	—	2	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	—	2	2	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
850	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
851	#107	C₂³×C₆₇	1	2	yes	—
852	#107	C₂³×C₆₇	1	2	yes	—
853	#107	C₂³×C₆₇	1	1	yes	characteristic
854	#107	C₂³×C₆₇	1	1	yes	characteristic
855	#107	C₂³×C₆₇	1	2	yes	—
856	#107	C₂³×C₆₇	1	2	yes	—
857	#106	C₂³×C₆₇	1	1	yes	characteristic
858	#106	C₂³×C₆₇	1	1	yes	characteristic
859	#106	C₂³×C₆₇	1	2	yes	—
860	#106	C₂³×C₆₇	1	2	yes	—
861	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
862	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
864	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
865	#103	C₂³×C₆₇	1	2	yes	—
866	#103	C₂³×C₆₇	1	2	yes	—
867	#103	C₂³×C₆₇	1	2	yes	—
868	#103	C₂³×C₆₇	1	2	yes	—
869	#103	C₂³×C₆₇	1	1	yes	characteristic
870	#103	C₂³×C₆₇	1	1	yes	characteristic
871	#103	C₂³×C₆₇	1	1	yes	characteristic
872	#103	C₂³×C₆₇	1	1	yes	characteristic
873	#103	C₂³×C₆₇	1	2	yes	—
874	#103	C₂³×C₆₇	1	2	yes	—
875	#103	C₂³×C₆₇	1	2	yes	—
876	#103	C₂³×C₆₇	1	2	yes	—
877	#103	C₂³×C₆₇	1	2	yes	—
878	#103	C₂³×C₆₇	1	2	yes	—
879	#102	C₂³×C₆₇	1	1	yes	characteristic
880	#102	C₂³×C₆₇	1	1	yes	characteristic
881	#102	C₂³×C₆₇	1	1	yes	characteristic
882	#102	C₂³×C₆₇	1	1	yes	characteristic
883	#102	C₂³×C₆₇	1	2	yes	—
884	#102	C₂³×C₆₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
889	#97	C₂³×C₆₇	1	2	yes	—
890	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
891	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
892	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₆₇	1	2	yes	—
895	#41	—	2	16	no	—
896	#41	—	2	8	no	—
897	#41	—	2	4	no	—
898	#41	—	2	4	no	—
899	#41	—	2	2	no	—
900	#41	—	2	2	no	—
901	#41	—	2	2	no	—
902	#41	—	2	2	no	—
903	#41	—	2	2	no	—
904	#41	#41×C₆₇	1	4	yes	—
905	C₂×Q₈	—	2	8	no	—
906	C₂×Q₈	—	2	4	no	—
907	C₂×Q₈	—	2	4	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	2	1	no	—
910	C₂×Q₈	—	2	1	no	—
911	C₂×Q₈	—	2	2	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	2	2	no	—
914	C₂×Q₈	—	2	2	no	—
915	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
916	C₂×Q₈	#41×C₆₇	1	4	yes	—
917	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
918	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
919	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
920	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	2	no	—
925	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
926	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
927	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
928	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂²×C₄	—	2	2	no	—
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
944	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
945	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
947	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
949	Q₁₆	—	2	4	no	—
950	Q₁₆	—	2	4	no	—
951	Q₁₆	—	2	2	no	—
952	Q₁₆	—	2	4	no	—
953	Q₁₆	—	2	4	no	—
954	SD₁₆	—	2	2	no	—
955	SD₁₆	—	2	4	no	—
956	SD₁₆	—	2	2	no	—
957	SD₁₆	—	2	4	no	—
958	D₈	—	2	2	no	—
959	M₁₆	—	2	2	no	—
960	M₁₆	—	2	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
966	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
968	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	2	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
994	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1018	C₄²	—	2	2	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	2	no	—
1022	C₄²	—	2	2	no	—
1023	C₄²	—	2	2	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1033	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1034	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1035	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1036	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₆₇	1	2	yes	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	1	no	—
1041	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1042	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1043	Q₈	—	2	8	no	—
1044	Q₈	—	2	2	no	—
1045	Q₈	—	2	4	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	2	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	2	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	4	2	no	—
1053	Q₈	—	8	2	no	—
1054	Q₈	C₂×#41×C₆₇	1	2	yes	—
1055	Q₈	C₂×#41×C₆₇	1	4	yes	—
1056	D₄	—	2	8	no	—
1057	D₄	—	2	4	no	—
1058	D₄	—	2	4	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	4	2	no	—
1064	D₄	—	8	2	no	—
1065	D₄	C₂×#41×C₆₇	1	2	yes	—
1066	C₂×C₄	—	2	8	no	—
1067	C₂×C₄	—	2	8	no	—
1068	C₂×C₄	—	2	4	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	4	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	4	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	2	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	4	1	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	4	2	no	—
1089	C₂×C₄	—	4	2	no	—
1090	C₂×C₄	—	8	1	no	—
1091	C₂×C₄	—	8	1	no	—
1092	C₂×C₄	—	8	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	1	no	—
1096	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1097	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1098	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1099	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1100	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1101	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1103	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1105	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1106	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1107	C₈	—	2	1	no	—
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	2	no	—
1112	C₈	—	2	2	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	2	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	#525×C₆₇	1	2	yes	—
1125	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1126	C₄	—	2	1	no	—
1127	C₄	—	2	2	no	—
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	2	2	no	—
1131	C₄	—	2	4	no	—
1132	C₄	—	2	2	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	4	1	no	—
1137	C₄	—	4	2	no	—
1138	C₄	—	4	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	2	no	—
1142	C₄	#525×C₆₇	1	2	yes	—
1143	C₄	#578×C₆₇	1	2	yes	—
1144	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1145	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	2	no	—
1148	C₂	—	4	2	no	—
1149	C₂	—	8	1	no	—
1150	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1151	C₂	C₂×#578×C₆₇	1	1	yes	characteristic
1152	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
prime radical	C₆₇×#3013	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3461	C₂	semidirect
2. C₄×2₋¹⁺⁴×C₆₇	C₂	semidirect
3. C₆₇×#3127	C₂	semidirect
4. C₆₇×#3124	C₂	semidirect
5. C₆₇×#3121	C₂	semidirect
6. C₆₇×#3120	C₂	semidirect
7. C₆₇×#3108	C₂	semidirect
8. C₆₇×#3107	C₂	semidirect
9. C₆₇×#3104	C₂	semidirect
10. C₆₇×#3102	C₂	semidirect
11. C₆₇×#3098	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3083	C₂	semidirect
14. C₆₇×#3082	C₂	semidirect
15. C₆₇×#3046	C₂	semidirect
16. C₆₇×#3044	C₂	semidirect
18. C₆₇×#3011	C₂	semidirect
19. C₄×#137×C₆₇	C₂	semidirect
20. C₄×#137×C₆₇	C₂	semidirect
21. C₄×#135×C₆₇	C₂	semidirect
22. C₂×C₄×Q₁₆×C₆₇	C₂	semidirect
23. C₆₇×#2922	C₂	semidirect
569. #60573	C₆₇	direct (N × H)
577. #3461	C₂×C₆₇	semidirect
578. C₄×2₋¹⁺⁴	C₂×C₆₇	semidirect
579. #3127	C₂×C₆₇	semidirect
580. #3124	C₂×C₆₇	semidirect
581. #3121	C₂×C₆₇	semidirect
582. #3120	C₂×C₆₇	semidirect
583. #3108	C₂×C₆₇	semidirect
584. #3107	C₂×C₆₇	semidirect
585. #3104	C₂×C₆₇	semidirect
586. #3102	C₂×C₆₇	semidirect
587. #3098	C₂×C₆₇	semidirect
588. #3097	C₂×C₆₇	semidirect
589. #3083	C₂×C₆₇	semidirect
590. #3082	C₂×C₆₇	semidirect
591. #3046	C₂×C₆₇	semidirect
592. #3044	C₂×C₆₇	semidirect
594. #3011	C₂×C₆₇	semidirect
595. C₄×#137	C₂×C₆₇	semidirect
596. C₄×#137	C₂×C₆₇	semidirect
597. C₄×#135	C₂×C₆₇	semidirect
598. C₂×C₄×Q₁₆	C₂×C₆₇	semidirect
599. #2922	C₂×C₆₇	semidirect
600. C₆₇	#60573	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3461	2
C₄×2₋¹⁺⁴×C₆₇	2
C₆₇×#3127	2
C₆₇×#3124	2
C₆₇×#3121	2
C₆₇×#3120	2
C₆₇×#3108	2
C₆₇×#3107	2
C₆₇×#3104	2
C₆₇×#3102	2
C₆₇×#3098	2
C₆₇×#3097	2
C₆₇×#3083	2
C₆₇×#3082	2
C₆₇×#3046	2
C₆₇×#3044	2
C₆₇×#3013	2
C₆₇×#3011	2
C₄×#137×C₆₇	2
C₄×#135×C₆₇	2
C₂×C₄×Q₁₆×C₆₇	2
C₆₇×#2922	2
#60573	67

Subgroups — C67×#60573 #30739824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60573 #30739824