Subgroups — C₆₇×#61219 #30740470

Order 17152.

2102 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3496	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3315	C₂	1	4	yes	maximal, complemented
4	C₆₇×#3314	C₂	1	4	yes	maximal, complemented
5	C₆₇×#3311	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3310	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#3098	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3063	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
13	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2897	C₂	1	2	yes	maximal, complemented
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
17	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
18	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
20	#559×C₆₇	—	2	1	no	—
21	#557×C₆₇	—	2	1	no	—
22	#556×C₆₇	—	2	2	no	—
23	#556×C₆₇	C₂²	1	2	yes	complemented
24	#554×C₆₇	C₂²	1	2	yes	complemented
25	#552×C₆₇	C₂²	1	4	yes	complemented
26	#547×C₆₇	—	2	1	no	—
27	#547×C₆₇	C₂²	1	2	yes	—
28	#546×C₆₇	—	2	2	no	—
29	#546×C₆₇	C₂²	1	4	yes	—
30	D₄²×C₆₇	—	2	1	no	—
31	D₄²×C₆₇	C₂²	1	2	yes	—
32	#539×C₆₇	—	2	2	no	—
33	#537×C₆₇	C₂²	1	2	yes	—
34	#536×C₆₇	C₂²	1	2	yes	complemented
35	#534×C₆₇	—	2	2	no	—
36	#533×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	#532×C₆₇	C₂²	1	1	yes	characteristic
38	#532×C₆₇	C₂²	1	1	yes	characteristic
39	#529×C₆₇	—	2	2	no	—
40	C₂×#121×C₆₇	—	2	2	no	—
41	#520×C₆₇	C₂²	1	2	yes	complemented
42	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
44	#491×C₆₇	C₂²	1	2	yes	complemented
45	#490×C₆₇	C₂²	1	2	yes	complemented
46	#489×C₆₇	C₂²	1	2	yes	complemented
47	#489×C₆₇	C₂²	1	2	yes	complemented
48	#485×C₆₇	C₂²	1	4	yes	complemented
49	#484×C₆₇	C₂²	1	4	yes	complemented
50	#482×C₆₇	C₂²	1	4	yes	complemented
51	#480×C₆₇	C₂²	1	4	yes	complemented
52	#478×C₆₇	C₂²	1	4	yes	complemented
53	#476×C₆₇	C₂²	1	2	yes	complemented
54	#474×C₆₇	C₂²	1	2	yes	complemented
55	#470×C₆₇	C₂²	1	4	yes	complemented
56	#468×C₆₇	C₂²	1	4	yes	complemented
57	#467×C₆₇	C₂²	1	4	yes	complemented
58	#465×C₆₇	C₂²	1	4	yes	complemented
59	#464×C₆₇	C₂²	1	4	yes	complemented
60	#462×C₆₇	C₂²	1	2	yes	complemented
61	#460×C₆₇	C₂²	1	2	yes	complemented
62	#452×C₆₇	C₂²	1	4	yes	complemented
63	#452×C₆₇	C₂²	1	4	yes	complemented
64	#450×C₆₇	C₂²	1	4	yes	complemented
65	#450×C₆₇	C₂²	1	4	yes	complemented
66	#440×C₆₇	C₂²	1	4	yes	complemented
67	#440×C₆₇	C₂²	1	4	yes	complemented
68	#435×C₆₇	C₂²	1	4	yes	complemented
69	#435×C₆₇	C₂²	1	4	yes	complemented
70	#428×C₆₇	C₂²	1	2	yes	complemented
71	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
72	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#418×C₆₇	C₂²	1	2	yes	—
74	#418×C₆₇	C₂²	1	4	yes	complemented
75	#417×C₆₇	C₂²	1	2	yes	complemented
76	#417×C₆₇	C₂²	1	4	yes	complemented
77	#416×C₆₇	C₂²	1	2	yes	complemented
78	#416×C₆₇	C₂²	1	4	yes	complemented
79	#416×C₆₇	C₂²	1	2	yes	complemented
80	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
82	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
83	#408×C₆₇	C₂²	1	2	yes	complemented
84	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
85	H(5,𝔽₂)×C₆₇	—	2	8	no	—
86	H(5,𝔽₂)×C₆₇	—	4	4	no	—
87	C₂×#41×C₆₇	—	2	2	no	—
88	C₂×#41×C₆₇	C₂³	1	2	yes	—
89	C₂×#41×C₆₇	C₂³	1	4	yes	—
90	C₂×#41×C₆₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₆₇	—	2	4	no	—
93	C₂²×D₄×C₆₇	—	2	2	no	—
94	C₂²×D₄×C₆₇	—	2	2	no	—
95	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
96	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	—	2	1	no	—
98	#137×C₆₇	—	4	4	no	—
99	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
100	C₂×SD₁₆×C₆₇	—	2	4	no	—
101	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
103	#131×C₆₇	—	4	4	no	—
104	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
105	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
106	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
109	C₄⋊Q₈×C₆₇	—	2	2	no	—
110	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
114	#127×C₆₇	D₄	1	1	yes	characteristic
115	#127×C₆₇	C₂³	1	1	yes	characteristic
116	#126×C₆₇	—	2	4	no	—
117	#126×C₆₇	—	2	4	no	—
118	#125×C₆₇	—	2	2	no	—
119	#125×C₆₇	—	2	4	no	—
120	#125×C₆₇	C₂³	1	2	yes	—
121	#124×C₆₇	—	2	2	no	—
122	#124×C₆₇	—	2	2	no	—
123	#124×C₆₇	D₄	1	2	yes	—
124	#124×C₆₇	C₂³	1	2	yes	—
125	#123×C₆₇	—	2	4	no	—
126	#123×C₆₇	—	2	4	no	—
127	#123×C₆₇	—	2	4	no	—
128	#123×C₆₇	—	2	4	no	—
129	C₂²⋊Q₈×C₆₇	—	2	2	no	—
130	C₂²⋊Q₈×C₆₇	—	2	1	no	—
131	C₂²⋊Q₈×C₆₇	—	2	1	no	—
132	C₂²⋊Q₈×C₆₇	—	2	4	no	—
133	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
134	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
135	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
136	#121×C₆₇	—	2	4	no	—
137	#121×C₆₇	—	2	2	no	—
138	#121×C₆₇	—	2	2	no	—
139	#121×C₆₇	—	2	1	no	—
140	#121×C₆₇	—	2	1	no	—
141	#121×C₆₇	—	2	2	no	—
142	#121×C₆₇	—	2	4	no	—
143	#121×C₆₇	D₄	1	2	yes	—
144	#121×C₆₇	D₄	1	2	yes	—
145	#121×C₆₇	C₂³	1	4	yes	—
146	#120×C₆₇	—	2	4	no	—
147	#120×C₆₇	—	2	4	no	—
148	C₄×Q₈×C₆₇	—	2	2	no	—
149	C₄×Q₈×C₆₇	—	2	2	no	—
150	C₄×Q₈×C₆₇	—	2	1	no	—
151	C₄×Q₈×C₆₇	—	2	1	no	—
152	C₄×Q₈×C₆₇	—	2	1	no	—
153	C₄×Q₈×C₆₇	—	2	1	no	—
154	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
155	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
156	C₄×D₄×C₆₇	—	2	4	no	—
157	C₄×D₄×C₆₇	—	2	2	no	—
158	C₄×D₄×C₆₇	—	2	2	no	—
159	C₄×D₄×C₆₇	—	2	1	no	—
160	C₄×D₄×C₆₇	—	2	1	no	—
161	C₄×D₄×C₆₇	—	2	1	no	—
162	C₄×D₄×C₆₇	—	2	1	no	—
163	C₄×D₄×C₆₇	C₂³	1	2	yes	—
164	C₄×D₄×C₆₇	C₂³	1	2	yes	—
165	C₄×D₄×C₆₇	C₂³	1	2	yes	—
166	C₄×D₄×C₆₇	C₂³	1	2	yes	—
167	#117×C₆₇	—	2	4	no	—
168	#117×C₆₇	C₂³	1	4	yes	—
169	#117×C₆₇	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
171	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
177	C₂×C₄²×C₆₇	—	2	1	no	—
178	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
179	#107×C₆₇	C₂³	1	4	yes	—
180	#107×C₆₇	C₂³	1	4	yes	—
181	#106×C₆₇	C₂³	1	4	yes	—
182	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
183	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
184	#103×C₆₇	C₂³	1	2	yes	—
185	#103×C₆₇	C₂³	1	2	yes	—
186	#103×C₆₇	C₂³	1	4	yes	—
187	#103×C₆₇	C₂³	1	4	yes	—
188	#103×C₆₇	C₂³	1	2	yes	—
189	#103×C₆₇	C₂³	1	2	yes	—
190	#102×C₆₇	C₂³	1	2	yes	—
191	#102×C₆₇	C₂³	1	2	yes	—
192	#102×C₆₇	C₂³	1	4	yes	—
193	#102×C₆₇	C₂³	1	4	yes	—
194	#102×C₆₇	C₂³	1	4	yes	—
195	#102×C₆₇	C₂³	1	2	yes	—
196	#102×C₆₇	C₂³	1	2	yes	—
197	#102×C₆₇	C₂³	1	4	yes	—
198	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
199	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
200	#97×C₆₇	C₂³	1	2	yes	—
201	#97×C₆₇	C₂³	1	2	yes	—
202	C₂⁴×C₆₇	—	2	1	no	—
203	C₂⁴×C₆₇	—	2	4	no	—
204	#41×C₆₇	—	2	4	no	—
205	#41×C₆₇	—	2	4	no	—
206	#41×C₆₇	—	2	8	no	—
207	#41×C₆₇	—	2	4	no	—
208	#41×C₆₇	—	2	4	no	—
209	#41×C₆₇	—	4	4	no	—
210	#41×C₆₇	—	4	8	no	—
211	C₂×Q₈×C₆₇	—	2	1	no	—
212	C₂×Q₈×C₆₇	—	2	1	no	—
213	C₂×Q₈×C₆₇	—	2	1	no	—
214	C₂×Q₈×C₆₇	—	2	2	no	—
215	C₂×Q₈×C₆₇	—	2	2	no	—
216	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
217	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
218	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
219	C₂×D₄×C₆₇	—	2	8	no	—
220	C₂×D₄×C₆₇	—	2	4	no	—
221	C₂×D₄×C₆₇	—	2	2	no	—
222	C₂×D₄×C₆₇	—	2	4	no	—
223	C₂×D₄×C₆₇	—	2	1	no	—
224	C₂×D₄×C₆₇	—	2	1	no	—
225	C₂×D₄×C₆₇	—	2	4	no	—
226	C₂×D₄×C₆₇	—	2	1	no	—
227	C₂×D₄×C₆₇	—	2	2	no	—
228	C₂×D₄×C₆₇	—	4	4	no	—
229	C₂×D₄×C₆₇	—	4	8	no	—
230	C₂×D₄×C₆₇	—	4	16	no	—
231	C₂×D₄×C₆₇	—	8	4	no	—
232	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
233	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
234	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₆₇	#41	1	4	yes	—
237	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
238	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₆₇	—	2	1	no	—
240	C₂²×C₄×C₆₇	—	2	1	no	—
241	C₂²×C₄×C₆₇	—	2	1	no	—
242	C₂²×C₄×C₆₇	—	2	4	no	—
243	C₂²×C₄×C₆₇	—	2	4	no	—
244	C₂²×C₄×C₆₇	—	2	2	no	—
245	C₂²×C₄×C₆₇	—	2	2	no	—
246	C₂²×C₄×C₆₇	—	2	2	no	—
247	C₂²×C₄×C₆₇	—	8	2	no	—
248	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
252	Q₁₆×C₆₇	—	4	4	no	—
253	SD₁₆×C₆₇	—	2	8	no	—
254	SD₁₆×C₆₇	—	4	4	no	—
255	M₁₆×C₆₇	—	2	4	no	—
256	M₁₆×C₆₇	—	4	4	no	—
257	C₂×C₈×C₆₇	—	2	2	no	—
258	C₂×C₈×C₆₇	—	2	2	no	—
259	C₂×C₈×C₆₇	—	4	4	no	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
262	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₇	—	2	1	no	—
264	C₄⋊C₄×C₆₇	—	2	2	no	—
265	C₄⋊C₄×C₆₇	—	2	2	no	—
266	C₄⋊C₄×C₆₇	—	2	4	no	—
267	C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₄⋊C₄×C₆₇	—	2	1	no	—
269	C₄⋊C₄×C₆₇	—	2	4	no	—
270	C₄⋊C₄×C₆₇	—	2	2	no	—
271	C₄⋊C₄×C₆₇	—	2	4	no	—
272	C₄⋊C₄×C₆₇	—	2	1	no	—
273	C₄⋊C₄×C₆₇	—	2	1	no	—
274	C₄⋊C₄×C₆₇	—	2	2	no	—
275	C₄⋊C₄×C₆₇	—	2	1	no	—
276	C₄⋊C₄×C₆₇	—	2	4	no	—
277	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
280	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₆₇	—	2	4	no	—
284	C₂²⋊C₄×C₆₇	—	2	4	no	—
285	C₂²⋊C₄×C₆₇	—	2	2	no	—
286	C₂²⋊C₄×C₆₇	—	2	4	no	—
287	C₂²⋊C₄×C₆₇	—	2	4	no	—
288	C₂²⋊C₄×C₆₇	—	2	2	no	—
289	C₂²⋊C₄×C₆₇	—	2	2	no	—
290	C₂²⋊C₄×C₆₇	—	2	2	no	—
291	C₂²⋊C₄×C₆₇	—	2	4	no	—
292	C₂²⋊C₄×C₆₇	—	2	2	no	—
293	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
294	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
295	C₄²×C₆₇	—	2	2	no	—
296	C₄²×C₆₇	—	2	2	no	—
297	C₄²×C₆₇	—	2	4	no	—
298	C₄²×C₆₇	—	2	2	no	—
299	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	4	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	4	8	no	—
307	C₂³×C₆₇	—	8	1	no	—
308	C₂³×C₆₇	—	8	1	no	—
309	C₂³×C₆₇	—	8	4	no	—
310	C₂³×C₆₇	—	8	4	no	—
311	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
312	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₆₇	—	2	4	no	—
314	Q₈×C₆₇	—	2	2	no	—
315	Q₈×C₆₇	—	2	2	no	—
316	Q₈×C₆₇	—	2	2	no	—
317	Q₈×C₆₇	—	2	2	no	—
318	Q₈×C₆₇	—	4	2	no	—
319	Q₈×C₆₇	—	4	2	no	—
320	Q₈×C₆₇	—	8	1	no	—
321	D₄×C₆₇	—	2	8	no	—
322	D₄×C₆₇	—	2	4	no	—
323	D₄×C₆₇	—	2	4	no	—
324	D₄×C₆₇	—	2	2	no	—
325	D₄×C₆₇	—	2	2	no	—
326	D₄×C₆₇	—	2	2	no	—
327	D₄×C₆₇	—	4	2	no	—
328	D₄×C₆₇	—	4	2	no	—
329	D₄×C₆₇	—	4	8	no	—
330	D₄×C₆₇	—	4	2	no	—
331	D₄×C₆₇	—	4	8	no	—
332	D₄×C₆₇	—	4	4	no	—
333	D₄×C₆₇	—	8	1	no	—
334	D₄×C₆₇	—	8	4	no	—
335	D₄×C₆₇	C₂×#41	1	4	yes	—
336	C₂×C₄×C₆₇	—	2	4	no	—
337	C₂×C₄×C₆₇	—	2	4	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	4	1	no	—
345	C₂×C₄×C₆₇	—	4	1	no	—
346	C₂×C₄×C₆₇	—	4	8	no	—
347	C₂×C₄×C₆₇	—	4	4	no	—
348	C₂×C₄×C₆₇	—	4	2	no	—
349	C₂×C₄×C₆₇	—	4	4	no	—
350	C₂×C₄×C₆₇	—	8	2	no	—
351	C₂×C₄×C₆₇	—	8	1	no	—
352	C₂×C₄×C₆₇	—	8	4	no	—
353	C₂×C₄×C₆₇	—	8	1	no	—
354	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
355	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
356	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
357	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
361	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
363	C₈×C₆₇	—	2	2	no	—
364	C₈×C₆₇	—	2	2	no	—
365	C₈×C₆₇	—	2	4	no	—
366	C₂²×C₆₇	—	2	1	no	—
367	C₂²×C₆₇	—	2	1	no	—
368	C₂²×C₆₇	—	2	4	no	—
369	C₂²×C₆₇	—	2	4	no	—
370	C₂²×C₆₇	—	2	4	no	—
371	C₂²×C₆₇	—	2	4	no	—
372	C₂²×C₆₇	—	4	2	no	—
373	C₂²×C₆₇	—	4	2	no	—
374	C₂²×C₆₇	—	4	2	no	—
375	C₂²×C₆₇	—	4	2	no	—
376	C₂²×C₆₇	—	4	2	no	—
377	C₂²×C₆₇	—	8	4	no	—
378	C₂²×C₆₇	—	16	8	no	—
379	C₂²×C₆₇	#546	1	2	yes	—
380	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
381	C₄×C₆₇	—	2	1	no	—
382	C₄×C₆₇	—	2	1	no	—
383	C₄×C₆₇	—	2	1	no	—
384	C₄×C₆₇	—	2	1	no	—
385	C₄×C₆₇	—	2	4	no	—
386	C₄×C₆₇	—	4	2	no	—
387	C₄×C₆₇	—	4	2	no	—
388	C₄×C₆₇	—	4	2	no	—
389	C₄×C₆₇	—	4	2	no	—
390	C₄×C₆₇	—	4	2	no	—
391	C₄×C₆₇	—	4	2	no	—
392	C₄×C₆₇	#546	1	2	yes	—
393	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
394	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
395	#61219	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂×C₆₇	—	2	2	no	—
397	C₂×C₆₇	—	4	4	no	—
398	C₂×C₆₇	—	4	4	no	—
399	C₂×C₆₇	—	8	2	no	—
400	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
401	C₂×C₆₇	#3585	1	1	yes	characteristic
402	C₂×C₆₇	#3586	1	1	yes	characteristic
403	#3507	C₂×C₆₇	1	1	yes	characteristic, complemented
404	#3496	C₂×C₆₇	1	1	yes	characteristic
405	#3315	C₂×C₆₇	1	4	yes	complemented
406	#3314	C₂×C₆₇	1	4	yes	complemented
407	#3311	C₂×C₆₇	1	4	yes	complemented
408	#3310	C₂×C₆₇	1	4	yes	complemented
409	#3135	C₂×C₆₇	1	1	yes	characteristic, complemented
410	#3098	C₂×C₆₇	1	2	yes	complemented
411	#3077	C₂×C₆₇	1	1	yes	characteristic, complemented
412	#3063	C₂×C₆₇	1	2	yes	complemented
413	#3037	C₂×C₆₇	1	1	yes	characteristic, complemented
414	#3009	C₂×C₆₇	1	2	yes	complemented
415	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
416	#2932	C₂×C₆₇	1	1	yes	characteristic, complemented
417	#2897	C₂×C₆₇	1	2	yes	complemented
418	C₆₇	#61219	1	1	yes	characteristic, direct product factor, Sylow
419	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
420	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
421	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
422	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
423	#559	—	2	1	no	—
424	#557	—	2	1	no	—
425	#556	—	2	2	no	—
426	#556	C₂²×C₆₇	1	2	yes	complemented
427	#554	C₂²×C₆₇	1	2	yes	complemented
428	#552	C₂²×C₆₇	1	4	yes	complemented
429	#547	—	2	1	no	—
430	#547	C₂²×C₆₇	1	2	yes	—
431	#546	—	2	2	no	—
432	#546	C₂²×C₆₇	1	4	yes	—
433	D₄²	—	2	1	no	—
434	D₄²	C₂²×C₆₇	1	2	yes	—
435	#539	—	2	2	no	—
436	#537	C₂²×C₆₇	1	2	yes	—
437	#536	C₂²×C₆₇	1	2	yes	complemented
438	#534	—	2	2	no	—
439	#533	C₂²×C₆₇	1	1	yes	characteristic, complemented
440	#532	C₂²×C₆₇	1	1	yes	characteristic
441	#532	C₂²×C₆₇	1	1	yes	characteristic
442	#529	—	2	2	no	—
443	C₂×#121	—	2	2	no	—
444	#520	C₂²×C₆₇	1	2	yes	complemented
445	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
446	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
447	#491	C₂²×C₆₇	1	2	yes	complemented
448	#490	C₂²×C₆₇	1	2	yes	complemented
449	#489	C₂²×C₆₇	1	2	yes	complemented
450	#489	C₂²×C₆₇	1	2	yes	complemented
451	#485	C₂²×C₆₇	1	4	yes	complemented
452	#484	C₂²×C₆₇	1	4	yes	complemented
453	#482	C₂²×C₆₇	1	4	yes	complemented
454	#480	C₂²×C₆₇	1	4	yes	complemented
455	#478	C₂²×C₆₇	1	4	yes	complemented
456	#476	C₂²×C₆₇	1	2	yes	complemented
457	#474	C₂²×C₆₇	1	2	yes	complemented
458	#470	C₂²×C₆₇	1	4	yes	complemented
459	#468	C₂²×C₆₇	1	4	yes	complemented
460	#467	C₂²×C₆₇	1	4	yes	complemented
461	#465	C₂²×C₆₇	1	4	yes	complemented
462	#464	C₂²×C₆₇	1	4	yes	complemented
463	#462	C₂²×C₆₇	1	2	yes	complemented
464	#460	C₂²×C₆₇	1	2	yes	complemented
465	#452	C₂²×C₆₇	1	4	yes	complemented
466	#452	C₂²×C₆₇	1	4	yes	complemented
467	#450	C₂²×C₆₇	1	4	yes	complemented
468	#450	C₂²×C₆₇	1	4	yes	complemented
469	#440	C₂²×C₆₇	1	4	yes	complemented
470	#440	C₂²×C₆₇	1	4	yes	complemented
471	#435	C₂²×C₆₇	1	4	yes	complemented
472	#435	C₂²×C₆₇	1	4	yes	complemented
473	#428	C₂²×C₆₇	1	2	yes	complemented
474	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
475	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
476	#418	C₂²×C₆₇	1	2	yes	—
477	#418	C₂²×C₆₇	1	4	yes	complemented
478	#417	C₂²×C₆₇	1	2	yes	complemented
479	#417	C₂²×C₆₇	1	4	yes	complemented
480	#416	C₂²×C₆₇	1	2	yes	complemented
481	#416	C₂²×C₆₇	1	2	yes	complemented
482	#416	C₂²×C₆₇	1	4	yes	complemented
483	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
484	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
485	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
486	#408	C₂²×C₆₇	1	2	yes	complemented
487	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
488	H(5,𝔽₂)	—	2	8	no	—
489	H(5,𝔽₂)	—	4	4	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	C₂³×C₆₇	1	2	yes	—
492	C₂×#41	C₂³×C₆₇	1	4	yes	—
493	C₂×#41	C₂³×C₆₇	1	2	yes	—
494	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
495	C₂²×D₄	—	2	4	no	—
496	C₂²×D₄	—	2	2	no	—
497	C₂²×D₄	—	2	2	no	—
498	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
499	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
500	C₂³×C₄	—	2	1	no	—
501	#137	—	4	4	no	—
502	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
503	C₂×SD₁₆	—	2	4	no	—
504	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
505	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
506	#131	—	4	4	no	—
507	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
508	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
509	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
511	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
512	C₄⋊Q₈	—	2	2	no	—
513	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
517	#127	D₄×C₆₇	1	1	yes	characteristic
518	#127	C₂³×C₆₇	1	1	yes	characteristic
519	#126	—	2	4	no	—
520	#126	—	2	4	no	—
521	#125	—	2	2	no	—
522	#125	—	2	4	no	—
523	#125	C₂³×C₆₇	1	2	yes	—
524	#124	—	2	2	no	—
525	#124	—	2	2	no	—
526	#124	D₄×C₆₇	1	2	yes	—
527	#124	C₂³×C₆₇	1	2	yes	—
528	#123	—	2	4	no	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	4	no	—
536	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
537	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
538	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
539	#121	—	2	4	no	—
540	#121	—	2	2	no	—
541	#121	—	2	2	no	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	2	no	—
545	#121	—	2	4	no	—
546	#121	D₄×C₆₇	1	2	yes	—
547	#121	D₄×C₆₇	1	2	yes	—
548	#121	C₂³×C₆₇	1	4	yes	—
549	#120	—	2	4	no	—
550	#120	—	2	4	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	1	no	—
554	C₄×Q₈	—	2	1	no	—
555	C₄×Q₈	—	2	1	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
558	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
559	C₄×D₄	—	2	4	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	C₂³×C₆₇	1	2	yes	—
567	C₄×D₄	C₂³×C₆₇	1	2	yes	—
568	C₄×D₄	C₂³×C₆₇	1	2	yes	—
569	C₄×D₄	C₂³×C₆₇	1	2	yes	—
570	#117	—	2	4	no	—
571	#117	C₂³×C₆₇	1	2	yes	—
572	#117	C₂³×C₆₇	1	4	yes	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	2	no	—
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
578	C₂×C₂²⋊C₄	—	2	1	no	—
579	C₂×C₂²⋊C₄	—	2	4	no	—
580	C₂×C₄²	—	2	1	no	—
581	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
582	#107	C₂³×C₆₇	1	4	yes	—
583	#107	C₂³×C₆₇	1	4	yes	—
584	#106	C₂³×C₆₇	1	4	yes	—
585	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
586	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
587	#103	C₂³×C₆₇	1	4	yes	—
588	#103	C₂³×C₆₇	1	2	yes	—
589	#103	C₂³×C₆₇	1	4	yes	—
590	#103	C₂³×C₆₇	1	2	yes	—
591	#103	C₂³×C₆₇	1	2	yes	—
592	#103	C₂³×C₆₇	1	2	yes	—
593	#102	C₂³×C₆₇	1	4	yes	—
594	#102	C₂³×C₆₇	1	2	yes	—
595	#102	C₂³×C₆₇	1	4	yes	—
596	#102	C₂³×C₆₇	1	4	yes	—
597	#102	C₂³×C₆₇	1	4	yes	—
598	#102	C₂³×C₆₇	1	2	yes	—
599	#102	C₂³×C₆₇	1	2	yes	—
600	#102	C₂³×C₆₇	1	2	yes	—
601	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
602	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
603	#97	C₂³×C₆₇	1	2	yes	—
604	#97	C₂³×C₆₇	1	2	yes	—
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	4	no	—
607	#41	—	2	4	no	—
608	#41	—	2	4	no	—
609	#41	—	2	8	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	8	no	—
614	C₂×Q₈	—	2	1	no	—
615	C₂×Q₈	—	2	1	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	2	2	no	—
619	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
621	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	2	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	—	4	8	no	—
633	C₂×D₄	—	4	16	no	—
634	C₂×D₄	—	8	4	no	—
635	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
636	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
637	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
638	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
639	C₂×D₄	#41×C₆₇	1	4	yes	—
640	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
641	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	4	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	8	2	no	—
651	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
654	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
655	Q₁₆	—	4	4	no	—
656	SD₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	M₁₆	—	2	4	no	—
659	M₁₆	—	4	4	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	4	4	no	—
663	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
664	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
665	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
666	C₄⋊C₄	—	2	1	no	—
667	C₄⋊C₄	—	2	2	no	—
668	C₄⋊C₄	—	2	2	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	1	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	4	no	—
680	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
681	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	2	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
697	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
698	C₄²	—	2	2	no	—
699	C₄²	—	2	2	no	—
700	C₄²	—	2	4	no	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
704	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
705	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
706	C₂³	—	2	2	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	4	8	no	—
710	C₂³	—	8	1	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	4	no	—
713	C₂³	—	8	4	no	—
714	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
715	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
716	Q₈	—	2	4	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	2	2	no	—
719	Q₈	—	2	2	no	—
720	Q₈	—	2	2	no	—
721	Q₈	—	4	2	no	—
722	Q₈	—	4	2	no	—
723	Q₈	—	8	1	no	—
724	D₄	—	2	8	no	—
725	D₄	—	2	4	no	—
726	D₄	—	2	4	no	—
727	D₄	—	2	2	no	—
728	D₄	—	2	2	no	—
729	D₄	—	2	2	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	2	no	—
732	D₄	—	4	8	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	8	no	—
735	D₄	—	4	4	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	4	no	—
738	D₄	C₂×#41×C₆₇	1	4	yes	—
739	C₂×C₄	—	2	4	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	4	1	no	—
748	C₂×C₄	—	4	1	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	4	no	—
751	C₂×C₄	—	4	2	no	—
752	C₂×C₄	—	4	4	no	—
753	C₂×C₄	—	8	2	no	—
754	C₂×C₄	—	8	1	no	—
755	C₂×C₄	—	8	1	no	—
756	C₂×C₄	—	8	4	no	—
757	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
758	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
759	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
760	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
761	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
763	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
764	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
765	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	2	2	no	—
768	C₈	—	2	4	no	—
769	C₂²	—	2	1	no	—
770	C₂²	—	2	1	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	4	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	8	4	no	—
781	C₂²	—	16	8	no	—
782	C₂²	#546×C₆₇	1	2	yes	—
783	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
784	C₄	—	2	1	no	—
785	C₄	—	2	1	no	—
786	C₄	—	2	1	no	—
787	C₄	—	2	1	no	—
788	C₄	—	2	4	no	—
789	C₄	—	4	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	#546×C₆₇	1	2	yes	—
796	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
797	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
798	C₂	—	2	2	no	—
799	C₂	—	4	4	no	—
800	C₂	—	4	4	no	—
801	C₂	—	8	2	no	—
802	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
803	C₂	C₆₇×#3585	1	1	yes	characteristic
804	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×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3507	C₂	semidirect
3. C₆₇×#3315	C₂	semidirect
4. C₆₇×#3314	C₂	semidirect
5. C₆₇×#3311	C₂	semidirect
6. C₆₇×#3310	C₂	semidirect
7. C₆₇×#3135	C₂	semidirect
8. C₆₇×#3098	C₂	semidirect
9. C₆₇×#3077	C₂	semidirect
10. C₆₇×#3063	C₂	semidirect
11. C₆₇×#3037	C₂	semidirect
12. C₆₇×#3009	C₂	semidirect
13. C₂×#440×C₆₇	C₂	semidirect
14. C₆₇×#2932	C₂	semidirect
15. C₆₇×#2897	C₂	semidirect
17. C₂×#137×C₆₇	C₂²	semidirect
19. C₂×#131×C₆₇	C₂²	semidirect
23. #556×C₆₇	C₂²	semidirect
24. #554×C₆₇	C₂²	semidirect
25. #552×C₆₇	C₂²	semidirect
34. #536×C₆₇	C₂²	semidirect
36. #533×C₆₇	C₂²	semidirect
41. #520×C₆₇	C₂²	semidirect
42. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
44. #491×C₆₇	C₂²	semidirect
45. #490×C₆₇	C₂²	semidirect
46. #489×C₆₇	C₂²	semidirect
47. #489×C₆₇	C₂²	semidirect
48. #485×C₆₇	C₂²	semidirect
49. #484×C₆₇	C₂²	semidirect
50. #482×C₆₇	C₂²	semidirect
51. #480×C₆₇	C₂²	semidirect
52. #478×C₆₇	C₂²	semidirect
53. #476×C₆₇	C₂²	semidirect
54. #474×C₆₇	C₂²	semidirect
55. #470×C₆₇	C₂²	semidirect
56. #468×C₆₇	C₂²	semidirect
57. #467×C₆₇	C₂²	semidirect
58. #465×C₆₇	C₂²	semidirect
59. #464×C₆₇	C₂²	semidirect
60. #462×C₆₇	C₂²	semidirect
61. #460×C₆₇	C₂²	semidirect
62. #452×C₆₇	C₂²	semidirect
63. #452×C₆₇	C₂²	semidirect
64. #450×C₆₇	C₂²	semidirect
65. #450×C₆₇	C₂²	semidirect
66. #440×C₆₇	C₂²	semidirect
67. #440×C₆₇	C₂²	semidirect
68. #435×C₆₇	C₂²	semidirect
69. #435×C₆₇	C₂²	semidirect
70. #428×C₆₇	C₂²	semidirect
71. C₂×#107×C₆₇	C₂²	semidirect
72. #423×C₆₇	C₂²	semidirect
74. #418×C₆₇	C₂²	semidirect
75. #417×C₆₇	C₂²	semidirect
76. #417×C₆₇	C₂²	semidirect
77. #416×C₆₇	C₂²	semidirect
78. #416×C₆₇	C₂²	semidirect
79. #416×C₆₇	C₂²	semidirect
80. C₂×#103×C₆₇	C₂²	semidirect
82. C₂×#102×C₆₇	C₂²	semidirect
83. #408×C₆₇	C₂²	semidirect
84. C₂×#97×C₆₇	C₂²	semidirect
395. #61219	C₆₇	direct (N × H)
403. #3507	C₂×C₆₇	semidirect
405. #3315	C₂×C₆₇	semidirect
406. #3314	C₂×C₆₇	semidirect
407. #3311	C₂×C₆₇	semidirect
408. #3310	C₂×C₆₇	semidirect
409. #3135	C₂×C₆₇	semidirect
410. #3098	C₂×C₆₇	semidirect
411. #3077	C₂×C₆₇	semidirect
412. #3063	C₂×C₆₇	semidirect
413. #3037	C₂×C₆₇	semidirect
414. #3009	C₂×C₆₇	semidirect
415. C₂×#440	C₂×C₆₇	semidirect
416. #2932	C₂×C₆₇	semidirect
417. #2897	C₂×C₆₇	semidirect
418. C₆₇	#61219	direct (N × H)
420. C₂×#137	C₂²×C₆₇	semidirect
422. C₂×#131	C₂²×C₆₇	semidirect
426. #556	C₂²×C₆₇	semidirect
427. #554	C₂²×C₆₇	semidirect
428. #552	C₂²×C₆₇	semidirect
437. #536	C₂²×C₆₇	semidirect
439. #533	C₂²×C₆₇	semidirect
444. #520	C₂²×C₆₇	semidirect
445. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
447. #491	C₂²×C₆₇	semidirect
448. #490	C₂²×C₆₇	semidirect
449. #489	C₂²×C₆₇	semidirect
450. #489	C₂²×C₆₇	semidirect
451. #485	C₂²×C₆₇	semidirect
452. #484	C₂²×C₆₇	semidirect
453. #482	C₂²×C₆₇	semidirect
454. #480	C₂²×C₆₇	semidirect
455. #478	C₂²×C₆₇	semidirect
456. #476	C₂²×C₆₇	semidirect
457. #474	C₂²×C₆₇	semidirect
458. #470	C₂²×C₆₇	semidirect
459. #468	C₂²×C₆₇	semidirect
460. #467	C₂²×C₆₇	semidirect
461. #465	C₂²×C₆₇	semidirect
462. #464	C₂²×C₆₇	semidirect
463. #462	C₂²×C₆₇	semidirect
464. #460	C₂²×C₆₇	semidirect
465. #452	C₂²×C₆₇	semidirect
466. #452	C₂²×C₆₇	semidirect
467. #450	C₂²×C₆₇	semidirect
468. #450	C₂²×C₆₇	semidirect
469. #440	C₂²×C₆₇	semidirect
470. #440	C₂²×C₆₇	semidirect
471. #435	C₂²×C₆₇	semidirect
472. #435	C₂²×C₆₇	semidirect
473. #428	C₂²×C₆₇	semidirect
474. C₂×#107	C₂²×C₆₇	semidirect
475. #423	C₂²×C₆₇	semidirect
477. #418	C₂²×C₆₇	semidirect
478. #417	C₂²×C₆₇	semidirect
479. #417	C₂²×C₆₇	semidirect
480. #416	C₂²×C₆₇	semidirect
481. #416	C₂²×C₆₇	semidirect
482. #416	C₂²×C₆₇	semidirect
483. C₂×#103	C₂²×C₆₇	semidirect
485. C₂×#102	C₂²×C₆₇	semidirect
486. #408	C₂²×C₆₇	semidirect
487. C₂×#97	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×#3507	2
C₆₇×#3496	2
C₆₇×#3315	2
C₆₇×#3314	2
C₆₇×#3311	2
C₆₇×#3310	2
C₆₇×#3135	2
C₆₇×#3098	2
C₆₇×#3077	2
C₆₇×#3063	2
C₆₇×#3037	2
C₆₇×#3009	2
C₂×#440×C₆₇	2
C₆₇×#2932	2
C₆₇×#2897	2
#61219	67

Subgroups — C67×#61219 #30740470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61219 #30740470